From f0af2624acf5236ba386bfb1d96141c3b2d36e66 Mon Sep 17 00:00:00 2001
From: Hu Zhao <zhao@mbd.rwth-aachen.de>
Date: Sat, 22 Apr 2023 06:36:20 +0200
Subject: [PATCH] docs: add built documentation

---
 docs/source/_build/doctrees/api.doctree       |   Bin 0 -> 2809 bytes
 docs/source/_build/doctrees/changelog.doctree |   Bin 0 -> 5265 bytes
 .../_build/doctrees/emulator/index.doctree    |   Bin 0 -> 5958 bytes
 .../doctrees/emulator/robustgasp.doctree      |   Bin 0 -> 202926 bytes
 .../source/_build/doctrees/environment.pickle |   Bin 0 -> 263253 bytes
 docs/source/_build/doctrees/examples.doctree  |   Bin 0 -> 2973 bytes
 docs/source/_build/doctrees/index.doctree     |   Bin 0 -> 3918 bytes
 .../inference/active_learning.doctree         |   Bin 0 -> 81785 bytes
 .../inference/bayes_inference.doctree         |   Bin 0 -> 88720 bytes
 .../_build/doctrees/inference/index.doctree   |   Bin 0 -> 5786 bytes
 .../source/_build/doctrees/quickstart.doctree |   Bin 0 -> 21390 bytes
 docs/source/_build/doctrees/refs.doctree      |   Bin 0 -> 3418 bytes
 .../_build/doctrees/sampler/index.doctree     |   Bin 0 -> 5340 bytes
 .../_build/doctrees/sampler/latin.doctree     |   Bin 0 -> 25111 bytes
 .../sampler/metropolis_hastings.doctree       |   Bin 0 -> 52323 bytes
 .../_build/doctrees/sampler/saltelli.doctree  |   Bin 0 -> 21705 bytes
 .../_build/doctrees/sensitivity/index.doctree |   Bin 0 -> 4034 bytes
 .../_build/doctrees/sensitivity/sobol.doctree |   Bin 0 -> 32057 bytes
 .../_build/doctrees/simulator/index.doctree   |   Bin 0 -> 12332 bytes
 .../simulator/mass_point_model.doctree        |   Bin 0 -> 48840 bytes
 .../doctrees/simulator/ravaflow24.doctree     |   Bin 0 -> 96224 bytes
 .../doctrees/simulator/run_simulator.doctree  |   Bin 0 -> 46850 bytes
 docs/source/_build/html/.buildinfo            |     4 +
 .../plot_run_ravaflow24.py                    |   212 +
 .../plot_mass_point_model.ipynb               |   165 +
 .../plot_latin.py                             |    91 +
 .../plot_bayes_inference.ipynb                |   140 +
 .../plot_latin.ipynb                          |   140 +
 .../simulator_python.zip                      |   Bin 0 -> 22289 bytes
 .../plot_run_mass_point_model.ipynb           |   251 +
 .../plot_bayes_inference.py                   |   116 +
 .../inference_python.zip                      |   Bin 0 -> 8376 bytes
 .../plot_active_learning.py                   |   127 +
 .../plot_run_mass_point_model.py              |   184 +
 .../plot_metropolis_hastings.py               |   116 +
 .../simulator_jupyter.zip                     |   Bin 0 -> 37421 bytes
 .../plot_saltelli.py                          |    82 +
 .../plot_ravaflow24.py                        |   150 +
 .../plot_metropolis_hastings.ipynb            |   151 +
 .../sampler_python.zip                        |   Bin 0 -> 8197 bytes
 .../plot_scalargasp.ipynb                     |   183 +
 .../plot_ravaflow24.ipynb                     |   201 +
 .../plot_mass_point_model.py                  |   128 +
 .../plot_ppgasp.ipynb                         |   183 +
 .../sampler_jupyter.zip                       |   Bin 0 -> 14963 bytes
 .../inference_jupyter.zip                     |   Bin 0 -> 12936 bytes
 .../plot_run_ravaflow24.ipynb                 |   316 +
 .../emulator_jupyter.zip                      |   Bin 0 -> 13821 bytes
 .../sensitivity_python.zip                    |   Bin 0 -> 7350 bytes
 .../plot_ppgasp.py                            |   112 +
 .../plot_scalargasp.py                        |   125 +
 .../plot_sobol_analyze.py                     |   213 +
 .../plot_active_learning.ipynb                |   133 +
 .../plot_saltelli.ipynb                       |   122 +
 .../plot_sobol_analyze.ipynb                  |   140 +
 .../emulator_python.zip                       |   Bin 0 -> 8028 bytes
 .../sensitivity_jupyter.zip                   |   Bin 0 -> 9747 bytes
 .../_build/html/_images/coordinate_system.png |   Bin 0 -> 595830 bytes
 .../latin_hypercube_sampling_sketch.png       |   Bin 0 -> 81075 bytes
 .../sphx_glr_plot_active_learning_001.png     |   Bin 0 -> 65560 bytes
 .../sphx_glr_plot_active_learning_thumb.png   |   Bin 0 -> 47840 bytes
 .../sphx_glr_plot_bayes_inference_001.png     |   Bin 0 -> 67321 bytes
 .../sphx_glr_plot_bayes_inference_002.png     |   Bin 0 -> 42106 bytes
 .../sphx_glr_plot_bayes_inference_thumb.png   |   Bin 0 -> 40749 bytes
 .../html/_images/sphx_glr_plot_latin_001.png  |   Bin 0 -> 13787 bytes
 .../html/_images/sphx_glr_plot_latin_002.png  |   Bin 0 -> 13574 bytes
 .../html/_images/sphx_glr_plot_latin_003.png  |   Bin 0 -> 13975 bytes
 .../_images/sphx_glr_plot_latin_thumb.png     |   Bin 0 -> 11800 bytes
 .../sphx_glr_plot_mass_point_model_001.png    |   Bin 0 -> 38383 bytes
 .../sphx_glr_plot_mass_point_model_002.png    |   Bin 0 -> 47182 bytes
 .../sphx_glr_plot_mass_point_model_thumb.png  |   Bin 0 -> 16576 bytes
 .../sphx_glr_plot_metropolis_hastings_001.png |   Bin 0 -> 14957 bytes
 .../sphx_glr_plot_metropolis_hastings_002.png |   Bin 0 -> 48807 bytes
 ...phx_glr_plot_metropolis_hastings_thumb.png |   Bin 0 -> 31329 bytes
 .../html/_images/sphx_glr_plot_ppgasp_001.png |   Bin 0 -> 127582 bytes
 .../_images/sphx_glr_plot_ppgasp_thumb.png    |   Bin 0 -> 19418 bytes
 .../_images/sphx_glr_plot_ravaflow24_001.png  |   Bin 0 -> 41809 bytes
 .../sphx_glr_plot_ravaflow24_thumb.png        |   Bin 0 -> 22497 bytes
 ...hx_glr_plot_run_mass_point_model_thumb.png |   Bin 0 -> 26794 bytes
 .../sphx_glr_plot_run_ravaflow24_thumb.png    |   Bin 0 -> 26794 bytes
 .../_images/sphx_glr_plot_saltelli_001.png    |   Bin 0 -> 151258 bytes
 .../_images/sphx_glr_plot_saltelli_002.png    |   Bin 0 -> 174197 bytes
 .../_images/sphx_glr_plot_saltelli_thumb.png  |   Bin 0 -> 81243 bytes
 .../_images/sphx_glr_plot_scalargasp_001.png  |   Bin 0 -> 21104 bytes
 .../_images/sphx_glr_plot_scalargasp_002.png  |   Bin 0 -> 40770 bytes
 .../_images/sphx_glr_plot_scalargasp_003.png  |   Bin 0 -> 56023 bytes
 .../sphx_glr_plot_scalargasp_thumb.png        |   Bin 0 -> 34836 bytes
 .../sphx_glr_plot_sobol_analyze_001.png       |   Bin 0 -> 20065 bytes
 .../sphx_glr_plot_sobol_analyze_002.png       |   Bin 0 -> 20113 bytes
 .../sphx_glr_plot_sobol_analyze_thumb.png     |   Bin 0 -> 28988 bytes
 docs/source/_build/html/_modules/index.html   |   119 +
 .../_modules/psimpy/emulator/robustgasp.html  |   724 +
 .../psimpy/inference/active_learning.html     |   576 +
 .../psimpy/inference/bayes_inference.html     |   357 +
 .../html/_modules/psimpy/sampler/latin.html   |   229 +
 .../psimpy/sampler/metropolis_hastings.html   |   335 +
 .../_modules/psimpy/sampler/saltelli.html     |   174 +
 .../_modules/psimpy/sensitivity/sobol.html    |   352 +
 .../psimpy/simulator/mass_point_model.html    |   378 +
 .../_modules/psimpy/simulator/ravaflow24.html |   502 +
 .../psimpy/simulator/run_simulator.html       |   348 +
 docs/source/_build/html/_sources/api.rst.txt  |    11 +
 .../_build/html/_sources/changelog.rst.txt    |     6 +
 .../html/_sources/emulator/index.rst.txt      |    27 +
 .../html/_sources/emulator/robustgasp.rst.txt |   211 +
 .../_build/html/_sources/examples.rst.txt     |    11 +
 .../source/_build/html/_sources/index.rst.txt |    21 +
 .../inference/active_learning.rst.txt         |    27 +
 .../inference/bayes_inference.rst.txt         |    63 +
 .../html/_sources/inference/index.rst.txt     |    21 +
 .../_build/html/_sources/quickstart.rst.txt   |    91 +
 docs/source/_build/html/_sources/refs.rst.txt |     4 +
 .../html/_sources/sampler/index.rst.txt       |    22 +
 .../html/_sources/sampler/latin.rst.txt       |    40 +
 .../sampler/metropolis_hastings.rst.txt       |    35 +
 .../html/_sources/sampler/saltelli.rst.txt    |    19 +
 .../html/_sources/sensitivity/index.rst.txt   |    16 +
 .../html/_sources/sensitivity/sobol.rst.txt   |    19 +
 .../html/_sources/simulator/index.rst.txt     |    38 +
 .../simulator/mass_point_model.rst.txt        |    86 +
 .../_sources/simulator/ravaflow24.rst.txt     |    24 +
 .../_sources/simulator/run_simulator.rst.txt  |    30 +
 .../_sphinx_javascript_frameworks_compat.js   |   134 +
 docs/source/_build/html/_static/basic.css     |   899 ++
 .../_build/html/_static/binder_badge_logo.svg |     1 +
 .../_build/html/_static/broken_example.png    |   Bin 0 -> 21404 bytes
 .../_build/html/_static/coordinate_system.png |   Bin 0 -> 595830 bytes
 .../_build/html/_static/css/badge_only.css    |     1 +
 .../source/_build/html/_static/css/custom.css |     6 +
 .../_static/css/fonts/Roboto-Slab-Bold.woff   |   Bin 0 -> 87624 bytes
 .../_static/css/fonts/Roboto-Slab-Bold.woff2  |   Bin 0 -> 67312 bytes
 .../css/fonts/Roboto-Slab-Regular.woff        |   Bin 0 -> 86288 bytes
 .../css/fonts/Roboto-Slab-Regular.woff2       |   Bin 0 -> 66444 bytes
 .../_static/css/fonts/fontawesome-webfont.eot |   Bin 0 -> 165742 bytes
 .../_static/css/fonts/fontawesome-webfont.svg |  2671 ++++
 .../_static/css/fonts/fontawesome-webfont.ttf |   Bin 0 -> 165548 bytes
 .../css/fonts/fontawesome-webfont.woff        |   Bin 0 -> 98024 bytes
 .../css/fonts/fontawesome-webfont.woff2       |   Bin 0 -> 77160 bytes
 .../_static/css/fonts/lato-bold-italic.woff   |   Bin 0 -> 323344 bytes
 .../_static/css/fonts/lato-bold-italic.woff2  |   Bin 0 -> 193308 bytes
 .../html/_static/css/fonts/lato-bold.woff     |   Bin 0 -> 309728 bytes
 .../html/_static/css/fonts/lato-bold.woff2    |   Bin 0 -> 184912 bytes
 .../_static/css/fonts/lato-normal-italic.woff |   Bin 0 -> 328412 bytes
 .../css/fonts/lato-normal-italic.woff2        |   Bin 0 -> 195704 bytes
 .../html/_static/css/fonts/lato-normal.woff   |   Bin 0 -> 309192 bytes
 .../html/_static/css/fonts/lato-normal.woff2  |   Bin 0 -> 182708 bytes
 docs/source/_build/html/_static/css/theme.css |     4 +
 docs/source/_build/html/_static/doctools.js   |   156 +
 .../html/_static/documentation_options.js     |    14 +
 docs/source/_build/html/_static/file.png      |   Bin 0 -> 286 bytes
 .../_build/html/_static/jquery-3.6.0.js       | 10881 ++++++++++++++++
 docs/source/_build/html/_static/jquery.js     |     2 +
 .../_build/html/_static/js/badge_only.js      |     1 +
 .../_static/js/html5shiv-printshiv.min.js     |     4 +
 .../_build/html/_static/js/html5shiv.min.js   |     4 +
 docs/source/_build/html/_static/js/theme.js   |     1 +
 .../_build/html/_static/language_data.js      |   199 +
 .../latin_hypercube_sampling_sketch.png       |   Bin 0 -> 81075 bytes
 docs/source/_build/html/_static/minus.png     |   Bin 0 -> 90 bytes
 docs/source/_build/html/_static/no_image.png  |   Bin 0 -> 4315 bytes
 docs/source/_build/html/_static/plus.png      |   Bin 0 -> 90 bytes
 docs/source/_build/html/_static/pygments.css  |    74 +
 .../source/_build/html/_static/searchtools.js |   566 +
 .../_build/html/_static/sg_gallery-binder.css |     6 +
 .../html/_static/sg_gallery-dataframe.css     |    46 +
 .../html/_static/sg_gallery-rendered-html.css |   224 +
 .../source/_build/html/_static/sg_gallery.css |   342 +
 .../_build/html/_static/sphinx_highlight.js   |   144 +
 .../_build/html/_static/underscore-1.13.1.js  |  2042 +++
 docs/source/_build/html/_static/underscore.js |     6 +
 docs/source/_build/html/api.html              |   134 +
 docs/source/_build/html/changelog.html        |   139 +
 docs/source/_build/html/emulator/index.html   |   145 +
 .../_build/html/emulator/robustgasp.html      |   619 +
 docs/source/_build/html/examples.html         |   134 +
 docs/source/_build/html/genindex.html         |   298 +
 docs/source/_build/html/index.html            |   156 +
 .../html/inference/active_learning.html       |   304 +
 .../html/inference/bayes_inference.html       |   319 +
 docs/source/_build/html/inference/index.html  |   139 +
 docs/source/_build/html/objects.inv           |   Bin 0 -> 1825 bytes
 docs/source/_build/html/quickstart.html       |   213 +
 docs/source/_build/html/refs.html             |   165 +
 docs/source/_build/html/sampler/index.html    |   140 +
 docs/source/_build/html/sampler/latin.html    |   207 +
 .../html/sampler/metropolis_hastings.html     |   236 +
 docs/source/_build/html/sampler/saltelli.html |   190 +
 docs/source/_build/html/search.html           |   129 +
 docs/source/_build/html/searchindex.js        |     1 +
 .../source/_build/html/sensitivity/index.html |   136 +
 .../source/_build/html/sensitivity/sobol.html |   210 +
 docs/source/_build/html/simulator/index.html  |   158 +
 .../html/simulator/mass_point_model.html      |   250 +
 .../_build/html/simulator/ravaflow24.html     |   348 +
 .../_build/html/simulator/run_simulator.html  |   247 +
 195 files changed, 32146 insertions(+)
 create mode 100644 docs/source/_build/doctrees/api.doctree
 create mode 100644 docs/source/_build/doctrees/changelog.doctree
 create mode 100644 docs/source/_build/doctrees/emulator/index.doctree
 create mode 100644 docs/source/_build/doctrees/emulator/robustgasp.doctree
 create mode 100644 docs/source/_build/doctrees/environment.pickle
 create mode 100644 docs/source/_build/doctrees/examples.doctree
 create mode 100644 docs/source/_build/doctrees/index.doctree
 create mode 100644 docs/source/_build/doctrees/inference/active_learning.doctree
 create mode 100644 docs/source/_build/doctrees/inference/bayes_inference.doctree
 create mode 100644 docs/source/_build/doctrees/inference/index.doctree
 create mode 100644 docs/source/_build/doctrees/quickstart.doctree
 create mode 100644 docs/source/_build/doctrees/refs.doctree
 create mode 100644 docs/source/_build/doctrees/sampler/index.doctree
 create mode 100644 docs/source/_build/doctrees/sampler/latin.doctree
 create mode 100644 docs/source/_build/doctrees/sampler/metropolis_hastings.doctree
 create mode 100644 docs/source/_build/doctrees/sampler/saltelli.doctree
 create mode 100644 docs/source/_build/doctrees/sensitivity/index.doctree
 create mode 100644 docs/source/_build/doctrees/sensitivity/sobol.doctree
 create mode 100644 docs/source/_build/doctrees/simulator/index.doctree
 create mode 100644 docs/source/_build/doctrees/simulator/mass_point_model.doctree
 create mode 100644 docs/source/_build/doctrees/simulator/ravaflow24.doctree
 create mode 100644 docs/source/_build/doctrees/simulator/run_simulator.doctree
 create mode 100644 docs/source/_build/html/.buildinfo
 create mode 100644 docs/source/_build/html/_downloads/06e1d1c67d64bdd5612e33cffc1295c5/plot_run_ravaflow24.py
 create mode 100644 docs/source/_build/html/_downloads/201f9a51be1f2378acae03891235a84e/plot_mass_point_model.ipynb
 create mode 100644 docs/source/_build/html/_downloads/213f7cd5e82a62f8d1da8c3af9caab35/plot_latin.py
 create mode 100644 docs/source/_build/html/_downloads/2d9fc590bc1edb11501b144674a0a949/plot_bayes_inference.ipynb
 create mode 100644 docs/source/_build/html/_downloads/3072e3885ecdb1bbb3b34893dcfd8def/plot_latin.ipynb
 create mode 100644 docs/source/_build/html/_downloads/31c796c77470b56d8b117051a799e0b5/simulator_python.zip
 create mode 100644 docs/source/_build/html/_downloads/39558f3ab53d6f797e2208e7c89063a5/plot_run_mass_point_model.ipynb
 create mode 100644 docs/source/_build/html/_downloads/44f0f511484d9bfd5f8d212c8f287e9e/plot_bayes_inference.py
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 create mode 100644 docs/source/_build/html/_downloads/6dd07bf8f59ed369971c33b38f420079/plot_saltelli.py
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 create mode 100644 docs/source/_build/html/_downloads/72c9aa931cd2028d7edb96ceb292a4a2/plot_metropolis_hastings.ipynb
 create mode 100644 docs/source/_build/html/_downloads/79d68b726b379b22e24e81ddc36bf480/sampler_python.zip
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 create mode 100644 docs/source/_build/html/_downloads/af73dbd4cdfb71a4d5cac0b204c855e0/emulator_jupyter.zip
 create mode 100644 docs/source/_build/html/_downloads/b20b8a8616a1c41193e9b38a6dd88919/sensitivity_python.zip
 create mode 100644 docs/source/_build/html/_downloads/bfca202fd55dbe4c4a07ec2f8128e4cc/plot_ppgasp.py
 create mode 100644 docs/source/_build/html/_downloads/ca97a6211ade4816b175cce5bc31a34b/plot_scalargasp.py
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 create mode 100644 docs/source/_build/html/_downloads/e02cb6046784acec18b4383ffbd83d67/plot_active_learning.ipynb
 create mode 100644 docs/source/_build/html/_downloads/e0b3048771af654ea83c8bb3f5bf6c0c/plot_saltelli.ipynb
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 create mode 100644 docs/source/_build/html/_images/sphx_glr_plot_ppgasp_thumb.png
 create mode 100644 docs/source/_build/html/_images/sphx_glr_plot_ravaflow24_001.png
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 create mode 100644 docs/source/_build/html/_images/sphx_glr_plot_saltelli_001.png
 create mode 100644 docs/source/_build/html/_images/sphx_glr_plot_saltelli_002.png
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 create mode 100644 docs/source/_build/html/_modules/psimpy/sampler/metropolis_hastings.html
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diff --git a/docs/source/_build/doctrees/simulator/run_simulator.doctree b/docs/source/_build/doctrees/simulator/run_simulator.doctree
new file mode 100644
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diff --git a/docs/source/_build/html/.buildinfo b/docs/source/_build/html/.buildinfo
new file mode 100644
index 0000000..c10e76a
--- /dev/null
+++ b/docs/source/_build/html/.buildinfo
@@ -0,0 +1,4 @@
+# Sphinx build info version 1
+# This file hashes the configuration used when building these files. When it is not found, a full rebuild will be done.
+config: 312d9d94b3d9ded8d89af6085a987f67
+tags: 645f666f9bcd5a90fca523b33c5a78b7
diff --git a/docs/source/_build/html/_downloads/06e1d1c67d64bdd5612e33cffc1295c5/plot_run_ravaflow24.py b/docs/source/_build/html/_downloads/06e1d1c67d64bdd5612e33cffc1295c5/plot_run_ravaflow24.py
new file mode 100644
index 0000000..6766651
--- /dev/null
+++ b/docs/source/_build/html/_downloads/06e1d1c67d64bdd5612e33cffc1295c5/plot_run_ravaflow24.py
@@ -0,0 +1,212 @@
+"""
+
+RunSimulator: Ravaflow24 Mixture Model
+======================================
+"""
+
+# %% md
+# 
+# This example shows how to run multiple Ravaflow24Mixture simulations in serial
+# and parallelly using :class:`.RunSimulator`.
+#
+
+# %% md
+# 
+# First, we import the class :class:`.Ravaflow24Mixture`.
+
+from psimpy.simulator import Ravaflow24Mixture
+
+# %% md
+# 
+# To create an instance of this class, we must specify the parameter ``dir_sim``.
+# It represents the directory in which output files generated by r.avaflow will be
+# saved.
+
+import os
+
+# Here we create a folder called `temp1_run_Ravaflow24Mixture_example` to save
+# output files generated by r.avaflow
+cwd = os.getcwd()
+if not os.path.exists('temp1_run_Ravaflow24Mixture_example'):
+    os.mkdir('temp1_run_Ravaflow24Mixture_example')
+dir_sim = os.path.join(cwd, 'temp1_run_Ravaflow24Mixture_example')
+
+# %% md
+# 
+# Given ``dir_sim``,  we can create an instance of :class:`.Ravaflow24Mixture`.
+# To reduce simulation time, we set ``time_end`` to :math:`50`. Other parameters
+# are set to their default values.
+
+voellmy_model = Ravaflow24Mixture(dir_sim, time_end=50)
+
+# %% md
+# 
+# The `simulator` in this example is defined based on ``voellmy_model`` as follows.
+# It takes required inputs and returns the overall impact area.
+
+import numpy as np
+
+def simulator(prefix, elevation, hrelease, basal_friction, turbulent_friction, EPSG):
+    """Preprocess required inputs, run simulation, and return output as a numpy array."""
+    grass_location, sh_file = voellmy_model.preprocess(prefix=prefix, elevation=elevation,
+        hrelease=hrelease, basal_friction=basal_friction, turbulent_friction=turbulent_friction, EPSG=EPSG)
+    voellmy_model.run(grass_location, sh_file) # run this line, r.avaflow will write outputs to dir_sim
+    impact_area = voellmy_model.extract_impact_area(prefix)
+    
+    return np.array([impact_area]) # define dir_out and set save_out to True, returned numpy array will be saved to dir_out
+
+
+# %% md
+# 
+# To demonstrate how to run multiple simulations using :class:`.RunSimulator`, 
+# we choose ``basal_friction`` and ``turbulent_friction`` as variable input
+# parameters. Each has two different values, leading to four simulations.
+
+import itertools
+
+var_inp_parameter = ['basal_friction', 'turbulent_friction']
+basal_friction = [20, 30] 
+turbulent_friction = [3, 4]
+var_samples = np.array(
+    [x for x in itertools.product(basal_friction, turbulent_friction)])
+
+
+# %% md
+#
+# Other parameters of the `simulator`, including ``elevation``, ``hrelease``, and
+# ``EPSG`` are treated as fixed input. It means that their values are the same in
+# all simulations.
+
+dir_data = os.path.abspath('../../../tests/data/')
+elevation = os.path.join(dir_data, 'synthetic_topo.tif')
+hrelease = os.path.join(dir_data, 'synthetic_rel.tif')
+fix_inp = {'elevation': elevation, 'hrelease': hrelease, 'EPSG': '2326'}
+
+# %% md
+# 
+# The parameter ``prefix`` of the `simulator` is special. It is not involved in
+# the computational model, but only used to name output files generated by r.avaflow.
+# Such parameter is not defined in ``var_inp_parameter`` or ``fix_inp`` of
+# :class:`.RunSimulator`. Instead, we use a seperate parameter, called ``o_parameter``
+# for this purpose.
+
+o_parameter = 'prefix'
+
+
+# %% md
+# 
+# We may want to save outputs returned by the `simulator` at each simulation for
+# later inspection or processing. In that case, we need to define ``dir_out`` and
+# set ``save_out`` as `True`.
+
+import os
+
+cwd = os.getcwd()
+if not os.path.exists('temp2_run_Ravaflow24Mixture_example'):
+    os.mkdir('temp2_run_Ravaflow24Mixture_example')
+dir_out = os.path.join(cwd, 'temp2_run_Ravaflow24Mixture_example')
+
+# %% md
+#
+# .. note:: Please note that ``dir_out`` and ``dir_sim`` are two different
+#    parameters for different purposes.
+#  
+#     - ``dir_out`` is a parameter of :class:`.RunSimulator`. The `simulator`
+#       returns output of interest as a numpy array for each simulation. If
+#       we want to save this returned output of interest (here impact area)
+#       to our local machine, we need to specify the value of ``dir_out`` which
+#       represents the directory in which output of interest will be saved and
+#       set ``save_out`` to `True`. Otherwise, we do not need ``dir_out`` and
+#       leave ``save_out`` to `False`.
+#     - ``dir_sim`` is a parameter of :class:`.Ravaflow24Mixture`. :class:`.Ravaflow24Mixture`
+#       relies on the third party software r.avaflow 2.4. When we call
+#       :py:meth:`.Ravaflow24Mixture.run` in the function body of above `simulator`,
+#       r.avaflow 2.4 will be run and it generates output files. The value of
+#       ``dir_sim`` specifies the directory in which output files generated by
+#       r.avaflow 2.4 are going to be saved.
+#
+#    The value of ``dir_out`` and ``dir_sim`` can be the same if file names 
+#    have no conflict. We recommend to keep them seperate. In addition, if the function
+#    body of the `simulator` does not write files to disk, ``dir_sim`` is not required. Our
+#    :class:`.MassPointModel` is an example. Similarly, if we do not want to save
+#    returned numpy array of the `simulator`, ``dir_out`` is not needed.
+
+# %% md
+#
+# Now we can define an object of :class:`.RunSimulator` by
+
+from psimpy.simulator import RunSimulator
+
+run_simulator = RunSimulator(simulator, var_inp_parameter, fix_inp, o_parameter,
+    dir_out, save_out=True)
+
+
+# %% md
+# 
+# Before running simulations, we need to specify values of ``prefixes`` which
+# will be used to name files generated by each r.avaflow simulation and
+# each returned numpy array of `simulator`.
+
+serial_prefixes = ["serial"+str(i) for i in range(len(var_samples))]
+parallel_prefixes = ["parallel"+str(i) for i in range(len(var_samples))]
+
+# %% md
+#
+# Now we can use :py:meth:`.RunSimulator.serial_run` method or
+# :py:meth:`.RunSimulator.parallel_run` method to run the simulations
+# in serial or parallelly.
+
+import time
+
+start = time.time()
+run_simulator.serial_run(var_samples=var_samples, prefixes=serial_prefixes)
+serial_time = time.time() - start
+serial_output = run_simulator.outputs
+print(f"serial_output: {serial_output}")
+
+start = time.time()
+# append setting to True means that simulation outputs of parallel run will be
+# appended to above serial run outputs
+run_simulator.parallel_run(var_samples, prefixes=parallel_prefixes,
+    max_workers=2, append=True)
+parallel_time = time.time() - start
+    
+parallel_output = run_simulator.outputs[len(var_samples):]
+print(f"parallel_output: {parallel_output}")
+
+    
+print("Serial run time: ", serial_time)
+print("Parallel run time: ", parallel_time)
+
+# %% md
+# 
+# All output files returned by the `simulator` are
+
+os.listdir(dir_out)
+
+# %% md
+# 
+# All output files/directories generated by r.avaflow simulations 
+# (including files/directories generated during preprocessing) are
+
+os.listdir(dir_sim)
+
+
+# %% md
+# .. warning:: If one simulation failed due to whatever reason, the error massage
+#    will be printed to the screen but other simulations will continue. In that 
+#    case, the output file of failed simulation will not be writted to ``dir_out``.
+#    Also, the element of :py:attr:`.RunSimulator.outputs` corresponding to that
+#    simulation will be a string representing the error message, instead of a
+#    numpy array.
+
+
+# %% md
+# 
+# In the end, we delete the folder `temp1_run_Ravaflow24Mixture_example` and
+# `temp2_run_Ravaflow24Mixture_example` and all files therein.
+
+import shutil
+
+shutil.rmtree(dir_sim)
+shutil.rmtree(dir_out)
\ No newline at end of file
diff --git a/docs/source/_build/html/_downloads/201f9a51be1f2378acae03891235a84e/plot_mass_point_model.ipynb b/docs/source/_build/html/_downloads/201f9a51be1f2378acae03891235a84e/plot_mass_point_model.ipynb
new file mode 100644
index 0000000..44810c7
--- /dev/null
+++ b/docs/source/_build/html/_downloads/201f9a51be1f2378acae03891235a84e/plot_mass_point_model.ipynb
@@ -0,0 +1,165 @@
+{
+  "cells": [
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "%matplotlib inline"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "\n# Mass Point Model\n"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "This example shows how to simulate the movement of a masspoint on a topography\nusing :class:`.MassPointModel`.\n\n\n\n"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "First, import the class :class:`.MassPointModel` and create an instance by\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "from psimpy.simulator import MassPointModel\n\nmpm = MassPointModel()"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "Required inputs for a simulation using :class:`.MassPointModel` include:\n    1. topographic data: digital elevation model (in `ESRI ascii` format)\n    2. friction coefficients: coulomb friction and turbulent friction coefficients\n    3. initial state: initial location and initial velocity of the masspoint\n    4. computational parameters: such as time step, end time, etc.\n\nThe synthetic topography ``synthetic_topo.asc`` is used here for illustration.\nIt is located at the `tests/data/` folder.\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "import os\nimport linecache\nimport numpy as np\n\ndir_data = os.path.abspath('../../../tests/data/')\nelevation = os.path.join(dir_data, 'synthetic_topo.asc')"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "<div class=\"alert alert-info\"><h4>Note</h4><p>You may need to modify ``dir_data`` according to where you save\n   ``synthetic_topo.asc`` on your local machine.</p></div>\n\n"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "We can load the elevation data and visulize it. The figure below shows how\nthe topography looks like, as well as the initial location of the masspoint\n(noted by the red dot).\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "header = [linecache.getline(elevation, i) for i in range(1,6)]\nheader_values = [float(h.split()[-1].strip()) for h in header]\nncols, nrows, xll, yll, cellsize = header_values\nncols = int(ncols)\nnrows = int(nrows)\n\nx_values = np.arange(xll, xll+(cellsize*ncols), cellsize)\ny_values = np.arange(yll, yll+(cellsize*nrows), cellsize)\n        \nz_values = np.loadtxt(elevation, skiprows=6)\nz_values = np.rot90(np.transpose(z_values))\n\n# initial location\nx0 = 200\ny0 = 2000\nz0 = z_values[0, int(x0/cellsize)]\n\nimport matplotlib.pyplot as plt\n\nfig, ax = plt.subplots(2, 1, figsize=(10,6), height_ratios=[3,2])\n\nfig0 = ax[0].contourf(x_values, y_values, z_values, levels=20)\nax[0].set_xlabel('x')\nax[0].set_ylabel('y')\nax[0].set_title('synthetic topography')\nax[0].scatter(x0, y0, s=10, c='r', marker='o')\ncbar = plt.colorbar(fig0, ax=ax[0], format='%d', orientation='horizontal',\n    fraction=0.1, pad=0.2)\ncbar.ax.set_ylabel('z')\n\n\nax[1].plot(x_values, z_values[0, :])\nax[1].scatter(x0, z0, s=10, c='r', marker='o')\nax[1].set_xlabel('x')\nax[1].set_ylabel('z')\nax[1].set_xlim(0, 5000)\nax[1].set_title('cross section at any y')\n\nplt.tight_layout()"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "We set the friction coefficients as\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "mu = 0.15\nxi = 1000"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "Given above topography, initial location, and friction coefficients, we can\ncall the :py:meth:`.MassPointModel.run` method to perform a simulation. Other\nparameters are set to their default values. (we suppress raised warnings )\n(other parameters are set to their default values).\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "import warnings\n\nwarnings.filterwarnings(\"ignore\")\noutput = mpm.run(elevation=elevation, coulomb_friction=mu, turbulent_friction=xi, x0=x0, y0=y0)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "The simulation returns time history of the mass point's location and velocity.\nFollowing plots show the simulation results.\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "fig, ax = plt.subplots(3, 1, figsize=(10,6))\n\nax[0].set_xlabel('time (s)')\nax[0].set_ylabel('x')\nax[0].set_title(\"x-t plot\")\nax[0].plot(output[:,0], output[:,1])\n\nax[1].set_xlabel('time (s)')\nax[1].set_ylabel('velocity')\nax[1].set_title(\"v-t plot\")\nax[1].plot(output[:,0], output[:,5])\n\nax[2].set_xlabel('x')\nax[2].set_ylabel('velocity')\nax[2].set_title(\"x-v plot\")\nax[2].plot(output[:,1], output[:,5])\n\nplt.tight_layout()"
+      ]
+    }
+  ],
+  "metadata": {
+    "kernelspec": {
+      "display_name": "Python 3",
+      "language": "python",
+      "name": "python3"
+    },
+    "language_info": {
+      "codemirror_mode": {
+        "name": "ipython",
+        "version": 3
+      },
+      "file_extension": ".py",
+      "mimetype": "text/x-python",
+      "name": "python",
+      "nbconvert_exporter": "python",
+      "pygments_lexer": "ipython3",
+      "version": "3.9.12"
+    }
+  },
+  "nbformat": 4,
+  "nbformat_minor": 0
+}
\ No newline at end of file
diff --git a/docs/source/_build/html/_downloads/213f7cd5e82a62f8d1da8c3af9caab35/plot_latin.py b/docs/source/_build/html/_downloads/213f7cd5e82a62f8d1da8c3af9caab35/plot_latin.py
new file mode 100644
index 0000000..1faa3cc
--- /dev/null
+++ b/docs/source/_build/html/_downloads/213f7cd5e82a62f8d1da8c3af9caab35/plot_latin.py
@@ -0,0 +1,91 @@
+"""
+
+Latin hypercube sampling
+========================
+"""
+
+# %% md
+# 
+# This example shows how to draw samples using Latin hypercube sampling.
+#
+# 
+
+# %% md
+# 
+# For the illustration purpose, let's have a look at a two-dimensional example
+# where we have two random variables X and Y. Each is uniformly distributed in its
+# range.
+
+import numpy as np
+
+ndim = 2
+# range of X is 10 to 20, range of Y is -10 to 0
+bounds = np.array([[10,20], [-10,0]])
+
+# %% md
+#
+# Given this setting, we can import :class:`.Latin`, create an instance, and
+# call the :py:meth:`.Latin.sample` method to draw required number of samples
+
+from psimpy.sampler import LHS
+
+# setting seed leads to same samples every time when the codes are run
+lhs_sampler = LHS(ndim, bounds, seed=10)
+lhs_samples = lhs_sampler.sample(nsamples=5)
+
+# %% md
+#
+# The samples are plotted in the following figure.
+
+import matplotlib.pyplot as plt
+
+fig , ax = plt.subplots(figsize=(6,4))
+
+ax.scatter(lhs_samples[:,0], lhs_samples[:,1], s=10, c='blue', marker='o')
+
+ax.set_xlabel('X')
+ax.set_ylabel('Y')
+ax.set_xlim(bounds[0])
+ax.set_ylim(bounds[1])
+ax.set_title("Latin hypercube samples (criterion='random')")
+_ = ax.grid(visible=True, which='major', axis='both')
+
+
+# %% md
+#
+# There are different criterions to pick samples in each hypercube. The default
+# is `random`, as used above. Other options are `center` and `maximin`. For instance,
+# we can use the `center` criterion to draw :math:`5` samples as follows:
+
+lhs_sampler = LHS(ndim, bounds, criterion='center', seed=10)
+lhs_samples = lhs_sampler.sample(nsamples=5)
+
+fig , ax = plt.subplots(figsize=(6,4))
+
+ax.scatter(lhs_samples[:,0], lhs_samples[:,1], s=10, c='blue', marker='o')
+
+ax.set_xlabel('X')
+ax.set_ylabel('Y')
+ax.set_xlim(bounds[0])
+ax.set_ylim(bounds[1])
+ax.set_title("Latin hypercube samples (criterion='center')")
+_ = ax.grid(visible=True, which='major', axis='both')
+
+
+# %% md
+#
+# And we can use the `maximin` criterion as follows:
+
+lhs_sampler = LHS(ndim, bounds, criterion='maximin', seed=10, iteration=500)
+lhs_samples = lhs_sampler.sample(nsamples=5)
+
+fig , ax = plt.subplots(figsize=(6,4))
+
+ax.scatter(lhs_samples[:,0], lhs_samples[:,1], s=10, c='blue', marker='o')
+
+ax.set_xlabel('X')
+ax.set_ylabel('Y')
+ax.set_xlim(bounds[0])
+ax.set_ylim(bounds[1])
+ax.set_title("Latin hypercube samples (criterion='maximin')")
+_ = ax.grid(visible=True, which='major', axis='both')
\ No newline at end of file
diff --git a/docs/source/_build/html/_downloads/2d9fc590bc1edb11501b144674a0a949/plot_bayes_inference.ipynb b/docs/source/_build/html/_downloads/2d9fc590bc1edb11501b144674a0a949/plot_bayes_inference.ipynb
new file mode 100644
index 0000000..1a2b1ea
--- /dev/null
+++ b/docs/source/_build/html/_downloads/2d9fc590bc1edb11501b144674a0a949/plot_bayes_inference.ipynb
@@ -0,0 +1,140 @@
+{
+  "cells": [
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "%matplotlib inline"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "\n# Bayesian inference\n"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "This example shows how to perform Bayesian inference given the uniform prior\n\n$p(\\mathbf{x})=p(x_1,x_2)=0.01$\n\nwhere $x_i \\in [-5,5], i=1,2$, and likelihood\n\n$L(\\mathbf{x}|\\mathbf{d})=\\exp \\left(-\\frac{1}{100}\\left(x_1-1\\right)^2-\\left(x_1^2-x_2\\right)^2\\right)$.\n\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "import numpy as np\n\nndim = 2\nbounds = np.array([[-5,5],[-5,5]])\n\ndef prior(x):\n        return 0.01\n\ndef likelihood(x):\n        return np.exp(-(x[0]-1)**2/100 - (x[0]**2-x[1])**2)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "To estimate the posterior using grid estimation, we need to import the\n:class:`.GridEstimation` class, create an instance, and call the \n:py:meth:`.GridEstimation.run` method.\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "from psimpy.inference.bayes_inference import GridEstimation\n\ngrid_estimator = GridEstimation(ndim, bounds, prior, likelihood)\nposterior, x_ndim = grid_estimator.run(nbins=[50,40])"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "The following figure plots the estimated posterior.\n\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "import matplotlib.pyplot as plt\n\nfig, ax = plt.subplots(1,1,figsize=(6,4))\n\n# mask insignificant values\nposterior = np.where(posterior < 1e-10, None, posterior)\n\ncontour = ax.contour(x_ndim[0], x_ndim[1], np.transpose(posterior), levels=10)\nplt.colorbar(contour, ax=ax)\nax.set_xlim(bounds[0,0], bounds[0,1])\nax.set_ylim(bounds[1,0], bounds[1,1])\nax.set_title('Grid estimation')\nax.set_xlabel('x1')\nax.set_ylabel('x2')\nplt.tight_layout()"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "To estimate the posterior using Metropolis Hastings estimation, we need to import\nthe :class:`.MetropolisHastingsEstimation` class, create an instance, and call the \n:py:meth:`.MetropolisHastingsEstimation.run` method. The \n:py:meth:`.MetropolisHastingsEstimation.run` method has a parameter, ``mh_sampler``,\nwhich takes an instance of :class:`.MetropolisHastings` as argument.\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "from psimpy.inference.bayes_inference import MetropolisHastingsEstimation\n\nmh_estimator = MetropolisHastingsEstimation(ndim, bounds, prior, likelihood)\n\n# create a mh_sampler\nfrom psimpy.sampler.metropolis_hastings import MetropolisHastings\nfrom scipy.stats import multivariate_normal\n\ninit_state = np.array([-4,-4])\nf_sample = multivariate_normal.rvs\nnburn = 100\nnthin = 10\nseed = 1\nkwgs_f_sample = {'random_state': np.random.default_rng(seed)}\n\nmh_sampler = MetropolisHastings(ndim=ndim, init_state=init_state,\n    f_sample=f_sample, bounds=bounds, nburn=nburn, nthin=nthin, seed=seed,\n    kwgs_f_sample=kwgs_f_sample)\n    \nnsamples = 5000\nmh_samples, mh_accept = mh_estimator.run(nsamples, mh_sampler)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "The following figure plots the samples drawn from the unnormalized posterior,\nwhich can be used to estimate the posterior and its poperties.\n\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "import matplotlib.pyplot as plt\n\nfig, ax = plt.subplots(1,1,figsize=(5,4))\n\nax.scatter(mh_samples[:,0], mh_samples[:,1], s=10, c='r', marker='o', alpha=0.1)\nax.set_xlim(bounds[0,0], bounds[0,1])\nax.set_ylim(bounds[1,0], bounds[1,1])\nax.set_title('MH estimation')\nax.set_xlabel('x1')\nax.set_ylabel('x2')\nplt.tight_layout()"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "<div class=\"alert alert-info\"><h4>Note</h4><p>Besides ``prior`` and ``likelihood``, one can also instantiate\n    the :class:`.MetropolisHastingsEstimation` class with\n\n     - ``ln_prior`` and ``ln_likelihood``: Natural logarithm of ``prior`` and ``likelihood``.\n     - ``ln_pxl``: Natural logarithm of the product of ``prior`` and ``likelihood``.</p></div>\n\n"
+      ]
+    }
+  ],
+  "metadata": {
+    "kernelspec": {
+      "display_name": "Python 3",
+      "language": "python",
+      "name": "python3"
+    },
+    "language_info": {
+      "codemirror_mode": {
+        "name": "ipython",
+        "version": 3
+      },
+      "file_extension": ".py",
+      "mimetype": "text/x-python",
+      "name": "python",
+      "nbconvert_exporter": "python",
+      "pygments_lexer": "ipython3",
+      "version": "3.9.12"
+    }
+  },
+  "nbformat": 4,
+  "nbformat_minor": 0
+}
\ No newline at end of file
diff --git a/docs/source/_build/html/_downloads/3072e3885ecdb1bbb3b34893dcfd8def/plot_latin.ipynb b/docs/source/_build/html/_downloads/3072e3885ecdb1bbb3b34893dcfd8def/plot_latin.ipynb
new file mode 100644
index 0000000..353f5cf
--- /dev/null
+++ b/docs/source/_build/html/_downloads/3072e3885ecdb1bbb3b34893dcfd8def/plot_latin.ipynb
@@ -0,0 +1,140 @@
+{
+  "cells": [
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "%matplotlib inline"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "\n# Latin hypercube sampling\n"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "This example shows how to draw samples using Latin hypercube sampling.\n\n\n\n"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "For the illustration purpose, let's have a look at a two-dimensional example\nwhere we have two random variables X and Y. Each is uniformly distributed in its\nrange.\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "import numpy as np\n\nndim = 2\n# range of X is 10 to 20, range of Y is -10 to 0\nbounds = np.array([[10,20], [-10,0]])"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "Given this setting, we can import :class:`.Latin`, create an instance, and\ncall the :py:meth:`.Latin.sample` method to draw required number of samples\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "from psimpy.sampler import LHS\n\n# setting seed leads to same samples every time when the codes are run\nlhs_sampler = LHS(ndim, bounds, seed=10)\nlhs_samples = lhs_sampler.sample(nsamples=5)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "The samples are plotted in the following figure.\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "import matplotlib.pyplot as plt\n\nfig , ax = plt.subplots(figsize=(6,4))\n\nax.scatter(lhs_samples[:,0], lhs_samples[:,1], s=10, c='blue', marker='o')\n\nax.set_xlabel('X')\nax.set_ylabel('Y')\nax.set_xlim(bounds[0])\nax.set_ylim(bounds[1])\nax.set_title(\"Latin hypercube samples (criterion='random')\")\n_ = ax.grid(visible=True, which='major', axis='both')"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "There are different criterions to pick samples in each hypercube. The default\nis `random`, as used above. Other options are `center` and `maximin`. For instance,\nwe can use the `center` criterion to draw $5$ samples as follows:\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "lhs_sampler = LHS(ndim, bounds, criterion='center', seed=10)\nlhs_samples = lhs_sampler.sample(nsamples=5)\n\nfig , ax = plt.subplots(figsize=(6,4))\n\nax.scatter(lhs_samples[:,0], lhs_samples[:,1], s=10, c='blue', marker='o')\n\nax.set_xlabel('X')\nax.set_ylabel('Y')\nax.set_xlim(bounds[0])\nax.set_ylim(bounds[1])\nax.set_title(\"Latin hypercube samples (criterion='center')\")\n_ = ax.grid(visible=True, which='major', axis='both')"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "And we can use the `maximin` criterion as follows:\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "lhs_sampler = LHS(ndim, bounds, criterion='maximin', seed=10, iteration=500)\nlhs_samples = lhs_sampler.sample(nsamples=5)\n\nfig , ax = plt.subplots(figsize=(6,4))\n\nax.scatter(lhs_samples[:,0], lhs_samples[:,1], s=10, c='blue', marker='o')\n\nax.set_xlabel('X')\nax.set_ylabel('Y')\nax.set_xlim(bounds[0])\nax.set_ylim(bounds[1])\nax.set_title(\"Latin hypercube samples (criterion='maximin')\")\n_ = ax.grid(visible=True, which='major', axis='both')"
+      ]
+    }
+  ],
+  "metadata": {
+    "kernelspec": {
+      "display_name": "Python 3",
+      "language": "python",
+      "name": "python3"
+    },
+    "language_info": {
+      "codemirror_mode": {
+        "name": "ipython",
+        "version": 3
+      },
+      "file_extension": ".py",
+      "mimetype": "text/x-python",
+      "name": "python",
+      "nbconvert_exporter": "python",
+      "pygments_lexer": "ipython3",
+      "version": "3.9.12"
+    }
+  },
+  "nbformat": 4,
+  "nbformat_minor": 0
+}
\ No newline at end of file
diff --git a/docs/source/_build/html/_downloads/31c796c77470b56d8b117051a799e0b5/simulator_python.zip b/docs/source/_build/html/_downloads/31c796c77470b56d8b117051a799e0b5/simulator_python.zip
new file mode 100644
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diff --git a/docs/source/_build/html/_downloads/39558f3ab53d6f797e2208e7c89063a5/plot_run_mass_point_model.ipynb b/docs/source/_build/html/_downloads/39558f3ab53d6f797e2208e7c89063a5/plot_run_mass_point_model.ipynb
new file mode 100644
index 0000000..a75fe8e
--- /dev/null
+++ b/docs/source/_build/html/_downloads/39558f3ab53d6f797e2208e7c89063a5/plot_run_mass_point_model.ipynb
@@ -0,0 +1,251 @@
+{
+  "cells": [
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "%matplotlib inline"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "\n# RunSimulator: Mass Point Model\n"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "This example shows how to run multiple MassPointModel simulations in serial\nand parallelly using :class:`.RunSimulator`.\n\n\n\n"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "First, we import the class :class:`.MassPointModel` and define a `simulator`\nbased on :py:meth:`.MassPointModel.run` method.\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "from psimpy.simulator import MassPointModel\n\nmpm = MassPointModel()\nmpm_simulator = mpm.run"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "This simulator takes required input data, solves the mass point model, and\nreturns time history of the mass point's location and velocity\n(see :py:meth:`.MassPointModel.run`).\n\nRequired inputs for `mpm_simulator` include:\n    1. topographic data: digital elevation model (in `ESRI ascii` format)\n    2. friction coefficients: coulomb friction and turbulent friction coefficients\n    3. initial state: initial location and initial velocity of the masspoint\n    4. computational parameters: such as time step, end time, etc.\n\nThe synthetic topography ``synthetic_topo.asc`` is used here for illustration.\nIt is located at the `/tests/data/` folder.\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "import os\n\ndir_data = os.path.abspath('../../../tests/data/')\nelevation = os.path.join(dir_data, 'synthetic_topo.asc')"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "<div class=\"alert alert-info\"><h4>Note</h4><p>You may need to modify ``dir_data`` according to where you save\n   ``synthetic_topo.asc`` on your local machine.</p></div>\n\n"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "For this example, we are going to run multiple simulations at different values\nof coulomb friction coefficient (``coulomb_friction``) and turbulent friction\ncoefficient (``turbulent_friction``) while keep other inputs fixed. Namely,\n``coulomb_friction`` and ``turbulent_friction`` are variable input parameters.\nAll other inputs are fixed input parameters.\n\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "import numpy as np\nimport itertools\n\n# Variable iput parameters are defined as a list of strings. Their values will be\n# passed as a numpy array (var_samples) when run simulations.\nvar_inp_parameter = ['coulomb_friction', 'turbulent_friction']\ncoulomb_friction = np.arange(0.1, 0.31, 0.1)\nturbulent_friction = np.arange(500, 2001, 400)\nvar_samples = np.array(\n    [x for x in itertools.product(coulomb_friction, turbulent_friction)])\nprint(\"Number of variable input samples are: \", len(var_samples))\n\n# Fixed input parameters are defined as a dictionary. Their values are given.\nfix_inp = {'elevation': elevation, 'x0': 200, 'y0': 2000, 'tend': 50}"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "<div class=\"alert alert-info\"><h4>Note</h4><p>Parameters of `mpm_simulator` which are not included in\n   ``var_inp_parameter`` and ``fix_inp``, such as ``ux0``, ``uy0`` and\n   ``curvature``, will automatically take their default values.</p></div>\n\n"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "We may want to save outputs returned by `mpm_simulator` at each simulation for\nlater inspection or processing. In that case, we need to define ``dir_out`` and\nset ``save_out`` as `True`.\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "import os\n\n# Here we create a folder called `temp_run_MassPointModel_example` to save outputs\n# returned at each simulation.\ncwd = os.getcwd()\nif not os.path.exists('temp_run_MassPointModel_example'):\n    os.mkdir('temp_run_MassPointModel_example')\ndir_out = os.path.join(cwd, 'temp_run_MassPointModel_example')"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "Now we can define an object of :class:`.RunSimulator` by\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "from psimpy.simulator import RunSimulator\n\nrun_mpm_simulator = RunSimulator(mpm_simulator, var_inp_parameter, fix_inp,\n    dir_out=dir_out, save_out=True)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "<div class=\"alert alert-info\"><h4>Note</h4><p>Since outputs of each simulation are saved in the same folder ``dir_out``,\n   we need to give each file a unique name in order to avoid conflict. This is\n   realized by defining ``prefixes``.</p></div>\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "serial_prefixes = [\"serial\"+str(i) for i in range(len(var_samples))]\nparallel_prefixes = [\"parallel\"+str(i) for i in range(len(var_samples))]"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "Using :py:meth:`.RunSimulator.serial_run` method or\n:py:meth:`.RunSimulator.parallel_run` method, we can run the simulations\nin serial or parallelly.\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "import time\n\nstart = time.time()\nrun_mpm_simulator.serial_run(var_samples=var_samples, prefixes=serial_prefixes)\nserial_time = time.time() - start\nserial_output = run_mpm_simulator.outputs\n\nstart = time.time()\n# max_workers controls maximum number of tasks running in parallel\nrun_mpm_simulator.parallel_run(var_samples, prefixes=parallel_prefixes, max_workers=4)\nparallel_time = time.time() - start\nparallel_output = run_mpm_simulator.outputs\n    \nprint(\"Serial run time: \", serial_time)\nprint(\"Parallel run time: \", parallel_time)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "Once a simulation is done, its output is saved to ``dir_out``. All output files\ngenerated by above simulations are as follows: \n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "os.listdir(dir_out)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "Once all simulations are done, their outputs can also be accessed by\n:py:attr:`.RunSimulator.outputs` attribute, which is a list.\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "# Here we print the maximum velocity of each simulation in the parallel run.\nmax_v = [np.max(output[:,5]) for output in parallel_output]\nprint(\n    f\"Maximum velocity of {parallel_prefixes[0]} to {parallel_prefixes[-1]} are: \",\n    '\\n',\n    max_v)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "<div class=\"alert alert-danger\"><h4>Warning</h4><p>If one simulation failed due to whatever reason, the error massage\n   will be printed to the screen but other simulations will continue. In that \n   case, the output file of failed simulation will not be writted to ``dir_out``.\n   Also, the element of :py:attr:`.RunSimulator.outputs` corresponding to that\n   simulation will be a string representing the error message, instead of a\n   numpy array.</p></div>\n\n"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "Here we delete the folder `temp_run_MassPointModel_example` and all files therein.\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "import shutil\n\nshutil.rmtree(dir_out)"
+      ]
+    }
+  ],
+  "metadata": {
+    "kernelspec": {
+      "display_name": "Python 3",
+      "language": "python",
+      "name": "python3"
+    },
+    "language_info": {
+      "codemirror_mode": {
+        "name": "ipython",
+        "version": 3
+      },
+      "file_extension": ".py",
+      "mimetype": "text/x-python",
+      "name": "python",
+      "nbconvert_exporter": "python",
+      "pygments_lexer": "ipython3",
+      "version": "3.9.12"
+    }
+  },
+  "nbformat": 4,
+  "nbformat_minor": 0
+}
\ No newline at end of file
diff --git a/docs/source/_build/html/_downloads/44f0f511484d9bfd5f8d212c8f287e9e/plot_bayes_inference.py b/docs/source/_build/html/_downloads/44f0f511484d9bfd5f8d212c8f287e9e/plot_bayes_inference.py
new file mode 100644
index 0000000..855d62b
--- /dev/null
+++ b/docs/source/_build/html/_downloads/44f0f511484d9bfd5f8d212c8f287e9e/plot_bayes_inference.py
@@ -0,0 +1,116 @@
+"""
+
+Bayesian inference
+==================
+"""
+
+# %% md
+# 
+# This example shows how to perform Bayesian inference given the uniform prior
+#
+# :math:`p(\mathbf{x})=p(x_1,x_2)=0.01`
+# 
+# where :math:`x_i \in [-5,5], i=1,2`, and likelihood
+#
+# :math:`L(\mathbf{x}|\mathbf{d})=\exp \left(-\frac{1}{100}\left(x_1-1\right)^2-\left(x_1^2-x_2\right)^2\right)`.
+#
+
+import numpy as np
+
+ndim = 2
+bounds = np.array([[-5,5],[-5,5]])
+
+def prior(x):
+        return 0.01
+
+def likelihood(x):
+        return np.exp(-(x[0]-1)**2/100 - (x[0]**2-x[1])**2)
+
+# %% md
+#
+# To estimate the posterior using grid estimation, we need to import the
+# :class:`.GridEstimation` class, create an instance, and call the 
+# :py:meth:`.GridEstimation.run` method.
+
+from psimpy.inference.bayes_inference import GridEstimation
+
+grid_estimator = GridEstimation(ndim, bounds, prior, likelihood)
+posterior, x_ndim = grid_estimator.run(nbins=[50,40])
+
+# %% md
+#
+# The following figure plots the estimated posterior.
+# 
+
+import matplotlib.pyplot as plt
+
+fig, ax = plt.subplots(1,1,figsize=(6,4))
+
+# mask insignificant values
+posterior = np.where(posterior < 1e-10, None, posterior)
+
+contour = ax.contour(x_ndim[0], x_ndim[1], np.transpose(posterior), levels=10)
+plt.colorbar(contour, ax=ax)
+ax.set_xlim(bounds[0,0], bounds[0,1])
+ax.set_ylim(bounds[1,0], bounds[1,1])
+ax.set_title('Grid estimation')
+ax.set_xlabel('x1')
+ax.set_ylabel('x2')
+plt.tight_layout()
+
+# %% md
+#
+# To estimate the posterior using Metropolis Hastings estimation, we need to import
+# the :class:`.MetropolisHastingsEstimation` class, create an instance, and call the 
+# :py:meth:`.MetropolisHastingsEstimation.run` method. The 
+# :py:meth:`.MetropolisHastingsEstimation.run` method has a parameter, ``mh_sampler``,
+# which takes an instance of :class:`.MetropolisHastings` as argument.
+
+from psimpy.inference.bayes_inference import MetropolisHastingsEstimation
+
+mh_estimator = MetropolisHastingsEstimation(ndim, bounds, prior, likelihood)
+
+# create a mh_sampler
+from psimpy.sampler.metropolis_hastings import MetropolisHastings
+from scipy.stats import multivariate_normal
+
+init_state = np.array([-4,-4])
+f_sample = multivariate_normal.rvs
+nburn = 100
+nthin = 10
+seed = 1
+kwgs_f_sample = {'random_state': np.random.default_rng(seed)}
+
+mh_sampler = MetropolisHastings(ndim=ndim, init_state=init_state,
+    f_sample=f_sample, bounds=bounds, nburn=nburn, nthin=nthin, seed=seed,
+    kwgs_f_sample=kwgs_f_sample)
+    
+nsamples = 5000
+mh_samples, mh_accept = mh_estimator.run(nsamples, mh_sampler)
+
+
+# %% md
+#
+# The following figure plots the samples drawn from the unnormalized posterior,
+# which can be used to estimate the posterior and its poperties.
+# 
+import matplotlib.pyplot as plt
+
+fig, ax = plt.subplots(1,1,figsize=(5,4))
+
+ax.scatter(mh_samples[:,0], mh_samples[:,1], s=10, c='r', marker='o', alpha=0.1)
+ax.set_xlim(bounds[0,0], bounds[0,1])
+ax.set_ylim(bounds[1,0], bounds[1,1])
+ax.set_title('MH estimation')
+ax.set_xlabel('x1')
+ax.set_ylabel('x2')
+plt.tight_layout()
+
+
+# %% md
+# .. note:: Besides ``prior`` and ``likelihood``, one can also instantiate
+#     the :class:`.MetropolisHastingsEstimation` class with
+#
+#      - ``ln_prior`` and ``ln_likelihood``: Natural logarithm of ``prior`` and ``likelihood``.
+#      - ``ln_pxl``: Natural logarithm of the product of ``prior`` and ``likelihood``.
+#
\ No newline at end of file
diff --git a/docs/source/_build/html/_downloads/4647ee707541b918a88f2f6fccfe8f6e/inference_python.zip b/docs/source/_build/html/_downloads/4647ee707541b918a88f2f6fccfe8f6e/inference_python.zip
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diff --git a/docs/source/_build/html/_downloads/49e9d5799ebf50f0ee6452a55ef932ec/plot_active_learning.py b/docs/source/_build/html/_downloads/49e9d5799ebf50f0ee6452a55ef932ec/plot_active_learning.py
new file mode 100644
index 0000000..5f341c0
--- /dev/null
+++ b/docs/source/_build/html/_downloads/49e9d5799ebf50f0ee6452a55ef932ec/plot_active_learning.py
@@ -0,0 +1,127 @@
+"""
+
+Active learning
+===============
+"""
+
+# %% md
+# 
+# This example shows how to use the :class:`.ActiveLearning` class to iteratively
+# build a Gaussian process emulator for an unnormalized posterior involving a
+# simulator. It should be noted that this example is only for illustration
+# purpose, rather than a real case. For simplicity, required arguments for
+# :class:`.ActiveLearning` (including `simulator`, `likelihood`, `data`, etc.) are purely
+# made up. For a realistic case of active learning, one can refer to :cite:t:`Zhao2022`.
+#
+# First, we define the simulator, prior distribution of its variable parameters,
+# observed data, and likelihood function. They basically define the Bayesian
+# inference problem. 
+
+import numpy as np
+
+ndim = 2 # dimension of variable parameters of the simulator
+bounds = bounds = np.array([[-5,5],[-5,5]]) # bounds of variable parameters
+data = np.array([1,0])
+
+def simulator(x1, x2):
+    """Simulator y=f(x)."""
+    y1, y2 = x1, x2
+    return np.array([y1, y2])
+
+def prior(x):
+    """Uniform prior."""
+    return 1/(10*10)
+
+def likelihood(y, data):
+    """Likelihood function L(y,data)."""
+    return np.exp(-(y[0]-data[0])**2/100 - (y[0]**2-y[1]-data[1])**2)
+
+# %% md
+#
+# Imagine that the simulator is a complex solver. It is not computationally feasible
+# to compute the posterior distribution of the variable parameters using grid estimation
+# or Metropolis Hastings estimation. This is because they require evaluating the likelihood
+# many times which essentially leads to many evaluations of the simulator. Therefore, we
+# resort to use active learning to build a Gaussian process emulator for the unnormalized
+# posterior (prior times likelihood) based on a small number of evaluations of the simulator.
+# The the posterior can be estimated using the emulator.
+#
+# To do so, we need to pass arguments to following parameters of the :class:`.ActiveLearning` class:
+#
+#   - run_sim_obj : instance of class :class:`.RunSimulator`. It carries information on how
+#     to run the simulator.
+#   - lhs_sampler : instance of class :class:`.LHS`. It is used to draw initial samples to run
+#     simulations in order to train an inital Gaussian process emulator.
+#   - scalar_gasp : instance of class :class:`.ScalarGaSP`. It sets up the emulator structure.
+#
+
+from psimpy.simulator import RunSimulator
+from psimpy.sampler import LHS
+from psimpy.emulator import ScalarGaSP
+
+run_simulator = RunSimulator(simulator, var_inp_parameter=['x1','x2'])
+lhs_sampler = LHS(ndim=ndim, bounds=bounds, seed=1)
+scalar_gasp = ScalarGaSP(ndim=ndim)
+
+# %%md
+#
+# Next, we create an object of the :class:`.ActiveLearning` class by
+
+from psimpy.inference import ActiveLearning
+
+active_learner = ActiveLearning(ndim, bounds, data, run_simulator, prior, likelihood,
+    lhs_sampler, scalar_gasp)
+
+# %%md
+#
+# Then we can call the :py:meth:`.ActiveLearning.initial_simulation` method to run initial
+# simulations and call the :py:meth:`.ActiveLearning.iterative_emulation` method to
+# iteratively run new simulation and build emulator. Here we allocate 40 simulations for
+# initial emulator training and 60 simulations for adaptive training.
+#
+n0 = 40
+niter = 60
+
+init_var_samples, init_sim_outputs = active_learner.initial_simulation(
+    n0, mode='parallel', max_workers=4)
+
+var_samples, _, _ = active_learner.iterative_emulation(
+    n0, init_var_samples, init_sim_outputs, niter=niter)
+
+# %%md
+#
+# Once the active learning process is finished, we obtain the final emulator for the
+# logarithm of the unnormalized posterior, which is given by the
+# :py:meth:`.ActiveLearning.approx_ln_pxl` method.
+# 
+# We can then estimate the posterior using grid estimation or Metropolis Hastings
+# estimation based on the emulator. An example is as follows. The contour plot shows
+# the estimated posterior. 
+#
+from psimpy.inference import GridEstimation
+import matplotlib.pyplot as plt
+
+grid_estimator = GridEstimation(ndim, bounds, ln_pxl=active_learner.approx_ln_pxl)
+posterior, x_ndim = grid_estimator.run(nbins=50)
+
+fig, ax = plt.subplots(1,1,figsize=(5,4))
+
+# initial training points
+ax.scatter(init_var_samples[:,0], init_var_samples[:,1], s=10, c='r', marker='o',
+    zorder=1, alpha=0.8, label='initial training points')
+# actively picked training points
+ax.scatter(var_samples[n0:,0], var_samples[n0:,1], s=15, c='k', marker='+',
+    zorder=2, alpha=0.8, label='iterative training points')
+
+# estimated posterior based on the final emulator
+posterior = np.where(posterior < 1e-10, None, posterior)
+contour = ax.contour(x_ndim[0], x_ndim[1], np.transpose(posterior), levels=10, zorder=0)
+plt.colorbar(contour, ax=ax)
+
+ax.legend()
+ax.set_title('Active learning')
+ax.set_xlabel('x1')
+ax.set_ylabel('x2')
+ax.set_xlim([-5,5])
+ax.set_ylim([-5,5])
+plt.tight_layout()
\ No newline at end of file
diff --git a/docs/source/_build/html/_downloads/4d495ff630306dd98ca342f01931251c/plot_run_mass_point_model.py b/docs/source/_build/html/_downloads/4d495ff630306dd98ca342f01931251c/plot_run_mass_point_model.py
new file mode 100644
index 0000000..2b073cf
--- /dev/null
+++ b/docs/source/_build/html/_downloads/4d495ff630306dd98ca342f01931251c/plot_run_mass_point_model.py
@@ -0,0 +1,184 @@
+"""
+
+RunSimulator: Mass Point Model
+==============================
+"""
+
+# %% md
+# 
+# This example shows how to run multiple MassPointModel simulations in serial
+# and parallelly using :class:`.RunSimulator`.
+#
+#
+
+
+# %% md
+# 
+# First, we import the class :class:`.MassPointModel` and define a `simulator`
+# based on :py:meth:`.MassPointModel.run` method.
+
+from psimpy.simulator import MassPointModel
+
+mpm = MassPointModel()
+mpm_simulator = mpm.run
+
+
+# %% md
+# 
+# This simulator takes required input data, solves the mass point model, and
+# returns time history of the mass point's location and velocity
+# (see :py:meth:`.MassPointModel.run`).
+#
+# Required inputs for `mpm_simulator` include:
+#     1. topographic data: digital elevation model (in `ESRI ascii` format)
+#     2. friction coefficients: coulomb friction and turbulent friction coefficients
+#     3. initial state: initial location and initial velocity of the masspoint
+#     4. computational parameters: such as time step, end time, etc.
+#
+# The synthetic topography ``synthetic_topo.asc`` is used here for illustration.
+# It is located at the `/tests/data/` folder.
+
+import os
+
+dir_data = os.path.abspath('../../../tests/data/')
+elevation = os.path.join(dir_data, 'synthetic_topo.asc')
+
+# %% md
+# .. note:: You may need to modify ``dir_data`` according to where you save
+#    ``synthetic_topo.asc`` on your local machine.
+
+# %% md
+# 
+# For this example, we are going to run multiple simulations at different values
+# of coulomb friction coefficient (``coulomb_friction``) and turbulent friction
+# coefficient (``turbulent_friction``) while keep other inputs fixed. Namely,
+# ``coulomb_friction`` and ``turbulent_friction`` are variable input parameters.
+# All other inputs are fixed input parameters.
+#
+
+import numpy as np
+import itertools
+
+# Variable iput parameters are defined as a list of strings. Their values will be
+# passed as a numpy array (var_samples) when run simulations.
+var_inp_parameter = ['coulomb_friction', 'turbulent_friction']
+coulomb_friction = np.arange(0.1, 0.31, 0.1)
+turbulent_friction = np.arange(500, 2001, 400)
+var_samples = np.array(
+    [x for x in itertools.product(coulomb_friction, turbulent_friction)])
+print("Number of variable input samples are: ", len(var_samples))
+
+# Fixed input parameters are defined as a dictionary. Their values are given.
+fix_inp = {'elevation': elevation, 'x0': 200, 'y0': 2000, 'tend': 50}
+
+# %% md
+# .. note:: Parameters of `mpm_simulator` which are not included in
+#    ``var_inp_parameter`` and ``fix_inp``, such as ``ux0``, ``uy0`` and
+#    ``curvature``, will automatically take their default values.
+
+# %% md
+# 
+# We may want to save outputs returned by `mpm_simulator` at each simulation for
+# later inspection or processing. In that case, we need to define ``dir_out`` and
+# set ``save_out`` as `True`.
+
+import os
+
+# Here we create a folder called `temp_run_MassPointModel_example` to save outputs
+# returned at each simulation.
+cwd = os.getcwd()
+if not os.path.exists('temp_run_MassPointModel_example'):
+    os.mkdir('temp_run_MassPointModel_example')
+dir_out = os.path.join(cwd, 'temp_run_MassPointModel_example')
+
+
+# %% md
+# 
+# Now we can define an object of :class:`.RunSimulator` by
+
+from psimpy.simulator import RunSimulator
+
+run_mpm_simulator = RunSimulator(mpm_simulator, var_inp_parameter, fix_inp,
+    dir_out=dir_out, save_out=True)
+
+# %% md
+# .. note:: Since outputs of each simulation are saved in the same folder ``dir_out``,
+#    we need to give each file a unique name in order to avoid conflict. This is
+#    realized by defining ``prefixes``.
+
+serial_prefixes = ["serial"+str(i) for i in range(len(var_samples))]
+parallel_prefixes = ["parallel"+str(i) for i in range(len(var_samples))]
+
+
+# %% md
+# 
+# Using :py:meth:`.RunSimulator.serial_run` method or
+# :py:meth:`.RunSimulator.parallel_run` method, we can run the simulations
+# in serial or parallelly.
+
+import time
+
+start = time.time()
+run_mpm_simulator.serial_run(var_samples=var_samples, prefixes=serial_prefixes)
+serial_time = time.time() - start
+serial_output = run_mpm_simulator.outputs
+
+start = time.time()
+# max_workers controls maximum number of tasks running in parallel
+run_mpm_simulator.parallel_run(var_samples, prefixes=parallel_prefixes, max_workers=4)
+parallel_time = time.time() - start
+parallel_output = run_mpm_simulator.outputs
+    
+print("Serial run time: ", serial_time)
+print("Parallel run time: ", parallel_time)
+
+
+# %% md
+# 
+# Once a simulation is done, its output is saved to ``dir_out``. All output files
+# generated by above simulations are as follows: 
+
+os.listdir(dir_out)
+
+
+# %% md
+# 
+# Once all simulations are done, their outputs can also be accessed by
+# :py:attr:`.RunSimulator.outputs` attribute, which is a list.
+
+# Here we print the maximum velocity of each simulation in the parallel run.
+max_v = [np.max(output[:,5]) for output in parallel_output]
+print(
+    f"Maximum velocity of {parallel_prefixes[0]} to {parallel_prefixes[-1]} are: ",
+    '\n',
+    max_v)
+
+
+# %% md
+# .. warning:: If one simulation failed due to whatever reason, the error massage
+#    will be printed to the screen but other simulations will continue. In that 
+#    case, the output file of failed simulation will not be writted to ``dir_out``.
+#    Also, the element of :py:attr:`.RunSimulator.outputs` corresponding to that
+#    simulation will be a string representing the error message, instead of a
+#    numpy array.
+
+
+# %% md
+# 
+# Here we delete the folder `temp_run_MassPointModel_example` and all files therein.
+
+import shutil
+
+shutil.rmtree(dir_out)
+
+
+ 
+
+
+
+
+
+
+
+
+
diff --git a/docs/source/_build/html/_downloads/50d02379952730d4e961434a77e23a62/plot_metropolis_hastings.py b/docs/source/_build/html/_downloads/50d02379952730d4e961434a77e23a62/plot_metropolis_hastings.py
new file mode 100644
index 0000000..d3654ff
--- /dev/null
+++ b/docs/source/_build/html/_downloads/50d02379952730d4e961434a77e23a62/plot_metropolis_hastings.py
@@ -0,0 +1,116 @@
+"""
+
+Metropolis Hastings sampling
+============================
+"""
+
+# %% md
+# 
+# This example shows how to draw samples using Metropolis Hastings sampling.
+# The target probability distribution is
+#
+# :math:`p(\mathbf{x})=p(x_1, x_2) \propto \exp \left(-\frac{1}{100}\left(x_1-1\right)^2-\left(x_1^2-x_2\right)^2\right)`
+#
+# where :math:`x_1 \in [-5,5]` and :math:`x_2 \in [-5,5]`.
+#
+# It should be noted that the right hand side of the equation is an unnormalized
+# probability density function since its integral is not equal to :math:`1`.
+# This can happen, for example, when the normalization constant is unknown or difficult
+# to compute.
+# 
+# We can define the target probability distribution in Python as follows:
+# 
+
+import numpy as np
+
+def target_dist(x):
+    if (x[0]>=-5 and x[0]<=5) and (x[1]>=-5 and x[1]<=5):
+        return np.exp(-0.01*(x[0]-1)**2 - (x[0]**2-x[1])**2)
+    else:
+        return 0
+
+# %% md
+# 
+# The figure below shows how the target distribution looks like.
+
+import matplotlib.pyplot as plt
+import itertools
+
+x1_values = np.linspace(-5,5.1,100)
+x2_values = np.linspace(-5,5.1,100)
+
+target_values = np.zeros((100, 100))
+for i, j in itertools.product(range(100), range(100)):
+    x1 = x1_values[i]
+    x2 = x2_values[j]
+    target_values[i,j] = target_dist(np.array([x1, x2]))
+
+fig , ax = plt.subplots(figsize=(4,4))
+
+ax.contourf(x1_values, x2_values, np.transpose(target_values), levels=10, cmap='Blues')
+
+ax.set_title('(unnormalized) target distribution')
+ax.set_xlabel(r'$x_1$')
+ax.set_ylabel(r'$x_2$')
+ax.set_xlim(-5,5)
+ax.set_ylim(-5,5)
+plt.tight_layout()
+
+
+# %% md
+# 
+# To perform Metropolis Hastings sampling, we need to choose a proposal distribution
+# which can be used to determine a new state ``x'`` given a current state ``x`` at
+# each iteration. This is defined by the parameter ``f_sample`` which should be a
+# function. A usual choice is to choose the new state from a Gaussian distribution
+# centered at the current state.
+#
+
+from scipy.stats import multivariate_normal
+
+f_sample = multivariate_normal.rvs
+# make the samples reproducible
+kwgs_f_sample = {'random_state': np.random.default_rng(seed=1)}
+
+# %% md
+# 
+# Then, we create an instance of :class:`.MetropolisHastings` class.
+
+from psimpy.sampler.metropolis_hastings import MetropolisHastings
+
+mh_sampler = MetropolisHastings(ndim=2, init_state=np.array([-4,-4]),
+    f_sample=f_sample, target=target_dist, nburn=1000, nthin=5,
+    seed=1, kwgs_f_sample=kwgs_f_sample)
+
+# %% md
+# 
+# Next, we call the :py:meth:`.MetropolisHastings.sample` method to draw required 
+# number of samples.
+
+mh_samples, mh_accept = mh_sampler.sample(nsamples=5000)
+
+print("Acceptance ratio: ", np.mean(mh_accept))
+
+
+# %% md
+# 
+# The following figure shows how the samples look like.
+
+import matplotlib.pyplot as plt
+import itertools
+
+# sphinx_gallery_thumbnail_number = 2
+fig , ax = plt.subplots(figsize=(4,4))
+
+ax.contourf(x1_values, x2_values, np.transpose(target_values), levels=10, cmap='Blues')
+ax.scatter(mh_samples[:,0], mh_samples[:,1], s=5, c='r', marker='o',alpha=0.05)
+
+ax.set_title('Metropolis Hastings samples')
+ax.set_xlabel(r'$x_1$')
+ax.set_ylabel(r'$x_2$')
+ax.set_xlim(-5,5)
+ax.set_ylim(-5,5)
+plt.tight_layout()
+
+
+
diff --git a/docs/source/_build/html/_downloads/6601ba25871fd56fd9acfef62ca40570/simulator_jupyter.zip b/docs/source/_build/html/_downloads/6601ba25871fd56fd9acfef62ca40570/simulator_jupyter.zip
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diff --git a/docs/source/_build/html/_downloads/6dd07bf8f59ed369971c33b38f420079/plot_saltelli.py b/docs/source/_build/html/_downloads/6dd07bf8f59ed369971c33b38f420079/plot_saltelli.py
new file mode 100644
index 0000000..fcc5023
--- /dev/null
+++ b/docs/source/_build/html/_downloads/6dd07bf8f59ed369971c33b38f420079/plot_saltelli.py
@@ -0,0 +1,82 @@
+"""
+
+Saltelli sampling
+=================
+"""
+
+# %% md
+# 
+# This example shows how to draw samples using Saltelli sampling. 
+# Assume that there is a three-dimensional problem where X, Y, and Z are the
+# three random variables.
+
+import numpy as np
+
+ndim = 3
+# range of X is 10 to 20, range of Y is 100 to 200, range of Z is 1000 to 2000
+bounds = np.array([[10,20], [100,200], [1000,2000]])
+
+# %% md
+#
+# Given this setting, we can import :class:`.Saltelli`, create an instance, and
+# call the :py:meth:`.Saltelli.sample` method to draw required number of samples.
+
+from psimpy.sampler import Saltelli
+
+saltelli_sampler = Saltelli(ndim, bounds, calc_second_order=False)
+saltelli_samples = saltelli_sampler.sample(nbase=128)
+
+# %% md
+#
+# In above codes, we set ``calc_second_order`` to `False`. It means that picked
+# samples can be used in following Sobol' analysis to compute first-order and
+# total-effect Sobol' indices but not second-order Sobol' indices. It leads to 
+# :math:`nbase*(ndim+2)` samples as shown below
+
+import matplotlib.pyplot as plt
+
+fig = plt.figure()
+ax = fig.add_subplot(projection='3d')
+
+ax.scatter(saltelli_samples[:,0], saltelli_samples[:,1], saltelli_samples[:,2], marker='o')
+ax.set_xlabel('X')
+ax.set_ylabel('Y')
+ax.set_zlabel('Z')
+
+plt.tight_layout()
+
+print('Number of samples: ', f'{len(saltelli_samples)}')
+
+
+# %% md
+#
+# If we want to draw samples which can also be used to compute second-order
+# Sobol' indices, we need to set ``calc_second_order`` to `True`.
+# It leads to :math:`nbase*(2*ndim+2)` samples.
+
+saltelli_sampler = Saltelli(ndim, bounds, calc_second_order=True)
+saltelli_samples = saltelli_sampler.sample(nbase=128)
+
+fig = plt.figure()
+ax = fig.add_subplot(projection='3d')
+
+ax.scatter(saltelli_samples[:,0], saltelli_samples[:,1], saltelli_samples[:,2], marker='o')
+ax.set_xlabel('X')
+ax.set_ylabel('Y')
+ax.set_zlabel('Z')
+
+plt.tight_layout()
+
+print('Number of samples: ', f'{len(saltelli_samples)}')
+
+
+# %% md
+# .. note:: If one has a two-dimensional problem, there is no need to set
+#     ``calc_second_order`` to `True`. The reason is that the second-order Sobol'
+#     index can be directly computed based on the first-order and total-effect
+#     Sobol' index in that case.
+
+
+
+
+
diff --git a/docs/source/_build/html/_downloads/70f25099189c12416e6ef5e4aa3ed8b4/plot_ravaflow24.py b/docs/source/_build/html/_downloads/70f25099189c12416e6ef5e4aa3ed8b4/plot_ravaflow24.py
new file mode 100644
index 0000000..b73fec3
--- /dev/null
+++ b/docs/source/_build/html/_downloads/70f25099189c12416e6ef5e4aa3ed8b4/plot_ravaflow24.py
@@ -0,0 +1,150 @@
+"""
+
+Ravaflow24 Mixture Model
+========================
+"""
+
+# %% md
+# 
+# This example shows how to simulate mass flow on a topography using
+# :class:`.Ravaflow24Mixture`.
+#
+#
+
+# %% md
+# 
+# First, import the class :class:`.Ravaflow24Mixture` by
+
+from psimpy.simulator import Ravaflow24Mixture
+
+# %% md
+# 
+# To create an instance of this class, we must specify the parameter ``dir_sim``.
+# It represents the directory in which output files generated by r.avaflow will be
+# saved.
+
+import os
+
+# Here we create a folder called `temp_Ravaflow24Mixture_example` to save output
+# files generated by r.avaflow
+cwd = os.getcwd()
+if not os.path.exists('temp_Ravaflow24Mixture_example'):
+    os.mkdir('temp_Ravaflow24Mixture_example')
+dir_sim = os.path.join(cwd, 'temp_Ravaflow24Mixture_example')
+
+# %% md
+# 
+# Now, we can create an instance of :class:`.Ravaflow24Mixture` by given
+# ``dir_sim`` and leaving other parameters to their default values
+# (Other parameters include ``time_step``, ``time_end``, ``curvature_control``,
+# ``entrainment_control``, ``stopping_control``, etc.)
+
+voellmy_model = Ravaflow24Mixture(dir_sim)
+
+# %% md
+#
+# To run a simulation using above `voellmy_model`, one needs to specify 
+#     1. ``elevation`` – Name of elevation raster file (including its path).
+#     2. ``hrelease`` – Name of release height raster file (including its path).
+#     3. ``prefix`` – Prefix required by r.avaflow to name output files.
+#     4. If ``elevation`` is not a georeferenced file which can be used to create
+#        a `GRASS Location`, ``EPSG`` must be provided.
+#
+# Other optional parameters include ``internal_friction``, ``basal_friction``,
+# ``turbulent_friction``, ``entrainment_coef`` etc.
+#
+# The synthetic topography ``synthetic_topo.tif`` and release mass ``synthetic_rel.tif``
+# are used here for illustration. They are located at the `/tests/data/` folder.
+
+dir_data = os.path.abspath('../../../tests/data/')
+elevation = os.path.join(dir_data, 'synthetic_topo.tif')
+hrelease = os.path.join(dir_data, 'synthetic_rel.tif')
+prefix = 'synthetic'
+
+# %% md
+#
+# .. note:: You may need to modify ``dir_data`` according to where you save them
+#    on your local machine.
+
+# %% md
+# 
+# Given above inputs, we can create a `GRASS Location` and a shell file by calling
+# :py:meth:`.Ravaflow24Mixture.preprocess` method, and run the simulation using
+# :py:meth:`.Ravaflow24Mixture.run` method
+
+grass_location, sh_file = voellmy_model.preprocess(
+    prefix=prefix, elevation=elevation, hrelease=hrelease, EPSG='2326')
+voellmy_model.run(grass_location, sh_file)
+
+# %% md
+# 
+# Once the simulation is finished, the results are located in the folder
+# `/dir_sim/your_prefix_results`. In this case, they are located in
+# `/temp_Ravaflow24Mixture_example/synthetic_results`. We can extract desired
+# outputs using respective method and visualize them.
+# For example, we can extract the overall impact area, maximum flow velocity, or
+# maximum flow velocity at specific locations:
+
+import numpy as np
+
+# overall impact area
+impact_area = voellmy_model.extract_impact_area(prefix)
+print(f"Impact_area is {impact_area} m^2")
+
+# overall maximum flow velocity
+v_mmax = voellmy_model.extract_qoi_max(prefix, 'v', aggregate=True)
+print(f"Maximum flow velocity is {v_mmax} m/s^2")
+
+# maximum flow velocity at specific locations
+loc = np.array([[500, 2000], [1500, 2000]])
+v_max_loc = voellmy_model.extract_qoi_max_loc(prefix, loc, 'v')
+print(f"Maximum flow velocity at location {loc[0]} is {v_max_loc[0]} m/s^2")
+print(f"Maximum flow velocity at location {loc[1]} is {v_max_loc[1]} m/s^2")
+
+# %% md
+# 
+# We can visulize point-wise maximum flow height and velocity using heatmaps:
+
+import matplotlib.pyplot as plt
+import linecache
+
+# extract head information of result ascii files and compute x and y coordinates
+hmax_asc = os.path.join(dir_sim, f'{prefix}_results', f'{prefix}_ascii', f'{prefix}_hflow_max.asc')
+        
+header = [linecache.getline(hmax_asc, i) for i in range(1,6)]
+header_values = [float(h.split()[-1].strip()) for h in header]
+ncols, nrows, xll, yll, cellsize = header_values
+ncols = int(ncols)
+nrows = int(nrows)
+
+x = np.arange(xll, xll+(cellsize*ncols), cellsize)
+y = np.arange(yll, yll+(cellsize*nrows), cellsize)
+
+# point-wise maximum flow height
+h_max = voellmy_model.extract_qoi_max(prefix, 'h', aggregate=False)
+# point-wise maximum flow velocity
+v_max = voellmy_model.extract_qoi_max(prefix, 'v', aggregate=False)
+
+fig, ax = plt.subplots(2, 1, figsize=(10,6))
+
+fig0 = ax[0].contourf(x, y, h_max, levels=20)
+ax[0].set_xlabel('x')
+ax[0].set_ylabel('y')
+ax[0].set_title('maximum flow height' + r' $(m/s)$')
+cbar0 = plt.colorbar(fig0, ax=ax[0], format='%.1f', orientation='vertical', fraction=0.1)
+
+fig1 = ax[1].contourf(x, y, v_max, levels=20)
+ax[1].set_xlabel('x')
+ax[1].set_ylabel('y')
+ax[1].set_title('maximum flow velocity' + r' ($m/s^2$)')
+cbar1 = plt.colorbar(fig1, ax=ax[1], format='%.1f', orientation='vertical', fraction=0.1)
+
+plt.tight_layout()
+
+# %% md
+# 
+# Here we delete the folder `temp_Ravaflow24Mixture_example` and all files therein.
+
+import shutil
+
+shutil.rmtree(dir_sim)
diff --git a/docs/source/_build/html/_downloads/72c9aa931cd2028d7edb96ceb292a4a2/plot_metropolis_hastings.ipynb b/docs/source/_build/html/_downloads/72c9aa931cd2028d7edb96ceb292a4a2/plot_metropolis_hastings.ipynb
new file mode 100644
index 0000000..6584ae1
--- /dev/null
+++ b/docs/source/_build/html/_downloads/72c9aa931cd2028d7edb96ceb292a4a2/plot_metropolis_hastings.ipynb
@@ -0,0 +1,151 @@
+{
+  "cells": [
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "%matplotlib inline"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "\n# Metropolis Hastings sampling\n"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "This example shows how to draw samples using Metropolis Hastings sampling.\nThe target probability distribution is\n\n$p(\\mathbf{x})=p(x_1, x_2) \\propto \\exp \\left(-\\frac{1}{100}\\left(x_1-1\\right)^2-\\left(x_1^2-x_2\\right)^2\\right)$\n\nwhere $x_1 \\in [-5,5]$ and $x_2 \\in [-5,5]$.\n\nIt should be noted that the right hand side of the equation is an unnormalized\nprobability density function since its integral is not equal to $1$.\nThis can happen, for example, when the normalization constant is unknown or difficult\nto compute.\n\nWe can define the target probability distribution in Python as follows:\n\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "import numpy as np\n\ndef target_dist(x):\n    if (x[0]>=-5 and x[0]<=5) and (x[1]>=-5 and x[1]<=5):\n        return np.exp(-0.01*(x[0]-1)**2 - (x[0]**2-x[1])**2)\n    else:\n        return 0"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "The figure below shows how the target distribution looks like.\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "import matplotlib.pyplot as plt\nimport itertools\n\nx1_values = np.linspace(-5,5.1,100)\nx2_values = np.linspace(-5,5.1,100)\n\ntarget_values = np.zeros((100, 100))\nfor i, j in itertools.product(range(100), range(100)):\n    x1 = x1_values[i]\n    x2 = x2_values[j]\n    target_values[i,j] = target_dist(np.array([x1, x2]))\n\nfig , ax = plt.subplots(figsize=(4,4))\n\nax.contourf(x1_values, x2_values, np.transpose(target_values), levels=10, cmap='Blues')\n\nax.set_title('(unnormalized) target distribution')\nax.set_xlabel(r'$x_1$')\nax.set_ylabel(r'$x_2$')\nax.set_xlim(-5,5)\nax.set_ylim(-5,5)\nplt.tight_layout()"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "To perform Metropolis Hastings sampling, we need to choose a proposal distribution\nwhich can be used to determine a new state ``x'`` given a current state ``x`` at\neach iteration. This is defined by the parameter ``f_sample`` which should be a\nfunction. A usual choice is to choose the new state from a Gaussian distribution\ncentered at the current state.\n\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "from scipy.stats import multivariate_normal\n\nf_sample = multivariate_normal.rvs\n# make the samples reproducible\nkwgs_f_sample = {'random_state': np.random.default_rng(seed=1)}"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "Then, we create an instance of :class:`.MetropolisHastings` class.\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "from psimpy.sampler.metropolis_hastings import MetropolisHastings\n\nmh_sampler = MetropolisHastings(ndim=2, init_state=np.array([-4,-4]),\n    f_sample=f_sample, target=target_dist, nburn=1000, nthin=5,\n    seed=1, kwgs_f_sample=kwgs_f_sample)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "Next, we call the :py:meth:`.MetropolisHastings.sample` method to draw required \nnumber of samples.\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "mh_samples, mh_accept = mh_sampler.sample(nsamples=5000)\n\nprint(\"Acceptance ratio: \", np.mean(mh_accept))"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "The following figure shows how the samples look like.\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "import matplotlib.pyplot as plt\nimport itertools\n\n# sphinx_gallery_thumbnail_number = 2\nfig , ax = plt.subplots(figsize=(4,4))\n\nax.contourf(x1_values, x2_values, np.transpose(target_values), levels=10, cmap='Blues')\nax.scatter(mh_samples[:,0], mh_samples[:,1], s=5, c='r', marker='o',alpha=0.05)\n\nax.set_title('Metropolis Hastings samples')\nax.set_xlabel(r'$x_1$')\nax.set_ylabel(r'$x_2$')\nax.set_xlim(-5,5)\nax.set_ylim(-5,5)\nplt.tight_layout()"
+      ]
+    }
+  ],
+  "metadata": {
+    "kernelspec": {
+      "display_name": "Python 3",
+      "language": "python",
+      "name": "python3"
+    },
+    "language_info": {
+      "codemirror_mode": {
+        "name": "ipython",
+        "version": 3
+      },
+      "file_extension": ".py",
+      "mimetype": "text/x-python",
+      "name": "python",
+      "nbconvert_exporter": "python",
+      "pygments_lexer": "ipython3",
+      "version": "3.9.12"
+    }
+  },
+  "nbformat": 4,
+  "nbformat_minor": 0
+}
\ No newline at end of file
diff --git a/docs/source/_build/html/_downloads/79d68b726b379b22e24e81ddc36bf480/sampler_python.zip b/docs/source/_build/html/_downloads/79d68b726b379b22e24e81ddc36bf480/sampler_python.zip
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diff --git a/docs/source/_build/html/_downloads/8c06e92daa6ae4230f607ca4f47a3769/plot_scalargasp.ipynb b/docs/source/_build/html/_downloads/8c06e92daa6ae4230f607ca4f47a3769/plot_scalargasp.ipynb
new file mode 100644
index 0000000..4583d35
--- /dev/null
+++ b/docs/source/_build/html/_downloads/8c06e92daa6ae4230f607ca4f47a3769/plot_scalargasp.ipynb
@@ -0,0 +1,183 @@
+{
+  "cells": [
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "%matplotlib inline"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "\n# ScalarGaSP: GP emulation for a single-output function\n"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "This example shows how to apply Gaussian process emulation to a single-output\nfunction using class :class:`.ScalarGaSP`.\n\nThe task is to build a GP emulator for the function $y = x * sin(x)$\nbased on a few number of training data.\n\n"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "First, import the class :class:`.ScalarGaSP` by\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "from psimpy.emulator import ScalarGaSP"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "Then, create an instance of :class:`.ScalarGaSP`.  The parameter ``ndim``\n(dimension of function input ``x``) must be specified. Optional parameters, such\nas ``method``, ``kernel_type``, etc., can be set up if desired. Here, we leave\nall the optional parameters to their default values.\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "emulator = ScalarGaSP(ndim=1)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "Given training input points ``design`` and corresponding output values ``response``,\nthe emulator can be trained using :py:meth:`.ScalarGaSP.train`. Below we train\nan emulator using $8$ selected points.\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "import numpy as np\n\ndef f(x):\n    #return x + 3*np.sin(x/2)\n    return x*np.sin(x)\n\nx = np.arange(2,10,1)\ny = f(x)\n\nemulator.train(design=x, response=y)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "We can validate the performance of the trained emulator using the leave-one-out\ncross validation method :py:meth:`loo_validate()`.\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "validation = emulator.loo_validate()"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "Let's plot emulator predictions vs actual outputs. The error bar indicates the\nstandard deviation.\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "import matplotlib.pyplot as plt\n\nfig , ax = plt.subplots(figsize=(4,4))\n\nax.set_xlabel('Actual y')\nax.set_ylabel('Emulator-predicted y')\nax.set_xlim(np.min(y)-1,np.max(y)+1)\nax.set_ylim(np.min(y)-1,np.max(y)+1)\n\n_ = ax.plot([np.min(y)-1,np.max(y)+1], [np.min(y)-1,np.max(y)+1])\n_ = ax.errorbar(y, validation[:,0], validation[:,1], fmt='.', linestyle='', label='prediction and std')\n_ = plt.legend()\nplt.tight_layout()"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "With the trained emulator at our deposit, we can use the\n:py:meth:`.ScalarGaSP.predict()` method to make predictions at \nany arbitrary set of input points (``testing_input``). It should be noted that,\n``testing_trend`` should be set according to ``trend`` used during emulator\ntraining. \n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "testing_input = np.arange(0,10,0.1)\npredictions = emulator.predict(testing_input)\n\nplt.plot(testing_input, predictions[:, 0], 'r-', label= \"mean\")\nplt.scatter(x, y, s=15, c='k', label=\"training data\", zorder=3)\nplt.plot(testing_input, f(testing_input), 'k:', zorder=2, label=\"true function\")\nplt.fill_between(testing_input, predictions[:, 1], predictions[:, 2], alpha=0.3, label=\"95% CI\")\nplt.xlabel('x')\nplt.ylabel('emulator-predicted y')\nplt.xlim(testing_input[0], testing_input[-1])\n_ = plt.legend()\nplt.tight_layout()"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "We can also draw any number of samples at ``testing_input``` using\n:py:meth:`.ScalarGaSP.sample()` method.\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "nsamples = 5\nsamples = emulator.sample(testing_input, nsamples=nsamples)\n\n# sphinx_gallery_thumbnail_number = 3\nfor i in range(nsamples):\n    plt.plot(testing_input, samples[:,i], '--', label=f'sample{i+1}')\n\nplt.scatter(x, y, s=15, c='k', label=\"training data\", zorder=2)\nplt.plot(testing_input, f(testing_input), 'k:', zorder=2, label=\"true function\")\nplt.fill_between(testing_input, predictions[:, 1], predictions[:, 2], alpha=0.3, label=\"95% CI\")\nplt.xlabel('x')\nplt.ylabel('emulator-predicted y')\nplt.xlim(testing_input[0], testing_input[-1])\n_ = plt.legend()\nplt.tight_layout()"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        ".. tip:: Above example shows how to train a GP emulator based on noise-free training data,\n   which is often the case of emulating a deterministic simulator. If you are dealing\n   with noisy training data, you can\n\n    - set the parameter ``nugget`` to a desired value, or\n    - set ``nugget`` to $0$ and ``nugget_est`` to `True`, meaning that ``nugget``\n      is estimated from the noisy training data.\n"
+      ]
+    }
+  ],
+  "metadata": {
+    "kernelspec": {
+      "display_name": "Python 3",
+      "language": "python",
+      "name": "python3"
+    },
+    "language_info": {
+      "codemirror_mode": {
+        "name": "ipython",
+        "version": 3
+      },
+      "file_extension": ".py",
+      "mimetype": "text/x-python",
+      "name": "python",
+      "nbconvert_exporter": "python",
+      "pygments_lexer": "ipython3",
+      "version": "3.9.12"
+    }
+  },
+  "nbformat": 4,
+  "nbformat_minor": 0
+}
\ No newline at end of file
diff --git a/docs/source/_build/html/_downloads/9847b46a66214926039e571c42505921/plot_ravaflow24.ipynb b/docs/source/_build/html/_downloads/9847b46a66214926039e571c42505921/plot_ravaflow24.ipynb
new file mode 100644
index 0000000..341d6d8
--- /dev/null
+++ b/docs/source/_build/html/_downloads/9847b46a66214926039e571c42505921/plot_ravaflow24.ipynb
@@ -0,0 +1,201 @@
+{
+  "cells": [
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "%matplotlib inline"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "\n# Ravaflow24 Mixture Model\n"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "This example shows how to simulate mass flow on a topography using\n:class:`.Ravaflow24Mixture`.\n\n\n\n"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "First, import the class :class:`.Ravaflow24Mixture` by\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "from psimpy.simulator import Ravaflow24Mixture"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "To create an instance of this class, we must specify the parameter ``dir_sim``.\nIt represents the directory in which output files generated by r.avaflow will be\nsaved.\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "import os\n\n# Here we create a folder called `temp_Ravaflow24Mixture_example` to save output\n# files generated by r.avaflow\ncwd = os.getcwd()\nif not os.path.exists('temp_Ravaflow24Mixture_example'):\n    os.mkdir('temp_Ravaflow24Mixture_example')\ndir_sim = os.path.join(cwd, 'temp_Ravaflow24Mixture_example')"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "Now, we can create an instance of :class:`.Ravaflow24Mixture` by given\n``dir_sim`` and leaving other parameters to their default values\n(Other parameters include ``time_step``, ``time_end``, ``curvature_control``,\n``entrainment_control``, ``stopping_control``, etc.)\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "voellmy_model = Ravaflow24Mixture(dir_sim)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "To run a simulation using above `voellmy_model`, one needs to specify \n    1. ``elevation`` \u2013 Name of elevation raster file (including its path).\n    2. ``hrelease`` \u2013 Name of release height raster file (including its path).\n    3. ``prefix`` \u2013 Prefix required by r.avaflow to name output files.\n    4. If ``elevation`` is not a georeferenced file which can be used to create\n       a `GRASS Location`, ``EPSG`` must be provided.\n\nOther optional parameters include ``internal_friction``, ``basal_friction``,\n``turbulent_friction``, ``entrainment_coef`` etc.\n\nThe synthetic topography ``synthetic_topo.tif`` and release mass ``synthetic_rel.tif``\nare used here for illustration. They are located at the `/tests/data/` folder.\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "dir_data = os.path.abspath('../../../tests/data/')\nelevation = os.path.join(dir_data, 'synthetic_topo.tif')\nhrelease = os.path.join(dir_data, 'synthetic_rel.tif')\nprefix = 'synthetic'"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "<div class=\"alert alert-info\"><h4>Note</h4><p>You may need to modify ``dir_data`` according to where you save them\n   on your local machine.</p></div>\n\n"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "Given above inputs, we can create a `GRASS Location` and a shell file by calling\n:py:meth:`.Ravaflow24Mixture.preprocess` method, and run the simulation using\n:py:meth:`.Ravaflow24Mixture.run` method\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "grass_location, sh_file = voellmy_model.preprocess(\n    prefix=prefix, elevation=elevation, hrelease=hrelease, EPSG='2326')\nvoellmy_model.run(grass_location, sh_file)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "Once the simulation is finished, the results are located in the folder\n`/dir_sim/your_prefix_results`. In this case, they are located in\n`/temp_Ravaflow24Mixture_example/synthetic_results`. We can extract desired\noutputs using respective method and visualize them.\nFor example, we can extract the overall impact area, maximum flow velocity, or\nmaximum flow velocity at specific locations:\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "import numpy as np\n\n# overall impact area\nimpact_area = voellmy_model.extract_impact_area(prefix)\nprint(f\"Impact_area is {impact_area} m^2\")\n\n# overall maximum flow velocity\nv_mmax = voellmy_model.extract_qoi_max(prefix, 'v', aggregate=True)\nprint(f\"Maximum flow velocity is {v_mmax} m/s^2\")\n\n# maximum flow velocity at specific locations\nloc = np.array([[500, 2000], [1500, 2000]])\nv_max_loc = voellmy_model.extract_qoi_max_loc(prefix, loc, 'v')\nprint(f\"Maximum flow velocity at location {loc[0]} is {v_max_loc[0]} m/s^2\")\nprint(f\"Maximum flow velocity at location {loc[1]} is {v_max_loc[1]} m/s^2\")"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "We can visulize point-wise maximum flow height and velocity using heatmaps:\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "import matplotlib.pyplot as plt\nimport linecache\n\n# extract head information of result ascii files and compute x and y coordinates\nhmax_asc = os.path.join(dir_sim, f'{prefix}_results', f'{prefix}_ascii', f'{prefix}_hflow_max.asc')\n        \nheader = [linecache.getline(hmax_asc, i) for i in range(1,6)]\nheader_values = [float(h.split()[-1].strip()) for h in header]\nncols, nrows, xll, yll, cellsize = header_values\nncols = int(ncols)\nnrows = int(nrows)\n\nx = np.arange(xll, xll+(cellsize*ncols), cellsize)\ny = np.arange(yll, yll+(cellsize*nrows), cellsize)\n\n# point-wise maximum flow height\nh_max = voellmy_model.extract_qoi_max(prefix, 'h', aggregate=False)\n# point-wise maximum flow velocity\nv_max = voellmy_model.extract_qoi_max(prefix, 'v', aggregate=False)\n\nfig, ax = plt.subplots(2, 1, figsize=(10,6))\n\nfig0 = ax[0].contourf(x, y, h_max, levels=20)\nax[0].set_xlabel('x')\nax[0].set_ylabel('y')\nax[0].set_title('maximum flow height' + r' $(m/s)$')\ncbar0 = plt.colorbar(fig0, ax=ax[0], format='%.1f', orientation='vertical', fraction=0.1)\n\nfig1 = ax[1].contourf(x, y, v_max, levels=20)\nax[1].set_xlabel('x')\nax[1].set_ylabel('y')\nax[1].set_title('maximum flow velocity' + r' ($m/s^2$)')\ncbar1 = plt.colorbar(fig1, ax=ax[1], format='%.1f', orientation='vertical', fraction=0.1)\n\nplt.tight_layout()"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "Here we delete the folder `temp_Ravaflow24Mixture_example` and all files therein.\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "import shutil\n\nshutil.rmtree(dir_sim)"
+      ]
+    }
+  ],
+  "metadata": {
+    "kernelspec": {
+      "display_name": "Python 3",
+      "language": "python",
+      "name": "python3"
+    },
+    "language_info": {
+      "codemirror_mode": {
+        "name": "ipython",
+        "version": 3
+      },
+      "file_extension": ".py",
+      "mimetype": "text/x-python",
+      "name": "python",
+      "nbconvert_exporter": "python",
+      "pygments_lexer": "ipython3",
+      "version": "3.9.12"
+    }
+  },
+  "nbformat": 4,
+  "nbformat_minor": 0
+}
\ No newline at end of file
diff --git a/docs/source/_build/html/_downloads/98a9fafc5e8001527da7060b5766f5b2/plot_mass_point_model.py b/docs/source/_build/html/_downloads/98a9fafc5e8001527da7060b5766f5b2/plot_mass_point_model.py
new file mode 100644
index 0000000..0b942fe
--- /dev/null
+++ b/docs/source/_build/html/_downloads/98a9fafc5e8001527da7060b5766f5b2/plot_mass_point_model.py
@@ -0,0 +1,128 @@
+"""
+
+Mass Point Model
+================
+"""
+
+# %% md
+# 
+# This example shows how to simulate the movement of a masspoint on a topography
+# using :class:`.MassPointModel`.
+#
+# 
+
+# %% md
+# 
+# First, import the class :class:`.MassPointModel` and create an instance by
+
+from psimpy.simulator import MassPointModel
+
+mpm = MassPointModel()
+
+# %% md
+# 
+# Required inputs for a simulation using :class:`.MassPointModel` include:
+#     1. topographic data: digital elevation model (in `ESRI ascii` format)
+#     2. friction coefficients: coulomb friction and turbulent friction coefficients
+#     3. initial state: initial location and initial velocity of the masspoint
+#     4. computational parameters: such as time step, end time, etc.
+#
+# The synthetic topography ``synthetic_topo.asc`` is used here for illustration.
+# It is located at the `tests/data/` folder.
+
+import os
+import linecache
+import numpy as np
+
+dir_data = os.path.abspath('../../../tests/data/')
+elevation = os.path.join(dir_data, 'synthetic_topo.asc')
+
+
+# %% md
+# .. note:: You may need to modify ``dir_data`` according to where you save
+#    ``synthetic_topo.asc`` on your local machine.
+
+# %% md
+# We can load the elevation data and visulize it. The figure below shows how
+# the topography looks like, as well as the initial location of the masspoint
+# (noted by the red dot).
+
+header = [linecache.getline(elevation, i) for i in range(1,6)]
+header_values = [float(h.split()[-1].strip()) for h in header]
+ncols, nrows, xll, yll, cellsize = header_values
+ncols = int(ncols)
+nrows = int(nrows)
+
+x_values = np.arange(xll, xll+(cellsize*ncols), cellsize)
+y_values = np.arange(yll, yll+(cellsize*nrows), cellsize)
+        
+z_values = np.loadtxt(elevation, skiprows=6)
+z_values = np.rot90(np.transpose(z_values))
+
+# initial location
+x0 = 200
+y0 = 2000
+z0 = z_values[0, int(x0/cellsize)]
+
+import matplotlib.pyplot as plt
+
+fig, ax = plt.subplots(2, 1, figsize=(10,6), height_ratios=[3,2])
+
+fig0 = ax[0].contourf(x_values, y_values, z_values, levels=20)
+ax[0].set_xlabel('x')
+ax[0].set_ylabel('y')
+ax[0].set_title('synthetic topography')
+ax[0].scatter(x0, y0, s=10, c='r', marker='o')
+cbar = plt.colorbar(fig0, ax=ax[0], format='%d', orientation='horizontal',
+    fraction=0.1, pad=0.2)
+cbar.ax.set_ylabel('z')
+
+
+ax[1].plot(x_values, z_values[0, :])
+ax[1].scatter(x0, z0, s=10, c='r', marker='o')
+ax[1].set_xlabel('x')
+ax[1].set_ylabel('z')
+ax[1].set_xlim(0, 5000)
+ax[1].set_title('cross section at any y')
+
+plt.tight_layout()
+
+# %% md
+# We set the friction coefficients as
+
+mu = 0.15
+xi = 1000
+
+# %% md
+# Given above topography, initial location, and friction coefficients, we can
+# call the :py:meth:`.MassPointModel.run` method to perform a simulation. Other
+# parameters are set to their default values. (we suppress raised warnings )
+# (other parameters are set to their default values).
+
+import warnings
+
+warnings.filterwarnings("ignore")
+output = mpm.run(elevation=elevation, coulomb_friction=mu, turbulent_friction=xi, x0=x0, y0=y0)
+
+# %% md
+# The simulation returns time history of the mass point's location and velocity.
+# Following plots show the simulation results.
+
+fig, ax = plt.subplots(3, 1, figsize=(10,6))
+
+ax[0].set_xlabel('time (s)')
+ax[0].set_ylabel('x')
+ax[0].set_title("x-t plot")
+ax[0].plot(output[:,0], output[:,1])
+
+ax[1].set_xlabel('time (s)')
+ax[1].set_ylabel('velocity')
+ax[1].set_title("v-t plot")
+ax[1].plot(output[:,0], output[:,5])
+
+ax[2].set_xlabel('x')
+ax[2].set_ylabel('velocity')
+ax[2].set_title("x-v plot")
+ax[2].plot(output[:,1], output[:,5])
+
+plt.tight_layout()
diff --git a/docs/source/_build/html/_downloads/9ac7682e0f10ab62297eb4ff29689bc8/plot_ppgasp.ipynb b/docs/source/_build/html/_downloads/9ac7682e0f10ab62297eb4ff29689bc8/plot_ppgasp.ipynb
new file mode 100644
index 0000000..868efae
--- /dev/null
+++ b/docs/source/_build/html/_downloads/9ac7682e0f10ab62297eb4ff29689bc8/plot_ppgasp.ipynb
@@ -0,0 +1,183 @@
+{
+  "cells": [
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "%matplotlib inline"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "\n# PPGaSP: GP emulation for multi-output functions\n"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "This example shows how to apply Gaussian process emulation to a multi-output\nfunction using class :class:`.PPGaSP`.\n\nThe multi-output function that we are going to look at is the `DIAMOND`\n(diplomatic and military operations in a non-warfighting domain) computer model.\nIt is used as a testbed to illustrate the `PP GaSP` emulator in the `R` package\n`RobustGaSP`, see :cite:t:`Gu2019` for more detail.\n\nThe simulator has $13$ input parameters and $5$ outputs. Namely,\n$\\mathbf{y}=f(\\mathbf{x})$ where $\\mathbf{x}=(x_1,\\ldots,x_{13})^T$\nand $\\mathbf{y}=(y_1,\\ldots,y_5)^T$.\n\nThe training and testing data are provided in the folder '.../tests/data/'.\nWe first load the training and testing data. \n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "import numpy as np\nimport os\n\ndir_data = os.path.abspath('../../../tests/data/')\n\nhumanityX = np.genfromtxt(os.path.join(dir_data, 'humanityX.csv'), delimiter=',')\nhumanityY = np.genfromtxt(os.path.join(dir_data, 'humanityY.csv'), delimiter=',')\nprint(f\"Number of training data points: \", humanityX.shape[0])\nprint(f\"Input dimension: \", humanityX.shape[1])\nprint(f\"Output dimension: \", humanityY.shape[1])\n\nhumanityXt = np.genfromtxt(os.path.join(dir_data, 'humanityXt.csv'), delimiter=',')\nhumanityYt = np.genfromtxt(os.path.join(dir_data, 'humanityYt.csv'), delimiter=',')\nprint(f\"Number of testing data points: \", humanityXt.shape[0])"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "<div class=\"alert alert-info\"><h4>Note</h4><p>You may need to modify ``dir_data`` according to where you save them\n   on your local machine.</p></div>\n\n"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "``humanityX`` and ``humanitY`` are the training data, corresponding to ``design``\nand ``response`` respectively. ``humanityXt`` are testing input data, at which\nwe are going to make predictions once the emulator is trained. ``humanityYt``\nare the true outputs at ``humanityXt``, which is then used to validate the\nperformance of the trained emulator.\n\n"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "To build a `PP GaSP` emulator for the above simulator,  first import class\n:class:`.PPGaSP` by\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "from psimpy.emulator import PPGaSP"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "Then, create an instance of :class:`.PPGaSP`.  The parameter ``ndim``\n(dimension of function input ``x``) must be specified. Optional parameters, such\nas ``method``, ``kernel_type``, etc., can be set up if desired. Here, we leave\nall the optional parameters to their default values.\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "emulator = PPGaSP(ndim=humanityX.shape[1])"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "Next, we train the `PP GaSP` emulator based on the training data using\n:py:meth:`.PPGaSP.train` method.\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "emulator.train(design=humanityX, response=humanityY)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "With the trained emulator, we can make predictions for any arbitrary set of\ninput points using :py:meth:`PPGaSP.predict` method.\nHere, we make predictions at testing input points ``humanityXt``.\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "predictions = emulator.predict(humanityXt)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "We can validate the performance of the trained emulator based on the true outputs\n``humanityYt``.\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "import matplotlib.pyplot as plt\n\nfig, ax = plt.subplots(5, 1, figsize=(6,15))\n\nfor i in range(humanityY.shape[1]):\n\n    ax[i].set_xlabel(f'Actual $y_{i+1}$')\n    ax[i].set_ylabel(f'Emulator-predicted $y_{i+1}$')\n    ax[i].set_xlim(np.min(humanityYt[:,i]),np.max(humanityYt[:,i]))\n    ax[i].set_ylim(np.min(humanityYt[:,i]),np.max(humanityYt[:,i]))\n\n    _ = ax[i].plot([np.min(humanityYt[:,i]),np.max(humanityYt[:,i])], [np.min(humanityYt[:,i]),np.max(humanityYt[:,i])])\n    _ = ax[i].errorbar(humanityYt[:,i], predictions[:,i,0], predictions[:,i,3], fmt='.', linestyle='', label='prediction and std')\n    _ = ax[i].legend()\n\nplt.tight_layout()"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "We can also draw any number of samples at testing input ``humanityXt`` using \n:py:meth:`.PPGaSPsample()` method.\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "samples = emulator.sample(humanityXt, nsamples=10)\nprint(\"Shape of samples: \", samples.shape)"
+      ]
+    }
+  ],
+  "metadata": {
+    "kernelspec": {
+      "display_name": "Python 3",
+      "language": "python",
+      "name": "python3"
+    },
+    "language_info": {
+      "codemirror_mode": {
+        "name": "ipython",
+        "version": 3
+      },
+      "file_extension": ".py",
+      "mimetype": "text/x-python",
+      "name": "python",
+      "nbconvert_exporter": "python",
+      "pygments_lexer": "ipython3",
+      "version": "3.9.12"
+    }
+  },
+  "nbformat": 4,
+  "nbformat_minor": 0
+}
\ No newline at end of file
diff --git a/docs/source/_build/html/_downloads/9be10f28a70b43dfd67c8234c21c2052/sampler_jupyter.zip b/docs/source/_build/html/_downloads/9be10f28a70b43dfd67c8234c21c2052/sampler_jupyter.zip
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diff --git a/docs/source/_build/html/_downloads/ad745ba736a627e1e1bb6fcec00ac417/plot_run_ravaflow24.ipynb b/docs/source/_build/html/_downloads/ad745ba736a627e1e1bb6fcec00ac417/plot_run_ravaflow24.ipynb
new file mode 100644
index 0000000..488bf46
--- /dev/null
+++ b/docs/source/_build/html/_downloads/ad745ba736a627e1e1bb6fcec00ac417/plot_run_ravaflow24.ipynb
@@ -0,0 +1,316 @@
+{
+  "cells": [
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "%matplotlib inline"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "\n# RunSimulator: Ravaflow24 Mixture Model\n"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "This example shows how to run multiple Ravaflow24Mixture simulations in serial\nand parallelly using :class:`.RunSimulator`.\n\n\n"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "First, we import the class :class:`.Ravaflow24Mixture`.\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "from psimpy.simulator import Ravaflow24Mixture"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "To create an instance of this class, we must specify the parameter ``dir_sim``.\nIt represents the directory in which output files generated by r.avaflow will be\nsaved.\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "import os\n\n# Here we create a folder called `temp1_run_Ravaflow24Mixture_example` to save\n# output files generated by r.avaflow\ncwd = os.getcwd()\nif not os.path.exists('temp1_run_Ravaflow24Mixture_example'):\n    os.mkdir('temp1_run_Ravaflow24Mixture_example')\ndir_sim = os.path.join(cwd, 'temp1_run_Ravaflow24Mixture_example')"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "Given ``dir_sim``,  we can create an instance of :class:`.Ravaflow24Mixture`.\nTo reduce simulation time, we set ``time_end`` to $50$. Other parameters\nare set to their default values.\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "voellmy_model = Ravaflow24Mixture(dir_sim, time_end=50)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "The `simulator` in this example is defined based on ``voellmy_model`` as follows.\nIt takes required inputs and returns the overall impact area.\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "import numpy as np\n\ndef simulator(prefix, elevation, hrelease, basal_friction, turbulent_friction, EPSG):\n    \"\"\"Preprocess required inputs, run simulation, and return output as a numpy array.\"\"\"\n    grass_location, sh_file = voellmy_model.preprocess(prefix=prefix, elevation=elevation,\n        hrelease=hrelease, basal_friction=basal_friction, turbulent_friction=turbulent_friction, EPSG=EPSG)\n    voellmy_model.run(grass_location, sh_file) # run this line, r.avaflow will write outputs to dir_sim\n    impact_area = voellmy_model.extract_impact_area(prefix)\n    \n    return np.array([impact_area]) # define dir_out and set save_out to True, returned numpy array will be saved to dir_out"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "To demonstrate how to run multiple simulations using :class:`.RunSimulator`, \nwe choose ``basal_friction`` and ``turbulent_friction`` as variable input\nparameters. Each has two different values, leading to four simulations.\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "import itertools\n\nvar_inp_parameter = ['basal_friction', 'turbulent_friction']\nbasal_friction = [20, 30] \nturbulent_friction = [3, 4]\nvar_samples = np.array(\n    [x for x in itertools.product(basal_friction, turbulent_friction)])"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "Other parameters of the `simulator`, including ``elevation``, ``hrelease``, and\n``EPSG`` are treated as fixed input. It means that their values are the same in\nall simulations.\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "dir_data = os.path.abspath('../../../tests/data/')\nelevation = os.path.join(dir_data, 'synthetic_topo.tif')\nhrelease = os.path.join(dir_data, 'synthetic_rel.tif')\nfix_inp = {'elevation': elevation, 'hrelease': hrelease, 'EPSG': '2326'}"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "The parameter ``prefix`` of the `simulator` is special. It is not involved in\nthe computational model, but only used to name output files generated by r.avaflow.\nSuch parameter is not defined in ``var_inp_parameter`` or ``fix_inp`` of\n:class:`.RunSimulator`. Instead, we use a seperate parameter, called ``o_parameter``\nfor this purpose.\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "o_parameter = 'prefix'"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "We may want to save outputs returned by the `simulator` at each simulation for\nlater inspection or processing. In that case, we need to define ``dir_out`` and\nset ``save_out`` as `True`.\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "import os\n\ncwd = os.getcwd()\nif not os.path.exists('temp2_run_Ravaflow24Mixture_example'):\n    os.mkdir('temp2_run_Ravaflow24Mixture_example')\ndir_out = os.path.join(cwd, 'temp2_run_Ravaflow24Mixture_example')"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "<div class=\"alert alert-info\"><h4>Note</h4><p>Please note that ``dir_out`` and ``dir_sim`` are two different\n   parameters for different purposes.\n\n    - ``dir_out`` is a parameter of :class:`.RunSimulator`. The `simulator`\n      returns output of interest as a numpy array for each simulation. If\n      we want to save this returned output of interest (here impact area)\n      to our local machine, we need to specify the value of ``dir_out`` which\n      represents the directory in which output of interest will be saved and\n      set ``save_out`` to `True`. Otherwise, we do not need ``dir_out`` and\n      leave ``save_out`` to `False`.\n    - ``dir_sim`` is a parameter of :class:`.Ravaflow24Mixture`. :class:`.Ravaflow24Mixture`\n      relies on the third party software r.avaflow 2.4. When we call\n      :py:meth:`.Ravaflow24Mixture.run` in the function body of above `simulator`,\n      r.avaflow 2.4 will be run and it generates output files. The value of\n      ``dir_sim`` specifies the directory in which output files generated by\n      r.avaflow 2.4 are going to be saved.\n\n   The value of ``dir_out`` and ``dir_sim`` can be the same if file names \n   have no conflict. We recommend to keep them seperate. In addition, if the function\n   body of the `simulator` does not write files to disk, ``dir_sim`` is not required. Our\n   :class:`.MassPointModel` is an example. Similarly, if we do not want to save\n   returned numpy array of the `simulator`, ``dir_out`` is not needed.</p></div>\n\n"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "Now we can define an object of :class:`.RunSimulator` by\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "from psimpy.simulator import RunSimulator\n\nrun_simulator = RunSimulator(simulator, var_inp_parameter, fix_inp, o_parameter,\n    dir_out, save_out=True)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "Before running simulations, we need to specify values of ``prefixes`` which\nwill be used to name files generated by each r.avaflow simulation and\neach returned numpy array of `simulator`.\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "serial_prefixes = [\"serial\"+str(i) for i in range(len(var_samples))]\nparallel_prefixes = [\"parallel\"+str(i) for i in range(len(var_samples))]"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "Now we can use :py:meth:`.RunSimulator.serial_run` method or\n:py:meth:`.RunSimulator.parallel_run` method to run the simulations\nin serial or parallelly.\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "import time\n\nstart = time.time()\nrun_simulator.serial_run(var_samples=var_samples, prefixes=serial_prefixes)\nserial_time = time.time() - start\nserial_output = run_simulator.outputs\nprint(f\"serial_output: {serial_output}\")\n\nstart = time.time()\n# append setting to True means that simulation outputs of parallel run will be\n# appended to above serial run outputs\nrun_simulator.parallel_run(var_samples, prefixes=parallel_prefixes,\n    max_workers=2, append=True)\nparallel_time = time.time() - start\n    \nparallel_output = run_simulator.outputs[len(var_samples):]\nprint(f\"parallel_output: {parallel_output}\")\n\n    \nprint(\"Serial run time: \", serial_time)\nprint(\"Parallel run time: \", parallel_time)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "All output files returned by the `simulator` are\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "os.listdir(dir_out)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "All output files/directories generated by r.avaflow simulations \n(including files/directories generated during preprocessing) are\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "os.listdir(dir_sim)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "<div class=\"alert alert-danger\"><h4>Warning</h4><p>If one simulation failed due to whatever reason, the error massage\n   will be printed to the screen but other simulations will continue. In that \n   case, the output file of failed simulation will not be writted to ``dir_out``.\n   Also, the element of :py:attr:`.RunSimulator.outputs` corresponding to that\n   simulation will be a string representing the error message, instead of a\n   numpy array.</p></div>\n\n"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "In the end, we delete the folder `temp1_run_Ravaflow24Mixture_example` and\n`temp2_run_Ravaflow24Mixture_example` and all files therein.\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "import shutil\n\nshutil.rmtree(dir_sim)\nshutil.rmtree(dir_out)"
+      ]
+    }
+  ],
+  "metadata": {
+    "kernelspec": {
+      "display_name": "Python 3",
+      "language": "python",
+      "name": "python3"
+    },
+    "language_info": {
+      "codemirror_mode": {
+        "name": "ipython",
+        "version": 3
+      },
+      "file_extension": ".py",
+      "mimetype": "text/x-python",
+      "name": "python",
+      "nbconvert_exporter": "python",
+      "pygments_lexer": "ipython3",
+      "version": "3.9.12"
+    }
+  },
+  "nbformat": 4,
+  "nbformat_minor": 0
+}
\ No newline at end of file
diff --git a/docs/source/_build/html/_downloads/af73dbd4cdfb71a4d5cac0b204c855e0/emulator_jupyter.zip b/docs/source/_build/html/_downloads/af73dbd4cdfb71a4d5cac0b204c855e0/emulator_jupyter.zip
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diff --git a/docs/source/_build/html/_downloads/bfca202fd55dbe4c4a07ec2f8128e4cc/plot_ppgasp.py b/docs/source/_build/html/_downloads/bfca202fd55dbe4c4a07ec2f8128e4cc/plot_ppgasp.py
new file mode 100644
index 0000000..5ae4059
--- /dev/null
+++ b/docs/source/_build/html/_downloads/bfca202fd55dbe4c4a07ec2f8128e4cc/plot_ppgasp.py
@@ -0,0 +1,112 @@
+"""
+
+PPGaSP: GP emulation for multi-output functions
+===============================================
+"""
+
+
+# %% md
+# 
+# This example shows how to apply Gaussian process emulation to a multi-output
+# function using class :class:`.PPGaSP`.
+#
+# The multi-output function that we are going to look at is the `DIAMOND`
+# (diplomatic and military operations in a non-warfighting domain) computer model.
+# It is used as a testbed to illustrate the `PP GaSP` emulator in the `R` package
+# `RobustGaSP`, see :cite:t:`Gu2019` for more detail.
+#
+# The simulator has :math:`13` input parameters and :math:`5` outputs. Namely,
+# :math:`\mathbf{y}=f(\mathbf{x})` where :math:`\mathbf{x}=(x_1,\ldots,x_{13})^T`
+# and :math:`\mathbf{y}=(y_1,\ldots,y_5)^T`.
+#
+# The training and testing data are provided in the folder '.../tests/data/'.
+# We first load the training and testing data. 
+
+import numpy as np
+import os
+
+dir_data = os.path.abspath('../../../tests/data/')
+
+humanityX = np.genfromtxt(os.path.join(dir_data, 'humanityX.csv'), delimiter=',')
+humanityY = np.genfromtxt(os.path.join(dir_data, 'humanityY.csv'), delimiter=',')
+print(f"Number of training data points: ", humanityX.shape[0])
+print(f"Input dimension: ", humanityX.shape[1])
+print(f"Output dimension: ", humanityY.shape[1])
+
+humanityXt = np.genfromtxt(os.path.join(dir_data, 'humanityXt.csv'), delimiter=',')
+humanityYt = np.genfromtxt(os.path.join(dir_data, 'humanityYt.csv'), delimiter=',')
+print(f"Number of testing data points: ", humanityXt.shape[0])
+
+# %% md
+# .. note:: You may need to modify ``dir_data`` according to where you save them
+#    on your local machine.
+
+# %% md
+# ``humanityX`` and ``humanitY`` are the training data, corresponding to ``design``
+# and ``response`` respectively. ``humanityXt`` are testing input data, at which
+# we are going to make predictions once the emulator is trained. ``humanityYt``
+# are the true outputs at ``humanityXt``, which is then used to validate the
+# performance of the trained emulator.
+
+# %% md
+# 
+# To build a `PP GaSP` emulator for the above simulator,  first import class
+# :class:`.PPGaSP` by
+
+from psimpy.emulator import PPGaSP
+
+# %% md
+# 
+# Then, create an instance of :class:`.PPGaSP`.  The parameter ``ndim``
+# (dimension of function input ``x``) must be specified. Optional parameters, such
+# as ``method``, ``kernel_type``, etc., can be set up if desired. Here, we leave
+# all the optional parameters to their default values.
+
+emulator = PPGaSP(ndim=humanityX.shape[1])
+
+
+# %% md
+# 
+# Next, we train the `PP GaSP` emulator based on the training data using
+# :py:meth:`.PPGaSP.train` method.
+
+emulator.train(design=humanityX, response=humanityY)
+
+# %% md
+#
+# With the trained emulator, we can make predictions for any arbitrary set of
+# input points using :py:meth:`PPGaSP.predict` method.
+# Here, we make predictions at testing input points ``humanityXt``.
+
+predictions = emulator.predict(humanityXt)
+
+# %% md
+# 
+# We can validate the performance of the trained emulator based on the true outputs
+# ``humanityYt``.
+
+import matplotlib.pyplot as plt
+
+fig, ax = plt.subplots(5, 1, figsize=(6,15))
+
+for i in range(humanityY.shape[1]):
+
+    ax[i].set_xlabel(f'Actual $y_{i+1}$')
+    ax[i].set_ylabel(f'Emulator-predicted $y_{i+1}$')
+    ax[i].set_xlim(np.min(humanityYt[:,i]),np.max(humanityYt[:,i]))
+    ax[i].set_ylim(np.min(humanityYt[:,i]),np.max(humanityYt[:,i]))
+
+    _ = ax[i].plot([np.min(humanityYt[:,i]),np.max(humanityYt[:,i])], [np.min(humanityYt[:,i]),np.max(humanityYt[:,i])])
+    _ = ax[i].errorbar(humanityYt[:,i], predictions[:,i,0], predictions[:,i,3], fmt='.', linestyle='', label='prediction and std')
+    _ = ax[i].legend()
+
+plt.tight_layout()
+
+
+# %%md
+#
+# We can also draw any number of samples at testing input ``humanityXt`` using 
+# :py:meth:`.PPGaSPsample()` method.
+
+samples = emulator.sample(humanityXt, nsamples=10)
+print("Shape of samples: ", samples.shape)
\ No newline at end of file
diff --git a/docs/source/_build/html/_downloads/ca97a6211ade4816b175cce5bc31a34b/plot_scalargasp.py b/docs/source/_build/html/_downloads/ca97a6211ade4816b175cce5bc31a34b/plot_scalargasp.py
new file mode 100644
index 0000000..54a5cbd
--- /dev/null
+++ b/docs/source/_build/html/_downloads/ca97a6211ade4816b175cce5bc31a34b/plot_scalargasp.py
@@ -0,0 +1,125 @@
+"""
+
+ScalarGaSP: GP emulation for a single-output function
+=====================================================
+"""
+
+# %% md
+# 
+# This example shows how to apply Gaussian process emulation to a single-output
+# function using class :class:`.ScalarGaSP`.
+#
+# The task is to build a GP emulator for the function :math:`y = x * sin(x)`
+# based on a few number of training data.
+
+# %% md
+# 
+# First, import the class :class:`.ScalarGaSP` by
+
+from psimpy.emulator import ScalarGaSP
+
+# %% md
+# 
+# Then, create an instance of :class:`.ScalarGaSP`.  The parameter ``ndim``
+# (dimension of function input ``x``) must be specified. Optional parameters, such
+# as ``method``, ``kernel_type``, etc., can be set up if desired. Here, we leave
+# all the optional parameters to their default values.
+
+emulator = ScalarGaSP(ndim=1)
+
+# %% md
+# 
+# Given training input points ``design`` and corresponding output values ``response``,
+# the emulator can be trained using :py:meth:`.ScalarGaSP.train`. Below we train
+# an emulator using :math:`8` selected points.
+
+import numpy as np
+
+def f(x):
+    #return x + 3*np.sin(x/2)
+    return x*np.sin(x)
+
+x = np.arange(2,10,1)
+y = f(x)
+
+emulator.train(design=x, response=y)
+
+# %% md
+# 
+# We can validate the performance of the trained emulator using the leave-one-out
+# cross validation method :py:meth:`loo_validate()`.
+
+validation = emulator.loo_validate()
+
+# %% md
+#
+# Let's plot emulator predictions vs actual outputs. The error bar indicates the
+# standard deviation.
+
+import matplotlib.pyplot as plt
+
+fig , ax = plt.subplots(figsize=(4,4))
+
+ax.set_xlabel('Actual y')
+ax.set_ylabel('Emulator-predicted y')
+ax.set_xlim(np.min(y)-1,np.max(y)+1)
+ax.set_ylim(np.min(y)-1,np.max(y)+1)
+
+_ = ax.plot([np.min(y)-1,np.max(y)+1], [np.min(y)-1,np.max(y)+1])
+_ = ax.errorbar(y, validation[:,0], validation[:,1], fmt='.', linestyle='', label='prediction and std')
+_ = plt.legend()
+plt.tight_layout()
+
+
+# %% md
+#
+# With the trained emulator at our deposit, we can use the
+# :py:meth:`.ScalarGaSP.predict()` method to make predictions at 
+# any arbitrary set of input points (``testing_input``). It should be noted that,
+# ``testing_trend`` should be set according to ``trend`` used during emulator
+# training. 
+
+testing_input = np.arange(0,10,0.1)
+predictions = emulator.predict(testing_input)
+
+plt.plot(testing_input, predictions[:, 0], 'r-', label= "mean")
+plt.scatter(x, y, s=15, c='k', label="training data", zorder=3)
+plt.plot(testing_input, f(testing_input), 'k:', zorder=2, label="true function")
+plt.fill_between(testing_input, predictions[:, 1], predictions[:, 2], alpha=0.3, label="95% CI")
+plt.xlabel('x')
+plt.ylabel('emulator-predicted y')
+plt.xlim(testing_input[0], testing_input[-1])
+_ = plt.legend()
+plt.tight_layout()
+
+# %% md
+#
+# We can also draw any number of samples at ``testing_input``` using
+# :py:meth:`.ScalarGaSP.sample()` method.
+
+nsamples = 5
+samples = emulator.sample(testing_input, nsamples=nsamples)
+
+# sphinx_gallery_thumbnail_number = 3
+for i in range(nsamples):
+    plt.plot(testing_input, samples[:,i], '--', label=f'sample{i+1}')
+
+plt.scatter(x, y, s=15, c='k', label="training data", zorder=2)
+plt.plot(testing_input, f(testing_input), 'k:', zorder=2, label="true function")
+plt.fill_between(testing_input, predictions[:, 1], predictions[:, 2], alpha=0.3, label="95% CI")
+plt.xlabel('x')
+plt.ylabel('emulator-predicted y')
+plt.xlim(testing_input[0], testing_input[-1])
+_ = plt.legend()
+plt.tight_layout()
+
+
+# %% md
+#
+# .. tip:: Above example shows how to train a GP emulator based on noise-free training data,
+#    which is often the case of emulating a deterministic simulator. If you are dealing
+#    with noisy training data, you can
+#
+#     - set the parameter ``nugget`` to a desired value, or
+#     - set ``nugget`` to :math:`0` and ``nugget_est`` to `True`, meaning that ``nugget``
+#       is estimated from the noisy training data.
\ No newline at end of file
diff --git a/docs/source/_build/html/_downloads/d3e17d759872695d3b37be8319e77dbf/plot_sobol_analyze.py b/docs/source/_build/html/_downloads/d3e17d759872695d3b37be8319e77dbf/plot_sobol_analyze.py
new file mode 100644
index 0000000..87bbad8
--- /dev/null
+++ b/docs/source/_build/html/_downloads/d3e17d759872695d3b37be8319e77dbf/plot_sobol_analyze.py
@@ -0,0 +1,213 @@
+"""
+
+Sobol' analysis
+===============
+"""
+
+# %% md
+# 
+# This example shows how to compute Sobol' sensitivity indices using
+# the :class:`.SobolAnalyze` class. 
+#
+# Let us consider the Ishigami function :cite:p:`LeGratiet2014`
+# 
+# :math:`y=f\left(x_1, x_2, x_3\right)=\sin \left(x_1\right)+7 \sin \left(\mathrm{x}_2\right)^2+0.1 x_3^4 \sin \left(x_1\right)`
+#
+# where :math:`x_i` is uniformly distributed on :math:`[-\pi, \pi]` for :math:`i \in [1,2,3]`. We define the function as follows:
+
+import numpy as np
+
+def f(x1,x2,x3):
+    return np.sin(x1) + 7*np.sin(x2)**2 + 0.1*x3**4*np.sin(x1)
+
+
+# %% md
+# 
+# The variation of each :math:`x_i` leads to the variation of :math:`y`. Sobol' analysis is used to quantify the contribution
+# of each :math:`x_i` and their interactions to the variation of :math:`y`. Steps of a Sobol' analysis are:
+#
+#  #. Draw samples of input.
+#  #. Evaluate the model at each input sample to obtain model output.
+#  #. Compute Sobol' indices based on model outputs.
+# 
+
+from psimpy.sampler import Saltelli
+from psimpy.sensitivity import SobolAnalyze
+
+ndim = 3
+bounds = np.array([[-np.pi, np.pi], [-np.pi, np.pi], [-np.pi, np.pi]])
+calc_second_order = False
+nbase = 1024
+
+# draw Saltelli samples
+saltelli_sampler = Saltelli(ndim, bounds, calc_second_order)
+saltelli_samples = saltelli_sampler.sample(nbase)
+
+# Evaluate the model to obtain model outputs
+Y = f(saltelli_samples[:,0], saltelli_samples[:,1], saltelli_samples[:, 2])
+
+# Compute Sobol' indices
+sobol_analyzer = SobolAnalyze(ndim, Y, calc_second_order, seed=2)
+S_res = sobol_analyzer.run()
+
+print("Estimated first-order Sobol' index: ", S_res['S1'][:,0])
+print("Analytical solution: [0.314, 0.442, 0]")
+
+
+# %% md
+# 
+# Figure below shows the results. The bar plots represent estimated first-order
+# and total-effect Sobol' indices, as well as their 95% confidence interval. The
+# red stars represent true values of the first-order Sobol' indices.
+#
+
+import matplotlib.pyplot as plt
+
+name_vars = [r'$x_1$',r'$x_2$',r'$x_3$']
+x = {'S1':[1,4,7], 'ST':[2,5,8]}
+color = {'S1':'#69b3a2', 'ST':'#3399e6'}
+width=0.8
+capsize=3
+
+fig, ax1 = plt.subplots(figsize=(4,3))
+
+# estimated first-order Sobol' indices and their confidence interval
+ax1.bar(x['S1'], S_res['S1'][:,0], width=width, yerr=S_res['S1'][:,2], color=color['S1'], capsize=capsize)
+
+ax1.axis([0,9,0,0.7])
+ax1.set_xticks([1.5,4.5,7.5])
+ax1.set_xticklabels(name_vars)
+ax1.tick_params(axis='both',bottom=False)
+ax1.tick_params(axis="y", labelcolor=color['S1'])
+ax1.yaxis.grid(True, linestyle='--', which='major', color='grey', alpha=.25)
+ax1.set_ylabel('First-order index', color=color['S1'])
+
+# analytical solution for first-order indices
+ax1.scatter(x['S1'], [0.314, 0.442, 0], s=30, c='red', marker='*')
+
+
+# estimated total-effect Sobol' indices and their confidence interval
+ax2 = ax1.twinx()
+ax2.bar(x['ST'], S_res['ST'][:,0], width=width, yerr=S_res['ST'][:,2], color=color['ST'], capsize=capsize)
+
+ax2.axis([0,9,0,0.7])
+ax2.set_xticks([1.5,4.5,7.5])
+ax2.tick_params(axis='both',bottom=False)
+ax2.tick_params(axis="y", labelcolor=color['ST'])
+ax2.yaxis.grid(True, linestyle='--', which='major', color='grey', alpha=.25)
+ax2.set_ylabel('Total-effect index', color=color['ST'])
+
+plt.tight_layout()
+
+
+# %% md
+# .. note:: The interaction between one parameter and all other parameters can be
+#     quantified by the difference between its first-order and total-effet Sobol'
+#     indices. If detailed information on interaction between any two parameters
+#     is needed, one can set ``calc_second_order`` to `True`.
+#  
+
+
+# %% md
+#
+# **Many models of interest in real-world applications are very computationally
+# expensive. In that case, we resort to emulation techniques in order to efficiently
+# conduct Sobol' analysis.** See :cite:t:`Zhao2021a` for the detailed theory.
+# 
+# Steps of such an analysis are:
+# 
+#  #. Draw input samples for emulator training.
+#  #. Evaluate the model at each training input point to obtain training data.
+#  #. Train an emulator for the computationally expensive model of interest.
+#  #. Draw samples of input for Sobol' analysis.
+#  #. Evaluate the emulator at each input sample at step 3 to obtain approximated model outputs.
+#  #. Compute Sobol' indices based on approximated model outputs.
+#
+# Assume that the above Ishigami function is computationally expensive, an emulator-based
+# Sobol' analysis can be conducted as follows:
+#
+
+import numpy as np
+from psimpy.sampler import LHS
+from psimpy.emulator import ScalarGaSP
+from psimpy.sampler import Saltelli
+from psimpy.sensitivity import SobolAnalyze
+
+# define the model
+def f(x1,x2,x3):
+    return np.sin(x1) + 7*np.sin(x2)**2 + 0.1*x3**4*np.sin(x1)
+
+ndim = 3
+bounds = np.array([[-np.pi, np.pi], [-np.pi, np.pi], [-np.pi, np.pi]])
+seed = 2
+
+# draw 100 input samples for emulator training using Latin hypercube sampling
+lhs_sampler = LHS(ndim, bounds, seed, criterion='maximin', iteration=200)
+design = lhs_sampler.sample(nsamples=100)
+
+# evaluate the model at each training input point
+response = f(design[:,0], design[:,1], design[:,2])
+
+# train an emulator
+scalar_gasp = ScalarGaSP(ndim)
+scalar_gasp.train(design, response)
+
+# the trained emulator needs to be validated before moving on
+# here we leave out this step for simplicity...
+
+# draw samples of input for Sobol' analysis
+calc_second_order = False
+nbase = 1024
+
+saltelli_sampler = Saltelli(ndim, bounds, calc_second_order)
+saltelli_samples = saltelli_sampler.sample(nbase)
+
+# evaluate the emulator to obtain approximated model output.
+# in order to take emulator-induced uncertainty into account, we draw 50 realizations
+# from the emulator
+Y = scalar_gasp.sample(saltelli_samples, 50)
+
+# Compute Sobol' indices based on approximated model outputs
+sobol_analyzer = SobolAnalyze(ndim, Y, calc_second_order, seed=seed)
+S_res = sobol_analyzer.run(mode='parallel', max_workers=5)
+
+print("\n")
+print("Emulator-based first-order Sobol' index: ", S_res['S1'][:,0])
+print("Analytical solution: [0.314, 0.442, 0]")
+
+# %% md
+# The following figure shows how the results of emulator-based Sobol' analysis
+# look like.
+#
+
+import matplotlib.pyplot as plt
+
+name_vars = [r'$x_1$',r'$x_2$',r'$x_3$']
+x = {'S1':[1,4,7], 'ST':[2,5,8]}
+color = {'S1':'#69b3a2', 'ST':'#3399e6'}
+width=0.8
+capsize=3
+
+fig, ax1 = plt.subplots(figsize=(4,3))
+
+ax1.bar(x['S1'], S_res['S1'][:,0], width=width, yerr=S_res['S1'][:,2], color=color['S1'], capsize=capsize)
+ax1.axis([0,9,0,0.7])
+ax1.set_xticks([1.5,4.5,7.5])
+ax1.set_xticklabels(name_vars)
+ax1.tick_params(axis='both',bottom=False)
+ax1.tick_params(axis="y", labelcolor=color['S1'])
+ax1.yaxis.grid(True, linestyle='--', which='major', color='grey', alpha=.25)
+ax1.set_ylabel('First-order index', color=color['S1'])
+
+ax1.scatter(x['S1'], [0.314, 0.442, 0], s=30, c='red', marker='*')
+
+ax2 = ax1.twinx()
+ax2.bar(x['ST'], S_res['ST'][:,0], width=width, yerr=S_res['ST'][:,2], color=color['ST'], capsize=capsize)
+ax2.axis([0,9,0,0.7])
+ax2.set_xticks([1.5,4.5,7.5])
+ax2.tick_params(axis='both',bottom=False)
+ax2.tick_params(axis="y", labelcolor=color['ST'])
+ax2.yaxis.grid(True, linestyle='--', which='major', color='grey', alpha=.25)
+ax2.set_ylabel('Total-effect index', color=color['ST'])
+
+plt.tight_layout()
\ No newline at end of file
diff --git a/docs/source/_build/html/_downloads/e02cb6046784acec18b4383ffbd83d67/plot_active_learning.ipynb b/docs/source/_build/html/_downloads/e02cb6046784acec18b4383ffbd83d67/plot_active_learning.ipynb
new file mode 100644
index 0000000..f7fbd77
--- /dev/null
+++ b/docs/source/_build/html/_downloads/e02cb6046784acec18b4383ffbd83d67/plot_active_learning.ipynb
@@ -0,0 +1,133 @@
+{
+  "cells": [
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "%matplotlib inline"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "\n# Active learning\n"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "This example shows how to use the :class:`.ActiveLearning` class to iteratively\nbuild a Gaussian process emulator for an unnormalized posterior involving a\nsimulator. It should be noted that this example is only for illustration\npurpose, rather than a real case. For simplicity, required arguments for\n:class:`.ActiveLearning` (including `simulator`, `likelihood`, `data`, etc.) are purely\nmade up. For a realistic case of active learning, one can refer to :cite:t:`Zhao2022`.\n\nFirst, we define the simulator, prior distribution of its variable parameters,\nobserved data, and likelihood function. They basically define the Bayesian\ninference problem. \n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "import numpy as np\n\nndim = 2 # dimension of variable parameters of the simulator\nbounds = bounds = np.array([[-5,5],[-5,5]]) # bounds of variable parameters\ndata = np.array([1,0])\n\ndef simulator(x1, x2):\n    \"\"\"Simulator y=f(x).\"\"\"\n    y1, y2 = x1, x2\n    return np.array([y1, y2])\n\ndef prior(x):\n    \"\"\"Uniform prior.\"\"\"\n    return 1/(10*10)\n\ndef likelihood(y, data):\n    \"\"\"Likelihood function L(y,data).\"\"\"\n    return np.exp(-(y[0]-data[0])**2/100 - (y[0]**2-y[1]-data[1])**2)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "Imagine that the simulator is a complex solver. It is not computationally feasible\nto compute the posterior distribution of the variable parameters using grid estimation\nor Metropolis Hastings estimation. This is because they require evaluating the likelihood\nmany times which essentially leads to many evaluations of the simulator. Therefore, we\nresort to use active learning to build a Gaussian process emulator for the unnormalized\nposterior (prior times likelihood) based on a small number of evaluations of the simulator.\nThe the posterior can be estimated using the emulator.\n\nTo do so, we need to pass arguments to following parameters of the :class:`.ActiveLearning` class:\n\n  - run_sim_obj : instance of class :class:`.RunSimulator`. It carries information on how\n    to run the simulator.\n  - lhs_sampler : instance of class :class:`.LHS`. It is used to draw initial samples to run\n    simulations in order to train an inital Gaussian process emulator.\n  - scalar_gasp : instance of class :class:`.ScalarGaSP`. It sets up the emulator structure.\n\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "from psimpy.simulator import RunSimulator\nfrom psimpy.sampler import LHS\nfrom psimpy.emulator import ScalarGaSP\n\nrun_simulator = RunSimulator(simulator, var_inp_parameter=['x1','x2'])\nlhs_sampler = LHS(ndim=ndim, bounds=bounds, seed=1)\nscalar_gasp = ScalarGaSP(ndim=ndim)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "Next, we create an object of the :class:`.ActiveLearning` class by\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "from psimpy.inference import ActiveLearning\n\nactive_learner = ActiveLearning(ndim, bounds, data, run_simulator, prior, likelihood,\n    lhs_sampler, scalar_gasp)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "Then we can call the :py:meth:`.ActiveLearning.initial_simulation` method to run initial\nsimulations and call the :py:meth:`.ActiveLearning.iterative_emulation` method to\niteratively run new simulation and build emulator. Here we allocate 40 simulations for\ninitial emulator training and 60 simulations for adaptive training.\n\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "n0 = 40\nniter = 60\n\ninit_var_samples, init_sim_outputs = active_learner.initial_simulation(\n    n0, mode='parallel', max_workers=4)\n\nvar_samples, _, _ = active_learner.iterative_emulation(\n    n0, init_var_samples, init_sim_outputs, niter=niter)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "Once the active learning process is finished, we obtain the final emulator for the\nlogarithm of the unnormalized posterior, which is given by the\n:py:meth:`.ActiveLearning.approx_ln_pxl` method.\n\nWe can then estimate the posterior using grid estimation or Metropolis Hastings\nestimation based on the emulator. An example is as follows. The contour plot shows\nthe estimated posterior. \n\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "from psimpy.inference import GridEstimation\nimport matplotlib.pyplot as plt\n\ngrid_estimator = GridEstimation(ndim, bounds, ln_pxl=active_learner.approx_ln_pxl)\nposterior, x_ndim = grid_estimator.run(nbins=50)\n\nfig, ax = plt.subplots(1,1,figsize=(5,4))\n\n# initial training points\nax.scatter(init_var_samples[:,0], init_var_samples[:,1], s=10, c='r', marker='o',\n    zorder=1, alpha=0.8, label='initial training points')\n# actively picked training points\nax.scatter(var_samples[n0:,0], var_samples[n0:,1], s=15, c='k', marker='+',\n    zorder=2, alpha=0.8, label='iterative training points')\n\n# estimated posterior based on the final emulator\nposterior = np.where(posterior < 1e-10, None, posterior)\ncontour = ax.contour(x_ndim[0], x_ndim[1], np.transpose(posterior), levels=10, zorder=0)\nplt.colorbar(contour, ax=ax)\n\nax.legend()\nax.set_title('Active learning')\nax.set_xlabel('x1')\nax.set_ylabel('x2')\nax.set_xlim([-5,5])\nax.set_ylim([-5,5])\nplt.tight_layout()"
+      ]
+    }
+  ],
+  "metadata": {
+    "kernelspec": {
+      "display_name": "Python 3",
+      "language": "python",
+      "name": "python3"
+    },
+    "language_info": {
+      "codemirror_mode": {
+        "name": "ipython",
+        "version": 3
+      },
+      "file_extension": ".py",
+      "mimetype": "text/x-python",
+      "name": "python",
+      "nbconvert_exporter": "python",
+      "pygments_lexer": "ipython3",
+      "version": "3.9.12"
+    }
+  },
+  "nbformat": 4,
+  "nbformat_minor": 0
+}
\ No newline at end of file
diff --git a/docs/source/_build/html/_downloads/e0b3048771af654ea83c8bb3f5bf6c0c/plot_saltelli.ipynb b/docs/source/_build/html/_downloads/e0b3048771af654ea83c8bb3f5bf6c0c/plot_saltelli.ipynb
new file mode 100644
index 0000000..bb713ea
--- /dev/null
+++ b/docs/source/_build/html/_downloads/e0b3048771af654ea83c8bb3f5bf6c0c/plot_saltelli.ipynb
@@ -0,0 +1,122 @@
+{
+  "cells": [
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "%matplotlib inline"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "\n# Saltelli sampling\n"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "This example shows how to draw samples using Saltelli sampling. \nAssume that there is a three-dimensional problem where X, Y, and Z are the\nthree random variables.\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "import numpy as np\n\nndim = 3\n# range of X is 10 to 20, range of Y is 100 to 200, range of Z is 1000 to 2000\nbounds = np.array([[10,20], [100,200], [1000,2000]])"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "Given this setting, we can import :class:`.Saltelli`, create an instance, and\ncall the :py:meth:`.Saltelli.sample` method to draw required number of samples.\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "from psimpy.sampler import Saltelli\n\nsaltelli_sampler = Saltelli(ndim, bounds, calc_second_order=False)\nsaltelli_samples = saltelli_sampler.sample(nbase=128)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "In above codes, we set ``calc_second_order`` to `False`. It means that picked\nsamples can be used in following Sobol' analysis to compute first-order and\ntotal-effect Sobol' indices but not second-order Sobol' indices. It leads to \n$nbase*(ndim+2)$ samples as shown below\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "import matplotlib.pyplot as plt\n\nfig = plt.figure()\nax = fig.add_subplot(projection='3d')\n\nax.scatter(saltelli_samples[:,0], saltelli_samples[:,1], saltelli_samples[:,2], marker='o')\nax.set_xlabel('X')\nax.set_ylabel('Y')\nax.set_zlabel('Z')\n\nplt.tight_layout()\n\nprint('Number of samples: ', f'{len(saltelli_samples)}')"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "If we want to draw samples which can also be used to compute second-order\nSobol' indices, we need to set ``calc_second_order`` to `True`.\nIt leads to $nbase*(2*ndim+2)$ samples.\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "saltelli_sampler = Saltelli(ndim, bounds, calc_second_order=True)\nsaltelli_samples = saltelli_sampler.sample(nbase=128)\n\nfig = plt.figure()\nax = fig.add_subplot(projection='3d')\n\nax.scatter(saltelli_samples[:,0], saltelli_samples[:,1], saltelli_samples[:,2], marker='o')\nax.set_xlabel('X')\nax.set_ylabel('Y')\nax.set_zlabel('Z')\n\nplt.tight_layout()\n\nprint('Number of samples: ', f'{len(saltelli_samples)}')"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "<div class=\"alert alert-info\"><h4>Note</h4><p>If one has a two-dimensional problem, there is no need to set\n    ``calc_second_order`` to `True`. The reason is that the second-order Sobol'\n    index can be directly computed based on the first-order and total-effect\n    Sobol' index in that case.</p></div>\n\n"
+      ]
+    }
+  ],
+  "metadata": {
+    "kernelspec": {
+      "display_name": "Python 3",
+      "language": "python",
+      "name": "python3"
+    },
+    "language_info": {
+      "codemirror_mode": {
+        "name": "ipython",
+        "version": 3
+      },
+      "file_extension": ".py",
+      "mimetype": "text/x-python",
+      "name": "python",
+      "nbconvert_exporter": "python",
+      "pygments_lexer": "ipython3",
+      "version": "3.9.12"
+    }
+  },
+  "nbformat": 4,
+  "nbformat_minor": 0
+}
\ No newline at end of file
diff --git a/docs/source/_build/html/_downloads/e6e32deb84b9140224f7120b34bdafda/plot_sobol_analyze.ipynb b/docs/source/_build/html/_downloads/e6e32deb84b9140224f7120b34bdafda/plot_sobol_analyze.ipynb
new file mode 100644
index 0000000..5667684
--- /dev/null
+++ b/docs/source/_build/html/_downloads/e6e32deb84b9140224f7120b34bdafda/plot_sobol_analyze.ipynb
@@ -0,0 +1,140 @@
+{
+  "cells": [
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "%matplotlib inline"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "\n# Sobol' analysis\n"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "This example shows how to compute Sobol' sensitivity indices using\nthe :class:`.SobolAnalyze` class. \n\nLet us consider the Ishigami function :cite:p:`LeGratiet2014`\n\n$y=f\\left(x_1, x_2, x_3\\right)=\\sin \\left(x_1\\right)+7 \\sin \\left(\\mathrm{x}_2\\right)^2+0.1 x_3^4 \\sin \\left(x_1\\right)$\n\nwhere $x_i$ is uniformly distributed on $[-\\pi, \\pi]$ for $i \\in [1,2,3]$. We define the function as follows:\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "import numpy as np\n\ndef f(x1,x2,x3):\n    return np.sin(x1) + 7*np.sin(x2)**2 + 0.1*x3**4*np.sin(x1)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "The variation of each $x_i$ leads to the variation of $y$. Sobol' analysis is used to quantify the contribution\nof each $x_i$ and their interactions to the variation of $y$. Steps of a Sobol' analysis are:\n\n #. Draw samples of input.\n #. Evaluate the model at each input sample to obtain model output.\n #. Compute Sobol' indices based on model outputs.\n\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "from psimpy.sampler import Saltelli\nfrom psimpy.sensitivity import SobolAnalyze\n\nndim = 3\nbounds = np.array([[-np.pi, np.pi], [-np.pi, np.pi], [-np.pi, np.pi]])\ncalc_second_order = False\nnbase = 1024\n\n# draw Saltelli samples\nsaltelli_sampler = Saltelli(ndim, bounds, calc_second_order)\nsaltelli_samples = saltelli_sampler.sample(nbase)\n\n# Evaluate the model to obtain model outputs\nY = f(saltelli_samples[:,0], saltelli_samples[:,1], saltelli_samples[:, 2])\n\n# Compute Sobol' indices\nsobol_analyzer = SobolAnalyze(ndim, Y, calc_second_order, seed=2)\nS_res = sobol_analyzer.run()\n\nprint(\"Estimated first-order Sobol' index: \", S_res['S1'][:,0])\nprint(\"Analytical solution: [0.314, 0.442, 0]\")"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "Figure below shows the results. The bar plots represent estimated first-order\nand total-effect Sobol' indices, as well as their 95% confidence interval. The\nred stars represent true values of the first-order Sobol' indices.\n\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "import matplotlib.pyplot as plt\n\nname_vars = [r'$x_1$',r'$x_2$',r'$x_3$']\nx = {'S1':[1,4,7], 'ST':[2,5,8]}\ncolor = {'S1':'#69b3a2', 'ST':'#3399e6'}\nwidth=0.8\ncapsize=3\n\nfig, ax1 = plt.subplots(figsize=(4,3))\n\n# estimated first-order Sobol' indices and their confidence interval\nax1.bar(x['S1'], S_res['S1'][:,0], width=width, yerr=S_res['S1'][:,2], color=color['S1'], capsize=capsize)\n\nax1.axis([0,9,0,0.7])\nax1.set_xticks([1.5,4.5,7.5])\nax1.set_xticklabels(name_vars)\nax1.tick_params(axis='both',bottom=False)\nax1.tick_params(axis=\"y\", labelcolor=color['S1'])\nax1.yaxis.grid(True, linestyle='--', which='major', color='grey', alpha=.25)\nax1.set_ylabel('First-order index', color=color['S1'])\n\n# analytical solution for first-order indices\nax1.scatter(x['S1'], [0.314, 0.442, 0], s=30, c='red', marker='*')\n\n\n# estimated total-effect Sobol' indices and their confidence interval\nax2 = ax1.twinx()\nax2.bar(x['ST'], S_res['ST'][:,0], width=width, yerr=S_res['ST'][:,2], color=color['ST'], capsize=capsize)\n\nax2.axis([0,9,0,0.7])\nax2.set_xticks([1.5,4.5,7.5])\nax2.tick_params(axis='both',bottom=False)\nax2.tick_params(axis=\"y\", labelcolor=color['ST'])\nax2.yaxis.grid(True, linestyle='--', which='major', color='grey', alpha=.25)\nax2.set_ylabel('Total-effect index', color=color['ST'])\n\nplt.tight_layout()"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "<div class=\"alert alert-info\"><h4>Note</h4><p>The interaction between one parameter and all other parameters can be\n    quantified by the difference between its first-order and total-effet Sobol'\n    indices. If detailed information on interaction between any two parameters\n    is needed, one can set ``calc_second_order`` to `True`.</p></div>\n\n\n"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "**Many models of interest in real-world applications are very computationally\nexpensive. In that case, we resort to emulation techniques in order to efficiently\nconduct Sobol' analysis.** See :cite:t:`Zhao2021a` for the detailed theory.\n\nSteps of such an analysis are:\n\n #. Draw input samples for emulator training.\n #. Evaluate the model at each training input point to obtain training data.\n #. Train an emulator for the computationally expensive model of interest.\n #. Draw samples of input for Sobol' analysis.\n #. Evaluate the emulator at each input sample at step 3 to obtain approximated model outputs.\n #. Compute Sobol' indices based on approximated model outputs.\n\nAssume that the above Ishigami function is computationally expensive, an emulator-based\nSobol' analysis can be conducted as follows:\n\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "import numpy as np\nfrom psimpy.sampler import LHS\nfrom psimpy.emulator import ScalarGaSP\nfrom psimpy.sampler import Saltelli\nfrom psimpy.sensitivity import SobolAnalyze\n\n# define the model\ndef f(x1,x2,x3):\n    return np.sin(x1) + 7*np.sin(x2)**2 + 0.1*x3**4*np.sin(x1)\n\nndim = 3\nbounds = np.array([[-np.pi, np.pi], [-np.pi, np.pi], [-np.pi, np.pi]])\nseed = 2\n\n# draw 100 input samples for emulator training using Latin hypercube sampling\nlhs_sampler = LHS(ndim, bounds, seed, criterion='maximin', iteration=200)\ndesign = lhs_sampler.sample(nsamples=100)\n\n# evaluate the model at each training input point\nresponse = f(design[:,0], design[:,1], design[:,2])\n\n# train an emulator\nscalar_gasp = ScalarGaSP(ndim)\nscalar_gasp.train(design, response)\n\n# the trained emulator needs to be validated before moving on\n# here we leave out this step for simplicity...\n\n# draw samples of input for Sobol' analysis\ncalc_second_order = False\nnbase = 1024\n\nsaltelli_sampler = Saltelli(ndim, bounds, calc_second_order)\nsaltelli_samples = saltelli_sampler.sample(nbase)\n\n# evaluate the emulator to obtain approximated model output.\n# in order to take emulator-induced uncertainty into account, we draw 50 realizations\n# from the emulator\nY = scalar_gasp.sample(saltelli_samples, 50)\n\n# Compute Sobol' indices based on approximated model outputs\nsobol_analyzer = SobolAnalyze(ndim, Y, calc_second_order, seed=seed)\nS_res = sobol_analyzer.run(mode='parallel', max_workers=5)\n\nprint(\"\\n\")\nprint(\"Emulator-based first-order Sobol' index: \", S_res['S1'][:,0])\nprint(\"Analytical solution: [0.314, 0.442, 0]\")"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "The following figure shows how the results of emulator-based Sobol' analysis\nlook like.\n\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "import matplotlib.pyplot as plt\n\nname_vars = [r'$x_1$',r'$x_2$',r'$x_3$']\nx = {'S1':[1,4,7], 'ST':[2,5,8]}\ncolor = {'S1':'#69b3a2', 'ST':'#3399e6'}\nwidth=0.8\ncapsize=3\n\nfig, ax1 = plt.subplots(figsize=(4,3))\n\nax1.bar(x['S1'], S_res['S1'][:,0], width=width, yerr=S_res['S1'][:,2], color=color['S1'], capsize=capsize)\nax1.axis([0,9,0,0.7])\nax1.set_xticks([1.5,4.5,7.5])\nax1.set_xticklabels(name_vars)\nax1.tick_params(axis='both',bottom=False)\nax1.tick_params(axis=\"y\", labelcolor=color['S1'])\nax1.yaxis.grid(True, linestyle='--', which='major', color='grey', alpha=.25)\nax1.set_ylabel('First-order index', color=color['S1'])\n\nax1.scatter(x['S1'], [0.314, 0.442, 0], s=30, c='red', marker='*')\n\nax2 = ax1.twinx()\nax2.bar(x['ST'], S_res['ST'][:,0], width=width, yerr=S_res['ST'][:,2], color=color['ST'], capsize=capsize)\nax2.axis([0,9,0,0.7])\nax2.set_xticks([1.5,4.5,7.5])\nax2.tick_params(axis='both',bottom=False)\nax2.tick_params(axis=\"y\", labelcolor=color['ST'])\nax2.yaxis.grid(True, linestyle='--', which='major', color='grey', alpha=.25)\nax2.set_ylabel('Total-effect index', color=color['ST'])\n\nplt.tight_layout()"
+      ]
+    }
+  ],
+  "metadata": {
+    "kernelspec": {
+      "display_name": "Python 3",
+      "language": "python",
+      "name": "python3"
+    },
+    "language_info": {
+      "codemirror_mode": {
+        "name": "ipython",
+        "version": 3
+      },
+      "file_extension": ".py",
+      "mimetype": "text/x-python",
+      "name": "python",
+      "nbconvert_exporter": "python",
+      "pygments_lexer": "ipython3",
+      "version": "3.9.12"
+    }
+  },
+  "nbformat": 4,
+  "nbformat_minor": 0
+}
\ No newline at end of file
diff --git a/docs/source/_build/html/_downloads/ff2071d6226ad5ba480d05dc9b72039e/emulator_python.zip b/docs/source/_build/html/_downloads/ff2071d6226ad5ba480d05dc9b72039e/emulator_python.zip
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diff --git a/docs/source/_build/html/_images/sphx_glr_plot_bayes_inference_001.png b/docs/source/_build/html/_images/sphx_glr_plot_bayes_inference_001.png
new file mode 100644
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diff --git a/docs/source/_build/html/_images/sphx_glr_plot_mass_point_model_thumb.png b/docs/source/_build/html/_images/sphx_glr_plot_mass_point_model_thumb.png
new file mode 100644
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diff --git a/docs/source/_build/html/_images/sphx_glr_plot_metropolis_hastings_thumb.png b/docs/source/_build/html/_images/sphx_glr_plot_metropolis_hastings_thumb.png
new file mode 100644
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literal 0
HcmV?d00001

diff --git a/docs/source/_build/html/_images/sphx_glr_plot_sobol_analyze_thumb.png b/docs/source/_build/html/_images/sphx_glr_plot_sobol_analyze_thumb.png
new file mode 100644
index 0000000000000000000000000000000000000000..e9d71aae8a897a39f06d760916579c41041db55d
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+  <h1>All modules for which code is available</h1>
+<ul><li><a href="psimpy/emulator/robustgasp.html">psimpy.emulator.robustgasp</a></li>
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+<li><a href="psimpy/simulator/mass_point_model.html">psimpy.simulator.mass_point_model</a></li>
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new file mode 100644
index 0000000..8c4bfda
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+++ b/docs/source/_build/html/_modules/psimpy/emulator/robustgasp.html
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+  <h1>Source code for psimpy.emulator.robustgasp</h1><div class="highlight"><pre>
+<span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">from</span> <span class="nn">rpy2.robjects.packages</span> <span class="kn">import</span> <span class="n">importr</span>
+<span class="kn">import</span> <span class="nn">rpy2.robjects.numpy2ri</span>
+<span class="kn">from</span> <span class="nn">rpy2.rinterface</span> <span class="kn">import</span> <span class="n">NA</span>
+<span class="kn">from</span> <span class="nn">rpy2.rinterface_lib.sexp</span> <span class="kn">import</span> <span class="n">NALogicalType</span>
+<span class="kn">from</span> <span class="nn">typing</span> <span class="kn">import</span> <span class="n">Union</span>
+<span class="kn">from</span> <span class="nn">beartype</span> <span class="kn">import</span> <span class="n">beartype</span>
+
+<span class="n">rpy2</span><span class="o">.</span><span class="n">robjects</span><span class="o">.</span><span class="n">numpy2ri</span><span class="o">.</span><span class="n">activate</span><span class="p">()</span>
+<span class="n">RobustGaSP</span> <span class="o">=</span> <span class="n">importr</span><span class="p">(</span><span class="s1">&#39;RobustGaSP&#39;</span><span class="p">)</span>
+
+<span class="c1"># fetch @</span>
+<span class="n">r_base</span> <span class="o">=</span> <span class="n">importr</span><span class="p">(</span><span class="s2">&quot;base&quot;</span><span class="p">)</span>
+<span class="n">r_at</span> <span class="o">=</span> <span class="n">r_base</span><span class="o">.</span><span class="vm">__dict__</span><span class="p">[</span><span class="s2">&quot;@&quot;</span><span class="p">]</span>
+
+<span class="k">class</span> <span class="nc">RobustGaSPBase</span><span class="p">:</span>
+
+    <span class="nd">@beartype</span>
+    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span>
+        <span class="bp">self</span><span class="p">,</span> <span class="n">ndim</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">zero_mean</span><span class="p">:</span> <span class="nb">str</span> <span class="o">=</span> <span class="s1">&#39;No&#39;</span><span class="p">,</span> <span class="n">nugget</span><span class="p">:</span> <span class="nb">float</span> <span class="o">=</span> <span class="mf">0.0</span><span class="p">,</span>
+        <span class="n">nugget_est</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="kc">False</span><span class="p">,</span>
+        <span class="n">range_par</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="n">NALogicalType</span><span class="p">]</span> <span class="o">=</span> <span class="n">NA</span><span class="p">,</span> 
+        <span class="n">method</span><span class="p">:</span> <span class="nb">str</span> <span class="o">=</span><span class="s1">&#39;post_mode&#39;</span><span class="p">,</span> <span class="n">prior_choice</span><span class="p">:</span> <span class="nb">str</span> <span class="o">=</span> <span class="s1">&#39;ref_approx&#39;</span><span class="p">,</span>
+        <span class="n">a</span><span class="p">:</span> <span class="nb">float</span> <span class="o">=</span> <span class="mf">0.2</span><span class="p">,</span> <span class="n">b</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">float</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
+        <span class="n">kernel_type</span><span class="p">:</span> <span class="nb">str</span> <span class="o">=</span> <span class="s1">&#39;matern_5_2&#39;</span><span class="p">,</span>
+        <span class="n">isotropic</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="kc">False</span><span class="p">,</span> <span class="n">optimization</span><span class="p">:</span> <span class="nb">str</span> <span class="o">=</span> <span class="s1">&#39;lbfgs&#39;</span><span class="p">,</span>
+        <span class="n">alpha</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span> <span class="n">lower_bound</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="kc">True</span><span class="p">,</span>
+        <span class="n">max_eval</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">int</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span> <span class="n">num_initial_values</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">2</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
+        <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Set up basic parameters of the emulator.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        ndim : int</span>
+<span class="sd">            Input parameter dimension.</span>
+<span class="sd">        zero_mean : str, optional </span>
+<span class="sd">            If `&#39;Yes&#39;`, the mean is set to zero. If `&#39;No&#39;`, the mean is</span>
+<span class="sd">            specified by ``trend``. Default is `&#39;No&#39;`.</span>
+<span class="sd">        nugget : float, optional</span>
+<span class="sd">            Nugget variance ratio. </span>
+<span class="sd">            If :math:`0`, there is no nugget or the nugget is estimated.</span>
+<span class="sd">            If not :math:`0`, it means a fixed nugget. Default is :math:`0`.</span>
+<span class="sd">        nugget_est : bool, optional</span>
+<span class="sd">            `True` means ``nugget`` should be estimated.</span>
+<span class="sd">            `False` means ``nugget`` is fixed or not estimated.</span>
+<span class="sd">            Default is `False`.</span>
+<span class="sd">        range_par : numpy array, optional</span>
+<span class="sd">            Range parameters. One dimension :class:`numpy.ndarray` of length</span>
+<span class="sd">            ``ndim``. If given, range parameters are set to the given values</span>
+<span class="sd">            rather than estimated based on training data.</span>
+<span class="sd">            By default `NA`, meaning that range parameters are estimated based</span>
+<span class="sd">            on training data.</span>
+<span class="sd">        method : str, optional</span>
+<span class="sd">            Method used for parameter estimation.</span>
+<span class="sd">            `&#39;post_mode&#39;`: marginal posterior mode estimation, resulted emulator</span>
+<span class="sd">            is a Student&#39;s t-process.</span>
+<span class="sd">            `&#39;mmle&#39;`: maximum marginal likelihood estimation, resulted emulator</span>
+<span class="sd">            is a Student&#39;s t-process.</span>
+<span class="sd">            `&#39;mle&#39;`: maximum likelihood estimation, resulted emulator is a</span>
+<span class="sd">            Gaussian process.</span>
+<span class="sd">            Default is `&#39;post_mode&#39;`.</span>
+<span class="sd">        prior_choice : str, optional</span>
+<span class="sd">            `&#39;ref_xi&#39;`, `&#39;ref_gamma&#39;`, or `&#39;ref_approx&#39;`.</span>
+<span class="sd">            Default is `&#39;ref_approx&#39;`.</span>
+<span class="sd">        a : float, optional</span>
+<span class="sd">            Prior parameters in the jointly robust prior. Default :math:`0.2`.</span>
+<span class="sd">        b : float, optional</span>
+<span class="sd">            Prior parameters in the jointly robust prior.</span>
+<span class="sd">            Default value is :math:`ntrain^{-1/ndim}(a+ndim)`, where ``ntrain``</span>
+<span class="sd">            is the number of training input points and ``ndim`` is input</span>
+<span class="sd">            parameter dimension.</span>
+<span class="sd">        kernel_type : str, optional</span>
+<span class="sd">            `&#39;matern_3_2&#39;`: Matern correlation with roughness parameter :math:`3/2`.</span>
+<span class="sd">            `&#39;matern_5_2&#39;`: Matern correlation with roughness parameter :math:`5/2`.</span>
+<span class="sd">            `&#39;pow_exp&#39;`: power exponential correlation with roughness parameter</span>
+<span class="sd">            ``alpha``.</span>
+<span class="sd">            Default is `&#39;matern_5_2&#39;`.</span>
+<span class="sd">        isotropic : bool, optional</span>
+<span class="sd">            `True`: isotropic kernel. `False`: separable kernel.</span>
+<span class="sd">            Default is `False`.</span>
+<span class="sd">        optimization : str, optional</span>
+<span class="sd">            Optimization method for kernel parameters.</span>
+<span class="sd">            `&#39;lbfgs&#39;`: low storage version of the Broyden-Fletcher-Goldarb-Shanno</span>
+<span class="sd">            method.</span>
+<span class="sd">            `&#39;nelder-mead&#39;`: Nelder and Mead method.</span>
+<span class="sd">            `&#39;brent&#39;`: Brent method for one-dimensional problems.</span>
+<span class="sd">        alpha : numpy array, optional</span>
+<span class="sd">            Roughness parameters in the `&#39;pow_exp&#39;` correlation functions. One</span>
+<span class="sd">            dimension :class:`numpy.ndarray` of length ``ndim``.</span>
+<span class="sd">            Default is a one dimension array with each entry being :math:`1.9`.</span>
+<span class="sd">        lower_bound : bool</span>
+<span class="sd">            `True`: the default lower bounds of the inverse range parameters are</span>
+<span class="sd">            used to constrain the optimization.</span>
+<span class="sd">            `False`: the optimization is unconstrained.</span>
+<span class="sd">            Default is `True`.</span>
+<span class="sd">        max_eval : int, optional</span>
+<span class="sd">            Maximum number of steps to estimate the range and nugget parameters.</span>
+<span class="sd">            Default is :math:`max(30,20+5*ndim)`.</span>
+<span class="sd">        num_initial_values : int, optional</span>
+<span class="sd">            Number of initial values of the kernel parameters in optimization.</span>
+<span class="sd">            Default is :math:`2`.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">ndim</span> <span class="o">=</span> <span class="n">ndim</span>
+
+        <span class="k">if</span> <span class="n">zero_mean</span> <span class="ow">not</span> <span class="ow">in</span> <span class="p">[</span><span class="s1">&#39;No&#39;</span><span class="p">,</span> <span class="s1">&#39;Yes&#39;</span><span class="p">]:</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;zero_mean can be either &#39;No&#39; or &#39;Yes&#39;.&quot;</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">zero_mean</span> <span class="o">=</span> <span class="n">zero_mean</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">nugget</span> <span class="o">=</span> <span class="nb">float</span><span class="p">(</span><span class="n">nugget</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">nugget_est</span> <span class="o">=</span> <span class="n">nugget_est</span>
+
+        <span class="k">if</span> <span class="n">range_par</span> <span class="ow">is</span> <span class="ow">not</span> <span class="n">NA</span><span class="p">:</span>
+            <span class="k">if</span> <span class="n">range_par</span><span class="o">.</span><span class="n">ndim</span> <span class="o">!=</span> <span class="mi">1</span> <span class="ow">or</span> <span class="nb">len</span><span class="p">(</span><span class="n">range_par</span><span class="p">)</span> <span class="o">!=</span> <span class="n">ndim</span><span class="p">:</span>
+                <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span>
+                    <span class="s2">&quot;range_par must be 1d numpy array of length ndim&quot;</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">range_par</span> <span class="o">=</span> <span class="n">range_par</span>
+
+        <span class="k">if</span> <span class="n">method</span> <span class="ow">not</span> <span class="ow">in</span> <span class="p">[</span><span class="s1">&#39;post_mode&#39;</span><span class="p">,</span> <span class="s1">&#39;mmle&#39;</span><span class="p">,</span> <span class="s1">&#39;mle&#39;</span><span class="p">]:</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span>
+                <span class="s2">&quot;method can only be &#39;post_mode&#39;, &#39;mmle&#39;, or &#39;mle&#39;.&quot;</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">method</span> <span class="o">=</span> <span class="n">method</span>
+
+        <span class="k">if</span> <span class="n">prior_choice</span> <span class="ow">not</span> <span class="ow">in</span> <span class="p">[</span><span class="s1">&#39;ref_xi&#39;</span><span class="p">,</span> <span class="s1">&#39;ref_gamma&#39;</span><span class="p">,</span> <span class="s1">&#39;ref_approx&#39;</span><span class="p">]:</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span>
+                <span class="s2">&quot;prior_choice can only be &#39;ref_xi&#39;, &#39;ref_gamma&#39;,&quot;</span>
+                <span class="s2">&quot; or &#39;ref_approx&#39;.&quot;</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">prior_choice</span> <span class="o">=</span> <span class="n">prior_choice</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">a</span> <span class="o">=</span> <span class="nb">float</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">b</span> <span class="o">=</span> <span class="n">b</span>
+
+        <span class="k">if</span> <span class="n">kernel_type</span> <span class="ow">not</span> <span class="ow">in</span> <span class="p">[</span><span class="s1">&#39;matern_3_2&#39;</span><span class="p">,</span> <span class="s1">&#39;matern_5_2&#39;</span><span class="p">,</span> <span class="s1">&#39;pow_exp&#39;</span><span class="p">]:</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span>
+                <span class="s2">&quot;kernel_type can only be &#39;matern_3_2&#39;, &#39;matern_5_2&#39;,&quot;</span>
+                <span class="s2">&quot; or &#39;pow_exp&#39;.&quot;</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">kernel_type</span> <span class="o">=</span> <span class="n">kernel_type</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">isotropic</span> <span class="o">=</span> <span class="n">isotropic</span>
+
+        <span class="k">if</span> <span class="n">optimization</span> <span class="ow">not</span> <span class="ow">in</span> <span class="p">[</span><span class="s1">&#39;lbfgs&#39;</span><span class="p">,</span> <span class="s1">&#39;nelder-mead&#39;</span><span class="p">,</span> <span class="s1">&#39;brent&#39;</span><span class="p">]:</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span>
+                <span class="s2">&quot;optimization can only be &#39;lbfgs&#39;, &#39;nelder-mead&#39;, or &#39;brent&#39;.&quot;</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">optimization</span> <span class="o">=</span> <span class="n">optimization</span>
+
+        <span class="k">if</span> <span class="n">alpha</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="n">alpha</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="n">ndim</span><span class="p">)</span> <span class="o">*</span> <span class="mf">1.9</span>
+        <span class="k">elif</span> <span class="n">alpha</span><span class="o">.</span><span class="n">ndim</span> <span class="o">!=</span> <span class="mi">1</span> <span class="ow">or</span> <span class="nb">len</span><span class="p">(</span><span class="n">alpha</span><span class="p">)</span> <span class="o">!=</span> <span class="n">ndim</span><span class="p">:</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;alpha must be 1d numpy array of length ndim&quot;</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">alpha</span> <span class="o">=</span> <span class="n">alpha</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">float32</span><span class="p">)</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">lower_bound</span> <span class="o">=</span> <span class="n">lower_bound</span>
+
+        <span class="k">if</span> <span class="n">max_eval</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="n">max_eval</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="nb">max</span><span class="p">(</span><span class="mi">30</span><span class="p">,</span> <span class="mi">20</span> <span class="o">+</span> <span class="mi">5</span><span class="o">*</span><span class="n">ndim</span><span class="p">))</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">max_eval</span> <span class="o">=</span> <span class="n">max_eval</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">num_initial_values</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">num_initial_values</span><span class="p">)</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">emulator</span> <span class="o">=</span> <span class="kc">None</span>
+    
+    <span class="k">def</span> <span class="nf">_preprocess_design_response_trend</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">design</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span>
+        <span class="n">response</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="n">trend</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
+        <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Preprocess design, response, and trend before train an emulator.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        design : numpy array</span>
+<span class="sd">            Training input points. Shape :code:`(ntrain, ndim)`.</span>
+<span class="sd">            ``ntrain`` is the number of training points, ``ndim`` is the input</span>
+<span class="sd">            dimension. If :math:`ndim=1`, both :code:`(ntrain, 1)` and</span>
+<span class="sd">            :code:`(ntrain,)` :class:`numpy.ndarray` are valid.</span>
+<span class="sd">        response : numpy array</span>
+<span class="sd">            Training output points. Shape :code:`(ntrain, nresponse)`.</span>
+<span class="sd">            ``nresponse`` is the number of QoIs of a single simulation.</span>
+<span class="sd">            ``ntrain`` output points corresponding to ``design``.</span>
+<span class="sd">            For child class :class:`.ScalarGaSP`, :math:`nresponse=1`.</span>
+<span class="sd">            For child class :class:`.PPGaSP`, :math:`nresponse&gt;1`.</span>
+<span class="sd">        trend : numpy array</span>
+<span class="sd">            Basis function matrix. Shape :code:`(ntrain, q)`.</span>
+<span class="sd">            If `None`, a :code:`(ntrain, 1)` matrix of ones is used.</span>
+<span class="sd">            If :math:`q=1`, both :code:`(ntrain, 1)` and :code:`(ntrain,)`</span>
+<span class="sd">            :class:`numpy.ndarray` are valid.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="ow">not</span> <span class="p">(</span><span class="n">design</span><span class="o">.</span><span class="n">ndim</span> <span class="o">==</span> <span class="mi">1</span> <span class="ow">or</span> <span class="n">design</span><span class="o">.</span><span class="n">ndim</span> <span class="o">==</span> <span class="mi">2</span><span class="p">):</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;design must be 1d or 2d numpy array.&quot;</span><span class="p">)</span>
+        <span class="k">elif</span> <span class="n">design</span><span class="o">.</span><span class="n">ndim</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
+            <span class="n">design</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">design</span><span class="p">,</span> <span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">design</span><span class="p">),</span> <span class="mi">1</span><span class="p">))</span>
+        
+        <span class="k">if</span> <span class="n">design</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">!=</span> <span class="bp">self</span><span class="o">.</span><span class="n">ndim</span><span class="p">:</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;design must match the input dimension ndim&quot;</span><span class="p">)</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">design</span> <span class="o">=</span> <span class="n">design</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">float32</span><span class="p">)</span>
+
+        <span class="k">if</span> <span class="ow">not</span> <span class="p">(</span><span class="n">response</span><span class="o">.</span><span class="n">ndim</span> <span class="o">==</span> <span class="mi">1</span> <span class="ow">or</span> <span class="n">response</span><span class="o">.</span><span class="n">ndim</span> <span class="o">==</span> <span class="mi">2</span><span class="p">):</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;response must be 1d or 2d numpy array.&quot;</span><span class="p">)</span>
+        <span class="k">elif</span> <span class="n">response</span><span class="o">.</span><span class="n">ndim</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
+            <span class="n">response</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">response</span><span class="p">,</span> <span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">response</span><span class="p">),</span> <span class="mi">1</span><span class="p">))</span>
+        <span class="k">if</span> <span class="n">response</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">!=</span> <span class="n">design</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]:</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span>
+                <span class="s2">&quot;response must have same number of points as design&quot;</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">response</span> <span class="o">=</span> <span class="n">response</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">float32</span><span class="p">)</span>
+
+        <span class="k">if</span> <span class="n">trend</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="n">trend</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">((</span><span class="n">design</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="mi">1</span><span class="p">))</span>
+        <span class="k">elif</span> <span class="ow">not</span> <span class="p">(</span><span class="n">trend</span><span class="o">.</span><span class="n">ndim</span> <span class="o">==</span> <span class="mi">1</span> <span class="ow">or</span> <span class="n">trend</span><span class="o">.</span><span class="n">ndim</span> <span class="o">==</span> <span class="mi">2</span><span class="p">):</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;trend must be 1d or 2d numpy array.&quot;</span><span class="p">)</span>
+        <span class="k">elif</span> <span class="n">trend</span><span class="o">.</span><span class="n">ndim</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
+            <span class="n">trend</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">trend</span><span class="p">,</span> <span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">trend</span><span class="p">),</span> <span class="mi">1</span><span class="p">))</span>
+        <span class="k">if</span> <span class="n">trend</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">!=</span> <span class="n">design</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]:</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;trend must have same numer of points as design&quot;</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">trend</span> <span class="o">=</span> <span class="n">trend</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">float32</span><span class="p">)</span>
+
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">zero_mean</span> <span class="o">==</span> <span class="s1">&#39;Yes&#39;</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">trend</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">design</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="mi">1</span><span class="p">),</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">float32</span><span class="p">)</span>
+        
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">b</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">_b</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span> <span class="o">/</span> <span class="n">design</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span><span class="o">**</span><span class="p">(</span><span class="mi">1</span> <span class="o">/</span> <span class="n">design</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span> <span class="o">*</span> \
+                <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">a</span> <span class="o">+</span> <span class="n">design</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">_b</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">b</span>
+
+    <span class="k">def</span> <span class="nf">_preprocess_testing_input_trend</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">testing_input</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span>
+        <span class="n">testing_trend</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
+        <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Preprocess testing_input and testing_trend before make prediction or</span>
+<span class="sd">        draw samples.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        testing_input : numpy array</span>
+<span class="sd">            Input matrix to make prediction or draw samples.</span>
+<span class="sd">            Shape :code:`(ntest, ndim)`.</span>
+<span class="sd">            If :math:`ndim=1`, both :code:`(ntest, 1)` and :code:`(ntest,)`</span>
+<span class="sd">            :class:`numpy.ndarray` are valid.</span>
+<span class="sd">        testing_trend : numpy array</span>
+<span class="sd">            Basis function matrix corresponds to ``testing_input``.</span>
+<span class="sd">            Shape :code:`(ntest, q)`.</span>
+<span class="sd">            By default :code:`(ntest, 1)` matrix of ones.</span>
+<span class="sd">            If :math:`q=1`, both :code:`(ntest, 1)` and :code:`(ntest,)`</span>
+<span class="sd">            :class:`numpy.ndarray` are valid.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="ow">not</span> <span class="p">(</span><span class="n">testing_input</span><span class="o">.</span><span class="n">ndim</span> <span class="o">==</span> <span class="mi">1</span> <span class="ow">or</span> <span class="n">testing_input</span><span class="o">.</span><span class="n">ndim</span> <span class="o">==</span> <span class="mi">2</span><span class="p">):</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;testing_input must be 1d or 2d numpy array.&quot;</span><span class="p">)</span>
+        <span class="k">elif</span> <span class="n">testing_input</span><span class="o">.</span><span class="n">ndim</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
+            <span class="n">testing_input</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">testing_input</span><span class="p">,</span> <span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">testing_input</span><span class="p">),</span> <span class="mi">1</span><span class="p">))</span>
+        
+        <span class="k">if</span> <span class="n">testing_input</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">!=</span> <span class="bp">self</span><span class="o">.</span><span class="n">ndim</span><span class="p">:</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span>
+                <span class="s2">&quot;testing_input must match the input dimension ndim&quot;</span><span class="p">)</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">testing_input</span> <span class="o">=</span> <span class="n">testing_input</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">float32</span><span class="p">)</span>
+
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">zero_mean</span> <span class="o">==</span> <span class="s2">&quot;Yes&quot;</span><span class="p">:</span>
+            <span class="n">testing_trend</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">testing_input</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="mi">1</span><span class="p">))</span>
+        <span class="k">elif</span> <span class="n">testing_trend</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="n">testing_trend</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">((</span><span class="n">testing_input</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="mi">1</span><span class="p">))</span>
+        <span class="k">elif</span> <span class="ow">not</span> <span class="p">(</span><span class="n">testing_trend</span><span class="o">.</span><span class="n">ndim</span> <span class="o">==</span> <span class="mi">1</span> <span class="ow">or</span> <span class="n">testing_trend</span><span class="o">.</span><span class="n">ndim</span> <span class="o">==</span> <span class="mi">2</span><span class="p">):</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;testing_trend must be 1d or 2d numpy array.&quot;</span><span class="p">)</span>
+        <span class="k">elif</span> <span class="n">testing_trend</span><span class="o">.</span><span class="n">ndim</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
+            <span class="n">testing_trend</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">testing_trend</span><span class="p">,</span> <span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">testing_trend</span><span class="p">),</span> <span class="mi">1</span><span class="p">))</span>
+        
+        <span class="bp">self</span><span class="o">.</span><span class="n">testing_trend</span> <span class="o">=</span> <span class="n">testing_trend</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">float32</span><span class="p">)</span>
+
+        <span class="k">if</span> <span class="n">testing_trend</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">!=</span> <span class="n">testing_input</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]:</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span>
+                <span class="s2">&quot;testing_trend must have same numer of points as testing_input&quot;</span><span class="p">)</span>
+
+        <span class="k">if</span> <span class="n">testing_trend</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">!=</span> <span class="bp">self</span><span class="o">.</span><span class="n">trend</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">]:</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span>
+                <span class="s2">&quot;testing_trend must have the same basis as the trend used&quot;</span>
+                <span class="s2">&quot; for emulator training.&quot;</span><span class="p">)</span>
+
+<div class="viewcode-block" id="ScalarGaSP"><a class="viewcode-back" href="../../../emulator/robustgasp.html#psimpy.emulator.robustgasp.ScalarGaSP">[docs]</a><span class="k">class</span> <span class="nc">ScalarGaSP</span><span class="p">(</span><span class="n">RobustGaSPBase</span><span class="p">):</span>
+
+<div class="viewcode-block" id="ScalarGaSP.train"><a class="viewcode-back" href="../../../emulator/robustgasp.html#psimpy.emulator.robustgasp.ScalarGaSP.train">[docs]</a>    <span class="nd">@beartype</span>
+    <span class="k">def</span> <span class="nf">train</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">design</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="n">response</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span>
+        <span class="n">trend</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
+        <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Train a scalar GP given training data.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        design : numpy array</span>
+<span class="sd">            Training input points. Shape :code:`(ntrain, ndim)`.</span>
+<span class="sd">            ``ntrain`` is the number of training points, ``ndim`` is the input</span>
+<span class="sd">            dimension. If :math:`ndim=1`, both :code:`(ntrain, 1)` and</span>
+<span class="sd">            :code:`(ntrain,)` :class:`numpy.ndarray` are valid.</span>
+<span class="sd">        response : numpy array</span>
+<span class="sd">            Training output points. Shape :code:`(ntrain, 1)` or</span>
+<span class="sd">            :code:`(ntrain,)`.</span>
+<span class="sd">        trend : numpy array, optional</span>
+<span class="sd">            Basis function matrix. Shape :code:`(ntrain, q)`.</span>
+<span class="sd">            If `None`, a :code:`(ntrain, 1)` matrix of ones is used.</span>
+<span class="sd">            If :math:`q=1`, both :code:`(ntrain, 1)` and :code:`(ntrain,)`</span>
+<span class="sd">            :class:`numpy.ndarray` are valid.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">_preprocess_design_response_trend</span><span class="p">(</span><span class="n">design</span><span class="p">,</span> <span class="n">response</span><span class="p">,</span> <span class="n">trend</span><span class="p">)</span>
+
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">response</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">!=</span> <span class="mi">1</span><span class="p">:</span>
+            <span class="k">raise</span> <span class="ne">RuntimeError</span><span class="p">(</span><span class="s2">&quot;ScalarGaSP only works for scalar-output model&quot;</span><span class="p">)</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">emulator</span> <span class="o">=</span> <span class="n">RobustGaSP</span><span class="o">.</span><span class="n">rgasp</span><span class="p">(</span>
+            <span class="n">design</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">design</span><span class="p">,</span>
+            <span class="n">response</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">response</span><span class="p">,</span>
+            <span class="n">trend</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">trend</span><span class="p">,</span>
+            <span class="n">zero_mean</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">zero_mean</span><span class="p">,</span>
+            <span class="n">nugget</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">nugget</span><span class="p">,</span>
+            <span class="n">nugget_est</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">nugget_est</span><span class="p">,</span>
+            <span class="n">range_par</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">range_par</span><span class="p">,</span>
+            <span class="n">method</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">method</span><span class="p">,</span>
+            <span class="n">prior_choice</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">prior_choice</span><span class="p">,</span>
+            <span class="n">a</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">a</span><span class="p">,</span>
+            <span class="n">b</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">_b</span><span class="p">,</span>
+            <span class="n">kernel_type</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">kernel_type</span><span class="p">,</span>
+            <span class="n">isotropic</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">isotropic</span><span class="p">,</span>
+            <span class="n">optimization</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">optimization</span><span class="p">,</span>
+            <span class="n">alpha</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">alpha</span><span class="p">,</span>
+            <span class="n">lower_bound</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">lower_bound</span><span class="p">,</span>
+            <span class="n">max_eval</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">max_eval</span><span class="p">,</span>
+            <span class="n">num_initial_values</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">num_initial_values</span><span class="p">)</span></div>
+    
+<div class="viewcode-block" id="ScalarGaSP.predict"><a class="viewcode-back" href="../../../emulator/robustgasp.html#psimpy.emulator.robustgasp.ScalarGaSP.predict">[docs]</a>    <span class="nd">@beartype</span>
+    <span class="k">def</span> <span class="nf">predict</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">testing_input</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span>
+        <span class="n">testing_trend</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">:</span>
+        <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Make prediction using the trained scalar GP emulator.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        testing_input : numpy array</span>
+<span class="sd">            Input points at which to make prediction. Shape :code:`(ntest, ndim)`.</span>
+<span class="sd">            ``ntest`` is the number of input points and ``ndim`` is the</span>
+<span class="sd">            input dimension. If :math:`ndim=1`, both :code:`(ntest, 1)` and</span>
+<span class="sd">            :code:`(ntest,)` :class:`numpy.ndarray` are valid.</span>
+<span class="sd">        testing_trend : numpy array, optional</span>
+<span class="sd">            Basis function matrix corresponds to ``testing_input``.</span>
+<span class="sd">            Shape :code:`(ntest, q)`. By default :code:`(ntest, 1)` matrix of ones.</span>
+<span class="sd">            If :math:`q=1`, both :code:`(ntest, 1)` and :code:`(ntest,)`</span>
+<span class="sd">            :class:`numpy.ndarray` are valid.</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        predictions : numpy array</span>
+<span class="sd">            Emulator-prediction at ``testing_input``. Shape :code:`(ntest, 4)`.</span>
+<span class="sd">            `predictions[:, 0]` - mean,</span>
+<span class="sd">            `predictions[:, 1]` - low95,</span>
+<span class="sd">            `predictions[:, 2]` - upper95, </span>
+<span class="sd">            `predictions[:, 3]` - sd</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">emulator</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="k">raise</span> <span class="ne">RuntimeError</span><span class="p">(</span><span class="s2">&quot;Emulator has not been trained!&quot;</span><span class="p">)</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">_preprocess_testing_input_trend</span><span class="p">(</span><span class="n">testing_input</span><span class="p">,</span> <span class="n">testing_trend</span><span class="p">)</span>
+
+        <span class="n">r_predictions</span> <span class="o">=</span> <span class="n">RobustGaSP</span><span class="o">.</span><span class="n">predict_rgasp</span><span class="p">(</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">emulator</span><span class="p">,</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">testing_input</span><span class="p">,</span>
+            <span class="n">testing_trend</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">testing_trend</span><span class="p">,</span>
+            <span class="n">interval_data</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
+            <span class="n">outasS3</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
+        <span class="n">predictions</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">transpose</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">r_predictions</span><span class="p">))</span>
+
+        <span class="k">return</span> <span class="n">predictions</span></div>
+
+<div class="viewcode-block" id="ScalarGaSP.sample"><a class="viewcode-back" href="../../../emulator/robustgasp.html#psimpy.emulator.robustgasp.ScalarGaSP.sample">[docs]</a>    <span class="nd">@beartype</span>
+    <span class="k">def</span> <span class="nf">sample</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">testing_input</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="n">nsamples</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">1</span><span class="p">,</span>
+        <span class="n">testing_trend</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">:</span>
+        <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Draw samples using the trained scalar GP emulator.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        testing_input : numpy array</span>
+<span class="sd">            Input points at which to draw samples. Shape :code:`(ntest, ndim)`.</span>
+<span class="sd">            ``ntest`` is the number of input points and ``ndim`` is the input</span>
+<span class="sd">            dimension. If :math:`ndim=1`, both :code:`(ntest, 1)` and</span>
+<span class="sd">            :code:`(ntest,)` :class:`numpy.ndarray` are valid.</span>
+<span class="sd">        nsamples : int, optional</span>
+<span class="sd">            Number of samples to be drawn.</span>
+<span class="sd">        testing_trend : numpy array, optional</span>
+<span class="sd">            Basis function matrix corresponds to ``testing_input``.</span>
+<span class="sd">            Shape :code:`(ntest, q)`. By default :code:`(ntest, 1)` matrix of ones.</span>
+<span class="sd">            If :math:`q=1`, both :code:`(ntest, 1)` and :code:`(ntest,)`</span>
+<span class="sd">            :class:`numpy.ndarray` are valid.</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        samples : numpy array</span>
+<span class="sd">            Shape :code:`(ntest, nsamples)`. Each column contains one realization</span>
+<span class="sd">            of the trained emulator at ``testing_input``.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">emulator</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="k">raise</span> <span class="ne">RuntimeError</span><span class="p">(</span><span class="s2">&quot;Emulator has not been trained!&quot;</span><span class="p">)</span>
+        
+        <span class="bp">self</span><span class="o">.</span><span class="n">_preprocess_testing_input_trend</span><span class="p">(</span><span class="n">testing_input</span><span class="p">,</span> <span class="n">testing_trend</span><span class="p">)</span>
+
+        <span class="n">r_samples</span> <span class="o">=</span> <span class="n">RobustGaSP</span><span class="o">.</span><span class="n">Sample</span><span class="p">(</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">emulator</span><span class="p">,</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">testing_input</span><span class="p">,</span>
+            <span class="n">num_sample</span><span class="o">=</span><span class="n">nsamples</span><span class="p">,</span>
+            <span class="n">testing_trend</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">testing_trend</span><span class="p">)</span>
+        <span class="n">samples</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">r_samples</span><span class="p">)</span>
+
+        <span class="k">return</span> <span class="n">samples</span></div>
+
+<div class="viewcode-block" id="ScalarGaSP.loo_validate"><a class="viewcode-back" href="../../../emulator/robustgasp.html#psimpy.emulator.robustgasp.ScalarGaSP.loo_validate">[docs]</a>    <span class="k">def</span> <span class="nf">loo_validate</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+        <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Validate trained scalar GP emulator using leave-one-out-cross-validation.</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        validation : numpy array</span>
+<span class="sd">            Shape :code:`(n, 2)`.</span>
+<span class="sd">            validation[:, 0] - leave one out fitted values,</span>
+<span class="sd">            validation[:, 1] - stand deviation of each prediction</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">emulator</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="k">raise</span> <span class="ne">RuntimeError</span><span class="p">(</span><span class="s2">&quot;Emulator has not been trained!&quot;</span><span class="p">)</span>
+
+        <span class="n">r_validation</span> <span class="o">=</span> <span class="n">RobustGaSP</span><span class="o">.</span><span class="n">leave_one_out_rgasp</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">emulator</span><span class="p">)</span>
+        <span class="n">validation</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">transpose</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">r_validation</span><span class="p">))</span>
+
+        <span class="k">return</span> <span class="n">validation</span></div></div>
+
+
+<div class="viewcode-block" id="PPGaSP"><a class="viewcode-back" href="../../../emulator/robustgasp.html#psimpy.emulator.robustgasp.PPGaSP">[docs]</a><span class="k">class</span> <span class="nc">PPGaSP</span><span class="p">(</span><span class="n">RobustGaSPBase</span><span class="p">):</span>
+
+<div class="viewcode-block" id="PPGaSP.train"><a class="viewcode-back" href="../../../emulator/robustgasp.html#psimpy.emulator.robustgasp.PPGaSP.train">[docs]</a>    <span class="nd">@beartype</span>
+    <span class="k">def</span> <span class="nf">train</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">design</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="n">response</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span>
+        <span class="n">trend</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
+        <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Train a parallel partial GP given training data.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        design : numpy array </span>
+<span class="sd">            Training input points. Shape :code:`(ntrain, ndim)`.</span>
+<span class="sd">            ``ntrain`` is the number of training points, ``ndim`` is the input</span>
+<span class="sd">            dimension. If :math:`ndim=1`, both :code:`(ndim, 1)` and</span>
+<span class="sd">            :code:`(ndim,)` :class:`numpy.ndarray` are valid.</span>
+<span class="sd">        response : numpy array</span>
+<span class="sd">            Training output points. Shape :code:`(ntrain, nresponse)`,</span>
+<span class="sd">            :math:`nresponse&gt;1`.</span>
+<span class="sd">        trend : numpy array, optional</span>
+<span class="sd">            Basis function matrix. Shape :code:`(ntrain, q)`.</span>
+<span class="sd">            If `None`, a :code:`(ntrain, 1)` matrix of ones is used.</span>
+<span class="sd">            If :math:`q=1`, both :code:`(ntrain, 1)` and :code:`(ntrain,)`</span>
+<span class="sd">            :class:`numpy.ndarray` are valid.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">_preprocess_design_response_trend</span><span class="p">(</span><span class="n">design</span><span class="p">,</span> <span class="n">response</span><span class="p">,</span> <span class="n">trend</span><span class="p">)</span>
+
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">response</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
+            <span class="k">raise</span> <span class="ne">RuntimeError</span><span class="p">(</span>
+                <span class="s2">&quot;PPGaSP should be used for models with vector output.&quot;</span>
+                <span class="s2">&quot; For scalar output model, please use ScalarGaSP.&quot;</span><span class="p">)</span>
+        
+        <span class="bp">self</span><span class="o">.</span><span class="n">emulator</span> <span class="o">=</span> <span class="n">RobustGaSP</span><span class="o">.</span><span class="n">ppgasp</span><span class="p">(</span>
+            <span class="n">design</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">design</span><span class="p">,</span>
+            <span class="n">response</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">response</span><span class="p">,</span>
+            <span class="n">trend</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">trend</span><span class="p">,</span>
+            <span class="n">zero_mean</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">zero_mean</span><span class="p">,</span>
+            <span class="n">nugget</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">nugget</span><span class="p">,</span>
+            <span class="n">nugget_est</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">nugget_est</span><span class="p">,</span>
+            <span class="n">range_par</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">range_par</span><span class="p">,</span>
+            <span class="n">method</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">method</span><span class="p">,</span>
+            <span class="n">prior_choice</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">prior_choice</span><span class="p">,</span>
+            <span class="n">a</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">a</span><span class="p">,</span>
+            <span class="n">b</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">_b</span><span class="p">,</span>
+            <span class="n">kernel_type</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">kernel_type</span><span class="p">,</span>
+            <span class="n">isotropic</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">isotropic</span><span class="p">,</span>
+            <span class="n">optimization</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">optimization</span><span class="p">,</span>
+            <span class="n">alpha</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">alpha</span><span class="p">,</span>
+            <span class="n">lower_bound</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">lower_bound</span><span class="p">,</span>
+            <span class="n">max_eval</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">max_eval</span><span class="p">,</span>
+            <span class="n">num_initial_values</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">num_initial_values</span><span class="p">)</span></div>
+
+<div class="viewcode-block" id="PPGaSP.predict"><a class="viewcode-back" href="../../../emulator/robustgasp.html#psimpy.emulator.robustgasp.PPGaSP.predict">[docs]</a>    <span class="nd">@beartype</span>
+    <span class="k">def</span> <span class="nf">predict</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">testing_input</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span>
+        <span class="n">testing_trend</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">:</span>
+        <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Make prediction using the trained parallel partial GP emulator.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        testing_input : numpy array</span>
+<span class="sd">            Input points at which to make prediction. Shape :code:`(ntest, ndim)`.</span>
+<span class="sd">            ``ntest`` is the number of input points and ``ndim`` is the input</span>
+<span class="sd">            dimension. If :math:`ndim=1`, both :code:`(ntest, 1)` and</span>
+<span class="sd">            :code:`(ntest,)` :class:`numpy.ndarray` are valid.</span>
+<span class="sd">        testing_trend : numpy array, optional</span>
+<span class="sd">            Basis function matrix corresponds to ``testing_input``.</span>
+<span class="sd">            Shape :code:`(ntest, q)`. By default :code:`(ntest, 1)` matrix of ones.</span>
+<span class="sd">            If :math:`q=1`, both :code:`(ntest, 1)` and :code:`(ntest,)`</span>
+<span class="sd">            :class:`numpy.ndarray` are valid.</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        predictions : numpy array</span>
+<span class="sd">            Emulator-prediction at ``testing_input``.</span>
+<span class="sd">            Shape :code:`(ntest, nresponse, 4)`.</span>
+<span class="sd">            `predictions[:, :, 0]` - mean,</span>
+<span class="sd">            `predictions[:, :, 1]` - low95,</span>
+<span class="sd">            `predictions[:, :, 2]` - upper95,</span>
+<span class="sd">            `predictions[:, :, 3]` - sd</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">emulator</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="k">raise</span> <span class="ne">RuntimeError</span><span class="p">(</span><span class="s2">&quot;Emulator has not been trained!&quot;</span><span class="p">)</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">_preprocess_testing_input_trend</span><span class="p">(</span><span class="n">testing_input</span><span class="p">,</span> <span class="n">testing_trend</span><span class="p">)</span>
+
+        <span class="n">r_predictions</span> <span class="o">=</span> <span class="n">RobustGaSP</span><span class="o">.</span><span class="n">predict_ppgasp</span><span class="p">(</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">emulator</span><span class="p">,</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">testing_input</span><span class="p">,</span>
+            <span class="n">testing_trend</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">testing_trend</span><span class="p">,</span>
+            <span class="n">interval_data</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
+            <span class="n">outasS3</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
+
+        <span class="n">ntest</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">testing_input</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
+        <span class="n">nresponse</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">response</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
+
+        <span class="n">predictions</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">ntest</span><span class="p">,</span> <span class="n">nresponse</span><span class="p">,</span> <span class="mi">4</span><span class="p">))</span>
+        <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">4</span><span class="p">):</span>
+            <span class="n">predictions</span><span class="p">[:,</span> <span class="p">:,</span> <span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">r_predictions</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
+
+        <span class="k">return</span> <span class="n">predictions</span></div>
+
+<div class="viewcode-block" id="PPGaSP.sample"><a class="viewcode-back" href="../../../emulator/robustgasp.html#psimpy.emulator.robustgasp.PPGaSP.sample">[docs]</a>    <span class="nd">@beartype</span>
+    <span class="k">def</span> <span class="nf">sample</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">testing_input</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="n">nsamples</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">1</span><span class="p">,</span>
+        <span class="n">testing_trend</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">:</span>
+        <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Draw samples using the trained parallel partial GaSP emulator.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        testing_input : numpy array</span>
+<span class="sd">            Input point at which to draw samples. Shape :code:`(ntest, ndim)`.</span>
+<span class="sd">            ``ntest`` is the number of input points and ``ndim`` is the input</span>
+<span class="sd">            dimension. If :math:`ndim=1`, both :code:`(ntest, 1)` and</span>
+<span class="sd">            :code:`(ntest,)` :class:`numpy.ndarray` are valid.</span>
+<span class="sd">        nsamples : int, optional</span>
+<span class="sd">            Number of samples to be drawn.</span>
+<span class="sd">        testing_trend : numpy array, optional</span>
+<span class="sd">            Basis function matrix corresponds to ``testing_input``.</span>
+<span class="sd">            Shape :code:`(ntest, q)`. By default :code:`(ntest, 1)` matrix of ones.</span>
+<span class="sd">            If :math:`q=1`, both :code:`(ntest, 1)` and :code:`(ntest,)`</span>
+<span class="sd">            :class:`numpy.ndarray` are valid.</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        samples : numpy array</span>
+<span class="sd">            Shape :code:`(ntest, nresponse, nsamples)`. </span>
+<span class="sd">            `samples[:, :, i]` corresponds to i-th realization of the trained</span>
+<span class="sd">            emulator at ``testing_input``, i=1, ..., ``nsamples``.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">emulator</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="k">raise</span> <span class="ne">RuntimeError</span><span class="p">(</span><span class="s2">&quot;Emulator has not been trained!&quot;</span><span class="p">)</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">_preprocess_testing_input_trend</span><span class="p">(</span><span class="n">testing_input</span><span class="p">,</span> <span class="n">testing_trend</span><span class="p">)</span>
+        
+        <span class="n">ntest</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">testing_input</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
+        <span class="n">nresponse</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">response</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
+        
+        <span class="c1"># extract trained parameters of ppgasp_emulator</span>
+        <span class="n">sigma2_hat</span> <span class="o">=</span> <span class="n">r_at</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">emulator</span><span class="p">,</span> <span class="s2">&quot;sigma2_hat&quot;</span><span class="p">)</span>
+        <span class="n">nugget</span> <span class="o">=</span> <span class="n">r_at</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">emulator</span><span class="p">,</span> <span class="s2">&quot;nugget&quot;</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
+        <span class="n">beta_hat</span> <span class="o">=</span> <span class="n">r_at</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">emulator</span><span class="p">,</span> <span class="s2">&quot;beta_hat&quot;</span><span class="p">)</span>
+        <span class="n">range_par</span> <span class="o">=</span> <span class="mi">1</span><span class="o">/</span><span class="n">beta_hat</span>
+        
+        <span class="c1"># set up a rgasp_emulator using trained parameters of ppgasp_emulator</span>
+        <span class="n">rgasp_emulator</span> <span class="o">=</span> <span class="n">RobustGaSP</span><span class="o">.</span><span class="n">rgasp</span><span class="p">(</span>
+            <span class="n">design</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">design</span><span class="p">,</span>
+            <span class="n">response</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">response</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span>
+            <span class="n">trend</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">trend</span><span class="p">,</span>
+            <span class="n">zero_mean</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">zero_mean</span><span class="p">,</span>
+            <span class="n">nugget</span><span class="o">=</span><span class="n">nugget</span><span class="p">,</span>
+            <span class="n">nugget_est</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span>
+            <span class="n">range_par</span><span class="o">=</span><span class="n">range_par</span><span class="p">,</span>
+            <span class="n">method</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">method</span><span class="p">,</span> 
+            <span class="n">prior_choice</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">prior_choice</span><span class="p">,</span>
+            <span class="n">a</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">a</span><span class="p">,</span>
+            <span class="n">b</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">_b</span><span class="p">,</span>
+            <span class="n">kernel_type</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">kernel_type</span><span class="p">,</span>
+            <span class="n">isotropic</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">isotropic</span><span class="p">,</span>
+            <span class="n">optimization</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">optimization</span><span class="p">,</span>
+            <span class="n">alpha</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">alpha</span><span class="p">,</span>
+            <span class="n">lower_bound</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">lower_bound</span><span class="p">,</span>
+            <span class="n">max_eval</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">max_eval</span><span class="p">,</span>
+            <span class="n">num_initial_values</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">num_initial_values</span><span class="p">)</span> 
+        
+        <span class="c1"># predictions and samples of y1 at testing_input using rgasp_emulator</span>
+        <span class="n">r_predictions_y1</span> <span class="o">=</span> <span class="n">RobustGaSP</span><span class="o">.</span><span class="n">predict_rgasp</span><span class="p">(</span>
+            <span class="n">rgasp_emulator</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">testing_input</span><span class="p">,</span> <span class="n">testing_trend</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">testing_trend</span><span class="p">)</span> 
+        <span class="n">predictions_y1</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">transpose</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">r_predictions_y1</span><span class="p">))</span>
+        <span class="n">predictions_mean_y1</span> <span class="o">=</span>  <span class="n">np</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">predictions_y1</span><span class="p">[:,</span><span class="mi">0</span><span class="p">],</span> <span class="p">(</span><span class="n">ntest</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span>
+        
+        <span class="n">r_samples_y1</span> <span class="o">=</span> <span class="n">RobustGaSP</span><span class="o">.</span><span class="n">Sample</span><span class="p">(</span>
+            <span class="n">rgasp_emulator</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">testing_input</span><span class="p">,</span> <span class="n">num_sample</span><span class="o">=</span><span class="n">nsamples</span><span class="p">,</span>
+            <span class="n">testing_trend</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">testing_trend</span><span class="p">)</span>
+        <span class="n">samples_y1</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">r_samples_y1</span><span class="p">)</span>
+
+        <span class="c1"># use predictions_mean and samples of y1 to calculate LW term</span>
+        <span class="n">LW_term</span> <span class="o">=</span> <span class="p">(</span><span class="n">samples_y1</span> <span class="o">-</span> <span class="n">predictions_mean_y1</span><span class="p">)</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">sigma2_hat</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
+        
+        <span class="c1"># predictions of y1,...,yk using ppgasp_emulator</span>
+        <span class="n">predictions</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">testing_input</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">testing_trend</span><span class="p">)</span>
+        <span class="n">predictions_mean</span> <span class="o">=</span> <span class="n">predictions</span><span class="p">[:,</span> <span class="p">:,</span> <span class="mi">0</span><span class="p">]</span>
+        
+        <span class="n">samples</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">ntest</span><span class="p">,</span> <span class="n">nresponse</span><span class="p">,</span> <span class="n">nsamples</span><span class="p">))</span>
+        <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">nresponse</span><span class="p">):</span>
+            <span class="n">samples</span><span class="p">[:,</span><span class="n">i</span><span class="p">,:]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">predictions_mean</span><span class="p">[:,</span> <span class="n">i</span><span class="p">],</span> <span class="p">(</span><span class="n">ntest</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span> <span class="o">+</span> \
+                             <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">sigma2_hat</span><span class="p">[</span><span class="n">i</span><span class="p">])</span> <span class="o">*</span> <span class="n">LW_term</span>
+            
+        <span class="k">return</span> <span class="n">samples</span></div></div>
+</pre></div>
+
+           </div>
+          </div>
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+
+  <hr/>
+
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+    <p>&#169; Copyright 2023, Hu Zhao.</p>
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diff --git a/docs/source/_build/html/_modules/psimpy/inference/active_learning.html b/docs/source/_build/html/_modules/psimpy/inference/active_learning.html
new file mode 100644
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@@ -0,0 +1,576 @@
+<!DOCTYPE html>
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+          <li class="breadcrumb-item"><a href="../../index.html">Module code</a></li>
+      <li class="breadcrumb-item active">psimpy.inference.active_learning</li>
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+             
+  <h1>Source code for psimpy.inference.active_learning</h1><div class="highlight"><pre>
+<span></span><span class="kn">import</span> <span class="nn">sys</span>
+<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">from</span> <span class="nn">scipy</span> <span class="kn">import</span> <span class="n">optimize</span>
+<span class="kn">from</span> <span class="nn">typing</span> <span class="kn">import</span> <span class="n">Union</span>
+<span class="kn">from</span> <span class="nn">beartype.typing</span> <span class="kn">import</span> <span class="n">Callable</span>
+<span class="kn">from</span> <span class="nn">beartype</span> <span class="kn">import</span> <span class="n">beartype</span>
+<span class="kn">from</span> <span class="nn">psimpy.simulator</span> <span class="kn">import</span> <span class="n">RunSimulator</span>
+<span class="kn">from</span> <span class="nn">psimpy.sampler</span> <span class="kn">import</span> <span class="n">LHS</span>
+<span class="kn">from</span> <span class="nn">psimpy.emulator</span> <span class="kn">import</span> <span class="n">ScalarGaSP</span>
+<span class="kn">from</span> <span class="nn">psimpy.utility</span> <span class="kn">import</span> <span class="n">check_bounds</span>
+
+<span class="n">_min_float</span> <span class="o">=</span> <span class="mi">10</span><span class="o">**</span><span class="p">(</span><span class="n">sys</span><span class="o">.</span><span class="n">float_info</span><span class="o">.</span><span class="n">min_10_exp</span><span class="p">)</span>
+
+<div class="viewcode-block" id="ActiveLearning"><a class="viewcode-back" href="../../../inference/active_learning.html#psimpy.inference.active_learning.ActiveLearning">[docs]</a><span class="k">class</span> <span class="nc">ActiveLearning</span><span class="p">:</span>
+
+    <span class="nd">@beartype</span>
+    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span>
+        <span class="bp">self</span><span class="p">,</span>
+        <span class="n">ndim</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span>
+        <span class="n">bounds</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span>
+        <span class="n">data</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span>
+        <span class="n">run_sim_obj</span><span class="p">:</span> <span class="n">RunSimulator</span><span class="p">,</span>
+        <span class="n">prior</span><span class="p">:</span> <span class="n">Callable</span><span class="p">,</span>
+        <span class="n">likelihood</span><span class="p">:</span> <span class="n">Callable</span><span class="p">,</span> 
+        <span class="n">lhs_sampler</span><span class="p">:</span> <span class="n">LHS</span><span class="p">,</span>
+        <span class="n">scalar_gasp</span><span class="p">:</span> <span class="n">ScalarGaSP</span><span class="p">,</span>
+        <span class="n">scalar_gasp_trend</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">str</span><span class="p">,</span> <span class="n">Callable</span><span class="p">[[</span><span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">],</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">]]</span> <span class="o">=</span> <span class="s1">&#39;constant&#39;</span><span class="p">,</span>
+        <span class="n">indicator</span><span class="p">:</span> <span class="nb">str</span> <span class="o">=</span> <span class="s1">&#39;entropy&#39;</span><span class="p">,</span>
+        <span class="n">optimizer</span><span class="p">:</span> <span class="n">Callable</span> <span class="o">=</span> <span class="n">optimize</span><span class="o">.</span><span class="n">brute</span><span class="p">,</span>
+        <span class="n">args_prior</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">list</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
+        <span class="n">kwgs_prior</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">dict</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
+        <span class="n">args_likelihood</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">list</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
+        <span class="n">kwgs_likelihood</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">dict</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
+        <span class="n">args_optimizer</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">list</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
+        <span class="n">kwgs_optimizer</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">dict</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
+        <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Contruct a scalar GP emulator for natural logarithm  of the product of</span>
+<span class="sd">        prior and likelihood (i.e. unnormalized posterior), via active learning. </span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        ndim : int</span>
+<span class="sd">            Dimension of parameter ``x``.</span>
+<span class="sd">        bounds : numpy array</span>
+<span class="sd">            Upper and lower boundaries of each parameter. Shape :code:`(ndim, 2)`.</span>
+<span class="sd">            `bounds[:, 0]` corresponds to lower boundaries of each parameter and</span>
+<span class="sd">            `bounds[:, 1]` to upper boundaries of each parameter. </span>
+<span class="sd">        data : numpy array</span>
+<span class="sd">            Observed data for parameter calibration.</span>
+<span class="sd">        run_sim_obj : instance of class :class:`.RunSimulator`</span>
+<span class="sd">            It has an attribute :py:attr:`simulator` and two methods to run </span>
+<span class="sd">            :py:attr:`simulator`, namely :meth:`.serial_run` and</span>
+<span class="sd">            :meth:`.parallel_run`. For each simulation, :py:attr:`simulator`</span>
+<span class="sd">            must return outputs ``y`` as a numpy array.</span>
+<span class="sd">        prior : Callable</span>
+<span class="sd">            Prior probability density function.</span>
+<span class="sd">            Call with :code:`prior(x, *args_prior, **kwgs_prior)` and return</span>
+<span class="sd">            the value of prior probability density at ``x``.</span>
+<span class="sd">        likelihood : Callable</span>
+<span class="sd">            Likelihood function constructed based on ``data`` and simulation</span>
+<span class="sd">            outputs ``y`` evaluated at ``x``. Call with</span>
+<span class="sd">            :code:`likelihood(y, data, *args_likelihood, **kwgs_likelihood)`</span>
+<span class="sd">            and return the likelihood value at ``x``.</span>
+<span class="sd">        lhs_sampler : instance of class :class:`.LHS`</span>
+<span class="sd">            Latin hypercube sampler used to draw initial samples of ``x``.</span>
+<span class="sd">            These initial samples are used to run initial simulations and build</span>
+<span class="sd">            initial emulator.</span>
+<span class="sd">        scalar_gasp : instance of class :class:`.ScalarGaSP`</span>
+<span class="sd">            An object which sets up the emulator structure. Providing training</span>
+<span class="sd">            data, the emulator can be trained and used to make predictions. </span>
+<span class="sd">        scalar_gasp_trend : str or Callable, optional</span>
+<span class="sd">            Mean function of ``scalar_gasp`` emulator, which is used to</span>
+<span class="sd">            determine the ``trend`` or ``testing_trend`` at given ``design`` or</span>
+<span class="sd">            ``testing_input``.</span>
+<span class="sd">            `&#39;zero&#39;` - trend is set to zero.</span>
+<span class="sd">            `&#39;constant&#39;` - trend is set to a constant.</span>
+<span class="sd">            `&#39;linear&#39;` - trend is linear to design or testing_input.</span>
+<span class="sd">            Callable - a function takes design or testing_input as parameter</span>
+<span class="sd">            and returns the trend.</span>
+<span class="sd">            Default is `&#39;constant&#39;`.</span>
+<span class="sd">        indicator : str, optional</span>
+<span class="sd">            Indicator of uncertainty. `&#39;entropy&#39;` or `&#39;variance&#39;`. Default is</span>
+<span class="sd">            `&#39;entropy&#39;`.</span>
+<span class="sd">        optimizer : Callable, optional</span>
+<span class="sd">            A function which finds the input point ``x`` that minimizes the</span>
+<span class="sd">            uncertainty ``indicator`` at each iteration step.</span>
+<span class="sd">            Call with :code:`optimizer(func, *args_optimizer, **kwgs_optimizer)`. </span>
+<span class="sd">            The objective function ``func`` is defined by the class method</span>
+<span class="sd">            :meth:`_uncertainty_indicator` which have only one argument ``x``.</span>
+<span class="sd">            The ``optimizer`` should return either the solution array, or a</span>
+<span class="sd">            :class:`scipy.optimize.OptimizeResult` object which has the attribute</span>
+<span class="sd">            :py:attr:`x` denoting the solution array.</span>
+<span class="sd">            By default is set to :py:func:`scipy.optimize.brute`.</span>
+<span class="sd">        args_prior : list, optional</span>
+<span class="sd">            Positional arguments for ``prior``.</span>
+<span class="sd">        kwgs_prior: dict, optional</span>
+<span class="sd">            Keyword arguments for ``prior``.</span>
+<span class="sd">        args_likelihood : list, optional</span>
+<span class="sd">            Positional arguments for ``likelihood``.</span>
+<span class="sd">        kwgs_likelihood : dict, optional</span>
+<span class="sd">            Keyword arguments for ``likelihood``.</span>
+<span class="sd">        args_optimizer : list, optional</span>
+<span class="sd">            Positional arguments for ``optimizer``.</span>
+<span class="sd">        kwgs_optimizer : dict, optional</span>
+<span class="sd">            Keyword arguments for ``optimizer``.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="n">ndim</span> <span class="o">!=</span> <span class="nb">len</span><span class="p">(</span><span class="n">run_sim_obj</span><span class="o">.</span><span class="n">var_inp_parameter</span><span class="p">):</span>
+            <span class="k">raise</span> <span class="ne">RuntimeError</span><span class="p">(</span><span class="s2">&quot;ndim and run_sim_obj are incompatible&quot;</span><span class="p">)</span>
+        <span class="k">if</span> <span class="n">ndim</span> <span class="o">!=</span> <span class="n">lhs_sampler</span><span class="o">.</span><span class="n">ndim</span><span class="p">:</span>
+            <span class="k">raise</span> <span class="ne">RuntimeError</span><span class="p">(</span><span class="s2">&quot;ndim and lhs_sampler are incompatible&quot;</span><span class="p">)</span>
+        <span class="k">if</span> <span class="n">ndim</span> <span class="o">!=</span> <span class="n">scalar_gasp</span><span class="o">.</span><span class="n">ndim</span><span class="p">:</span>
+            <span class="k">raise</span> <span class="ne">RuntimeError</span><span class="p">(</span><span class="s2">&quot;ndim and scalar_gasp are incompatible&quot;</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">ndim</span> <span class="o">=</span> <span class="n">ndim</span>
+
+        <span class="n">check_bounds</span><span class="p">(</span><span class="n">ndim</span><span class="p">,</span> <span class="n">bounds</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">bounds</span> <span class="o">=</span> <span class="n">bounds</span>           
+        
+        <span class="bp">self</span><span class="o">.</span><span class="n">data</span> <span class="o">=</span> <span class="n">data</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">run_sim_obj</span> <span class="o">=</span> <span class="n">run_sim_obj</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">prior</span> <span class="o">=</span> <span class="n">prior</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">likelihood</span> <span class="o">=</span> <span class="n">likelihood</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">lhs_sampler</span> <span class="o">=</span> <span class="n">lhs_sampler</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">lhs_sampler</span><span class="o">.</span><span class="n">bounds</span> <span class="o">=</span> <span class="n">bounds</span>
+        
+        <span class="bp">self</span><span class="o">.</span><span class="n">scalar_gasp</span> <span class="o">=</span> <span class="n">scalar_gasp</span>
+
+        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">scalar_gasp_trend</span><span class="p">,</span> <span class="nb">str</span><span class="p">):</span>
+            <span class="k">if</span> <span class="n">scalar_gasp_trend</span> <span class="ow">not</span> <span class="ow">in</span> <span class="p">[</span><span class="s2">&quot;zero&quot;</span><span class="p">,</span><span class="s2">&quot;constant&quot;</span><span class="p">,</span><span class="s2">&quot;linear&quot;</span><span class="p">]:</span>
+                <span class="k">raise</span> <span class="ne">NotImplementedError</span><span class="p">(</span>
+                    <span class="sa">f</span><span class="s2">&quot;unsupported scalar_gasp_trend </span><span class="si">{</span><span class="n">scalar_gasp_trend</span><span class="si">}</span><span class="s2">&quot;</span>
+                    <span class="sa">f</span><span class="s2">&quot; please choose from &#39;zero&#39;, &#39;constant&#39;, and &#39;linear&#39;&quot;</span>
+                    <span class="sa">f</span><span class="s2">&quot; or pass it as a function&quot;</span><span class="p">)</span>            
+        <span class="bp">self</span><span class="o">.</span><span class="n">scalar_gasp_trend</span> <span class="o">=</span> <span class="n">scalar_gasp_trend</span>
+        
+        <span class="k">if</span> <span class="n">indicator</span> <span class="ow">not</span> <span class="ow">in</span> <span class="p">[</span><span class="s2">&quot;entropy&quot;</span><span class="p">,</span> <span class="s2">&quot;variance&quot;</span><span class="p">]:</span>
+            <span class="k">raise</span> <span class="ne">NotImplementedError</span><span class="p">(</span>
+                <span class="sa">f</span><span class="s2">&quot;unsupported indicator </span><span class="si">{</span><span class="n">indicator</span><span class="si">}</span><span class="s2">. Please choose from&quot;</span>
+                <span class="sa">f</span><span class="s2">&quot; &#39;entropy&#39; and &#39;variance&#39;&quot;</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">indicator</span> <span class="o">=</span> <span class="n">indicator</span>
+    
+        <span class="k">if</span> <span class="n">optimizer</span> <span class="ow">is</span> <span class="n">optimize</span><span class="o">.</span><span class="n">brute</span><span class="p">:</span>
+            <span class="n">ranges</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="nb">tuple</span><span class="p">(</span><span class="n">bounds</span><span class="p">[</span><span class="n">i</span><span class="p">])</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">ndim</span><span class="p">))</span>
+            <span class="n">args_optimizer</span> <span class="o">=</span> <span class="p">[</span><span class="n">ranges</span><span class="p">]</span>
+            <span class="k">if</span> <span class="n">kwgs_optimizer</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+                <span class="n">allowed_keys</span> <span class="o">=</span> <span class="p">{</span><span class="s2">&quot;Ns&quot;</span><span class="p">,</span> <span class="s2">&quot;workers&quot;</span><span class="p">}</span>
+                <span class="k">if</span> <span class="ow">not</span> <span class="nb">set</span><span class="p">(</span><span class="n">kwgs_optimizer</span><span class="o">.</span><span class="n">keys</span><span class="p">())</span><span class="o">.</span><span class="n">issubset</span><span class="p">(</span><span class="n">allowed_keys</span><span class="p">):</span>
+                    <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span>
+                        <span class="s2">&quot;allowed keys are &#39;Ns&#39; and &#39;workers&#39; for&quot;</span>
+                        <span class="s2">&quot; optimize.brute&quot;</span><span class="p">)</span>
+            <span class="k">else</span><span class="p">:</span>
+                <span class="n">kwgs_optimizer</span> <span class="o">=</span> <span class="p">{</span><span class="s2">&quot;Ns&quot;</span><span class="p">:</span> <span class="mi">50</span><span class="p">}</span>
+            <span class="n">kwgs_optimizer</span><span class="o">.</span><span class="n">update</span><span class="p">({</span><span class="s2">&quot;finish&quot;</span><span class="p">:</span> <span class="kc">None</span><span class="p">})</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">optimizer</span> <span class="o">=</span> <span class="n">optimizer</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">args_prior</span> <span class="o">=</span> <span class="p">()</span> <span class="k">if</span> <span class="n">args_prior</span> <span class="ow">is</span> <span class="kc">None</span> <span class="k">else</span> <span class="n">args_prior</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">kwgs_prior</span> <span class="o">=</span> <span class="p">{}</span> <span class="k">if</span> <span class="n">kwgs_prior</span> <span class="ow">is</span> <span class="kc">None</span> <span class="k">else</span> <span class="n">kwgs_prior</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">args_likelihood</span> <span class="o">=</span> <span class="p">()</span> <span class="k">if</span> <span class="n">args_likelihood</span> <span class="ow">is</span> <span class="kc">None</span> <span class="k">else</span> <span class="n">args_likelihood</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">kwgs_likelihood</span> <span class="o">=</span> <span class="p">{}</span> <span class="k">if</span> <span class="n">kwgs_likelihood</span> <span class="ow">is</span> <span class="kc">None</span> <span class="k">else</span> <span class="n">kwgs_likelihood</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">args_optimizer</span><span class="o">=</span><span class="p">()</span> <span class="k">if</span> <span class="n">args_optimizer</span> <span class="ow">is</span> <span class="kc">None</span> <span class="k">else</span> <span class="n">args_optimizer</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">kwgs_optimizer</span><span class="o">=</span><span class="p">{}</span> <span class="k">if</span> <span class="n">kwgs_optimizer</span> <span class="ow">is</span> <span class="kc">None</span> <span class="k">else</span> <span class="n">kwgs_optimizer</span>
+
+
+<div class="viewcode-block" id="ActiveLearning.initial_simulation"><a class="viewcode-back" href="../../../inference/active_learning.html#psimpy.inference.active_learning.ActiveLearning.initial_simulation">[docs]</a>    <span class="nd">@beartype</span>
+    <span class="k">def</span> <span class="nf">initial_simulation</span><span class="p">(</span>
+        <span class="bp">self</span><span class="p">,</span>
+        <span class="n">n0</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span>
+        <span class="n">prefixes</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="nb">str</span><span class="p">],</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
+        <span class="n">mode</span><span class="p">:</span> <span class="nb">str</span> <span class="o">=</span> <span class="s1">&#39;serial&#39;</span><span class="p">,</span>
+        <span class="n">max_workers</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">int</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">tuple</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">]:</span>
+        <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Run ``n0`` initial simulations.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        n0 : int</span>
+<span class="sd">            Number of initial simulation runs.</span>
+<span class="sd">        prefixes : list of str, optional</span>
+<span class="sd">            Consist of ``n0`` strings. Each is used to name corresponding</span>
+<span class="sd">            simulation output file(s).</span>
+<span class="sd">            If `None`, `&#39;sim0&#39;`, `&#39;sim1&#39;`, ... are used.   </span>
+<span class="sd">        mode : str, optional</span>
+<span class="sd">            `&#39;parallel&#39;` or `&#39;serial&#39;`. Run `n0` simulations in parallel or</span>
+<span class="sd">            in serial.</span>
+<span class="sd">        max_workers : int, optional</span>
+<span class="sd">            Controls the maximum number of tasks running in parallel.</span>
+<span class="sd">            Default is the number of CPUs on the host.</span>
+<span class="sd">        </span>
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        init_var_samples: numpy array</span>
+<span class="sd">            Variable input samples for ``n0`` initial simulations.</span>
+<span class="sd">            Shape of :code:`(n0, ndim)`.</span>
+<span class="sd">        init_sim_outputs : numpy array</span>
+<span class="sd">            Outputs of ``n0`` intial simulations.</span>
+<span class="sd">            :code:`init_sim_outputs.shape[0]` is ``n0``.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">init_var_samples</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">lhs_sampler</span><span class="o">.</span><span class="n">sample</span><span class="p">(</span><span class="n">n0</span><span class="p">)</span>
+
+        <span class="k">if</span> <span class="n">mode</span> <span class="o">==</span> <span class="s1">&#39;parallel&#39;</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">run_sim_obj</span><span class="o">.</span><span class="n">parallel_run</span><span class="p">(</span><span class="n">init_var_samples</span><span class="p">,</span> <span class="n">prefixes</span><span class="p">,</span>
+                <span class="n">append</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">max_workers</span><span class="o">=</span><span class="n">max_workers</span><span class="p">)</span>
+        <span class="k">elif</span> <span class="n">mode</span> <span class="o">==</span> <span class="s1">&#39;serial&#39;</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">run_sim_obj</span><span class="o">.</span><span class="n">serial_run</span><span class="p">(</span><span class="n">init_var_samples</span><span class="p">,</span> <span class="n">prefixes</span><span class="p">,</span>
+                <span class="n">append</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;mode must be &#39;parallel&#39; or &#39;serial&#39;&quot;</span><span class="p">)</span>
+        
+        <span class="n">init_sim_outputs</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">run_sim_obj</span><span class="o">.</span><span class="n">outputs</span><span class="p">)</span>
+
+        <span class="k">return</span> <span class="n">init_var_samples</span><span class="p">,</span> <span class="n">init_sim_outputs</span></div>
+    
+<div class="viewcode-block" id="ActiveLearning.iterative_emulation"><a class="viewcode-back" href="../../../inference/active_learning.html#psimpy.inference.active_learning.ActiveLearning.iterative_emulation">[docs]</a>    <span class="nd">@beartype</span>
+    <span class="k">def</span> <span class="nf">iterative_emulation</span><span class="p">(</span>
+        <span class="bp">self</span><span class="p">,</span>
+        <span class="n">ninit</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span>
+        <span class="n">init_var_samples</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span>
+        <span class="n">init_sim_outputs</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span>
+        <span class="n">niter</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span>
+        <span class="n">iter_prefixes</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="nb">str</span><span class="p">],</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span>
+        <span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">tuple</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">]:</span>
+        <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Sequentially pick ``niter`` new input points based on ``ninit``</span>
+<span class="sd">        simulations.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        niter : int</span>
+<span class="sd">            Number of interative simulaitons.</span>
+<span class="sd">        ninit : int</span>
+<span class="sd">            Number of initial simulations.</span>
+<span class="sd">        init_var_samples: numpy array</span>
+<span class="sd">            Variable input samples for ``ninit`` simulations.</span>
+<span class="sd">            Shape of :code:`(ninit, ndim)`.</span>
+<span class="sd">        init_sim_outputs : numpy array</span>
+<span class="sd">            Outputs of ``ninit`` simulations.</span>
+<span class="sd">            :code:`init_sim_outputs.shape[0]` is ``ninit``. </span>
+<span class="sd">        iter_prefixes : list of str, optional</span>
+<span class="sd">            Consist of ``niter`` strings. Each is used to name</span>
+<span class="sd">            corresponding iterative simulation output file(s).</span>
+<span class="sd">            If `None`, `&#39;iter_sim0&#39;`, `&#39;iter_sim1&#39;`, ... are used.</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        var_samples : numpy array</span>
+<span class="sd">            Variable input samples of ``ninit`` simulations and ``niter``</span>
+<span class="sd">            iterative simulations. Shape of :code:`(ninit+niter, ndim)`.</span>
+<span class="sd">        sim_outputs : numpy array</span>
+<span class="sd">            Outputs of ``ninit`` and ``niter`` simulations. </span>
+<span class="sd">            :code:`sim_outputs.shape[0]` is :math:`ninit+niter`.</span>
+<span class="sd">        ln_pxl_values : numpy array</span>
+<span class="sd">            Natural logarithm values of the product of prior and likelihood </span>
+<span class="sd">            at ``ninit`` and ``niter`` simulations. </span>
+<span class="sd">            Shape of :code:`(ninit+niter,)`.</span>
+<span class="sd">        </span>
+<span class="sd">        Notes</span>
+<span class="sd">        -----</span>
+<span class="sd">        If a duplicated iteration point is returned by the ``optimizer``, the</span>
+<span class="sd">        iteration will be stopped right away. In that case, the first dimension</span>
+<span class="sd">        of returned ``var_samples``, ``sim_outputs``, ``ln_pxl_values`` is smaller</span>
+<span class="sd">        than :math:`ninit+niter`.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="n">init_var_samples</span><span class="o">.</span><span class="n">shape</span> <span class="o">!=</span> <span class="p">(</span><span class="n">ninit</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">ndim</span><span class="p">):</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;init_var_samples must be of shape (ninit, ndim)&quot;</span><span class="p">)</span>
+        
+        <span class="k">if</span> <span class="n">init_sim_outputs</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">!=</span> <span class="n">ninit</span><span class="p">:</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span>
+                <span class="s2">&quot;init_sim_outputs.shape[0] must equal to ninit&quot;</span><span class="p">)</span>
+        
+        <span class="k">if</span> <span class="n">iter_prefixes</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="n">iter_prefixes</span> <span class="o">=</span> <span class="p">[</span><span class="sa">f</span><span class="s1">&#39;iter_sim</span><span class="si">{</span><span class="n">i</span><span class="si">}</span><span class="s1">&#39;</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">niter</span><span class="p">)]</span>
+        <span class="k">elif</span> <span class="nb">len</span><span class="p">(</span><span class="n">iter_prefixes</span><span class="p">)</span> <span class="o">!=</span> <span class="n">niter</span><span class="p">:</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;iter_prefixes must have niter number of items&quot;</span><span class="p">)</span>
+        <span class="k">elif</span> <span class="nb">len</span><span class="p">(</span><span class="nb">set</span><span class="p">(</span><span class="n">iter_prefixes</span><span class="p">))</span> <span class="o">!=</span> <span class="n">niter</span><span class="p">:</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;Each item of iter_prefixes must be unique&quot;</span><span class="p">)</span>
+        
+        <span class="n">ln_pxl_values</span> <span class="o">=</span> <span class="p">[</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">_compute_ln_pxl</span><span class="p">(</span><span class="n">init_var_samples</span><span class="p">[</span><span class="n">i</span><span class="p">,:],</span> <span class="n">init_sim_outputs</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
+            <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">ninit</span><span class="p">)</span>
+            <span class="p">]</span>
+        <span class="n">var_samples</span> <span class="o">=</span> <span class="n">init_var_samples</span>
+        <span class="n">sim_outputs</span> <span class="o">=</span> <span class="n">init_sim_outputs</span>
+        
+        <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">niter</span><span class="p">):</span>
+            
+            <span class="bp">self</span><span class="o">.</span><span class="n">_emulate_ln_pxl</span><span class="p">(</span><span class="n">var_samples</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">ln_pxl_values</span><span class="p">))</span>
+
+            <span class="n">opt_res</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">optimizer</span><span class="p">(</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">_uncertainty_indicator</span><span class="p">,</span>
+                <span class="o">*</span><span class="bp">self</span><span class="o">.</span><span class="n">args_optimizer</span><span class="p">,</span>
+                <span class="o">**</span><span class="bp">self</span><span class="o">.</span><span class="n">kwgs_optimizer</span><span class="p">)</span>
+            <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">opt_res</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">):</span>
+                <span class="n">next_var_sample</span> <span class="o">=</span> <span class="n">opt_res</span>
+            <span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">opt_res</span><span class="p">,</span> <span class="n">optimize</span><span class="o">.</span><span class="n">OptimizeResult</span><span class="p">):</span>
+                <span class="n">next_var_sample</span> <span class="o">=</span> <span class="n">opt_res</span><span class="o">.</span><span class="n">x</span>
+            <span class="k">else</span><span class="p">:</span>
+                <span class="k">raise</span> <span class="ne">RuntimeError</span><span class="p">(</span>
+                    <span class="s2">&quot;Optimizer must return a 1d numpy array representing the&quot;</span>
+                    <span class="s2">&quot; solution or a OptimizeResult object having x attribute&quot;</span><span class="p">)</span>
+            
+            <span class="n">next_var_sample</span> <span class="o">=</span> <span class="n">next_var_sample</span><span class="o">.</span><span class="n">reshape</span><span class="p">((</span><span class="mi">1</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">ndim</span><span class="p">))</span>
+            <span class="n">temp_var_samples</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">vstack</span><span class="p">((</span><span class="n">var_samples</span><span class="p">,</span> <span class="n">next_var_sample</span><span class="p">))</span>
+
+            <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">unique</span><span class="p">(</span><span class="n">temp_var_samples</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">))</span> <span class="o">!=</span> <span class="nb">len</span><span class="p">(</span><span class="n">var_samples</span><span class="p">)</span> <span class="o">+</span> <span class="mi">1</span><span class="p">:</span>
+                <span class="nb">print</span><span class="p">(</span>
+                    <span class="s2">&quot;Optimizer finds duplicated next_var_sample at&quot;</span>
+                    <span class="s2">&quot; iteration </span><span class="si">{i}</span><span class="s2">. The active learning process will&quot;</span>
+                    <span class="s2">&quot; be terminated.&quot;</span><span class="p">)</span>
+                <span class="k">break</span>
+
+            <span class="n">var_samples</span> <span class="o">=</span> <span class="n">temp_var_samples</span>
+
+            <span class="bp">self</span><span class="o">.</span><span class="n">run_sim_obj</span><span class="o">.</span><span class="n">serial_run</span><span class="p">(</span><span class="n">next_var_sample</span><span class="p">,</span> <span class="p">[</span><span class="n">iter_prefixes</span><span class="p">[</span><span class="n">i</span><span class="p">]],</span>
+                <span class="n">append</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span>
+            <span class="n">next_sim_output</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">run_sim_obj</span><span class="o">.</span><span class="n">outputs</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
+            <span class="n">sim_outputs</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">vstack</span><span class="p">((</span><span class="n">sim_outputs</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">next_sim_output</span><span class="p">])))</span>
+
+            <span class="n">next_ln_pxl_value</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_compute_ln_pxl</span><span class="p">(</span>
+                <span class="n">next_var_sample</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">),</span> <span class="n">next_sim_output</span><span class="p">)</span>
+            <span class="n">ln_pxl_values</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">next_ln_pxl_value</span><span class="p">)</span>
+        
+        <span class="c1"># train final scalar gasp</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">_emulate_ln_pxl</span><span class="p">(</span><span class="n">var_samples</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">ln_pxl_values</span><span class="p">))</span>
+        
+        <span class="n">ln_pxl_values</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">ln_pxl_values</span><span class="p">)</span>
+        
+        <span class="k">return</span> <span class="n">var_samples</span><span class="p">,</span> <span class="n">sim_outputs</span><span class="p">,</span> <span class="n">ln_pxl_values</span></div>
+
+<div class="viewcode-block" id="ActiveLearning.approx_ln_pxl"><a class="viewcode-back" href="../../../inference/active_learning.html#psimpy.inference.active_learning.ActiveLearning.approx_ln_pxl">[docs]</a>    <span class="nd">@beartype</span>
+    <span class="k">def</span> <span class="nf">approx_ln_pxl</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">float</span><span class="p">:</span>
+        <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Approximate `ln_pxl` value at ``x`` based on the trained emulator.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        x : numpy array</span>
+<span class="sd">            One variable sample at which `ln_pxl` is to be approximated. Shape of</span>
+<span class="sd">            :code:`(ndim,)`.</span>
+<span class="sd">        </span>
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        A float value which is the emulator-predicted `ln_pxl` value at ``x``.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">predict</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_predict_ln_pxl</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
+
+        <span class="k">return</span> <span class="nb">float</span><span class="p">(</span><span class="n">predict</span><span class="p">[:,</span><span class="mi">0</span><span class="p">])</span></div>
+
+    
+    <span class="k">def</span> <span class="nf">_compute_ln_pxl</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="n">y</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">float</span><span class="p">:</span>
+        <span class="sd">&quot;&quot;&quot;Compute natural logarithm of the product of prior and likelihood.</span>
+<span class="sd">        </span>
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        x : numpy array</span>
+<span class="sd">            Variable input of :py:func:`simulator`. Shape of :code:`(ndim,)`.</span>
+<span class="sd">        y : numpy array</span>
+<span class="sd">            Simulation outputs at ``x``.</span>
+<span class="sd">        </span>
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        ln_pxl_val : float</span>
+<span class="sd">            Natural logarithm of the product of prior and likelihood at ``x``.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">prior_val</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">prior</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="o">*</span><span class="bp">self</span><span class="o">.</span><span class="n">args_prior</span><span class="p">,</span> <span class="o">**</span><span class="bp">self</span><span class="o">.</span><span class="n">kwgs_prior</span><span class="p">)</span>
+        <span class="n">likelihood_val</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">likelihood</span><span class="p">(</span><span class="n">y</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">data</span><span class="p">,</span> <span class="o">*</span><span class="bp">self</span><span class="o">.</span><span class="n">args_likelihood</span><span class="p">,</span>
+            <span class="o">**</span><span class="bp">self</span><span class="o">.</span><span class="n">kwgs_likelihood</span><span class="p">)</span>
+        <span class="n">pxl_val</span> <span class="o">=</span> <span class="n">prior_val</span> <span class="o">*</span> <span class="n">likelihood_val</span>
+        
+        <span class="k">return</span> <span class="nb">float</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">maximum</span><span class="p">(</span><span class="n">pxl_val</span><span class="p">,</span> <span class="n">_min_float</span><span class="p">)))</span>
+
+    
+    <span class="k">def</span> <span class="nf">_emulate_ln_pxl</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">var_samples</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="n">ln_pxl_values</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span>
+        <span class="p">)</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
+        <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Train scalar gasp emulator for natural lograthim of the product of prior</span>
+<span class="sd">        and likelihood based on ``n`` simulations.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        var_samples: numpy array</span>
+<span class="sd">            Variable inputs samples for ``n`` simulations. Shape of</span>
+<span class="sd">            :code:`(n, ndim)`.</span>
+<span class="sd">        ln_pxl_values : numpy array</span>
+<span class="sd">            Natural lograthim values of the product of prior and likelhood</span>
+<span class="sd">            corresponding to ``n`` simulations. Shape of :code:`(n,)`.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">var_samples</span><span class="p">)</span> 
+
+        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">scalar_gasp_trend</span><span class="p">,</span> <span class="nb">str</span><span class="p">):</span>
+            <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">scalar_gasp_trend</span> <span class="o">==</span> <span class="s2">&quot;zero&quot;</span><span class="p">:</span>
+                <span class="n">trend</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">n</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span>
+            <span class="k">elif</span> <span class="bp">self</span><span class="o">.</span><span class="n">scalar_gasp_trend</span> <span class="o">==</span> <span class="s2">&quot;constant&quot;</span><span class="p">:</span>
+                <span class="n">trend</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">((</span><span class="n">n</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span>
+            <span class="k">elif</span> <span class="bp">self</span><span class="o">.</span><span class="n">scalar_gasp_trend</span> <span class="o">==</span> <span class="s2">&quot;linear&quot;</span><span class="p">:</span>
+                <span class="n">trend</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">c_</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="n">n</span><span class="p">),</span> <span class="n">var_samples</span><span class="p">]</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="n">trend</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">scalar_gasp_trend</span><span class="p">(</span><span class="n">var_samples</span><span class="p">)</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">scalar_gasp</span><span class="o">.</span><span class="n">train</span><span class="p">(</span><span class="n">var_samples</span><span class="p">,</span> <span class="n">ln_pxl_values</span><span class="p">,</span> <span class="n">trend</span><span class="p">)</span>
+    
+    <span class="k">def</span> <span class="nf">_predict_ln_pxl</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">:</span>
+        <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Make prediction of `ln_pxl` at ``x`` using the emulator.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        x : numpy array</span>
+<span class="sd">            One variable input point. Shape of :code:`(ndim,)`.</span>
+<span class="sd">        </span>
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        predict : numpy array</span>
+<span class="sd">            Emulator-prediction at ``x``. Shape :code:`(1, 4)`.</span>
+<span class="sd">            `predict[0, 0]` - mean,</span>
+<span class="sd">            `predict[0, 1]` - low95,</span>
+<span class="sd">            `predict[0, 2]` - upper95,</span>
+<span class="sd">            `predict[0, 3]` - sd.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">x</span> <span class="o">=</span> <span class="n">x</span><span class="o">.</span><span class="n">reshape</span><span class="p">((</span><span class="mi">1</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">ndim</span><span class="p">))</span>
+
+        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">scalar_gasp_trend</span><span class="p">,</span> <span class="nb">str</span><span class="p">):</span> 
+            <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">scalar_gasp_trend</span> <span class="o">==</span> <span class="s2">&quot;zero&quot;</span><span class="p">:</span>
+                <span class="n">trend</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span>
+            <span class="k">elif</span> <span class="bp">self</span><span class="o">.</span><span class="n">scalar_gasp_trend</span> <span class="o">==</span> <span class="s2">&quot;constant&quot;</span><span class="p">:</span>
+                <span class="n">trend</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">((</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span>
+            <span class="k">elif</span> <span class="bp">self</span><span class="o">.</span><span class="n">scalar_gasp_trend</span> <span class="o">==</span> <span class="s2">&quot;linear&quot;</span><span class="p">:</span>
+                <span class="n">trend</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">c_</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="mi">1</span><span class="p">),</span> <span class="n">x</span><span class="p">]</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="n">trend</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">scalar_gasp_trend</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
+        
+        <span class="n">predict</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">scalar_gasp</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">trend</span><span class="p">)</span>
+
+        <span class="k">return</span> <span class="n">predict</span>
+
+    <span class="k">def</span> <span class="nf">_uncertainty_indicator</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">float</span><span class="p">:</span>
+        <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Indicator of uncertainty.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        x : numpy array</span>
+<span class="sd">            One variable input point. Shape of :code:`(ndim,)`.</span>
+<span class="sd">        </span>
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        neg_val : float</span>
+<span class="sd">            Negative value of uncertainty indicator at ``x``.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">predict</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_predict_ln_pxl</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
+        
+        <span class="n">mean</span> <span class="o">=</span> <span class="n">predict</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">]</span>
+        <span class="n">std</span> <span class="o">=</span> <span class="n">predict</span><span class="p">[:,</span> <span class="mi">3</span><span class="p">]</span>
+
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">indicator</span> <span class="o">==</span> <span class="s2">&quot;entropy&quot;</span><span class="p">:</span>
+            <span class="n">neg_val</span> <span class="o">=</span> <span class="o">-</span><span class="n">mean</span> <span class="o">-</span> <span class="mf">0.5</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">log</span><span class="p">(</span>
+                <span class="n">np</span><span class="o">.</span><span class="n">maximum</span><span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">e</span><span class="o">*</span><span class="n">std</span><span class="o">**</span><span class="mi">2</span><span class="p">,</span> <span class="n">_min_float</span><span class="p">)</span>
+                <span class="p">)</span>
+        <span class="k">elif</span> <span class="bp">self</span><span class="o">.</span><span class="n">indicator</span> <span class="o">==</span> <span class="s2">&quot;variance&quot;</span><span class="p">:</span>
+            <span class="n">neg_val</span> <span class="o">=</span> <span class="o">-</span><span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="n">mean</span> <span class="o">+</span> <span class="mi">2</span><span class="o">*</span><span class="n">std</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">log</span><span class="p">(</span>
+                <span class="n">np</span><span class="o">.</span><span class="n">maximum</span><span class="p">(</span><span class="mi">1</span><span class="o">-</span><span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="n">std</span><span class="o">**</span><span class="mi">2</span><span class="p">),</span> <span class="n">_min_float</span><span class="p">)</span>
+                <span class="p">)</span>
+        
+        <span class="k">return</span> <span class="nb">float</span><span class="p">(</span><span class="n">neg_val</span><span class="p">)</span></div>
+</pre></div>
+
+           </div>
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+
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+  <h1>Source code for psimpy.inference.bayes_inference</h1><div class="highlight"><pre>
+<span></span><span class="kn">import</span> <span class="nn">sys</span>
+<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">from</span> <span class="nn">abc</span> <span class="kn">import</span> <span class="n">ABC</span>
+<span class="kn">from</span> <span class="nn">abc</span> <span class="kn">import</span> <span class="n">abstractmethod</span>
+<span class="kn">from</span> <span class="nn">typing</span> <span class="kn">import</span> <span class="n">Union</span>
+<span class="kn">from</span> <span class="nn">beartype.typing</span> <span class="kn">import</span> <span class="n">Callable</span>
+<span class="kn">from</span> <span class="nn">beartype</span> <span class="kn">import</span> <span class="n">beartype</span>
+<span class="kn">from</span> <span class="nn">psimpy.sampler</span> <span class="kn">import</span> <span class="n">MetropolisHastings</span>
+<span class="kn">from</span> <span class="nn">psimpy.utility</span> <span class="kn">import</span> <span class="n">check_bounds</span>
+
+<span class="n">_min_float</span> <span class="o">=</span> <span class="mi">10</span><span class="o">**</span><span class="p">(</span><span class="n">sys</span><span class="o">.</span><span class="n">float_info</span><span class="o">.</span><span class="n">min_10_exp</span><span class="p">)</span>
+<span class="n">_max_float</span> <span class="o">=</span> <span class="mi">10</span><span class="o">**</span><span class="p">(</span><span class="n">sys</span><span class="o">.</span><span class="n">float_info</span><span class="o">.</span><span class="n">max_10_exp</span><span class="p">)</span>
+<span class="n">_max_e</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">_max_float</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="nb">float</span><span class="p">))</span>
+
+<span class="k">class</span> <span class="nc">BayesInferenceBase</span><span class="p">(</span><span class="n">ABC</span><span class="p">):</span>
+
+    <span class="nd">@beartype</span>
+    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span>
+        <span class="bp">self</span><span class="p">,</span>
+        <span class="n">ndim</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span>
+        <span class="n">bounds</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
+        <span class="n">prior</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="n">Callable</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
+        <span class="n">likelihood</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="n">Callable</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
+        <span class="n">ln_prior</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="n">Callable</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
+        <span class="n">ln_likelihood</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="n">Callable</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
+        <span class="n">ln_pxl</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="n">Callable</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
+        <span class="n">args_prior</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">list</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
+        <span class="n">kwgs_prior</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">dict</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
+        <span class="n">args_likelihood</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">list</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
+        <span class="n">kwgs_likelihood</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">dict</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+        <span class="n">args_ln_pxl</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">list</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
+        <span class="n">kwgs_ln_pxl</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">dict</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span><span class="o">=</span><span class="kc">None</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
+        <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Set up basic input for Bayesian inference.</span>
+<span class="sd">    </span>
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        ndim : int</span>
+<span class="sd">            Dimension of parameter ``x``.</span>
+<span class="sd">        bounds : numpy array</span>
+<span class="sd">            Upper and lower boundaries of each parameter.</span>
+<span class="sd">            Shape :code:`(ndim, 2)`. </span>
+<span class="sd">            `bounds[:, 0]` corresponds to lower boundaries of each parameter and</span>
+<span class="sd">            `bounds[:, 1]` to upper boundaries of each parameter. </span>
+<span class="sd">        prior : Callable</span>
+<span class="sd">            Prior probability density function.</span>
+<span class="sd">            Call with :code:`prior(x, *args_prior, **kwgs_prior)`.</span>
+<span class="sd">            Return the prior probability density value at ``x``, where ``x`` is</span>
+<span class="sd">            a one dimension :class:`numpy.ndarray` of shape :code:`(ndim,)`.</span>
+<span class="sd">        likelihood : Callable</span>
+<span class="sd">            Likelihood function.</span>
+<span class="sd">            Call with :code:`likelihood(x, *args_likelihood, **kwgs_likelihood)`.</span>
+<span class="sd">            Return the likelihood value at ``x``.</span>
+<span class="sd">        ln_prior : Callable</span>
+<span class="sd">            Natural logarithm of prior probability density function.</span>
+<span class="sd">            Call with :code:`ln_prior(x, *args_prior, **kwgs_prior)`.</span>
+<span class="sd">            Return the value of natural logarithm of prior probability density</span>
+<span class="sd">            at ``x``.</span>
+<span class="sd">        ln_likelihood : Callable</span>
+<span class="sd">            Natural logarithm of likelihood function.</span>
+<span class="sd">            Call with :code:`ln_likelihood(x, *args_likelihood, **kwgs_likelihood)`.</span>
+<span class="sd">            Return the value of natural logarithm of likelihood at ``x``.</span>
+<span class="sd">        ln_pxl : Callable</span>
+<span class="sd">            Natural logarithm of the product of prior and likelihood.</span>
+<span class="sd">            Call with :code:`ln_pxl(x, *args_ln_pxl, **kwgs_ln_pxl)`.</span>
+<span class="sd">            Return the value of natural logarithm of the product of prior and</span>
+<span class="sd">            likelihood at ``x``.    </span>
+<span class="sd">        args_prior : list, optional</span>
+<span class="sd">            Positional arguments for ``prior`` or ``ln_prior``.</span>
+<span class="sd">        kwgs_prior: dict, optional</span>
+<span class="sd">            Keyword arguments for ``prior`` or ``ln_prior``.</span>
+<span class="sd">        args_likelihood : list, optional</span>
+<span class="sd">            Positional arguments for ``likelihood`` or ``ln_likelihood``.</span>
+<span class="sd">        kwgs_likelihood : dict, optional</span>
+<span class="sd">            Keyword arguments for ``likelihood`` or ``ln_likelihood``.</span>
+<span class="sd">        args_ln_pxl : list, optional</span>
+<span class="sd">            Positional arguments for ``ln_pxl``.</span>
+<span class="sd">        kwgs_ln_pxl : dict, optional</span>
+<span class="sd">            Keyword arguments for ``ln_pxl``.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">ndim</span> <span class="o">=</span> <span class="n">ndim</span>            
+        <span class="bp">self</span><span class="o">.</span><span class="n">bounds</span> <span class="o">=</span> <span class="n">bounds</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">args_prior</span> <span class="o">=</span> <span class="p">()</span> <span class="k">if</span> <span class="n">args_prior</span> <span class="ow">is</span> <span class="kc">None</span> <span class="k">else</span> <span class="n">args_prior</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">kwgs_prior</span> <span class="o">=</span> <span class="p">{}</span> <span class="k">if</span> <span class="n">kwgs_prior</span> <span class="ow">is</span> <span class="kc">None</span> <span class="k">else</span> <span class="n">kwgs_prior</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">args_likelihood</span> <span class="o">=</span> <span class="p">()</span> <span class="k">if</span> <span class="n">args_likelihood</span> <span class="ow">is</span> <span class="kc">None</span> <span class="k">else</span> <span class="n">args_likelihood</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">kwgs_likelihood</span> <span class="o">=</span> <span class="p">{}</span> <span class="k">if</span> <span class="n">kwgs_likelihood</span> <span class="ow">is</span> <span class="kc">None</span> <span class="k">else</span> <span class="n">kwgs_likelihood</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">args_ln_pxl</span> <span class="o">=</span> <span class="p">()</span> <span class="k">if</span> <span class="n">args_ln_pxl</span> <span class="ow">is</span> <span class="kc">None</span> <span class="k">else</span> <span class="n">args_ln_pxl</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">kwgs_ln_pxl</span> <span class="o">=</span> <span class="p">{}</span> <span class="k">if</span> <span class="n">kwgs_ln_pxl</span> <span class="ow">is</span> <span class="kc">None</span> <span class="k">else</span> <span class="n">kwgs_ln_pxl</span>
+
+        <span class="k">if</span> <span class="n">ln_pxl</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">ln_pxl</span> <span class="o">=</span> <span class="n">ln_pxl</span>
+        <span class="k">elif</span> <span class="p">(</span><span class="n">ln_prior</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">)</span> <span class="ow">and</span> <span class="p">(</span><span class="n">ln_likelihood</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">):</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">ln_prior</span> <span class="o">=</span> <span class="n">ln_prior</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">ln_likelihood</span> <span class="o">=</span> <span class="n">ln_likelihood</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">ln_pxl</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_ln_pxl_1</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">args_ln_pxl</span> <span class="o">=</span> <span class="p">()</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">kwgs_ln_pxl</span> <span class="o">=</span> <span class="p">{}</span>
+        <span class="k">elif</span> <span class="p">(</span><span class="n">prior</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">)</span> <span class="ow">and</span> <span class="p">(</span><span class="n">likelihood</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">):</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">prior</span> <span class="o">=</span> <span class="n">prior</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">likelihood</span> <span class="o">=</span> <span class="n">likelihood</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">ln_pxl</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_ln_pxl_2</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">args_ln_pxl</span> <span class="o">=</span> <span class="p">()</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">kwgs_ln_pxl</span> <span class="o">=</span> <span class="p">{}</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">((</span>
+                <span class="s2">&quot;One of the following inputs is necessary:&quot;</span>
+                <span class="s2">&quot; (1) `ln_pxl`&quot;</span>
+                <span class="s2">&quot; (2) `ln_prior` and `ln_likelihood`&quot;</span>
+                <span class="s2">&quot; (3) `prior` and `likelihood`&quot;</span><span class="p">))</span>
+    
+    <span class="k">def</span> <span class="nf">_ln_pxl_1</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">float</span><span class="p">:</span>
+        <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Construct ``ln_pxl``, given ``ln_prior`` and ``ln_likelihood``.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">ln_pxl</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">ln_prior</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="o">*</span><span class="bp">self</span><span class="o">.</span><span class="n">args_prior</span><span class="p">,</span> <span class="o">**</span><span class="bp">self</span><span class="o">.</span><span class="n">kwgs_prior</span><span class="p">)</span> <span class="o">+</span> \
+            <span class="bp">self</span><span class="o">.</span><span class="n">ln_likelihood</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="o">*</span><span class="bp">self</span><span class="o">.</span><span class="n">args_likelihood</span><span class="p">,</span> <span class="o">**</span><span class="bp">self</span><span class="o">.</span><span class="n">kwgs_likelihood</span><span class="p">)</span>
+
+        <span class="k">return</span> <span class="nb">float</span><span class="p">(</span><span class="n">ln_pxl</span><span class="p">)</span>
+    
+    <span class="k">def</span> <span class="nf">_ln_pxl_2</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">float</span><span class="p">:</span>
+        <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Construct ``ln_pxl``, given ``prior`` and ``likelihood``.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">pxl</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">prior</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="o">*</span><span class="bp">self</span><span class="o">.</span><span class="n">args_prior</span><span class="p">,</span> <span class="o">**</span><span class="bp">self</span><span class="o">.</span><span class="n">kwgs_prior</span><span class="p">)</span> <span class="o">*</span> \
+            <span class="bp">self</span><span class="o">.</span><span class="n">likelihood</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="o">*</span><span class="bp">self</span><span class="o">.</span><span class="n">args_likelihood</span><span class="p">,</span> <span class="o">**</span><span class="bp">self</span><span class="o">.</span><span class="n">kwgs_likelihood</span><span class="p">)</span>
+        <span class="n">ln_pxl</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">maximum</span><span class="p">(</span><span class="n">pxl</span><span class="p">,</span> <span class="n">_min_float</span><span class="p">))</span>
+        
+        <span class="k">return</span> <span class="nb">float</span><span class="p">(</span><span class="n">ln_pxl</span><span class="p">)</span>
+
+    <span class="nd">@abstractmethod</span>
+    <span class="k">def</span> <span class="nf">run</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwgs</span><span class="p">):</span>
+        <span class="k">pass</span>
+
+
+<div class="viewcode-block" id="GridEstimation"><a class="viewcode-back" href="../../../inference/bayes_inference.html#psimpy.inference.bayes_inference.GridEstimation">[docs]</a><span class="k">class</span> <span class="nc">GridEstimation</span><span class="p">(</span><span class="n">BayesInferenceBase</span><span class="p">):</span>
+    
+<div class="viewcode-block" id="GridEstimation.run"><a class="viewcode-back" href="../../../inference/bayes_inference.html#psimpy.inference.bayes_inference.GridEstimation.run">[docs]</a>    <span class="nd">@beartype</span>
+    <span class="k">def</span> <span class="nf">run</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">nbins</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">int</span><span class="p">,</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]]</span>
+        <span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">tuple</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="nb">list</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">]]:</span>
+        <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Use Grid approximation to estimate the posterior.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        nbins : int or list of ints</span>
+<span class="sd">            Number of bins for each parameter.</span>
+<span class="sd">            If `int`, the same value is used for each parameter.</span>
+<span class="sd">            If `list of int`, it should be of length ``ndim``.</span>
+<span class="sd">        </span>
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        posterior : numpy array</span>
+<span class="sd">            Estimated posterior probability density values at grid points.</span>
+<span class="sd">            Shape of :code:`(nbins[0], nbins[1], ..., nbins[ndim])`.</span>
+<span class="sd">        x_ndim : list of numpy array</span>
+<span class="sd">            Contain ``ndim`` 1d :class:`numpy.ndarray` `x1`, `x2`, ... Each `xi`</span>
+<span class="sd">            is a 1d array of length ``nbins[i]``, representing the 1d coordinate</span>
+<span class="sd">            array along the i-th axis.</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">nbins</span><span class="p">,</span> <span class="nb">int</span><span class="p">):</span>
+            <span class="n">nbins</span> <span class="o">=</span> <span class="p">[</span><span class="n">nbins</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ndim</span>
+        <span class="k">elif</span> <span class="nb">len</span><span class="p">(</span><span class="n">nbins</span><span class="p">)</span> <span class="o">!=</span> <span class="bp">self</span><span class="o">.</span><span class="n">ndim</span><span class="p">:</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span>
+                <span class="s2">&quot;nbins must be an integer or a list of ndim integers&quot;</span><span class="p">)</span>
+
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">bounds</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;bounds must be provided for grid estimation&quot;</span><span class="p">)</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="n">check_bounds</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ndim</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">bounds</span><span class="p">)</span>
+        
+        <span class="n">steps</span> <span class="o">=</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">bounds</span><span class="p">[:,</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">bounds</span><span class="p">[:,</span><span class="mi">0</span><span class="p">])</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">nbins</span><span class="p">)</span> 
+        <span class="n">starts</span> <span class="o">=</span> <span class="n">steps</span><span class="o">/</span><span class="mi">2</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">bounds</span><span class="p">[:,</span><span class="mi">0</span><span class="p">]</span>
+        <span class="n">stops</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">bounds</span><span class="p">[:,</span><span class="mi">1</span><span class="p">]</span>  
+        
+        <span class="n">x_ndim</span> <span class="o">=</span> <span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">starts</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">stops</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">steps</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
+            <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ndim</span><span class="p">)]</span>
+        <span class="n">xx_matrices</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">meshgrid</span><span class="p">(</span><span class="o">*</span><span class="n">x_ndim</span><span class="p">,</span> <span class="n">indexing</span><span class="o">=</span><span class="s1">&#39;ij&#39;</span><span class="p">)</span>
+        <span class="n">grid_point_coords</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">hstack</span><span class="p">(</span>
+            <span class="nb">tuple</span><span class="p">(</span><span class="n">matrix</span><span class="o">.</span><span class="n">reshape</span><span class="p">((</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="mi">1</span><span class="p">))</span> <span class="k">for</span> <span class="n">matrix</span> <span class="ow">in</span> <span class="n">xx_matrices</span><span class="p">)</span>
+            <span class="p">)</span>
+        
+        <span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">grid_point_coords</span><span class="p">)</span>
+        <span class="n">ln_unnorm_posterior</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+        <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
+            <span class="n">point_i</span> <span class="o">=</span> <span class="n">grid_point_coords</span><span class="p">[</span><span class="n">i</span><span class="p">,:]</span>
+            <span class="n">ln_unnorm_posterior</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> \
+                <span class="bp">self</span><span class="o">.</span><span class="n">ln_pxl</span><span class="p">(</span><span class="n">point_i</span><span class="p">,</span> <span class="o">*</span><span class="bp">self</span><span class="o">.</span><span class="n">args_ln_pxl</span><span class="p">,</span> <span class="o">**</span><span class="bp">self</span><span class="o">.</span><span class="n">kwgs_ln_pxl</span><span class="p">)</span>
+        
+        <span class="n">ln_unnorm_posterior</span> <span class="o">=</span> <span class="n">ln_unnorm_posterior</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">xx_matrices</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>
+        <span class="n">ln_unnorm_posterior</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">where</span><span class="p">(</span>
+            <span class="n">ln_unnorm_posterior</span> <span class="o">&gt;=</span> <span class="n">_max_e</span><span class="p">,</span> <span class="n">_max_e</span><span class="p">,</span> <span class="n">ln_unnorm_posterior</span><span class="p">)</span>
+        <span class="n">unnorm_posterior</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="n">ln_unnorm_posterior</span><span class="p">)</span>
+        <span class="n">posterior</span> <span class="o">=</span> <span class="n">unnorm_posterior</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">unnorm_posterior</span><span class="p">)</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">prod</span><span class="p">(</span><span class="n">steps</span><span class="p">)</span>
+        
+        <span class="k">return</span> <span class="n">posterior</span><span class="p">,</span> <span class="n">x_ndim</span></div></div>
+
+
+<div class="viewcode-block" id="MetropolisHastingsEstimation"><a class="viewcode-back" href="../../../inference/bayes_inference.html#psimpy.inference.bayes_inference.MetropolisHastingsEstimation">[docs]</a><span class="k">class</span> <span class="nc">MetropolisHastingsEstimation</span><span class="p">(</span><span class="n">BayesInferenceBase</span><span class="p">):</span>
+
+<div class="viewcode-block" id="MetropolisHastingsEstimation.run"><a class="viewcode-back" href="../../../inference/bayes_inference.html#psimpy.inference.bayes_inference.MetropolisHastingsEstimation.run">[docs]</a>    <span class="k">def</span> <span class="nf">run</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">nsamples</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">mh_sampler</span><span class="p">:</span> <span class="n">MetropolisHastings</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">tuple</span><span class="p">[</span>
+        <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">]:</span>
+        <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Use Metropolis Hastings sampling to draw samples from the posterior.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        nsamples : int</span>
+<span class="sd">            Number of samples to be drawn.</span>
+<span class="sd">        mh_sampler : instance of :class:`.MetropolisHastings`</span>
+<span class="sd">            Metropolis Hastings sampler.</span>
+<span class="sd">        </span>
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        mh_samples : numpy array</span>
+<span class="sd">            Samples drawn from the posterior. Shape of :code:`(nsamples, ndim)`.</span>
+<span class="sd">        mh_accept : numpy array</span>
+<span class="sd">            Shape of :code:`(nsamples,)`. Each element indicates whether the</span>
+<span class="sd">            corresponding sample is the proposed new state (value 1) or the old</span>
+<span class="sd">            state (value 0). :code:`np.mean(mh_accept)` thus gives the overall</span>
+<span class="sd">            acceptance ratio.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="n">mh_sampler</span><span class="o">.</span><span class="n">ndim</span> <span class="o">!=</span> <span class="bp">self</span><span class="o">.</span><span class="n">ndim</span><span class="p">:</span>
+            <span class="k">raise</span> <span class="ne">RuntimeError</span><span class="p">(</span>
+                <span class="s2">&quot;ndim of mh_sampler and ndim defined in this class must be&quot;</span>
+                <span class="s2">&quot; consistent&quot;</span><span class="p">)</span>
+        
+        <span class="k">if</span> <span class="nb">type</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">bounds</span><span class="p">)</span> <span class="o">!=</span> <span class="nb">type</span><span class="p">(</span><span class="n">mh_sampler</span><span class="o">.</span><span class="n">bounds</span><span class="p">):</span>
+            <span class="k">raise</span> <span class="ne">RuntimeError</span><span class="p">(</span>
+                <span class="s2">&quot;bounds of mh_sampler and bounds defined in this class must be&quot;</span>
+                <span class="s2">&quot; consistent&quot;</span><span class="p">)</span>
+        <span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">bounds</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">)</span> <span class="ow">and</span> \
+            <span class="ow">not</span> <span class="n">np</span><span class="o">.</span><span class="n">all</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">equal</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">bounds</span><span class="p">,</span> <span class="n">mh_sampler</span><span class="o">.</span><span class="n">bounds</span><span class="p">)):</span>
+            <span class="k">raise</span> <span class="ne">RuntimeError</span><span class="p">(</span>
+                <span class="s2">&quot;bounds of mh_sampler and bounds defined in this class must be&quot;</span>
+                <span class="s2">&quot; consistent&quot;</span><span class="p">)</span>
+
+        <span class="n">mh_sampler</span><span class="o">.</span><span class="n">ln_target</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">ln_pxl</span>
+        <span class="n">mh_sampler</span><span class="o">.</span><span class="n">args_target</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">args_ln_pxl</span>
+        <span class="n">mh_sampler</span><span class="o">.</span><span class="n">kwgs_target</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">kwgs_ln_pxl</span>
+        
+        <span class="n">mh_samples</span><span class="p">,</span> <span class="n">mh_accept</span> <span class="o">=</span> <span class="n">mh_sampler</span><span class="o">.</span><span class="n">sample</span><span class="p">(</span><span class="n">nsamples</span><span class="p">)</span>
+
+        <span class="k">return</span> <span class="n">mh_samples</span><span class="p">,</span> <span class="n">mh_accept</span></div></div>
+</pre></div>
+
+           </div>
+          </div>
+          <footer>
+
+  <hr/>
+
+  <div role="contentinfo">
+    <p>&#169; Copyright 2023, Hu Zhao.</p>
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diff --git a/docs/source/_build/html/_modules/psimpy/sampler/latin.html b/docs/source/_build/html/_modules/psimpy/sampler/latin.html
new file mode 100644
index 0000000..f1b1f55
--- /dev/null
+++ b/docs/source/_build/html/_modules/psimpy/sampler/latin.html
@@ -0,0 +1,229 @@
+<!DOCTYPE html>
+<html class="writer-html5" lang="en" >
+<head>
+  <meta charset="utf-8" />
+  <meta name="viewport" content="width=device-width, initial-scale=1.0" />
+  <title>psimpy.sampler.latin &mdash; PSimPy&#39;s documentation</title>
+      <link rel="stylesheet" href="../../../_static/pygments.css" type="text/css" />
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+      <li class="breadcrumb-item active">psimpy.sampler.latin</li>
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+           <div itemprop="articleBody">
+             
+  <h1>Source code for psimpy.sampler.latin</h1><div class="highlight"><pre>
+<span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">from</span> <span class="nn">scipy.spatial.distance</span> <span class="kn">import</span> <span class="n">pdist</span>
+<span class="kn">from</span> <span class="nn">typing</span> <span class="kn">import</span> <span class="n">Union</span>
+<span class="kn">from</span> <span class="nn">beartype</span> <span class="kn">import</span> <span class="n">beartype</span>
+<span class="kn">from</span> <span class="nn">psimpy.utility</span> <span class="kn">import</span> <span class="n">check_bounds</span><span class="p">,</span> <span class="n">scale_samples</span>
+
+<div class="viewcode-block" id="LHS"><a class="viewcode-back" href="../../../sampler/latin.html#psimpy.sampler.latin.LHS">[docs]</a><span class="k">class</span> <span class="nc">LHS</span><span class="p">:</span>
+    
+    <span class="nd">@beartype</span>
+    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span>
+        <span class="bp">self</span><span class="p">,</span> <span class="n">ndim</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">bounds</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
+        <span class="n">seed</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">int</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span> <span class="n">criterion</span><span class="p">:</span> <span class="nb">str</span> <span class="o">=</span> <span class="s1">&#39;random&#39;</span><span class="p">,</span> 
+        <span class="n">iteration</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">int</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
+        <span class="sd">&quot;&quot;&quot;Latin hypercube sampling.</span>
+<span class="sd">    </span>
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        ndim : int</span>
+<span class="sd">            Dimension of parameters.</span>
+<span class="sd">        bounds : numpy array</span>
+<span class="sd">            Upper and lower boundaries of each parameter. Shape :code:`(ndim, 2)`.</span>
+<span class="sd">            `bounds[:, 0]` corresponds to lower boundaries of each parameter and</span>
+<span class="sd">            `bounds[:, 1]` to upper boundaries of each parameter.</span>
+<span class="sd">        seed : int, optional</span>
+<span class="sd">            Seed to initialize the pseudo-random number generator.</span>
+<span class="sd">        criterion : str, optional</span>
+<span class="sd">            Criterion for generating Latin hypercube samples.</span>
+<span class="sd">            `&#39;random&#39;` - randomly locate samples in each bin.</span>
+<span class="sd">            `&#39;center&#39;` - locate samples in bin centers.</span>
+<span class="sd">            `&#39;maximin&#39;` - locate samples in each bin by maximizing their minimum</span>
+<span class="sd">            distance.</span>
+<span class="sd">            Default is `&#39;random&#39;`.</span>
+<span class="sd">        iteration : int, optional</span>
+<span class="sd">            Number of iterations if :code:`criterion=&#39;maximin&#39;`.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">ndim</span> <span class="o">=</span> <span class="n">ndim</span>
+
+        <span class="k">if</span> <span class="n">bounds</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="n">check_bounds</span><span class="p">(</span><span class="n">ndim</span><span class="p">,</span> <span class="n">bounds</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">bounds</span> <span class="o">=</span> <span class="n">bounds</span>
+        
+        <span class="bp">self</span><span class="o">.</span><span class="n">rng</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">default_rng</span><span class="p">(</span><span class="n">seed</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">seed</span> <span class="o">=</span> <span class="n">seed</span>
+        
+        <span class="k">if</span> <span class="n">criterion</span> <span class="ow">not</span> <span class="ow">in</span> <span class="p">(</span><span class="s1">&#39;random&#39;</span><span class="p">,</span> <span class="s1">&#39;center&#39;</span><span class="p">,</span> <span class="s1">&#39;maximin&#39;</span><span class="p">):</span>
+            <span class="k">raise</span> <span class="ne">NotImplementedError</span><span class="p">(</span>
+                <span class="sa">f</span><span class="s2">&quot;criterion </span><span class="si">{</span><span class="n">criterion</span><span class="si">}</span><span class="s2"> is not implemented.&quot;</span>
+                <span class="sa">f</span><span class="s2">&quot; Supported criterion includes: &#39;random&#39;, &#39;center&#39;, &#39;maximin&#39;&quot;</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">criterion</span> <span class="o">=</span> <span class="n">criterion</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">iteration</span> <span class="o">=</span> <span class="n">iteration</span>
+        
+    
+<div class="viewcode-block" id="LHS.sample"><a class="viewcode-back" href="../../../sampler/latin.html#psimpy.sampler.latin.LHS.sample">[docs]</a>    <span class="k">def</span> <span class="nf">sample</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">nsamples</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">:</span>
+        <span class="sd">&quot;&quot;&quot;Draw Latin hypercube samples.</span>
+<span class="sd">        </span>
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        nsamples : int</span>
+<span class="sd">            Number of samples to be drawn.</span>
+<span class="sd">        </span>
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        lhs_samples : numpy array</span>
+<span class="sd">            Latin hypercube samples. Shape :code:`(nsamples, ndim)`.  </span>
+<span class="sd">        &quot;&quot;&quot;</span>        
+        <span class="bp">self</span><span class="o">.</span><span class="n">nsamples</span> <span class="o">=</span> <span class="n">nsamples</span>
+        
+        <span class="c1"># create nsamples bins in the interval [0, 1]</span>
+        <span class="n">bin_edges</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="n">nsamples</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">_lower_edges</span> <span class="o">=</span> <span class="n">bin_edges</span><span class="p">[:</span><span class="n">nsamples</span><span class="p">]</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">_upper_edges</span> <span class="o">=</span> <span class="n">bin_edges</span><span class="p">[</span><span class="mi">1</span> <span class="p">:</span> <span class="n">nsamples</span><span class="o">+</span><span class="mi">1</span><span class="p">]</span>      
+        
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">criterion</span> <span class="o">==</span> <span class="s1">&#39;random&#39;</span><span class="p">:</span>
+            <span class="n">lhs_samples</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_random</span><span class="p">()</span>
+        <span class="k">elif</span> <span class="bp">self</span><span class="o">.</span><span class="n">criterion</span> <span class="o">==</span> <span class="s1">&#39;center&#39;</span><span class="p">:</span>
+            <span class="n">lhs_samples</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_center</span><span class="p">()</span>
+        <span class="k">elif</span> <span class="bp">self</span><span class="o">.</span><span class="n">criterion</span> <span class="o">==</span> <span class="s1">&#39;maximin&#39;</span><span class="p">:</span>
+            <span class="n">lhs_samples</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_maximin</span><span class="p">()</span>     
+        
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">bounds</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="n">lhs_samples</span> <span class="o">=</span> <span class="n">scale_samples</span><span class="p">(</span><span class="n">lhs_samples</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">bounds</span><span class="p">)</span>
+        
+        <span class="k">return</span> <span class="n">lhs_samples</span></div>
+    
+    <span class="k">def</span> <span class="nf">_random</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">:</span>
+        <span class="sd">&quot;&quot;&quot;&quot;Draw samples by randomly picking points in each bin.&quot;&quot;&quot;</span>
+        <span class="n">samples</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">rng</span><span class="o">.</span><span class="n">uniform</span><span class="p">(</span><span class="n">size</span><span class="o">=</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">nsamples</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">ndim</span><span class="p">))</span>
+        <span class="n">lhs_samples</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros_like</span><span class="p">(</span><span class="n">samples</span><span class="p">)</span>
+        <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ndim</span><span class="p">):</span>
+            <span class="n">samples</span><span class="p">[:,</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">samples</span><span class="p">[:,</span><span class="n">j</span><span class="p">]</span><span class="o">*</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_upper_edges</span><span class="o">-</span><span class="bp">self</span><span class="o">.</span><span class="n">_lower_edges</span><span class="p">)</span> \
+                <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">_lower_edges</span>
+            <span class="n">lhs_samples</span><span class="p">[:,</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">rng</span><span class="o">.</span><span class="n">permutation</span><span class="p">(</span><span class="n">samples</span><span class="p">[:,</span><span class="n">j</span><span class="p">])</span>
+        <span class="k">return</span> <span class="n">lhs_samples</span>
+    
+    <span class="k">def</span> <span class="nf">_center</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">:</span>
+        <span class="sd">&quot;&quot;&quot;&quot;Draw samples by picking points at the center of each bin.&quot;&quot;&quot;</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">_center_points</span> <span class="o">=</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_lower_edges</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">_upper_edges</span><span class="p">)</span> <span class="o">/</span> <span class="mi">2</span>
+        <span class="n">lhs_samples</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="bp">self</span><span class="o">.</span><span class="n">nsamples</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">ndim</span><span class="p">))</span>
+        <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ndim</span><span class="p">):</span>
+            <span class="n">lhs_samples</span><span class="p">[:,</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">rng</span><span class="o">.</span><span class="n">permutation</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_center_points</span><span class="p">)</span> 
+        <span class="k">return</span> <span class="n">lhs_samples</span>
+
+    <span class="k">def</span> <span class="nf">_maximin</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">:</span>
+        <span class="sd">&quot;&quot;&quot;&quot;</span>
+<span class="sd">        Draw samples by maximizing the minimum distance between samples.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">iteration</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">iteration</span> <span class="o">=</span> <span class="mi">100</span>
+        
+        <span class="c1"># max --&gt; min?</span>
+        <span class="n">min_distance</span> <span class="o">=</span> <span class="mi">0</span>
+        <span class="n">lhs_samples</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="bp">self</span><span class="o">.</span><span class="n">nsamples</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">ndim</span><span class="p">))</span>
+        <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">iteration</span><span class="p">):</span>
+            <span class="n">temp_samples</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_random</span><span class="p">()</span>
+            <span class="n">temp_distance</span> <span class="o">=</span> <span class="n">pdist</span><span class="p">(</span><span class="n">temp_samples</span><span class="p">)</span>
+            <span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">min</span><span class="p">(</span><span class="n">temp_distance</span><span class="p">)</span> <span class="o">&gt;</span> <span class="n">min_distance</span><span class="p">:</span>
+                <span class="n">min_distance</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">min</span><span class="p">(</span><span class="n">temp_distance</span><span class="p">)</span>
+                <span class="n">lhs_samples</span> <span class="o">=</span> <span class="n">temp_samples</span>
+        <span class="k">return</span> <span class="n">lhs_samples</span></div>
+</pre></div>
+
+           </div>
+          </div>
+          <footer>
+
+  <hr/>
+
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+    <p>&#169; Copyright 2023, Hu Zhao.</p>
+  </div>
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diff --git a/docs/source/_build/html/_modules/psimpy/sampler/metropolis_hastings.html b/docs/source/_build/html/_modules/psimpy/sampler/metropolis_hastings.html
new file mode 100644
index 0000000..bae9853
--- /dev/null
+++ b/docs/source/_build/html/_modules/psimpy/sampler/metropolis_hastings.html
@@ -0,0 +1,335 @@
+<!DOCTYPE html>
+<html class="writer-html5" lang="en" >
+<head>
+  <meta charset="utf-8" />
+  <meta name="viewport" content="width=device-width, initial-scale=1.0" />
+  <title>psimpy.sampler.metropolis_hastings &mdash; PSimPy&#39;s documentation</title>
+      <link rel="stylesheet" href="../../../_static/pygments.css" type="text/css" />
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+      <li class="breadcrumb-item active">psimpy.sampler.metropolis_hastings</li>
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+      </li>
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+          <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article">
+           <div itemprop="articleBody">
+             
+  <h1>Source code for psimpy.sampler.metropolis_hastings</h1><div class="highlight"><pre>
+<span></span><span class="kn">import</span> <span class="nn">sys</span>
+<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">from</span> <span class="nn">typing</span> <span class="kn">import</span> <span class="n">Union</span>
+<span class="kn">from</span> <span class="nn">beartype.typing</span> <span class="kn">import</span> <span class="n">Callable</span>
+<span class="kn">from</span> <span class="nn">beartype</span> <span class="kn">import</span> <span class="n">beartype</span>
+<span class="kn">from</span> <span class="nn">psimpy.utility</span> <span class="kn">import</span> <span class="n">check_bounds</span>
+
+<span class="n">_min_float</span> <span class="o">=</span> <span class="mi">10</span><span class="o">**</span><span class="p">(</span><span class="n">sys</span><span class="o">.</span><span class="n">float_info</span><span class="o">.</span><span class="n">min_10_exp</span><span class="p">)</span>
+
+<div class="viewcode-block" id="MetropolisHastings"><a class="viewcode-back" href="../../../sampler/metropolis_hastings.html#psimpy.sampler.metropolis_hastings.MetropolisHastings">[docs]</a><span class="k">class</span> <span class="nc">MetropolisHastings</span><span class="p">:</span>
+    
+    <span class="nd">@beartype</span>
+    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span>
+        <span class="bp">self</span><span class="p">,</span>
+        <span class="n">ndim</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span>
+        <span class="n">init_state</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span>
+        <span class="n">f_sample</span><span class="p">:</span> <span class="n">Callable</span><span class="p">,</span>
+        <span class="n">target</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="n">Callable</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
+        <span class="n">ln_target</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="n">Callable</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
+        <span class="n">bounds</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
+        <span class="n">f_density</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="n">Callable</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
+        <span class="n">symmetric</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="kc">True</span><span class="p">,</span>
+        <span class="n">nburn</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">0</span><span class="p">,</span>
+        <span class="n">nthin</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">1</span><span class="p">,</span>
+        <span class="n">seed</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">int</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
+        <span class="n">args_target</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">list</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
+        <span class="n">kwgs_target</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">dict</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
+        <span class="n">args_f_sample</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">list</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span> 
+        <span class="n">kwgs_f_sample</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">dict</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
+        <span class="n">args_f_density</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">list</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
+        <span class="n">kwgs_f_density</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">dict</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span><span class="kc">None</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
+        <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Metropolis Hastings sampling.</span>
+<span class="sd">    </span>
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        ndim : int</span>
+<span class="sd">            Dimension of parameter ``x``.</span>
+<span class="sd">        init_state : numpy array</span>
+<span class="sd">            Contains ``ndim`` numeric values representing the starting point of</span>
+<span class="sd">            the Metropolis hastings chain. Shape :code:`(ndim,)`.</span>
+<span class="sd">        f_sample : Callable</span>
+<span class="sd">            A function which proposes a new state ``x&#39;`` given a current state</span>
+<span class="sd">            ``x``. Call with :code:`f_sample(x, *args_f_sample, **kwgs_f_sample)`.</span>
+<span class="sd">            Return the proposed state ``x&#39;`` as a :class:`numpy.ndarray` of</span>
+<span class="sd">            shape :code:`(ndim,)`. If :math:`ndim=1`, ``f_sample`` may also</span>
+<span class="sd">            return a scalar value.</span>
+<span class="sd">        target : Callable, optional</span>
+<span class="sd">            Target probability density function, up to a normalizing constant. </span>
+<span class="sd">            Call with :code:`target(x, *args_target, **kwgs_target)`.</span>
+<span class="sd">            Return the probability density value at ``x``. </span>
+<span class="sd">            If ``target`` is not given, ``ln_target`` must be provided.</span>
+<span class="sd">        ln_target : Callable, optional</span>
+<span class="sd">            Natural logarithm of target probability density function.</span>
+<span class="sd">            Call with :code:`ln_target(x, *args_target, **kwgs_target)`.</span>
+<span class="sd">            Return the value of natural logarithm of target probability density</span>
+<span class="sd">            value at ``x``.</span>
+<span class="sd">            If ``ln_target`` is not given, ``target`` must be provided.</span>
+<span class="sd">        bounds : numpy array, optional</span>
+<span class="sd">            Upper and lower boundaries of each parameter. Shape :code:`(ndim, 2)`.</span>
+<span class="sd">            `bounds[:, 0]` corresponds to lower boundaries of each parameter and</span>
+<span class="sd">            `bounds[:, 1]` to upper boundaries of each parameter. </span>
+<span class="sd">        f_density : Callable, optional</span>
+<span class="sd">            Call with :code:`f_density(x1, x2, *args_f_density, **kwgs_f_density)`.</span>
+<span class="sd">            Return the probability density at state ``x1`` given state ``x2``.</span>
+<span class="sd">            It must be provided if ``symmetric`` is set to `False`.</span>
+<span class="sd">        symmetric : bool, optional</span>
+<span class="sd">            Whether ``f_density`` is symmetric or asymmetric.</span>
+<span class="sd">        nburn : int, optional</span>
+<span class="sd">            Number of burnin. Default no burnin.</span>
+<span class="sd">        nthin : int, optional</span>
+<span class="sd">            Number of thining to reduce dependency. Default no thining.</span>
+<span class="sd">        seed : int, optional</span>
+<span class="sd">            Seed to initialize the pseudo-random number generator.</span>
+<span class="sd">            Default `None`.</span>
+<span class="sd">        args_target : list, optional</span>
+<span class="sd">            Positional arguments for ``target`` or ``ln_target``.</span>
+<span class="sd">        kwgs_target : dict, optional</span>
+<span class="sd">            Keyword arguments for ``target`` or ``ln_target``.</span>
+<span class="sd">        args_f_sample : list, optional</span>
+<span class="sd">            Positional arguments for ``f_sample``.</span>
+<span class="sd">        kwgs_f_sample : dict, optional</span>
+<span class="sd">            Keyword arguments for ``f_sample``.</span>
+<span class="sd">        args_f_density : list, optional</span>
+<span class="sd">            Positional arguments for ``f_density``.</span>
+<span class="sd">        kwgs_f_density : dict, optional</span>
+<span class="sd">            Keyword arguments for ``f_density``.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">init_state</span><span class="p">)</span> <span class="o">!=</span> <span class="n">ndim</span><span class="p">:</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;init_state must contain ndim=</span><span class="si">{</span><span class="n">ndim</span><span class="si">}</span><span class="s2"> elements&quot;</span><span class="p">)</span>
+        
+        <span class="k">if</span> <span class="n">bounds</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="n">check_bounds</span><span class="p">(</span><span class="n">ndim</span><span class="p">,</span> <span class="n">bounds</span><span class="p">)</span>
+
+            <span class="k">if</span> <span class="ow">not</span> <span class="nb">all</span><span class="p">([</span>
+                <span class="n">init_state</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">&gt;=</span> <span class="n">bounds</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="mi">0</span><span class="p">]</span> <span class="ow">and</span>
+                <span class="n">init_state</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">&lt;=</span> <span class="n">bounds</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="mi">1</span><span class="p">]</span>
+                <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">ndim</span><span class="p">)</span>
+            <span class="p">]):</span>
+                <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;init_state violates bounds&quot;</span><span class="p">)</span>
+
+        <span class="k">if</span> <span class="p">(</span><span class="ow">not</span> <span class="n">symmetric</span><span class="p">)</span> <span class="ow">and</span> <span class="p">(</span><span class="n">f_density</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">):</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;f_density must be provided if asymmetric&quot;</span><span class="p">)</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">ndim</span> <span class="o">=</span> <span class="n">ndim</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">init_state</span> <span class="o">=</span> <span class="n">init_state</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">f_sample</span> <span class="o">=</span> <span class="n">f_sample</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">target</span> <span class="o">=</span> <span class="n">target</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">ln_target</span> <span class="o">=</span> <span class="n">ln_target</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">bounds</span> <span class="o">=</span> <span class="n">bounds</span>
+        
+        <span class="bp">self</span><span class="o">.</span><span class="n">f_density</span> <span class="o">=</span> <span class="n">f_density</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">symmetric</span> <span class="o">=</span> <span class="n">symmetric</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">nburn</span> <span class="o">=</span> <span class="n">nburn</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">nthin</span> <span class="o">=</span> <span class="n">nthin</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">rng</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">default_rng</span><span class="p">(</span><span class="n">seed</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">seed</span> <span class="o">=</span> <span class="n">seed</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">args_target</span> <span class="o">=</span> <span class="p">()</span> <span class="k">if</span> <span class="n">args_target</span> <span class="ow">is</span> <span class="kc">None</span> <span class="k">else</span> <span class="n">args_target</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">args_f_sample</span> <span class="o">=</span> <span class="p">()</span> <span class="k">if</span> <span class="n">args_f_sample</span> <span class="ow">is</span> <span class="kc">None</span> <span class="k">else</span> <span class="n">args_f_sample</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">args_f_density</span> <span class="o">=</span> <span class="p">()</span> <span class="k">if</span> <span class="n">args_f_density</span> <span class="ow">is</span> <span class="kc">None</span> <span class="k">else</span> <span class="n">args_f_density</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">kwgs_target</span> <span class="o">=</span> <span class="p">{}</span> <span class="k">if</span> <span class="n">kwgs_target</span> <span class="ow">is</span> <span class="kc">None</span> <span class="k">else</span> <span class="n">kwgs_target</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">kwgs_f_sample</span> <span class="o">=</span> <span class="p">{}</span> <span class="k">if</span> <span class="n">kwgs_f_sample</span> <span class="ow">is</span> <span class="kc">None</span> <span class="k">else</span> <span class="n">kwgs_f_sample</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">kwgs_f_density</span> <span class="o">=</span> <span class="p">{}</span> <span class="k">if</span> <span class="n">kwgs_f_density</span> <span class="ow">is</span> <span class="kc">None</span> <span class="k">else</span> <span class="n">kwgs_f_density</span>        
+    
+<div class="viewcode-block" id="MetropolisHastings.sample"><a class="viewcode-back" href="../../../sampler/metropolis_hastings.html#psimpy.sampler.metropolis_hastings.MetropolisHastings.sample">[docs]</a>    <span class="k">def</span> <span class="nf">sample</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">nsamples</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">tuple</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">]:</span>
+        <span class="sd">&quot;&quot;&quot;Draw samples.</span>
+<span class="sd">        </span>
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        nsamples : int</span>
+<span class="sd">            Number of samples to be drawn.</span>
+<span class="sd">        </span>
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        mh_samples : numpy array</span>
+<span class="sd">            Samples drawn from ``target``. Shape :code:`(nsamples, ndim)`.</span>
+<span class="sd">        mh_accept : numpy array</span>
+<span class="sd">            Shape of :code:`(nsamples,)`. Each element indicates whether the</span>
+<span class="sd">            corresponding sample is the proposed new state (value 1) or the old</span>
+<span class="sd">            state (value 0). :code:`np.mean(mh_accept)` thus gives the overall</span>
+<span class="sd">            acceptance ratio.</span>
+<span class="sd">        &quot;&quot;&quot;</span> 
+        <span class="k">if</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">target</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">)</span> <span class="ow">and</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ln_target</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">):</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span>
+                <span class="s2">&quot;Either target or ln_target must be provided before call the&quot;</span>
+                <span class="s2">&quot; sample method&quot;</span><span class="p">)</span>
+                 
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">ln_target</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="n">init_t</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">target</span><span class="p">(</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">init_state</span><span class="p">,</span> <span class="o">*</span><span class="bp">self</span><span class="o">.</span><span class="n">args_target</span><span class="p">,</span> <span class="o">**</span><span class="bp">self</span><span class="o">.</span><span class="n">kwgs_target</span><span class="p">)</span>
+            <span class="n">ln_init_t</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">maximum</span><span class="p">(</span><span class="n">init_t</span><span class="p">,</span> <span class="n">_min_float</span><span class="p">))</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="n">ln_init_t</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">ln_target</span><span class="p">(</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">init_state</span><span class="p">,</span> <span class="o">*</span><span class="bp">self</span><span class="o">.</span><span class="n">args_target</span><span class="p">,</span> <span class="o">**</span><span class="bp">self</span><span class="o">.</span><span class="n">kwgs_target</span><span class="p">)</span>
+
+        <span class="nb">iter</span> <span class="o">=</span> <span class="mi">0</span>
+        <span class="n">niter</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">nburn</span> <span class="o">+</span> <span class="p">(</span><span class="n">nsamples</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span><span class="o">*</span><span class="bp">self</span><span class="o">.</span><span class="n">nthin</span> <span class="o">+</span> <span class="mi">1</span>
+        
+        <span class="n">_samples</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">niter</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">ndim</span><span class="p">))</span>
+        <span class="n">_accept</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">niter</span><span class="p">)</span>
+        
+        <span class="n">current_state</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">init_state</span>
+        <span class="n">ln_current_t</span> <span class="o">=</span> <span class="n">ln_init_t</span>
+
+        <span class="k">while</span> <span class="nb">iter</span> <span class="o">&lt;</span> <span class="n">niter</span><span class="p">:</span>
+
+            <span class="n">candidate_state</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">f_sample</span><span class="p">(</span>
+                <span class="n">current_state</span><span class="p">,</span> <span class="o">*</span><span class="bp">self</span><span class="o">.</span><span class="n">args_f_sample</span><span class="p">,</span> <span class="o">**</span><span class="bp">self</span><span class="o">.</span><span class="n">kwgs_f_sample</span><span class="p">)</span>
+            <span class="n">candidate_state</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">candidate_state</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span>
+            
+            <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">bounds</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+                <span class="k">if</span> <span class="ow">not</span> <span class="nb">all</span><span class="p">([</span>
+                    <span class="n">candidate_state</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">&gt;=</span> <span class="bp">self</span><span class="o">.</span><span class="n">bounds</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="mi">0</span><span class="p">]</span> <span class="ow">and</span>
+                    <span class="n">candidate_state</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">&lt;=</span> <span class="bp">self</span><span class="o">.</span><span class="n">bounds</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="mi">1</span><span class="p">]</span>
+                    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ndim</span><span class="p">)</span>
+                <span class="p">]):</span>
+                    <span class="n">_samples</span><span class="p">[</span><span class="nb">iter</span><span class="p">,</span> <span class="p">:]</span> <span class="o">=</span> <span class="n">current_state</span>
+                    <span class="n">_accept</span><span class="p">[</span><span class="nb">iter</span><span class="p">]</span> <span class="o">=</span> <span class="mi">0</span>
+                    <span class="nb">iter</span> <span class="o">+=</span> <span class="mi">1</span>
+                    <span class="k">continue</span>
+            
+            <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">ln_target</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+                <span class="n">candidate_t</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">target</span><span class="p">(</span>
+                    <span class="n">candidate_state</span><span class="p">,</span> <span class="o">*</span><span class="bp">self</span><span class="o">.</span><span class="n">args_target</span><span class="p">,</span> <span class="o">**</span><span class="bp">self</span><span class="o">.</span><span class="n">kwgs_target</span><span class="p">)</span>
+                <span class="n">ln_candidate_t</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">maximum</span><span class="p">(</span><span class="n">candidate_t</span><span class="p">,</span> <span class="n">_min_float</span><span class="p">))</span>
+            <span class="k">else</span><span class="p">:</span>
+                <span class="n">ln_candidate_t</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">ln_target</span><span class="p">(</span>
+                    <span class="n">candidate_state</span><span class="p">,</span> <span class="o">*</span><span class="bp">self</span><span class="o">.</span><span class="n">args_target</span><span class="p">,</span> <span class="o">**</span><span class="bp">self</span><span class="o">.</span><span class="n">kwgs_target</span><span class="p">)</span>
+
+            <span class="n">diff_ln_t</span> <span class="o">=</span> <span class="n">ln_candidate_t</span> <span class="o">-</span> <span class="n">ln_current_t</span>
+
+            <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">symmetric</span><span class="p">:</span>
+                <span class="n">ln_accept</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">min</span><span class="p">(</span><span class="n">diff_ln_t</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
+            <span class="k">else</span><span class="p">:</span>
+                <span class="n">current_f</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">f_density</span><span class="p">(</span><span class="n">current_state</span><span class="p">,</span> <span class="n">candidate_state</span><span class="p">,</span>
+                    <span class="o">*</span><span class="bp">self</span><span class="o">.</span><span class="n">args_f_density</span><span class="p">,</span> <span class="o">**</span><span class="bp">self</span><span class="o">.</span><span class="n">kwgs_f_density</span><span class="p">)</span>
+                <span class="n">ln_current_f</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">maximum</span><span class="p">(</span><span class="n">current_f</span><span class="p">,</span> <span class="n">_min_float</span><span class="p">))</span>
+
+                <span class="n">candidate_f</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">f_density</span><span class="p">(</span><span class="n">candidate_state</span><span class="p">,</span> <span class="n">current_state</span><span class="p">,</span>
+                    <span class="o">*</span><span class="bp">self</span><span class="o">.</span><span class="n">args_f_density</span><span class="p">,</span> <span class="o">**</span><span class="bp">self</span><span class="o">.</span><span class="n">kwgs_f_density</span><span class="p">)</span>
+                <span class="n">ln_candidate_f</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">maximum</span><span class="p">(</span><span class="n">candidate_f</span><span class="p">,</span> <span class="n">_min_float</span><span class="p">))</span>
+                
+                <span class="n">diff_ln_f</span> <span class="o">=</span> <span class="n">ln_candidate_f</span> <span class="o">-</span> <span class="n">ln_current_f</span> 
+                <span class="n">ln_accept</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">min</span><span class="p">(</span><span class="n">diff_ln_t</span> <span class="o">-</span> <span class="n">diff_ln_f</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
+            
+            <span class="k">if</span> <span class="n">ln_accept</span> <span class="o">&gt;=</span> <span class="n">np</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">maximum</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">rng</span><span class="o">.</span><span class="n">random</span><span class="p">(),</span> <span class="n">_min_float</span><span class="p">)):</span>
+                <span class="n">current_state</span> <span class="o">=</span> <span class="n">candidate_state</span>
+                <span class="n">ln_current_t</span> <span class="o">=</span> <span class="n">ln_candidate_t</span>
+
+                <span class="n">_samples</span><span class="p">[</span><span class="nb">iter</span><span class="p">,</span> <span class="p">:]</span> <span class="o">=</span> <span class="n">candidate_state</span>
+                <span class="n">_accept</span><span class="p">[</span><span class="nb">iter</span><span class="p">]</span> <span class="o">=</span> <span class="mi">1</span>
+
+            <span class="k">else</span><span class="p">:</span>
+                <span class="n">_samples</span><span class="p">[</span><span class="nb">iter</span><span class="p">,</span> <span class="p">:]</span> <span class="o">=</span> <span class="n">current_state</span>
+                <span class="n">_accept</span><span class="p">[</span><span class="nb">iter</span><span class="p">]</span> <span class="o">=</span> <span class="mi">0</span>
+
+            <span class="nb">iter</span> <span class="o">+=</span> <span class="mi">1</span>
+        
+        <span class="n">mh_samples</span> <span class="o">=</span> <span class="n">_samples</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">nburn</span><span class="p">:</span><span class="n">niter</span><span class="p">:</span><span class="bp">self</span><span class="o">.</span><span class="n">nthin</span><span class="p">,</span> <span class="p">:]</span>
+        <span class="n">mh_accept</span> <span class="o">=</span> <span class="n">_accept</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">nburn</span><span class="p">:</span><span class="n">niter</span><span class="p">:</span><span class="bp">self</span><span class="o">.</span><span class="n">nthin</span><span class="p">]</span>
+
+        <span class="k">return</span> <span class="n">mh_samples</span><span class="p">,</span> <span class="n">mh_accept</span></div></div>
+</pre></div>
+
+           </div>
+          </div>
+          <footer>
+
+  <hr/>
+
+  <div role="contentinfo">
+    <p>&#169; Copyright 2023, Hu Zhao.</p>
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+    <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a>
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diff --git a/docs/source/_build/html/_modules/psimpy/sampler/saltelli.html b/docs/source/_build/html/_modules/psimpy/sampler/saltelli.html
new file mode 100644
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+<!DOCTYPE html>
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+             
+  <h1>Source code for psimpy.sampler.saltelli</h1><div class="highlight"><pre>
+<span></span><span class="kn">from</span> <span class="nn">SALib.sample</span> <span class="kn">import</span> <span class="n">saltelli</span>
+<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">from</span> <span class="nn">typing</span> <span class="kn">import</span> <span class="n">Union</span>
+<span class="kn">from</span> <span class="nn">beartype</span> <span class="kn">import</span> <span class="n">beartype</span>
+<span class="kn">from</span> <span class="nn">psimpy.utility</span> <span class="kn">import</span> <span class="n">check_bounds</span>
+
+<div class="viewcode-block" id="Saltelli"><a class="viewcode-back" href="../../../sampler/saltelli.html#psimpy.sampler.saltelli.Saltelli">[docs]</a><span class="k">class</span> <span class="nc">Saltelli</span><span class="p">:</span>
+    
+    <span class="nd">@beartype</span>
+    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span>
+        <span class="bp">self</span><span class="p">,</span> <span class="n">ndim</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">bounds</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
+        <span class="n">calc_second_order</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="kc">True</span><span class="p">,</span> <span class="n">skip_values</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">int</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span>
+        <span class="p">)</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
+        <span class="sd">&quot;&quot;&quot;Saltelli&#39;s version of Sobol&#39; sampling.</span>
+<span class="sd">        </span>
+<span class="sd">        Parameters</span>
+<span class="sd">        -------------</span>
+<span class="sd">        ndim : int</span>
+<span class="sd">            Dimension of parameters.</span>
+<span class="sd">        bounds : numpy array, optional</span>
+<span class="sd">            Upper and lower boundaries of each parameter. Shape :code:`(ndim, 2)`.</span>
+<span class="sd">            `bounds[:, 0]` corresponds to lower boundaries of each parameter and</span>
+<span class="sd">            `bounds[:, 1]` to upper boundaries of each parameter. </span>
+<span class="sd">        calc_second_order : bool, optional</span>
+<span class="sd">            If `True`, calculate second-order Sobol&#39; indices.</span>
+<span class="sd">            If `False`, second-order Sobol&#39; indices are not computed.</span>
+<span class="sd">        skip_values : int, optional</span>
+<span class="sd">            Number of points to skip in the Sobol&#39; sequence. It should be </span>
+<span class="sd">            ideally a value of base :math:`2`.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="n">bounds</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="n">bounds</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">]</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">ndim</span><span class="p">)])</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="n">check_bounds</span><span class="p">(</span><span class="n">ndim</span><span class="p">,</span> <span class="n">bounds</span><span class="p">)</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">problem</span> <span class="o">=</span> <span class="p">{</span>
+            <span class="s1">&#39;num_vars&#39;</span><span class="p">:</span> <span class="n">ndim</span><span class="p">,</span>
+            <span class="s1">&#39;names&#39;</span><span class="p">:</span> <span class="p">[</span><span class="sa">f</span><span class="s2">&quot;x</span><span class="si">{</span><span class="n">i</span><span class="si">}</span><span class="s2">&quot;</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">ndim</span><span class="p">)],</span>
+            <span class="s1">&#39;bounds&#39;</span><span class="p">:</span> <span class="n">bounds</span>
+        <span class="p">}</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">calc_second_order</span> <span class="o">=</span> <span class="n">calc_second_order</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">skip_values</span> <span class="o">=</span> <span class="n">skip_values</span>
+    
+<div class="viewcode-block" id="Saltelli.sample"><a class="viewcode-back" href="../../../sampler/saltelli.html#psimpy.sampler.saltelli.Saltelli.sample">[docs]</a>    <span class="k">def</span> <span class="nf">sample</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">nbase</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">:</span>
+        <span class="sd">&quot;&quot;&quot;Draw samples using Saltelli&#39;s extension of the Sobol&#39; sequence.</span>
+<span class="sd">        </span>
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        nbase : int</span>
+<span class="sd">            Number of base samples. Correspond to the parameter ``N`` of </span>
+<span class="sd">            :py:func:`SALib.sample.saltelli.sample`.</span>
+<span class="sd">        </span>
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        samples : numpy array</span>
+<span class="sd">            Shape of :code:`(nbase*(2*ndim+2), ndim)` if ``calc_second_order``</span>
+<span class="sd">            is `True`. Shape of :code:`(nbase*(ndim+2), ndim)` if</span>
+<span class="sd">            ``calc_second_order`` is `False`. </span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">samples</span> <span class="o">=</span> <span class="n">saltelli</span><span class="o">.</span><span class="n">sample</span><span class="p">(</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">problem</span><span class="p">,</span> <span class="n">nbase</span><span class="p">,</span> <span class="n">calc_second_order</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">calc_second_order</span><span class="p">,</span>
+            <span class="n">skip_values</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">skip_values</span><span class="p">)</span>
+        
+        <span class="k">return</span> <span class="n">samples</span></div></div>
+</pre></div>
+
+           </div>
+          </div>
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+
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+
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+  <h1>Source code for psimpy.sensitivity.sobol</h1><div class="highlight"><pre>
+<span></span><span class="kn">from</span> <span class="nn">SALib.analyze</span> <span class="kn">import</span> <span class="n">sobol</span>
+<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">from</span> <span class="nn">concurrent.futures</span> <span class="kn">import</span> <span class="n">ProcessPoolExecutor</span>
+<span class="kn">from</span> <span class="nn">scipy.stats</span> <span class="kn">import</span> <span class="n">norm</span>
+<span class="kn">from</span> <span class="nn">typing</span> <span class="kn">import</span> <span class="n">Union</span>
+<span class="kn">from</span> <span class="nn">beartype</span> <span class="kn">import</span> <span class="n">beartype</span>
+
+<div class="viewcode-block" id="SobolAnalyze"><a class="viewcode-back" href="../../../sensitivity/sobol.html#psimpy.sensitivity.sobol.SobolAnalyze">[docs]</a><span class="k">class</span> <span class="nc">SobolAnalyze</span><span class="p">:</span>
+
+    <span class="nd">@beartype</span>
+    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span>
+        <span class="bp">self</span><span class="p">,</span> <span class="n">ndim</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">Y</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="n">calc_second_order</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="kc">True</span><span class="p">,</span>
+        <span class="n">nresamples</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">100</span><span class="p">,</span> <span class="n">conf_level</span><span class="p">:</span> <span class="nb">float</span> <span class="o">=</span> <span class="mf">0.95</span><span class="p">,</span>
+        <span class="n">seed</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">int</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
+        <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Sobol&#39; sensitivity analysis.</span>
+<span class="sd">        This class is built based on :py:func:`SALib.analyze.sobol`.</span>
+<span class="sd">        </span>
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        ndim : int</span>
+<span class="sd">            Dimension of parameter ``x``.</span>
+<span class="sd">        Y : numpy array</span>
+<span class="sd">            Model outputs evaluated at varaible input points drawn by Saltelli</span>
+<span class="sd">            sampling. Shape of :code:`(nsaltelli, nrealizations)`. ``nsaltelli``</span>
+<span class="sd">            is the number of Saltelli sample points, and ``nrealizations`` is</span>
+<span class="sd">            the number of  realizations of model output at one input point.</span>
+<span class="sd">            More specially: :math:`nrealizations=1` for a deterministic model</span>
+<span class="sd">            which returns a scalar output at one input point,</span>
+<span class="sd">            and :math:`nrealizations&gt;1` for a stochastic model which returns</span>
+<span class="sd">            multiple realizations of a scalar output at one input point (such</span>
+<span class="sd">            as a Gaussian process model).</span>
+<span class="sd">            If :math:`nrealizations=1`, an array of shape :code:`(nsaltelli,)`</span>
+<span class="sd">            is also valid.</span>
+<span class="sd">        calc_second_order : bool, optional</span>
+<span class="sd">            If `True`, calculate secord order Sobol&#39; indices.</span>
+<span class="sd">        nresamples : int, optional</span>
+<span class="sd">            Size of bootstrap sampling.</span>
+<span class="sd">        conf_level : float, optional</span>
+<span class="sd">            Confidence interval level. Must be a value within the range</span>
+<span class="sd">            :math:`(0,1)`.</span>
+<span class="sd">        seed : int, optional</span>
+<span class="sd">            Seed to initialize the pseudo-random number generator.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">ndim</span> <span class="o">=</span> <span class="n">ndim</span>
+
+        <span class="k">if</span> <span class="ow">not</span> <span class="p">(</span><span class="n">Y</span><span class="o">.</span><span class="n">ndim</span> <span class="o">==</span> <span class="mi">1</span> <span class="ow">or</span> <span class="n">Y</span><span class="o">.</span><span class="n">ndim</span> <span class="o">==</span> <span class="mi">2</span><span class="p">):</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;Y must be a one or two dimensional numpy array&quot;</span><span class="p">)</span>
+        <span class="k">elif</span> <span class="n">Y</span><span class="o">.</span><span class="n">ndim</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
+            <span class="n">Y</span> <span class="o">=</span> <span class="n">Y</span><span class="o">.</span><span class="n">reshape</span><span class="p">((</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span>
+        
+        <span class="k">if</span> <span class="n">calc_second_order</span> <span class="ow">and</span> <span class="n">Y</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">%</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">ndim</span> <span class="o">+</span> <span class="mi">2</span><span class="p">)</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
+            <span class="n">nbase</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">Y</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">/</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">ndim</span> <span class="o">+</span> <span class="mi">2</span><span class="p">))</span>
+        <span class="k">elif</span> <span class="ow">not</span> <span class="n">calc_second_order</span> <span class="ow">and</span> <span class="n">Y</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">%</span> <span class="p">(</span><span class="n">ndim</span> <span class="o">+</span> <span class="mi">2</span><span class="p">)</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
+            <span class="n">nbase</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">Y</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">/</span> <span class="p">(</span><span class="n">ndim</span> <span class="o">+</span> <span class="mi">2</span><span class="p">))</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="k">raise</span> <span class="ne">RuntimeError</span><span class="p">(</span><span class="s2">&quot;Y does not match ndim and calc_second_order&quot;</span><span class="p">)</span>
+        
+        <span class="bp">self</span><span class="o">.</span><span class="n">Y</span> <span class="o">=</span> <span class="n">Y</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">nbase</span> <span class="o">=</span> <span class="n">nbase</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">nrealizations</span> <span class="o">=</span> <span class="n">Y</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">calc_second_order</span> <span class="o">=</span> <span class="n">calc_second_order</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">nresamples</span> <span class="o">=</span> <span class="n">nresamples</span>
+        
+        <span class="k">if</span> <span class="ow">not</span> <span class="p">(</span><span class="n">conf_level</span> <span class="o">&gt;</span> <span class="mi">0</span> <span class="ow">and</span> <span class="n">conf_level</span> <span class="o">&lt;</span> <span class="mi">1</span><span class="p">):</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;conf_level must be within 0 and 1&quot;</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">conf_level</span> <span class="o">=</span> <span class="n">conf_level</span>
+        
+        <span class="bp">self</span><span class="o">.</span><span class="n">rng</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">default_rng</span><span class="p">(</span><span class="n">seed</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">seed</span> <span class="o">=</span> <span class="n">seed</span>
+    
+<div class="viewcode-block" id="SobolAnalyze.run"><a class="viewcode-back" href="../../../sensitivity/sobol.html#psimpy.sensitivity.sobol.SobolAnalyze.run">[docs]</a>    <span class="nd">@beartype</span>
+    <span class="k">def</span> <span class="nf">run</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">mode</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">str</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
+        <span class="n">max_workers</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">int</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">dict</span><span class="p">[</span><span class="nb">str</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">]:</span>
+        <span class="sd">&quot;&quot;&quot;Perform Sobol&#39; analysis.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        mode : str, optional</span>
+<span class="sd">            `&#39;parallel&#39;` or `&#39;serial&#39;`. Run sobol&#39; analysis for each colomn of</span>
+<span class="sd">            ``Y`` in parallel or in serial. Only relevant when</span>
+<span class="sd">            :math:`nrealizations&gt;1`.</span>
+<span class="sd">        max_workers : int, optional</span>
+<span class="sd">            The maximum number of tasks running in parallel.</span>
+<span class="sd">            Default is the number of CPUs on the host.</span>
+<span class="sd">            Only relevant when :math:`nrealizations&gt;1`.</span>
+<span class="sd">        </span>
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        S_res : dict</span>
+<span class="sd">            Sobol&#39; sensitivity indices.</span>
+<span class="sd">            `S_res[&#39;S1&#39;]` - :class:`numpy.ndarray` of shape :code:`(ndim, 3)`,</span>
+<span class="sd">            first-order Sobol&#39; index, its std, and conf_level for each parameter.</span>
+<span class="sd">            `S_res[&#39;ST&#39;]` - :class:`numpy.ndarray` of shape :code:`(ndim, 3)`,</span>
+<span class="sd">            total-effect Sobol&#39; index, its std, and conf_level for each parameter.</span>
+<span class="sd">            `S_res[&#39;S2&#39;]` - :class:`numpy.ndarray` of shape</span>
+<span class="sd">            :code:`(ndim*(ndim-1)/2, 3)`, second-order Sobol&#39; index, its std,</span>
+<span class="sd">            and conf_level for each pair of parameters. </span>
+<span class="sd">            `S_res[&#39;S2&#39;]` is only available if ``calc_second_order`` is True.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="p">(</span><span class="n">mode</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">)</span> <span class="ow">and</span> <span class="p">(</span><span class="n">mode</span> <span class="ow">not</span> <span class="ow">in</span> <span class="p">[</span><span class="s2">&quot;parallel&quot;</span><span class="p">,</span> <span class="s2">&quot;serial&quot;</span><span class="p">]):</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span>
+                <span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="n">mode</span><span class="si">}</span><span class="s2"> is not supported. Choose &#39;parallel&#39; or &#39;serial&#39;&quot;</span><span class="p">)</span>
+
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">nrealizations</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
+            <span class="n">S_all</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_base_analyze</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">Y</span><span class="p">[:,</span><span class="mi">0</span><span class="p">])</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="k">if</span> <span class="n">mode</span> <span class="o">==</span> <span class="s2">&quot;parallel&quot;</span><span class="p">:</span>
+                <span class="n">S_all</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_parallel_run</span><span class="p">(</span><span class="n">max_workers</span><span class="p">)</span>
+            <span class="k">else</span><span class="p">:</span>
+                <span class="n">S_all</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_serial_run</span><span class="p">()</span>    
+                
+        <span class="n">z</span> <span class="o">=</span> <span class="n">norm</span><span class="o">.</span><span class="n">ppf</span><span class="p">(</span><span class="mf">0.5</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">conf_level</span><span class="o">/</span><span class="mi">2</span><span class="p">)</span>
+
+        <span class="n">S_res</span> <span class="o">=</span> <span class="p">{</span><span class="s1">&#39;S1&#39;</span> <span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="bp">self</span><span class="o">.</span><span class="n">ndim</span><span class="p">,</span><span class="mi">3</span><span class="p">)),</span> <span class="s1">&#39;ST&#39;</span> <span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="bp">self</span><span class="o">.</span><span class="n">ndim</span><span class="p">,</span><span class="mi">3</span><span class="p">))}</span>
+
+        <span class="n">S_res</span><span class="p">[</span><span class="s1">&#39;S1&#39;</span><span class="p">][:,</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">S_all</span><span class="p">[</span><span class="s1">&#39;S1&#39;</span><span class="p">],</span> <span class="n">axis</span><span class="o">=</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">))</span>
+        <span class="n">S_res</span><span class="p">[</span><span class="s1">&#39;S1&#39;</span><span class="p">][:,</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">std</span><span class="p">(</span><span class="n">S_all</span><span class="p">[</span><span class="s1">&#39;S1&#39;</span><span class="p">],</span> <span class="n">axis</span><span class="o">=</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">))</span>
+        <span class="n">S_res</span><span class="p">[</span><span class="s1">&#39;S1&#39;</span><span class="p">][:,</span><span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="n">S_res</span><span class="p">[</span><span class="s1">&#39;S1&#39;</span><span class="p">][:,</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">z</span>
+        
+        <span class="n">S_res</span><span class="p">[</span><span class="s1">&#39;ST&#39;</span><span class="p">][:,</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">S_all</span><span class="p">[</span><span class="s1">&#39;ST&#39;</span><span class="p">],</span> <span class="n">axis</span><span class="o">=</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">))</span>
+        <span class="n">S_res</span><span class="p">[</span><span class="s1">&#39;ST&#39;</span><span class="p">][:,</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">std</span><span class="p">(</span><span class="n">S_all</span><span class="p">[</span><span class="s1">&#39;ST&#39;</span><span class="p">],</span> <span class="n">axis</span><span class="o">=</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">))</span>
+        <span class="n">S_res</span><span class="p">[</span><span class="s1">&#39;ST&#39;</span><span class="p">][:,</span><span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="n">S_res</span><span class="p">[</span><span class="s1">&#39;ST&#39;</span><span class="p">][:,</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">z</span>
+
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">calc_second_order</span><span class="p">:</span>
+            <span class="n">S_res</span><span class="o">.</span><span class="n">update</span><span class="p">(</span>
+                <span class="p">{</span><span class="s1">&#39;S2&#39;</span> <span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="nb">int</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ndim</span> <span class="o">*</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ndim</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">/</span> <span class="mi">2</span><span class="p">),</span> <span class="mi">3</span><span class="p">))}</span>
+            <span class="p">)</span>
+            <span class="n">S_res</span><span class="p">[</span><span class="s1">&#39;S2&#39;</span><span class="p">][:,</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">S_all</span><span class="p">[</span><span class="s1">&#39;S2&#39;</span><span class="p">],</span> <span class="n">axis</span><span class="o">=</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">))</span>
+            <span class="n">S_res</span><span class="p">[</span><span class="s1">&#39;S2&#39;</span><span class="p">][:,</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">std</span><span class="p">(</span><span class="n">S_all</span><span class="p">[</span><span class="s1">&#39;S2&#39;</span><span class="p">],</span> <span class="n">axis</span><span class="o">=</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">))</span>
+            <span class="n">S_res</span><span class="p">[</span><span class="s1">&#39;S2&#39;</span><span class="p">][:,</span><span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="n">S_res</span><span class="p">[</span><span class="s1">&#39;S2&#39;</span><span class="p">][:,</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">z</span>
+        
+        <span class="k">return</span> <span class="n">S_res</span></div>
+
+    
+    <span class="k">def</span> <span class="nf">_serial_run</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+        <span class="sd">&quot;&quot;&quot;Run Sobol&#39; analysis for each colomn of ``Y`` in serial.&quot;&quot;&quot;</span>
+        <span class="n">S_all</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_create_S_dict</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">nrealizations</span><span class="p">)</span>
+
+        <span class="k">for</span> <span class="n">nr</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">nrealizations</span><span class="p">):</span>
+            <span class="n">S</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_base_analyze</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">Y</span><span class="p">[:,</span><span class="n">nr</span><span class="p">])</span>
+            <span class="n">S_all</span><span class="p">[</span><span class="s1">&#39;S1&#39;</span><span class="p">][:,:,</span><span class="n">nr</span><span class="p">]</span> <span class="o">=</span> <span class="n">S</span><span class="p">[</span><span class="s1">&#39;S1&#39;</span><span class="p">][:,:,</span><span class="mi">0</span><span class="p">]</span>
+            <span class="n">S_all</span><span class="p">[</span><span class="s1">&#39;ST&#39;</span><span class="p">][:,:,</span><span class="n">nr</span><span class="p">]</span> <span class="o">=</span> <span class="n">S</span><span class="p">[</span><span class="s1">&#39;ST&#39;</span><span class="p">][:,:,</span><span class="mi">0</span><span class="p">]</span>
+            <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">calc_second_order</span><span class="p">:</span>
+                <span class="n">S_all</span><span class="p">[</span><span class="s1">&#39;S2&#39;</span><span class="p">][:,:,</span><span class="n">nr</span><span class="p">]</span> <span class="o">=</span> <span class="n">S</span><span class="p">[</span><span class="s1">&#39;S2&#39;</span><span class="p">][:,:,</span><span class="mi">0</span><span class="p">]</span>
+        
+        <span class="k">return</span> <span class="n">S_all</span>
+            
+
+    <span class="k">def</span> <span class="nf">_parallel_run</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">max_workers</span><span class="p">):</span>
+        <span class="sd">&quot;&quot;&quot;Run Sobol&#39; analysis for each colomn of ``Y`` in parallel.&quot;&quot;&quot;</span>
+        <span class="n">S_all</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_create_S_dict</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">nrealizations</span><span class="p">)</span>
+
+        <span class="k">with</span> <span class="n">ProcessPoolExecutor</span><span class="p">(</span><span class="n">max_workers</span><span class="o">=</span><span class="n">max_workers</span><span class="p">)</span> <span class="k">as</span> <span class="n">executor</span><span class="p">:</span>
+            <span class="n">futures</span> <span class="o">=</span> <span class="p">[</span><span class="n">executor</span><span class="o">.</span><span class="n">submit</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_base_analyze</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">Y</span><span class="p">[:,</span><span class="n">nr</span><span class="p">])</span>
+                <span class="k">for</span> <span class="n">nr</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">nrealizations</span><span class="p">)]</span>
+            
+            <span class="k">for</span> <span class="n">nr</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">nrealizations</span><span class="p">):</span>
+                <span class="n">S</span> <span class="o">=</span> <span class="n">futures</span><span class="p">[</span><span class="n">nr</span><span class="p">]</span><span class="o">.</span><span class="n">result</span><span class="p">()</span>
+                <span class="n">S_all</span><span class="p">[</span><span class="s1">&#39;S1&#39;</span><span class="p">][:,:,</span><span class="n">nr</span><span class="p">]</span> <span class="o">=</span> <span class="n">S</span><span class="p">[</span><span class="s1">&#39;S1&#39;</span><span class="p">][:,:,</span><span class="mi">0</span><span class="p">]</span>
+                <span class="n">S_all</span><span class="p">[</span><span class="s1">&#39;ST&#39;</span><span class="p">][:,:,</span><span class="n">nr</span><span class="p">]</span> <span class="o">=</span> <span class="n">S</span><span class="p">[</span><span class="s1">&#39;ST&#39;</span><span class="p">][:,:,</span><span class="mi">0</span><span class="p">]</span>
+                <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">calc_second_order</span><span class="p">:</span>
+                    <span class="n">S_all</span><span class="p">[</span><span class="s1">&#39;S2&#39;</span><span class="p">][:,:,</span><span class="n">nr</span><span class="p">]</span> <span class="o">=</span> <span class="n">S</span><span class="p">[</span><span class="s1">&#39;S2&#39;</span><span class="p">][:,:,</span><span class="mi">0</span><span class="p">]</span>
+        
+        <span class="k">return</span> <span class="n">S_all</span>
+
+    
+    <span class="k">def</span> <span class="nf">_base_analyze</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">y</span><span class="p">):</span>
+        <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Perform Sobol&#39; sensitivity analysis for a deterministic model.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        y : numpy array</span>
+<span class="sd">            Model outputs evaluated at varaible input points drawn by Saltelli</span>
+<span class="sd">            sampling. 1d array of shape :code:`(nsaltelli, )`.</span>
+<span class="sd">        </span>
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        S: dict</span>
+<span class="sd">            Sobol&#39;s sensitivity indices.</span>
+<span class="sd">            `S[&#39;S1&#39;]` - :class:`numpy.ndarray` of shape</span>
+<span class="sd">            :code:`(ndim, nresamples+1, 1)`, first-order Sobol&#39; indices of</span>
+<span class="sd">            each parameter.</span>
+<span class="sd">            `S[&#39;ST&#39;]` - :class:`numpy.ndarray` of shape</span>
+<span class="sd">            :code:`(ndim, nresamples+1, 1)`, total-effect Sobol&#39; indices of</span>
+<span class="sd">            each parameter.</span>
+<span class="sd">            `S[&#39;S2&#39;]` - :class:`numpy.ndarray` of shape</span>
+<span class="sd">            :code:`(ndim*(ndim-1)/2, nresamples+1, 1)`, second-order Sobol&#39;</span>
+<span class="sd">            indices for each pair of parameters.</span>
+<span class="sd">            `S[&#39;S2&#39;]` is only available if ``calc_second_order`` is True.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">S</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_create_S_dict</span><span class="p">(</span><span class="n">nrealizations</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
+        
+        <span class="k">if</span> <span class="n">y</span><span class="o">.</span><span class="n">std</span><span class="p">()</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
+            <span class="k">return</span> <span class="n">S</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="n">y</span> <span class="o">=</span> <span class="p">(</span><span class="n">y</span> <span class="o">-</span> <span class="n">y</span><span class="o">.</span><span class="n">mean</span><span class="p">())</span> <span class="o">/</span> <span class="n">y</span><span class="o">.</span><span class="n">std</span><span class="p">()</span>
+        
+        <span class="n">A</span><span class="p">,</span> <span class="n">B</span><span class="p">,</span> <span class="n">AB</span><span class="p">,</span> <span class="n">BA</span> <span class="o">=</span> <span class="n">sobol</span><span class="o">.</span><span class="n">separate_output_values</span><span class="p">(</span>
+            <span class="n">y</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">ndim</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">nbase</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">calc_second_order</span><span class="p">)</span>
+        <span class="n">r</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">rng</span><span class="o">.</span><span class="n">integers</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">nbase</span><span class="p">,</span> <span class="n">size</span><span class="o">=</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">nbase</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">nresamples</span><span class="p">))</span>
+
+        <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ndim</span><span class="p">):</span>
+            <span class="n">S</span><span class="p">[</span><span class="s1">&#39;S1&#39;</span><span class="p">][</span><span class="n">j</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">sobol</span><span class="o">.</span><span class="n">first_order</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">AB</span><span class="p">[:,</span> <span class="n">j</span><span class="p">],</span> <span class="n">B</span><span class="p">)</span>
+            <span class="n">S</span><span class="p">[</span><span class="s1">&#39;ST&#39;</span><span class="p">][</span><span class="n">j</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">sobol</span><span class="o">.</span><span class="n">total_order</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">AB</span><span class="p">[:,</span> <span class="n">j</span><span class="p">],</span> <span class="n">B</span><span class="p">)</span>
+
+            <span class="n">S</span><span class="p">[</span><span class="s1">&#39;S1&#39;</span><span class="p">][</span><span class="n">j</span><span class="p">,</span><span class="mi">1</span><span class="p">:,</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">sobol</span><span class="o">.</span><span class="n">first_order</span><span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="n">r</span><span class="p">],</span> <span class="n">AB</span><span class="p">[</span><span class="n">r</span><span class="p">,</span> <span class="n">j</span><span class="p">],</span> <span class="n">B</span><span class="p">[</span><span class="n">r</span><span class="p">])</span>
+            <span class="n">S</span><span class="p">[</span><span class="s1">&#39;ST&#39;</span><span class="p">][</span><span class="n">j</span><span class="p">,</span><span class="mi">1</span><span class="p">:,</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">sobol</span><span class="o">.</span><span class="n">total_order</span><span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="n">r</span><span class="p">],</span> <span class="n">AB</span><span class="p">[</span><span class="n">r</span><span class="p">,</span> <span class="n">j</span><span class="p">],</span> <span class="n">B</span><span class="p">[</span><span class="n">r</span><span class="p">])</span>
+        
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">calc_second_order</span><span class="p">:</span>
+            <span class="n">s2_sequence</span> <span class="o">=</span> <span class="mi">0</span>
+            <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ndim</span><span class="p">):</span>
+                <span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">j</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">ndim</span><span class="p">):</span>
+                    <span class="n">S</span><span class="p">[</span><span class="s1">&#39;S2&#39;</span><span class="p">][</span><span class="n">s2_sequence</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">sobol</span><span class="o">.</span><span class="n">second_order</span><span class="p">(</span>
+                        <span class="n">A</span><span class="p">,</span> <span class="n">AB</span><span class="p">[:,</span> <span class="n">j</span><span class="p">],</span> <span class="n">AB</span><span class="p">[:,</span> <span class="n">k</span><span class="p">],</span> <span class="n">BA</span><span class="p">[:,</span> <span class="n">j</span><span class="p">],</span> <span class="n">B</span><span class="p">)</span>
+                    <span class="n">S</span><span class="p">[</span><span class="s1">&#39;S2&#39;</span><span class="p">][</span><span class="n">s2_sequence</span><span class="p">,</span><span class="mi">1</span><span class="p">:,</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">sobol</span><span class="o">.</span><span class="n">second_order</span><span class="p">(</span>
+                        <span class="n">A</span><span class="p">[</span><span class="n">r</span><span class="p">],</span> <span class="n">AB</span><span class="p">[</span><span class="n">r</span><span class="p">,</span> <span class="n">j</span><span class="p">],</span> <span class="n">AB</span><span class="p">[</span><span class="n">r</span><span class="p">,</span> <span class="n">k</span><span class="p">],</span> <span class="n">BA</span><span class="p">[</span><span class="n">r</span><span class="p">,</span> <span class="n">j</span><span class="p">],</span> <span class="n">B</span><span class="p">[</span><span class="n">r</span><span class="p">])</span>
+                    <span class="n">s2_sequence</span> <span class="o">+=</span> <span class="mi">1</span>
+        
+        <span class="k">return</span> <span class="n">S</span>
+
+    <span class="k">def</span> <span class="nf">_create_S_dict</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">nrealizations</span><span class="p">):</span>
+        <span class="sd">&quot;&quot;&quot;Create dict to store results.&quot;&quot;&quot;</span>
+        <span class="n">S</span> <span class="o">=</span> <span class="p">{</span>
+            <span class="s1">&#39;S1&#39;</span> <span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="bp">self</span><span class="o">.</span><span class="n">ndim</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">nresamples</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">nrealizations</span><span class="p">)),</span>
+            <span class="s1">&#39;ST&#39;</span> <span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="bp">self</span><span class="o">.</span><span class="n">ndim</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">nresamples</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">nrealizations</span><span class="p">))</span>
+            <span class="p">}</span>
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">calc_second_order</span><span class="p">:</span>
+            <span class="n">S</span><span class="o">.</span><span class="n">update</span><span class="p">(</span>
+                <span class="p">{</span><span class="s1">&#39;S2&#39;</span> <span class="p">:</span> 
+                <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span>
+                    <span class="nb">int</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ndim</span> <span class="o">*</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ndim</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">/</span> <span class="mi">2</span><span class="p">),</span>
+                    <span class="bp">self</span><span class="o">.</span><span class="n">nresamples</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span>
+                    <span class="n">nrealizations</span><span class="p">))</span>
+                <span class="p">}</span>
+            <span class="p">)</span>
+
+        <span class="k">return</span> <span class="n">S</span></div>
+
+</pre></div>
+
+           </div>
+          </div>
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+
+  <hr/>
+
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+    <p>&#169; Copyright 2023, Hu Zhao.</p>
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diff --git a/docs/source/_build/html/_modules/psimpy/simulator/mass_point_model.html b/docs/source/_build/html/_modules/psimpy/simulator/mass_point_model.html
new file mode 100644
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+++ b/docs/source/_build/html/_modules/psimpy/simulator/mass_point_model.html
@@ -0,0 +1,378 @@
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+             
+  <h1>Source code for psimpy.simulator.mass_point_model</h1><div class="highlight"><pre>
+<span></span><span class="kn">import</span> <span class="nn">os</span>
+<span class="kn">import</span> <span class="nn">math</span>
+<span class="kn">import</span> <span class="nn">linecache</span>
+<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">from</span> <span class="nn">scipy.integrate</span> <span class="kn">import</span> <span class="n">ode</span>
+<span class="kn">from</span> <span class="nn">scipy.interpolate</span> <span class="kn">import</span> <span class="n">interp2d</span>
+<span class="kn">from</span> <span class="nn">typing</span> <span class="kn">import</span> <span class="n">Union</span>
+<span class="kn">from</span> <span class="nn">beartype</span> <span class="kn">import</span> <span class="n">beartype</span>
+
+<div class="viewcode-block" id="MassPointModel"><a class="viewcode-back" href="../../../simulator/mass_point_model.html#psimpy.simulator.mass_point_model.MassPointModel">[docs]</a><span class="k">class</span> <span class="nc">MassPointModel</span><span class="p">:</span>
+
+    <span class="sd">&quot;&quot;&quot;Simulate the movement of a masspoint on a topography.&quot;&quot;&quot;</span>
+    
+    <span class="nd">@staticmethod</span>
+    <span class="k">def</span> <span class="nf">_preprocess</span><span class="p">(</span><span class="n">elevation</span><span class="p">,</span> <span class="n">x0</span><span class="p">,</span> <span class="n">y0</span><span class="p">):</span>
+        <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Preprocess input data.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        elevation : str</span>
+<span class="sd">            Name of the elevation raster file, in ESRI ascii format, including</span>
+<span class="sd">            the path.</span>
+<span class="sd">        x0 : float or int</span>
+<span class="sd">            x coordinate of initial position.</span>
+<span class="sd">        y0 : float or int</span>
+<span class="sd">            y coordinate of initial position.</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        fgrad_x : Callable</span>
+<span class="sd">            Call with :code:`fgrad_x(x, y)`. Return first order partial</span>
+<span class="sd">            derivative of ``elevation`` with respect to `x` at location</span>
+<span class="sd">            `(x, y)`.</span>
+<span class="sd">        fgrad_y : callable</span>
+<span class="sd">            Call with :code:`fgrad_y(x, y)`. Return first order partial</span>
+<span class="sd">            derivative of ``elevation`` with respect to `y` at location</span>
+<span class="sd">            `(x, y)`.</span>
+<span class="sd">        fgrad_xx : Callable</span>
+<span class="sd">            Call with :code:`fgrad_xx(x, y)`. Return second order partial</span>
+<span class="sd">            derivative of ``elevation`` with respect to `x` at location `(x, y)`.</span>
+<span class="sd">        fgrad_yy : Callable</span>
+<span class="sd">            Call with :code:`fgrad_yy(x, y)`. Return second order partial</span>
+<span class="sd">            derivative of ``elevation`` with respect to `y` at location `(x, y)`.</span>
+<span class="sd">        fgrad_xy : Callable</span>
+<span class="sd">            Call with :code:`fgrad_xy(x ,y)`. Return second order partial</span>
+<span class="sd">            derivative of ``elevation`` with respect to `x` and `y` at location</span>
+<span class="sd">            `(x, y)`.</span>
+<span class="sd">        &quot;&quot;&quot;</span>        
+        <span class="k">if</span> <span class="ow">not</span> <span class="n">os</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">exists</span><span class="p">(</span><span class="n">elevation</span><span class="p">):</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="n">elevation</span><span class="si">}</span><span class="s2"> does not exist&quot;</span><span class="p">)</span>
+
+        <span class="n">header</span> <span class="o">=</span> <span class="p">[</span><span class="n">linecache</span><span class="o">.</span><span class="n">getline</span><span class="p">(</span><span class="n">elevation</span><span class="p">,</span> <span class="n">i</span><span class="p">)</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="mi">6</span><span class="p">)]</span>
+        <span class="n">header_values</span> <span class="o">=</span> <span class="p">[</span><span class="nb">float</span><span class="p">(</span><span class="n">h</span><span class="o">.</span><span class="n">split</span><span class="p">()[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">strip</span><span class="p">())</span> <span class="k">for</span> <span class="n">h</span> <span class="ow">in</span> <span class="n">header</span><span class="p">]</span>
+        <span class="n">ncols</span><span class="p">,</span> <span class="n">nrows</span><span class="p">,</span> <span class="n">xll</span><span class="p">,</span> <span class="n">yll</span><span class="p">,</span> <span class="n">cellsize</span> <span class="o">=</span> <span class="n">header_values</span>
+        <span class="n">ncols</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">ncols</span><span class="p">)</span>
+        <span class="n">nrows</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">nrows</span><span class="p">)</span>
+
+        <span class="n">x_values</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">xll</span><span class="p">,</span> <span class="n">xll</span><span class="o">+</span><span class="p">(</span><span class="n">cellsize</span><span class="o">*</span><span class="n">ncols</span><span class="p">),</span> <span class="n">cellsize</span><span class="p">)</span>
+        <span class="n">y_values</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">yll</span><span class="p">,</span> <span class="n">yll</span><span class="o">+</span><span class="p">(</span><span class="n">cellsize</span><span class="o">*</span><span class="n">nrows</span><span class="p">),</span> <span class="n">cellsize</span><span class="p">)</span>
+
+        <span class="k">if</span> <span class="ow">not</span> <span class="nb">all</span><span class="p">([</span><span class="n">x0</span><span class="o">&gt;</span><span class="n">x_values</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">x0</span><span class="o">&lt;</span><span class="n">x_values</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="n">y0</span><span class="o">&gt;</span><span class="n">y_values</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span>
+            <span class="n">y0</span><span class="o">&lt;</span><span class="n">y_values</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]]):</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span>
+                <span class="s2">&quot;x0 and y0 must be within the boundary of elevation&quot;</span><span class="p">)</span>
+        
+        <span class="n">z_values</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">loadtxt</span><span class="p">(</span><span class="n">elevation</span><span class="p">,</span> <span class="n">skiprows</span><span class="o">=</span><span class="mi">6</span><span class="p">)</span>
+        <span class="n">z_values</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">rot90</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">transpose</span><span class="p">(</span><span class="n">z_values</span><span class="p">))</span>
+        
+        <span class="n">dzdx</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">gradient</span><span class="p">(</span><span class="n">z_values</span><span class="p">,</span> <span class="n">x_values</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
+        <span class="n">dzdy</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">gradient</span><span class="p">(</span><span class="n">z_values</span><span class="p">,</span> <span class="n">y_values</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
+        
+        <span class="n">dzdxx</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">gradient</span><span class="p">(</span><span class="n">dzdx</span><span class="p">,</span> <span class="n">x_values</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
+        <span class="n">dzdyy</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">gradient</span><span class="p">(</span><span class="n">dzdy</span><span class="p">,</span> <span class="n">y_values</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
+        <span class="n">dzdxy</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">gradient</span><span class="p">(</span><span class="n">dzdx</span><span class="p">,</span> <span class="n">y_values</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
+        
+        <span class="n">fgrad_x</span> <span class="o">=</span> <span class="n">interp2d</span><span class="p">(</span><span class="n">x_values</span><span class="p">,</span> <span class="n">y_values</span><span class="p">,</span> <span class="n">dzdx</span><span class="p">)</span>
+        <span class="n">fgrad_y</span> <span class="o">=</span> <span class="n">interp2d</span><span class="p">(</span><span class="n">x_values</span><span class="p">,</span> <span class="n">y_values</span><span class="p">,</span> <span class="n">dzdy</span><span class="p">)</span>
+        <span class="n">fgrad_xx</span> <span class="o">=</span> <span class="n">interp2d</span><span class="p">(</span><span class="n">x_values</span><span class="p">,</span> <span class="n">y_values</span><span class="p">,</span> <span class="n">dzdxx</span><span class="p">)</span>
+        <span class="n">fgrad_yy</span> <span class="o">=</span> <span class="n">interp2d</span><span class="p">(</span><span class="n">x_values</span><span class="p">,</span> <span class="n">y_values</span><span class="p">,</span> <span class="n">dzdyy</span><span class="p">)</span>
+        <span class="n">fgrad_xy</span> <span class="o">=</span> <span class="n">interp2d</span><span class="p">(</span><span class="n">x_values</span><span class="p">,</span> <span class="n">y_values</span><span class="p">,</span> <span class="n">dzdxy</span><span class="p">)</span>
+
+        <span class="k">return</span> <span class="n">fgrad_x</span><span class="p">,</span> <span class="n">fgrad_y</span><span class="p">,</span> <span class="n">fgrad_xx</span><span class="p">,</span> <span class="n">fgrad_yy</span><span class="p">,</span> <span class="n">fgrad_xy</span>
+
+    
+    <span class="nd">@staticmethod</span>
+    <span class="k">def</span> <span class="nf">_mass_point_model</span><span class="p">(</span>
+        <span class="n">t</span><span class="p">,</span> <span class="n">alpha</span><span class="p">,</span> <span class="n">coulomb_friction</span><span class="p">,</span> <span class="n">turbulent_friction</span><span class="p">,</span> <span class="n">fgrad_x</span><span class="p">,</span> <span class="n">fgrad_y</span><span class="p">,</span>
+        <span class="n">fgrad_xx</span><span class="p">,</span> <span class="n">fgrad_yy</span><span class="p">,</span> <span class="n">fgrad_xy</span><span class="p">,</span> <span class="n">g</span><span class="p">,</span> <span class="n">curvature</span><span class="p">):</span>
+        <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Define mass point model (3d) which serves as the callable function</span>
+<span class="sd">        :code:`f(t,alpha,*f_args)` in :class:`scipy.integrate.ode(f)`.</span>
+
+<span class="sd">        Parameters:</span>
+<span class="sd">        -----------</span>
+<span class="sd">        t : float or int</span>
+<span class="sd">            Time in seconds.</span>
+<span class="sd">        alpha : list</span>
+<span class="sd">            Contains `x`, `y`, `ux`, `uy` at time `t`, i.e.,</span>
+<span class="sd">            `[x(t), y(t), ux(t), uy(t)]`.</span>
+<span class="sd">        coulomb_friction : float</span>
+<span class="sd">            Dry Coulomb friction coefficient.</span>
+<span class="sd">        turbulent_friction : float or int</span>
+<span class="sd">            Turbulent friction coefficient, in :math:`m/s^2`.</span>
+<span class="sd">        fgrad_x : Callable</span>
+<span class="sd">            Call with :code:`fgrad_x(x, y)`. Return first order partial</span>
+<span class="sd">            derivative of ``elevation`` with respect to `x` at location `(x, y)`.</span>
+<span class="sd">        fgrad_y : Callable</span>
+<span class="sd">            Call with :code:`fgrad_y(x, y)`. Return first order partial</span>
+<span class="sd">            derivative of ``elevation`` with respect to `y` at location `(x, y)`.</span>
+<span class="sd">        fgrad_xx : Callable</span>
+<span class="sd">            Call with :code:`fgrad_xx(x, y)`. Return second order partial</span>
+<span class="sd">            derivative of ``elevation`` with respect to `x` at location `(x, y)`.</span>
+<span class="sd">        fgrad_yy : Callable</span>
+<span class="sd">            Call with :code:`fgrad_yy(x, y)`. Return second order partial</span>
+<span class="sd">            derivative of ``elevation`` with respect to `y` at location `(x, y)`.</span>
+<span class="sd">        fgrad_xy : Callable</span>
+<span class="sd">            Call with :code:`fgrad_xy(x ,y)`. Return second order partial</span>
+<span class="sd">            derivative of ``elevation`` with respect to `x` and `y` at location</span>
+<span class="sd">            `(x, y)`.</span>
+<span class="sd">        g : float or int</span>
+<span class="sd">            Gravity acceleration, in :math:`m/s^2`.</span>
+<span class="sd">        curvature : bool</span>
+<span class="sd">            If `True`, take the curvature effect into account.</span>
+<span class="sd">        </span>
+<span class="sd">        Return:</span>
+<span class="sd">        -------</span>
+<span class="sd">        dalphadt : numpy array </span>
+<span class="sd">            Right hand side of the mass point model.</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">ux</span><span class="p">,</span> <span class="n">uy</span> <span class="o">=</span> <span class="n">alpha</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">alpha</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">alpha</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="n">alpha</span><span class="p">[</span><span class="mi">3</span><span class="p">]</span>
+
+        <span class="n">gradx</span><span class="p">,</span> <span class="n">grady</span><span class="p">,</span> <span class="n">gradxx</span><span class="p">,</span> <span class="n">gradyy</span><span class="p">,</span> <span class="n">gradxy</span> <span class="o">=</span> <span class="n">fgrad_x</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n">y</span><span class="p">),</span> <span class="n">fgrad_y</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n">y</span><span class="p">),</span> \
+            <span class="n">fgrad_xx</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n">y</span><span class="p">),</span> <span class="n">fgrad_yy</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n">y</span><span class="p">),</span> <span class="n">fgrad_xy</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n">y</span><span class="p">)</span>
+
+        <span class="n">sqrt_x</span> <span class="o">=</span> <span class="n">math</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="n">gradx</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span>
+        <span class="n">sqrt_y</span> <span class="o">=</span> <span class="n">math</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="n">grady</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span>
+        <span class="n">sqrt_xy</span> <span class="o">=</span> <span class="n">math</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="n">gradx</span><span class="o">**</span><span class="mi">2</span> <span class="o">+</span> <span class="n">grady</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span>
+
+        <span class="n">gx</span> <span class="o">=</span> <span class="n">gradx</span> <span class="o">*</span> <span class="p">(</span><span class="o">-</span><span class="n">g</span><span class="p">)</span> <span class="o">/</span> <span class="n">sqrt_x</span>
+        <span class="n">gy</span> <span class="o">=</span> <span class="n">grady</span> <span class="o">*</span> <span class="p">(</span><span class="o">-</span><span class="n">g</span><span class="p">)</span> <span class="o">/</span> <span class="n">sqrt_y</span>
+        <span class="n">gn</span> <span class="o">=</span> <span class="n">g</span> <span class="o">/</span> <span class="n">sqrt_xy</span>
+
+        <span class="k">if</span> <span class="n">curvature</span><span class="p">:</span>
+            <span class="n">kx</span> <span class="o">=</span> <span class="n">gradxx</span> <span class="o">/</span> <span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="n">gradx</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="o">/</span> <span class="n">sqrt_xy</span>
+            <span class="n">kxy</span> <span class="o">=</span> <span class="n">gradxy</span> <span class="o">/</span> <span class="n">sqrt_x</span> <span class="o">/</span> <span class="n">sqrt_y</span> <span class="o">/</span> <span class="n">sqrt_xy</span>
+            <span class="n">ky</span> <span class="o">=</span> <span class="n">gradyy</span> <span class="o">/</span> <span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="n">grady</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="o">/</span> <span class="n">sqrt_xy</span>
+            <span class="n">uku</span> <span class="o">=</span> <span class="n">kx</span><span class="o">*</span><span class="n">ux</span><span class="o">**</span><span class="mi">2</span> <span class="o">+</span> <span class="mi">2</span><span class="o">*</span><span class="n">kxy</span><span class="o">*</span><span class="n">ux</span><span class="o">*</span><span class="n">uy</span> <span class="o">+</span> <span class="n">ky</span><span class="o">*</span><span class="n">uy</span><span class="o">**</span><span class="mi">2</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="n">uku</span> <span class="o">=</span> <span class="mi">0</span>
+        
+        <span class="n">u</span> <span class="o">=</span> <span class="n">math</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">ux</span><span class="o">**</span><span class="mi">2</span> <span class="o">+</span> <span class="n">uy</span><span class="o">**</span><span class="mi">2</span> <span class="o">+</span> <span class="mi">2</span><span class="o">*</span><span class="n">ux</span><span class="o">*</span><span class="n">uy</span><span class="o">*</span><span class="n">gradx</span><span class="o">*</span><span class="n">grady</span><span class="o">/</span><span class="n">sqrt_x</span><span class="o">/</span><span class="n">sqrt_y</span><span class="p">)</span>
+        
+        <span class="n">dalphadt</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">alpha</span><span class="p">))</span>
+
+        <span class="n">dalphadt</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">ux</span> <span class="o">/</span> <span class="n">sqrt_x</span>
+        <span class="n">dalphadt</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">uy</span> <span class="o">/</span> <span class="n">sqrt_y</span>
+
+        <span class="k">if</span> <span class="n">u</span> <span class="o">!=</span> <span class="mi">0</span><span class="p">:</span>
+            <span class="n">friction</span> <span class="o">=</span> <span class="n">coulomb_friction</span><span class="o">*</span><span class="p">(</span><span class="n">gn</span><span class="o">+</span><span class="n">uku</span><span class="p">)</span> <span class="o">+</span> <span class="n">g</span><span class="o">*</span><span class="n">u</span><span class="o">**</span><span class="mi">2</span><span class="o">/</span><span class="n">turbulent_friction</span>
+            <span class="n">dalphadt</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="n">gx</span> <span class="o">-</span> <span class="p">(</span><span class="n">ux</span><span class="o">/</span><span class="n">u</span><span class="p">)</span><span class="o">*</span><span class="n">friction</span>
+            <span class="n">dalphadt</span><span class="p">[</span><span class="mi">3</span><span class="p">]</span> <span class="o">=</span> <span class="n">gy</span> <span class="o">-</span> <span class="p">(</span><span class="n">uy</span><span class="o">/</span><span class="n">u</span><span class="p">)</span><span class="o">*</span><span class="n">friction</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="n">friction</span> <span class="o">=</span> <span class="n">coulomb_friction</span><span class="o">*</span><span class="n">gn</span>
+            <span class="n">dalphadt</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="n">gx</span> <span class="o">+</span> <span class="n">friction</span><span class="o">*</span><span class="n">gradx</span><span class="o">*</span><span class="p">(</span><span class="mi">1</span><span class="o">+</span><span class="n">gradx</span><span class="o">**</span><span class="mi">2</span><span class="o">+</span><span class="n">grady</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span><span class="o">/</span><span class="n">sqrt_x</span><span class="o">/</span>   \
+                <span class="n">math</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">gradx</span><span class="o">**</span><span class="mi">2</span><span class="o">+</span><span class="n">grady</span><span class="o">**</span><span class="mi">2</span><span class="o">+</span><span class="p">(</span><span class="n">gradx</span><span class="o">**</span><span class="mi">2</span><span class="o">+</span><span class="n">grady</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span>
+            <span class="n">dalphadt</span><span class="p">[</span><span class="mi">3</span><span class="p">]</span> <span class="o">=</span> <span class="n">gy</span> <span class="o">+</span> <span class="n">friction</span><span class="o">*</span><span class="n">grady</span><span class="o">*</span><span class="p">(</span><span class="mi">1</span><span class="o">+</span><span class="n">gradx</span><span class="o">**</span><span class="mi">2</span><span class="o">+</span><span class="n">grady</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span><span class="o">/</span><span class="n">sqrt_y</span><span class="o">/</span>   \
+                <span class="n">math</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">gradx</span><span class="o">**</span><span class="mi">2</span><span class="o">+</span><span class="n">grady</span><span class="o">**</span><span class="mi">2</span><span class="o">+</span><span class="p">(</span><span class="n">gradx</span><span class="o">**</span><span class="mi">2</span><span class="o">+</span><span class="n">grady</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span>
+
+        <span class="k">return</span> <span class="n">dalphadt</span>
+
+<div class="viewcode-block" id="MassPointModel.run"><a class="viewcode-back" href="../../../simulator/mass_point_model.html#psimpy.simulator.mass_point_model.MassPointModel.run">[docs]</a>    <span class="nd">@beartype</span>
+    <span class="k">def</span> <span class="nf">run</span><span class="p">(</span>
+        <span class="bp">self</span><span class="p">,</span> <span class="n">elevation</span><span class="p">:</span> <span class="nb">str</span><span class="p">,</span> <span class="n">coulomb_friction</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span>
+        <span class="n">turbulent_friction</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">float</span><span class="p">,</span> <span class="nb">int</span><span class="p">],</span> <span class="n">x0</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">float</span><span class="p">,</span> <span class="nb">int</span><span class="p">],</span>
+        <span class="n">y0</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">float</span><span class="p">,</span> <span class="nb">int</span><span class="p">],</span> <span class="n">ux0</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">float</span><span class="p">,</span> <span class="nb">int</span><span class="p">]</span> <span class="o">=</span> <span class="mi">0</span><span class="p">,</span>
+        <span class="n">uy0</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">float</span><span class="p">,</span> <span class="nb">int</span><span class="p">]</span> <span class="o">=</span> <span class="mi">0</span><span class="p">,</span> <span class="n">dt</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">float</span><span class="p">,</span> <span class="nb">int</span><span class="p">]</span> <span class="o">=</span> <span class="mi">1</span><span class="p">,</span>
+        <span class="n">tend</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">float</span><span class="p">,</span> <span class="nb">int</span><span class="p">]</span> <span class="o">=</span> <span class="mi">300</span><span class="p">,</span> <span class="n">t0</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">float</span><span class="p">,</span> <span class="nb">int</span><span class="p">]</span> <span class="o">=</span> <span class="mi">0</span><span class="p">,</span>
+        <span class="n">g</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">float</span><span class="p">,</span> <span class="nb">int</span><span class="p">]</span> <span class="o">=</span> <span class="mf">9.8</span><span class="p">,</span> <span class="n">atol</span><span class="p">:</span> <span class="nb">float</span> <span class="o">=</span> <span class="mf">1e-6</span><span class="p">,</span> <span class="n">rtol</span><span class="p">:</span> <span class="nb">float</span> <span class="o">=</span> <span class="mf">1e-6</span><span class="p">,</span>
+        <span class="n">curvature</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="kc">False</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">:</span>
+        <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Solve the mass point model using :class:`scipy.integrate.ode` solver</span>
+<span class="sd">        given required input data.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        elevation : str</span>
+<span class="sd">            Name of the elevation raster file, in ESRI ascii format, including</span>
+<span class="sd">            the path.</span>
+<span class="sd">        coulomb_friction : float</span>
+<span class="sd">            Dry Coulomb friction coefficient.</span>
+<span class="sd">        turbulent_friction : float or int</span>
+<span class="sd">            Turbulent friction coefficient, in :math:`m/s^2`.</span>
+<span class="sd">        x0 : float or int</span>
+<span class="sd">            `x` coordinate of initial position.</span>
+<span class="sd">        y0 : float or int</span>
+<span class="sd">            `y` coordinate of initial position.</span>
+<span class="sd">        ux0 : float or int</span>
+<span class="sd">            Initial velocity in `x` direction.</span>
+<span class="sd">        uy0 : float or int</span>
+<span class="sd">            Initial velocity in `y` direction.</span>
+<span class="sd">        dt : float or int</span>
+<span class="sd">            Time step in seconds.</span>
+<span class="sd">        tend : float or int</span>
+<span class="sd">            End time in seconds.</span>
+<span class="sd">        t0 : float or int</span>
+<span class="sd">            Initial time.</span>
+<span class="sd">        g : float or int</span>
+<span class="sd">            Gravity acceleration, in :math:`m/s^2`.</span>
+<span class="sd">        atol : float</span>
+<span class="sd">            Absolute tolerance for solution.</span>
+<span class="sd">        rtol : float</span>
+<span class="sd">            Relative tolerance for solution.</span>
+<span class="sd">        curvature : bool</span>
+<span class="sd">            If `True`, take the curvature effect into account.</span>
+<span class="sd">        </span>
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        output: numpy array</span>
+<span class="sd">            Time history of the mass point&#39;s location and velocity.</span>
+<span class="sd">            2d :class:`numpy.ndarray`. Each row corresponds to a time step and</span>
+<span class="sd">            each column corresponds to a quantity. In total :math:`6` columns,</span>
+<span class="sd">            namely :code:`output.shape[1]=6`. More specifically:</span>
+<span class="sd">            :code:`output[:,0]` are the time steps,</span>
+<span class="sd">            :code:`output[:,1]` are the `x` coordinates,</span>
+<span class="sd">            :code:`output[:,2]` are the `y` coordinates,</span>
+<span class="sd">            :code:`output[:,3]` are velocity values in `x` direction,</span>
+<span class="sd">            :code:`output[:,4]` are velocity values in `y` direction,</span>
+<span class="sd">            :code:`output[:,5]` are total velocity values.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">fgrad_x</span><span class="p">,</span> <span class="n">fgrad_y</span><span class="p">,</span> <span class="n">fgrad_xx</span><span class="p">,</span> <span class="n">fgrad_yy</span><span class="p">,</span> <span class="n">fgrad_xy</span> <span class="o">=</span> \
+            <span class="bp">self</span><span class="o">.</span><span class="n">_preprocess</span><span class="p">(</span><span class="n">elevation</span><span class="p">,</span> <span class="n">x0</span><span class="p">,</span> <span class="n">y0</span><span class="p">)</span>
+        
+        <span class="n">s</span> <span class="o">=</span> <span class="n">ode</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_mass_point_model</span><span class="p">)</span><span class="o">.</span><span class="n">set_integrator</span><span class="p">(</span><span class="s1">&#39;dopri5&#39;</span><span class="p">,</span> <span class="n">method</span><span class="o">=</span><span class="s1">&#39;bdf&#39;</span><span class="p">,</span>
+            <span class="n">atol</span><span class="o">=</span><span class="n">atol</span><span class="p">,</span> <span class="n">rtol</span><span class="o">=</span><span class="n">rtol</span><span class="p">)</span>
+        
+        <span class="n">s</span><span class="o">.</span><span class="n">set_f_params</span><span class="p">(</span><span class="n">coulomb_friction</span><span class="p">,</span> <span class="n">turbulent_friction</span><span class="p">,</span> <span class="n">fgrad_x</span><span class="p">,</span> <span class="n">fgrad_y</span><span class="p">,</span>
+            <span class="n">fgrad_xx</span><span class="p">,</span><span class="n">fgrad_yy</span><span class="p">,</span><span class="n">fgrad_xy</span><span class="p">,</span> <span class="n">g</span><span class="p">,</span> <span class="n">curvature</span><span class="p">)</span>
+        
+        <span class="n">alpha0</span> <span class="o">=</span> <span class="p">[</span><span class="n">x0</span><span class="p">,</span> <span class="n">y0</span><span class="p">,</span> <span class="n">ux0</span><span class="p">,</span> <span class="n">uy0</span><span class="p">]</span>
+        <span class="n">s</span><span class="o">.</span><span class="n">set_initial_value</span><span class="p">(</span><span class="n">alpha0</span><span class="p">,</span> <span class="n">t0</span><span class="p">)</span>
+
+        <span class="n">t_all</span> <span class="o">=</span> <span class="p">[</span><span class="n">t0</span><span class="p">]</span>
+        <span class="n">alpha_all</span> <span class="o">=</span> <span class="p">[</span><span class="n">alpha0</span><span class="p">]</span>
+
+        <span class="k">while</span> <span class="n">s</span><span class="o">.</span><span class="n">successful</span><span class="p">()</span> <span class="ow">and</span> <span class="n">s</span><span class="o">.</span><span class="n">t</span> <span class="o">&lt;</span> <span class="n">tend</span><span class="p">:</span>
+            <span class="n">s</span><span class="o">.</span><span class="n">integrate</span><span class="p">(</span><span class="n">s</span><span class="o">.</span><span class="n">t</span> <span class="o">+</span> <span class="n">dt</span><span class="p">)</span>
+            <span class="n">t_all</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">s</span><span class="o">.</span><span class="n">t</span><span class="p">)</span>
+            <span class="n">alpha_all</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">s</span><span class="o">.</span><span class="n">y</span><span class="p">)</span>
+        
+        <span class="n">t_all</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">t_all</span><span class="p">)</span>
+        <span class="n">alpha_all</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">alpha_all</span><span class="p">)</span>
+
+        <span class="n">u</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">t_all</span><span class="p">))</span>
+        <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">t_all</span><span class="p">)):</span>
+            <span class="n">gradx</span> <span class="o">=</span> <span class="n">fgrad_x</span><span class="p">(</span><span class="n">alpha_all</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="mi">0</span><span class="p">],</span> <span class="n">alpha_all</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="mi">1</span><span class="p">])</span>
+            <span class="n">grady</span> <span class="o">=</span> <span class="n">fgrad_y</span><span class="p">(</span><span class="n">alpha_all</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="mi">0</span><span class="p">],</span> <span class="n">alpha_all</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="mi">1</span><span class="p">])</span>
+            <span class="n">ux</span> <span class="o">=</span> <span class="n">alpha_all</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="mi">2</span><span class="p">]</span>
+            <span class="n">uy</span> <span class="o">=</span> <span class="n">alpha_all</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="mi">3</span><span class="p">]</span>
+            <span class="n">u</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">math</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">ux</span><span class="o">**</span><span class="mi">2</span> <span class="o">+</span> <span class="n">uy</span><span class="o">**</span><span class="mi">2</span> <span class="o">+</span> <span class="mi">2</span><span class="o">*</span><span class="n">ux</span><span class="o">*</span><span class="n">uy</span><span class="o">*</span><span class="n">gradx</span><span class="o">*</span><span class="n">grady</span><span class="o">/</span>
+                <span class="n">math</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">1</span><span class="o">+</span><span class="n">gradx</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span><span class="o">/</span><span class="n">math</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">1</span><span class="o">+</span><span class="n">grady</span><span class="o">**</span><span class="mi">2</span><span class="p">))</span>
+            
+        <span class="n">t_all</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">t_all</span><span class="p">,(</span><span class="nb">len</span><span class="p">(</span><span class="n">t_all</span><span class="p">),</span><span class="o">-</span><span class="mi">1</span><span class="p">))</span>
+        <span class="n">u</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">u</span><span class="p">,(</span><span class="nb">len</span><span class="p">(</span><span class="n">u</span><span class="p">),</span><span class="o">-</span><span class="mi">1</span><span class="p">))</span>
+        <span class="n">output</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">t_all</span><span class="p">,</span> <span class="n">alpha_all</span><span class="p">,</span> <span class="n">u</span><span class="p">),</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
+        
+        <span class="k">return</span> <span class="n">output</span></div></div>
+</pre></div>
+
+           </div>
+          </div>
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+
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+
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diff --git a/docs/source/_build/html/_modules/psimpy/simulator/ravaflow24.html b/docs/source/_build/html/_modules/psimpy/simulator/ravaflow24.html
new file mode 100644
index 0000000..ea31444
--- /dev/null
+++ b/docs/source/_build/html/_modules/psimpy/simulator/ravaflow24.html
@@ -0,0 +1,502 @@
+<!DOCTYPE html>
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+           <div itemprop="articleBody">
+             
+  <h1>Source code for psimpy.simulator.ravaflow24</h1><div class="highlight"><pre>
+<span></span><span class="kn">import</span> <span class="nn">os</span>
+<span class="kn">import</span> <span class="nn">linecache</span>
+<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">from</span> <span class="nn">scipy.interpolate</span> <span class="kn">import</span> <span class="n">interp2d</span>
+<span class="kn">from</span> <span class="nn">typing</span> <span class="kn">import</span> <span class="n">Union</span>
+<span class="kn">from</span> <span class="nn">beartype</span> <span class="kn">import</span> <span class="n">beartype</span>
+
+<div class="viewcode-block" id="Ravaflow24Mixture"><a class="viewcode-back" href="../../../simulator/ravaflow24.html#psimpy.simulator.ravaflow24.Ravaflow24Mixture">[docs]</a><span class="k">class</span> <span class="nc">Ravaflow24Mixture</span><span class="p">:</span>
+    
+    <span class="nd">@beartype</span>
+    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span>
+        <span class="bp">self</span><span class="p">,</span> <span class="n">dir_sim</span><span class="p">:</span> <span class="nb">str</span><span class="p">,</span> <span class="n">time_step</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">float</span><span class="p">,</span> <span class="nb">int</span><span class="p">]</span> <span class="o">=</span> <span class="mi">10</span><span class="p">,</span>
+        <span class="n">time_end</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">float</span><span class="p">,</span> <span class="nb">int</span><span class="p">]</span> <span class="o">=</span> <span class="mi">300</span><span class="p">,</span> <span class="n">cfl</span><span class="p">:</span> <span class="nb">float</span> <span class="o">=</span> <span class="mf">0.4</span><span class="p">,</span> 
+        <span class="n">time_step_length</span><span class="p">:</span> <span class="nb">float</span> <span class="o">=</span> <span class="mf">0.001</span><span class="p">,</span> <span class="n">conversion_control</span><span class="p">:</span> <span class="nb">str</span> <span class="o">=</span> <span class="s1">&#39;0&#39;</span><span class="p">,</span>
+        <span class="n">curvature_control</span><span class="p">:</span> <span class="nb">str</span> <span class="o">=</span> <span class="s1">&#39;1&#39;</span><span class="p">,</span> <span class="n">surface_control</span><span class="p">:</span> <span class="nb">str</span> <span class="o">=</span> <span class="s1">&#39;0&#39;</span><span class="p">,</span>
+        <span class="n">entrainment_control</span><span class="p">:</span> <span class="nb">str</span> <span class="o">=</span> <span class="s1">&#39;0&#39;</span><span class="p">,</span> <span class="n">shear_velocity_coef</span><span class="p">:</span> <span class="nb">float</span> <span class="o">=</span> <span class="mf">0.05</span><span class="p">,</span>
+        <span class="n">basal_friction_diff</span><span class="p">:</span> <span class="nb">float</span> <span class="o">=</span> <span class="mf">0.0</span><span class="p">,</span> <span class="n">stopping_control</span><span class="p">:</span> <span class="nb">str</span> <span class="o">=</span> <span class="s1">&#39;0&#39;</span><span class="p">,</span>
+        <span class="n">stopping_threshold</span><span class="p">:</span> <span class="nb">float</span> <span class="o">=</span> <span class="mf">0.0</span><span class="p">,</span> <span class="n">friction_control</span><span class="p">:</span> <span class="nb">str</span> <span class="o">=</span> <span class="s1">&#39;0&#39;</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
+        <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        `r.avaflow 2.4 Mixture model` (Voellmy-type shallow flow model).</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        dir_sim : str</span>
+<span class="sd">            Directory to save output files generated by `r.avaflow`.</span>
+<span class="sd">        time_step : float or int</span>
+<span class="sd">            Time step for simulation, in seconds.</span>
+<span class="sd">        time_end : float or int</span>
+<span class="sd">            End time for simulation, in seconds.</span>
+<span class="sd">        cfl : float</span>
+<span class="sd">            CFL criterion, a value being equal or smaller than 0.5.</span>
+<span class="sd">        time_step_length : float</span>
+<span class="sd">            If ``cfl`` is not applicable, ``time_step_length`` is used.</span>
+<span class="sd">            In seconds. Recommended range is around :math:`0.1` to :math:`0.5`.</span>
+<span class="sd">        conversion_control : str</span>
+<span class="sd">            `&#39;0&#39;`: no conversion of flow heights to flow depths.</span>
+<span class="sd">            `&#39;1&#39;`: conversion is applied.</span>
+<span class="sd">        curvature_control : str</span>
+<span class="sd">            `&#39;0&#39;`: curvature is neglected.</span>
+<span class="sd">            `&#39;1&#39;`: curvature is considered in the decelerating source terms.</span>
+<span class="sd">            `&#39;2&#39;`: curvature is considered in all relevant terms.</span>
+<span class="sd">        surface_control : str</span>
+<span class="sd">            `&#39;0&#39;`: no balancing of forces.</span>
+<span class="sd">            `&#39;1&#39;`: apply balancing of forces.</span>
+<span class="sd">        entrainment_control : str</span>
+<span class="sd">            `&#39;0&#39;`: no entrainment.</span>
+<span class="sd">            `&#39;1&#39;`: the entrainment coefficient is multiplied with flow momentum.</span>
+<span class="sd">            `&#39;2&#39;`: simplified entrainment and deposition model is used.</span>
+<span class="sd">            `&#39;3&#39;`: combination of `&#39;1&#39;` for entrainmnet and `&#39;2&#39;` for deposition.</span>
+<span class="sd">            `&#39;4&#39;`: acceleration-deceleration entrainment and deposition model.</span>
+<span class="sd">        shear_velocity_coef : float</span>
+<span class="sd">            Only used with ``entrainment_control`` being `&#39;2&#39;` or `&#39;3&#39;`, range</span>
+<span class="sd">            :math:`[0,1]`.</span>
+<span class="sd">        basal_friction_diff : float</span>
+<span class="sd">            Difference between the basal friction angles of the basal surface</span>
+<span class="sd">            and the flow, in degrees. Only used with ``entrainment_control``</span>
+<span class="sd">            being `&#39;2&#39;` or `&#39;3&#39;`.</span>
+<span class="sd">        stopping_control : str</span>
+<span class="sd">            `&#39;0&#39;`: no stopping control is used.</span>
+<span class="sd">            `&#39;1&#39;`: stop if the flow kinetic energy is equal or smaller than a</span>
+<span class="sd">            given threshold.</span>
+<span class="sd">            `&#39;2&#39;`: stop if the flow momentum is equal or smaller than a given</span>
+<span class="sd">            threshold.</span>
+<span class="sd">            `&#39;3&#39;`: stop if the dynamic flow pressure of all raster cells is</span>
+<span class="sd">            euqal or smaller than a given threshold.</span>
+<span class="sd">        stopping_threshold : float</span>
+<span class="sd">            Threshold value for ``stopping_control``.</span>
+<span class="sd">            If ``stopping_control`` is `&#39;1&#39;` or `&#39;2&#39;`, ``stopping_threshold``</span>
+<span class="sd">            has to be given as the maximum value reached during the flow.</span>
+<span class="sd">            If ``stopping_control`` is `&#39;3&#39;`, the pressure threshold has to be</span>
+<span class="sd">            specified.</span>
+<span class="sd">        friction_control : str, optional</span>
+<span class="sd">            `&#39;0&#39;`: no dynamic adaptation of friction parameters.</span>
+<span class="sd">            `&#39;1&#39;`: dynamic adaptation of friction parameters (ignored for the</span>
+<span class="sd">            mixture model).</span>
+<span class="sd">        </span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="ow">not</span> <span class="n">os</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">isdir</span><span class="p">(</span><span class="n">dir_sim</span><span class="p">):</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="n">dir_sim</span><span class="si">}</span><span class="s2"> does not exist or is not a directory&quot;</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">dir_sim</span> <span class="o">=</span> <span class="n">dir_sim</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">time_step</span> <span class="o">=</span> <span class="n">time_step</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">time_end</span> <span class="o">=</span> <span class="n">time_end</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">cfl</span> <span class="o">=</span> <span class="n">cfl</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">time_step_length</span> <span class="o">=</span> <span class="n">time_step_length</span>
+        
+        <span class="k">if</span> <span class="n">conversion_control</span> <span class="ow">not</span> <span class="ow">in</span> <span class="p">[</span><span class="s1">&#39;0&#39;</span><span class="p">,</span><span class="s1">&#39;1&#39;</span><span class="p">]:</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;convresion_control must be &#39;0&#39; or &#39;1&#39;&quot;</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">conversion_control</span> <span class="o">=</span> <span class="n">conversion_control</span>
+        
+        <span class="k">if</span> <span class="n">curvature_control</span> <span class="ow">not</span> <span class="ow">in</span> <span class="p">[</span><span class="s1">&#39;0&#39;</span><span class="p">,</span><span class="s1">&#39;1&#39;</span><span class="p">,</span><span class="s1">&#39;2&#39;</span><span class="p">]:</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;curvature_control must be &#39;0&#39; or &#39;1&#39; or &#39;2&#39;&quot;</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">curvature_control</span> <span class="o">=</span> <span class="n">curvature_control</span> 
+        
+        <span class="k">if</span> <span class="n">surface_control</span> <span class="ow">not</span> <span class="ow">in</span> <span class="p">[</span><span class="s1">&#39;0&#39;</span><span class="p">,</span><span class="s1">&#39;1&#39;</span><span class="p">]:</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;surface_control must be &#39;0&#39; or &#39;1&#39;&quot;</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">surface_control</span> <span class="o">=</span> <span class="n">surface_control</span>
+        
+        <span class="k">if</span> <span class="n">entrainment_control</span> <span class="ow">not</span> <span class="ow">in</span> <span class="p">[</span><span class="s1">&#39;0&#39;</span><span class="p">,</span><span class="s1">&#39;1&#39;</span><span class="p">,</span><span class="s1">&#39;2&#39;</span><span class="p">,</span><span class="s1">&#39;3&#39;</span><span class="p">,</span><span class="s1">&#39;4&#39;</span><span class="p">]:</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span>
+                <span class="s2">&quot;entrainment_control must be &#39;0&#39;, &#39;1&#39;, &#39;2&#39;, &#39;3&#39;, or &#39;4&#39;&quot;</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">entrainment_control</span> <span class="o">=</span> <span class="n">entrainment_control</span>
+        
+        <span class="bp">self</span><span class="o">.</span><span class="n">shear_velocity_coef</span> <span class="o">=</span> <span class="n">shear_velocity_coef</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">basal_friction_diff</span> <span class="o">=</span> <span class="n">basal_friction_diff</span>
+        
+        <span class="k">if</span> <span class="n">stopping_control</span> <span class="ow">not</span> <span class="ow">in</span> <span class="p">[</span><span class="s1">&#39;0&#39;</span><span class="p">,</span><span class="s1">&#39;1&#39;</span><span class="p">,</span><span class="s1">&#39;2&#39;</span><span class="p">,</span><span class="s1">&#39;3&#39;</span><span class="p">]:</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;stopping_control must be &#39;0&#39;, &#39;1&#39;, &#39;2&#39;, or &#39;3&#39;&quot;</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">stopping_control</span> <span class="o">=</span> <span class="n">stopping_control</span>
+                 
+        <span class="bp">self</span><span class="o">.</span><span class="n">stopping_threshold</span> <span class="o">=</span> <span class="n">stopping_threshold</span>
+
+        <span class="k">if</span> <span class="n">friction_control</span> <span class="ow">not</span> <span class="ow">in</span> <span class="p">[</span><span class="s1">&#39;0&#39;</span><span class="p">,</span><span class="s1">&#39;1&#39;</span><span class="p">]:</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;friction_control must be &#39;0&#39; or &#39;1&#39;&quot;</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">friction_control</span> <span class="o">=</span> <span class="n">friction_control</span>
+    
+<div class="viewcode-block" id="Ravaflow24Mixture.preprocess"><a class="viewcode-back" href="../../../simulator/ravaflow24.html#psimpy.simulator.ravaflow24.Ravaflow24Mixture.preprocess">[docs]</a>    <span class="nd">@beartype</span>
+    <span class="k">def</span> <span class="nf">preprocess</span><span class="p">(</span>
+        <span class="bp">self</span><span class="p">,</span> <span class="n">prefix</span><span class="p">:</span> <span class="nb">str</span><span class="p">,</span> <span class="n">elevation</span><span class="p">:</span> <span class="nb">str</span><span class="p">,</span> <span class="n">hrelease</span><span class="p">:</span> <span class="nb">str</span><span class="p">,</span>
+        <span class="n">cellsize</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">float</span><span class="p">,</span> <span class="nb">int</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">floating</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">integer</span><span class="p">]</span> <span class="o">=</span> <span class="mi">20</span><span class="p">,</span>
+        <span class="n">hrelease_ratio</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">float</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">integer</span><span class="p">]</span> <span class="o">=</span> <span class="mf">1.0</span><span class="p">,</span> 
+        <span class="n">internal_friction</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">float</span><span class="p">,</span> <span class="nb">int</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">floating</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">integer</span><span class="p">]</span> <span class="o">=</span> <span class="mi">35</span><span class="p">,</span>
+        <span class="n">basal_friction</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">float</span><span class="p">,</span> <span class="nb">int</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">floating</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">integer</span><span class="p">]</span> <span class="o">=</span> <span class="mi">20</span><span class="p">,</span>
+        <span class="n">turbulent_friction</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">float</span><span class="p">,</span> <span class="nb">int</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">floating</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">integer</span><span class="p">]</span> <span class="o">=</span> <span class="mi">3</span><span class="p">,</span>
+        <span class="n">entrainment_coef</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">float</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">floating</span><span class="p">]</span> <span class="o">=</span> <span class="o">-</span><span class="mf">7.0</span><span class="p">,</span>
+        <span class="n">EPSG</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">str</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">tuple</span><span class="p">[</span><span class="nb">str</span><span class="p">,</span> <span class="nb">str</span><span class="p">]:</span>
+        <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Preprocess simulation input data simulation.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        prefix : str</span>
+<span class="sd">            Prefix required by `r.avaflow` to name output files.</span>
+<span class="sd">        elevation : str</span>
+<span class="sd">            Name of elevation raster file (including its path).</span>
+<span class="sd">            The file format should be supported by `GDAL`.</span>
+<span class="sd">            Its unit is in meters.</span>
+<span class="sd">        hrelease : str</span>
+<span class="sd">            Name of release height raster file (including its path).</span>
+<span class="sd">            The file format should be supported by `GDAL`.</span>
+<span class="sd">            Its unit is in meters.</span>
+<span class="sd">        cellsize : float or int, optional</span>
+<span class="sd">            Cell size in meters to be used for simulation.</span>
+<span class="sd">        hrelease_ratio : float, optional</span>
+<span class="sd">            A positive value to multiple ``hrelease`` in order to control</span>
+<span class="sd">            the release volume.</span>
+<span class="sd">        internal_friction : float or int, optional</span>
+<span class="sd">            Internal friction angle, in degrees, range :math:`[0,90)`.</span>
+<span class="sd">        basal_friction : float or int, optional</span>
+<span class="sd">            Basal friction angle, in degrees, range :math:`[0,90)`.</span>
+<span class="sd">        turbulent_friction : float or int, optional</span>
+<span class="sd">            Logarithm with base :math:`10` of the turbulent friction, in</span>
+<span class="sd">            :math:`m/s^2`.</span>
+<span class="sd">        entrainment_coef : float, optional</span>
+<span class="sd">            Logarithm with base :math:`10` of the entrainment coefficient,</span>
+<span class="sd">            except for :math:`0` meaning no entrainment.</span>
+<span class="sd">        EPSG : str, optional</span>
+<span class="sd">            `EPSG` (European Petroleum Survey Group) code to create</span>
+<span class="sd">            `GRASS Location &lt;https://grass.osgeo.org/grass82/manuals/grass_database.html&gt;`_.</span>
+<span class="sd">            If `None`, ``elevation`` must be a georeferenced file which has</span>
+<span class="sd">            metadata to create the `GRASS Location`. </span>
+<span class="sd">        </span>
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        grass_location : str</span>
+<span class="sd">            Name of the `GRASS Location` (including path).</span>
+<span class="sd">        sh_file : str</span>
+<span class="sd">            Name of the shell file (including path), which will be called by</span>
+<span class="sd">            `GRASS &lt;https://grass.osgeo.org/&gt;`_ to run the simulation. </span>
+<span class="sd">        &quot;&quot;&quot;</span>        
+        <span class="n">sh_file</span> <span class="o">=</span> <span class="n">os</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">dir_sim</span><span class="p">,</span> <span class="sa">f</span><span class="s1">&#39;</span><span class="si">{</span><span class="n">prefix</span><span class="si">}</span><span class="s1">_shell.sh&#39;</span><span class="p">)</span>
+        <span class="n">grass_location</span> <span class="o">=</span> <span class="n">os</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">dir_sim</span><span class="p">,</span> <span class="sa">f</span><span class="s1">&#39;</span><span class="si">{</span><span class="n">prefix</span><span class="si">}</span><span class="s1">_glocation&#39;</span><span class="p">)</span>
+        <span class="n">results_dir</span> <span class="o">=</span> <span class="n">os</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">dir_sim</span><span class="p">,</span> <span class="sa">f</span><span class="s1">&#39;</span><span class="si">{</span><span class="n">prefix</span><span class="si">}</span><span class="s1">_results&#39;</span><span class="p">)</span>
+
+        <span class="k">if</span> <span class="n">os</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">exists</span><span class="p">(</span><span class="n">sh_file</span><span class="p">)</span> <span class="ow">or</span> <span class="n">os</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">exists</span><span class="p">(</span><span class="n">grass_location</span><span class="p">)</span> <span class="ow">or</span> \
+            <span class="n">os</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">exists</span><span class="p">(</span><span class="n">results_dir</span><span class="p">):</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span>
+                <span class="sa">f</span><span class="s2">&quot;File(s) with prefix=</span><span class="si">{</span><span class="n">prefix</span><span class="si">}</span><span class="s2"> already exists in </span><span class="si">{</span><span class="bp">self</span><span class="o">.</span><span class="n">dir_sim</span><span class="si">}</span><span class="s2">.&quot;</span>
+                <span class="sa">f</span><span class="s2">&quot; Move or delete conflicting files, or use another prefix.&quot;</span><span class="p">)</span>
+        
+        <span class="k">if</span> <span class="ow">not</span> <span class="n">os</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">exists</span><span class="p">(</span><span class="n">elevation</span><span class="p">):</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="n">elevation</span><span class="si">}</span><span class="s2"> does not exist&quot;</span><span class="p">)</span>
+        
+        <span class="k">if</span> <span class="ow">not</span> <span class="n">os</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">exists</span><span class="p">(</span><span class="n">hrelease</span><span class="p">):</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="n">hrelease</span><span class="si">}</span><span class="s2"> does not exist&quot;</span><span class="p">)</span>
+        
+        <span class="c1"># create grass location</span>
+        <span class="k">if</span> <span class="n">EPSG</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="n">os</span><span class="o">.</span><span class="n">system</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;grass -e -c </span><span class="si">{</span><span class="n">elevation</span><span class="si">}</span><span class="s2"> </span><span class="si">{</span><span class="n">grass_location</span><span class="si">}</span><span class="s2">&quot;</span><span class="p">)</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="n">os</span><span class="o">.</span><span class="n">system</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;grass -e -c EPSG:</span><span class="si">{</span><span class="n">EPSG</span><span class="si">}</span><span class="s2"> </span><span class="si">{</span><span class="n">grass_location</span><span class="si">}</span><span class="s2">&quot;</span><span class="p">)</span>
+
+        <span class="c1"># create shell file</span>
+        <span class="k">with</span> <span class="nb">open</span><span class="p">(</span><span class="n">sh_file</span><span class="p">,</span> <span class="s1">&#39;w&#39;</span><span class="p">)</span> <span class="k">as</span> <span class="n">sh</span><span class="p">:</span>
+
+            <span class="n">sh</span><span class="o">.</span><span class="n">write</span><span class="p">(</span><span class="s2">&quot;# import elevation raster </span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">)</span>
+            <span class="n">sh</span><span class="o">.</span><span class="n">write</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;r.in.gdal -o input=</span><span class="si">{</span><span class="n">elevation</span><span class="si">}</span><span class="s2"> output=elev --overwrite&quot;</span><span class="p">)</span>
+            <span class="n">sh</span><span class="o">.</span><span class="n">write</span><span class="p">(</span><span class="s2">&quot;</span><span class="se">\n\n</span><span class="s2">&quot;</span><span class="p">)</span>
+
+            <span class="n">sh</span><span class="o">.</span><span class="n">write</span><span class="p">(</span><span class="s2">&quot;# set region based on elev </span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">)</span>
+            <span class="n">sh</span><span class="o">.</span><span class="n">write</span><span class="p">(</span><span class="s2">&quot;g.region raster=elev </span><span class="se">\n\n</span><span class="s2">&quot;</span><span class="p">)</span>
+            
+            <span class="n">sh</span><span class="o">.</span><span class="n">write</span><span class="p">(</span><span class="s1">&#39;# import hrelease raster </span><span class="se">\n</span><span class="s1">&#39;</span><span class="p">)</span>
+            <span class="n">sh</span><span class="o">.</span><span class="n">write</span><span class="p">(</span>
+                <span class="sa">f</span><span class="s2">&quot;r.in.gdal -o input=</span><span class="si">{</span><span class="n">hrelease</span><span class="si">}</span><span class="s2"> output=raw_hrel --overwrite&quot;</span><span class="p">)</span>
+            <span class="n">sh</span><span class="o">.</span><span class="n">write</span><span class="p">(</span><span class="s2">&quot;</span><span class="se">\n\n</span><span class="s2">&quot;</span><span class="p">)</span>
+
+            <span class="n">sh</span><span class="o">.</span><span class="n">write</span><span class="p">(</span>
+                <span class="sa">f</span><span class="s2">&quot;r.mapcalc </span><span class="se">\&quot;</span><span class="s2">hrel = raw_hrel*</span><span class="si">{</span><span class="n">hrelease_ratio</span><span class="si">}</span><span class="se">\&quot;</span><span class="s2"> --overwrite&quot;</span><span class="p">)</span>
+            <span class="n">sh</span><span class="o">.</span><span class="n">write</span><span class="p">(</span><span class="s2">&quot;</span><span class="se">\n\n</span><span class="s2">&quot;</span><span class="p">)</span>
+            
+            <span class="n">sh</span><span class="o">.</span><span class="n">write</span><span class="p">(</span>
+                <span class="sa">f</span><span class="s2">&quot;r.avaflow -e -a prefix=</span><span class="si">{</span><span class="n">prefix</span><span class="si">}</span><span class="s2"> cellsize=</span><span class="si">{</span><span class="n">cellsize</span><span class="si">}</span><span class="s2"> phases=x &quot;</span>
+                <span class="sa">f</span><span class="s2">&quot;elevation=elev hrelease=hrel &quot;</span>
+                <span class="sa">f</span><span class="s2">&quot;friction=</span><span class="si">{</span><span class="n">internal_friction</span><span class="si">}</span><span class="s2">,</span><span class="si">{</span><span class="n">basal_friction</span><span class="si">}</span><span class="s2">,&quot;</span>
+                <span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="n">turbulent_friction</span><span class="si">}</span><span class="s2"> &quot;</span>
+                <span class="sa">f</span><span class="s2">&quot;basal=</span><span class="si">{</span><span class="n">entrainment_coef</span><span class="si">}</span><span class="s2">,</span><span class="si">{</span><span class="bp">self</span><span class="o">.</span><span class="n">shear_velocity_coef</span><span class="si">}</span><span class="s2">,&quot;</span>
+                <span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="bp">self</span><span class="o">.</span><span class="n">basal_friction_diff</span><span class="si">}</span><span class="s2">,</span><span class="si">{</span><span class="bp">self</span><span class="o">.</span><span class="n">stopping_threshold</span><span class="si">}</span><span class="s2"> &quot;</span>
+                <span class="sa">f</span><span class="s2">&quot;controls=</span><span class="si">{</span><span class="bp">self</span><span class="o">.</span><span class="n">conversion_control</span><span class="si">}</span><span class="s2">,</span><span class="si">{</span><span class="bp">self</span><span class="o">.</span><span class="n">curvature_control</span><span class="si">}</span><span class="s2">,&quot;</span>
+                <span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="bp">self</span><span class="o">.</span><span class="n">surface_control</span><span class="si">}</span><span class="s2">,</span><span class="si">{</span><span class="bp">self</span><span class="o">.</span><span class="n">entrainment_control</span><span class="si">}</span><span class="s2">,&quot;</span>
+                <span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="bp">self</span><span class="o">.</span><span class="n">stopping_control</span><span class="si">}</span><span class="s2">,</span><span class="si">{</span><span class="bp">self</span><span class="o">.</span><span class="n">friction_control</span><span class="si">}</span><span class="s2"> &quot;</span>
+                <span class="sa">f</span><span class="s2">&quot;time=</span><span class="si">{</span><span class="bp">self</span><span class="o">.</span><span class="n">time_step</span><span class="si">}</span><span class="s2">,</span><span class="si">{</span><span class="bp">self</span><span class="o">.</span><span class="n">time_end</span><span class="si">}</span><span class="s2"> &quot;</span>
+                <span class="sa">f</span><span class="s2">&quot;cfl=</span><span class="si">{</span><span class="bp">self</span><span class="o">.</span><span class="n">cfl</span><span class="si">}</span><span class="s2">,</span><span class="si">{</span><span class="bp">self</span><span class="o">.</span><span class="n">time_step_length</span><span class="si">}</span><span class="s2">&quot;</span><span class="p">)</span>
+        
+        <span class="k">return</span> <span class="n">grass_location</span><span class="p">,</span> <span class="n">sh_file</span></div>
+
+<div class="viewcode-block" id="Ravaflow24Mixture.run"><a class="viewcode-back" href="../../../simulator/ravaflow24.html#psimpy.simulator.ravaflow24.Ravaflow24Mixture.run">[docs]</a>    <span class="nd">@beartype</span>
+    <span class="k">def</span> <span class="nf">run</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">grass_location</span><span class="p">:</span> <span class="nb">str</span><span class="p">,</span> <span class="n">sh_file</span><span class="p">:</span> <span class="nb">str</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
+        <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Run simulation.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        grass_location : str</span>
+<span class="sd">            Name of the `GRASS Location` (including path).</span>
+<span class="sd">        sh_file : str</span>
+<span class="sd">            Name of the shell file (including path).</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="ow">not</span> <span class="n">os</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">exists</span><span class="p">(</span><span class="n">grass_location</span><span class="p">):</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="n">grass_location</span><span class="si">}</span><span class="s2"> does not exist&quot;</span><span class="p">)</span>
+        <span class="k">if</span> <span class="ow">not</span> <span class="n">os</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">exists</span><span class="p">(</span><span class="n">os</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="n">grass_location</span><span class="p">,</span> <span class="s2">&quot;PERMANENT&quot;</span><span class="p">)):</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="n">grass_location</span><span class="si">}</span><span class="s2"> is not a grass location&quot;</span><span class="p">)</span>
+        
+        <span class="k">if</span> <span class="ow">not</span> <span class="n">os</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">exists</span><span class="p">(</span><span class="n">sh_file</span><span class="p">):</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="n">sh_file</span><span class="si">}</span><span class="s2"> does not exist&quot;</span><span class="p">)</span>
+        
+        <span class="n">grass_mapset</span> <span class="o">=</span> <span class="n">os</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="n">grass_location</span><span class="p">,</span> <span class="s2">&quot;PERMANENT&quot;</span><span class="p">,</span> <span class="s2">&quot;&quot;</span><span class="p">)</span>
+
+        <span class="n">os</span><span class="o">.</span><span class="n">chdir</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">dir_sim</span><span class="p">)</span>
+        <span class="n">os</span><span class="o">.</span><span class="n">system</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;grass </span><span class="si">{</span><span class="n">grass_mapset</span><span class="si">}</span><span class="s2"> --exec sh </span><span class="si">{</span><span class="n">sh_file</span><span class="si">}</span><span class="s2">&quot;</span><span class="p">)</span></div>
+
+
+<div class="viewcode-block" id="Ravaflow24Mixture.extract_impact_area"><a class="viewcode-back" href="../../../simulator/ravaflow24.html#psimpy.simulator.ravaflow24.Ravaflow24Mixture.extract_impact_area">[docs]</a>    <span class="k">def</span> <span class="nf">extract_impact_area</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">prefix</span><span class="p">:</span> <span class="nb">str</span><span class="p">,</span> <span class="n">qoi</span><span class="p">:</span> <span class="nb">str</span> <span class="o">=</span> <span class="s1">&#39;h&#39;</span><span class="p">,</span>
+        <span class="n">threshold</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">float</span><span class="p">,</span> <span class="nb">int</span><span class="p">]</span> <span class="o">=</span> <span class="mf">0.5</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">float</span><span class="p">:</span>
+        <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Extract impact area defined by a given quantity of interest and its</span>
+<span class="sd">        threshold.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        prefix : str</span>
+<span class="sd">            Prefix used by `r.avaflow` to name output files.</span>
+<span class="sd">        qoi : str</span>
+<span class="sd">            Quantity of interest to determine the impact area.</span>
+<span class="sd">            `&#39;h&#39;`: maximum flow height, in meters.</span>
+<span class="sd">            `&#39;v&#39;`: maximum flow velocity, in :math:`m/s`.</span>
+<span class="sd">            `&#39;p&#39;`: maximum flow pressure, in :math:`Pa`.</span>
+<span class="sd">            `&#39;t&#39;`: maximum flow kinetic energy, in :math:`J`.</span>
+<span class="sd">        threshold : float or int</span>
+<span class="sd">            Threshold of ``qoi`` to determine impact area. Areas where ``qoi``</span>
+<span class="sd">            is larger than ``threshold`` are regarded as impar area.</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        impact_area : float</span>
+<span class="sd">            A scalar value representing the overall impact area.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="n">qoi</span> <span class="ow">not</span> <span class="ow">in</span> <span class="p">[</span><span class="s1">&#39;h&#39;</span><span class="p">,</span><span class="s1">&#39;v&#39;</span><span class="p">,</span><span class="s1">&#39;p&#39;</span><span class="p">,</span><span class="s1">&#39;t&#39;</span><span class="p">]:</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;qoi must be &#39;h&#39;, &#39;v&#39;, &#39;p&#39;, or &#39;t&#39;&quot;</span><span class="p">)</span>
+
+        <span class="n">qoi_max_raster_asc</span> <span class="o">=</span> <span class="n">os</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">dir_sim</span><span class="p">,</span> <span class="sa">f</span><span class="s1">&#39;</span><span class="si">{</span><span class="n">prefix</span><span class="si">}</span><span class="s1">_results&#39;</span><span class="p">,</span>
+            <span class="sa">f</span><span class="s1">&#39;</span><span class="si">{</span><span class="n">prefix</span><span class="si">}</span><span class="s1">_ascii&#39;</span><span class="p">,</span> <span class="sa">f</span><span class="s1">&#39;</span><span class="si">{</span><span class="n">prefix</span><span class="si">}</span><span class="s1">_</span><span class="si">{</span><span class="n">qoi</span><span class="si">}</span><span class="s1">flow_max.asc&#39;</span><span class="p">)</span>
+        <span class="n">qoi_max_raster</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">loadtxt</span><span class="p">(</span><span class="n">qoi_max_raster_asc</span><span class="p">,</span> <span class="n">skiprows</span><span class="o">=</span><span class="mi">6</span><span class="p">)</span>
+
+        <span class="n">cellsize</span> <span class="o">=</span> <span class="n">linecache</span><span class="o">.</span><span class="n">getline</span><span class="p">(</span><span class="n">qoi_max_raster_asc</span><span class="p">,</span> <span class="mi">5</span><span class="p">)</span>
+        <span class="n">cellsize</span> <span class="o">=</span> <span class="nb">float</span><span class="p">(</span><span class="n">cellsize</span><span class="o">.</span><span class="n">split</span><span class="p">()[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">strip</span><span class="p">())</span>
+
+        <span class="n">impact_area</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">where</span><span class="p">(</span><span class="n">qoi_max_raster</span><span class="o">&gt;</span><span class="n">threshold</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">0</span><span class="p">))</span> <span class="o">*</span> \
+            <span class="p">(</span><span class="n">cellsize</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span>
+            
+        <span class="k">return</span> <span class="nb">float</span><span class="p">(</span><span class="n">impact_area</span><span class="p">)</span></div>
+
+<div class="viewcode-block" id="Ravaflow24Mixture.extract_qoi_max"><a class="viewcode-back" href="../../../simulator/ravaflow24.html#psimpy.simulator.ravaflow24.Ravaflow24Mixture.extract_qoi_max">[docs]</a>    <span class="k">def</span> <span class="nf">extract_qoi_max</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">prefix</span><span class="p">:</span> <span class="nb">str</span><span class="p">,</span> <span class="n">qoi</span><span class="p">:</span> <span class="nb">str</span><span class="p">,</span>
+        <span class="n">aggregate</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="kc">True</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">Union</span><span class="p">[</span><span class="nb">float</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">]:</span>
+        <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Extract the maximum value(s) of a quantity of interest.</span>
+<span class="sd">        </span>
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        prefix : str</span>
+<span class="sd">            Prefix used by `r.avaflow` to name output files.</span>
+<span class="sd">        qoi : str</span>
+<span class="sd">            Quantity of interest.</span>
+<span class="sd">            `&#39;h&#39;`: maximum flow height, in meters.</span>
+<span class="sd">            `&#39;v&#39;`: maximum flow velocity, in :math:`m/s`.</span>
+<span class="sd">            `&#39;p&#39;`: maximum flow pressure, in :math:`Pa`.</span>
+<span class="sd">            `&#39;t&#39;`: maximum flow kinetic energy, in :math:`J`.</span>
+<span class="sd">        aggregate : bool</span>
+<span class="sd">            If `True`, returns the overall maximum value over all spatio-tempo</span>
+<span class="sd">            grids. If `False`, returns the maximum values over all time steps at</span>
+<span class="sd">            each spatio location, namely a raster of maximum values.</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        qoi_max : float or numpy array</span>
+<span class="sd">            Maximum value(s) of ``qoi`` in one simulation.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="n">qoi</span> <span class="ow">not</span> <span class="ow">in</span> <span class="p">[</span><span class="s1">&#39;h&#39;</span><span class="p">,</span><span class="s1">&#39;v&#39;</span><span class="p">,</span><span class="s1">&#39;p&#39;</span><span class="p">,</span><span class="s1">&#39;t&#39;</span><span class="p">]:</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;qoi must be &#39;h&#39;, &#39;v&#39;, &#39;p&#39;, or &#39;t&#39;&quot;</span><span class="p">)</span>
+        
+        <span class="n">qoi_max_raster_asc</span> <span class="o">=</span> <span class="n">os</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">dir_sim</span><span class="p">,</span> <span class="sa">f</span><span class="s1">&#39;</span><span class="si">{</span><span class="n">prefix</span><span class="si">}</span><span class="s1">_results&#39;</span><span class="p">,</span>
+            <span class="sa">f</span><span class="s1">&#39;</span><span class="si">{</span><span class="n">prefix</span><span class="si">}</span><span class="s1">_ascii&#39;</span><span class="p">,</span> <span class="sa">f</span><span class="s1">&#39;</span><span class="si">{</span><span class="n">prefix</span><span class="si">}</span><span class="s1">_</span><span class="si">{</span><span class="n">qoi</span><span class="si">}</span><span class="s1">flow_max.asc&#39;</span><span class="p">)</span>
+        <span class="n">qoi_max_raster</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">loadtxt</span><span class="p">(</span><span class="n">qoi_max_raster_asc</span><span class="p">,</span> <span class="n">skiprows</span><span class="o">=</span><span class="mi">6</span><span class="p">)</span>
+
+        <span class="k">if</span> <span class="n">aggregate</span><span class="p">:</span>
+            <span class="k">return</span> <span class="nb">float</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">max</span><span class="p">(</span><span class="n">qoi_max_raster</span><span class="p">))</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">rot90</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">transpose</span><span class="p">(</span><span class="n">qoi_max_raster</span><span class="p">))</span></div>
+
+
+<div class="viewcode-block" id="Ravaflow24Mixture.extract_qoi_max_loc"><a class="viewcode-back" href="../../../simulator/ravaflow24.html#psimpy.simulator.ravaflow24.Ravaflow24Mixture.extract_qoi_max_loc">[docs]</a>    <span class="k">def</span> <span class="nf">extract_qoi_max_loc</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">prefix</span><span class="p">:</span> <span class="nb">str</span><span class="p">,</span> <span class="n">loc</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span>
+        <span class="n">qoi</span><span class="p">:</span> <span class="nb">str</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">:</span>
+        <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Extract maximum value(s) of a quantity of interest at specific</span>
+<span class="sd">        location(s).</span>
+<span class="sd">        </span>
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        prefix : str</span>
+<span class="sd">            Prefix used by `r.avaflow` to name output files.</span>
+<span class="sd">        loc : numpy array</span>
+<span class="sd">            Coordinates of interested locations. Shape :code:`(nloc, 2)`, where</span>
+<span class="sd">            ``nloc`` is the number of interested locations.</span>
+<span class="sd">            :code:`loc[:,0]` corresponds to `x` coordinates and</span>
+<span class="sd">            :code:`loc[:,1]` to `y` coordinates.</span>
+<span class="sd">        qoi : str</span>
+<span class="sd">            Quantity of interest.</span>
+<span class="sd">            `&#39;h&#39;`: maximum flow height, in meters.</span>
+<span class="sd">            `&#39;v&#39;`: maximum flow velocity, in :math:`m/s`.</span>
+<span class="sd">            `&#39;p&#39;`: maximum flow pressure, in :math:`Pa`.</span>
+<span class="sd">            `&#39;t&#39;`: maximum flow kinetic energy, in :math:`J`.</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        qoi_max_loc : numpy array</span>
+<span class="sd">            Consist of maximum value(s) of ``qoi`` at each location.</span>
+<span class="sd">            Shape of :code:`(nloc,)`.</span>
+<span class="sd">        &quot;&quot;&quot;</span>       
+        <span class="k">if</span> <span class="ow">not</span> <span class="p">(</span><span class="n">loc</span><span class="o">.</span><span class="n">ndim</span> <span class="o">==</span> <span class="mi">2</span> <span class="ow">and</span> <span class="n">loc</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">==</span> <span class="mi">2</span><span class="p">):</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span>
+                <span class="s2">&quot;loc must be a 2d numpy array with first axis corresponding to&quot;</span>
+                <span class="s2">&quot; the number of locations and second axis to x and y coords&quot;</span><span class="p">)</span>
+
+        <span class="k">if</span> <span class="n">qoi</span> <span class="ow">not</span> <span class="ow">in</span> <span class="p">[</span><span class="s1">&#39;h&#39;</span><span class="p">,</span><span class="s1">&#39;v&#39;</span><span class="p">,</span><span class="s1">&#39;p&#39;</span><span class="p">,</span><span class="s1">&#39;t&#39;</span><span class="p">]:</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;qoi must be &#39;h&#39;, &#39;v&#39;, &#39;p&#39;, or &#39;t&#39;&quot;</span><span class="p">)</span>
+        
+        <span class="n">qoi_max_raster_asc</span> <span class="o">=</span> <span class="n">os</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">dir_sim</span><span class="p">,</span> <span class="sa">f</span><span class="s1">&#39;</span><span class="si">{</span><span class="n">prefix</span><span class="si">}</span><span class="s1">_results&#39;</span><span class="p">,</span>
+            <span class="sa">f</span><span class="s1">&#39;</span><span class="si">{</span><span class="n">prefix</span><span class="si">}</span><span class="s1">_ascii&#39;</span><span class="p">,</span> <span class="sa">f</span><span class="s1">&#39;</span><span class="si">{</span><span class="n">prefix</span><span class="si">}</span><span class="s1">_</span><span class="si">{</span><span class="n">qoi</span><span class="si">}</span><span class="s1">flow_max.asc&#39;</span><span class="p">)</span>
+        
+        <span class="n">header</span> <span class="o">=</span> <span class="p">[</span><span class="n">linecache</span><span class="o">.</span><span class="n">getline</span><span class="p">(</span><span class="n">qoi_max_raster_asc</span><span class="p">,</span> <span class="n">i</span><span class="p">)</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="mi">6</span><span class="p">)]</span>
+        <span class="n">header_values</span> <span class="o">=</span> <span class="p">[</span><span class="nb">float</span><span class="p">(</span><span class="n">h</span><span class="o">.</span><span class="n">split</span><span class="p">()[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">strip</span><span class="p">())</span> <span class="k">for</span> <span class="n">h</span> <span class="ow">in</span> <span class="n">header</span><span class="p">]</span>
+        <span class="n">ncols</span><span class="p">,</span> <span class="n">nrows</span><span class="p">,</span> <span class="n">xll</span><span class="p">,</span> <span class="n">yll</span><span class="p">,</span> <span class="n">cellsize</span> <span class="o">=</span> <span class="n">header_values</span>
+        <span class="n">ncols</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">ncols</span><span class="p">)</span>
+        <span class="n">nrows</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">nrows</span><span class="p">)</span>
+
+        <span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">xll</span><span class="p">,</span> <span class="n">xll</span><span class="o">+</span><span class="p">(</span><span class="n">cellsize</span><span class="o">*</span><span class="n">ncols</span><span class="p">),</span> <span class="n">cellsize</span><span class="p">)</span>
+        <span class="n">y</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">yll</span><span class="p">,</span> <span class="n">yll</span><span class="o">+</span><span class="p">(</span><span class="n">cellsize</span><span class="o">*</span><span class="n">nrows</span><span class="p">),</span> <span class="n">cellsize</span><span class="p">)</span>
+
+        <span class="k">if</span> <span class="ow">not</span> <span class="nb">all</span><span class="p">([</span><span class="n">loc</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="mi">0</span><span class="p">]</span><span class="o">&gt;=</span><span class="n">x</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="ow">and</span> <span class="n">loc</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="mi">0</span><span class="p">]</span><span class="o">&lt;=</span><span class="n">x</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="ow">and</span> <span class="n">loc</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="mi">1</span><span class="p">]</span><span class="o">&gt;=</span><span class="n">y</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="ow">and</span> \
+            <span class="n">loc</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="mi">1</span><span class="p">]</span><span class="o">&lt;=</span><span class="n">y</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">loc</span><span class="p">))]):</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span>
+                <span class="s2">&quot;Coordinates in loc must be within the boundary of topography&quot;</span><span class="p">)</span>
+
+        <span class="n">qoi_max_raster</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">loadtxt</span><span class="p">(</span><span class="n">qoi_max_raster_asc</span><span class="p">,</span> <span class="n">skiprows</span><span class="o">=</span><span class="mi">6</span><span class="p">)</span>
+        <span class="n">qoi_max_raster</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">rot90</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">transpose</span><span class="p">(</span><span class="n">qoi_max_raster</span><span class="p">))</span>
+
+        <span class="n">f_qoi_max</span> <span class="o">=</span> <span class="n">interp2d</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">qoi_max_raster</span><span class="p">)</span>
+
+        <span class="n">qoi_max_loc</span> <span class="o">=</span> <span class="p">[</span><span class="nb">float</span><span class="p">(</span><span class="n">f_qoi_max</span><span class="p">(</span><span class="n">loc</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="mi">0</span><span class="p">],</span> <span class="n">loc</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="mi">1</span><span class="p">]))</span> \
+            <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">loc</span><span class="p">))]</span>
+
+        <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">qoi_max_loc</span><span class="p">)</span></div></div>
+</pre></div>
+
+           </div>
+          </div>
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+
+  <hr/>
+
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+    <p>&#169; Copyright 2023, Hu Zhao.</p>
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diff --git a/docs/source/_build/html/_modules/psimpy/simulator/run_simulator.html b/docs/source/_build/html/_modules/psimpy/simulator/run_simulator.html
new file mode 100644
index 0000000..2d473eb
--- /dev/null
+++ b/docs/source/_build/html/_modules/psimpy/simulator/run_simulator.html
@@ -0,0 +1,348 @@
+<!DOCTYPE html>
+<html class="writer-html5" lang="en" >
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+          <li class="breadcrumb-item"><a href="../../index.html">Module code</a></li>
+      <li class="breadcrumb-item active">psimpy.simulator.run_simulator</li>
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+           <div itemprop="articleBody">
+             
+  <h1>Source code for psimpy.simulator.run_simulator</h1><div class="highlight"><pre>
+<span></span><span class="kn">import</span> <span class="nn">os</span>
+<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">from</span> <span class="nn">concurrent.futures</span> <span class="kn">import</span> <span class="n">ProcessPoolExecutor</span>
+<span class="kn">from</span> <span class="nn">beartype.typing</span> <span class="kn">import</span> <span class="n">Callable</span>
+<span class="kn">from</span> <span class="nn">beartype</span> <span class="kn">import</span> <span class="n">beartype</span>
+<span class="kn">from</span> <span class="nn">typing</span> <span class="kn">import</span> <span class="n">Union</span>
+
+<div class="viewcode-block" id="RunSimulator"><a class="viewcode-back" href="../../../simulator/run_simulator.html#psimpy.simulator.run_simulator.RunSimulator">[docs]</a><span class="k">class</span> <span class="nc">RunSimulator</span><span class="p">:</span>
+
+    <span class="nd">@beartype</span>
+    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span>
+        <span class="bp">self</span><span class="p">,</span> <span class="n">simulator</span><span class="p">:</span> <span class="n">Callable</span><span class="p">,</span> <span class="n">var_inp_parameter</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">str</span><span class="p">],</span> 
+        <span class="n">fix_inp</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">dict</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
+        <span class="n">o_parameter</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">str</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span> <span class="n">dir_out</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">str</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
+        <span class="n">save_out</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="kc">False</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
+        <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Serial or parallel execution of a given simulator.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        simulator : Callable</span>
+<span class="sd">            A Python function defining the simulator. Its parameters are defined</span>
+<span class="sd">            in three parts:</span>
+<span class="sd">            ``var_inp_parameter`` defines variable parameters;</span>
+<span class="sd">            ``fix_inp`` defines fixed parameters (``fix_inp.keys()``) and their</span>
+<span class="sd">            values (``fix_inp.values()``);</span>
+<span class="sd">            ``o_parameter`` defines an additional variable which is used to</span>
+<span class="sd">            name files saved onto the disk within the function body of</span>
+<span class="sd">            ``simulator``.</span>
+<span class="sd">            The simulator should return outputs of interest as </span>
+<span class="sd">            :class:`numpy.ndarray`.</span>
+<span class="sd">        var_inp_parameter :  list of str</span>
+<span class="sd">            A list consists of all variable input parameters of ``simulator``.</span>
+<span class="sd">        fix_inp : dict, optional</span>
+<span class="sd">            A dictionary consists of key-value pairs of all fixed input of the</span>
+<span class="sd">            ``simulator``.</span>
+<span class="sd">        o_parameter : str, optional</span>
+<span class="sd">            Keyword parameter of ``simulator`` which is used to name internally</span>
+<span class="sd">            saved files (if defined). It is only relevant if the function body</span>
+<span class="sd">            of ``simulator`` saves data onto the disk.  </span>
+<span class="sd">        dir_out : str, optional</span>
+<span class="sd">            Directory to save outputs of interest returned by ``simulator``.</span>
+<span class="sd">        save_out : bool, optional</span>
+<span class="sd">            Whether to save returned values of ``simulator``. If `True`,</span>
+<span class="sd">            ``dir_out`` must be given. </span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">simulator</span> <span class="o">=</span> <span class="n">simulator</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">var_inp_parameter</span> <span class="o">=</span> <span class="n">var_inp_parameter</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">fix_inp</span> <span class="o">=</span> <span class="p">{}</span> <span class="k">if</span> <span class="n">fix_inp</span> <span class="ow">is</span> <span class="kc">None</span> <span class="k">else</span> <span class="n">fix_inp</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">o_parameter</span> <span class="o">=</span> <span class="n">o_parameter</span>
+
+        <span class="k">if</span> <span class="n">save_out</span><span class="p">:</span>
+            <span class="k">if</span> <span class="n">dir_out</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+                <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span>
+                    <span class="s2">&quot;dir_out must be defined if save_out is True&quot;</span><span class="p">)</span>
+            <span class="k">elif</span> <span class="ow">not</span> <span class="n">os</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">isdir</span><span class="p">(</span><span class="n">dir_out</span><span class="p">):</span>
+                <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span>
+                    <span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="n">dir_out</span><span class="si">}</span><span class="s2"> does not exist or is not a directory&quot;</span><span class="p">)</span> 
+        <span class="bp">self</span><span class="o">.</span><span class="n">dir_out</span> <span class="o">=</span> <span class="n">dir_out</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">save_out</span> <span class="o">=</span> <span class="n">save_out</span>
+        
+        <span class="bp">self</span><span class="o">.</span><span class="n">var_samples</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([])</span>
+        <span class="sd">&quot;&quot;&quot;Samples of variable input parameters.&quot;&quot;&quot;</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">outputs</span><span class="p">:</span> <span class="nb">list</span> <span class="o">=</span> <span class="p">[]</span>
+        <span class="sd">&quot;&quot;&quot;Simulation outputs.&quot;&quot;&quot;</span>
+
+<div class="viewcode-block" id="RunSimulator.serial_run"><a class="viewcode-back" href="../../../simulator/run_simulator.html#psimpy.simulator.run_simulator.RunSimulator.serial_run">[docs]</a>    <span class="nd">@beartype</span>
+    <span class="k">def</span> <span class="nf">serial_run</span><span class="p">(</span>
+        <span class="bp">self</span><span class="p">,</span> <span class="n">var_samples</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="n">prefixes</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="nb">str</span><span class="p">],</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
+        <span class="n">append</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="kc">False</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
+        <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Perform serial execution of ``simulator`` at a set of ``var_samples``.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        var_samples : numpy array</span>
+<span class="sd">            Samples of variable input parameters. The first axis</span>
+<span class="sd">            (:code:`var_samples.shape[0]`) corresponds to the number of samples.</span>
+<span class="sd">            The second axis (:code:`var_samples.shape[1]`) corresponds to the</span>
+<span class="sd">            number of variable input parameters. </span>
+<span class="sd">        prefixes :  list of str, optional</span>
+<span class="sd">            Contains :code:`len(var_samples)` prefixes. Each of them is used to</span>
+<span class="sd">            name corresponding simulation output file. </span>
+<span class="sd">        append : bool, optional</span>
+<span class="sd">            If `True`, append ``var_samples`` to existing samples and</span>
+<span class="sd">            correspondingly append simulation outputs.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">num_pre_run</span><span class="p">,</span> <span class="n">num_new_run</span><span class="p">,</span> <span class="n">kwargs_num_new_run</span><span class="p">,</span> <span class="n">prefixes</span> <span class="o">=</span> \
+            <span class="bp">self</span><span class="o">.</span><span class="n">_preprocess</span><span class="p">(</span><span class="n">var_samples</span><span class="p">,</span> <span class="n">prefixes</span><span class="p">,</span> <span class="n">append</span><span class="p">)</span>
+        
+        <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">num_new_run</span><span class="p">):</span>
+            <span class="n">kwargs</span> <span class="o">=</span> <span class="n">kwargs_num_new_run</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+
+            <span class="k">try</span><span class="p">:</span>
+                <span class="n">output</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">simulator</span><span class="p">(</span><span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">outputs</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">output</span><span class="p">)</span>
+                
+                <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">save_out</span><span class="p">:</span>
+                    <span class="n">fname</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="n">prefixes</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="si">}</span><span class="s2">_output.npy&quot;</span>
+                    <span class="n">np</span><span class="o">.</span><span class="n">save</span><span class="p">(</span><span class="n">os</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">dir_out</span><span class="p">,</span> <span class="n">fname</span><span class="p">),</span> <span class="n">output</span><span class="p">)</span>
+
+            <span class="k">except</span> <span class="ne">Exception</span> <span class="k">as</span> <span class="n">e</span><span class="p">:</span>
+                <span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;Exception occurred in simulation </span><span class="si">{</span><span class="n">prefixes</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="si">}</span><span class="s2">.&quot;</span>
+                      <span class="sa">f</span><span class="s2">&quot;The error message is: </span><span class="si">{</span><span class="nb">str</span><span class="p">(</span><span class="n">e</span><span class="p">)</span><span class="si">}</span><span class="s2">&quot;</span><span class="p">)</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">outputs</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">str</span><span class="p">(</span><span class="n">e</span><span class="p">))</span></div>
+            
+<div class="viewcode-block" id="RunSimulator.parallel_run"><a class="viewcode-back" href="../../../simulator/run_simulator.html#psimpy.simulator.run_simulator.RunSimulator.parallel_run">[docs]</a>    <span class="nd">@beartype</span>
+    <span class="k">def</span> <span class="nf">parallel_run</span><span class="p">(</span>
+        <span class="bp">self</span><span class="p">,</span> <span class="n">var_samples</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="n">prefixes</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="nb">str</span><span class="p">],</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
+        <span class="n">append</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="kc">False</span><span class="p">,</span> <span class="n">max_workers</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">int</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
+        <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Perform parallel execution of ``simulator`` at a set of ``var_samples``.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        var_samples : numpy array</span>
+<span class="sd">            Samples of variable input parameters. The first axis</span>
+<span class="sd">            (:code:`var_samples.shape[0]`) corresponds to the number of samples.</span>
+<span class="sd">            The second axis (:code:`var_samples.shape[1]`) corresponds to the</span>
+<span class="sd">            number of variable input parameters.</span>
+<span class="sd">        prefixes :  list of str, optional</span>
+<span class="sd">            Contains :code:`len(var_samples)` prefixes. Each of them is used to</span>
+<span class="sd">            name corresponding simulation output file.</span>
+<span class="sd">        append : bool, optional</span>
+<span class="sd">            If `True`, append ``var_samples`` to existing samples and</span>
+<span class="sd">            correspondingly append simulation outputs.</span>
+<span class="sd">        max_workers : int, optional</span>
+<span class="sd">            Controls the maximum number of tasks running in parallel.</span>
+<span class="sd">            Default is the number of CPUs on the host.        </span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">num_pre_run</span><span class="p">,</span> <span class="n">num_new_run</span><span class="p">,</span> <span class="n">kwargs_num_new_run</span><span class="p">,</span> <span class="n">prefixes</span> <span class="o">=</span> \
+            <span class="bp">self</span><span class="o">.</span><span class="n">_preprocess</span><span class="p">(</span><span class="n">var_samples</span><span class="p">,</span> <span class="n">prefixes</span><span class="p">,</span> <span class="n">append</span><span class="p">)</span>
+
+        <span class="k">with</span> <span class="n">ProcessPoolExecutor</span><span class="p">(</span><span class="n">max_workers</span><span class="o">=</span><span class="n">max_workers</span><span class="p">)</span> <span class="k">as</span> <span class="n">executor</span><span class="p">:</span>
+            <span class="n">futures</span> <span class="o">=</span> <span class="p">[</span><span class="n">executor</span><span class="o">.</span><span class="n">submit</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">simulator</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
+                       <span class="k">for</span> <span class="n">kwargs</span> <span class="ow">in</span> <span class="n">kwargs_num_new_run</span><span class="p">]</span>
+            <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">num_new_run</span><span class="p">):</span>
+                <span class="k">try</span><span class="p">:</span>
+                    <span class="n">output</span> <span class="o">=</span> <span class="n">futures</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">.</span><span class="n">result</span><span class="p">()</span>
+                    <span class="bp">self</span><span class="o">.</span><span class="n">outputs</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">output</span><span class="p">)</span>
+
+                    <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">save_out</span><span class="p">:</span>
+                        <span class="n">fname</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="n">prefixes</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="si">}</span><span class="s2">_output.npy&quot;</span>
+                        <span class="n">np</span><span class="o">.</span><span class="n">save</span><span class="p">(</span><span class="n">os</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">dir_out</span><span class="p">,</span> <span class="n">fname</span><span class="p">),</span> <span class="n">output</span><span class="p">)</span>
+
+                <span class="k">except</span> <span class="ne">Exception</span> <span class="k">as</span> <span class="n">e</span><span class="p">:</span>
+                    <span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;Exception occurred in simulation </span><span class="si">{</span><span class="n">prefixes</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="si">}</span><span class="s2">.&quot;</span>
+                          <span class="sa">f</span><span class="s2">&quot;The error message is: </span><span class="si">{</span><span class="nb">str</span><span class="p">(</span><span class="n">e</span><span class="p">)</span><span class="si">}</span><span class="s2">&quot;</span><span class="p">)</span>
+                    <span class="bp">self</span><span class="o">.</span><span class="n">outputs</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">str</span><span class="p">(</span><span class="n">e</span><span class="p">))</span></div>
+    
+
+    <span class="k">def</span> <span class="nf">_preprocess</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">var_samples</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="n">prefixes</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">str</span><span class="p">],</span>
+        <span class="n">append</span><span class="p">:</span> <span class="nb">bool</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">tuple</span><span class="p">[</span><span class="nb">int</span><span class="p">,</span> <span class="nb">int</span><span class="p">,</span> <span class="nb">list</span><span class="p">[</span><span class="nb">dict</span><span class="p">],</span> <span class="nb">list</span><span class="p">[</span><span class="nb">str</span><span class="p">]]:</span>
+        <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Preprocess inputs for :meth:`.serial_run` and :meth:`parallel_run`.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        var_samples : numpy array</span>
+<span class="sd">            Samples of variable input parameters. The first axis</span>
+<span class="sd">            (:code:`var_samples.shape[0]`) corresponds to the number of samples.</span>
+<span class="sd">            The second axis (:code:`var_samples.shape[1]`) corresponds to the</span>
+<span class="sd">            number of variable input parameters.</span>
+<span class="sd">        prefixes :  list of str, optional</span>
+<span class="sd">            Contains :code:`len(var_samples)` prefixes. Each of them is used to</span>
+<span class="sd">            name corresponding simulation output file.</span>
+<span class="sd">        append : bool</span>
+<span class="sd">            If `True`, append ``var_samples`` to existing samples and</span>
+<span class="sd">            correspondingly append simulation outputs.</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        num_pre_run : int</span>
+<span class="sd">            Number of existing runs.</span>
+<span class="sd">        num_new_run : int</span>
+<span class="sd">            Number of new runs. </span>
+<span class="sd">        kwargs_num_new_run: list</span>
+<span class="sd">            Contains ``num_new_run`` dictionaries, each of which corresponds to </span>
+<span class="sd">            ``kwargs`` of one simulation.     </span>
+<span class="sd">        prefixes : list of str</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="n">var_samples</span><span class="o">.</span><span class="n">ndim</span> <span class="o">==</span> <span class="mi">0</span> <span class="ow">or</span> <span class="n">var_samples</span><span class="o">.</span><span class="n">ndim</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
+            <span class="n">var_samples</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">var_samples</span><span class="p">,</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">))</span>           
+
+        <span class="k">if</span> <span class="n">var_samples</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">!=</span> <span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">var_inp_parameter</span><span class="p">):</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span>
+                <span class="s2">&quot;var_samples should have the same number of&quot;</span> 
+                <span class="s2">&quot; variable inputs as defined by var_input_parameter&quot;</span><span class="p">)</span>
+        
+        <span class="n">num_new_run</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">var_samples</span><span class="p">)</span>
+        
+        <span class="k">if</span> <span class="ow">not</span> <span class="n">append</span><span class="p">:</span>
+            <span class="n">num_pre_run</span> <span class="o">=</span> <span class="mi">0</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">outputs</span> <span class="o">=</span> <span class="p">[]</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">var_samples</span> <span class="o">=</span> <span class="n">var_samples</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="n">num_pre_run</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">var_samples</span><span class="p">)</span>
+            <span class="k">if</span> <span class="n">num_pre_run</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
+                <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span>
+                    <span class="s2">&quot;append is True but no previous var_samples exist&quot;</span><span class="p">)</span>
+            <span class="k">else</span><span class="p">:</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">var_samples</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">vstack</span><span class="p">((</span><span class="bp">self</span><span class="o">.</span><span class="n">var_samples</span><span class="p">,</span> <span class="n">var_samples</span><span class="p">))</span>
+        
+        <span class="k">if</span> <span class="n">prefixes</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="n">prefixes</span> <span class="o">=</span> <span class="p">[</span><span class="sa">f</span><span class="s1">&#39;sim</span><span class="si">{</span><span class="n">i</span><span class="o">+</span><span class="n">num_pre_run</span><span class="si">}</span><span class="s1">&#39;</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">num_new_run</span><span class="p">)]</span>
+        <span class="k">elif</span> <span class="nb">len</span><span class="p">(</span><span class="n">prefixes</span><span class="p">)</span> <span class="o">!=</span> <span class="n">num_new_run</span><span class="p">:</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span>
+                <span class="s2">&quot;prefixes should have same number of items as var_samples&quot;</span><span class="p">)</span>
+        <span class="k">elif</span> <span class="nb">len</span><span class="p">(</span><span class="nb">set</span><span class="p">(</span><span class="n">prefixes</span><span class="p">))</span> <span class="o">!=</span> <span class="n">num_new_run</span><span class="p">:</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;Each element of prefixes should be unique&quot;</span><span class="p">)</span>
+
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">save_out</span><span class="p">:</span>
+            <span class="n">new_filenames</span> <span class="o">=</span> \
+                <span class="p">[</span><span class="sa">f</span><span class="s1">&#39;</span><span class="si">{</span><span class="n">prefixes</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="si">}</span><span class="s1">_output.npy&#39;</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">num_new_run</span><span class="p">)]</span>
+            <span class="n">exist_filenames</span> <span class="o">=</span> <span class="n">os</span><span class="o">.</span><span class="n">listdir</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">dir_out</span><span class="p">)</span>
+            <span class="n">common_filenames</span> <span class="o">=</span> <span class="nb">set</span><span class="p">(</span><span class="n">new_filenames</span><span class="p">)</span><span class="o">.</span><span class="n">intersection</span><span class="p">(</span><span class="n">exist_filenames</span><span class="p">)</span>
+            
+            <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">common_filenames</span><span class="p">)</span> <span class="o">!=</span> <span class="mi">0</span><span class="p">:</span>
+                <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span>
+                    <span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="bp">self</span><span class="o">.</span><span class="n">dir_out</span><span class="si">}</span><span class="s2"> contains files named with prefixes. &quot;</span>
+                    <span class="sa">f</span><span class="s2">&quot;Please move or delete the files before starting runs, &quot;</span>
+                    <span class="sa">f</span><span class="s2">&quot;or provide different prefixes.&quot;</span><span class="p">)</span>
+        
+        <span class="n">kwargs_num_new_run</span> <span class="o">=</span> <span class="p">[]</span>
+        <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">num_new_run</span><span class="p">):</span>
+            
+            <span class="n">var_sample</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">var_samples</span><span class="p">[</span><span class="n">i</span><span class="o">+</span><span class="n">num_pre_run</span><span class="p">]</span>
+            <span class="n">kwargs</span> <span class="o">=</span> <span class="p">{</span><span class="bp">self</span><span class="o">.</span><span class="n">var_inp_parameter</span><span class="p">[</span><span class="n">j</span><span class="p">]:</span> <span class="n">var_sample</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> 
+                <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">var_sample</span><span class="p">))}</span>
+            
+            <span class="n">kwargs</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">fix_inp</span><span class="p">)</span>
+
+            <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">o_parameter</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+                <span class="n">kwargs</span><span class="o">.</span><span class="n">update</span><span class="p">({</span><span class="sa">f</span><span class="s1">&#39;</span><span class="si">{</span><span class="bp">self</span><span class="o">.</span><span class="n">o_parameter</span><span class="si">}</span><span class="s1">&#39;</span><span class="p">:</span> <span class="sa">f</span><span class="s1">&#39;</span><span class="si">{</span><span class="n">prefixes</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="si">}</span><span class="s1">&#39;</span><span class="p">})</span>
+            
+            <span class="n">kwargs_num_new_run</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">kwargs</span><span class="p">)</span>
+
+        <span class="k">return</span> <span class="n">num_pre_run</span><span class="p">,</span> <span class="n">num_new_run</span><span class="p">,</span> <span class="n">kwargs_num_new_run</span><span class="p">,</span> <span class="n">prefixes</span></div>
+</pre></div>
+
+           </div>
+          </div>
+          <footer>
+
+  <hr/>
+
+  <div role="contentinfo">
+    <p>&#169; Copyright 2023, Hu Zhao.</p>
+  </div>
+
+  Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a
+    <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a>
+    provided by <a href="https://readthedocs.org">Read the Docs</a>.
+   
+
+</footer>
+        </div>
+      </div>
+    </section>
+  </div>
+  <script>
+      jQuery(function () {
+          SphinxRtdTheme.Navigation.enable(true);
+      });
+  </script> 
+
+</body>
+</html>
\ No newline at end of file
diff --git a/docs/source/_build/html/_sources/api.rst.txt b/docs/source/_build/html/_sources/api.rst.txt
new file mode 100644
index 0000000..1dfc308
--- /dev/null
+++ b/docs/source/_build/html/_sources/api.rst.txt
@@ -0,0 +1,11 @@
+API & Theory
+============
+
+.. toctree::
+   :maxdepth: 2
+
+   /emulator/index
+   /inference/index
+   /sampler/index
+   /sensitivity/index
+   /simulator/index
\ No newline at end of file
diff --git a/docs/source/_build/html/_sources/changelog.rst.txt b/docs/source/_build/html/_sources/changelog.rst.txt
new file mode 100644
index 0000000..198a10c
--- /dev/null
+++ b/docs/source/_build/html/_sources/changelog.rst.txt
@@ -0,0 +1,6 @@
+:tocdepth: 1
+
+Changes
+=======
+
+.. include:: ../../CHANGELOG.md
diff --git a/docs/source/_build/html/_sources/emulator/index.rst.txt b/docs/source/_build/html/_sources/emulator/index.rst.txt
new file mode 100644
index 0000000..1ffa6d7
--- /dev/null
+++ b/docs/source/_build/html/_sources/emulator/index.rst.txt
@@ -0,0 +1,27 @@
+********
+Emulator
+********
+
+This module hosts functionality for emulation methods.
+
+Emulation, also known as surrogate modeling or meta-modeling, is a type of
+method which is used to build cheap-to-evaluate emulators (surrogate models) to
+approximate expensive-to-evaluate simulators. It can greatly reduce
+computational costs of tasks in which a computationally intensive simulator
+needs to be run multiple times, such as a global sensitivity anlaysis,
+uncertainty quantification, or parameter calibration.
+
+Currently implemented classes in this module are:
+
+* :class:`.ScalarGaSP`: Gaussian process emulation for simulators which return a
+  scalar value as output.
+
+* :class:`.PPGaSP`: Gaussian process emulation for simulators which return
+  multiple values as output. 
+
+.. toctree::
+   :maxdepth: 2
+   :hidden:
+   :caption: Emulator
+
+    RobustGaSP <robustgasp>
\ No newline at end of file
diff --git a/docs/source/_build/html/_sources/emulator/robustgasp.rst.txt b/docs/source/_build/html/_sources/emulator/robustgasp.rst.txt
new file mode 100644
index 0000000..d5c587f
--- /dev/null
+++ b/docs/source/_build/html/_sources/emulator/robustgasp.rst.txt
@@ -0,0 +1,211 @@
+RobustGaSP
+==========
+
+`RobustGaSP`, standing for `Robust Gaussian Stochastic Process Emulation`, is a
+`R` package developed by :cite:t:`Gu2019`. It implements robust methods to
+estimate the unknown parameters which can greatly improve predictive performance
+of the built emulator. In addition, it implements the `PP GaSP` (parallel partial
+Gaussian stochastic process) emulator for simulators which return multiple values
+as output, see :cite:t:`Gu2016` for more detail.
+
+In :py:mod:`PSimPy.emulator.robustgasp`, we have implemented class
+:class:`.ScalarGaSP` and  class :class:`.PPGaSP` based on `RobustGaSP` and
+`rpy2`, which allows us to use `RobustGaSP` directly from within `Python`.
+
+Theory recap of GP emulation
+----------------------------
+
+A simulator represents a mapping from an input space to an output space.
+Gaussian process emulation treats a computationally expensive simulator as an
+unknown function from a Bayesian perspective: the prior belief of the simulator,
+namely a Gaussian process, is updated based on a modest number of simulation runs,
+leading to a posterior which can be evaluated much faster than the simulator and
+can then be used for computationally demanding analyses :cite:p:`Zhao2021a`. A recap
+of Gaussian process emulation is provided below, which is adapted from `Chapter 3`
+of :cite:t:`Zhao2021b`.
+
+GP prior
+^^^^^^^^
+
+Let :math:`f(\cdot)` denote a simulator that one wants to approximate. It
+defines a mapping from a :math:`p`-dimensional input
+:math:`\mathbf{x}=(x_1,\ldots,x_p)^T \in \mathcal{X} \subset{\mathbb{R}^p}`
+to a scalar output :math:`y \in \mathbb{R}`. 
+
+From the Bayesian perspective, the prior belief of the simulator is modeled by
+a Gaussian process, namely
+
+.. math:: f(\cdot) \sim \mathcal{GP}(m(\cdot), C(\cdot,\cdot)).
+    :label: GP
+
+The Gaussian process is fully specified by its mean function :math:`m(\cdot)`
+and covariance function :math:`C(\cdot,\cdot)`. The mean function is usually
+modeled by parametric regression
+
+.. math:: m(\mathbf{x})=\mathbf{h}^T(\mathbf{x}) \boldsymbol{\beta}=\sum_{t=1}^{q} h_{t}(\mathbf{x}) \beta_{t},
+    :label: GPmean
+
+with :math:`q`-dimensional vectors
+:math:`\mathbf{h}(\mathbf{x})=\left(h_{1}(\mathbf{x}), h_{2}(\mathbf{x}), \ldots, h_{q}(\mathbf{x})\right)^T`
+and :math:`\boldsymbol{\beta}=\left(\beta_{1}, \beta_{2}, \ldots, \beta_{q}\right)^T`
+denoting the chosen basis functions and unknown regression parameters respectively.
+The basis functions are commonly chosen as constant :math:`\mathbf{h}(\mathbf{x})=1`
+or some prescribed polynomials like :math:`\mathbf{h}(\mathbf{x})=(1,x_1,\ldots,x_p)^T`.
+
+The covariance function is often assumed to be stationary and typically has a
+separable form of
+
+.. math::  C\left(\mathbf{x}_{i}, \mathbf{x}_{j}\right)=\sigma^2 c\left(\mathbf{x}_{i}, \mathbf{x}_{j}\right)=\sigma^2 \prod_{l=1}^{p} c_{l}\left(x_{i l}, x_{j l}\right),
+    :label: GPcovariance
+
+where :math:`c\left(\mathbf{x}_{i}, \mathbf{x}_{j}\right)` is the correlation
+function, and :math:`c_{l}\left(x_{i l}, x_{j l}\right)` corresponds to the
+correlation between the :math:`l`-th component of :math:`\mathbf{x}_i`` and
+the counterpart of :math:`\mathbf{x}_j`. Various correlation functions can be
+chosen for :math:`c_{l}\left(x_{i l}, x_{j l}\right)`. In what follows a specific
+correlation function from the Matern family is chosen to illustrate the theory.
+It should be noted that it can be replaced by any other correlation function
+without loss of generality.
+
+.. math:: c_{l}\left(x_{i l}, x_{j l}\right) = \left(1+\frac{\sqrt{5}||x_{il}-x_{jl}||}{\psi_l}+\frac{5||x_{il}-x_{jl}||^2}{3\psi_{l}^{2}} \right) \exp{\left(-\frac{\sqrt{5}||x_{il}-x_{jl}||}{\psi_l}\right)},
+    :label: GPcorrelation
+
+where :math:`\psi_l` is the correlation length parameter in the :math:`l`-th
+dimension. The unknowns in the covariance function
+:math:`C\left(\mathbf{x}_{i}, \mathbf{x}_{j}\right)` are the variance
+:math:`\sigma^2` and the :math:`p` correlation length parameters
+:math:`\boldsymbol{\psi}=(\psi_1,\ldots,\psi_p)^T`.
+
+GP posterior
+^^^^^^^^^^^^
+
+Equations :eq:`GP` to :eq:`GPcorrelation` encode prior knowledge of the simulator
+:math:`f(\cdot)`. From the Bayesian viewpoint, this prior knowledge can be updated
+to a posterior based on a limited number of training data. Training data here refer
+to :math:`n^{tr}` pairs of input-output data of :math:`f(\cdot)`.
+
+Let :math:`\mathbf{x}^{tr}:=\{\mathbf{x}_i\}_{i=1}^{n^{tr}}` and 
+:math:`\mathbf{y}^{tr}:=\{f(\mathbf{x}_i)\}_{i=1}^{n^{tr}}` denote the training
+inputs and outputs respectively. Since any finite number of random variables
+from a Gaussian process are jointly Gaussian distributed, the joint distribution
+of the :math:`n^{tr}` outputs :math:`\mathbf{y}^{tr}` follow a
+:math:`n^{tr}`-dimensional Gaussian distribution
+
+.. math:: p(\mathbf{y}^{tr} | \boldsymbol{\beta}, \sigma^{2}, \boldsymbol{\psi})  \sim \mathcal{N}_{n^{tr}}\left(\mathbf{H}\boldsymbol{\beta}, \sigma^{2} \mathbf{R}\right),
+    :label: GPlikelihood1
+
+where :math:`\mathbf{H}=\left[\mathbf{h}(\mathbf{x}_{1}), \ldots, \mathbf{h}(\mathbf{x}_{n^{tr}}) \right]^T`
+is the :math:`n^{tr} \times q` basis design matrix and :math:`\mathbf{R}` is the
+:math:`n^{tr} \times n^{tr}` correlation matrix with :math:`(i,j)` element
+:math:`c(\mathbf{x}_{i}, \mathbf{x}_{j})`. Equation :eq:`GPlikelihood1` is known
+as the likelihood function.
+
+Similarly, the joint distribution of the function output :math:`y^*` at any
+untried input :math:`\mathbf{x}^*` and :math:`\mathbf{y}^{tr}` follows a
+:math:`(n^{tr}+1)`-dimensional Gaussian distribution
+
+.. math:: p(y^*, \mathbf{y}^{tr} \mid \boldsymbol{\beta}, \sigma^{2}, \boldsymbol{\psi}) \sim \mathcal{N}_{n^{tr}+1}\left(\left[\begin{array}{c}
+    \mathbf{h}^T\left(\mathbf{x}^*\right) \\
+    \mathbf{H}
+    \end{array}\right] \boldsymbol{\beta}, \sigma^{2}\left[\begin{array}{cc}
+    c\left(\mathbf{x}^*, \mathbf{x}^*\right) & \mathbf{r}^T\left(\mathbf{x}^*\right) \\
+    \mathbf{r}\left(\mathbf{x}^*\right) & \mathbf{R}
+    \end{array}\right]\right)
+    :label: jointystarytr
+
+where :math:`\mathbf{r}(\mathbf{x}^*)=\left(c(\mathbf{x}^*, \mathbf{x}_{1}), \ldots, c(\mathbf{x}^*, \mathbf{x}_{n^{tr}}) \right)^T`.
+According to the property of the multivariate Gaussian distribution, the conditional
+distribution of :math:`y^*` conditioned on :math:`\mathbf{y}^{tr}` is again a
+Gaussian distribution, namely
+
+.. math:: p(y^* | \mathbf{y}^{tr}, \boldsymbol{\beta}, \sigma^{2}, \boldsymbol{\psi}) \sim  \mathcal{N}
+    \left(m', \sigma^2 c' \right),\label{eq:conditionalGaussian}
+    :label: conditionalGaussian
+
+.. math:: m'=\mathbf{h}^T(\mathbf{x}^*) \boldsymbol{\beta} + \mathbf{r}^T(\mathbf{x}^*) \mathbf{R}^{-1} (\mathbf{y}^{tr}-\mathbf{H}\boldsymbol{\beta})
+    :label: conditionalGaussianM
+
+.. math:: c'=c(\mathbf{x}^*, \mathbf{x}^*) - \mathbf{r}^T(\mathbf{x}^*) \mathbf{R}^{-1} \mathbf{r}(\mathbf{x}^*).
+    :label: conditionalGaussianC
+
+Equations :eq:`conditionalGaussian` to :eq:`conditionalGaussianC` can be easily
+extended to any dimensionality since the joint distribution of the function
+outputs at any number of untried inputs and :math:`\mathbf{y}^{tr}` also follows
+a multivariate Gaussian distribution. Equations :eq:`conditionalGaussian` to 
+:eq:`conditionalGaussianC` therefore essentially define the posterior which is an
+updated Gaussian process, given the unknown regression parameters
+:math:`\boldsymbol{\beta}`, variance :math:`\sigma^2`, and correlation length
+parameters :math:`\boldsymbol{\psi}`. 
+
+For any new input :math:`\mathbf{x}^*`, the output :math:`y^*` can be almost
+instantaneously predicted, given by the mean :math:`m'`, namely equation
+:eq:`conditionalGaussianM`. Moreover, the uncertainty associated with the prediction
+can be estimated by for example the variance :math:`\sigma^2c'`. Depending on how
+the unknown parameters (:math:`\boldsymbol{\beta}`, :math:`\sigma^2`, and :math:`\boldsymbol{\psi}`)
+are learned based on the training data, the posterior can have various forms, see
+`Section 3.3` of :cite:t:`Zhao2021b`.
+
+Sample from GP
+^^^^^^^^^^^^^^
+A Gaussian process, either the prior or the posterior, defines a distribution over
+functions. Once its mean function :math:`m(\cdot)` and covariance function
+:math:`C(\cdot,\cdot)` are specified, the Gaussian process can be evaluated at a
+finite number :math:`s` of input points :math:`\{\mathbf{x}_i\}_{i=1}^{s}`.
+The joint distribution of :math:`\{y_i=f(\mathbf{x}_i)\}_{i=1}^{s}` follows a
+:math:`s`-variate Gaussian distribution. A sample of the :math:`s`-variate Gaussian
+distribution, denoted as :math:`\tilde{\mathbf{y}}:=(\tilde{y}_1,\ldots,\tilde{y}_s)^T`,
+can be viewed as a sample of the Gaussian process (evaluated at a finite number of points).
+To generate :math:`\tilde{\mathbf{y}}`, the :math:`s \times s` covariance matrix
+:math:`\boldsymbol{\Sigma}` needs to be decomposed into the product of a lower triangular
+matrix :math:`\mathbf{L}` and its conjugate transpose :math:`\mathbf{L}^T` using the Cholesky
+decomposition
+
+.. math:: \boldsymbol{\Sigma}=\left(\begin{array}{cccc}
+    C\left(\mathbf{x}_{1}, \mathbf{x}_{1}\right) & C\left(\mathbf{x}_{1}, \mathbf{x}_{2}\right) & \ldots & C\left(\mathbf{x}_{1}, \mathbf{x}_{s}\right) \\
+    C\left(\mathbf{x}_{2}, \mathbf{x}_{1}\right) & C\left(\mathbf{x}_{2}, \mathbf{x}_{2}\right) & \ldots & C\left(\mathbf{x}_{2}, \mathbf{x}_{s}\right) \\
+    \vdots & \vdots & \ddots & \vdots \\
+    C\left(\mathbf{x}_{s}, \mathbf{x}_{1}\right) & \ldots & \ldots & C\left(\mathbf{x}_{s}, \mathbf{x}_{s}\right)
+    \end{array}\right)=\mathbf{L}\mathbf{L}^T.
+    :label: Choleskydecomposition
+
+Then a sample :math:`\tilde{\mathbf{y}}` can be obtained as follows:
+
+.. math:: \tilde{\mathbf{y}} = (m(\mathbf{x}_i),\ldots,m(\mathbf{x}_s))^T + \mathbf{L}\mathbf{w},
+    :label: GPsample
+
+where :math:`\mathbf{w}:=(w_1,\dots,w_s)^T` denotes a :math:`s`-dimensional random vector
+consisting of :math:`s` independent standard normal random variables :math:`w_i,i \in \{1,\ldots,s\}`.
+
+
+ScalarGaSP Class
+----------------
+
+Class :class:`.ScalarGaSP` provides Gaussian process emulation for simulators 
+which return a scalar value as output, namely :math:`y \in \mathbb{R}`. Please
+refer to :cite:t:`Gu2018` for the detailed theory.
+
+It is imported by::
+    
+    from psimpy.emulator.robustgasp import ScalarGaSP
+
+Methods
+^^^^^^^
+.. autoclass:: psimpy.emulator.robustgasp.ScalarGaSP
+    :members: train, predict, sample, loo_validate
+
+
+PPGaSP Class
+------------
+
+Class :class:`.PPGaSP` provides Gaussian process emulation for simulators 
+which return multiple values as output, namely :math:`y \in \mathbb{R}^k, k>1`.
+Please refer to :cite:t:`Gu2016` for the detailed theory.
+
+It is imported by::
+    
+    from psimpy.emulator.robustgasp import PPGaSP
+
+Methods
+^^^^^^^
+.. autoclass:: psimpy.emulator.robustgasp.PPGaSP
+    :members: train, predict, sample
diff --git a/docs/source/_build/html/_sources/examples.rst.txt b/docs/source/_build/html/_sources/examples.rst.txt
new file mode 100644
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+++ b/docs/source/_build/html/_sources/examples.rst.txt
@@ -0,0 +1,11 @@
+Example Gallery
+===============
+
+.. toctree::
+
+   Emulator <../auto_examples/emulator/index>
+   Inference <../auto_examples/inference/index>
+   Sampler <../auto_examples/sampler/index>
+   Sensitivity <../auto_examples/sensitivity/index>
+   Simulator <../auto_examples/simulator/index>
+   
\ No newline at end of file
diff --git a/docs/source/_build/html/_sources/index.rst.txt b/docs/source/_build/html/_sources/index.rst.txt
new file mode 100644
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@@ -0,0 +1,21 @@
+:gitlab_url: https://git-ce.rwth-aachen.de/mbd/psimpy
+
+Welcome to PSimPy's documentation!
+==================================
+
+:Release: |release|
+:Date: |today|
+
+
+Contents
+--------
+
+.. toctree::
+   :maxdepth: 2
+
+   Home <self>
+   quickstart
+   api
+   examples
+   changelog
+   refs
diff --git a/docs/source/_build/html/_sources/inference/active_learning.rst.txt b/docs/source/_build/html/_sources/inference/active_learning.rst.txt
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+Active Learning
+===============
+
+Active learning is a machine learning technique that involves selecting the most
+informative data points for the purpose of training an emulator. The idea behind
+active learning is to reduce the amount of training data required for a machine
+learning model to achieve a certain level of accuracy. This is achieved by iteratively
+choosing a new data point that is expected to be the most informative.
+
+In this module, the :class:`.ActiveLearning` class is implemented to actively build a
+Gaussian process emulator for the natural logarithm of the unnormalized posterior in
+Bayesian inference. It is supposed to facilitate efficient parameter calibration of
+computationally expensive simulators. For detailed theories, please refer to 
+:cite:t:`Wang2018`, :cite:t:`Kandasamy2017`, and :cite:t:`Zhao2022`.
+
+
+ActiveLearning Class
+--------------------
+
+The :class:`.ActiveLearning` class is imported by::
+    
+    from psimpy.inference.active_learning import ActiveLearning
+
+Methods
+^^^^^^^
+.. autoclass:: psimpy.inference.active_learning.ActiveLearning
+    :members: initial_simulation, iterative_emulation, approx_ln_pxl
\ No newline at end of file
diff --git a/docs/source/_build/html/_sources/inference/bayes_inference.rst.txt b/docs/source/_build/html/_sources/inference/bayes_inference.rst.txt
new file mode 100644
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+Bayes Inference
+===============
+
+Bayesian inference is a statistical method for making probabilistic inference about
+unknown parameters based on observed data and prior knowledge. The update from
+prior knowledge to posterior in light of observed data is based on Bayes' theorem:
+
+.. math:: p(\mathbf{x} \mid \mathbf{d}) = \frac{L(\mathbf{x} \mid \mathbf{d}) p(\mathbf{x})}
+    {\int L(\mathbf{x} \mid \mathbf{d}) p(\mathbf{x}) d \mathbf{x}}
+    :label: bayes
+
+where :math:`\mathbf{x}` represents the collection of unknown parameters and
+:math:`\mathbf{d}` represents the collection of observed data. The prior probability
+distribution, :math:`p(\mathbf{x})`, represents the degree of belief in the parameters before
+any data is observed. The likelihood function, :math:`L(\mathbf{x} \mid \mathbf{d})`, represents
+the probability of observing the data given the parameters. The posterior distribution,
+:math:`p(\mathbf{x} \mid \mathbf{d})`, is obtained by multiplying the prior probability
+distribution by the likelihood function and then normalizing the result. Bayesian inference
+allows for incorporating subjective prior beliefs, which can be updated as new data becomes available.
+
+For many real world problems, it is hardly possible to analytically compute the posterior due to
+the complexity of the denominator in equation :eq:`bayes`, namely the nomalizing constant. In this
+module, two numerical approximations are implemented: grid estimation and Metropolis Hastings
+estimation.
+
+In grid estimation, the denominator in equation :eq:`bayes` is approximated by numerical integration
+on a regular grid and the posterior value at each grid point is computed, as shown in equation
+:eq:`grid_estimation`. The number of grid points increases dramatically with the increase of the number
+of unknown parameters. Grid estimation is therefore limited to low-dimensional problems.
+
+.. math:: p(\mathbf{x} \mid \mathbf{d}) \approx \frac{L(\mathbf{x} \mid \mathbf{d}) p(\mathbf{x})}
+    {\sum_{i=1}^N L\left(\mathbf{x}_i \mid \mathbf{d}\right) p\left(\mathbf{x}_i\right) \Delta \mathbf{x}_i}
+    :label: grid_estimation
+
+Metropolis Hastings estimation directly draw samples from the unnormalized posterior distribution, namely
+the numerator of equation :eq:`bayes`. The samples are then used to estimate properties of the posterior
+distribution, like the mean and variance, or to estimate the posterior distribution.
+
+
+GridEstimation Class
+--------------------
+
+The :class:`.GridEstimation` class is imported by::
+    
+    from psimpy.inference.bayes_inference import GridEstimation
+
+Methods
+^^^^^^^
+.. autoclass:: psimpy.inference.bayes_inference.GridEstimation
+    :members: run
+
+
+MetropolisHastingsEstimation Class
+----------------------------------
+
+The :class:`.MetropolisHastingsEstimation` class is imported by::
+    
+    from psimpy.inference.bayes_inference import MetropolisHastingsEstimation
+
+Methods
+^^^^^^^
+.. autoclass:: psimpy.inference.bayes_inference.MetropolisHastingsEstimation
+    :members: run
diff --git a/docs/source/_build/html/_sources/inference/index.rst.txt b/docs/source/_build/html/_sources/inference/index.rst.txt
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+*********
+Inference
+*********
+
+This module hosts functionality for inference methods.
+
+Currently implemented classes are:
+
+* :class:`.ActiveLearning`: Construct a Gaussian process emulator for an unnormalized posterior. 
+
+* :class:`.GridEstimation`: Estimate a posterior distribution by grid estimation.
+
+* :class:`.MetropolisHastingsEstimation`: Estimate a posterior by Metropolis Hastings estimation.
+
+.. toctree::
+   :maxdepth: 1
+   :hidden:
+   :caption: Inference
+
+    Active Learning <active_learning>
+    Bayes Inference <bayes_inference>
\ No newline at end of file
diff --git a/docs/source/_build/html/_sources/quickstart.rst.txt b/docs/source/_build/html/_sources/quickstart.rst.txt
new file mode 100644
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@@ -0,0 +1,91 @@
+
+Getting Started
+===============
+
+Overview
+--------
+
+PSimPy (Predictive and probabilistic simulation with Python) implements
+a Gaussian process emulation-based framework that enables systematically and
+efficiently performing uncertainty-related analyses of physics-based
+models, which are often computationlly expensive. Examples are variance-based
+global sensitvity analysis, uncertainty quantification, and parameter
+calibration.
+
+Installation
+------------
+
+:py:mod:`PSimPy` is a pure Python package. All Python-related dependencies are
+automatically taken care of. It should be noted that some modules rely on or use
+non-Python package and software. More specifically, the emulator module
+:py:mod:`robustgasp.py` relies on the R package
+`RobustGaSP <https://cran.r-project.org/web/packages/RobustGaSP/>`_;
+the simulator module :py:mod:`ravaflow24.py` relies on the open source software
+`r.avaflow 2.4 <https://www.landslidemodels.org/r.avaflow/>`_.
+
+If the simulator module :py:mod:`ravaflow24.py` is desired, you may follow the
+official `r.avaflow User manual <https://www.landslidemodels.org/r.avaflow/manual.php>`_
+to install it. The installation of the R package `RobustGaSP` is covered in
+following steps.
+
+We recommond you to install :py:mod:`PSimPy` in a virtual environment such as a
+`conda` environment. You may want to first install `Anaconda` or `Miniconda` if you
+haven't. The steps afterwards are as follows.
+
+1. Create a conda environment with Python 3.9::
+    
+    conda create --name your_env_name python=3.9
+
+2. Install `R` if you don't have it on your machine (if you have `R`, you can
+   skip this step; alternatively, you can still follow this step to install `R` in
+   the conda environment)::
+    
+    conda activate your_env_name
+    conda install -c conda-forge r-base=3.6
+
+3. Install the R package `RobustGaSP` in the R terminal::
+    
+    R
+    install.packages("RobustGaSP",repos="https://cran.r-project.org",version="0.6.4")
+
+   Try if it is successfully installed by::
+    
+    library("RobustGaSP")
+
+4. Configure the environment variable `R_HOME` so that `rpy2` knows where to find
+   `R` packages. You can find your `R_HOME` by typing the following command in the
+   R terminal::
+    
+    R.home()
+    q()
+
+   It is a path like ".../lib/R". Set the environment variable `R_HOME` in your
+   conda environment by::
+    
+    conda env config vars set R_HOME=your_R_HOME
+
+   Afterwards reactivate your conda environment to make the change take effect by::
+    
+    conda deactivate
+    conda activate your_env_name
+
+5. Install :py:mod:`PSimPy` using `pip` in your conda environment by::
+    
+    conda install -c conda-forge pip
+    pip install psimpy
+
+Now you should have :py:mod:`PSimPy` and its dependencies successfully installed
+in your conda environment. You can use it in the Python terminal or in your
+Python IDE.
+
+If you would like to use it with Jupyter Notebook (iPython Notebook), there is
+one extra step needed to set your conda environment on your Notebook:
+
+6. Install `ipykernel` and install a kernel that points to your conda environment
+   by::
+
+    conda install -c conda-forge ipykernel
+    python -m ipykernel install --user --name=your_env_name
+
+Now you can start your Notebook, change the kernel to your conda environment, and
+use :py:mod:`PSimPy`.
\ No newline at end of file
diff --git a/docs/source/_build/html/_sources/refs.rst.txt b/docs/source/_build/html/_sources/refs.rst.txt
new file mode 100644
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+++ b/docs/source/_build/html/_sources/refs.rst.txt
@@ -0,0 +1,4 @@
+References
+==========
+
+.. bibliography::
\ No newline at end of file
diff --git a/docs/source/_build/html/_sources/sampler/index.rst.txt b/docs/source/_build/html/_sources/sampler/index.rst.txt
new file mode 100644
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@@ -0,0 +1,22 @@
+*******
+Sampler
+*******
+
+This module hosts functionality for sampling methods.
+
+Currently implemented classes are:
+
+* :class:`.LHS`: Latin hypercube sampling.
+
+* :class:`.MetropolisHastings`: Metropolis Hastings sampling.
+
+* :class:`.Saltelli`: Saltelli's version of Sobol' sampling.
+
+.. toctree::
+   :maxdepth: 1
+   :hidden:
+   :caption: Sampler
+
+    Latin Hypercube <latin>
+    Metropolis Hastings <metropolis_hastings>
+    Saltelli <saltelli>
\ No newline at end of file
diff --git a/docs/source/_build/html/_sources/sampler/latin.rst.txt b/docs/source/_build/html/_sources/sampler/latin.rst.txt
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@@ -0,0 +1,40 @@
+Latin Hypercube Sampling
+========================
+
+Latin hypercube sampling is one type of space-filling sampling method. It is often
+used to draw input points for emulator training. The following figure gives a
+three-dimensional example.
+
+.. image:: ../_static/latin_hypercube_sampling_sketch.png
+   :width: 800
+   :alt: an illustration of Latin hypercube sampling
+   :align: center
+
+Three random variables :math:`X`, :math:`Y`, and :math:`Z` consist of
+a three-dimensional space. If we want to draw :math:`6` samples from this space
+using Latin hypercube sampling, we first divide the range of each variable into
+:math:`6` equally probable intervals as shown on the left. In each interval,
+we pick a value for the corresponding variable. Then we shuffle the picked values
+of each variable (e.g. :math:`x_1` to :math:`x_6`) as shown in the middle. Last,
+each combination gives us one sample of the three variables as shown on the right.
+It should be noted that each sample excludes any other samples from the intervals
+that it locates in. This can be straightforwardly extended to draw :math:`M` samples
+from :math:`N`-dimensional space consisting of :math:`N` random variables.
+  
+
+LHS Class
+---------
+
+The :class:`.LHS` class is imported by::
+    
+    from psimpy.sampler.latin import LHS
+
+Methods
+^^^^^^^
+.. autoclass:: psimpy.sampler.latin.LHS
+    :members: sample
+
+
+.. warning:: The :class:`.LHS` class considers each random variable being uniformly
+    distributed in its range. If this is not the case, one needs to transform picked
+    samples accordingly. 
\ No newline at end of file
diff --git a/docs/source/_build/html/_sources/sampler/metropolis_hastings.rst.txt b/docs/source/_build/html/_sources/sampler/metropolis_hastings.rst.txt
new file mode 100644
index 0000000..cedb0b5
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@@ -0,0 +1,35 @@
+Metropolis Hastings Sampling
+============================
+
+Metropolis Hastings sampling is a widely used Markov Chain Monte Carlo (MCMC)
+algorithm for generating a sequence of samples from a target probability
+distribution where direct sampling is difficult. The samples can be used to
+estimate properties of the target distribution, like its mean, variance, and higher
+moments. The samples can also be used to approximate the target distribution,
+for example via a histogram. The algorithm works by constructing a Markov chain
+with a stationary distribution equal to the target distribution. 
+
+Steps of the algorithm are as follows:
+
+  1. Choose an initial state for the Markov chain, usually from the target distribution.
+  2. At each iteration, propose a new state by sampling from a proposal distribution.
+  3. Calculate the acceptance probability.
+  4. Accept or reject the proposed state based on the acceptance probability.
+  5. Repeat steps 2-4 for a large number of iterations to obtain a sequence of samples.
+  6. Apply "burn-in" and "thining".
+
+Final samples from the Markov chain can then be used to estimate the target
+distribution or its properties.
+       
+
+MetropolisHastings Class
+------------------------
+
+The :class:`.MetropolisHastings` class is imported by::
+    
+    from psimpy.sampler.metropolis_hastings import MetropolisHastings
+
+Methods
+^^^^^^^
+.. autoclass:: psimpy.sampler.metropolis_hastings.MetropolisHastings
+    :members: sample
\ No newline at end of file
diff --git a/docs/source/_build/html/_sources/sampler/saltelli.rst.txt b/docs/source/_build/html/_sources/sampler/saltelli.rst.txt
new file mode 100644
index 0000000..d875a00
--- /dev/null
+++ b/docs/source/_build/html/_sources/sampler/saltelli.rst.txt
@@ -0,0 +1,19 @@
+Saltelli Sampling
+=================
+
+Saltelli sampling is a method to draw samples for the purpose of Sobol'
+sensitvity analysis (variance-based sensitivity analysis). Detailed description
+of the theory can be found in :cite:t:`Saltelli2002` and :cite:t:`Saltelli2010`.
+The :class:`.Saltelli` class relies on the Python package `SALib` :cite:p:`Herman2017`.
+
+Saltelli Class
+--------------
+
+The :class:`.Saltelli` class is imported by::
+    
+    from psimpy.sampler.saltelli import Saltelli
+
+Methods
+^^^^^^^
+.. autoclass:: psimpy.sampler.saltelli.Saltelli
+    :members: sample
\ No newline at end of file
diff --git a/docs/source/_build/html/_sources/sensitivity/index.rst.txt b/docs/source/_build/html/_sources/sensitivity/index.rst.txt
new file mode 100644
index 0000000..75d67ed
--- /dev/null
+++ b/docs/source/_build/html/_sources/sensitivity/index.rst.txt
@@ -0,0 +1,16 @@
+***********
+Sensitivity
+***********
+
+This module hosts functionality for sensitivity analysis methods.
+
+Currently implemented classes are:
+
+* :class:`.SobolAnalyze`: Compute Sobol' sensitivity indices.
+
+.. toctree::
+   :maxdepth: 1
+   :hidden:
+   :caption: Sensitivity
+
+    Sobol Analyze <sobol>
\ No newline at end of file
diff --git a/docs/source/_build/html/_sources/sensitivity/sobol.rst.txt b/docs/source/_build/html/_sources/sensitivity/sobol.rst.txt
new file mode 100644
index 0000000..b140e4d
--- /dev/null
+++ b/docs/source/_build/html/_sources/sensitivity/sobol.rst.txt
@@ -0,0 +1,19 @@
+Sobol' Sensitivity Analysis
+===========================
+
+This module is used to compute Sobol' indices given model (e.g. simulator or emulator)
+outputs evaluated at chosen Saltelli samples (see the :class:`.Saltelli` class).
+Detailed description of the theory can be found in :cite:t:`Saltelli2002` and :cite:t:`Saltelli2010`.
+The :class:`.SobolAnalyze` class relies on the Python package `SALib` :cite:p:`Herman2017`.
+
+SobolAnalyze Class
+------------------
+
+The :class:`.SobolAnalyze` class is imported by::
+    
+    from psimpy.sensitivity.sobol import SobolAnalyze
+
+Methods
+^^^^^^^
+.. autoclass:: psimpy.sensitivity.sobol.SobolAnalyze
+    :members: run
\ No newline at end of file
diff --git a/docs/source/_build/html/_sources/simulator/index.rst.txt b/docs/source/_build/html/_sources/simulator/index.rst.txt
new file mode 100644
index 0000000..66c9249
--- /dev/null
+++ b/docs/source/_build/html/_sources/simulator/index.rst.txt
@@ -0,0 +1,38 @@
+*********
+Simulator
+*********
+
+Computer simulations are widely used to study real-world systems in many fields.
+Such a simulation model, so-called `simulator`, essentially defines a mapping from
+an input space :math:`\mathcal{X}` to an output space :math:`\mathcal{Y}`.
+More specifically, given a simulator :math:`\mathbf{y}=\mathbf{f}(\mathbf{x})`,
+it maps a :math:`p`-dimensional input :math:`\mathbf{x} \in \mathcal{X} \subset{\mathbb{R}^p}`
+to a :math:`k`-dimensional output :math:`\mathbf{y} \in \mathcal{Y} \subset{\mathbb{R}^k}`.
+The mapping :math:`\mathbf{f}` can vary from simple linear equations which can be analytically
+solved to complex partial differential equations which requires numerical schemes such as
+finite element methods.
+
+This module hosts simulators and functionality for running simulators. Currently
+implemented classes are:
+
+* :class:`.RunSimulator`: Serial and parallel execution of simulators.
+
+* :class:`.MassPointModel`: Mass point model for landslide run-out simulation.
+
+* :class:`.Ravaflow24Mixture`: Voellmy-type shallow flow model for landslide run-out simulation.
+
+.. toctree::
+   :maxdepth: 1
+   :hidden:
+   :caption: Simulator
+
+    Run Simulator <run_simulator>
+    Mass Point Model <mass_point_model>
+    Ravaflow Mixture Model <ravaflow24>
+
+.. note::
+   :class:`.MassPointModel` and :class:`.Ravaflow24Mixture` are only relevant if
+   the user wants to perform run-out simulation. :class:`.MassPointModel` is purely
+   Python-based and can be used right away. :class:`.Ravaflow24Mixture` depends on 
+   `r.avaflow 2.4 <https://www.landslidemodels.org/r.avaflow/>`_, which needs to be
+   installed by the user.
\ No newline at end of file
diff --git a/docs/source/_build/html/_sources/simulator/mass_point_model.rst.txt b/docs/source/_build/html/_sources/simulator/mass_point_model.rst.txt
new file mode 100644
index 0000000..e56f07d
--- /dev/null
+++ b/docs/source/_build/html/_sources/simulator/mass_point_model.rst.txt
@@ -0,0 +1,86 @@
+Mass Point Model
+================
+
+Theory of mass point model
+--------------------------
+
+A `mass point model` is an extremely simplified model to simulate mass movement
+on a given topography. It assumes that the flow mass is condensed to a single point.
+
+Let :math:`Z(x,y)` define a topography in a Cartesian
+coordinate system :math:`\{x, y, z\}`. It induces a local non-orthogonal
+coordinate system :math:`\{T_x, T_y, T_n\}`, where :math:`T_x` and :math:`T_y`
+denote surface tangent directions and :math:`T_n` denote surface normal direction
+:math:`T_n`, as shown by the following figure :cite:p:`Zhao2021b`
+
+.. image:: ../_static/coordinate_system.png
+   :width: 300
+   :alt: a surface-induced coordinate system
+   :align: center
+
+The govening equations describing the movement of a masspoint on the surface are
+given by
+
+.. math:: \frac{d x}{d t} = U_{T_x} \frac{1}{\sqrt{1+\left(\partial_x Z(x, y)\right)^2}}
+    :label: dxdt
+
+.. math:: \frac{d y}{d t} = U_{T_y} \frac{1}{\sqrt{1+\left(\partial_y Z(x, y)\right)^2}}
+    :label: dydt
+    
+.. math:: \frac{d U_{T_x}}{d t}=g_{T_x} - \frac{U_{T_x}}{\|\boldsymbol{U}\|} 
+    \cdot \left(\mu\left(g_N+\boldsymbol{U}^T \boldsymbol{K} \boldsymbol{U}\right) + 
+    \frac{g}{\xi}\|\boldsymbol{U}\|^2\right)
+    :label: dUTxdt
+    
+.. math:: \frac{d U_{T_y}}{d t} = g_{T_y} - \frac{U_{T_y}}{\|\boldsymbol{U}\|} 
+    \cdot\left(\mu\left(g_N+\boldsymbol{U}^T \boldsymbol{K} \boldsymbol{U}\right) + 
+    \frac{g}{\xi}\|\boldsymbol{U}\|^2\right)
+    :label: dUTydt
+
+where :math:`\mu` and :math:`\xi` are dry-Coulomb and turbulent friction coefficient
+respectively (Voellmy friction model is used here). :math:`\mathbf{K}` is the
+curvature tensor :cite:p:`Fischer2012`. :math:`\mathbf{U}` represents the masspoint's
+velocity. :math:`U_{T_x}` and :math:`U_{T_y}` are the velocity components along :math:`T_x`
+and :math:`T_y` direction respectively.
+
+Equations :eq:`dxdt` to :eq:`dUTydt` can be rewritten in the vector format as
+
+.. math:: \frac{d \boldsymbol{\alpha}}{d t}=\boldsymbol{f}(t, \boldsymbol{\alpha})
+    :label: dalphadt
+
+.. math:: \boldsymbol{\alpha}=\left[\begin{array}{c}
+    x(t) \\
+    y(t) \\
+    U_{T_x}(t) \\
+    U_{T_y}(t)
+    \end{array}\right]
+    :label: alpha
+    
+.. math:: \boldsymbol{f}=\left[\begin{array}{c}
+    U_{T_x} \frac{1}{\sqrt{1+\left(\partial_x Z(x, y)^2\right.}} \\
+    U_{T_y} \frac{1}{\sqrt{1+\left(\partial_y Z(x, y)^2\right.}} \\
+    g_{T_x}-\frac{U_{T_x}}{\|\boldsymbol{U}\|} \cdot\left(\mu\left(g_N+\boldsymbol{U}^T 
+    \boldsymbol{K} \boldsymbol{U}\right)+\frac{g}{\xi}\|\boldsymbol{U}\|^2\right) \\
+    g_{T_y}-\frac{U_{T_y}}{\|\boldsymbol{U}\|} \cdot\left(\mu\left(g_N+\boldsymbol{U}^T 
+    \boldsymbol{K} \boldsymbol{U}\right)+\frac{g}{\xi}\|\boldsymbol{U}\|^2\right)
+    \end{array}\right]
+    :label: vector-f
+
+Equation :eq:`dalphadt` defines an initial value problem. Given initial
+:math:`\boldsymbol{\alpha}_0`, the system can be solved forward in time using
+numerical schemes such as the runge-kutta method. Class :class:`.MassPointModel`
+utilizes the explicit runge-kutta method ``dopri5`` provided by
+:class:`scipy.integrate.ode`.
+
+
+MassPointModel Class
+--------------------
+
+The :class:`.MassPointModel` class is imported by::
+    
+    from psimpy.simulator.mass_point_model import MassPointModel
+
+Methods
+^^^^^^^
+.. autoclass:: psimpy.simulator.mass_point_model.MassPointModel
+    :members: run
\ No newline at end of file
diff --git a/docs/source/_build/html/_sources/simulator/ravaflow24.rst.txt b/docs/source/_build/html/_sources/simulator/ravaflow24.rst.txt
new file mode 100644
index 0000000..fc5aa6d
--- /dev/null
+++ b/docs/source/_build/html/_sources/simulator/ravaflow24.rst.txt
@@ -0,0 +1,24 @@
+Ravaflow24 Mixture Model
+========================
+
+`r.avaflow 2.4` is a GIS-supported open source software for mass flow modeling.
+It is developed by :cite:t:`Mergili2017`. For more information see its official
+user manual `here <https://www.landslidemodels.org/r.avaflow/>`_. 
+
+In :py:mod:`PSimPy.simulator.ravaflow24`, we have implemented class 
+:class:`.Ravaflow24Mixture`. It provides an Python interface to directly run
+the `Voellmy-tpye shallow flow model` of `r.avaflow 2.4` from within Python.
+For detailed theory of `Voellmy-tpye shallow flow model`, one can refer to
+:cite:t:`Christen2010` and :cite:t:`Fischer2012`.
+
+Ravaflow24Mixture Class
+-----------------------
+
+The :class:`.Ravaflow24Mixture` class is imported by::
+    
+    from psimpy.simulator.ravaflow24 import Ravaflow24Mixture
+
+Methods
+^^^^^^^
+.. autoclass:: psimpy.simulator.ravaflow24.Ravaflow24Mixture
+    :members: preprocess, run, extract_impact_area, extract_qoi_max, extract_qoi_max_loc
\ No newline at end of file
diff --git a/docs/source/_build/html/_sources/simulator/run_simulator.rst.txt b/docs/source/_build/html/_sources/simulator/run_simulator.rst.txt
new file mode 100644
index 0000000..5a24b32
--- /dev/null
+++ b/docs/source/_build/html/_sources/simulator/run_simulator.rst.txt
@@ -0,0 +1,30 @@
+Run Simulator
+=============
+
+A `simulator` which describes certain real-world system is often subject to
+uncertainties. Uncertainty-related analyses require running the `simulator`
+multiple times at different variable input points. Class :class:`.RunSimulator`
+implemented in this module provides functionality to sequentially or parallelly
+execute `simulator` at a number of varaible input points.
+
+The user needs to define their `simulator`, implement an interface (essentially
+a Python function) to call the `simulator` from within Python and return output
+of interest, and inform :class:`.RunSimulator` the signature of the interface.
+
+
+RunSimulator Class
+------------------
+
+The :class:`.RunSimulator` class is imported by::
+    
+    from psimpy.simulator.run_simulator import RunSimulator
+
+Methods
+^^^^^^^
+.. autoclass:: psimpy.simulator.run_simulator.RunSimulator
+    :members: serial_run, parallel_run
+
+Attributes
+^^^^^^^^^^
+.. autoattribute:: psimpy.simulator.run_simulator.RunSimulator.var_samples
+.. autoattribute:: psimpy.simulator.run_simulator.RunSimulator.outputs
\ No newline at end of file
diff --git a/docs/source/_build/html/_static/_sphinx_javascript_frameworks_compat.js b/docs/source/_build/html/_static/_sphinx_javascript_frameworks_compat.js
new file mode 100644
index 0000000..8549469
--- /dev/null
+++ b/docs/source/_build/html/_static/_sphinx_javascript_frameworks_compat.js
@@ -0,0 +1,134 @@
+/*
+ * _sphinx_javascript_frameworks_compat.js
+ * ~~~~~~~~~~
+ *
+ * Compatability shim for jQuery and underscores.js.
+ *
+ * WILL BE REMOVED IN Sphinx 6.0
+ * xref RemovedInSphinx60Warning
+ *
+ */
+
+/**
+ * select a different prefix for underscore
+ */
+$u = _.noConflict();
+
+
+/**
+ * small helper function to urldecode strings
+ *
+ * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/decodeURIComponent#Decoding_query_parameters_from_a_URL
+ */
+jQuery.urldecode = function(x) {
+    if (!x) {
+        return x
+    }
+    return decodeURIComponent(x.replace(/\+/g, ' '));
+};
+
+/**
+ * small helper function to urlencode strings
+ */
+jQuery.urlencode = encodeURIComponent;
+
+/**
+ * This function returns the parsed url parameters of the
+ * current request. Multiple values per key are supported,
+ * it will always return arrays of strings for the value parts.
+ */
+jQuery.getQueryParameters = function(s) {
+    if (typeof s === 'undefined')
+        s = document.location.search;
+    var parts = s.substr(s.indexOf('?') + 1).split('&');
+    var result = {};
+    for (var i = 0; i < parts.length; i++) {
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+        var key = jQuery.urldecode(tmp[0]);
+        var value = jQuery.urldecode(tmp[1]);
+        if (key in result)
+            result[key].push(value);
+        else
+            result[key] = [value];
+    }
+    return result;
+};
+
+/**
+ * highlight a given string on a jquery object by wrapping it in
+ * span elements with the given class name.
+ */
+jQuery.fn.highlightText = function(text, className) {
+    function highlight(node, addItems) {
+        if (node.nodeType === 3) {
+            var val = node.nodeValue;
+            var pos = val.toLowerCase().indexOf(text);
+            if (pos >= 0 &&
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+                var span;
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+                if (isInSVG) {
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+                } else {
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+                    span.className = className;
+                }
+                span.appendChild(document.createTextNode(val.substr(pos, text.length)));
+                node.parentNode.insertBefore(span, node.parentNode.insertBefore(
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+                node.nodeValue = val.substr(0, pos);
+                if (isInSVG) {
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+                    rect.setAttribute('class', className);
+                    addItems.push({
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+                }
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+        else if (!jQuery(node).is("button, select, textarea")) {
+            jQuery.each(node.childNodes, function() {
+                highlight(this, addItems);
+            });
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+    var addItems = [];
+    var result = this.each(function() {
+        highlight(this, addItems);
+    });
+    for (var i = 0; i < addItems.length; ++i) {
+        jQuery(addItems[i].parent).before(addItems[i].target);
+    }
+    return result;
+};
+
+/*
+ * backward compatibility for jQuery.browser
+ * This will be supported until firefox bug is fixed.
+ */
+if (!jQuery.browser) {
+    jQuery.uaMatch = function(ua) {
+        ua = ua.toLowerCase();
+
+        var match = /(chrome)[ \/]([\w.]+)/.exec(ua) ||
+            /(webkit)[ \/]([\w.]+)/.exec(ua) ||
+            /(opera)(?:.*version|)[ \/]([\w.]+)/.exec(ua) ||
+            /(msie) ([\w.]+)/.exec(ua) ||
+            ua.indexOf("compatible") < 0 && /(mozilla)(?:.*? rv:([\w.]+)|)/.exec(ua) ||
+            [];
+
+        return {
+            browser: match[ 1 ] || "",
+            version: match[ 2 ] || "0"
+        };
+    };
+    jQuery.browser = {};
+    jQuery.browser[jQuery.uaMatch(navigator.userAgent).browser] = true;
+}
diff --git a/docs/source/_build/html/_static/basic.css b/docs/source/_build/html/_static/basic.css
new file mode 100644
index 0000000..eeb0519
--- /dev/null
+++ b/docs/source/_build/html/_static/basic.css
@@ -0,0 +1,899 @@
+/*
+ * basic.css
+ * ~~~~~~~~~
+ *
+ * Sphinx stylesheet -- basic theme.
+ *
+ * :copyright: Copyright 2007-2022 by the Sphinx team, see AUTHORS.
+ * :license: BSD, see LICENSE for details.
+ *
+ */
+
+/* -- main layout ----------------------------------------------------------- */
+
+div.clearer {
+    clear: both;
+}
+
+div.section::after {
+    display: block;
+    content: '';
+    clear: left;
+}
+
+/* -- relbar ---------------------------------------------------------------- */
+
+div.related {
+    width: 100%;
+    font-size: 90%;
+}
+
+div.related h3 {
+    display: none;
+}
+
+div.related ul {
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+
+div.related li {
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+div.related li.right {
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+/* -- sidebar --------------------------------------------------------------- */
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+div.sphinxsidebarwrapper {
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+}
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+    clear: left;
+    float: left;
+    margin-right: 1em;
+}
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+img.align-right, figure.align-right, .figure.align-right, object.align-right {
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+    float: right;
+    margin-left: 1em;
+}
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+  display: block;
+  margin-left: auto;
+  margin-right: auto;
+}
+
+img.align-default, figure.align-default, .figure.align-default {
+  display: block;
+  margin-left: auto;
+  margin-right: auto;
+}
+
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+    text-align: left;
+}
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+    text-align: center;
+}
+
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+    text-align: center;
+}
+
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+    text-align: right;
+}
+
+/* -- sidebars -------------------------------------------------------------- */
+
+div.sidebar,
+aside.sidebar {
+    margin: 0 0 0.5em 1em;
+    border: 1px solid #ddb;
+    padding: 7px;
+    background-color: #ffe;
+    width: 40%;
+    float: right;
+    clear: right;
+    overflow-x: auto;
+}
+
+p.sidebar-title {
+    font-weight: bold;
+}
+div.admonition, div.topic, blockquote {
+    clear: left;
+}
+
+/* -- topics ---------------------------------------------------------------- */
+div.topic {
+    border: 1px solid #ccc;
+    padding: 7px;
+    margin: 10px 0 10px 0;
+}
+
+p.topic-title {
+    font-size: 1.1em;
+    font-weight: bold;
+    margin-top: 10px;
+}
+
+/* -- admonitions ----------------------------------------------------------- */
+
+div.admonition {
+    margin-top: 10px;
+    margin-bottom: 10px;
+    padding: 7px;
+}
+
+div.admonition dt {
+    font-weight: bold;
+}
+
+p.admonition-title {
+    margin: 0px 10px 5px 0px;
+    font-weight: bold;
+}
+
+div.body p.centered {
+    text-align: center;
+    margin-top: 25px;
+}
+
+/* -- content of sidebars/topics/admonitions -------------------------------- */
+
+div.sidebar > :last-child,
+aside.sidebar > :last-child,
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+    margin-bottom: 0;
+}
+
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+aside.sidebar::after,
+div.topic::after,
+div.admonition::after,
+blockquote::after {
+    display: block;
+    content: '';
+    clear: both;
+}
+
+/* -- tables ---------------------------------------------------------------- */
+
+table.docutils {
+    margin-top: 10px;
+    margin-bottom: 10px;
+    border: 0;
+    border-collapse: collapse;
+}
+
+table.align-center {
+    margin-left: auto;
+    margin-right: auto;
+}
+
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+    margin-left: auto;
+    margin-right: auto;
+}
+
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+    font-style: italic;
+}
+
+table caption span.caption-text {
+}
+
+table.docutils td, table.docutils th {
+    padding: 1px 8px 1px 5px;
+    border-top: 0;
+    border-left: 0;
+    border-right: 0;
+    border-bottom: 1px solid #aaa;
+}
+
+th {
+    text-align: left;
+    padding-right: 5px;
+}
+
+table.citation {
+    border-left: solid 1px gray;
+    margin-left: 1px;
+}
+
+table.citation td {
+    border-bottom: none;
+}
+
+th > :first-child,
+td > :first-child {
+    margin-top: 0px;
+}
+
+th > :last-child,
+td > :last-child {
+    margin-bottom: 0px;
+}
+
+/* -- figures --------------------------------------------------------------- */
+
+div.figure, figure {
+    margin: 0.5em;
+    padding: 0.5em;
+}
+
+div.figure p.caption, figcaption {
+    padding: 0.3em;
+}
+
+div.figure p.caption span.caption-number,
+figcaption span.caption-number {
+    font-style: italic;
+}
+
+div.figure p.caption span.caption-text,
+figcaption span.caption-text {
+}
+
+/* -- field list styles ----------------------------------------------------- */
+
+table.field-list td, table.field-list th {
+    border: 0 !important;
+}
+
+.field-list ul {
+    margin: 0;
+    padding-left: 1em;
+}
+
+.field-list p {
+    margin: 0;
+}
+
+.field-name {
+    -moz-hyphens: manual;
+    -ms-hyphens: manual;
+    -webkit-hyphens: manual;
+    hyphens: manual;
+}
+
+/* -- hlist styles ---------------------------------------------------------- */
+
+table.hlist {
+    margin: 1em 0;
+}
+
+table.hlist td {
+    vertical-align: top;
+}
+
+/* -- object description styles --------------------------------------------- */
+
+.sig {
+	font-family: 'Consolas', 'Menlo', 'DejaVu Sans Mono', 'Bitstream Vera Sans Mono', monospace;
+}
+
+.sig-name, code.descname {
+    background-color: transparent;
+    font-weight: bold;
+}
+
+.sig-name {
+	font-size: 1.1em;
+}
+
+code.descname {
+    font-size: 1.2em;
+}
+
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+    background-color: transparent;
+}
+
+.optional {
+    font-size: 1.3em;
+}
+
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+    font-size: larger;
+}
+
+.sig-param.n {
+	font-style: italic;
+}
+
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+
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+.sig-inline.cpp-texpr {
+	font-family: unset;
+}
+
+.sig.c   .k, .sig.c   .kt,
+.sig.cpp .k, .sig.cpp .kt {
+	color: #0033B3;
+}
+
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+	color: #1750EB;
+}
+
+.sig.c   .s, .sig.c   .sc,
+.sig.cpp .s, .sig.cpp .sc {
+	color: #067D17;
+}
+
+
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+
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+    list-style: decimal;
+}
+
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+    list-style: lower-alpha;
+}
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+    list-style: upper-alpha;
+}
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+}
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+    list-style: upper-roman;
+}
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+    margin-top: 0px;
+}
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+:not(li) > ul > li:last-child > :last-child {
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+}
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+    margin-top: 0;
+}
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+}
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+}
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+    margin-right: 0.5em;
+}
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+    margin-bottom: 0em;
+}
+
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+    clear: both;
+}
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+    display: grid;
+    grid-template-columns: fit-content(30%) auto;
+}
+
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+    font-weight: bold;
+    word-break: break-word;
+    padding-left: 0.5em;
+    padding-right: 5px;
+}
+dl.field-list > dt:after {
+    content: ":";
+}
+
+
+dl.field-list > dd {
+    padding-left: 0.5em;
+    margin-top: 0em;
+    margin-left: 0em;
+    margin-bottom: 0em;
+}
+
+dl {
+    margin-bottom: 15px;
+}
+
+dd > :first-child {
+    margin-top: 0px;
+}
+
+dd ul, dd table {
+    margin-bottom: 10px;
+}
+
+dd {
+    margin-top: 3px;
+    margin-bottom: 10px;
+    margin-left: 30px;
+}
+
+dl > dd:last-child,
+dl > dd:last-child > :last-child {
+    margin-bottom: 0;
+}
+
+dt:target, span.highlighted {
+    background-color: #fbe54e;
+}
+
+rect.highlighted {
+    fill: #fbe54e;
+}
+
+dl.glossary dt {
+    font-weight: bold;
+    font-size: 1.1em;
+}
+
+.versionmodified {
+    font-style: italic;
+}
+
+.system-message {
+    background-color: #fda;
+    padding: 5px;
+    border: 3px solid red;
+}
+
+.footnote:target  {
+    background-color: #ffa;
+}
+
+.line-block {
+    display: block;
+    margin-top: 1em;
+    margin-bottom: 1em;
+}
+
+.line-block .line-block {
+    margin-top: 0;
+    margin-bottom: 0;
+    margin-left: 1.5em;
+}
+
+.guilabel, .menuselection {
+    font-family: sans-serif;
+}
+
+.accelerator {
+    text-decoration: underline;
+}
+
+.classifier {
+    font-style: oblique;
+}
+
+.classifier:before {
+    font-style: normal;
+    margin: 0 0.5em;
+    content: ":";
+    display: inline-block;
+}
+
+abbr, acronym {
+    border-bottom: dotted 1px;
+    cursor: help;
+}
+
+/* -- code displays --------------------------------------------------------- */
+
+pre {
+    overflow: auto;
+    overflow-y: hidden;  /* fixes display issues on Chrome browsers */
+}
+
+pre, div[class*="highlight-"] {
+    clear: both;
+}
+
+span.pre {
+    -moz-hyphens: none;
+    -ms-hyphens: none;
+    -webkit-hyphens: none;
+    hyphens: none;
+    white-space: nowrap;
+}
+
+div[class*="highlight-"] {
+    margin: 1em 0;
+}
+
+td.linenos pre {
+    border: 0;
+    background-color: transparent;
+    color: #aaa;
+}
+
+table.highlighttable {
+    display: block;
+}
+
+table.highlighttable tbody {
+    display: block;
+}
+
+table.highlighttable tr {
+    display: flex;
+}
+
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+    margin: 0;
+    padding: 0;
+}
+
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+    padding-right: 0.5em;
+}
+
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+    flex: 1;
+    overflow: hidden;
+}
+
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+    display: block;
+}
+
+div.highlight pre,
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+    margin: 0;
+}
+
+div.code-block-caption + div {
+    margin-top: 0;
+}
+
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+    margin-top: 1em;
+    padding: 2px 5px;
+    font-size: small;
+}
+
+div.code-block-caption code {
+    background-color: transparent;
+}
+
+table.highlighttable td.linenos,
+span.linenos,
+div.highlight span.gp {  /* gp: Generic.Prompt */
+  user-select: none;
+  -webkit-user-select: text; /* Safari fallback only */
+  -webkit-user-select: none; /* Chrome/Safari */
+  -moz-user-select: none; /* Firefox */
+  -ms-user-select: none; /* IE10+ */
+}
+
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+    font-style: italic;
+}
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+}
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+}
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+    font-weight: bold;
+}
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+}
+
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+}
+
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+    font-family: sans-serif;
+}
+
+div.viewcode-block:target {
+    margin: -1px -10px;
+    padding: 0 10px;
+}
+
+/* -- math display ---------------------------------------------------------- */
+
+img.math {
+    vertical-align: middle;
+}
+
+div.body div.math p {
+    text-align: center;
+}
+
+span.eqno {
+    float: right;
+}
+
+span.eqno a.headerlink {
+    position: absolute;
+    z-index: 1;
+}
+
+div.math:hover a.headerlink {
+    visibility: visible;
+}
+
+/* -- printout stylesheet --------------------------------------------------- */
+
+@media print {
+    div.document,
+    div.documentwrapper,
+    div.bodywrapper {
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+        width: 100%;
+    }
+
+    div.sphinxsidebar,
+    div.related,
+    div.footer,
+    #top-link {
+        display: none;
+    }
+}
\ No newline at end of file
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index 0000000..855c845
--- /dev/null
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new file mode 100644
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diff --git a/docs/source/_build/html/_static/css/fonts/fontawesome-webfont.woff2 b/docs/source/_build/html/_static/css/fonts/fontawesome-webfont.woff2
new file mode 100644
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diff --git a/docs/source/_build/html/_static/css/fonts/lato-normal.woff b/docs/source/_build/html/_static/css/fonts/lato-normal.woff
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diff --git a/docs/source/_build/html/_static/css/fonts/lato-normal.woff2 b/docs/source/_build/html/_static/css/fonts/lato-normal.woff2
new file mode 100644
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format("woff2"),url(fonts/Roboto-Slab-Bold.woff?bed5564a116b05148e3b3bea6fb1162a) format("woff");font-display:block}
\ No newline at end of file
diff --git a/docs/source/_build/html/_static/doctools.js b/docs/source/_build/html/_static/doctools.js
new file mode 100644
index 0000000..527b876
--- /dev/null
+++ b/docs/source/_build/html/_static/doctools.js
@@ -0,0 +1,156 @@
+/*
+ * doctools.js
+ * ~~~~~~~~~~~
+ *
+ * Base JavaScript utilities for all Sphinx HTML documentation.
+ *
+ * :copyright: Copyright 2007-2022 by the Sphinx team, see AUTHORS.
+ * :license: BSD, see LICENSE for details.
+ *
+ */
+"use strict";
+
+const BLACKLISTED_KEY_CONTROL_ELEMENTS = new Set([
+  "TEXTAREA",
+  "INPUT",
+  "SELECT",
+  "BUTTON",
+]);
+
+const _ready = (callback) => {
+  if (document.readyState !== "loading") {
+    callback();
+  } else {
+    document.addEventListener("DOMContentLoaded", callback);
+  }
+};
+
+/**
+ * Small JavaScript module for the documentation.
+ */
+const Documentation = {
+  init: () => {
+    Documentation.initDomainIndexTable();
+    Documentation.initOnKeyListeners();
+  },
+
+  /**
+   * i18n support
+   */
+  TRANSLATIONS: {},
+  PLURAL_EXPR: (n) => (n === 1 ? 0 : 1),
+  LOCALE: "unknown",
+
+  // gettext and ngettext don't access this so that the functions
+  // can safely bound to a different name (_ = Documentation.gettext)
+  gettext: (string) => {
+    const translated = Documentation.TRANSLATIONS[string];
+    switch (typeof translated) {
+      case "undefined":
+        return string; // no translation
+      case "string":
+        return translated; // translation exists
+      default:
+        return translated[0]; // (singular, plural) translation tuple exists
+    }
+  },
+
+  ngettext: (singular, plural, n) => {
+    const translated = Documentation.TRANSLATIONS[singular];
+    if (typeof translated !== "undefined")
+      return translated[Documentation.PLURAL_EXPR(n)];
+    return n === 1 ? singular : plural;
+  },
+
+  addTranslations: (catalog) => {
+    Object.assign(Documentation.TRANSLATIONS, catalog.messages);
+    Documentation.PLURAL_EXPR = new Function(
+      "n",
+      `return (${catalog.plural_expr})`
+    );
+    Documentation.LOCALE = catalog.locale;
+  },
+
+  /**
+   * helper function to focus on search bar
+   */
+  focusSearchBar: () => {
+    document.querySelectorAll("input[name=q]")[0]?.focus();
+  },
+
+  /**
+   * Initialise the domain index toggle buttons
+   */
+  initDomainIndexTable: () => {
+    const toggler = (el) => {
+      const idNumber = el.id.substr(7);
+      const toggledRows = document.querySelectorAll(`tr.cg-${idNumber}`);
+      if (el.src.substr(-9) === "minus.png") {
+        el.src = `${el.src.substr(0, el.src.length - 9)}plus.png`;
+        toggledRows.forEach((el) => (el.style.display = "none"));
+      } else {
+        el.src = `${el.src.substr(0, el.src.length - 8)}minus.png`;
+        toggledRows.forEach((el) => (el.style.display = ""));
+      }
+    };
+
+    const togglerElements = document.querySelectorAll("img.toggler");
+    togglerElements.forEach((el) =>
+      el.addEventListener("click", (event) => toggler(event.currentTarget))
+    );
+    togglerElements.forEach((el) => (el.style.display = ""));
+    if (DOCUMENTATION_OPTIONS.COLLAPSE_INDEX) togglerElements.forEach(toggler);
+  },
+
+  initOnKeyListeners: () => {
+    // only install a listener if it is really needed
+    if (
+      !DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS &&
+      !DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS
+    )
+      return;
+
+    document.addEventListener("keydown", (event) => {
+      // bail for input elements
+      if (BLACKLISTED_KEY_CONTROL_ELEMENTS.has(document.activeElement.tagName)) return;
+      // bail with special keys
+      if (event.altKey || event.ctrlKey || event.metaKey) return;
+
+      if (!event.shiftKey) {
+        switch (event.key) {
+          case "ArrowLeft":
+            if (!DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS) break;
+
+            const prevLink = document.querySelector('link[rel="prev"]');
+            if (prevLink && prevLink.href) {
+              window.location.href = prevLink.href;
+              event.preventDefault();
+            }
+            break;
+          case "ArrowRight":
+            if (!DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS) break;
+
+            const nextLink = document.querySelector('link[rel="next"]');
+            if (nextLink && nextLink.href) {
+              window.location.href = nextLink.href;
+              event.preventDefault();
+            }
+            break;
+        }
+      }
+
+      // some keyboard layouts may need Shift to get /
+      switch (event.key) {
+        case "/":
+          if (!DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS) break;
+          Documentation.focusSearchBar();
+          event.preventDefault();
+      }
+    });
+  },
+};
+
+// quick alias for translations
+const _ = Documentation.gettext;
+
+_ready(Documentation.init);
diff --git a/docs/source/_build/html/_static/documentation_options.js b/docs/source/_build/html/_static/documentation_options.js
new file mode 100644
index 0000000..c99fee7
--- /dev/null
+++ b/docs/source/_build/html/_static/documentation_options.js
@@ -0,0 +1,14 @@
+var DOCUMENTATION_OPTIONS = {
+    URL_ROOT: document.getElementById("documentation_options").getAttribute('data-url_root'),
+    VERSION: '0.1.2',
+    LANGUAGE: 'en',
+    COLLAPSE_INDEX: false,
+    BUILDER: 'html',
+    FILE_SUFFIX: '.html',
+    LINK_SUFFIX: '.html',
+    HAS_SOURCE: true,
+    SOURCELINK_SUFFIX: '.txt',
+    NAVIGATION_WITH_KEYS: false,
+    SHOW_SEARCH_SUMMARY: true,
+    ENABLE_SEARCH_SHORTCUTS: true,
+};
\ No newline at end of file
diff --git a/docs/source/_build/html/_static/file.png b/docs/source/_build/html/_static/file.png
new file mode 100644
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diff --git a/docs/source/_build/html/_static/jquery-3.6.0.js b/docs/source/_build/html/_static/jquery-3.6.0.js
new file mode 100644
index 0000000..fc6c299
--- /dev/null
+++ b/docs/source/_build/html/_static/jquery-3.6.0.js
@@ -0,0 +1,10881 @@
+/*!
+ * jQuery JavaScript Library v3.6.0
+ * https://jquery.com/
+ *
+ * Includes Sizzle.js
+ * https://sizzlejs.com/
+ *
+ * Copyright OpenJS Foundation and other contributors
+ * Released under the MIT license
+ * https://jquery.org/license
+ *
+ * Date: 2021-03-02T17:08Z
+ */
+( function( global, factory ) {
+
+	"use strict";
+
+	if ( typeof module === "object" && typeof module.exports === "object" ) {
+
+		// For CommonJS and CommonJS-like environments where a proper `window`
+		// is present, execute the factory and get jQuery.
+		// For environments that do not have a `window` with a `document`
+		// (such as Node.js), expose a factory as module.exports.
+		// This accentuates the need for the creation of a real `window`.
+		// e.g. var jQuery = require("jquery")(window);
+		// See ticket #14549 for more info.
+		module.exports = global.document ?
+			factory( global, true ) :
+			function( w ) {
+				if ( !w.document ) {
+					throw new Error( "jQuery requires a window with a document" );
+				}
+				return factory( w );
+			};
+	} else {
+		factory( global );
+	}
+
+// Pass this if window is not defined yet
+} )( typeof window !== "undefined" ? window : this, function( window, noGlobal ) {
+
+// Edge <= 12 - 13+, Firefox <=18 - 45+, IE 10 - 11, Safari 5.1 - 9+, iOS 6 - 9.1
+// throw exceptions when non-strict code (e.g., ASP.NET 4.5) accesses strict mode
+// arguments.callee.caller (trac-13335). But as of jQuery 3.0 (2016), strict mode should be common
+// enough that all such attempts are guarded in a try block.
+"use strict";
+
+var arr = [];
+
+var getProto = Object.getPrototypeOf;
+
+var slice = arr.slice;
+
+var flat = arr.flat ? function( array ) {
+	return arr.flat.call( array );
+} : function( array ) {
+	return arr.concat.apply( [], array );
+};
+
+
+var push = arr.push;
+
+var indexOf = arr.indexOf;
+
+var class2type = {};
+
+var toString = class2type.toString;
+
+var hasOwn = class2type.hasOwnProperty;
+
+var fnToString = hasOwn.toString;
+
+var ObjectFunctionString = fnToString.call( Object );
+
+var support = {};
+
+var isFunction = function isFunction( obj ) {
+
+		// Support: Chrome <=57, Firefox <=52
+		// In some browsers, typeof returns "function" for HTML <object> elements
+		// (i.e., `typeof document.createElement( "object" ) === "function"`).
+		// We don't want to classify *any* DOM node as a function.
+		// Support: QtWeb <=3.8.5, WebKit <=534.34, wkhtmltopdf tool <=0.12.5
+		// Plus for old WebKit, typeof returns "function" for HTML collections
+		// (e.g., `typeof document.getElementsByTagName("div") === "function"`). (gh-4756)
+		return typeof obj === "function" && typeof obj.nodeType !== "number" &&
+			typeof obj.item !== "function";
+	};
+
+
+var isWindow = function isWindow( obj ) {
+		return obj != null && obj === obj.window;
+	};
+
+
+var document = window.document;
+
+
+
+	var preservedScriptAttributes = {
+		type: true,
+		src: true,
+		nonce: true,
+		noModule: true
+	};
+
+	function DOMEval( code, node, doc ) {
+		doc = doc || document;
+
+		var i, val,
+			script = doc.createElement( "script" );
+
+		script.text = code;
+		if ( node ) {
+			for ( i in preservedScriptAttributes ) {
+
+				// Support: Firefox 64+, Edge 18+
+				// Some browsers don't support the "nonce" property on scripts.
+				// On the other hand, just using `getAttribute` is not enough as
+				// the `nonce` attribute is reset to an empty string whenever it
+				// becomes browsing-context connected.
+				// See https://github.com/whatwg/html/issues/2369
+				// See https://html.spec.whatwg.org/#nonce-attributes
+				// The `node.getAttribute` check was added for the sake of
+				// `jQuery.globalEval` so that it can fake a nonce-containing node
+				// via an object.
+				val = node[ i ] || node.getAttribute && node.getAttribute( i );
+				if ( val ) {
+					script.setAttribute( i, val );
+				}
+			}
+		}
+		doc.head.appendChild( script ).parentNode.removeChild( script );
+	}
+
+
+function toType( obj ) {
+	if ( obj == null ) {
+		return obj + "";
+	}
+
+	// Support: Android <=2.3 only (functionish RegExp)
+	return typeof obj === "object" || typeof obj === "function" ?
+		class2type[ toString.call( obj ) ] || "object" :
+		typeof obj;
+}
+/* global Symbol */
+// Defining this global in .eslintrc.json would create a danger of using the global
+// unguarded in another place, it seems safer to define global only for this module
+
+
+
+var
+	version = "3.6.0",
+
+	// Define a local copy of jQuery
+	jQuery = function( selector, context ) {
+
+		// The jQuery object is actually just the init constructor 'enhanced'
+		// Need init if jQuery is called (just allow error to be thrown if not included)
+		return new jQuery.fn.init( selector, context );
+	};
+
+jQuery.fn = jQuery.prototype = {
+
+	// The current version of jQuery being used
+	jquery: version,
+
+	constructor: jQuery,
+
+	// The default length of a jQuery object is 0
+	length: 0,
+
+	toArray: function() {
+		return slice.call( this );
+	},
+
+	// Get the Nth element in the matched element set OR
+	// Get the whole matched element set as a clean array
+	get: function( num ) {
+
+		// Return all the elements in a clean array
+		if ( num == null ) {
+			return slice.call( this );
+		}
+
+		// Return just the one element from the set
+		return num < 0 ? this[ num + this.length ] : this[ num ];
+	},
+
+	// Take an array of elements and push it onto the stack
+	// (returning the new matched element set)
+	pushStack: function( elems ) {
+
+		// Build a new jQuery matched element set
+		var ret = jQuery.merge( this.constructor(), elems );
+
+		// Add the old object onto the stack (as a reference)
+		ret.prevObject = this;
+
+		// Return the newly-formed element set
+		return ret;
+	},
+
+	// Execute a callback for every element in the matched set.
+	each: function( callback ) {
+		return jQuery.each( this, callback );
+	},
+
+	map: function( callback ) {
+		return this.pushStack( jQuery.map( this, function( elem, i ) {
+			return callback.call( elem, i, elem );
+		} ) );
+	},
+
+	slice: function() {
+		return this.pushStack( slice.apply( this, arguments ) );
+	},
+
+	first: function() {
+		return this.eq( 0 );
+	},
+
+	last: function() {
+		return this.eq( -1 );
+	},
+
+	even: function() {
+		return this.pushStack( jQuery.grep( this, function( _elem, i ) {
+			return ( i + 1 ) % 2;
+		} ) );
+	},
+
+	odd: function() {
+		return this.pushStack( jQuery.grep( this, function( _elem, i ) {
+			return i % 2;
+		} ) );
+	},
+
+	eq: function( i ) {
+		var len = this.length,
+			j = +i + ( i < 0 ? len : 0 );
+		return this.pushStack( j >= 0 && j < len ? [ this[ j ] ] : [] );
+	},
+
+	end: function() {
+		return this.prevObject || this.constructor();
+	},
+
+	// For internal use only.
+	// Behaves like an Array's method, not like a jQuery method.
+	push: push,
+	sort: arr.sort,
+	splice: arr.splice
+};
+
+jQuery.extend = jQuery.fn.extend = function() {
+	var options, name, src, copy, copyIsArray, clone,
+		target = arguments[ 0 ] || {},
+		i = 1,
+		length = arguments.length,
+		deep = false;
+
+	// Handle a deep copy situation
+	if ( typeof target === "boolean" ) {
+		deep = target;
+
+		// Skip the boolean and the target
+		target = arguments[ i ] || {};
+		i++;
+	}
+
+	// Handle case when target is a string or something (possible in deep copy)
+	if ( typeof target !== "object" && !isFunction( target ) ) {
+		target = {};
+	}
+
+	// Extend jQuery itself if only one argument is passed
+	if ( i === length ) {
+		target = this;
+		i--;
+	}
+
+	for ( ; i < length; i++ ) {
+
+		// Only deal with non-null/undefined values
+		if ( ( options = arguments[ i ] ) != null ) {
+
+			// Extend the base object
+			for ( name in options ) {
+				copy = options[ name ];
+
+				// Prevent Object.prototype pollution
+				// Prevent never-ending loop
+				if ( name === "__proto__" || target === copy ) {
+					continue;
+				}
+
+				// Recurse if we're merging plain objects or arrays
+				if ( deep && copy && ( jQuery.isPlainObject( copy ) ||
+					( copyIsArray = Array.isArray( copy ) ) ) ) {
+					src = target[ name ];
+
+					// Ensure proper type for the source value
+					if ( copyIsArray && !Array.isArray( src ) ) {
+						clone = [];
+					} else if ( !copyIsArray && !jQuery.isPlainObject( src ) ) {
+						clone = {};
+					} else {
+						clone = src;
+					}
+					copyIsArray = false;
+
+					// Never move original objects, clone them
+					target[ name ] = jQuery.extend( deep, clone, copy );
+
+				// Don't bring in undefined values
+				} else if ( copy !== undefined ) {
+					target[ name ] = copy;
+				}
+			}
+		}
+	}
+
+	// Return the modified object
+	return target;
+};
+
+jQuery.extend( {
+
+	// Unique for each copy of jQuery on the page
+	expando: "jQuery" + ( version + Math.random() ).replace( /\D/g, "" ),
+
+	// Assume jQuery is ready without the ready module
+	isReady: true,
+
+	error: function( msg ) {
+		throw new Error( msg );
+	},
+
+	noop: function() {},
+
+	isPlainObject: function( obj ) {
+		var proto, Ctor;
+
+		// Detect obvious negatives
+		// Use toString instead of jQuery.type to catch host objects
+		if ( !obj || toString.call( obj ) !== "[object Object]" ) {
+			return false;
+		}
+
+		proto = getProto( obj );
+
+		// Objects with no prototype (e.g., `Object.create( null )`) are plain
+		if ( !proto ) {
+			return true;
+		}
+
+		// Objects with prototype are plain iff they were constructed by a global Object function
+		Ctor = hasOwn.call( proto, "constructor" ) && proto.constructor;
+		return typeof Ctor === "function" && fnToString.call( Ctor ) === ObjectFunctionString;
+	},
+
+	isEmptyObject: function( obj ) {
+		var name;
+
+		for ( name in obj ) {
+			return false;
+		}
+		return true;
+	},
+
+	// Evaluates a script in a provided context; falls back to the global one
+	// if not specified.
+	globalEval: function( code, options, doc ) {
+		DOMEval( code, { nonce: options && options.nonce }, doc );
+	},
+
+	each: function( obj, callback ) {
+		var length, i = 0;
+
+		if ( isArrayLike( obj ) ) {
+			length = obj.length;
+			for ( ; i < length; i++ ) {
+				if ( callback.call( obj[ i ], i, obj[ i ] ) === false ) {
+					break;
+				}
+			}
+		} else {
+			for ( i in obj ) {
+				if ( callback.call( obj[ i ], i, obj[ i ] ) === false ) {
+					break;
+				}
+			}
+		}
+
+		return obj;
+	},
+
+	// results is for internal usage only
+	makeArray: function( arr, results ) {
+		var ret = results || [];
+
+		if ( arr != null ) {
+			if ( isArrayLike( Object( arr ) ) ) {
+				jQuery.merge( ret,
+					typeof arr === "string" ?
+						[ arr ] : arr
+				);
+			} else {
+				push.call( ret, arr );
+			}
+		}
+
+		return ret;
+	},
+
+	inArray: function( elem, arr, i ) {
+		return arr == null ? -1 : indexOf.call( arr, elem, i );
+	},
+
+	// Support: Android <=4.0 only, PhantomJS 1 only
+	// push.apply(_, arraylike) throws on ancient WebKit
+	merge: function( first, second ) {
+		var len = +second.length,
+			j = 0,
+			i = first.length;
+
+		for ( ; j < len; j++ ) {
+			first[ i++ ] = second[ j ];
+		}
+
+		first.length = i;
+
+		return first;
+	},
+
+	grep: function( elems, callback, invert ) {
+		var callbackInverse,
+			matches = [],
+			i = 0,
+			length = elems.length,
+			callbackExpect = !invert;
+
+		// Go through the array, only saving the items
+		// that pass the validator function
+		for ( ; i < length; i++ ) {
+			callbackInverse = !callback( elems[ i ], i );
+			if ( callbackInverse !== callbackExpect ) {
+				matches.push( elems[ i ] );
+			}
+		}
+
+		return matches;
+	},
+
+	// arg is for internal usage only
+	map: function( elems, callback, arg ) {
+		var length, value,
+			i = 0,
+			ret = [];
+
+		// Go through the array, translating each of the items to their new values
+		if ( isArrayLike( elems ) ) {
+			length = elems.length;
+			for ( ; i < length; i++ ) {
+				value = callback( elems[ i ], i, arg );
+
+				if ( value != null ) {
+					ret.push( value );
+				}
+			}
+
+		// Go through every key on the object,
+		} else {
+			for ( i in elems ) {
+				value = callback( elems[ i ], i, arg );
+
+				if ( value != null ) {
+					ret.push( value );
+				}
+			}
+		}
+
+		// Flatten any nested arrays
+		return flat( ret );
+	},
+
+	// A global GUID counter for objects
+	guid: 1,
+
+	// jQuery.support is not used in Core but other projects attach their
+	// properties to it so it needs to exist.
+	support: support
+} );
+
+if ( typeof Symbol === "function" ) {
+	jQuery.fn[ Symbol.iterator ] = arr[ Symbol.iterator ];
+}
+
+// Populate the class2type map
+jQuery.each( "Boolean Number String Function Array Date RegExp Object Error Symbol".split( " " ),
+	function( _i, name ) {
+		class2type[ "[object " + name + "]" ] = name.toLowerCase();
+	} );
+
+function isArrayLike( obj ) {
+
+	// Support: real iOS 8.2 only (not reproducible in simulator)
+	// `in` check used to prevent JIT error (gh-2145)
+	// hasOwn isn't used here due to false negatives
+	// regarding Nodelist length in IE
+	var length = !!obj && "length" in obj && obj.length,
+		type = toType( obj );
+
+	if ( isFunction( obj ) || isWindow( obj ) ) {
+		return false;
+	}
+
+	return type === "array" || length === 0 ||
+		typeof length === "number" && length > 0 && ( length - 1 ) in obj;
+}
+var Sizzle =
+/*!
+ * Sizzle CSS Selector Engine v2.3.6
+ * https://sizzlejs.com/
+ *
+ * Copyright JS Foundation and other contributors
+ * Released under the MIT license
+ * https://js.foundation/
+ *
+ * Date: 2021-02-16
+ */
+( function( window ) {
+var i,
+	support,
+	Expr,
+	getText,
+	isXML,
+	tokenize,
+	compile,
+	select,
+	outermostContext,
+	sortInput,
+	hasDuplicate,
+
+	// Local document vars
+	setDocument,
+	document,
+	docElem,
+	documentIsHTML,
+	rbuggyQSA,
+	rbuggyMatches,
+	matches,
+	contains,
+
+	// Instance-specific data
+	expando = "sizzle" + 1 * new Date(),
+	preferredDoc = window.document,
+	dirruns = 0,
+	done = 0,
+	classCache = createCache(),
+	tokenCache = createCache(),
+	compilerCache = createCache(),
+	nonnativeSelectorCache = createCache(),
+	sortOrder = function( a, b ) {
+		if ( a === b ) {
+			hasDuplicate = true;
+		}
+		return 0;
+	},
+
+	// Instance methods
+	hasOwn = ( {} ).hasOwnProperty,
+	arr = [],
+	pop = arr.pop,
+	pushNative = arr.push,
+	push = arr.push,
+	slice = arr.slice,
+
+	// Use a stripped-down indexOf as it's faster than native
+	// https://jsperf.com/thor-indexof-vs-for/5
+	indexOf = function( list, elem ) {
+		var i = 0,
+			len = list.length;
+		for ( ; i < len; i++ ) {
+			if ( list[ i ] === elem ) {
+				return i;
+			}
+		}
+		return -1;
+	},
+
+	booleans = "checked|selected|async|autofocus|autoplay|controls|defer|disabled|hidden|" +
+		"ismap|loop|multiple|open|readonly|required|scoped",
+
+	// Regular expressions
+
+	// http://www.w3.org/TR/css3-selectors/#whitespace
+	whitespace = "[\\x20\\t\\r\\n\\f]",
+
+	// https://www.w3.org/TR/css-syntax-3/#ident-token-diagram
+	identifier = "(?:\\\\[\\da-fA-F]{1,6}" + whitespace +
+		"?|\\\\[^\\r\\n\\f]|[\\w-]|[^\0-\\x7f])+",
+
+	// Attribute selectors: http://www.w3.org/TR/selectors/#attribute-selectors
+	attributes = "\\[" + whitespace + "*(" + identifier + ")(?:" + whitespace +
+
+		// Operator (capture 2)
+		"*([*^$|!~]?=)" + whitespace +
+
+		// "Attribute values must be CSS identifiers [capture 5]
+		// or strings [capture 3 or capture 4]"
+		"*(?:'((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\"|(" + identifier + "))|)" +
+		whitespace + "*\\]",
+
+	pseudos = ":(" + identifier + ")(?:\\((" +
+
+		// To reduce the number of selectors needing tokenize in the preFilter, prefer arguments:
+		// 1. quoted (capture 3; capture 4 or capture 5)
+		"('((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\")|" +
+
+		// 2. simple (capture 6)
+		"((?:\\\\.|[^\\\\()[\\]]|" + attributes + ")*)|" +
+
+		// 3. anything else (capture 2)
+		".*" +
+		")\\)|)",
+
+	// Leading and non-escaped trailing whitespace, capturing some non-whitespace characters preceding the latter
+	rwhitespace = new RegExp( whitespace + "+", "g" ),
+	rtrim = new RegExp( "^" + whitespace + "+|((?:^|[^\\\\])(?:\\\\.)*)" +
+		whitespace + "+$", "g" ),
+
+	rcomma = new RegExp( "^" + whitespace + "*," + whitespace + "*" ),
+	rcombinators = new RegExp( "^" + whitespace + "*([>+~]|" + whitespace + ")" + whitespace +
+		"*" ),
+	rdescend = new RegExp( whitespace + "|>" ),
+
+	rpseudo = new RegExp( pseudos ),
+	ridentifier = new RegExp( "^" + identifier + "$" ),
+
+	matchExpr = {
+		"ID": new RegExp( "^#(" + identifier + ")" ),
+		"CLASS": new RegExp( "^\\.(" + identifier + ")" ),
+		"TAG": new RegExp( "^(" + identifier + "|[*])" ),
+		"ATTR": new RegExp( "^" + attributes ),
+		"PSEUDO": new RegExp( "^" + pseudos ),
+		"CHILD": new RegExp( "^:(only|first|last|nth|nth-last)-(child|of-type)(?:\\(" +
+			whitespace + "*(even|odd|(([+-]|)(\\d*)n|)" + whitespace + "*(?:([+-]|)" +
+			whitespace + "*(\\d+)|))" + whitespace + "*\\)|)", "i" ),
+		"bool": new RegExp( "^(?:" + booleans + ")$", "i" ),
+
+		// For use in libraries implementing .is()
+		// We use this for POS matching in `select`
+		"needsContext": new RegExp( "^" + whitespace +
+			"*[>+~]|:(even|odd|eq|gt|lt|nth|first|last)(?:\\(" + whitespace +
+			"*((?:-\\d)?\\d*)" + whitespace + "*\\)|)(?=[^-]|$)", "i" )
+	},
+
+	rhtml = /HTML$/i,
+	rinputs = /^(?:input|select|textarea|button)$/i,
+	rheader = /^h\d$/i,
+
+	rnative = /^[^{]+\{\s*\[native \w/,
+
+	// Easily-parseable/retrievable ID or TAG or CLASS selectors
+	rquickExpr = /^(?:#([\w-]+)|(\w+)|\.([\w-]+))$/,
+
+	rsibling = /[+~]/,
+
+	// CSS escapes
+	// http://www.w3.org/TR/CSS21/syndata.html#escaped-characters
+	runescape = new RegExp( "\\\\[\\da-fA-F]{1,6}" + whitespace + "?|\\\\([^\\r\\n\\f])", "g" ),
+	funescape = function( escape, nonHex ) {
+		var high = "0x" + escape.slice( 1 ) - 0x10000;
+
+		return nonHex ?
+
+			// Strip the backslash prefix from a non-hex escape sequence
+			nonHex :
+
+			// Replace a hexadecimal escape sequence with the encoded Unicode code point
+			// Support: IE <=11+
+			// For values outside the Basic Multilingual Plane (BMP), manually construct a
+			// surrogate pair
+			high < 0 ?
+				String.fromCharCode( high + 0x10000 ) :
+				String.fromCharCode( high >> 10 | 0xD800, high & 0x3FF | 0xDC00 );
+	},
+
+	// CSS string/identifier serialization
+	// https://drafts.csswg.org/cssom/#common-serializing-idioms
+	rcssescape = /([\0-\x1f\x7f]|^-?\d)|^-$|[^\0-\x1f\x7f-\uFFFF\w-]/g,
+	fcssescape = function( ch, asCodePoint ) {
+		if ( asCodePoint ) {
+
+			// U+0000 NULL becomes U+FFFD REPLACEMENT CHARACTER
+			if ( ch === "\0" ) {
+				return "\uFFFD";
+			}
+
+			// Control characters and (dependent upon position) numbers get escaped as code points
+			return ch.slice( 0, -1 ) + "\\" +
+				ch.charCodeAt( ch.length - 1 ).toString( 16 ) + " ";
+		}
+
+		// Other potentially-special ASCII characters get backslash-escaped
+		return "\\" + ch;
+	},
+
+	// Used for iframes
+	// See setDocument()
+	// Removing the function wrapper causes a "Permission Denied"
+	// error in IE
+	unloadHandler = function() {
+		setDocument();
+	},
+
+	inDisabledFieldset = addCombinator(
+		function( elem ) {
+			return elem.disabled === true && elem.nodeName.toLowerCase() === "fieldset";
+		},
+		{ dir: "parentNode", next: "legend" }
+	);
+
+// Optimize for push.apply( _, NodeList )
+try {
+	push.apply(
+		( arr = slice.call( preferredDoc.childNodes ) ),
+		preferredDoc.childNodes
+	);
+
+	// Support: Android<4.0
+	// Detect silently failing push.apply
+	// eslint-disable-next-line no-unused-expressions
+	arr[ preferredDoc.childNodes.length ].nodeType;
+} catch ( e ) {
+	push = { apply: arr.length ?
+
+		// Leverage slice if possible
+		function( target, els ) {
+			pushNative.apply( target, slice.call( els ) );
+		} :
+
+		// Support: IE<9
+		// Otherwise append directly
+		function( target, els ) {
+			var j = target.length,
+				i = 0;
+
+			// Can't trust NodeList.length
+			while ( ( target[ j++ ] = els[ i++ ] ) ) {}
+			target.length = j - 1;
+		}
+	};
+}
+
+function Sizzle( selector, context, results, seed ) {
+	var m, i, elem, nid, match, groups, newSelector,
+		newContext = context && context.ownerDocument,
+
+		// nodeType defaults to 9, since context defaults to document
+		nodeType = context ? context.nodeType : 9;
+
+	results = results || [];
+
+	// Return early from calls with invalid selector or context
+	if ( typeof selector !== "string" || !selector ||
+		nodeType !== 1 && nodeType !== 9 && nodeType !== 11 ) {
+
+		return results;
+	}
+
+	// Try to shortcut find operations (as opposed to filters) in HTML documents
+	if ( !seed ) {
+		setDocument( context );
+		context = context || document;
+
+		if ( documentIsHTML ) {
+
+			// If the selector is sufficiently simple, try using a "get*By*" DOM method
+			// (excepting DocumentFragment context, where the methods don't exist)
+			if ( nodeType !== 11 && ( match = rquickExpr.exec( selector ) ) ) {
+
+				// ID selector
+				if ( ( m = match[ 1 ] ) ) {
+
+					// Document context
+					if ( nodeType === 9 ) {
+						if ( ( elem = context.getElementById( m ) ) ) {
+
+							// Support: IE, Opera, Webkit
+							// TODO: identify versions
+							// getElementById can match elements by name instead of ID
+							if ( elem.id === m ) {
+								results.push( elem );
+								return results;
+							}
+						} else {
+							return results;
+						}
+
+					// Element context
+					} else {
+
+						// Support: IE, Opera, Webkit
+						// TODO: identify versions
+						// getElementById can match elements by name instead of ID
+						if ( newContext && ( elem = newContext.getElementById( m ) ) &&
+							contains( context, elem ) &&
+							elem.id === m ) {
+
+							results.push( elem );
+							return results;
+						}
+					}
+
+				// Type selector
+				} else if ( match[ 2 ] ) {
+					push.apply( results, context.getElementsByTagName( selector ) );
+					return results;
+
+				// Class selector
+				} else if ( ( m = match[ 3 ] ) && support.getElementsByClassName &&
+					context.getElementsByClassName ) {
+
+					push.apply( results, context.getElementsByClassName( m ) );
+					return results;
+				}
+			}
+
+			// Take advantage of querySelectorAll
+			if ( support.qsa &&
+				!nonnativeSelectorCache[ selector + " " ] &&
+				( !rbuggyQSA || !rbuggyQSA.test( selector ) ) &&
+
+				// Support: IE 8 only
+				// Exclude object elements
+				( nodeType !== 1 || context.nodeName.toLowerCase() !== "object" ) ) {
+
+				newSelector = selector;
+				newContext = context;
+
+				// qSA considers elements outside a scoping root when evaluating child or
+				// descendant combinators, which is not what we want.
+				// In such cases, we work around the behavior by prefixing every selector in the
+				// list with an ID selector referencing the scope context.
+				// The technique has to be used as well when a leading combinator is used
+				// as such selectors are not recognized by querySelectorAll.
+				// Thanks to Andrew Dupont for this technique.
+				if ( nodeType === 1 &&
+					( rdescend.test( selector ) || rcombinators.test( selector ) ) ) {
+
+					// Expand context for sibling selectors
+					newContext = rsibling.test( selector ) && testContext( context.parentNode ) ||
+						context;
+
+					// We can use :scope instead of the ID hack if the browser
+					// supports it & if we're not changing the context.
+					if ( newContext !== context || !support.scope ) {
+
+						// Capture the context ID, setting it first if necessary
+						if ( ( nid = context.getAttribute( "id" ) ) ) {
+							nid = nid.replace( rcssescape, fcssescape );
+						} else {
+							context.setAttribute( "id", ( nid = expando ) );
+						}
+					}
+
+					// Prefix every selector in the list
+					groups = tokenize( selector );
+					i = groups.length;
+					while ( i-- ) {
+						groups[ i ] = ( nid ? "#" + nid : ":scope" ) + " " +
+							toSelector( groups[ i ] );
+					}
+					newSelector = groups.join( "," );
+				}
+
+				try {
+					push.apply( results,
+						newContext.querySelectorAll( newSelector )
+					);
+					return results;
+				} catch ( qsaError ) {
+					nonnativeSelectorCache( selector, true );
+				} finally {
+					if ( nid === expando ) {
+						context.removeAttribute( "id" );
+					}
+				}
+			}
+		}
+	}
+
+	// All others
+	return select( selector.replace( rtrim, "$1" ), context, results, seed );
+}
+
+/**
+ * Create key-value caches of limited size
+ * @returns {function(string, object)} Returns the Object data after storing it on itself with
+ *	property name the (space-suffixed) string and (if the cache is larger than Expr.cacheLength)
+ *	deleting the oldest entry
+ */
+function createCache() {
+	var keys = [];
+
+	function cache( key, value ) {
+
+		// Use (key + " ") to avoid collision with native prototype properties (see Issue #157)
+		if ( keys.push( key + " " ) > Expr.cacheLength ) {
+
+			// Only keep the most recent entries
+			delete cache[ keys.shift() ];
+		}
+		return ( cache[ key + " " ] = value );
+	}
+	return cache;
+}
+
+/**
+ * Mark a function for special use by Sizzle
+ * @param {Function} fn The function to mark
+ */
+function markFunction( fn ) {
+	fn[ expando ] = true;
+	return fn;
+}
+
+/**
+ * Support testing using an element
+ * @param {Function} fn Passed the created element and returns a boolean result
+ */
+function assert( fn ) {
+	var el = document.createElement( "fieldset" );
+
+	try {
+		return !!fn( el );
+	} catch ( e ) {
+		return false;
+	} finally {
+
+		// Remove from its parent by default
+		if ( el.parentNode ) {
+			el.parentNode.removeChild( el );
+		}
+
+		// release memory in IE
+		el = null;
+	}
+}
+
+/**
+ * Adds the same handler for all of the specified attrs
+ * @param {String} attrs Pipe-separated list of attributes
+ * @param {Function} handler The method that will be applied
+ */
+function addHandle( attrs, handler ) {
+	var arr = attrs.split( "|" ),
+		i = arr.length;
+
+	while ( i-- ) {
+		Expr.attrHandle[ arr[ i ] ] = handler;
+	}
+}
+
+/**
+ * Checks document order of two siblings
+ * @param {Element} a
+ * @param {Element} b
+ * @returns {Number} Returns less than 0 if a precedes b, greater than 0 if a follows b
+ */
+function siblingCheck( a, b ) {
+	var cur = b && a,
+		diff = cur && a.nodeType === 1 && b.nodeType === 1 &&
+			a.sourceIndex - b.sourceIndex;
+
+	// Use IE sourceIndex if available on both nodes
+	if ( diff ) {
+		return diff;
+	}
+
+	// Check if b follows a
+	if ( cur ) {
+		while ( ( cur = cur.nextSibling ) ) {
+			if ( cur === b ) {
+				return -1;
+			}
+		}
+	}
+
+	return a ? 1 : -1;
+}
+
+/**
+ * Returns a function to use in pseudos for input types
+ * @param {String} type
+ */
+function createInputPseudo( type ) {
+	return function( elem ) {
+		var name = elem.nodeName.toLowerCase();
+		return name === "input" && elem.type === type;
+	};
+}
+
+/**
+ * Returns a function to use in pseudos for buttons
+ * @param {String} type
+ */
+function createButtonPseudo( type ) {
+	return function( elem ) {
+		var name = elem.nodeName.toLowerCase();
+		return ( name === "input" || name === "button" ) && elem.type === type;
+	};
+}
+
+/**
+ * Returns a function to use in pseudos for :enabled/:disabled
+ * @param {Boolean} disabled true for :disabled; false for :enabled
+ */
+function createDisabledPseudo( disabled ) {
+
+	// Known :disabled false positives: fieldset[disabled] > legend:nth-of-type(n+2) :can-disable
+	return function( elem ) {
+
+		// Only certain elements can match :enabled or :disabled
+		// https://html.spec.whatwg.org/multipage/scripting.html#selector-enabled
+		// https://html.spec.whatwg.org/multipage/scripting.html#selector-disabled
+		if ( "form" in elem ) {
+
+			// Check for inherited disabledness on relevant non-disabled elements:
+			// * listed form-associated elements in a disabled fieldset
+			//   https://html.spec.whatwg.org/multipage/forms.html#category-listed
+			//   https://html.spec.whatwg.org/multipage/forms.html#concept-fe-disabled
+			// * option elements in a disabled optgroup
+			//   https://html.spec.whatwg.org/multipage/forms.html#concept-option-disabled
+			// All such elements have a "form" property.
+			if ( elem.parentNode && elem.disabled === false ) {
+
+				// Option elements defer to a parent optgroup if present
+				if ( "label" in elem ) {
+					if ( "label" in elem.parentNode ) {
+						return elem.parentNode.disabled === disabled;
+					} else {
+						return elem.disabled === disabled;
+					}
+				}
+
+				// Support: IE 6 - 11
+				// Use the isDisabled shortcut property to check for disabled fieldset ancestors
+				return elem.isDisabled === disabled ||
+
+					// Where there is no isDisabled, check manually
+					/* jshint -W018 */
+					elem.isDisabled !== !disabled &&
+					inDisabledFieldset( elem ) === disabled;
+			}
+
+			return elem.disabled === disabled;
+
+		// Try to winnow out elements that can't be disabled before trusting the disabled property.
+		// Some victims get caught in our net (label, legend, menu, track), but it shouldn't
+		// even exist on them, let alone have a boolean value.
+		} else if ( "label" in elem ) {
+			return elem.disabled === disabled;
+		}
+
+		// Remaining elements are neither :enabled nor :disabled
+		return false;
+	};
+}
+
+/**
+ * Returns a function to use in pseudos for positionals
+ * @param {Function} fn
+ */
+function createPositionalPseudo( fn ) {
+	return markFunction( function( argument ) {
+		argument = +argument;
+		return markFunction( function( seed, matches ) {
+			var j,
+				matchIndexes = fn( [], seed.length, argument ),
+				i = matchIndexes.length;
+
+			// Match elements found at the specified indexes
+			while ( i-- ) {
+				if ( seed[ ( j = matchIndexes[ i ] ) ] ) {
+					seed[ j ] = !( matches[ j ] = seed[ j ] );
+				}
+			}
+		} );
+	} );
+}
+
+/**
+ * Checks a node for validity as a Sizzle context
+ * @param {Element|Object=} context
+ * @returns {Element|Object|Boolean} The input node if acceptable, otherwise a falsy value
+ */
+function testContext( context ) {
+	return context && typeof context.getElementsByTagName !== "undefined" && context;
+}
+
+// Expose support vars for convenience
+support = Sizzle.support = {};
+
+/**
+ * Detects XML nodes
+ * @param {Element|Object} elem An element or a document
+ * @returns {Boolean} True iff elem is a non-HTML XML node
+ */
+isXML = Sizzle.isXML = function( elem ) {
+	var namespace = elem && elem.namespaceURI,
+		docElem = elem && ( elem.ownerDocument || elem ).documentElement;
+
+	// Support: IE <=8
+	// Assume HTML when documentElement doesn't yet exist, such as inside loading iframes
+	// https://bugs.jquery.com/ticket/4833
+	return !rhtml.test( namespace || docElem && docElem.nodeName || "HTML" );
+};
+
+/**
+ * Sets document-related variables once based on the current document
+ * @param {Element|Object} [doc] An element or document object to use to set the document
+ * @returns {Object} Returns the current document
+ */
+setDocument = Sizzle.setDocument = function( node ) {
+	var hasCompare, subWindow,
+		doc = node ? node.ownerDocument || node : preferredDoc;
+
+	// Return early if doc is invalid or already selected
+	// Support: IE 11+, Edge 17 - 18+
+	// IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+	// two documents; shallow comparisons work.
+	// eslint-disable-next-line eqeqeq
+	if ( doc == document || doc.nodeType !== 9 || !doc.documentElement ) {
+		return document;
+	}
+
+	// Update global variables
+	document = doc;
+	docElem = document.documentElement;
+	documentIsHTML = !isXML( document );
+
+	// Support: IE 9 - 11+, Edge 12 - 18+
+	// Accessing iframe documents after unload throws "permission denied" errors (jQuery #13936)
+	// Support: IE 11+, Edge 17 - 18+
+	// IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+	// two documents; shallow comparisons work.
+	// eslint-disable-next-line eqeqeq
+	if ( preferredDoc != document &&
+		( subWindow = document.defaultView ) && subWindow.top !== subWindow ) {
+
+		// Support: IE 11, Edge
+		if ( subWindow.addEventListener ) {
+			subWindow.addEventListener( "unload", unloadHandler, false );
+
+		// Support: IE 9 - 10 only
+		} else if ( subWindow.attachEvent ) {
+			subWindow.attachEvent( "onunload", unloadHandler );
+		}
+	}
+
+	// Support: IE 8 - 11+, Edge 12 - 18+, Chrome <=16 - 25 only, Firefox <=3.6 - 31 only,
+	// Safari 4 - 5 only, Opera <=11.6 - 12.x only
+	// IE/Edge & older browsers don't support the :scope pseudo-class.
+	// Support: Safari 6.0 only
+	// Safari 6.0 supports :scope but it's an alias of :root there.
+	support.scope = assert( function( el ) {
+		docElem.appendChild( el ).appendChild( document.createElement( "div" ) );
+		return typeof el.querySelectorAll !== "undefined" &&
+			!el.querySelectorAll( ":scope fieldset div" ).length;
+	} );
+
+	/* Attributes
+	---------------------------------------------------------------------- */
+
+	// Support: IE<8
+	// Verify that getAttribute really returns attributes and not properties
+	// (excepting IE8 booleans)
+	support.attributes = assert( function( el ) {
+		el.className = "i";
+		return !el.getAttribute( "className" );
+	} );
+
+	/* getElement(s)By*
+	---------------------------------------------------------------------- */
+
+	// Check if getElementsByTagName("*") returns only elements
+	support.getElementsByTagName = assert( function( el ) {
+		el.appendChild( document.createComment( "" ) );
+		return !el.getElementsByTagName( "*" ).length;
+	} );
+
+	// Support: IE<9
+	support.getElementsByClassName = rnative.test( document.getElementsByClassName );
+
+	// Support: IE<10
+	// Check if getElementById returns elements by name
+	// The broken getElementById methods don't pick up programmatically-set names,
+	// so use a roundabout getElementsByName test
+	support.getById = assert( function( el ) {
+		docElem.appendChild( el ).id = expando;
+		return !document.getElementsByName || !document.getElementsByName( expando ).length;
+	} );
+
+	// ID filter and find
+	if ( support.getById ) {
+		Expr.filter[ "ID" ] = function( id ) {
+			var attrId = id.replace( runescape, funescape );
+			return function( elem ) {
+				return elem.getAttribute( "id" ) === attrId;
+			};
+		};
+		Expr.find[ "ID" ] = function( id, context ) {
+			if ( typeof context.getElementById !== "undefined" && documentIsHTML ) {
+				var elem = context.getElementById( id );
+				return elem ? [ elem ] : [];
+			}
+		};
+	} else {
+		Expr.filter[ "ID" ] =  function( id ) {
+			var attrId = id.replace( runescape, funescape );
+			return function( elem ) {
+				var node = typeof elem.getAttributeNode !== "undefined" &&
+					elem.getAttributeNode( "id" );
+				return node && node.value === attrId;
+			};
+		};
+
+		// Support: IE 6 - 7 only
+		// getElementById is not reliable as a find shortcut
+		Expr.find[ "ID" ] = function( id, context ) {
+			if ( typeof context.getElementById !== "undefined" && documentIsHTML ) {
+				var node, i, elems,
+					elem = context.getElementById( id );
+
+				if ( elem ) {
+
+					// Verify the id attribute
+					node = elem.getAttributeNode( "id" );
+					if ( node && node.value === id ) {
+						return [ elem ];
+					}
+
+					// Fall back on getElementsByName
+					elems = context.getElementsByName( id );
+					i = 0;
+					while ( ( elem = elems[ i++ ] ) ) {
+						node = elem.getAttributeNode( "id" );
+						if ( node && node.value === id ) {
+							return [ elem ];
+						}
+					}
+				}
+
+				return [];
+			}
+		};
+	}
+
+	// Tag
+	Expr.find[ "TAG" ] = support.getElementsByTagName ?
+		function( tag, context ) {
+			if ( typeof context.getElementsByTagName !== "undefined" ) {
+				return context.getElementsByTagName( tag );
+
+			// DocumentFragment nodes don't have gEBTN
+			} else if ( support.qsa ) {
+				return context.querySelectorAll( tag );
+			}
+		} :
+
+		function( tag, context ) {
+			var elem,
+				tmp = [],
+				i = 0,
+
+				// By happy coincidence, a (broken) gEBTN appears on DocumentFragment nodes too
+				results = context.getElementsByTagName( tag );
+
+			// Filter out possible comments
+			if ( tag === "*" ) {
+				while ( ( elem = results[ i++ ] ) ) {
+					if ( elem.nodeType === 1 ) {
+						tmp.push( elem );
+					}
+				}
+
+				return tmp;
+			}
+			return results;
+		};
+
+	// Class
+	Expr.find[ "CLASS" ] = support.getElementsByClassName && function( className, context ) {
+		if ( typeof context.getElementsByClassName !== "undefined" && documentIsHTML ) {
+			return context.getElementsByClassName( className );
+		}
+	};
+
+	/* QSA/matchesSelector
+	---------------------------------------------------------------------- */
+
+	// QSA and matchesSelector support
+
+	// matchesSelector(:active) reports false when true (IE9/Opera 11.5)
+	rbuggyMatches = [];
+
+	// qSa(:focus) reports false when true (Chrome 21)
+	// We allow this because of a bug in IE8/9 that throws an error
+	// whenever `document.activeElement` is accessed on an iframe
+	// So, we allow :focus to pass through QSA all the time to avoid the IE error
+	// See https://bugs.jquery.com/ticket/13378
+	rbuggyQSA = [];
+
+	if ( ( support.qsa = rnative.test( document.querySelectorAll ) ) ) {
+
+		// Build QSA regex
+		// Regex strategy adopted from Diego Perini
+		assert( function( el ) {
+
+			var input;
+
+			// Select is set to empty string on purpose
+			// This is to test IE's treatment of not explicitly
+			// setting a boolean content attribute,
+			// since its presence should be enough
+			// https://bugs.jquery.com/ticket/12359
+			docElem.appendChild( el ).innerHTML = "<a id='" + expando + "'></a>" +
+				"<select id='" + expando + "-\r\\' msallowcapture=''>" +
+				"<option selected=''></option></select>";
+
+			// Support: IE8, Opera 11-12.16
+			// Nothing should be selected when empty strings follow ^= or $= or *=
+			// The test attribute must be unknown in Opera but "safe" for WinRT
+			// https://msdn.microsoft.com/en-us/library/ie/hh465388.aspx#attribute_section
+			if ( el.querySelectorAll( "[msallowcapture^='']" ).length ) {
+				rbuggyQSA.push( "[*^$]=" + whitespace + "*(?:''|\"\")" );
+			}
+
+			// Support: IE8
+			// Boolean attributes and "value" are not treated correctly
+			if ( !el.querySelectorAll( "[selected]" ).length ) {
+				rbuggyQSA.push( "\\[" + whitespace + "*(?:value|" + booleans + ")" );
+			}
+
+			// Support: Chrome<29, Android<4.4, Safari<7.0+, iOS<7.0+, PhantomJS<1.9.8+
+			if ( !el.querySelectorAll( "[id~=" + expando + "-]" ).length ) {
+				rbuggyQSA.push( "~=" );
+			}
+
+			// Support: IE 11+, Edge 15 - 18+
+			// IE 11/Edge don't find elements on a `[name='']` query in some cases.
+			// Adding a temporary attribute to the document before the selection works
+			// around the issue.
+			// Interestingly, IE 10 & older don't seem to have the issue.
+			input = document.createElement( "input" );
+			input.setAttribute( "name", "" );
+			el.appendChild( input );
+			if ( !el.querySelectorAll( "[name='']" ).length ) {
+				rbuggyQSA.push( "\\[" + whitespace + "*name" + whitespace + "*=" +
+					whitespace + "*(?:''|\"\")" );
+			}
+
+			// Webkit/Opera - :checked should return selected option elements
+			// http://www.w3.org/TR/2011/REC-css3-selectors-20110929/#checked
+			// IE8 throws error here and will not see later tests
+			if ( !el.querySelectorAll( ":checked" ).length ) {
+				rbuggyQSA.push( ":checked" );
+			}
+
+			// Support: Safari 8+, iOS 8+
+			// https://bugs.webkit.org/show_bug.cgi?id=136851
+			// In-page `selector#id sibling-combinator selector` fails
+			if ( !el.querySelectorAll( "a#" + expando + "+*" ).length ) {
+				rbuggyQSA.push( ".#.+[+~]" );
+			}
+
+			// Support: Firefox <=3.6 - 5 only
+			// Old Firefox doesn't throw on a badly-escaped identifier.
+			el.querySelectorAll( "\\\f" );
+			rbuggyQSA.push( "[\\r\\n\\f]" );
+		} );
+
+		assert( function( el ) {
+			el.innerHTML = "<a href='' disabled='disabled'></a>" +
+				"<select disabled='disabled'><option/></select>";
+
+			// Support: Windows 8 Native Apps
+			// The type and name attributes are restricted during .innerHTML assignment
+			var input = document.createElement( "input" );
+			input.setAttribute( "type", "hidden" );
+			el.appendChild( input ).setAttribute( "name", "D" );
+
+			// Support: IE8
+			// Enforce case-sensitivity of name attribute
+			if ( el.querySelectorAll( "[name=d]" ).length ) {
+				rbuggyQSA.push( "name" + whitespace + "*[*^$|!~]?=" );
+			}
+
+			// FF 3.5 - :enabled/:disabled and hidden elements (hidden elements are still enabled)
+			// IE8 throws error here and will not see later tests
+			if ( el.querySelectorAll( ":enabled" ).length !== 2 ) {
+				rbuggyQSA.push( ":enabled", ":disabled" );
+			}
+
+			// Support: IE9-11+
+			// IE's :disabled selector does not pick up the children of disabled fieldsets
+			docElem.appendChild( el ).disabled = true;
+			if ( el.querySelectorAll( ":disabled" ).length !== 2 ) {
+				rbuggyQSA.push( ":enabled", ":disabled" );
+			}
+
+			// Support: Opera 10 - 11 only
+			// Opera 10-11 does not throw on post-comma invalid pseudos
+			el.querySelectorAll( "*,:x" );
+			rbuggyQSA.push( ",.*:" );
+		} );
+	}
+
+	if ( ( support.matchesSelector = rnative.test( ( matches = docElem.matches ||
+		docElem.webkitMatchesSelector ||
+		docElem.mozMatchesSelector ||
+		docElem.oMatchesSelector ||
+		docElem.msMatchesSelector ) ) ) ) {
+
+		assert( function( el ) {
+
+			// Check to see if it's possible to do matchesSelector
+			// on a disconnected node (IE 9)
+			support.disconnectedMatch = matches.call( el, "*" );
+
+			// This should fail with an exception
+			// Gecko does not error, returns false instead
+			matches.call( el, "[s!='']:x" );
+			rbuggyMatches.push( "!=", pseudos );
+		} );
+	}
+
+	rbuggyQSA = rbuggyQSA.length && new RegExp( rbuggyQSA.join( "|" ) );
+	rbuggyMatches = rbuggyMatches.length && new RegExp( rbuggyMatches.join( "|" ) );
+
+	/* Contains
+	---------------------------------------------------------------------- */
+	hasCompare = rnative.test( docElem.compareDocumentPosition );
+
+	// Element contains another
+	// Purposefully self-exclusive
+	// As in, an element does not contain itself
+	contains = hasCompare || rnative.test( docElem.contains ) ?
+		function( a, b ) {
+			var adown = a.nodeType === 9 ? a.documentElement : a,
+				bup = b && b.parentNode;
+			return a === bup || !!( bup && bup.nodeType === 1 && (
+				adown.contains ?
+					adown.contains( bup ) :
+					a.compareDocumentPosition && a.compareDocumentPosition( bup ) & 16
+			) );
+		} :
+		function( a, b ) {
+			if ( b ) {
+				while ( ( b = b.parentNode ) ) {
+					if ( b === a ) {
+						return true;
+					}
+				}
+			}
+			return false;
+		};
+
+	/* Sorting
+	---------------------------------------------------------------------- */
+
+	// Document order sorting
+	sortOrder = hasCompare ?
+	function( a, b ) {
+
+		// Flag for duplicate removal
+		if ( a === b ) {
+			hasDuplicate = true;
+			return 0;
+		}
+
+		// Sort on method existence if only one input has compareDocumentPosition
+		var compare = !a.compareDocumentPosition - !b.compareDocumentPosition;
+		if ( compare ) {
+			return compare;
+		}
+
+		// Calculate position if both inputs belong to the same document
+		// Support: IE 11+, Edge 17 - 18+
+		// IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+		// two documents; shallow comparisons work.
+		// eslint-disable-next-line eqeqeq
+		compare = ( a.ownerDocument || a ) == ( b.ownerDocument || b ) ?
+			a.compareDocumentPosition( b ) :
+
+			// Otherwise we know they are disconnected
+			1;
+
+		// Disconnected nodes
+		if ( compare & 1 ||
+			( !support.sortDetached && b.compareDocumentPosition( a ) === compare ) ) {
+
+			// Choose the first element that is related to our preferred document
+			// Support: IE 11+, Edge 17 - 18+
+			// IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+			// two documents; shallow comparisons work.
+			// eslint-disable-next-line eqeqeq
+			if ( a == document || a.ownerDocument == preferredDoc &&
+				contains( preferredDoc, a ) ) {
+				return -1;
+			}
+
+			// Support: IE 11+, Edge 17 - 18+
+			// IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+			// two documents; shallow comparisons work.
+			// eslint-disable-next-line eqeqeq
+			if ( b == document || b.ownerDocument == preferredDoc &&
+				contains( preferredDoc, b ) ) {
+				return 1;
+			}
+
+			// Maintain original order
+			return sortInput ?
+				( indexOf( sortInput, a ) - indexOf( sortInput, b ) ) :
+				0;
+		}
+
+		return compare & 4 ? -1 : 1;
+	} :
+	function( a, b ) {
+
+		// Exit early if the nodes are identical
+		if ( a === b ) {
+			hasDuplicate = true;
+			return 0;
+		}
+
+		var cur,
+			i = 0,
+			aup = a.parentNode,
+			bup = b.parentNode,
+			ap = [ a ],
+			bp = [ b ];
+
+		// Parentless nodes are either documents or disconnected
+		if ( !aup || !bup ) {
+
+			// Support: IE 11+, Edge 17 - 18+
+			// IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+			// two documents; shallow comparisons work.
+			/* eslint-disable eqeqeq */
+			return a == document ? -1 :
+				b == document ? 1 :
+				/* eslint-enable eqeqeq */
+				aup ? -1 :
+				bup ? 1 :
+				sortInput ?
+				( indexOf( sortInput, a ) - indexOf( sortInput, b ) ) :
+				0;
+
+		// If the nodes are siblings, we can do a quick check
+		} else if ( aup === bup ) {
+			return siblingCheck( a, b );
+		}
+
+		// Otherwise we need full lists of their ancestors for comparison
+		cur = a;
+		while ( ( cur = cur.parentNode ) ) {
+			ap.unshift( cur );
+		}
+		cur = b;
+		while ( ( cur = cur.parentNode ) ) {
+			bp.unshift( cur );
+		}
+
+		// Walk down the tree looking for a discrepancy
+		while ( ap[ i ] === bp[ i ] ) {
+			i++;
+		}
+
+		return i ?
+
+			// Do a sibling check if the nodes have a common ancestor
+			siblingCheck( ap[ i ], bp[ i ] ) :
+
+			// Otherwise nodes in our document sort first
+			// Support: IE 11+, Edge 17 - 18+
+			// IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+			// two documents; shallow comparisons work.
+			/* eslint-disable eqeqeq */
+			ap[ i ] == preferredDoc ? -1 :
+			bp[ i ] == preferredDoc ? 1 :
+			/* eslint-enable eqeqeq */
+			0;
+	};
+
+	return document;
+};
+
+Sizzle.matches = function( expr, elements ) {
+	return Sizzle( expr, null, null, elements );
+};
+
+Sizzle.matchesSelector = function( elem, expr ) {
+	setDocument( elem );
+
+	if ( support.matchesSelector && documentIsHTML &&
+		!nonnativeSelectorCache[ expr + " " ] &&
+		( !rbuggyMatches || !rbuggyMatches.test( expr ) ) &&
+		( !rbuggyQSA     || !rbuggyQSA.test( expr ) ) ) {
+
+		try {
+			var ret = matches.call( elem, expr );
+
+			// IE 9's matchesSelector returns false on disconnected nodes
+			if ( ret || support.disconnectedMatch ||
+
+				// As well, disconnected nodes are said to be in a document
+				// fragment in IE 9
+				elem.document && elem.document.nodeType !== 11 ) {
+				return ret;
+			}
+		} catch ( e ) {
+			nonnativeSelectorCache( expr, true );
+		}
+	}
+
+	return Sizzle( expr, document, null, [ elem ] ).length > 0;
+};
+
+Sizzle.contains = function( context, elem ) {
+
+	// Set document vars if needed
+	// Support: IE 11+, Edge 17 - 18+
+	// IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+	// two documents; shallow comparisons work.
+	// eslint-disable-next-line eqeqeq
+	if ( ( context.ownerDocument || context ) != document ) {
+		setDocument( context );
+	}
+	return contains( context, elem );
+};
+
+Sizzle.attr = function( elem, name ) {
+
+	// Set document vars if needed
+	// Support: IE 11+, Edge 17 - 18+
+	// IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+	// two documents; shallow comparisons work.
+	// eslint-disable-next-line eqeqeq
+	if ( ( elem.ownerDocument || elem ) != document ) {
+		setDocument( elem );
+	}
+
+	var fn = Expr.attrHandle[ name.toLowerCase() ],
+
+		// Don't get fooled by Object.prototype properties (jQuery #13807)
+		val = fn && hasOwn.call( Expr.attrHandle, name.toLowerCase() ) ?
+			fn( elem, name, !documentIsHTML ) :
+			undefined;
+
+	return val !== undefined ?
+		val :
+		support.attributes || !documentIsHTML ?
+			elem.getAttribute( name ) :
+			( val = elem.getAttributeNode( name ) ) && val.specified ?
+				val.value :
+				null;
+};
+
+Sizzle.escape = function( sel ) {
+	return ( sel + "" ).replace( rcssescape, fcssescape );
+};
+
+Sizzle.error = function( msg ) {
+	throw new Error( "Syntax error, unrecognized expression: " + msg );
+};
+
+/**
+ * Document sorting and removing duplicates
+ * @param {ArrayLike} results
+ */
+Sizzle.uniqueSort = function( results ) {
+	var elem,
+		duplicates = [],
+		j = 0,
+		i = 0;
+
+	// Unless we *know* we can detect duplicates, assume their presence
+	hasDuplicate = !support.detectDuplicates;
+	sortInput = !support.sortStable && results.slice( 0 );
+	results.sort( sortOrder );
+
+	if ( hasDuplicate ) {
+		while ( ( elem = results[ i++ ] ) ) {
+			if ( elem === results[ i ] ) {
+				j = duplicates.push( i );
+			}
+		}
+		while ( j-- ) {
+			results.splice( duplicates[ j ], 1 );
+		}
+	}
+
+	// Clear input after sorting to release objects
+	// See https://github.com/jquery/sizzle/pull/225
+	sortInput = null;
+
+	return results;
+};
+
+/**
+ * Utility function for retrieving the text value of an array of DOM nodes
+ * @param {Array|Element} elem
+ */
+getText = Sizzle.getText = function( elem ) {
+	var node,
+		ret = "",
+		i = 0,
+		nodeType = elem.nodeType;
+
+	if ( !nodeType ) {
+
+		// If no nodeType, this is expected to be an array
+		while ( ( node = elem[ i++ ] ) ) {
+
+			// Do not traverse comment nodes
+			ret += getText( node );
+		}
+	} else if ( nodeType === 1 || nodeType === 9 || nodeType === 11 ) {
+
+		// Use textContent for elements
+		// innerText usage removed for consistency of new lines (jQuery #11153)
+		if ( typeof elem.textContent === "string" ) {
+			return elem.textContent;
+		} else {
+
+			// Traverse its children
+			for ( elem = elem.firstChild; elem; elem = elem.nextSibling ) {
+				ret += getText( elem );
+			}
+		}
+	} else if ( nodeType === 3 || nodeType === 4 ) {
+		return elem.nodeValue;
+	}
+
+	// Do not include comment or processing instruction nodes
+
+	return ret;
+};
+
+Expr = Sizzle.selectors = {
+
+	// Can be adjusted by the user
+	cacheLength: 50,
+
+	createPseudo: markFunction,
+
+	match: matchExpr,
+
+	attrHandle: {},
+
+	find: {},
+
+	relative: {
+		">": { dir: "parentNode", first: true },
+		" ": { dir: "parentNode" },
+		"+": { dir: "previousSibling", first: true },
+		"~": { dir: "previousSibling" }
+	},
+
+	preFilter: {
+		"ATTR": function( match ) {
+			match[ 1 ] = match[ 1 ].replace( runescape, funescape );
+
+			// Move the given value to match[3] whether quoted or unquoted
+			match[ 3 ] = ( match[ 3 ] || match[ 4 ] ||
+				match[ 5 ] || "" ).replace( runescape, funescape );
+
+			if ( match[ 2 ] === "~=" ) {
+				match[ 3 ] = " " + match[ 3 ] + " ";
+			}
+
+			return match.slice( 0, 4 );
+		},
+
+		"CHILD": function( match ) {
+
+			/* matches from matchExpr["CHILD"]
+				1 type (only|nth|...)
+				2 what (child|of-type)
+				3 argument (even|odd|\d*|\d*n([+-]\d+)?|...)
+				4 xn-component of xn+y argument ([+-]?\d*n|)
+				5 sign of xn-component
+				6 x of xn-component
+				7 sign of y-component
+				8 y of y-component
+			*/
+			match[ 1 ] = match[ 1 ].toLowerCase();
+
+			if ( match[ 1 ].slice( 0, 3 ) === "nth" ) {
+
+				// nth-* requires argument
+				if ( !match[ 3 ] ) {
+					Sizzle.error( match[ 0 ] );
+				}
+
+				// numeric x and y parameters for Expr.filter.CHILD
+				// remember that false/true cast respectively to 0/1
+				match[ 4 ] = +( match[ 4 ] ?
+					match[ 5 ] + ( match[ 6 ] || 1 ) :
+					2 * ( match[ 3 ] === "even" || match[ 3 ] === "odd" ) );
+				match[ 5 ] = +( ( match[ 7 ] + match[ 8 ] ) || match[ 3 ] === "odd" );
+
+				// other types prohibit arguments
+			} else if ( match[ 3 ] ) {
+				Sizzle.error( match[ 0 ] );
+			}
+
+			return match;
+		},
+
+		"PSEUDO": function( match ) {
+			var excess,
+				unquoted = !match[ 6 ] && match[ 2 ];
+
+			if ( matchExpr[ "CHILD" ].test( match[ 0 ] ) ) {
+				return null;
+			}
+
+			// Accept quoted arguments as-is
+			if ( match[ 3 ] ) {
+				match[ 2 ] = match[ 4 ] || match[ 5 ] || "";
+
+			// Strip excess characters from unquoted arguments
+			} else if ( unquoted && rpseudo.test( unquoted ) &&
+
+				// Get excess from tokenize (recursively)
+				( excess = tokenize( unquoted, true ) ) &&
+
+				// advance to the next closing parenthesis
+				( excess = unquoted.indexOf( ")", unquoted.length - excess ) - unquoted.length ) ) {
+
+				// excess is a negative index
+				match[ 0 ] = match[ 0 ].slice( 0, excess );
+				match[ 2 ] = unquoted.slice( 0, excess );
+			}
+
+			// Return only captures needed by the pseudo filter method (type and argument)
+			return match.slice( 0, 3 );
+		}
+	},
+
+	filter: {
+
+		"TAG": function( nodeNameSelector ) {
+			var nodeName = nodeNameSelector.replace( runescape, funescape ).toLowerCase();
+			return nodeNameSelector === "*" ?
+				function() {
+					return true;
+				} :
+				function( elem ) {
+					return elem.nodeName && elem.nodeName.toLowerCase() === nodeName;
+				};
+		},
+
+		"CLASS": function( className ) {
+			var pattern = classCache[ className + " " ];
+
+			return pattern ||
+				( pattern = new RegExp( "(^|" + whitespace +
+					")" + className + "(" + whitespace + "|$)" ) ) && classCache(
+						className, function( elem ) {
+							return pattern.test(
+								typeof elem.className === "string" && elem.className ||
+								typeof elem.getAttribute !== "undefined" &&
+									elem.getAttribute( "class" ) ||
+								""
+							);
+				} );
+		},
+
+		"ATTR": function( name, operator, check ) {
+			return function( elem ) {
+				var result = Sizzle.attr( elem, name );
+
+				if ( result == null ) {
+					return operator === "!=";
+				}
+				if ( !operator ) {
+					return true;
+				}
+
+				result += "";
+
+				/* eslint-disable max-len */
+
+				return operator === "=" ? result === check :
+					operator === "!=" ? result !== check :
+					operator === "^=" ? check && result.indexOf( check ) === 0 :
+					operator === "*=" ? check && result.indexOf( check ) > -1 :
+					operator === "$=" ? check && result.slice( -check.length ) === check :
+					operator === "~=" ? ( " " + result.replace( rwhitespace, " " ) + " " ).indexOf( check ) > -1 :
+					operator === "|=" ? result === check || result.slice( 0, check.length + 1 ) === check + "-" :
+					false;
+				/* eslint-enable max-len */
+
+			};
+		},
+
+		"CHILD": function( type, what, _argument, first, last ) {
+			var simple = type.slice( 0, 3 ) !== "nth",
+				forward = type.slice( -4 ) !== "last",
+				ofType = what === "of-type";
+
+			return first === 1 && last === 0 ?
+
+				// Shortcut for :nth-*(n)
+				function( elem ) {
+					return !!elem.parentNode;
+				} :
+
+				function( elem, _context, xml ) {
+					var cache, uniqueCache, outerCache, node, nodeIndex, start,
+						dir = simple !== forward ? "nextSibling" : "previousSibling",
+						parent = elem.parentNode,
+						name = ofType && elem.nodeName.toLowerCase(),
+						useCache = !xml && !ofType,
+						diff = false;
+
+					if ( parent ) {
+
+						// :(first|last|only)-(child|of-type)
+						if ( simple ) {
+							while ( dir ) {
+								node = elem;
+								while ( ( node = node[ dir ] ) ) {
+									if ( ofType ?
+										node.nodeName.toLowerCase() === name :
+										node.nodeType === 1 ) {
+
+										return false;
+									}
+								}
+
+								// Reverse direction for :only-* (if we haven't yet done so)
+								start = dir = type === "only" && !start && "nextSibling";
+							}
+							return true;
+						}
+
+						start = [ forward ? parent.firstChild : parent.lastChild ];
+
+						// non-xml :nth-child(...) stores cache data on `parent`
+						if ( forward && useCache ) {
+
+							// Seek `elem` from a previously-cached index
+
+							// ...in a gzip-friendly way
+							node = parent;
+							outerCache = node[ expando ] || ( node[ expando ] = {} );
+
+							// Support: IE <9 only
+							// Defend against cloned attroperties (jQuery gh-1709)
+							uniqueCache = outerCache[ node.uniqueID ] ||
+								( outerCache[ node.uniqueID ] = {} );
+
+							cache = uniqueCache[ type ] || [];
+							nodeIndex = cache[ 0 ] === dirruns && cache[ 1 ];
+							diff = nodeIndex && cache[ 2 ];
+							node = nodeIndex && parent.childNodes[ nodeIndex ];
+
+							while ( ( node = ++nodeIndex && node && node[ dir ] ||
+
+								// Fallback to seeking `elem` from the start
+								( diff = nodeIndex = 0 ) || start.pop() ) ) {
+
+								// When found, cache indexes on `parent` and break
+								if ( node.nodeType === 1 && ++diff && node === elem ) {
+									uniqueCache[ type ] = [ dirruns, nodeIndex, diff ];
+									break;
+								}
+							}
+
+						} else {
+
+							// Use previously-cached element index if available
+							if ( useCache ) {
+
+								// ...in a gzip-friendly way
+								node = elem;
+								outerCache = node[ expando ] || ( node[ expando ] = {} );
+
+								// Support: IE <9 only
+								// Defend against cloned attroperties (jQuery gh-1709)
+								uniqueCache = outerCache[ node.uniqueID ] ||
+									( outerCache[ node.uniqueID ] = {} );
+
+								cache = uniqueCache[ type ] || [];
+								nodeIndex = cache[ 0 ] === dirruns && cache[ 1 ];
+								diff = nodeIndex;
+							}
+
+							// xml :nth-child(...)
+							// or :nth-last-child(...) or :nth(-last)?-of-type(...)
+							if ( diff === false ) {
+
+								// Use the same loop as above to seek `elem` from the start
+								while ( ( node = ++nodeIndex && node && node[ dir ] ||
+									( diff = nodeIndex = 0 ) || start.pop() ) ) {
+
+									if ( ( ofType ?
+										node.nodeName.toLowerCase() === name :
+										node.nodeType === 1 ) &&
+										++diff ) {
+
+										// Cache the index of each encountered element
+										if ( useCache ) {
+											outerCache = node[ expando ] ||
+												( node[ expando ] = {} );
+
+											// Support: IE <9 only
+											// Defend against cloned attroperties (jQuery gh-1709)
+											uniqueCache = outerCache[ node.uniqueID ] ||
+												( outerCache[ node.uniqueID ] = {} );
+
+											uniqueCache[ type ] = [ dirruns, diff ];
+										}
+
+										if ( node === elem ) {
+											break;
+										}
+									}
+								}
+							}
+						}
+
+						// Incorporate the offset, then check against cycle size
+						diff -= last;
+						return diff === first || ( diff % first === 0 && diff / first >= 0 );
+					}
+				};
+		},
+
+		"PSEUDO": function( pseudo, argument ) {
+
+			// pseudo-class names are case-insensitive
+			// http://www.w3.org/TR/selectors/#pseudo-classes
+			// Prioritize by case sensitivity in case custom pseudos are added with uppercase letters
+			// Remember that setFilters inherits from pseudos
+			var args,
+				fn = Expr.pseudos[ pseudo ] || Expr.setFilters[ pseudo.toLowerCase() ] ||
+					Sizzle.error( "unsupported pseudo: " + pseudo );
+
+			// The user may use createPseudo to indicate that
+			// arguments are needed to create the filter function
+			// just as Sizzle does
+			if ( fn[ expando ] ) {
+				return fn( argument );
+			}
+
+			// But maintain support for old signatures
+			if ( fn.length > 1 ) {
+				args = [ pseudo, pseudo, "", argument ];
+				return Expr.setFilters.hasOwnProperty( pseudo.toLowerCase() ) ?
+					markFunction( function( seed, matches ) {
+						var idx,
+							matched = fn( seed, argument ),
+							i = matched.length;
+						while ( i-- ) {
+							idx = indexOf( seed, matched[ i ] );
+							seed[ idx ] = !( matches[ idx ] = matched[ i ] );
+						}
+					} ) :
+					function( elem ) {
+						return fn( elem, 0, args );
+					};
+			}
+
+			return fn;
+		}
+	},
+
+	pseudos: {
+
+		// Potentially complex pseudos
+		"not": markFunction( function( selector ) {
+
+			// Trim the selector passed to compile
+			// to avoid treating leading and trailing
+			// spaces as combinators
+			var input = [],
+				results = [],
+				matcher = compile( selector.replace( rtrim, "$1" ) );
+
+			return matcher[ expando ] ?
+				markFunction( function( seed, matches, _context, xml ) {
+					var elem,
+						unmatched = matcher( seed, null, xml, [] ),
+						i = seed.length;
+
+					// Match elements unmatched by `matcher`
+					while ( i-- ) {
+						if ( ( elem = unmatched[ i ] ) ) {
+							seed[ i ] = !( matches[ i ] = elem );
+						}
+					}
+				} ) :
+				function( elem, _context, xml ) {
+					input[ 0 ] = elem;
+					matcher( input, null, xml, results );
+
+					// Don't keep the element (issue #299)
+					input[ 0 ] = null;
+					return !results.pop();
+				};
+		} ),
+
+		"has": markFunction( function( selector ) {
+			return function( elem ) {
+				return Sizzle( selector, elem ).length > 0;
+			};
+		} ),
+
+		"contains": markFunction( function( text ) {
+			text = text.replace( runescape, funescape );
+			return function( elem ) {
+				return ( elem.textContent || getText( elem ) ).indexOf( text ) > -1;
+			};
+		} ),
+
+		// "Whether an element is represented by a :lang() selector
+		// is based solely on the element's language value
+		// being equal to the identifier C,
+		// or beginning with the identifier C immediately followed by "-".
+		// The matching of C against the element's language value is performed case-insensitively.
+		// The identifier C does not have to be a valid language name."
+		// http://www.w3.org/TR/selectors/#lang-pseudo
+		"lang": markFunction( function( lang ) {
+
+			// lang value must be a valid identifier
+			if ( !ridentifier.test( lang || "" ) ) {
+				Sizzle.error( "unsupported lang: " + lang );
+			}
+			lang = lang.replace( runescape, funescape ).toLowerCase();
+			return function( elem ) {
+				var elemLang;
+				do {
+					if ( ( elemLang = documentIsHTML ?
+						elem.lang :
+						elem.getAttribute( "xml:lang" ) || elem.getAttribute( "lang" ) ) ) {
+
+						elemLang = elemLang.toLowerCase();
+						return elemLang === lang || elemLang.indexOf( lang + "-" ) === 0;
+					}
+				} while ( ( elem = elem.parentNode ) && elem.nodeType === 1 );
+				return false;
+			};
+		} ),
+
+		// Miscellaneous
+		"target": function( elem ) {
+			var hash = window.location && window.location.hash;
+			return hash && hash.slice( 1 ) === elem.id;
+		},
+
+		"root": function( elem ) {
+			return elem === docElem;
+		},
+
+		"focus": function( elem ) {
+			return elem === document.activeElement &&
+				( !document.hasFocus || document.hasFocus() ) &&
+				!!( elem.type || elem.href || ~elem.tabIndex );
+		},
+
+		// Boolean properties
+		"enabled": createDisabledPseudo( false ),
+		"disabled": createDisabledPseudo( true ),
+
+		"checked": function( elem ) {
+
+			// In CSS3, :checked should return both checked and selected elements
+			// http://www.w3.org/TR/2011/REC-css3-selectors-20110929/#checked
+			var nodeName = elem.nodeName.toLowerCase();
+			return ( nodeName === "input" && !!elem.checked ) ||
+				( nodeName === "option" && !!elem.selected );
+		},
+
+		"selected": function( elem ) {
+
+			// Accessing this property makes selected-by-default
+			// options in Safari work properly
+			if ( elem.parentNode ) {
+				// eslint-disable-next-line no-unused-expressions
+				elem.parentNode.selectedIndex;
+			}
+
+			return elem.selected === true;
+		},
+
+		// Contents
+		"empty": function( elem ) {
+
+			// http://www.w3.org/TR/selectors/#empty-pseudo
+			// :empty is negated by element (1) or content nodes (text: 3; cdata: 4; entity ref: 5),
+			//   but not by others (comment: 8; processing instruction: 7; etc.)
+			// nodeType < 6 works because attributes (2) do not appear as children
+			for ( elem = elem.firstChild; elem; elem = elem.nextSibling ) {
+				if ( elem.nodeType < 6 ) {
+					return false;
+				}
+			}
+			return true;
+		},
+
+		"parent": function( elem ) {
+			return !Expr.pseudos[ "empty" ]( elem );
+		},
+
+		// Element/input types
+		"header": function( elem ) {
+			return rheader.test( elem.nodeName );
+		},
+
+		"input": function( elem ) {
+			return rinputs.test( elem.nodeName );
+		},
+
+		"button": function( elem ) {
+			var name = elem.nodeName.toLowerCase();
+			return name === "input" && elem.type === "button" || name === "button";
+		},
+
+		"text": function( elem ) {
+			var attr;
+			return elem.nodeName.toLowerCase() === "input" &&
+				elem.type === "text" &&
+
+				// Support: IE<8
+				// New HTML5 attribute values (e.g., "search") appear with elem.type === "text"
+				( ( attr = elem.getAttribute( "type" ) ) == null ||
+					attr.toLowerCase() === "text" );
+		},
+
+		// Position-in-collection
+		"first": createPositionalPseudo( function() {
+			return [ 0 ];
+		} ),
+
+		"last": createPositionalPseudo( function( _matchIndexes, length ) {
+			return [ length - 1 ];
+		} ),
+
+		"eq": createPositionalPseudo( function( _matchIndexes, length, argument ) {
+			return [ argument < 0 ? argument + length : argument ];
+		} ),
+
+		"even": createPositionalPseudo( function( matchIndexes, length ) {
+			var i = 0;
+			for ( ; i < length; i += 2 ) {
+				matchIndexes.push( i );
+			}
+			return matchIndexes;
+		} ),
+
+		"odd": createPositionalPseudo( function( matchIndexes, length ) {
+			var i = 1;
+			for ( ; i < length; i += 2 ) {
+				matchIndexes.push( i );
+			}
+			return matchIndexes;
+		} ),
+
+		"lt": createPositionalPseudo( function( matchIndexes, length, argument ) {
+			var i = argument < 0 ?
+				argument + length :
+				argument > length ?
+					length :
+					argument;
+			for ( ; --i >= 0; ) {
+				matchIndexes.push( i );
+			}
+			return matchIndexes;
+		} ),
+
+		"gt": createPositionalPseudo( function( matchIndexes, length, argument ) {
+			var i = argument < 0 ? argument + length : argument;
+			for ( ; ++i < length; ) {
+				matchIndexes.push( i );
+			}
+			return matchIndexes;
+		} )
+	}
+};
+
+Expr.pseudos[ "nth" ] = Expr.pseudos[ "eq" ];
+
+// Add button/input type pseudos
+for ( i in { radio: true, checkbox: true, file: true, password: true, image: true } ) {
+	Expr.pseudos[ i ] = createInputPseudo( i );
+}
+for ( i in { submit: true, reset: true } ) {
+	Expr.pseudos[ i ] = createButtonPseudo( i );
+}
+
+// Easy API for creating new setFilters
+function setFilters() {}
+setFilters.prototype = Expr.filters = Expr.pseudos;
+Expr.setFilters = new setFilters();
+
+tokenize = Sizzle.tokenize = function( selector, parseOnly ) {
+	var matched, match, tokens, type,
+		soFar, groups, preFilters,
+		cached = tokenCache[ selector + " " ];
+
+	if ( cached ) {
+		return parseOnly ? 0 : cached.slice( 0 );
+	}
+
+	soFar = selector;
+	groups = [];
+	preFilters = Expr.preFilter;
+
+	while ( soFar ) {
+
+		// Comma and first run
+		if ( !matched || ( match = rcomma.exec( soFar ) ) ) {
+			if ( match ) {
+
+				// Don't consume trailing commas as valid
+				soFar = soFar.slice( match[ 0 ].length ) || soFar;
+			}
+			groups.push( ( tokens = [] ) );
+		}
+
+		matched = false;
+
+		// Combinators
+		if ( ( match = rcombinators.exec( soFar ) ) ) {
+			matched = match.shift();
+			tokens.push( {
+				value: matched,
+
+				// Cast descendant combinators to space
+				type: match[ 0 ].replace( rtrim, " " )
+			} );
+			soFar = soFar.slice( matched.length );
+		}
+
+		// Filters
+		for ( type in Expr.filter ) {
+			if ( ( match = matchExpr[ type ].exec( soFar ) ) && ( !preFilters[ type ] ||
+				( match = preFilters[ type ]( match ) ) ) ) {
+				matched = match.shift();
+				tokens.push( {
+					value: matched,
+					type: type,
+					matches: match
+				} );
+				soFar = soFar.slice( matched.length );
+			}
+		}
+
+		if ( !matched ) {
+			break;
+		}
+	}
+
+	// Return the length of the invalid excess
+	// if we're just parsing
+	// Otherwise, throw an error or return tokens
+	return parseOnly ?
+		soFar.length :
+		soFar ?
+			Sizzle.error( selector ) :
+
+			// Cache the tokens
+			tokenCache( selector, groups ).slice( 0 );
+};
+
+function toSelector( tokens ) {
+	var i = 0,
+		len = tokens.length,
+		selector = "";
+	for ( ; i < len; i++ ) {
+		selector += tokens[ i ].value;
+	}
+	return selector;
+}
+
+function addCombinator( matcher, combinator, base ) {
+	var dir = combinator.dir,
+		skip = combinator.next,
+		key = skip || dir,
+		checkNonElements = base && key === "parentNode",
+		doneName = done++;
+
+	return combinator.first ?
+
+		// Check against closest ancestor/preceding element
+		function( elem, context, xml ) {
+			while ( ( elem = elem[ dir ] ) ) {
+				if ( elem.nodeType === 1 || checkNonElements ) {
+					return matcher( elem, context, xml );
+				}
+			}
+			return false;
+		} :
+
+		// Check against all ancestor/preceding elements
+		function( elem, context, xml ) {
+			var oldCache, uniqueCache, outerCache,
+				newCache = [ dirruns, doneName ];
+
+			// We can't set arbitrary data on XML nodes, so they don't benefit from combinator caching
+			if ( xml ) {
+				while ( ( elem = elem[ dir ] ) ) {
+					if ( elem.nodeType === 1 || checkNonElements ) {
+						if ( matcher( elem, context, xml ) ) {
+							return true;
+						}
+					}
+				}
+			} else {
+				while ( ( elem = elem[ dir ] ) ) {
+					if ( elem.nodeType === 1 || checkNonElements ) {
+						outerCache = elem[ expando ] || ( elem[ expando ] = {} );
+
+						// Support: IE <9 only
+						// Defend against cloned attroperties (jQuery gh-1709)
+						uniqueCache = outerCache[ elem.uniqueID ] ||
+							( outerCache[ elem.uniqueID ] = {} );
+
+						if ( skip && skip === elem.nodeName.toLowerCase() ) {
+							elem = elem[ dir ] || elem;
+						} else if ( ( oldCache = uniqueCache[ key ] ) &&
+							oldCache[ 0 ] === dirruns && oldCache[ 1 ] === doneName ) {
+
+							// Assign to newCache so results back-propagate to previous elements
+							return ( newCache[ 2 ] = oldCache[ 2 ] );
+						} else {
+
+							// Reuse newcache so results back-propagate to previous elements
+							uniqueCache[ key ] = newCache;
+
+							// A match means we're done; a fail means we have to keep checking
+							if ( ( newCache[ 2 ] = matcher( elem, context, xml ) ) ) {
+								return true;
+							}
+						}
+					}
+				}
+			}
+			return false;
+		};
+}
+
+function elementMatcher( matchers ) {
+	return matchers.length > 1 ?
+		function( elem, context, xml ) {
+			var i = matchers.length;
+			while ( i-- ) {
+				if ( !matchers[ i ]( elem, context, xml ) ) {
+					return false;
+				}
+			}
+			return true;
+		} :
+		matchers[ 0 ];
+}
+
+function multipleContexts( selector, contexts, results ) {
+	var i = 0,
+		len = contexts.length;
+	for ( ; i < len; i++ ) {
+		Sizzle( selector, contexts[ i ], results );
+	}
+	return results;
+}
+
+function condense( unmatched, map, filter, context, xml ) {
+	var elem,
+		newUnmatched = [],
+		i = 0,
+		len = unmatched.length,
+		mapped = map != null;
+
+	for ( ; i < len; i++ ) {
+		if ( ( elem = unmatched[ i ] ) ) {
+			if ( !filter || filter( elem, context, xml ) ) {
+				newUnmatched.push( elem );
+				if ( mapped ) {
+					map.push( i );
+				}
+			}
+		}
+	}
+
+	return newUnmatched;
+}
+
+function setMatcher( preFilter, selector, matcher, postFilter, postFinder, postSelector ) {
+	if ( postFilter && !postFilter[ expando ] ) {
+		postFilter = setMatcher( postFilter );
+	}
+	if ( postFinder && !postFinder[ expando ] ) {
+		postFinder = setMatcher( postFinder, postSelector );
+	}
+	return markFunction( function( seed, results, context, xml ) {
+		var temp, i, elem,
+			preMap = [],
+			postMap = [],
+			preexisting = results.length,
+
+			// Get initial elements from seed or context
+			elems = seed || multipleContexts(
+				selector || "*",
+				context.nodeType ? [ context ] : context,
+				[]
+			),
+
+			// Prefilter to get matcher input, preserving a map for seed-results synchronization
+			matcherIn = preFilter && ( seed || !selector ) ?
+				condense( elems, preMap, preFilter, context, xml ) :
+				elems,
+
+			matcherOut = matcher ?
+
+				// If we have a postFinder, or filtered seed, or non-seed postFilter or preexisting results,
+				postFinder || ( seed ? preFilter : preexisting || postFilter ) ?
+
+					// ...intermediate processing is necessary
+					[] :
+
+					// ...otherwise use results directly
+					results :
+				matcherIn;
+
+		// Find primary matches
+		if ( matcher ) {
+			matcher( matcherIn, matcherOut, context, xml );
+		}
+
+		// Apply postFilter
+		if ( postFilter ) {
+			temp = condense( matcherOut, postMap );
+			postFilter( temp, [], context, xml );
+
+			// Un-match failing elements by moving them back to matcherIn
+			i = temp.length;
+			while ( i-- ) {
+				if ( ( elem = temp[ i ] ) ) {
+					matcherOut[ postMap[ i ] ] = !( matcherIn[ postMap[ i ] ] = elem );
+				}
+			}
+		}
+
+		if ( seed ) {
+			if ( postFinder || preFilter ) {
+				if ( postFinder ) {
+
+					// Get the final matcherOut by condensing this intermediate into postFinder contexts
+					temp = [];
+					i = matcherOut.length;
+					while ( i-- ) {
+						if ( ( elem = matcherOut[ i ] ) ) {
+
+							// Restore matcherIn since elem is not yet a final match
+							temp.push( ( matcherIn[ i ] = elem ) );
+						}
+					}
+					postFinder( null, ( matcherOut = [] ), temp, xml );
+				}
+
+				// Move matched elements from seed to results to keep them synchronized
+				i = matcherOut.length;
+				while ( i-- ) {
+					if ( ( elem = matcherOut[ i ] ) &&
+						( temp = postFinder ? indexOf( seed, elem ) : preMap[ i ] ) > -1 ) {
+
+						seed[ temp ] = !( results[ temp ] = elem );
+					}
+				}
+			}
+
+		// Add elements to results, through postFinder if defined
+		} else {
+			matcherOut = condense(
+				matcherOut === results ?
+					matcherOut.splice( preexisting, matcherOut.length ) :
+					matcherOut
+			);
+			if ( postFinder ) {
+				postFinder( null, results, matcherOut, xml );
+			} else {
+				push.apply( results, matcherOut );
+			}
+		}
+	} );
+}
+
+function matcherFromTokens( tokens ) {
+	var checkContext, matcher, j,
+		len = tokens.length,
+		leadingRelative = Expr.relative[ tokens[ 0 ].type ],
+		implicitRelative = leadingRelative || Expr.relative[ " " ],
+		i = leadingRelative ? 1 : 0,
+
+		// The foundational matcher ensures that elements are reachable from top-level context(s)
+		matchContext = addCombinator( function( elem ) {
+			return elem === checkContext;
+		}, implicitRelative, true ),
+		matchAnyContext = addCombinator( function( elem ) {
+			return indexOf( checkContext, elem ) > -1;
+		}, implicitRelative, true ),
+		matchers = [ function( elem, context, xml ) {
+			var ret = ( !leadingRelative && ( xml || context !== outermostContext ) ) || (
+				( checkContext = context ).nodeType ?
+					matchContext( elem, context, xml ) :
+					matchAnyContext( elem, context, xml ) );
+
+			// Avoid hanging onto element (issue #299)
+			checkContext = null;
+			return ret;
+		} ];
+
+	for ( ; i < len; i++ ) {
+		if ( ( matcher = Expr.relative[ tokens[ i ].type ] ) ) {
+			matchers = [ addCombinator( elementMatcher( matchers ), matcher ) ];
+		} else {
+			matcher = Expr.filter[ tokens[ i ].type ].apply( null, tokens[ i ].matches );
+
+			// Return special upon seeing a positional matcher
+			if ( matcher[ expando ] ) {
+
+				// Find the next relative operator (if any) for proper handling
+				j = ++i;
+				for ( ; j < len; j++ ) {
+					if ( Expr.relative[ tokens[ j ].type ] ) {
+						break;
+					}
+				}
+				return setMatcher(
+					i > 1 && elementMatcher( matchers ),
+					i > 1 && toSelector(
+
+					// If the preceding token was a descendant combinator, insert an implicit any-element `*`
+					tokens
+						.slice( 0, i - 1 )
+						.concat( { value: tokens[ i - 2 ].type === " " ? "*" : "" } )
+					).replace( rtrim, "$1" ),
+					matcher,
+					i < j && matcherFromTokens( tokens.slice( i, j ) ),
+					j < len && matcherFromTokens( ( tokens = tokens.slice( j ) ) ),
+					j < len && toSelector( tokens )
+				);
+			}
+			matchers.push( matcher );
+		}
+	}
+
+	return elementMatcher( matchers );
+}
+
+function matcherFromGroupMatchers( elementMatchers, setMatchers ) {
+	var bySet = setMatchers.length > 0,
+		byElement = elementMatchers.length > 0,
+		superMatcher = function( seed, context, xml, results, outermost ) {
+			var elem, j, matcher,
+				matchedCount = 0,
+				i = "0",
+				unmatched = seed && [],
+				setMatched = [],
+				contextBackup = outermostContext,
+
+				// We must always have either seed elements or outermost context
+				elems = seed || byElement && Expr.find[ "TAG" ]( "*", outermost ),
+
+				// Use integer dirruns iff this is the outermost matcher
+				dirrunsUnique = ( dirruns += contextBackup == null ? 1 : Math.random() || 0.1 ),
+				len = elems.length;
+
+			if ( outermost ) {
+
+				// Support: IE 11+, Edge 17 - 18+
+				// IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+				// two documents; shallow comparisons work.
+				// eslint-disable-next-line eqeqeq
+				outermostContext = context == document || context || outermost;
+			}
+
+			// Add elements passing elementMatchers directly to results
+			// Support: IE<9, Safari
+			// Tolerate NodeList properties (IE: "length"; Safari: <number>) matching elements by id
+			for ( ; i !== len && ( elem = elems[ i ] ) != null; i++ ) {
+				if ( byElement && elem ) {
+					j = 0;
+
+					// Support: IE 11+, Edge 17 - 18+
+					// IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+					// two documents; shallow comparisons work.
+					// eslint-disable-next-line eqeqeq
+					if ( !context && elem.ownerDocument != document ) {
+						setDocument( elem );
+						xml = !documentIsHTML;
+					}
+					while ( ( matcher = elementMatchers[ j++ ] ) ) {
+						if ( matcher( elem, context || document, xml ) ) {
+							results.push( elem );
+							break;
+						}
+					}
+					if ( outermost ) {
+						dirruns = dirrunsUnique;
+					}
+				}
+
+				// Track unmatched elements for set filters
+				if ( bySet ) {
+
+					// They will have gone through all possible matchers
+					if ( ( elem = !matcher && elem ) ) {
+						matchedCount--;
+					}
+
+					// Lengthen the array for every element, matched or not
+					if ( seed ) {
+						unmatched.push( elem );
+					}
+				}
+			}
+
+			// `i` is now the count of elements visited above, and adding it to `matchedCount`
+			// makes the latter nonnegative.
+			matchedCount += i;
+
+			// Apply set filters to unmatched elements
+			// NOTE: This can be skipped if there are no unmatched elements (i.e., `matchedCount`
+			// equals `i`), unless we didn't visit _any_ elements in the above loop because we have
+			// no element matchers and no seed.
+			// Incrementing an initially-string "0" `i` allows `i` to remain a string only in that
+			// case, which will result in a "00" `matchedCount` that differs from `i` but is also
+			// numerically zero.
+			if ( bySet && i !== matchedCount ) {
+				j = 0;
+				while ( ( matcher = setMatchers[ j++ ] ) ) {
+					matcher( unmatched, setMatched, context, xml );
+				}
+
+				if ( seed ) {
+
+					// Reintegrate element matches to eliminate the need for sorting
+					if ( matchedCount > 0 ) {
+						while ( i-- ) {
+							if ( !( unmatched[ i ] || setMatched[ i ] ) ) {
+								setMatched[ i ] = pop.call( results );
+							}
+						}
+					}
+
+					// Discard index placeholder values to get only actual matches
+					setMatched = condense( setMatched );
+				}
+
+				// Add matches to results
+				push.apply( results, setMatched );
+
+				// Seedless set matches succeeding multiple successful matchers stipulate sorting
+				if ( outermost && !seed && setMatched.length > 0 &&
+					( matchedCount + setMatchers.length ) > 1 ) {
+
+					Sizzle.uniqueSort( results );
+				}
+			}
+
+			// Override manipulation of globals by nested matchers
+			if ( outermost ) {
+				dirruns = dirrunsUnique;
+				outermostContext = contextBackup;
+			}
+
+			return unmatched;
+		};
+
+	return bySet ?
+		markFunction( superMatcher ) :
+		superMatcher;
+}
+
+compile = Sizzle.compile = function( selector, match /* Internal Use Only */ ) {
+	var i,
+		setMatchers = [],
+		elementMatchers = [],
+		cached = compilerCache[ selector + " " ];
+
+	if ( !cached ) {
+
+		// Generate a function of recursive functions that can be used to check each element
+		if ( !match ) {
+			match = tokenize( selector );
+		}
+		i = match.length;
+		while ( i-- ) {
+			cached = matcherFromTokens( match[ i ] );
+			if ( cached[ expando ] ) {
+				setMatchers.push( cached );
+			} else {
+				elementMatchers.push( cached );
+			}
+		}
+
+		// Cache the compiled function
+		cached = compilerCache(
+			selector,
+			matcherFromGroupMatchers( elementMatchers, setMatchers )
+		);
+
+		// Save selector and tokenization
+		cached.selector = selector;
+	}
+	return cached;
+};
+
+/**
+ * A low-level selection function that works with Sizzle's compiled
+ *  selector functions
+ * @param {String|Function} selector A selector or a pre-compiled
+ *  selector function built with Sizzle.compile
+ * @param {Element} context
+ * @param {Array} [results]
+ * @param {Array} [seed] A set of elements to match against
+ */
+select = Sizzle.select = function( selector, context, results, seed ) {
+	var i, tokens, token, type, find,
+		compiled = typeof selector === "function" && selector,
+		match = !seed && tokenize( ( selector = compiled.selector || selector ) );
+
+	results = results || [];
+
+	// Try to minimize operations if there is only one selector in the list and no seed
+	// (the latter of which guarantees us context)
+	if ( match.length === 1 ) {
+
+		// Reduce context if the leading compound selector is an ID
+		tokens = match[ 0 ] = match[ 0 ].slice( 0 );
+		if ( tokens.length > 2 && ( token = tokens[ 0 ] ).type === "ID" &&
+			context.nodeType === 9 && documentIsHTML && Expr.relative[ tokens[ 1 ].type ] ) {
+
+			context = ( Expr.find[ "ID" ]( token.matches[ 0 ]
+				.replace( runescape, funescape ), context ) || [] )[ 0 ];
+			if ( !context ) {
+				return results;
+
+			// Precompiled matchers will still verify ancestry, so step up a level
+			} else if ( compiled ) {
+				context = context.parentNode;
+			}
+
+			selector = selector.slice( tokens.shift().value.length );
+		}
+
+		// Fetch a seed set for right-to-left matching
+		i = matchExpr[ "needsContext" ].test( selector ) ? 0 : tokens.length;
+		while ( i-- ) {
+			token = tokens[ i ];
+
+			// Abort if we hit a combinator
+			if ( Expr.relative[ ( type = token.type ) ] ) {
+				break;
+			}
+			if ( ( find = Expr.find[ type ] ) ) {
+
+				// Search, expanding context for leading sibling combinators
+				if ( ( seed = find(
+					token.matches[ 0 ].replace( runescape, funescape ),
+					rsibling.test( tokens[ 0 ].type ) && testContext( context.parentNode ) ||
+						context
+				) ) ) {
+
+					// If seed is empty or no tokens remain, we can return early
+					tokens.splice( i, 1 );
+					selector = seed.length && toSelector( tokens );
+					if ( !selector ) {
+						push.apply( results, seed );
+						return results;
+					}
+
+					break;
+				}
+			}
+		}
+	}
+
+	// Compile and execute a filtering function if one is not provided
+	// Provide `match` to avoid retokenization if we modified the selector above
+	( compiled || compile( selector, match ) )(
+		seed,
+		context,
+		!documentIsHTML,
+		results,
+		!context || rsibling.test( selector ) && testContext( context.parentNode ) || context
+	);
+	return results;
+};
+
+// One-time assignments
+
+// Sort stability
+support.sortStable = expando.split( "" ).sort( sortOrder ).join( "" ) === expando;
+
+// Support: Chrome 14-35+
+// Always assume duplicates if they aren't passed to the comparison function
+support.detectDuplicates = !!hasDuplicate;
+
+// Initialize against the default document
+setDocument();
+
+// Support: Webkit<537.32 - Safari 6.0.3/Chrome 25 (fixed in Chrome 27)
+// Detached nodes confoundingly follow *each other*
+support.sortDetached = assert( function( el ) {
+
+	// Should return 1, but returns 4 (following)
+	return el.compareDocumentPosition( document.createElement( "fieldset" ) ) & 1;
+} );
+
+// Support: IE<8
+// Prevent attribute/property "interpolation"
+// https://msdn.microsoft.com/en-us/library/ms536429%28VS.85%29.aspx
+if ( !assert( function( el ) {
+	el.innerHTML = "<a href='#'></a>";
+	return el.firstChild.getAttribute( "href" ) === "#";
+} ) ) {
+	addHandle( "type|href|height|width", function( elem, name, isXML ) {
+		if ( !isXML ) {
+			return elem.getAttribute( name, name.toLowerCase() === "type" ? 1 : 2 );
+		}
+	} );
+}
+
+// Support: IE<9
+// Use defaultValue in place of getAttribute("value")
+if ( !support.attributes || !assert( function( el ) {
+	el.innerHTML = "<input/>";
+	el.firstChild.setAttribute( "value", "" );
+	return el.firstChild.getAttribute( "value" ) === "";
+} ) ) {
+	addHandle( "value", function( elem, _name, isXML ) {
+		if ( !isXML && elem.nodeName.toLowerCase() === "input" ) {
+			return elem.defaultValue;
+		}
+	} );
+}
+
+// Support: IE<9
+// Use getAttributeNode to fetch booleans when getAttribute lies
+if ( !assert( function( el ) {
+	return el.getAttribute( "disabled" ) == null;
+} ) ) {
+	addHandle( booleans, function( elem, name, isXML ) {
+		var val;
+		if ( !isXML ) {
+			return elem[ name ] === true ? name.toLowerCase() :
+				( val = elem.getAttributeNode( name ) ) && val.specified ?
+					val.value :
+					null;
+		}
+	} );
+}
+
+return Sizzle;
+
+} )( window );
+
+
+
+jQuery.find = Sizzle;
+jQuery.expr = Sizzle.selectors;
+
+// Deprecated
+jQuery.expr[ ":" ] = jQuery.expr.pseudos;
+jQuery.uniqueSort = jQuery.unique = Sizzle.uniqueSort;
+jQuery.text = Sizzle.getText;
+jQuery.isXMLDoc = Sizzle.isXML;
+jQuery.contains = Sizzle.contains;
+jQuery.escapeSelector = Sizzle.escape;
+
+
+
+
+var dir = function( elem, dir, until ) {
+	var matched = [],
+		truncate = until !== undefined;
+
+	while ( ( elem = elem[ dir ] ) && elem.nodeType !== 9 ) {
+		if ( elem.nodeType === 1 ) {
+			if ( truncate && jQuery( elem ).is( until ) ) {
+				break;
+			}
+			matched.push( elem );
+		}
+	}
+	return matched;
+};
+
+
+var siblings = function( n, elem ) {
+	var matched = [];
+
+	for ( ; n; n = n.nextSibling ) {
+		if ( n.nodeType === 1 && n !== elem ) {
+			matched.push( n );
+		}
+	}
+
+	return matched;
+};
+
+
+var rneedsContext = jQuery.expr.match.needsContext;
+
+
+
+function nodeName( elem, name ) {
+
+	return elem.nodeName && elem.nodeName.toLowerCase() === name.toLowerCase();
+
+}
+var rsingleTag = ( /^<([a-z][^\/\0>:\x20\t\r\n\f]*)[\x20\t\r\n\f]*\/?>(?:<\/\1>|)$/i );
+
+
+
+// Implement the identical functionality for filter and not
+function winnow( elements, qualifier, not ) {
+	if ( isFunction( qualifier ) ) {
+		return jQuery.grep( elements, function( elem, i ) {
+			return !!qualifier.call( elem, i, elem ) !== not;
+		} );
+	}
+
+	// Single element
+	if ( qualifier.nodeType ) {
+		return jQuery.grep( elements, function( elem ) {
+			return ( elem === qualifier ) !== not;
+		} );
+	}
+
+	// Arraylike of elements (jQuery, arguments, Array)
+	if ( typeof qualifier !== "string" ) {
+		return jQuery.grep( elements, function( elem ) {
+			return ( indexOf.call( qualifier, elem ) > -1 ) !== not;
+		} );
+	}
+
+	// Filtered directly for both simple and complex selectors
+	return jQuery.filter( qualifier, elements, not );
+}
+
+jQuery.filter = function( expr, elems, not ) {
+	var elem = elems[ 0 ];
+
+	if ( not ) {
+		expr = ":not(" + expr + ")";
+	}
+
+	if ( elems.length === 1 && elem.nodeType === 1 ) {
+		return jQuery.find.matchesSelector( elem, expr ) ? [ elem ] : [];
+	}
+
+	return jQuery.find.matches( expr, jQuery.grep( elems, function( elem ) {
+		return elem.nodeType === 1;
+	} ) );
+};
+
+jQuery.fn.extend( {
+	find: function( selector ) {
+		var i, ret,
+			len = this.length,
+			self = this;
+
+		if ( typeof selector !== "string" ) {
+			return this.pushStack( jQuery( selector ).filter( function() {
+				for ( i = 0; i < len; i++ ) {
+					if ( jQuery.contains( self[ i ], this ) ) {
+						return true;
+					}
+				}
+			} ) );
+		}
+
+		ret = this.pushStack( [] );
+
+		for ( i = 0; i < len; i++ ) {
+			jQuery.find( selector, self[ i ], ret );
+		}
+
+		return len > 1 ? jQuery.uniqueSort( ret ) : ret;
+	},
+	filter: function( selector ) {
+		return this.pushStack( winnow( this, selector || [], false ) );
+	},
+	not: function( selector ) {
+		return this.pushStack( winnow( this, selector || [], true ) );
+	},
+	is: function( selector ) {
+		return !!winnow(
+			this,
+
+			// If this is a positional/relative selector, check membership in the returned set
+			// so $("p:first").is("p:last") won't return true for a doc with two "p".
+			typeof selector === "string" && rneedsContext.test( selector ) ?
+				jQuery( selector ) :
+				selector || [],
+			false
+		).length;
+	}
+} );
+
+
+// Initialize a jQuery object
+
+
+// A central reference to the root jQuery(document)
+var rootjQuery,
+
+	// A simple way to check for HTML strings
+	// Prioritize #id over <tag> to avoid XSS via location.hash (#9521)
+	// Strict HTML recognition (#11290: must start with <)
+	// Shortcut simple #id case for speed
+	rquickExpr = /^(?:\s*(<[\w\W]+>)[^>]*|#([\w-]+))$/,
+
+	init = jQuery.fn.init = function( selector, context, root ) {
+		var match, elem;
+
+		// HANDLE: $(""), $(null), $(undefined), $(false)
+		if ( !selector ) {
+			return this;
+		}
+
+		// Method init() accepts an alternate rootjQuery
+		// so migrate can support jQuery.sub (gh-2101)
+		root = root || rootjQuery;
+
+		// Handle HTML strings
+		if ( typeof selector === "string" ) {
+			if ( selector[ 0 ] === "<" &&
+				selector[ selector.length - 1 ] === ">" &&
+				selector.length >= 3 ) {
+
+				// Assume that strings that start and end with <> are HTML and skip the regex check
+				match = [ null, selector, null ];
+
+			} else {
+				match = rquickExpr.exec( selector );
+			}
+
+			// Match html or make sure no context is specified for #id
+			if ( match && ( match[ 1 ] || !context ) ) {
+
+				// HANDLE: $(html) -> $(array)
+				if ( match[ 1 ] ) {
+					context = context instanceof jQuery ? context[ 0 ] : context;
+
+					// Option to run scripts is true for back-compat
+					// Intentionally let the error be thrown if parseHTML is not present
+					jQuery.merge( this, jQuery.parseHTML(
+						match[ 1 ],
+						context && context.nodeType ? context.ownerDocument || context : document,
+						true
+					) );
+
+					// HANDLE: $(html, props)
+					if ( rsingleTag.test( match[ 1 ] ) && jQuery.isPlainObject( context ) ) {
+						for ( match in context ) {
+
+							// Properties of context are called as methods if possible
+							if ( isFunction( this[ match ] ) ) {
+								this[ match ]( context[ match ] );
+
+							// ...and otherwise set as attributes
+							} else {
+								this.attr( match, context[ match ] );
+							}
+						}
+					}
+
+					return this;
+
+				// HANDLE: $(#id)
+				} else {
+					elem = document.getElementById( match[ 2 ] );
+
+					if ( elem ) {
+
+						// Inject the element directly into the jQuery object
+						this[ 0 ] = elem;
+						this.length = 1;
+					}
+					return this;
+				}
+
+			// HANDLE: $(expr, $(...))
+			} else if ( !context || context.jquery ) {
+				return ( context || root ).find( selector );
+
+			// HANDLE: $(expr, context)
+			// (which is just equivalent to: $(context).find(expr)
+			} else {
+				return this.constructor( context ).find( selector );
+			}
+
+		// HANDLE: $(DOMElement)
+		} else if ( selector.nodeType ) {
+			this[ 0 ] = selector;
+			this.length = 1;
+			return this;
+
+		// HANDLE: $(function)
+		// Shortcut for document ready
+		} else if ( isFunction( selector ) ) {
+			return root.ready !== undefined ?
+				root.ready( selector ) :
+
+				// Execute immediately if ready is not present
+				selector( jQuery );
+		}
+
+		return jQuery.makeArray( selector, this );
+	};
+
+// Give the init function the jQuery prototype for later instantiation
+init.prototype = jQuery.fn;
+
+// Initialize central reference
+rootjQuery = jQuery( document );
+
+
+var rparentsprev = /^(?:parents|prev(?:Until|All))/,
+
+	// Methods guaranteed to produce a unique set when starting from a unique set
+	guaranteedUnique = {
+		children: true,
+		contents: true,
+		next: true,
+		prev: true
+	};
+
+jQuery.fn.extend( {
+	has: function( target ) {
+		var targets = jQuery( target, this ),
+			l = targets.length;
+
+		return this.filter( function() {
+			var i = 0;
+			for ( ; i < l; i++ ) {
+				if ( jQuery.contains( this, targets[ i ] ) ) {
+					return true;
+				}
+			}
+		} );
+	},
+
+	closest: function( selectors, context ) {
+		var cur,
+			i = 0,
+			l = this.length,
+			matched = [],
+			targets = typeof selectors !== "string" && jQuery( selectors );
+
+		// Positional selectors never match, since there's no _selection_ context
+		if ( !rneedsContext.test( selectors ) ) {
+			for ( ; i < l; i++ ) {
+				for ( cur = this[ i ]; cur && cur !== context; cur = cur.parentNode ) {
+
+					// Always skip document fragments
+					if ( cur.nodeType < 11 && ( targets ?
+						targets.index( cur ) > -1 :
+
+						// Don't pass non-elements to Sizzle
+						cur.nodeType === 1 &&
+							jQuery.find.matchesSelector( cur, selectors ) ) ) {
+
+						matched.push( cur );
+						break;
+					}
+				}
+			}
+		}
+
+		return this.pushStack( matched.length > 1 ? jQuery.uniqueSort( matched ) : matched );
+	},
+
+	// Determine the position of an element within the set
+	index: function( elem ) {
+
+		// No argument, return index in parent
+		if ( !elem ) {
+			return ( this[ 0 ] && this[ 0 ].parentNode ) ? this.first().prevAll().length : -1;
+		}
+
+		// Index in selector
+		if ( typeof elem === "string" ) {
+			return indexOf.call( jQuery( elem ), this[ 0 ] );
+		}
+
+		// Locate the position of the desired element
+		return indexOf.call( this,
+
+			// If it receives a jQuery object, the first element is used
+			elem.jquery ? elem[ 0 ] : elem
+		);
+	},
+
+	add: function( selector, context ) {
+		return this.pushStack(
+			jQuery.uniqueSort(
+				jQuery.merge( this.get(), jQuery( selector, context ) )
+			)
+		);
+	},
+
+	addBack: function( selector ) {
+		return this.add( selector == null ?
+			this.prevObject : this.prevObject.filter( selector )
+		);
+	}
+} );
+
+function sibling( cur, dir ) {
+	while ( ( cur = cur[ dir ] ) && cur.nodeType !== 1 ) {}
+	return cur;
+}
+
+jQuery.each( {
+	parent: function( elem ) {
+		var parent = elem.parentNode;
+		return parent && parent.nodeType !== 11 ? parent : null;
+	},
+	parents: function( elem ) {
+		return dir( elem, "parentNode" );
+	},
+	parentsUntil: function( elem, _i, until ) {
+		return dir( elem, "parentNode", until );
+	},
+	next: function( elem ) {
+		return sibling( elem, "nextSibling" );
+	},
+	prev: function( elem ) {
+		return sibling( elem, "previousSibling" );
+	},
+	nextAll: function( elem ) {
+		return dir( elem, "nextSibling" );
+	},
+	prevAll: function( elem ) {
+		return dir( elem, "previousSibling" );
+	},
+	nextUntil: function( elem, _i, until ) {
+		return dir( elem, "nextSibling", until );
+	},
+	prevUntil: function( elem, _i, until ) {
+		return dir( elem, "previousSibling", until );
+	},
+	siblings: function( elem ) {
+		return siblings( ( elem.parentNode || {} ).firstChild, elem );
+	},
+	children: function( elem ) {
+		return siblings( elem.firstChild );
+	},
+	contents: function( elem ) {
+		if ( elem.contentDocument != null &&
+
+			// Support: IE 11+
+			// <object> elements with no `data` attribute has an object
+			// `contentDocument` with a `null` prototype.
+			getProto( elem.contentDocument ) ) {
+
+			return elem.contentDocument;
+		}
+
+		// Support: IE 9 - 11 only, iOS 7 only, Android Browser <=4.3 only
+		// Treat the template element as a regular one in browsers that
+		// don't support it.
+		if ( nodeName( elem, "template" ) ) {
+			elem = elem.content || elem;
+		}
+
+		return jQuery.merge( [], elem.childNodes );
+	}
+}, function( name, fn ) {
+	jQuery.fn[ name ] = function( until, selector ) {
+		var matched = jQuery.map( this, fn, until );
+
+		if ( name.slice( -5 ) !== "Until" ) {
+			selector = until;
+		}
+
+		if ( selector && typeof selector === "string" ) {
+			matched = jQuery.filter( selector, matched );
+		}
+
+		if ( this.length > 1 ) {
+
+			// Remove duplicates
+			if ( !guaranteedUnique[ name ] ) {
+				jQuery.uniqueSort( matched );
+			}
+
+			// Reverse order for parents* and prev-derivatives
+			if ( rparentsprev.test( name ) ) {
+				matched.reverse();
+			}
+		}
+
+		return this.pushStack( matched );
+	};
+} );
+var rnothtmlwhite = ( /[^\x20\t\r\n\f]+/g );
+
+
+
+// Convert String-formatted options into Object-formatted ones
+function createOptions( options ) {
+	var object = {};
+	jQuery.each( options.match( rnothtmlwhite ) || [], function( _, flag ) {
+		object[ flag ] = true;
+	} );
+	return object;
+}
+
+/*
+ * Create a callback list using the following parameters:
+ *
+ *	options: an optional list of space-separated options that will change how
+ *			the callback list behaves or a more traditional option object
+ *
+ * By default a callback list will act like an event callback list and can be
+ * "fired" multiple times.
+ *
+ * Possible options:
+ *
+ *	once:			will ensure the callback list can only be fired once (like a Deferred)
+ *
+ *	memory:			will keep track of previous values and will call any callback added
+ *					after the list has been fired right away with the latest "memorized"
+ *					values (like a Deferred)
+ *
+ *	unique:			will ensure a callback can only be added once (no duplicate in the list)
+ *
+ *	stopOnFalse:	interrupt callings when a callback returns false
+ *
+ */
+jQuery.Callbacks = function( options ) {
+
+	// Convert options from String-formatted to Object-formatted if needed
+	// (we check in cache first)
+	options = typeof options === "string" ?
+		createOptions( options ) :
+		jQuery.extend( {}, options );
+
+	var // Flag to know if list is currently firing
+		firing,
+
+		// Last fire value for non-forgettable lists
+		memory,
+
+		// Flag to know if list was already fired
+		fired,
+
+		// Flag to prevent firing
+		locked,
+
+		// Actual callback list
+		list = [],
+
+		// Queue of execution data for repeatable lists
+		queue = [],
+
+		// Index of currently firing callback (modified by add/remove as needed)
+		firingIndex = -1,
+
+		// Fire callbacks
+		fire = function() {
+
+			// Enforce single-firing
+			locked = locked || options.once;
+
+			// Execute callbacks for all pending executions,
+			// respecting firingIndex overrides and runtime changes
+			fired = firing = true;
+			for ( ; queue.length; firingIndex = -1 ) {
+				memory = queue.shift();
+				while ( ++firingIndex < list.length ) {
+
+					// Run callback and check for early termination
+					if ( list[ firingIndex ].apply( memory[ 0 ], memory[ 1 ] ) === false &&
+						options.stopOnFalse ) {
+
+						// Jump to end and forget the data so .add doesn't re-fire
+						firingIndex = list.length;
+						memory = false;
+					}
+				}
+			}
+
+			// Forget the data if we're done with it
+			if ( !options.memory ) {
+				memory = false;
+			}
+
+			firing = false;
+
+			// Clean up if we're done firing for good
+			if ( locked ) {
+
+				// Keep an empty list if we have data for future add calls
+				if ( memory ) {
+					list = [];
+
+				// Otherwise, this object is spent
+				} else {
+					list = "";
+				}
+			}
+		},
+
+		// Actual Callbacks object
+		self = {
+
+			// Add a callback or a collection of callbacks to the list
+			add: function() {
+				if ( list ) {
+
+					// If we have memory from a past run, we should fire after adding
+					if ( memory && !firing ) {
+						firingIndex = list.length - 1;
+						queue.push( memory );
+					}
+
+					( function add( args ) {
+						jQuery.each( args, function( _, arg ) {
+							if ( isFunction( arg ) ) {
+								if ( !options.unique || !self.has( arg ) ) {
+									list.push( arg );
+								}
+							} else if ( arg && arg.length && toType( arg ) !== "string" ) {
+
+								// Inspect recursively
+								add( arg );
+							}
+						} );
+					} )( arguments );
+
+					if ( memory && !firing ) {
+						fire();
+					}
+				}
+				return this;
+			},
+
+			// Remove a callback from the list
+			remove: function() {
+				jQuery.each( arguments, function( _, arg ) {
+					var index;
+					while ( ( index = jQuery.inArray( arg, list, index ) ) > -1 ) {
+						list.splice( index, 1 );
+
+						// Handle firing indexes
+						if ( index <= firingIndex ) {
+							firingIndex--;
+						}
+					}
+				} );
+				return this;
+			},
+
+			// Check if a given callback is in the list.
+			// If no argument is given, return whether or not list has callbacks attached.
+			has: function( fn ) {
+				return fn ?
+					jQuery.inArray( fn, list ) > -1 :
+					list.length > 0;
+			},
+
+			// Remove all callbacks from the list
+			empty: function() {
+				if ( list ) {
+					list = [];
+				}
+				return this;
+			},
+
+			// Disable .fire and .add
+			// Abort any current/pending executions
+			// Clear all callbacks and values
+			disable: function() {
+				locked = queue = [];
+				list = memory = "";
+				return this;
+			},
+			disabled: function() {
+				return !list;
+			},
+
+			// Disable .fire
+			// Also disable .add unless we have memory (since it would have no effect)
+			// Abort any pending executions
+			lock: function() {
+				locked = queue = [];
+				if ( !memory && !firing ) {
+					list = memory = "";
+				}
+				return this;
+			},
+			locked: function() {
+				return !!locked;
+			},
+
+			// Call all callbacks with the given context and arguments
+			fireWith: function( context, args ) {
+				if ( !locked ) {
+					args = args || [];
+					args = [ context, args.slice ? args.slice() : args ];
+					queue.push( args );
+					if ( !firing ) {
+						fire();
+					}
+				}
+				return this;
+			},
+
+			// Call all the callbacks with the given arguments
+			fire: function() {
+				self.fireWith( this, arguments );
+				return this;
+			},
+
+			// To know if the callbacks have already been called at least once
+			fired: function() {
+				return !!fired;
+			}
+		};
+
+	return self;
+};
+
+
+function Identity( v ) {
+	return v;
+}
+function Thrower( ex ) {
+	throw ex;
+}
+
+function adoptValue( value, resolve, reject, noValue ) {
+	var method;
+
+	try {
+
+		// Check for promise aspect first to privilege synchronous behavior
+		if ( value && isFunction( ( method = value.promise ) ) ) {
+			method.call( value ).done( resolve ).fail( reject );
+
+		// Other thenables
+		} else if ( value && isFunction( ( method = value.then ) ) ) {
+			method.call( value, resolve, reject );
+
+		// Other non-thenables
+		} else {
+
+			// Control `resolve` arguments by letting Array#slice cast boolean `noValue` to integer:
+			// * false: [ value ].slice( 0 ) => resolve( value )
+			// * true: [ value ].slice( 1 ) => resolve()
+			resolve.apply( undefined, [ value ].slice( noValue ) );
+		}
+
+	// For Promises/A+, convert exceptions into rejections
+	// Since jQuery.when doesn't unwrap thenables, we can skip the extra checks appearing in
+	// Deferred#then to conditionally suppress rejection.
+	} catch ( value ) {
+
+		// Support: Android 4.0 only
+		// Strict mode functions invoked without .call/.apply get global-object context
+		reject.apply( undefined, [ value ] );
+	}
+}
+
+jQuery.extend( {
+
+	Deferred: function( func ) {
+		var tuples = [
+
+				// action, add listener, callbacks,
+				// ... .then handlers, argument index, [final state]
+				[ "notify", "progress", jQuery.Callbacks( "memory" ),
+					jQuery.Callbacks( "memory" ), 2 ],
+				[ "resolve", "done", jQuery.Callbacks( "once memory" ),
+					jQuery.Callbacks( "once memory" ), 0, "resolved" ],
+				[ "reject", "fail", jQuery.Callbacks( "once memory" ),
+					jQuery.Callbacks( "once memory" ), 1, "rejected" ]
+			],
+			state = "pending",
+			promise = {
+				state: function() {
+					return state;
+				},
+				always: function() {
+					deferred.done( arguments ).fail( arguments );
+					return this;
+				},
+				"catch": function( fn ) {
+					return promise.then( null, fn );
+				},
+
+				// Keep pipe for back-compat
+				pipe: function( /* fnDone, fnFail, fnProgress */ ) {
+					var fns = arguments;
+
+					return jQuery.Deferred( function( newDefer ) {
+						jQuery.each( tuples, function( _i, tuple ) {
+
+							// Map tuples (progress, done, fail) to arguments (done, fail, progress)
+							var fn = isFunction( fns[ tuple[ 4 ] ] ) && fns[ tuple[ 4 ] ];
+
+							// deferred.progress(function() { bind to newDefer or newDefer.notify })
+							// deferred.done(function() { bind to newDefer or newDefer.resolve })
+							// deferred.fail(function() { bind to newDefer or newDefer.reject })
+							deferred[ tuple[ 1 ] ]( function() {
+								var returned = fn && fn.apply( this, arguments );
+								if ( returned && isFunction( returned.promise ) ) {
+									returned.promise()
+										.progress( newDefer.notify )
+										.done( newDefer.resolve )
+										.fail( newDefer.reject );
+								} else {
+									newDefer[ tuple[ 0 ] + "With" ](
+										this,
+										fn ? [ returned ] : arguments
+									);
+								}
+							} );
+						} );
+						fns = null;
+					} ).promise();
+				},
+				then: function( onFulfilled, onRejected, onProgress ) {
+					var maxDepth = 0;
+					function resolve( depth, deferred, handler, special ) {
+						return function() {
+							var that = this,
+								args = arguments,
+								mightThrow = function() {
+									var returned, then;
+
+									// Support: Promises/A+ section 2.3.3.3.3
+									// https://promisesaplus.com/#point-59
+									// Ignore double-resolution attempts
+									if ( depth < maxDepth ) {
+										return;
+									}
+
+									returned = handler.apply( that, args );
+
+									// Support: Promises/A+ section 2.3.1
+									// https://promisesaplus.com/#point-48
+									if ( returned === deferred.promise() ) {
+										throw new TypeError( "Thenable self-resolution" );
+									}
+
+									// Support: Promises/A+ sections 2.3.3.1, 3.5
+									// https://promisesaplus.com/#point-54
+									// https://promisesaplus.com/#point-75
+									// Retrieve `then` only once
+									then = returned &&
+
+										// Support: Promises/A+ section 2.3.4
+										// https://promisesaplus.com/#point-64
+										// Only check objects and functions for thenability
+										( typeof returned === "object" ||
+											typeof returned === "function" ) &&
+										returned.then;
+
+									// Handle a returned thenable
+									if ( isFunction( then ) ) {
+
+										// Special processors (notify) just wait for resolution
+										if ( special ) {
+											then.call(
+												returned,
+												resolve( maxDepth, deferred, Identity, special ),
+												resolve( maxDepth, deferred, Thrower, special )
+											);
+
+										// Normal processors (resolve) also hook into progress
+										} else {
+
+											// ...and disregard older resolution values
+											maxDepth++;
+
+											then.call(
+												returned,
+												resolve( maxDepth, deferred, Identity, special ),
+												resolve( maxDepth, deferred, Thrower, special ),
+												resolve( maxDepth, deferred, Identity,
+													deferred.notifyWith )
+											);
+										}
+
+									// Handle all other returned values
+									} else {
+
+										// Only substitute handlers pass on context
+										// and multiple values (non-spec behavior)
+										if ( handler !== Identity ) {
+											that = undefined;
+											args = [ returned ];
+										}
+
+										// Process the value(s)
+										// Default process is resolve
+										( special || deferred.resolveWith )( that, args );
+									}
+								},
+
+								// Only normal processors (resolve) catch and reject exceptions
+								process = special ?
+									mightThrow :
+									function() {
+										try {
+											mightThrow();
+										} catch ( e ) {
+
+											if ( jQuery.Deferred.exceptionHook ) {
+												jQuery.Deferred.exceptionHook( e,
+													process.stackTrace );
+											}
+
+											// Support: Promises/A+ section 2.3.3.3.4.1
+											// https://promisesaplus.com/#point-61
+											// Ignore post-resolution exceptions
+											if ( depth + 1 >= maxDepth ) {
+
+												// Only substitute handlers pass on context
+												// and multiple values (non-spec behavior)
+												if ( handler !== Thrower ) {
+													that = undefined;
+													args = [ e ];
+												}
+
+												deferred.rejectWith( that, args );
+											}
+										}
+									};
+
+							// Support: Promises/A+ section 2.3.3.3.1
+							// https://promisesaplus.com/#point-57
+							// Re-resolve promises immediately to dodge false rejection from
+							// subsequent errors
+							if ( depth ) {
+								process();
+							} else {
+
+								// Call an optional hook to record the stack, in case of exception
+								// since it's otherwise lost when execution goes async
+								if ( jQuery.Deferred.getStackHook ) {
+									process.stackTrace = jQuery.Deferred.getStackHook();
+								}
+								window.setTimeout( process );
+							}
+						};
+					}
+
+					return jQuery.Deferred( function( newDefer ) {
+
+						// progress_handlers.add( ... )
+						tuples[ 0 ][ 3 ].add(
+							resolve(
+								0,
+								newDefer,
+								isFunction( onProgress ) ?
+									onProgress :
+									Identity,
+								newDefer.notifyWith
+							)
+						);
+
+						// fulfilled_handlers.add( ... )
+						tuples[ 1 ][ 3 ].add(
+							resolve(
+								0,
+								newDefer,
+								isFunction( onFulfilled ) ?
+									onFulfilled :
+									Identity
+							)
+						);
+
+						// rejected_handlers.add( ... )
+						tuples[ 2 ][ 3 ].add(
+							resolve(
+								0,
+								newDefer,
+								isFunction( onRejected ) ?
+									onRejected :
+									Thrower
+							)
+						);
+					} ).promise();
+				},
+
+				// Get a promise for this deferred
+				// If obj is provided, the promise aspect is added to the object
+				promise: function( obj ) {
+					return obj != null ? jQuery.extend( obj, promise ) : promise;
+				}
+			},
+			deferred = {};
+
+		// Add list-specific methods
+		jQuery.each( tuples, function( i, tuple ) {
+			var list = tuple[ 2 ],
+				stateString = tuple[ 5 ];
+
+			// promise.progress = list.add
+			// promise.done = list.add
+			// promise.fail = list.add
+			promise[ tuple[ 1 ] ] = list.add;
+
+			// Handle state
+			if ( stateString ) {
+				list.add(
+					function() {
+
+						// state = "resolved" (i.e., fulfilled)
+						// state = "rejected"
+						state = stateString;
+					},
+
+					// rejected_callbacks.disable
+					// fulfilled_callbacks.disable
+					tuples[ 3 - i ][ 2 ].disable,
+
+					// rejected_handlers.disable
+					// fulfilled_handlers.disable
+					tuples[ 3 - i ][ 3 ].disable,
+
+					// progress_callbacks.lock
+					tuples[ 0 ][ 2 ].lock,
+
+					// progress_handlers.lock
+					tuples[ 0 ][ 3 ].lock
+				);
+			}
+
+			// progress_handlers.fire
+			// fulfilled_handlers.fire
+			// rejected_handlers.fire
+			list.add( tuple[ 3 ].fire );
+
+			// deferred.notify = function() { deferred.notifyWith(...) }
+			// deferred.resolve = function() { deferred.resolveWith(...) }
+			// deferred.reject = function() { deferred.rejectWith(...) }
+			deferred[ tuple[ 0 ] ] = function() {
+				deferred[ tuple[ 0 ] + "With" ]( this === deferred ? undefined : this, arguments );
+				return this;
+			};
+
+			// deferred.notifyWith = list.fireWith
+			// deferred.resolveWith = list.fireWith
+			// deferred.rejectWith = list.fireWith
+			deferred[ tuple[ 0 ] + "With" ] = list.fireWith;
+		} );
+
+		// Make the deferred a promise
+		promise.promise( deferred );
+
+		// Call given func if any
+		if ( func ) {
+			func.call( deferred, deferred );
+		}
+
+		// All done!
+		return deferred;
+	},
+
+	// Deferred helper
+	when: function( singleValue ) {
+		var
+
+			// count of uncompleted subordinates
+			remaining = arguments.length,
+
+			// count of unprocessed arguments
+			i = remaining,
+
+			// subordinate fulfillment data
+			resolveContexts = Array( i ),
+			resolveValues = slice.call( arguments ),
+
+			// the primary Deferred
+			primary = jQuery.Deferred(),
+
+			// subordinate callback factory
+			updateFunc = function( i ) {
+				return function( value ) {
+					resolveContexts[ i ] = this;
+					resolveValues[ i ] = arguments.length > 1 ? slice.call( arguments ) : value;
+					if ( !( --remaining ) ) {
+						primary.resolveWith( resolveContexts, resolveValues );
+					}
+				};
+			};
+
+		// Single- and empty arguments are adopted like Promise.resolve
+		if ( remaining <= 1 ) {
+			adoptValue( singleValue, primary.done( updateFunc( i ) ).resolve, primary.reject,
+				!remaining );
+
+			// Use .then() to unwrap secondary thenables (cf. gh-3000)
+			if ( primary.state() === "pending" ||
+				isFunction( resolveValues[ i ] && resolveValues[ i ].then ) ) {
+
+				return primary.then();
+			}
+		}
+
+		// Multiple arguments are aggregated like Promise.all array elements
+		while ( i-- ) {
+			adoptValue( resolveValues[ i ], updateFunc( i ), primary.reject );
+		}
+
+		return primary.promise();
+	}
+} );
+
+
+// These usually indicate a programmer mistake during development,
+// warn about them ASAP rather than swallowing them by default.
+var rerrorNames = /^(Eval|Internal|Range|Reference|Syntax|Type|URI)Error$/;
+
+jQuery.Deferred.exceptionHook = function( error, stack ) {
+
+	// Support: IE 8 - 9 only
+	// Console exists when dev tools are open, which can happen at any time
+	if ( window.console && window.console.warn && error && rerrorNames.test( error.name ) ) {
+		window.console.warn( "jQuery.Deferred exception: " + error.message, error.stack, stack );
+	}
+};
+
+
+
+
+jQuery.readyException = function( error ) {
+	window.setTimeout( function() {
+		throw error;
+	} );
+};
+
+
+
+
+// The deferred used on DOM ready
+var readyList = jQuery.Deferred();
+
+jQuery.fn.ready = function( fn ) {
+
+	readyList
+		.then( fn )
+
+		// Wrap jQuery.readyException in a function so that the lookup
+		// happens at the time of error handling instead of callback
+		// registration.
+		.catch( function( error ) {
+			jQuery.readyException( error );
+		} );
+
+	return this;
+};
+
+jQuery.extend( {
+
+	// Is the DOM ready to be used? Set to true once it occurs.
+	isReady: false,
+
+	// A counter to track how many items to wait for before
+	// the ready event fires. See #6781
+	readyWait: 1,
+
+	// Handle when the DOM is ready
+	ready: function( wait ) {
+
+		// Abort if there are pending holds or we're already ready
+		if ( wait === true ? --jQuery.readyWait : jQuery.isReady ) {
+			return;
+		}
+
+		// Remember that the DOM is ready
+		jQuery.isReady = true;
+
+		// If a normal DOM Ready event fired, decrement, and wait if need be
+		if ( wait !== true && --jQuery.readyWait > 0 ) {
+			return;
+		}
+
+		// If there are functions bound, to execute
+		readyList.resolveWith( document, [ jQuery ] );
+	}
+} );
+
+jQuery.ready.then = readyList.then;
+
+// The ready event handler and self cleanup method
+function completed() {
+	document.removeEventListener( "DOMContentLoaded", completed );
+	window.removeEventListener( "load", completed );
+	jQuery.ready();
+}
+
+// Catch cases where $(document).ready() is called
+// after the browser event has already occurred.
+// Support: IE <=9 - 10 only
+// Older IE sometimes signals "interactive" too soon
+if ( document.readyState === "complete" ||
+	( document.readyState !== "loading" && !document.documentElement.doScroll ) ) {
+
+	// Handle it asynchronously to allow scripts the opportunity to delay ready
+	window.setTimeout( jQuery.ready );
+
+} else {
+
+	// Use the handy event callback
+	document.addEventListener( "DOMContentLoaded", completed );
+
+	// A fallback to window.onload, that will always work
+	window.addEventListener( "load", completed );
+}
+
+
+
+
+// Multifunctional method to get and set values of a collection
+// The value/s can optionally be executed if it's a function
+var access = function( elems, fn, key, value, chainable, emptyGet, raw ) {
+	var i = 0,
+		len = elems.length,
+		bulk = key == null;
+
+	// Sets many values
+	if ( toType( key ) === "object" ) {
+		chainable = true;
+		for ( i in key ) {
+			access( elems, fn, i, key[ i ], true, emptyGet, raw );
+		}
+
+	// Sets one value
+	} else if ( value !== undefined ) {
+		chainable = true;
+
+		if ( !isFunction( value ) ) {
+			raw = true;
+		}
+
+		if ( bulk ) {
+
+			// Bulk operations run against the entire set
+			if ( raw ) {
+				fn.call( elems, value );
+				fn = null;
+
+			// ...except when executing function values
+			} else {
+				bulk = fn;
+				fn = function( elem, _key, value ) {
+					return bulk.call( jQuery( elem ), value );
+				};
+			}
+		}
+
+		if ( fn ) {
+			for ( ; i < len; i++ ) {
+				fn(
+					elems[ i ], key, raw ?
+						value :
+						value.call( elems[ i ], i, fn( elems[ i ], key ) )
+				);
+			}
+		}
+	}
+
+	if ( chainable ) {
+		return elems;
+	}
+
+	// Gets
+	if ( bulk ) {
+		return fn.call( elems );
+	}
+
+	return len ? fn( elems[ 0 ], key ) : emptyGet;
+};
+
+
+// Matches dashed string for camelizing
+var rmsPrefix = /^-ms-/,
+	rdashAlpha = /-([a-z])/g;
+
+// Used by camelCase as callback to replace()
+function fcamelCase( _all, letter ) {
+	return letter.toUpperCase();
+}
+
+// Convert dashed to camelCase; used by the css and data modules
+// Support: IE <=9 - 11, Edge 12 - 15
+// Microsoft forgot to hump their vendor prefix (#9572)
+function camelCase( string ) {
+	return string.replace( rmsPrefix, "ms-" ).replace( rdashAlpha, fcamelCase );
+}
+var acceptData = function( owner ) {
+
+	// Accepts only:
+	//  - Node
+	//    - Node.ELEMENT_NODE
+	//    - Node.DOCUMENT_NODE
+	//  - Object
+	//    - Any
+	return owner.nodeType === 1 || owner.nodeType === 9 || !( +owner.nodeType );
+};
+
+
+
+
+function Data() {
+	this.expando = jQuery.expando + Data.uid++;
+}
+
+Data.uid = 1;
+
+Data.prototype = {
+
+	cache: function( owner ) {
+
+		// Check if the owner object already has a cache
+		var value = owner[ this.expando ];
+
+		// If not, create one
+		if ( !value ) {
+			value = {};
+
+			// We can accept data for non-element nodes in modern browsers,
+			// but we should not, see #8335.
+			// Always return an empty object.
+			if ( acceptData( owner ) ) {
+
+				// If it is a node unlikely to be stringify-ed or looped over
+				// use plain assignment
+				if ( owner.nodeType ) {
+					owner[ this.expando ] = value;
+
+				// Otherwise secure it in a non-enumerable property
+				// configurable must be true to allow the property to be
+				// deleted when data is removed
+				} else {
+					Object.defineProperty( owner, this.expando, {
+						value: value,
+						configurable: true
+					} );
+				}
+			}
+		}
+
+		return value;
+	},
+	set: function( owner, data, value ) {
+		var prop,
+			cache = this.cache( owner );
+
+		// Handle: [ owner, key, value ] args
+		// Always use camelCase key (gh-2257)
+		if ( typeof data === "string" ) {
+			cache[ camelCase( data ) ] = value;
+
+		// Handle: [ owner, { properties } ] args
+		} else {
+
+			// Copy the properties one-by-one to the cache object
+			for ( prop in data ) {
+				cache[ camelCase( prop ) ] = data[ prop ];
+			}
+		}
+		return cache;
+	},
+	get: function( owner, key ) {
+		return key === undefined ?
+			this.cache( owner ) :
+
+			// Always use camelCase key (gh-2257)
+			owner[ this.expando ] && owner[ this.expando ][ camelCase( key ) ];
+	},
+	access: function( owner, key, value ) {
+
+		// In cases where either:
+		//
+		//   1. No key was specified
+		//   2. A string key was specified, but no value provided
+		//
+		// Take the "read" path and allow the get method to determine
+		// which value to return, respectively either:
+		//
+		//   1. The entire cache object
+		//   2. The data stored at the key
+		//
+		if ( key === undefined ||
+				( ( key && typeof key === "string" ) && value === undefined ) ) {
+
+			return this.get( owner, key );
+		}
+
+		// When the key is not a string, or both a key and value
+		// are specified, set or extend (existing objects) with either:
+		//
+		//   1. An object of properties
+		//   2. A key and value
+		//
+		this.set( owner, key, value );
+
+		// Since the "set" path can have two possible entry points
+		// return the expected data based on which path was taken[*]
+		return value !== undefined ? value : key;
+	},
+	remove: function( owner, key ) {
+		var i,
+			cache = owner[ this.expando ];
+
+		if ( cache === undefined ) {
+			return;
+		}
+
+		if ( key !== undefined ) {
+
+			// Support array or space separated string of keys
+			if ( Array.isArray( key ) ) {
+
+				// If key is an array of keys...
+				// We always set camelCase keys, so remove that.
+				key = key.map( camelCase );
+			} else {
+				key = camelCase( key );
+
+				// If a key with the spaces exists, use it.
+				// Otherwise, create an array by matching non-whitespace
+				key = key in cache ?
+					[ key ] :
+					( key.match( rnothtmlwhite ) || [] );
+			}
+
+			i = key.length;
+
+			while ( i-- ) {
+				delete cache[ key[ i ] ];
+			}
+		}
+
+		// Remove the expando if there's no more data
+		if ( key === undefined || jQuery.isEmptyObject( cache ) ) {
+
+			// Support: Chrome <=35 - 45
+			// Webkit & Blink performance suffers when deleting properties
+			// from DOM nodes, so set to undefined instead
+			// https://bugs.chromium.org/p/chromium/issues/detail?id=378607 (bug restricted)
+			if ( owner.nodeType ) {
+				owner[ this.expando ] = undefined;
+			} else {
+				delete owner[ this.expando ];
+			}
+		}
+	},
+	hasData: function( owner ) {
+		var cache = owner[ this.expando ];
+		return cache !== undefined && !jQuery.isEmptyObject( cache );
+	}
+};
+var dataPriv = new Data();
+
+var dataUser = new Data();
+
+
+
+//	Implementation Summary
+//
+//	1. Enforce API surface and semantic compatibility with 1.9.x branch
+//	2. Improve the module's maintainability by reducing the storage
+//		paths to a single mechanism.
+//	3. Use the same single mechanism to support "private" and "user" data.
+//	4. _Never_ expose "private" data to user code (TODO: Drop _data, _removeData)
+//	5. Avoid exposing implementation details on user objects (eg. expando properties)
+//	6. Provide a clear path for implementation upgrade to WeakMap in 2014
+
+var rbrace = /^(?:\{[\w\W]*\}|\[[\w\W]*\])$/,
+	rmultiDash = /[A-Z]/g;
+
+function getData( data ) {
+	if ( data === "true" ) {
+		return true;
+	}
+
+	if ( data === "false" ) {
+		return false;
+	}
+
+	if ( data === "null" ) {
+		return null;
+	}
+
+	// Only convert to a number if it doesn't change the string
+	if ( data === +data + "" ) {
+		return +data;
+	}
+
+	if ( rbrace.test( data ) ) {
+		return JSON.parse( data );
+	}
+
+	return data;
+}
+
+function dataAttr( elem, key, data ) {
+	var name;
+
+	// If nothing was found internally, try to fetch any
+	// data from the HTML5 data-* attribute
+	if ( data === undefined && elem.nodeType === 1 ) {
+		name = "data-" + key.replace( rmultiDash, "-$&" ).toLowerCase();
+		data = elem.getAttribute( name );
+
+		if ( typeof data === "string" ) {
+			try {
+				data = getData( data );
+			} catch ( e ) {}
+
+			// Make sure we set the data so it isn't changed later
+			dataUser.set( elem, key, data );
+		} else {
+			data = undefined;
+		}
+	}
+	return data;
+}
+
+jQuery.extend( {
+	hasData: function( elem ) {
+		return dataUser.hasData( elem ) || dataPriv.hasData( elem );
+	},
+
+	data: function( elem, name, data ) {
+		return dataUser.access( elem, name, data );
+	},
+
+	removeData: function( elem, name ) {
+		dataUser.remove( elem, name );
+	},
+
+	// TODO: Now that all calls to _data and _removeData have been replaced
+	// with direct calls to dataPriv methods, these can be deprecated.
+	_data: function( elem, name, data ) {
+		return dataPriv.access( elem, name, data );
+	},
+
+	_removeData: function( elem, name ) {
+		dataPriv.remove( elem, name );
+	}
+} );
+
+jQuery.fn.extend( {
+	data: function( key, value ) {
+		var i, name, data,
+			elem = this[ 0 ],
+			attrs = elem && elem.attributes;
+
+		// Gets all values
+		if ( key === undefined ) {
+			if ( this.length ) {
+				data = dataUser.get( elem );
+
+				if ( elem.nodeType === 1 && !dataPriv.get( elem, "hasDataAttrs" ) ) {
+					i = attrs.length;
+					while ( i-- ) {
+
+						// Support: IE 11 only
+						// The attrs elements can be null (#14894)
+						if ( attrs[ i ] ) {
+							name = attrs[ i ].name;
+							if ( name.indexOf( "data-" ) === 0 ) {
+								name = camelCase( name.slice( 5 ) );
+								dataAttr( elem, name, data[ name ] );
+							}
+						}
+					}
+					dataPriv.set( elem, "hasDataAttrs", true );
+				}
+			}
+
+			return data;
+		}
+
+		// Sets multiple values
+		if ( typeof key === "object" ) {
+			return this.each( function() {
+				dataUser.set( this, key );
+			} );
+		}
+
+		return access( this, function( value ) {
+			var data;
+
+			// The calling jQuery object (element matches) is not empty
+			// (and therefore has an element appears at this[ 0 ]) and the
+			// `value` parameter was not undefined. An empty jQuery object
+			// will result in `undefined` for elem = this[ 0 ] which will
+			// throw an exception if an attempt to read a data cache is made.
+			if ( elem && value === undefined ) {
+
+				// Attempt to get data from the cache
+				// The key will always be camelCased in Data
+				data = dataUser.get( elem, key );
+				if ( data !== undefined ) {
+					return data;
+				}
+
+				// Attempt to "discover" the data in
+				// HTML5 custom data-* attrs
+				data = dataAttr( elem, key );
+				if ( data !== undefined ) {
+					return data;
+				}
+
+				// We tried really hard, but the data doesn't exist.
+				return;
+			}
+
+			// Set the data...
+			this.each( function() {
+
+				// We always store the camelCased key
+				dataUser.set( this, key, value );
+			} );
+		}, null, value, arguments.length > 1, null, true );
+	},
+
+	removeData: function( key ) {
+		return this.each( function() {
+			dataUser.remove( this, key );
+		} );
+	}
+} );
+
+
+jQuery.extend( {
+	queue: function( elem, type, data ) {
+		var queue;
+
+		if ( elem ) {
+			type = ( type || "fx" ) + "queue";
+			queue = dataPriv.get( elem, type );
+
+			// Speed up dequeue by getting out quickly if this is just a lookup
+			if ( data ) {
+				if ( !queue || Array.isArray( data ) ) {
+					queue = dataPriv.access( elem, type, jQuery.makeArray( data ) );
+				} else {
+					queue.push( data );
+				}
+			}
+			return queue || [];
+		}
+	},
+
+	dequeue: function( elem, type ) {
+		type = type || "fx";
+
+		var queue = jQuery.queue( elem, type ),
+			startLength = queue.length,
+			fn = queue.shift(),
+			hooks = jQuery._queueHooks( elem, type ),
+			next = function() {
+				jQuery.dequeue( elem, type );
+			};
+
+		// If the fx queue is dequeued, always remove the progress sentinel
+		if ( fn === "inprogress" ) {
+			fn = queue.shift();
+			startLength--;
+		}
+
+		if ( fn ) {
+
+			// Add a progress sentinel to prevent the fx queue from being
+			// automatically dequeued
+			if ( type === "fx" ) {
+				queue.unshift( "inprogress" );
+			}
+
+			// Clear up the last queue stop function
+			delete hooks.stop;
+			fn.call( elem, next, hooks );
+		}
+
+		if ( !startLength && hooks ) {
+			hooks.empty.fire();
+		}
+	},
+
+	// Not public - generate a queueHooks object, or return the current one
+	_queueHooks: function( elem, type ) {
+		var key = type + "queueHooks";
+		return dataPriv.get( elem, key ) || dataPriv.access( elem, key, {
+			empty: jQuery.Callbacks( "once memory" ).add( function() {
+				dataPriv.remove( elem, [ type + "queue", key ] );
+			} )
+		} );
+	}
+} );
+
+jQuery.fn.extend( {
+	queue: function( type, data ) {
+		var setter = 2;
+
+		if ( typeof type !== "string" ) {
+			data = type;
+			type = "fx";
+			setter--;
+		}
+
+		if ( arguments.length < setter ) {
+			return jQuery.queue( this[ 0 ], type );
+		}
+
+		return data === undefined ?
+			this :
+			this.each( function() {
+				var queue = jQuery.queue( this, type, data );
+
+				// Ensure a hooks for this queue
+				jQuery._queueHooks( this, type );
+
+				if ( type === "fx" && queue[ 0 ] !== "inprogress" ) {
+					jQuery.dequeue( this, type );
+				}
+			} );
+	},
+	dequeue: function( type ) {
+		return this.each( function() {
+			jQuery.dequeue( this, type );
+		} );
+	},
+	clearQueue: function( type ) {
+		return this.queue( type || "fx", [] );
+	},
+
+	// Get a promise resolved when queues of a certain type
+	// are emptied (fx is the type by default)
+	promise: function( type, obj ) {
+		var tmp,
+			count = 1,
+			defer = jQuery.Deferred(),
+			elements = this,
+			i = this.length,
+			resolve = function() {
+				if ( !( --count ) ) {
+					defer.resolveWith( elements, [ elements ] );
+				}
+			};
+
+		if ( typeof type !== "string" ) {
+			obj = type;
+			type = undefined;
+		}
+		type = type || "fx";
+
+		while ( i-- ) {
+			tmp = dataPriv.get( elements[ i ], type + "queueHooks" );
+			if ( tmp && tmp.empty ) {
+				count++;
+				tmp.empty.add( resolve );
+			}
+		}
+		resolve();
+		return defer.promise( obj );
+	}
+} );
+var pnum = ( /[+-]?(?:\d*\.|)\d+(?:[eE][+-]?\d+|)/ ).source;
+
+var rcssNum = new RegExp( "^(?:([+-])=|)(" + pnum + ")([a-z%]*)$", "i" );
+
+
+var cssExpand = [ "Top", "Right", "Bottom", "Left" ];
+
+var documentElement = document.documentElement;
+
+
+
+	var isAttached = function( elem ) {
+			return jQuery.contains( elem.ownerDocument, elem );
+		},
+		composed = { composed: true };
+
+	// Support: IE 9 - 11+, Edge 12 - 18+, iOS 10.0 - 10.2 only
+	// Check attachment across shadow DOM boundaries when possible (gh-3504)
+	// Support: iOS 10.0-10.2 only
+	// Early iOS 10 versions support `attachShadow` but not `getRootNode`,
+	// leading to errors. We need to check for `getRootNode`.
+	if ( documentElement.getRootNode ) {
+		isAttached = function( elem ) {
+			return jQuery.contains( elem.ownerDocument, elem ) ||
+				elem.getRootNode( composed ) === elem.ownerDocument;
+		};
+	}
+var isHiddenWithinTree = function( elem, el ) {
+
+		// isHiddenWithinTree might be called from jQuery#filter function;
+		// in that case, element will be second argument
+		elem = el || elem;
+
+		// Inline style trumps all
+		return elem.style.display === "none" ||
+			elem.style.display === "" &&
+
+			// Otherwise, check computed style
+			// Support: Firefox <=43 - 45
+			// Disconnected elements can have computed display: none, so first confirm that elem is
+			// in the document.
+			isAttached( elem ) &&
+
+			jQuery.css( elem, "display" ) === "none";
+	};
+
+
+
+function adjustCSS( elem, prop, valueParts, tween ) {
+	var adjusted, scale,
+		maxIterations = 20,
+		currentValue = tween ?
+			function() {
+				return tween.cur();
+			} :
+			function() {
+				return jQuery.css( elem, prop, "" );
+			},
+		initial = currentValue(),
+		unit = valueParts && valueParts[ 3 ] || ( jQuery.cssNumber[ prop ] ? "" : "px" ),
+
+		// Starting value computation is required for potential unit mismatches
+		initialInUnit = elem.nodeType &&
+			( jQuery.cssNumber[ prop ] || unit !== "px" && +initial ) &&
+			rcssNum.exec( jQuery.css( elem, prop ) );
+
+	if ( initialInUnit && initialInUnit[ 3 ] !== unit ) {
+
+		// Support: Firefox <=54
+		// Halve the iteration target value to prevent interference from CSS upper bounds (gh-2144)
+		initial = initial / 2;
+
+		// Trust units reported by jQuery.css
+		unit = unit || initialInUnit[ 3 ];
+
+		// Iteratively approximate from a nonzero starting point
+		initialInUnit = +initial || 1;
+
+		while ( maxIterations-- ) {
+
+			// Evaluate and update our best guess (doubling guesses that zero out).
+			// Finish if the scale equals or crosses 1 (making the old*new product non-positive).
+			jQuery.style( elem, prop, initialInUnit + unit );
+			if ( ( 1 - scale ) * ( 1 - ( scale = currentValue() / initial || 0.5 ) ) <= 0 ) {
+				maxIterations = 0;
+			}
+			initialInUnit = initialInUnit / scale;
+
+		}
+
+		initialInUnit = initialInUnit * 2;
+		jQuery.style( elem, prop, initialInUnit + unit );
+
+		// Make sure we update the tween properties later on
+		valueParts = valueParts || [];
+	}
+
+	if ( valueParts ) {
+		initialInUnit = +initialInUnit || +initial || 0;
+
+		// Apply relative offset (+=/-=) if specified
+		adjusted = valueParts[ 1 ] ?
+			initialInUnit + ( valueParts[ 1 ] + 1 ) * valueParts[ 2 ] :
+			+valueParts[ 2 ];
+		if ( tween ) {
+			tween.unit = unit;
+			tween.start = initialInUnit;
+			tween.end = adjusted;
+		}
+	}
+	return adjusted;
+}
+
+
+var defaultDisplayMap = {};
+
+function getDefaultDisplay( elem ) {
+	var temp,
+		doc = elem.ownerDocument,
+		nodeName = elem.nodeName,
+		display = defaultDisplayMap[ nodeName ];
+
+	if ( display ) {
+		return display;
+	}
+
+	temp = doc.body.appendChild( doc.createElement( nodeName ) );
+	display = jQuery.css( temp, "display" );
+
+	temp.parentNode.removeChild( temp );
+
+	if ( display === "none" ) {
+		display = "block";
+	}
+	defaultDisplayMap[ nodeName ] = display;
+
+	return display;
+}
+
+function showHide( elements, show ) {
+	var display, elem,
+		values = [],
+		index = 0,
+		length = elements.length;
+
+	// Determine new display value for elements that need to change
+	for ( ; index < length; index++ ) {
+		elem = elements[ index ];
+		if ( !elem.style ) {
+			continue;
+		}
+
+		display = elem.style.display;
+		if ( show ) {
+
+			// Since we force visibility upon cascade-hidden elements, an immediate (and slow)
+			// check is required in this first loop unless we have a nonempty display value (either
+			// inline or about-to-be-restored)
+			if ( display === "none" ) {
+				values[ index ] = dataPriv.get( elem, "display" ) || null;
+				if ( !values[ index ] ) {
+					elem.style.display = "";
+				}
+			}
+			if ( elem.style.display === "" && isHiddenWithinTree( elem ) ) {
+				values[ index ] = getDefaultDisplay( elem );
+			}
+		} else {
+			if ( display !== "none" ) {
+				values[ index ] = "none";
+
+				// Remember what we're overwriting
+				dataPriv.set( elem, "display", display );
+			}
+		}
+	}
+
+	// Set the display of the elements in a second loop to avoid constant reflow
+	for ( index = 0; index < length; index++ ) {
+		if ( values[ index ] != null ) {
+			elements[ index ].style.display = values[ index ];
+		}
+	}
+
+	return elements;
+}
+
+jQuery.fn.extend( {
+	show: function() {
+		return showHide( this, true );
+	},
+	hide: function() {
+		return showHide( this );
+	},
+	toggle: function( state ) {
+		if ( typeof state === "boolean" ) {
+			return state ? this.show() : this.hide();
+		}
+
+		return this.each( function() {
+			if ( isHiddenWithinTree( this ) ) {
+				jQuery( this ).show();
+			} else {
+				jQuery( this ).hide();
+			}
+		} );
+	}
+} );
+var rcheckableType = ( /^(?:checkbox|radio)$/i );
+
+var rtagName = ( /<([a-z][^\/\0>\x20\t\r\n\f]*)/i );
+
+var rscriptType = ( /^$|^module$|\/(?:java|ecma)script/i );
+
+
+
+( function() {
+	var fragment = document.createDocumentFragment(),
+		div = fragment.appendChild( document.createElement( "div" ) ),
+		input = document.createElement( "input" );
+
+	// Support: Android 4.0 - 4.3 only
+	// Check state lost if the name is set (#11217)
+	// Support: Windows Web Apps (WWA)
+	// `name` and `type` must use .setAttribute for WWA (#14901)
+	input.setAttribute( "type", "radio" );
+	input.setAttribute( "checked", "checked" );
+	input.setAttribute( "name", "t" );
+
+	div.appendChild( input );
+
+	// Support: Android <=4.1 only
+	// Older WebKit doesn't clone checked state correctly in fragments
+	support.checkClone = div.cloneNode( true ).cloneNode( true ).lastChild.checked;
+
+	// Support: IE <=11 only
+	// Make sure textarea (and checkbox) defaultValue is properly cloned
+	div.innerHTML = "<textarea>x</textarea>";
+	support.noCloneChecked = !!div.cloneNode( true ).lastChild.defaultValue;
+
+	// Support: IE <=9 only
+	// IE <=9 replaces <option> tags with their contents when inserted outside of
+	// the select element.
+	div.innerHTML = "<option></option>";
+	support.option = !!div.lastChild;
+} )();
+
+
+// We have to close these tags to support XHTML (#13200)
+var wrapMap = {
+
+	// XHTML parsers do not magically insert elements in the
+	// same way that tag soup parsers do. So we cannot shorten
+	// this by omitting <tbody> or other required elements.
+	thead: [ 1, "<table>", "</table>" ],
+	col: [ 2, "<table><colgroup>", "</colgroup></table>" ],
+	tr: [ 2, "<table><tbody>", "</tbody></table>" ],
+	td: [ 3, "<table><tbody><tr>", "</tr></tbody></table>" ],
+
+	_default: [ 0, "", "" ]
+};
+
+wrapMap.tbody = wrapMap.tfoot = wrapMap.colgroup = wrapMap.caption = wrapMap.thead;
+wrapMap.th = wrapMap.td;
+
+// Support: IE <=9 only
+if ( !support.option ) {
+	wrapMap.optgroup = wrapMap.option = [ 1, "<select multiple='multiple'>", "</select>" ];
+}
+
+
+function getAll( context, tag ) {
+
+	// Support: IE <=9 - 11 only
+	// Use typeof to avoid zero-argument method invocation on host objects (#15151)
+	var ret;
+
+	if ( typeof context.getElementsByTagName !== "undefined" ) {
+		ret = context.getElementsByTagName( tag || "*" );
+
+	} else if ( typeof context.querySelectorAll !== "undefined" ) {
+		ret = context.querySelectorAll( tag || "*" );
+
+	} else {
+		ret = [];
+	}
+
+	if ( tag === undefined || tag && nodeName( context, tag ) ) {
+		return jQuery.merge( [ context ], ret );
+	}
+
+	return ret;
+}
+
+
+// Mark scripts as having already been evaluated
+function setGlobalEval( elems, refElements ) {
+	var i = 0,
+		l = elems.length;
+
+	for ( ; i < l; i++ ) {
+		dataPriv.set(
+			elems[ i ],
+			"globalEval",
+			!refElements || dataPriv.get( refElements[ i ], "globalEval" )
+		);
+	}
+}
+
+
+var rhtml = /<|&#?\w+;/;
+
+function buildFragment( elems, context, scripts, selection, ignored ) {
+	var elem, tmp, tag, wrap, attached, j,
+		fragment = context.createDocumentFragment(),
+		nodes = [],
+		i = 0,
+		l = elems.length;
+
+	for ( ; i < l; i++ ) {
+		elem = elems[ i ];
+
+		if ( elem || elem === 0 ) {
+
+			// Add nodes directly
+			if ( toType( elem ) === "object" ) {
+
+				// Support: Android <=4.0 only, PhantomJS 1 only
+				// push.apply(_, arraylike) throws on ancient WebKit
+				jQuery.merge( nodes, elem.nodeType ? [ elem ] : elem );
+
+			// Convert non-html into a text node
+			} else if ( !rhtml.test( elem ) ) {
+				nodes.push( context.createTextNode( elem ) );
+
+			// Convert html into DOM nodes
+			} else {
+				tmp = tmp || fragment.appendChild( context.createElement( "div" ) );
+
+				// Deserialize a standard representation
+				tag = ( rtagName.exec( elem ) || [ "", "" ] )[ 1 ].toLowerCase();
+				wrap = wrapMap[ tag ] || wrapMap._default;
+				tmp.innerHTML = wrap[ 1 ] + jQuery.htmlPrefilter( elem ) + wrap[ 2 ];
+
+				// Descend through wrappers to the right content
+				j = wrap[ 0 ];
+				while ( j-- ) {
+					tmp = tmp.lastChild;
+				}
+
+				// Support: Android <=4.0 only, PhantomJS 1 only
+				// push.apply(_, arraylike) throws on ancient WebKit
+				jQuery.merge( nodes, tmp.childNodes );
+
+				// Remember the top-level container
+				tmp = fragment.firstChild;
+
+				// Ensure the created nodes are orphaned (#12392)
+				tmp.textContent = "";
+			}
+		}
+	}
+
+	// Remove wrapper from fragment
+	fragment.textContent = "";
+
+	i = 0;
+	while ( ( elem = nodes[ i++ ] ) ) {
+
+		// Skip elements already in the context collection (trac-4087)
+		if ( selection && jQuery.inArray( elem, selection ) > -1 ) {
+			if ( ignored ) {
+				ignored.push( elem );
+			}
+			continue;
+		}
+
+		attached = isAttached( elem );
+
+		// Append to fragment
+		tmp = getAll( fragment.appendChild( elem ), "script" );
+
+		// Preserve script evaluation history
+		if ( attached ) {
+			setGlobalEval( tmp );
+		}
+
+		// Capture executables
+		if ( scripts ) {
+			j = 0;
+			while ( ( elem = tmp[ j++ ] ) ) {
+				if ( rscriptType.test( elem.type || "" ) ) {
+					scripts.push( elem );
+				}
+			}
+		}
+	}
+
+	return fragment;
+}
+
+
+var rtypenamespace = /^([^.]*)(?:\.(.+)|)/;
+
+function returnTrue() {
+	return true;
+}
+
+function returnFalse() {
+	return false;
+}
+
+// Support: IE <=9 - 11+
+// focus() and blur() are asynchronous, except when they are no-op.
+// So expect focus to be synchronous when the element is already active,
+// and blur to be synchronous when the element is not already active.
+// (focus and blur are always synchronous in other supported browsers,
+// this just defines when we can count on it).
+function expectSync( elem, type ) {
+	return ( elem === safeActiveElement() ) === ( type === "focus" );
+}
+
+// Support: IE <=9 only
+// Accessing document.activeElement can throw unexpectedly
+// https://bugs.jquery.com/ticket/13393
+function safeActiveElement() {
+	try {
+		return document.activeElement;
+	} catch ( err ) { }
+}
+
+function on( elem, types, selector, data, fn, one ) {
+	var origFn, type;
+
+	// Types can be a map of types/handlers
+	if ( typeof types === "object" ) {
+
+		// ( types-Object, selector, data )
+		if ( typeof selector !== "string" ) {
+
+			// ( types-Object, data )
+			data = data || selector;
+			selector = undefined;
+		}
+		for ( type in types ) {
+			on( elem, type, selector, data, types[ type ], one );
+		}
+		return elem;
+	}
+
+	if ( data == null && fn == null ) {
+
+		// ( types, fn )
+		fn = selector;
+		data = selector = undefined;
+	} else if ( fn == null ) {
+		if ( typeof selector === "string" ) {
+
+			// ( types, selector, fn )
+			fn = data;
+			data = undefined;
+		} else {
+
+			// ( types, data, fn )
+			fn = data;
+			data = selector;
+			selector = undefined;
+		}
+	}
+	if ( fn === false ) {
+		fn = returnFalse;
+	} else if ( !fn ) {
+		return elem;
+	}
+
+	if ( one === 1 ) {
+		origFn = fn;
+		fn = function( event ) {
+
+			// Can use an empty set, since event contains the info
+			jQuery().off( event );
+			return origFn.apply( this, arguments );
+		};
+
+		// Use same guid so caller can remove using origFn
+		fn.guid = origFn.guid || ( origFn.guid = jQuery.guid++ );
+	}
+	return elem.each( function() {
+		jQuery.event.add( this, types, fn, data, selector );
+	} );
+}
+
+/*
+ * Helper functions for managing events -- not part of the public interface.
+ * Props to Dean Edwards' addEvent library for many of the ideas.
+ */
+jQuery.event = {
+
+	global: {},
+
+	add: function( elem, types, handler, data, selector ) {
+
+		var handleObjIn, eventHandle, tmp,
+			events, t, handleObj,
+			special, handlers, type, namespaces, origType,
+			elemData = dataPriv.get( elem );
+
+		// Only attach events to objects that accept data
+		if ( !acceptData( elem ) ) {
+			return;
+		}
+
+		// Caller can pass in an object of custom data in lieu of the handler
+		if ( handler.handler ) {
+			handleObjIn = handler;
+			handler = handleObjIn.handler;
+			selector = handleObjIn.selector;
+		}
+
+		// Ensure that invalid selectors throw exceptions at attach time
+		// Evaluate against documentElement in case elem is a non-element node (e.g., document)
+		if ( selector ) {
+			jQuery.find.matchesSelector( documentElement, selector );
+		}
+
+		// Make sure that the handler has a unique ID, used to find/remove it later
+		if ( !handler.guid ) {
+			handler.guid = jQuery.guid++;
+		}
+
+		// Init the element's event structure and main handler, if this is the first
+		if ( !( events = elemData.events ) ) {
+			events = elemData.events = Object.create( null );
+		}
+		if ( !( eventHandle = elemData.handle ) ) {
+			eventHandle = elemData.handle = function( e ) {
+
+				// Discard the second event of a jQuery.event.trigger() and
+				// when an event is called after a page has unloaded
+				return typeof jQuery !== "undefined" && jQuery.event.triggered !== e.type ?
+					jQuery.event.dispatch.apply( elem, arguments ) : undefined;
+			};
+		}
+
+		// Handle multiple events separated by a space
+		types = ( types || "" ).match( rnothtmlwhite ) || [ "" ];
+		t = types.length;
+		while ( t-- ) {
+			tmp = rtypenamespace.exec( types[ t ] ) || [];
+			type = origType = tmp[ 1 ];
+			namespaces = ( tmp[ 2 ] || "" ).split( "." ).sort();
+
+			// There *must* be a type, no attaching namespace-only handlers
+			if ( !type ) {
+				continue;
+			}
+
+			// If event changes its type, use the special event handlers for the changed type
+			special = jQuery.event.special[ type ] || {};
+
+			// If selector defined, determine special event api type, otherwise given type
+			type = ( selector ? special.delegateType : special.bindType ) || type;
+
+			// Update special based on newly reset type
+			special = jQuery.event.special[ type ] || {};
+
+			// handleObj is passed to all event handlers
+			handleObj = jQuery.extend( {
+				type: type,
+				origType: origType,
+				data: data,
+				handler: handler,
+				guid: handler.guid,
+				selector: selector,
+				needsContext: selector && jQuery.expr.match.needsContext.test( selector ),
+				namespace: namespaces.join( "." )
+			}, handleObjIn );
+
+			// Init the event handler queue if we're the first
+			if ( !( handlers = events[ type ] ) ) {
+				handlers = events[ type ] = [];
+				handlers.delegateCount = 0;
+
+				// Only use addEventListener if the special events handler returns false
+				if ( !special.setup ||
+					special.setup.call( elem, data, namespaces, eventHandle ) === false ) {
+
+					if ( elem.addEventListener ) {
+						elem.addEventListener( type, eventHandle );
+					}
+				}
+			}
+
+			if ( special.add ) {
+				special.add.call( elem, handleObj );
+
+				if ( !handleObj.handler.guid ) {
+					handleObj.handler.guid = handler.guid;
+				}
+			}
+
+			// Add to the element's handler list, delegates in front
+			if ( selector ) {
+				handlers.splice( handlers.delegateCount++, 0, handleObj );
+			} else {
+				handlers.push( handleObj );
+			}
+
+			// Keep track of which events have ever been used, for event optimization
+			jQuery.event.global[ type ] = true;
+		}
+
+	},
+
+	// Detach an event or set of events from an element
+	remove: function( elem, types, handler, selector, mappedTypes ) {
+
+		var j, origCount, tmp,
+			events, t, handleObj,
+			special, handlers, type, namespaces, origType,
+			elemData = dataPriv.hasData( elem ) && dataPriv.get( elem );
+
+		if ( !elemData || !( events = elemData.events ) ) {
+			return;
+		}
+
+		// Once for each type.namespace in types; type may be omitted
+		types = ( types || "" ).match( rnothtmlwhite ) || [ "" ];
+		t = types.length;
+		while ( t-- ) {
+			tmp = rtypenamespace.exec( types[ t ] ) || [];
+			type = origType = tmp[ 1 ];
+			namespaces = ( tmp[ 2 ] || "" ).split( "." ).sort();
+
+			// Unbind all events (on this namespace, if provided) for the element
+			if ( !type ) {
+				for ( type in events ) {
+					jQuery.event.remove( elem, type + types[ t ], handler, selector, true );
+				}
+				continue;
+			}
+
+			special = jQuery.event.special[ type ] || {};
+			type = ( selector ? special.delegateType : special.bindType ) || type;
+			handlers = events[ type ] || [];
+			tmp = tmp[ 2 ] &&
+				new RegExp( "(^|\\.)" + namespaces.join( "\\.(?:.*\\.|)" ) + "(\\.|$)" );
+
+			// Remove matching events
+			origCount = j = handlers.length;
+			while ( j-- ) {
+				handleObj = handlers[ j ];
+
+				if ( ( mappedTypes || origType === handleObj.origType ) &&
+					( !handler || handler.guid === handleObj.guid ) &&
+					( !tmp || tmp.test( handleObj.namespace ) ) &&
+					( !selector || selector === handleObj.selector ||
+						selector === "**" && handleObj.selector ) ) {
+					handlers.splice( j, 1 );
+
+					if ( handleObj.selector ) {
+						handlers.delegateCount--;
+					}
+					if ( special.remove ) {
+						special.remove.call( elem, handleObj );
+					}
+				}
+			}
+
+			// Remove generic event handler if we removed something and no more handlers exist
+			// (avoids potential for endless recursion during removal of special event handlers)
+			if ( origCount && !handlers.length ) {
+				if ( !special.teardown ||
+					special.teardown.call( elem, namespaces, elemData.handle ) === false ) {
+
+					jQuery.removeEvent( elem, type, elemData.handle );
+				}
+
+				delete events[ type ];
+			}
+		}
+
+		// Remove data and the expando if it's no longer used
+		if ( jQuery.isEmptyObject( events ) ) {
+			dataPriv.remove( elem, "handle events" );
+		}
+	},
+
+	dispatch: function( nativeEvent ) {
+
+		var i, j, ret, matched, handleObj, handlerQueue,
+			args = new Array( arguments.length ),
+
+			// Make a writable jQuery.Event from the native event object
+			event = jQuery.event.fix( nativeEvent ),
+
+			handlers = (
+				dataPriv.get( this, "events" ) || Object.create( null )
+			)[ event.type ] || [],
+			special = jQuery.event.special[ event.type ] || {};
+
+		// Use the fix-ed jQuery.Event rather than the (read-only) native event
+		args[ 0 ] = event;
+
+		for ( i = 1; i < arguments.length; i++ ) {
+			args[ i ] = arguments[ i ];
+		}
+
+		event.delegateTarget = this;
+
+		// Call the preDispatch hook for the mapped type, and let it bail if desired
+		if ( special.preDispatch && special.preDispatch.call( this, event ) === false ) {
+			return;
+		}
+
+		// Determine handlers
+		handlerQueue = jQuery.event.handlers.call( this, event, handlers );
+
+		// Run delegates first; they may want to stop propagation beneath us
+		i = 0;
+		while ( ( matched = handlerQueue[ i++ ] ) && !event.isPropagationStopped() ) {
+			event.currentTarget = matched.elem;
+
+			j = 0;
+			while ( ( handleObj = matched.handlers[ j++ ] ) &&
+				!event.isImmediatePropagationStopped() ) {
+
+				// If the event is namespaced, then each handler is only invoked if it is
+				// specially universal or its namespaces are a superset of the event's.
+				if ( !event.rnamespace || handleObj.namespace === false ||
+					event.rnamespace.test( handleObj.namespace ) ) {
+
+					event.handleObj = handleObj;
+					event.data = handleObj.data;
+
+					ret = ( ( jQuery.event.special[ handleObj.origType ] || {} ).handle ||
+						handleObj.handler ).apply( matched.elem, args );
+
+					if ( ret !== undefined ) {
+						if ( ( event.result = ret ) === false ) {
+							event.preventDefault();
+							event.stopPropagation();
+						}
+					}
+				}
+			}
+		}
+
+		// Call the postDispatch hook for the mapped type
+		if ( special.postDispatch ) {
+			special.postDispatch.call( this, event );
+		}
+
+		return event.result;
+	},
+
+	handlers: function( event, handlers ) {
+		var i, handleObj, sel, matchedHandlers, matchedSelectors,
+			handlerQueue = [],
+			delegateCount = handlers.delegateCount,
+			cur = event.target;
+
+		// Find delegate handlers
+		if ( delegateCount &&
+
+			// Support: IE <=9
+			// Black-hole SVG <use> instance trees (trac-13180)
+			cur.nodeType &&
+
+			// Support: Firefox <=42
+			// Suppress spec-violating clicks indicating a non-primary pointer button (trac-3861)
+			// https://www.w3.org/TR/DOM-Level-3-Events/#event-type-click
+			// Support: IE 11 only
+			// ...but not arrow key "clicks" of radio inputs, which can have `button` -1 (gh-2343)
+			!( event.type === "click" && event.button >= 1 ) ) {
+
+			for ( ; cur !== this; cur = cur.parentNode || this ) {
+
+				// Don't check non-elements (#13208)
+				// Don't process clicks on disabled elements (#6911, #8165, #11382, #11764)
+				if ( cur.nodeType === 1 && !( event.type === "click" && cur.disabled === true ) ) {
+					matchedHandlers = [];
+					matchedSelectors = {};
+					for ( i = 0; i < delegateCount; i++ ) {
+						handleObj = handlers[ i ];
+
+						// Don't conflict with Object.prototype properties (#13203)
+						sel = handleObj.selector + " ";
+
+						if ( matchedSelectors[ sel ] === undefined ) {
+							matchedSelectors[ sel ] = handleObj.needsContext ?
+								jQuery( sel, this ).index( cur ) > -1 :
+								jQuery.find( sel, this, null, [ cur ] ).length;
+						}
+						if ( matchedSelectors[ sel ] ) {
+							matchedHandlers.push( handleObj );
+						}
+					}
+					if ( matchedHandlers.length ) {
+						handlerQueue.push( { elem: cur, handlers: matchedHandlers } );
+					}
+				}
+			}
+		}
+
+		// Add the remaining (directly-bound) handlers
+		cur = this;
+		if ( delegateCount < handlers.length ) {
+			handlerQueue.push( { elem: cur, handlers: handlers.slice( delegateCount ) } );
+		}
+
+		return handlerQueue;
+	},
+
+	addProp: function( name, hook ) {
+		Object.defineProperty( jQuery.Event.prototype, name, {
+			enumerable: true,
+			configurable: true,
+
+			get: isFunction( hook ) ?
+				function() {
+					if ( this.originalEvent ) {
+						return hook( this.originalEvent );
+					}
+				} :
+				function() {
+					if ( this.originalEvent ) {
+						return this.originalEvent[ name ];
+					}
+				},
+
+			set: function( value ) {
+				Object.defineProperty( this, name, {
+					enumerable: true,
+					configurable: true,
+					writable: true,
+					value: value
+				} );
+			}
+		} );
+	},
+
+	fix: function( originalEvent ) {
+		return originalEvent[ jQuery.expando ] ?
+			originalEvent :
+			new jQuery.Event( originalEvent );
+	},
+
+	special: {
+		load: {
+
+			// Prevent triggered image.load events from bubbling to window.load
+			noBubble: true
+		},
+		click: {
+
+			// Utilize native event to ensure correct state for checkable inputs
+			setup: function( data ) {
+
+				// For mutual compressibility with _default, replace `this` access with a local var.
+				// `|| data` is dead code meant only to preserve the variable through minification.
+				var el = this || data;
+
+				// Claim the first handler
+				if ( rcheckableType.test( el.type ) &&
+					el.click && nodeName( el, "input" ) ) {
+
+					// dataPriv.set( el, "click", ... )
+					leverageNative( el, "click", returnTrue );
+				}
+
+				// Return false to allow normal processing in the caller
+				return false;
+			},
+			trigger: function( data ) {
+
+				// For mutual compressibility with _default, replace `this` access with a local var.
+				// `|| data` is dead code meant only to preserve the variable through minification.
+				var el = this || data;
+
+				// Force setup before triggering a click
+				if ( rcheckableType.test( el.type ) &&
+					el.click && nodeName( el, "input" ) ) {
+
+					leverageNative( el, "click" );
+				}
+
+				// Return non-false to allow normal event-path propagation
+				return true;
+			},
+
+			// For cross-browser consistency, suppress native .click() on links
+			// Also prevent it if we're currently inside a leveraged native-event stack
+			_default: function( event ) {
+				var target = event.target;
+				return rcheckableType.test( target.type ) &&
+					target.click && nodeName( target, "input" ) &&
+					dataPriv.get( target, "click" ) ||
+					nodeName( target, "a" );
+			}
+		},
+
+		beforeunload: {
+			postDispatch: function( event ) {
+
+				// Support: Firefox 20+
+				// Firefox doesn't alert if the returnValue field is not set.
+				if ( event.result !== undefined && event.originalEvent ) {
+					event.originalEvent.returnValue = event.result;
+				}
+			}
+		}
+	}
+};
+
+// Ensure the presence of an event listener that handles manually-triggered
+// synthetic events by interrupting progress until reinvoked in response to
+// *native* events that it fires directly, ensuring that state changes have
+// already occurred before other listeners are invoked.
+function leverageNative( el, type, expectSync ) {
+
+	// Missing expectSync indicates a trigger call, which must force setup through jQuery.event.add
+	if ( !expectSync ) {
+		if ( dataPriv.get( el, type ) === undefined ) {
+			jQuery.event.add( el, type, returnTrue );
+		}
+		return;
+	}
+
+	// Register the controller as a special universal handler for all event namespaces
+	dataPriv.set( el, type, false );
+	jQuery.event.add( el, type, {
+		namespace: false,
+		handler: function( event ) {
+			var notAsync, result,
+				saved = dataPriv.get( this, type );
+
+			if ( ( event.isTrigger & 1 ) && this[ type ] ) {
+
+				// Interrupt processing of the outer synthetic .trigger()ed event
+				// Saved data should be false in such cases, but might be a leftover capture object
+				// from an async native handler (gh-4350)
+				if ( !saved.length ) {
+
+					// Store arguments for use when handling the inner native event
+					// There will always be at least one argument (an event object), so this array
+					// will not be confused with a leftover capture object.
+					saved = slice.call( arguments );
+					dataPriv.set( this, type, saved );
+
+					// Trigger the native event and capture its result
+					// Support: IE <=9 - 11+
+					// focus() and blur() are asynchronous
+					notAsync = expectSync( this, type );
+					this[ type ]();
+					result = dataPriv.get( this, type );
+					if ( saved !== result || notAsync ) {
+						dataPriv.set( this, type, false );
+					} else {
+						result = {};
+					}
+					if ( saved !== result ) {
+
+						// Cancel the outer synthetic event
+						event.stopImmediatePropagation();
+						event.preventDefault();
+
+						// Support: Chrome 86+
+						// In Chrome, if an element having a focusout handler is blurred by
+						// clicking outside of it, it invokes the handler synchronously. If
+						// that handler calls `.remove()` on the element, the data is cleared,
+						// leaving `result` undefined. We need to guard against this.
+						return result && result.value;
+					}
+
+				// If this is an inner synthetic event for an event with a bubbling surrogate
+				// (focus or blur), assume that the surrogate already propagated from triggering the
+				// native event and prevent that from happening again here.
+				// This technically gets the ordering wrong w.r.t. to `.trigger()` (in which the
+				// bubbling surrogate propagates *after* the non-bubbling base), but that seems
+				// less bad than duplication.
+				} else if ( ( jQuery.event.special[ type ] || {} ).delegateType ) {
+					event.stopPropagation();
+				}
+
+			// If this is a native event triggered above, everything is now in order
+			// Fire an inner synthetic event with the original arguments
+			} else if ( saved.length ) {
+
+				// ...and capture the result
+				dataPriv.set( this, type, {
+					value: jQuery.event.trigger(
+
+						// Support: IE <=9 - 11+
+						// Extend with the prototype to reset the above stopImmediatePropagation()
+						jQuery.extend( saved[ 0 ], jQuery.Event.prototype ),
+						saved.slice( 1 ),
+						this
+					)
+				} );
+
+				// Abort handling of the native event
+				event.stopImmediatePropagation();
+			}
+		}
+	} );
+}
+
+jQuery.removeEvent = function( elem, type, handle ) {
+
+	// This "if" is needed for plain objects
+	if ( elem.removeEventListener ) {
+		elem.removeEventListener( type, handle );
+	}
+};
+
+jQuery.Event = function( src, props ) {
+
+	// Allow instantiation without the 'new' keyword
+	if ( !( this instanceof jQuery.Event ) ) {
+		return new jQuery.Event( src, props );
+	}
+
+	// Event object
+	if ( src && src.type ) {
+		this.originalEvent = src;
+		this.type = src.type;
+
+		// Events bubbling up the document may have been marked as prevented
+		// by a handler lower down the tree; reflect the correct value.
+		this.isDefaultPrevented = src.defaultPrevented ||
+				src.defaultPrevented === undefined &&
+
+				// Support: Android <=2.3 only
+				src.returnValue === false ?
+			returnTrue :
+			returnFalse;
+
+		// Create target properties
+		// Support: Safari <=6 - 7 only
+		// Target should not be a text node (#504, #13143)
+		this.target = ( src.target && src.target.nodeType === 3 ) ?
+			src.target.parentNode :
+			src.target;
+
+		this.currentTarget = src.currentTarget;
+		this.relatedTarget = src.relatedTarget;
+
+	// Event type
+	} else {
+		this.type = src;
+	}
+
+	// Put explicitly provided properties onto the event object
+	if ( props ) {
+		jQuery.extend( this, props );
+	}
+
+	// Create a timestamp if incoming event doesn't have one
+	this.timeStamp = src && src.timeStamp || Date.now();
+
+	// Mark it as fixed
+	this[ jQuery.expando ] = true;
+};
+
+// jQuery.Event is based on DOM3 Events as specified by the ECMAScript Language Binding
+// https://www.w3.org/TR/2003/WD-DOM-Level-3-Events-20030331/ecma-script-binding.html
+jQuery.Event.prototype = {
+	constructor: jQuery.Event,
+	isDefaultPrevented: returnFalse,
+	isPropagationStopped: returnFalse,
+	isImmediatePropagationStopped: returnFalse,
+	isSimulated: false,
+
+	preventDefault: function() {
+		var e = this.originalEvent;
+
+		this.isDefaultPrevented = returnTrue;
+
+		if ( e && !this.isSimulated ) {
+			e.preventDefault();
+		}
+	},
+	stopPropagation: function() {
+		var e = this.originalEvent;
+
+		this.isPropagationStopped = returnTrue;
+
+		if ( e && !this.isSimulated ) {
+			e.stopPropagation();
+		}
+	},
+	stopImmediatePropagation: function() {
+		var e = this.originalEvent;
+
+		this.isImmediatePropagationStopped = returnTrue;
+
+		if ( e && !this.isSimulated ) {
+			e.stopImmediatePropagation();
+		}
+
+		this.stopPropagation();
+	}
+};
+
+// Includes all common event props including KeyEvent and MouseEvent specific props
+jQuery.each( {
+	altKey: true,
+	bubbles: true,
+	cancelable: true,
+	changedTouches: true,
+	ctrlKey: true,
+	detail: true,
+	eventPhase: true,
+	metaKey: true,
+	pageX: true,
+	pageY: true,
+	shiftKey: true,
+	view: true,
+	"char": true,
+	code: true,
+	charCode: true,
+	key: true,
+	keyCode: true,
+	button: true,
+	buttons: true,
+	clientX: true,
+	clientY: true,
+	offsetX: true,
+	offsetY: true,
+	pointerId: true,
+	pointerType: true,
+	screenX: true,
+	screenY: true,
+	targetTouches: true,
+	toElement: true,
+	touches: true,
+	which: true
+}, jQuery.event.addProp );
+
+jQuery.each( { focus: "focusin", blur: "focusout" }, function( type, delegateType ) {
+	jQuery.event.special[ type ] = {
+
+		// Utilize native event if possible so blur/focus sequence is correct
+		setup: function() {
+
+			// Claim the first handler
+			// dataPriv.set( this, "focus", ... )
+			// dataPriv.set( this, "blur", ... )
+			leverageNative( this, type, expectSync );
+
+			// Return false to allow normal processing in the caller
+			return false;
+		},
+		trigger: function() {
+
+			// Force setup before trigger
+			leverageNative( this, type );
+
+			// Return non-false to allow normal event-path propagation
+			return true;
+		},
+
+		// Suppress native focus or blur as it's already being fired
+		// in leverageNative.
+		_default: function() {
+			return true;
+		},
+
+		delegateType: delegateType
+	};
+} );
+
+// Create mouseenter/leave events using mouseover/out and event-time checks
+// so that event delegation works in jQuery.
+// Do the same for pointerenter/pointerleave and pointerover/pointerout
+//
+// Support: Safari 7 only
+// Safari sends mouseenter too often; see:
+// https://bugs.chromium.org/p/chromium/issues/detail?id=470258
+// for the description of the bug (it existed in older Chrome versions as well).
+jQuery.each( {
+	mouseenter: "mouseover",
+	mouseleave: "mouseout",
+	pointerenter: "pointerover",
+	pointerleave: "pointerout"
+}, function( orig, fix ) {
+	jQuery.event.special[ orig ] = {
+		delegateType: fix,
+		bindType: fix,
+
+		handle: function( event ) {
+			var ret,
+				target = this,
+				related = event.relatedTarget,
+				handleObj = event.handleObj;
+
+			// For mouseenter/leave call the handler if related is outside the target.
+			// NB: No relatedTarget if the mouse left/entered the browser window
+			if ( !related || ( related !== target && !jQuery.contains( target, related ) ) ) {
+				event.type = handleObj.origType;
+				ret = handleObj.handler.apply( this, arguments );
+				event.type = fix;
+			}
+			return ret;
+		}
+	};
+} );
+
+jQuery.fn.extend( {
+
+	on: function( types, selector, data, fn ) {
+		return on( this, types, selector, data, fn );
+	},
+	one: function( types, selector, data, fn ) {
+		return on( this, types, selector, data, fn, 1 );
+	},
+	off: function( types, selector, fn ) {
+		var handleObj, type;
+		if ( types && types.preventDefault && types.handleObj ) {
+
+			// ( event )  dispatched jQuery.Event
+			handleObj = types.handleObj;
+			jQuery( types.delegateTarget ).off(
+				handleObj.namespace ?
+					handleObj.origType + "." + handleObj.namespace :
+					handleObj.origType,
+				handleObj.selector,
+				handleObj.handler
+			);
+			return this;
+		}
+		if ( typeof types === "object" ) {
+
+			// ( types-object [, selector] )
+			for ( type in types ) {
+				this.off( type, selector, types[ type ] );
+			}
+			return this;
+		}
+		if ( selector === false || typeof selector === "function" ) {
+
+			// ( types [, fn] )
+			fn = selector;
+			selector = undefined;
+		}
+		if ( fn === false ) {
+			fn = returnFalse;
+		}
+		return this.each( function() {
+			jQuery.event.remove( this, types, fn, selector );
+		} );
+	}
+} );
+
+
+var
+
+	// Support: IE <=10 - 11, Edge 12 - 13 only
+	// In IE/Edge using regex groups here causes severe slowdowns.
+	// See https://connect.microsoft.com/IE/feedback/details/1736512/
+	rnoInnerhtml = /<script|<style|<link/i,
+
+	// checked="checked" or checked
+	rchecked = /checked\s*(?:[^=]|=\s*.checked.)/i,
+	rcleanScript = /^\s*<!(?:\[CDATA\[|--)|(?:\]\]|--)>\s*$/g;
+
+// Prefer a tbody over its parent table for containing new rows
+function manipulationTarget( elem, content ) {
+	if ( nodeName( elem, "table" ) &&
+		nodeName( content.nodeType !== 11 ? content : content.firstChild, "tr" ) ) {
+
+		return jQuery( elem ).children( "tbody" )[ 0 ] || elem;
+	}
+
+	return elem;
+}
+
+// Replace/restore the type attribute of script elements for safe DOM manipulation
+function disableScript( elem ) {
+	elem.type = ( elem.getAttribute( "type" ) !== null ) + "/" + elem.type;
+	return elem;
+}
+function restoreScript( elem ) {
+	if ( ( elem.type || "" ).slice( 0, 5 ) === "true/" ) {
+		elem.type = elem.type.slice( 5 );
+	} else {
+		elem.removeAttribute( "type" );
+	}
+
+	return elem;
+}
+
+function cloneCopyEvent( src, dest ) {
+	var i, l, type, pdataOld, udataOld, udataCur, events;
+
+	if ( dest.nodeType !== 1 ) {
+		return;
+	}
+
+	// 1. Copy private data: events, handlers, etc.
+	if ( dataPriv.hasData( src ) ) {
+		pdataOld = dataPriv.get( src );
+		events = pdataOld.events;
+
+		if ( events ) {
+			dataPriv.remove( dest, "handle events" );
+
+			for ( type in events ) {
+				for ( i = 0, l = events[ type ].length; i < l; i++ ) {
+					jQuery.event.add( dest, type, events[ type ][ i ] );
+				}
+			}
+		}
+	}
+
+	// 2. Copy user data
+	if ( dataUser.hasData( src ) ) {
+		udataOld = dataUser.access( src );
+		udataCur = jQuery.extend( {}, udataOld );
+
+		dataUser.set( dest, udataCur );
+	}
+}
+
+// Fix IE bugs, see support tests
+function fixInput( src, dest ) {
+	var nodeName = dest.nodeName.toLowerCase();
+
+	// Fails to persist the checked state of a cloned checkbox or radio button.
+	if ( nodeName === "input" && rcheckableType.test( src.type ) ) {
+		dest.checked = src.checked;
+
+	// Fails to return the selected option to the default selected state when cloning options
+	} else if ( nodeName === "input" || nodeName === "textarea" ) {
+		dest.defaultValue = src.defaultValue;
+	}
+}
+
+function domManip( collection, args, callback, ignored ) {
+
+	// Flatten any nested arrays
+	args = flat( args );
+
+	var fragment, first, scripts, hasScripts, node, doc,
+		i = 0,
+		l = collection.length,
+		iNoClone = l - 1,
+		value = args[ 0 ],
+		valueIsFunction = isFunction( value );
+
+	// We can't cloneNode fragments that contain checked, in WebKit
+	if ( valueIsFunction ||
+			( l > 1 && typeof value === "string" &&
+				!support.checkClone && rchecked.test( value ) ) ) {
+		return collection.each( function( index ) {
+			var self = collection.eq( index );
+			if ( valueIsFunction ) {
+				args[ 0 ] = value.call( this, index, self.html() );
+			}
+			domManip( self, args, callback, ignored );
+		} );
+	}
+
+	if ( l ) {
+		fragment = buildFragment( args, collection[ 0 ].ownerDocument, false, collection, ignored );
+		first = fragment.firstChild;
+
+		if ( fragment.childNodes.length === 1 ) {
+			fragment = first;
+		}
+
+		// Require either new content or an interest in ignored elements to invoke the callback
+		if ( first || ignored ) {
+			scripts = jQuery.map( getAll( fragment, "script" ), disableScript );
+			hasScripts = scripts.length;
+
+			// Use the original fragment for the last item
+			// instead of the first because it can end up
+			// being emptied incorrectly in certain situations (#8070).
+			for ( ; i < l; i++ ) {
+				node = fragment;
+
+				if ( i !== iNoClone ) {
+					node = jQuery.clone( node, true, true );
+
+					// Keep references to cloned scripts for later restoration
+					if ( hasScripts ) {
+
+						// Support: Android <=4.0 only, PhantomJS 1 only
+						// push.apply(_, arraylike) throws on ancient WebKit
+						jQuery.merge( scripts, getAll( node, "script" ) );
+					}
+				}
+
+				callback.call( collection[ i ], node, i );
+			}
+
+			if ( hasScripts ) {
+				doc = scripts[ scripts.length - 1 ].ownerDocument;
+
+				// Reenable scripts
+				jQuery.map( scripts, restoreScript );
+
+				// Evaluate executable scripts on first document insertion
+				for ( i = 0; i < hasScripts; i++ ) {
+					node = scripts[ i ];
+					if ( rscriptType.test( node.type || "" ) &&
+						!dataPriv.access( node, "globalEval" ) &&
+						jQuery.contains( doc, node ) ) {
+
+						if ( node.src && ( node.type || "" ).toLowerCase()  !== "module" ) {
+
+							// Optional AJAX dependency, but won't run scripts if not present
+							if ( jQuery._evalUrl && !node.noModule ) {
+								jQuery._evalUrl( node.src, {
+									nonce: node.nonce || node.getAttribute( "nonce" )
+								}, doc );
+							}
+						} else {
+							DOMEval( node.textContent.replace( rcleanScript, "" ), node, doc );
+						}
+					}
+				}
+			}
+		}
+	}
+
+	return collection;
+}
+
+function remove( elem, selector, keepData ) {
+	var node,
+		nodes = selector ? jQuery.filter( selector, elem ) : elem,
+		i = 0;
+
+	for ( ; ( node = nodes[ i ] ) != null; i++ ) {
+		if ( !keepData && node.nodeType === 1 ) {
+			jQuery.cleanData( getAll( node ) );
+		}
+
+		if ( node.parentNode ) {
+			if ( keepData && isAttached( node ) ) {
+				setGlobalEval( getAll( node, "script" ) );
+			}
+			node.parentNode.removeChild( node );
+		}
+	}
+
+	return elem;
+}
+
+jQuery.extend( {
+	htmlPrefilter: function( html ) {
+		return html;
+	},
+
+	clone: function( elem, dataAndEvents, deepDataAndEvents ) {
+		var i, l, srcElements, destElements,
+			clone = elem.cloneNode( true ),
+			inPage = isAttached( elem );
+
+		// Fix IE cloning issues
+		if ( !support.noCloneChecked && ( elem.nodeType === 1 || elem.nodeType === 11 ) &&
+				!jQuery.isXMLDoc( elem ) ) {
+
+			// We eschew Sizzle here for performance reasons: https://jsperf.com/getall-vs-sizzle/2
+			destElements = getAll( clone );
+			srcElements = getAll( elem );
+
+			for ( i = 0, l = srcElements.length; i < l; i++ ) {
+				fixInput( srcElements[ i ], destElements[ i ] );
+			}
+		}
+
+		// Copy the events from the original to the clone
+		if ( dataAndEvents ) {
+			if ( deepDataAndEvents ) {
+				srcElements = srcElements || getAll( elem );
+				destElements = destElements || getAll( clone );
+
+				for ( i = 0, l = srcElements.length; i < l; i++ ) {
+					cloneCopyEvent( srcElements[ i ], destElements[ i ] );
+				}
+			} else {
+				cloneCopyEvent( elem, clone );
+			}
+		}
+
+		// Preserve script evaluation history
+		destElements = getAll( clone, "script" );
+		if ( destElements.length > 0 ) {
+			setGlobalEval( destElements, !inPage && getAll( elem, "script" ) );
+		}
+
+		// Return the cloned set
+		return clone;
+	},
+
+	cleanData: function( elems ) {
+		var data, elem, type,
+			special = jQuery.event.special,
+			i = 0;
+
+		for ( ; ( elem = elems[ i ] ) !== undefined; i++ ) {
+			if ( acceptData( elem ) ) {
+				if ( ( data = elem[ dataPriv.expando ] ) ) {
+					if ( data.events ) {
+						for ( type in data.events ) {
+							if ( special[ type ] ) {
+								jQuery.event.remove( elem, type );
+
+							// This is a shortcut to avoid jQuery.event.remove's overhead
+							} else {
+								jQuery.removeEvent( elem, type, data.handle );
+							}
+						}
+					}
+
+					// Support: Chrome <=35 - 45+
+					// Assign undefined instead of using delete, see Data#remove
+					elem[ dataPriv.expando ] = undefined;
+				}
+				if ( elem[ dataUser.expando ] ) {
+
+					// Support: Chrome <=35 - 45+
+					// Assign undefined instead of using delete, see Data#remove
+					elem[ dataUser.expando ] = undefined;
+				}
+			}
+		}
+	}
+} );
+
+jQuery.fn.extend( {
+	detach: function( selector ) {
+		return remove( this, selector, true );
+	},
+
+	remove: function( selector ) {
+		return remove( this, selector );
+	},
+
+	text: function( value ) {
+		return access( this, function( value ) {
+			return value === undefined ?
+				jQuery.text( this ) :
+				this.empty().each( function() {
+					if ( this.nodeType === 1 || this.nodeType === 11 || this.nodeType === 9 ) {
+						this.textContent = value;
+					}
+				} );
+		}, null, value, arguments.length );
+	},
+
+	append: function() {
+		return domManip( this, arguments, function( elem ) {
+			if ( this.nodeType === 1 || this.nodeType === 11 || this.nodeType === 9 ) {
+				var target = manipulationTarget( this, elem );
+				target.appendChild( elem );
+			}
+		} );
+	},
+
+	prepend: function() {
+		return domManip( this, arguments, function( elem ) {
+			if ( this.nodeType === 1 || this.nodeType === 11 || this.nodeType === 9 ) {
+				var target = manipulationTarget( this, elem );
+				target.insertBefore( elem, target.firstChild );
+			}
+		} );
+	},
+
+	before: function() {
+		return domManip( this, arguments, function( elem ) {
+			if ( this.parentNode ) {
+				this.parentNode.insertBefore( elem, this );
+			}
+		} );
+	},
+
+	after: function() {
+		return domManip( this, arguments, function( elem ) {
+			if ( this.parentNode ) {
+				this.parentNode.insertBefore( elem, this.nextSibling );
+			}
+		} );
+	},
+
+	empty: function() {
+		var elem,
+			i = 0;
+
+		for ( ; ( elem = this[ i ] ) != null; i++ ) {
+			if ( elem.nodeType === 1 ) {
+
+				// Prevent memory leaks
+				jQuery.cleanData( getAll( elem, false ) );
+
+				// Remove any remaining nodes
+				elem.textContent = "";
+			}
+		}
+
+		return this;
+	},
+
+	clone: function( dataAndEvents, deepDataAndEvents ) {
+		dataAndEvents = dataAndEvents == null ? false : dataAndEvents;
+		deepDataAndEvents = deepDataAndEvents == null ? dataAndEvents : deepDataAndEvents;
+
+		return this.map( function() {
+			return jQuery.clone( this, dataAndEvents, deepDataAndEvents );
+		} );
+	},
+
+	html: function( value ) {
+		return access( this, function( value ) {
+			var elem = this[ 0 ] || {},
+				i = 0,
+				l = this.length;
+
+			if ( value === undefined && elem.nodeType === 1 ) {
+				return elem.innerHTML;
+			}
+
+			// See if we can take a shortcut and just use innerHTML
+			if ( typeof value === "string" && !rnoInnerhtml.test( value ) &&
+				!wrapMap[ ( rtagName.exec( value ) || [ "", "" ] )[ 1 ].toLowerCase() ] ) {
+
+				value = jQuery.htmlPrefilter( value );
+
+				try {
+					for ( ; i < l; i++ ) {
+						elem = this[ i ] || {};
+
+						// Remove element nodes and prevent memory leaks
+						if ( elem.nodeType === 1 ) {
+							jQuery.cleanData( getAll( elem, false ) );
+							elem.innerHTML = value;
+						}
+					}
+
+					elem = 0;
+
+				// If using innerHTML throws an exception, use the fallback method
+				} catch ( e ) {}
+			}
+
+			if ( elem ) {
+				this.empty().append( value );
+			}
+		}, null, value, arguments.length );
+	},
+
+	replaceWith: function() {
+		var ignored = [];
+
+		// Make the changes, replacing each non-ignored context element with the new content
+		return domManip( this, arguments, function( elem ) {
+			var parent = this.parentNode;
+
+			if ( jQuery.inArray( this, ignored ) < 0 ) {
+				jQuery.cleanData( getAll( this ) );
+				if ( parent ) {
+					parent.replaceChild( elem, this );
+				}
+			}
+
+		// Force callback invocation
+		}, ignored );
+	}
+} );
+
+jQuery.each( {
+	appendTo: "append",
+	prependTo: "prepend",
+	insertBefore: "before",
+	insertAfter: "after",
+	replaceAll: "replaceWith"
+}, function( name, original ) {
+	jQuery.fn[ name ] = function( selector ) {
+		var elems,
+			ret = [],
+			insert = jQuery( selector ),
+			last = insert.length - 1,
+			i = 0;
+
+		for ( ; i <= last; i++ ) {
+			elems = i === last ? this : this.clone( true );
+			jQuery( insert[ i ] )[ original ]( elems );
+
+			// Support: Android <=4.0 only, PhantomJS 1 only
+			// .get() because push.apply(_, arraylike) throws on ancient WebKit
+			push.apply( ret, elems.get() );
+		}
+
+		return this.pushStack( ret );
+	};
+} );
+var rnumnonpx = new RegExp( "^(" + pnum + ")(?!px)[a-z%]+$", "i" );
+
+var getStyles = function( elem ) {
+
+		// Support: IE <=11 only, Firefox <=30 (#15098, #14150)
+		// IE throws on elements created in popups
+		// FF meanwhile throws on frame elements through "defaultView.getComputedStyle"
+		var view = elem.ownerDocument.defaultView;
+
+		if ( !view || !view.opener ) {
+			view = window;
+		}
+
+		return view.getComputedStyle( elem );
+	};
+
+var swap = function( elem, options, callback ) {
+	var ret, name,
+		old = {};
+
+	// Remember the old values, and insert the new ones
+	for ( name in options ) {
+		old[ name ] = elem.style[ name ];
+		elem.style[ name ] = options[ name ];
+	}
+
+	ret = callback.call( elem );
+
+	// Revert the old values
+	for ( name in options ) {
+		elem.style[ name ] = old[ name ];
+	}
+
+	return ret;
+};
+
+
+var rboxStyle = new RegExp( cssExpand.join( "|" ), "i" );
+
+
+
+( function() {
+
+	// Executing both pixelPosition & boxSizingReliable tests require only one layout
+	// so they're executed at the same time to save the second computation.
+	function computeStyleTests() {
+
+		// This is a singleton, we need to execute it only once
+		if ( !div ) {
+			return;
+		}
+
+		container.style.cssText = "position:absolute;left:-11111px;width:60px;" +
+			"margin-top:1px;padding:0;border:0";
+		div.style.cssText =
+			"position:relative;display:block;box-sizing:border-box;overflow:scroll;" +
+			"margin:auto;border:1px;padding:1px;" +
+			"width:60%;top:1%";
+		documentElement.appendChild( container ).appendChild( div );
+
+		var divStyle = window.getComputedStyle( div );
+		pixelPositionVal = divStyle.top !== "1%";
+
+		// Support: Android 4.0 - 4.3 only, Firefox <=3 - 44
+		reliableMarginLeftVal = roundPixelMeasures( divStyle.marginLeft ) === 12;
+
+		// Support: Android 4.0 - 4.3 only, Safari <=9.1 - 10.1, iOS <=7.0 - 9.3
+		// Some styles come back with percentage values, even though they shouldn't
+		div.style.right = "60%";
+		pixelBoxStylesVal = roundPixelMeasures( divStyle.right ) === 36;
+
+		// Support: IE 9 - 11 only
+		// Detect misreporting of content dimensions for box-sizing:border-box elements
+		boxSizingReliableVal = roundPixelMeasures( divStyle.width ) === 36;
+
+		// Support: IE 9 only
+		// Detect overflow:scroll screwiness (gh-3699)
+		// Support: Chrome <=64
+		// Don't get tricked when zoom affects offsetWidth (gh-4029)
+		div.style.position = "absolute";
+		scrollboxSizeVal = roundPixelMeasures( div.offsetWidth / 3 ) === 12;
+
+		documentElement.removeChild( container );
+
+		// Nullify the div so it wouldn't be stored in the memory and
+		// it will also be a sign that checks already performed
+		div = null;
+	}
+
+	function roundPixelMeasures( measure ) {
+		return Math.round( parseFloat( measure ) );
+	}
+
+	var pixelPositionVal, boxSizingReliableVal, scrollboxSizeVal, pixelBoxStylesVal,
+		reliableTrDimensionsVal, reliableMarginLeftVal,
+		container = document.createElement( "div" ),
+		div = document.createElement( "div" );
+
+	// Finish early in limited (non-browser) environments
+	if ( !div.style ) {
+		return;
+	}
+
+	// Support: IE <=9 - 11 only
+	// Style of cloned element affects source element cloned (#8908)
+	div.style.backgroundClip = "content-box";
+	div.cloneNode( true ).style.backgroundClip = "";
+	support.clearCloneStyle = div.style.backgroundClip === "content-box";
+
+	jQuery.extend( support, {
+		boxSizingReliable: function() {
+			computeStyleTests();
+			return boxSizingReliableVal;
+		},
+		pixelBoxStyles: function() {
+			computeStyleTests();
+			return pixelBoxStylesVal;
+		},
+		pixelPosition: function() {
+			computeStyleTests();
+			return pixelPositionVal;
+		},
+		reliableMarginLeft: function() {
+			computeStyleTests();
+			return reliableMarginLeftVal;
+		},
+		scrollboxSize: function() {
+			computeStyleTests();
+			return scrollboxSizeVal;
+		},
+
+		// Support: IE 9 - 11+, Edge 15 - 18+
+		// IE/Edge misreport `getComputedStyle` of table rows with width/height
+		// set in CSS while `offset*` properties report correct values.
+		// Behavior in IE 9 is more subtle than in newer versions & it passes
+		// some versions of this test; make sure not to make it pass there!
+		//
+		// Support: Firefox 70+
+		// Only Firefox includes border widths
+		// in computed dimensions. (gh-4529)
+		reliableTrDimensions: function() {
+			var table, tr, trChild, trStyle;
+			if ( reliableTrDimensionsVal == null ) {
+				table = document.createElement( "table" );
+				tr = document.createElement( "tr" );
+				trChild = document.createElement( "div" );
+
+				table.style.cssText = "position:absolute;left:-11111px;border-collapse:separate";
+				tr.style.cssText = "border:1px solid";
+
+				// Support: Chrome 86+
+				// Height set through cssText does not get applied.
+				// Computed height then comes back as 0.
+				tr.style.height = "1px";
+				trChild.style.height = "9px";
+
+				// Support: Android 8 Chrome 86+
+				// In our bodyBackground.html iframe,
+				// display for all div elements is set to "inline",
+				// which causes a problem only in Android 8 Chrome 86.
+				// Ensuring the div is display: block
+				// gets around this issue.
+				trChild.style.display = "block";
+
+				documentElement
+					.appendChild( table )
+					.appendChild( tr )
+					.appendChild( trChild );
+
+				trStyle = window.getComputedStyle( tr );
+				reliableTrDimensionsVal = ( parseInt( trStyle.height, 10 ) +
+					parseInt( trStyle.borderTopWidth, 10 ) +
+					parseInt( trStyle.borderBottomWidth, 10 ) ) === tr.offsetHeight;
+
+				documentElement.removeChild( table );
+			}
+			return reliableTrDimensionsVal;
+		}
+	} );
+} )();
+
+
+function curCSS( elem, name, computed ) {
+	var width, minWidth, maxWidth, ret,
+
+		// Support: Firefox 51+
+		// Retrieving style before computed somehow
+		// fixes an issue with getting wrong values
+		// on detached elements
+		style = elem.style;
+
+	computed = computed || getStyles( elem );
+
+	// getPropertyValue is needed for:
+	//   .css('filter') (IE 9 only, #12537)
+	//   .css('--customProperty) (#3144)
+	if ( computed ) {
+		ret = computed.getPropertyValue( name ) || computed[ name ];
+
+		if ( ret === "" && !isAttached( elem ) ) {
+			ret = jQuery.style( elem, name );
+		}
+
+		// A tribute to the "awesome hack by Dean Edwards"
+		// Android Browser returns percentage for some values,
+		// but width seems to be reliably pixels.
+		// This is against the CSSOM draft spec:
+		// https://drafts.csswg.org/cssom/#resolved-values
+		if ( !support.pixelBoxStyles() && rnumnonpx.test( ret ) && rboxStyle.test( name ) ) {
+
+			// Remember the original values
+			width = style.width;
+			minWidth = style.minWidth;
+			maxWidth = style.maxWidth;
+
+			// Put in the new values to get a computed value out
+			style.minWidth = style.maxWidth = style.width = ret;
+			ret = computed.width;
+
+			// Revert the changed values
+			style.width = width;
+			style.minWidth = minWidth;
+			style.maxWidth = maxWidth;
+		}
+	}
+
+	return ret !== undefined ?
+
+		// Support: IE <=9 - 11 only
+		// IE returns zIndex value as an integer.
+		ret + "" :
+		ret;
+}
+
+
+function addGetHookIf( conditionFn, hookFn ) {
+
+	// Define the hook, we'll check on the first run if it's really needed.
+	return {
+		get: function() {
+			if ( conditionFn() ) {
+
+				// Hook not needed (or it's not possible to use it due
+				// to missing dependency), remove it.
+				delete this.get;
+				return;
+			}
+
+			// Hook needed; redefine it so that the support test is not executed again.
+			return ( this.get = hookFn ).apply( this, arguments );
+		}
+	};
+}
+
+
+var cssPrefixes = [ "Webkit", "Moz", "ms" ],
+	emptyStyle = document.createElement( "div" ).style,
+	vendorProps = {};
+
+// Return a vendor-prefixed property or undefined
+function vendorPropName( name ) {
+
+	// Check for vendor prefixed names
+	var capName = name[ 0 ].toUpperCase() + name.slice( 1 ),
+		i = cssPrefixes.length;
+
+	while ( i-- ) {
+		name = cssPrefixes[ i ] + capName;
+		if ( name in emptyStyle ) {
+			return name;
+		}
+	}
+}
+
+// Return a potentially-mapped jQuery.cssProps or vendor prefixed property
+function finalPropName( name ) {
+	var final = jQuery.cssProps[ name ] || vendorProps[ name ];
+
+	if ( final ) {
+		return final;
+	}
+	if ( name in emptyStyle ) {
+		return name;
+	}
+	return vendorProps[ name ] = vendorPropName( name ) || name;
+}
+
+
+var
+
+	// Swappable if display is none or starts with table
+	// except "table", "table-cell", or "table-caption"
+	// See here for display values: https://developer.mozilla.org/en-US/docs/CSS/display
+	rdisplayswap = /^(none|table(?!-c[ea]).+)/,
+	rcustomProp = /^--/,
+	cssShow = { position: "absolute", visibility: "hidden", display: "block" },
+	cssNormalTransform = {
+		letterSpacing: "0",
+		fontWeight: "400"
+	};
+
+function setPositiveNumber( _elem, value, subtract ) {
+
+	// Any relative (+/-) values have already been
+	// normalized at this point
+	var matches = rcssNum.exec( value );
+	return matches ?
+
+		// Guard against undefined "subtract", e.g., when used as in cssHooks
+		Math.max( 0, matches[ 2 ] - ( subtract || 0 ) ) + ( matches[ 3 ] || "px" ) :
+		value;
+}
+
+function boxModelAdjustment( elem, dimension, box, isBorderBox, styles, computedVal ) {
+	var i = dimension === "width" ? 1 : 0,
+		extra = 0,
+		delta = 0;
+
+	// Adjustment may not be necessary
+	if ( box === ( isBorderBox ? "border" : "content" ) ) {
+		return 0;
+	}
+
+	for ( ; i < 4; i += 2 ) {
+
+		// Both box models exclude margin
+		if ( box === "margin" ) {
+			delta += jQuery.css( elem, box + cssExpand[ i ], true, styles );
+		}
+
+		// If we get here with a content-box, we're seeking "padding" or "border" or "margin"
+		if ( !isBorderBox ) {
+
+			// Add padding
+			delta += jQuery.css( elem, "padding" + cssExpand[ i ], true, styles );
+
+			// For "border" or "margin", add border
+			if ( box !== "padding" ) {
+				delta += jQuery.css( elem, "border" + cssExpand[ i ] + "Width", true, styles );
+
+			// But still keep track of it otherwise
+			} else {
+				extra += jQuery.css( elem, "border" + cssExpand[ i ] + "Width", true, styles );
+			}
+
+		// If we get here with a border-box (content + padding + border), we're seeking "content" or
+		// "padding" or "margin"
+		} else {
+
+			// For "content", subtract padding
+			if ( box === "content" ) {
+				delta -= jQuery.css( elem, "padding" + cssExpand[ i ], true, styles );
+			}
+
+			// For "content" or "padding", subtract border
+			if ( box !== "margin" ) {
+				delta -= jQuery.css( elem, "border" + cssExpand[ i ] + "Width", true, styles );
+			}
+		}
+	}
+
+	// Account for positive content-box scroll gutter when requested by providing computedVal
+	if ( !isBorderBox && computedVal >= 0 ) {
+
+		// offsetWidth/offsetHeight is a rounded sum of content, padding, scroll gutter, and border
+		// Assuming integer scroll gutter, subtract the rest and round down
+		delta += Math.max( 0, Math.ceil(
+			elem[ "offset" + dimension[ 0 ].toUpperCase() + dimension.slice( 1 ) ] -
+			computedVal -
+			delta -
+			extra -
+			0.5
+
+		// If offsetWidth/offsetHeight is unknown, then we can't determine content-box scroll gutter
+		// Use an explicit zero to avoid NaN (gh-3964)
+		) ) || 0;
+	}
+
+	return delta;
+}
+
+function getWidthOrHeight( elem, dimension, extra ) {
+
+	// Start with computed style
+	var styles = getStyles( elem ),
+
+		// To avoid forcing a reflow, only fetch boxSizing if we need it (gh-4322).
+		// Fake content-box until we know it's needed to know the true value.
+		boxSizingNeeded = !support.boxSizingReliable() || extra,
+		isBorderBox = boxSizingNeeded &&
+			jQuery.css( elem, "boxSizing", false, styles ) === "border-box",
+		valueIsBorderBox = isBorderBox,
+
+		val = curCSS( elem, dimension, styles ),
+		offsetProp = "offset" + dimension[ 0 ].toUpperCase() + dimension.slice( 1 );
+
+	// Support: Firefox <=54
+	// Return a confounding non-pixel value or feign ignorance, as appropriate.
+	if ( rnumnonpx.test( val ) ) {
+		if ( !extra ) {
+			return val;
+		}
+		val = "auto";
+	}
+
+
+	// Support: IE 9 - 11 only
+	// Use offsetWidth/offsetHeight for when box sizing is unreliable.
+	// In those cases, the computed value can be trusted to be border-box.
+	if ( ( !support.boxSizingReliable() && isBorderBox ||
+
+		// Support: IE 10 - 11+, Edge 15 - 18+
+		// IE/Edge misreport `getComputedStyle` of table rows with width/height
+		// set in CSS while `offset*` properties report correct values.
+		// Interestingly, in some cases IE 9 doesn't suffer from this issue.
+		!support.reliableTrDimensions() && nodeName( elem, "tr" ) ||
+
+		// Fall back to offsetWidth/offsetHeight when value is "auto"
+		// This happens for inline elements with no explicit setting (gh-3571)
+		val === "auto" ||
+
+		// Support: Android <=4.1 - 4.3 only
+		// Also use offsetWidth/offsetHeight for misreported inline dimensions (gh-3602)
+		!parseFloat( val ) && jQuery.css( elem, "display", false, styles ) === "inline" ) &&
+
+		// Make sure the element is visible & connected
+		elem.getClientRects().length ) {
+
+		isBorderBox = jQuery.css( elem, "boxSizing", false, styles ) === "border-box";
+
+		// Where available, offsetWidth/offsetHeight approximate border box dimensions.
+		// Where not available (e.g., SVG), assume unreliable box-sizing and interpret the
+		// retrieved value as a content box dimension.
+		valueIsBorderBox = offsetProp in elem;
+		if ( valueIsBorderBox ) {
+			val = elem[ offsetProp ];
+		}
+	}
+
+	// Normalize "" and auto
+	val = parseFloat( val ) || 0;
+
+	// Adjust for the element's box model
+	return ( val +
+		boxModelAdjustment(
+			elem,
+			dimension,
+			extra || ( isBorderBox ? "border" : "content" ),
+			valueIsBorderBox,
+			styles,
+
+			// Provide the current computed size to request scroll gutter calculation (gh-3589)
+			val
+		)
+	) + "px";
+}
+
+jQuery.extend( {
+
+	// Add in style property hooks for overriding the default
+	// behavior of getting and setting a style property
+	cssHooks: {
+		opacity: {
+			get: function( elem, computed ) {
+				if ( computed ) {
+
+					// We should always get a number back from opacity
+					var ret = curCSS( elem, "opacity" );
+					return ret === "" ? "1" : ret;
+				}
+			}
+		}
+	},
+
+	// Don't automatically add "px" to these possibly-unitless properties
+	cssNumber: {
+		"animationIterationCount": true,
+		"columnCount": true,
+		"fillOpacity": true,
+		"flexGrow": true,
+		"flexShrink": true,
+		"fontWeight": true,
+		"gridArea": true,
+		"gridColumn": true,
+		"gridColumnEnd": true,
+		"gridColumnStart": true,
+		"gridRow": true,
+		"gridRowEnd": true,
+		"gridRowStart": true,
+		"lineHeight": true,
+		"opacity": true,
+		"order": true,
+		"orphans": true,
+		"widows": true,
+		"zIndex": true,
+		"zoom": true
+	},
+
+	// Add in properties whose names you wish to fix before
+	// setting or getting the value
+	cssProps: {},
+
+	// Get and set the style property on a DOM Node
+	style: function( elem, name, value, extra ) {
+
+		// Don't set styles on text and comment nodes
+		if ( !elem || elem.nodeType === 3 || elem.nodeType === 8 || !elem.style ) {
+			return;
+		}
+
+		// Make sure that we're working with the right name
+		var ret, type, hooks,
+			origName = camelCase( name ),
+			isCustomProp = rcustomProp.test( name ),
+			style = elem.style;
+
+		// Make sure that we're working with the right name. We don't
+		// want to query the value if it is a CSS custom property
+		// since they are user-defined.
+		if ( !isCustomProp ) {
+			name = finalPropName( origName );
+		}
+
+		// Gets hook for the prefixed version, then unprefixed version
+		hooks = jQuery.cssHooks[ name ] || jQuery.cssHooks[ origName ];
+
+		// Check if we're setting a value
+		if ( value !== undefined ) {
+			type = typeof value;
+
+			// Convert "+=" or "-=" to relative numbers (#7345)
+			if ( type === "string" && ( ret = rcssNum.exec( value ) ) && ret[ 1 ] ) {
+				value = adjustCSS( elem, name, ret );
+
+				// Fixes bug #9237
+				type = "number";
+			}
+
+			// Make sure that null and NaN values aren't set (#7116)
+			if ( value == null || value !== value ) {
+				return;
+			}
+
+			// If a number was passed in, add the unit (except for certain CSS properties)
+			// The isCustomProp check can be removed in jQuery 4.0 when we only auto-append
+			// "px" to a few hardcoded values.
+			if ( type === "number" && !isCustomProp ) {
+				value += ret && ret[ 3 ] || ( jQuery.cssNumber[ origName ] ? "" : "px" );
+			}
+
+			// background-* props affect original clone's values
+			if ( !support.clearCloneStyle && value === "" && name.indexOf( "background" ) === 0 ) {
+				style[ name ] = "inherit";
+			}
+
+			// If a hook was provided, use that value, otherwise just set the specified value
+			if ( !hooks || !( "set" in hooks ) ||
+				( value = hooks.set( elem, value, extra ) ) !== undefined ) {
+
+				if ( isCustomProp ) {
+					style.setProperty( name, value );
+				} else {
+					style[ name ] = value;
+				}
+			}
+
+		} else {
+
+			// If a hook was provided get the non-computed value from there
+			if ( hooks && "get" in hooks &&
+				( ret = hooks.get( elem, false, extra ) ) !== undefined ) {
+
+				return ret;
+			}
+
+			// Otherwise just get the value from the style object
+			return style[ name ];
+		}
+	},
+
+	css: function( elem, name, extra, styles ) {
+		var val, num, hooks,
+			origName = camelCase( name ),
+			isCustomProp = rcustomProp.test( name );
+
+		// Make sure that we're working with the right name. We don't
+		// want to modify the value if it is a CSS custom property
+		// since they are user-defined.
+		if ( !isCustomProp ) {
+			name = finalPropName( origName );
+		}
+
+		// Try prefixed name followed by the unprefixed name
+		hooks = jQuery.cssHooks[ name ] || jQuery.cssHooks[ origName ];
+
+		// If a hook was provided get the computed value from there
+		if ( hooks && "get" in hooks ) {
+			val = hooks.get( elem, true, extra );
+		}
+
+		// Otherwise, if a way to get the computed value exists, use that
+		if ( val === undefined ) {
+			val = curCSS( elem, name, styles );
+		}
+
+		// Convert "normal" to computed value
+		if ( val === "normal" && name in cssNormalTransform ) {
+			val = cssNormalTransform[ name ];
+		}
+
+		// Make numeric if forced or a qualifier was provided and val looks numeric
+		if ( extra === "" || extra ) {
+			num = parseFloat( val );
+			return extra === true || isFinite( num ) ? num || 0 : val;
+		}
+
+		return val;
+	}
+} );
+
+jQuery.each( [ "height", "width" ], function( _i, dimension ) {
+	jQuery.cssHooks[ dimension ] = {
+		get: function( elem, computed, extra ) {
+			if ( computed ) {
+
+				// Certain elements can have dimension info if we invisibly show them
+				// but it must have a current display style that would benefit
+				return rdisplayswap.test( jQuery.css( elem, "display" ) ) &&
+
+					// Support: Safari 8+
+					// Table columns in Safari have non-zero offsetWidth & zero
+					// getBoundingClientRect().width unless display is changed.
+					// Support: IE <=11 only
+					// Running getBoundingClientRect on a disconnected node
+					// in IE throws an error.
+					( !elem.getClientRects().length || !elem.getBoundingClientRect().width ) ?
+					swap( elem, cssShow, function() {
+						return getWidthOrHeight( elem, dimension, extra );
+					} ) :
+					getWidthOrHeight( elem, dimension, extra );
+			}
+		},
+
+		set: function( elem, value, extra ) {
+			var matches,
+				styles = getStyles( elem ),
+
+				// Only read styles.position if the test has a chance to fail
+				// to avoid forcing a reflow.
+				scrollboxSizeBuggy = !support.scrollboxSize() &&
+					styles.position === "absolute",
+
+				// To avoid forcing a reflow, only fetch boxSizing if we need it (gh-3991)
+				boxSizingNeeded = scrollboxSizeBuggy || extra,
+				isBorderBox = boxSizingNeeded &&
+					jQuery.css( elem, "boxSizing", false, styles ) === "border-box",
+				subtract = extra ?
+					boxModelAdjustment(
+						elem,
+						dimension,
+						extra,
+						isBorderBox,
+						styles
+					) :
+					0;
+
+			// Account for unreliable border-box dimensions by comparing offset* to computed and
+			// faking a content-box to get border and padding (gh-3699)
+			if ( isBorderBox && scrollboxSizeBuggy ) {
+				subtract -= Math.ceil(
+					elem[ "offset" + dimension[ 0 ].toUpperCase() + dimension.slice( 1 ) ] -
+					parseFloat( styles[ dimension ] ) -
+					boxModelAdjustment( elem, dimension, "border", false, styles ) -
+					0.5
+				);
+			}
+
+			// Convert to pixels if value adjustment is needed
+			if ( subtract && ( matches = rcssNum.exec( value ) ) &&
+				( matches[ 3 ] || "px" ) !== "px" ) {
+
+				elem.style[ dimension ] = value;
+				value = jQuery.css( elem, dimension );
+			}
+
+			return setPositiveNumber( elem, value, subtract );
+		}
+	};
+} );
+
+jQuery.cssHooks.marginLeft = addGetHookIf( support.reliableMarginLeft,
+	function( elem, computed ) {
+		if ( computed ) {
+			return ( parseFloat( curCSS( elem, "marginLeft" ) ) ||
+				elem.getBoundingClientRect().left -
+					swap( elem, { marginLeft: 0 }, function() {
+						return elem.getBoundingClientRect().left;
+					} )
+			) + "px";
+		}
+	}
+);
+
+// These hooks are used by animate to expand properties
+jQuery.each( {
+	margin: "",
+	padding: "",
+	border: "Width"
+}, function( prefix, suffix ) {
+	jQuery.cssHooks[ prefix + suffix ] = {
+		expand: function( value ) {
+			var i = 0,
+				expanded = {},
+
+				// Assumes a single number if not a string
+				parts = typeof value === "string" ? value.split( " " ) : [ value ];
+
+			for ( ; i < 4; i++ ) {
+				expanded[ prefix + cssExpand[ i ] + suffix ] =
+					parts[ i ] || parts[ i - 2 ] || parts[ 0 ];
+			}
+
+			return expanded;
+		}
+	};
+
+	if ( prefix !== "margin" ) {
+		jQuery.cssHooks[ prefix + suffix ].set = setPositiveNumber;
+	}
+} );
+
+jQuery.fn.extend( {
+	css: function( name, value ) {
+		return access( this, function( elem, name, value ) {
+			var styles, len,
+				map = {},
+				i = 0;
+
+			if ( Array.isArray( name ) ) {
+				styles = getStyles( elem );
+				len = name.length;
+
+				for ( ; i < len; i++ ) {
+					map[ name[ i ] ] = jQuery.css( elem, name[ i ], false, styles );
+				}
+
+				return map;
+			}
+
+			return value !== undefined ?
+				jQuery.style( elem, name, value ) :
+				jQuery.css( elem, name );
+		}, name, value, arguments.length > 1 );
+	}
+} );
+
+
+function Tween( elem, options, prop, end, easing ) {
+	return new Tween.prototype.init( elem, options, prop, end, easing );
+}
+jQuery.Tween = Tween;
+
+Tween.prototype = {
+	constructor: Tween,
+	init: function( elem, options, prop, end, easing, unit ) {
+		this.elem = elem;
+		this.prop = prop;
+		this.easing = easing || jQuery.easing._default;
+		this.options = options;
+		this.start = this.now = this.cur();
+		this.end = end;
+		this.unit = unit || ( jQuery.cssNumber[ prop ] ? "" : "px" );
+	},
+	cur: function() {
+		var hooks = Tween.propHooks[ this.prop ];
+
+		return hooks && hooks.get ?
+			hooks.get( this ) :
+			Tween.propHooks._default.get( this );
+	},
+	run: function( percent ) {
+		var eased,
+			hooks = Tween.propHooks[ this.prop ];
+
+		if ( this.options.duration ) {
+			this.pos = eased = jQuery.easing[ this.easing ](
+				percent, this.options.duration * percent, 0, 1, this.options.duration
+			);
+		} else {
+			this.pos = eased = percent;
+		}
+		this.now = ( this.end - this.start ) * eased + this.start;
+
+		if ( this.options.step ) {
+			this.options.step.call( this.elem, this.now, this );
+		}
+
+		if ( hooks && hooks.set ) {
+			hooks.set( this );
+		} else {
+			Tween.propHooks._default.set( this );
+		}
+		return this;
+	}
+};
+
+Tween.prototype.init.prototype = Tween.prototype;
+
+Tween.propHooks = {
+	_default: {
+		get: function( tween ) {
+			var result;
+
+			// Use a property on the element directly when it is not a DOM element,
+			// or when there is no matching style property that exists.
+			if ( tween.elem.nodeType !== 1 ||
+				tween.elem[ tween.prop ] != null && tween.elem.style[ tween.prop ] == null ) {
+				return tween.elem[ tween.prop ];
+			}
+
+			// Passing an empty string as a 3rd parameter to .css will automatically
+			// attempt a parseFloat and fallback to a string if the parse fails.
+			// Simple values such as "10px" are parsed to Float;
+			// complex values such as "rotate(1rad)" are returned as-is.
+			result = jQuery.css( tween.elem, tween.prop, "" );
+
+			// Empty strings, null, undefined and "auto" are converted to 0.
+			return !result || result === "auto" ? 0 : result;
+		},
+		set: function( tween ) {
+
+			// Use step hook for back compat.
+			// Use cssHook if its there.
+			// Use .style if available and use plain properties where available.
+			if ( jQuery.fx.step[ tween.prop ] ) {
+				jQuery.fx.step[ tween.prop ]( tween );
+			} else if ( tween.elem.nodeType === 1 && (
+				jQuery.cssHooks[ tween.prop ] ||
+					tween.elem.style[ finalPropName( tween.prop ) ] != null ) ) {
+				jQuery.style( tween.elem, tween.prop, tween.now + tween.unit );
+			} else {
+				tween.elem[ tween.prop ] = tween.now;
+			}
+		}
+	}
+};
+
+// Support: IE <=9 only
+// Panic based approach to setting things on disconnected nodes
+Tween.propHooks.scrollTop = Tween.propHooks.scrollLeft = {
+	set: function( tween ) {
+		if ( tween.elem.nodeType && tween.elem.parentNode ) {
+			tween.elem[ tween.prop ] = tween.now;
+		}
+	}
+};
+
+jQuery.easing = {
+	linear: function( p ) {
+		return p;
+	},
+	swing: function( p ) {
+		return 0.5 - Math.cos( p * Math.PI ) / 2;
+	},
+	_default: "swing"
+};
+
+jQuery.fx = Tween.prototype.init;
+
+// Back compat <1.8 extension point
+jQuery.fx.step = {};
+
+
+
+
+var
+	fxNow, inProgress,
+	rfxtypes = /^(?:toggle|show|hide)$/,
+	rrun = /queueHooks$/;
+
+function schedule() {
+	if ( inProgress ) {
+		if ( document.hidden === false && window.requestAnimationFrame ) {
+			window.requestAnimationFrame( schedule );
+		} else {
+			window.setTimeout( schedule, jQuery.fx.interval );
+		}
+
+		jQuery.fx.tick();
+	}
+}
+
+// Animations created synchronously will run synchronously
+function createFxNow() {
+	window.setTimeout( function() {
+		fxNow = undefined;
+	} );
+	return ( fxNow = Date.now() );
+}
+
+// Generate parameters to create a standard animation
+function genFx( type, includeWidth ) {
+	var which,
+		i = 0,
+		attrs = { height: type };
+
+	// If we include width, step value is 1 to do all cssExpand values,
+	// otherwise step value is 2 to skip over Left and Right
+	includeWidth = includeWidth ? 1 : 0;
+	for ( ; i < 4; i += 2 - includeWidth ) {
+		which = cssExpand[ i ];
+		attrs[ "margin" + which ] = attrs[ "padding" + which ] = type;
+	}
+
+	if ( includeWidth ) {
+		attrs.opacity = attrs.width = type;
+	}
+
+	return attrs;
+}
+
+function createTween( value, prop, animation ) {
+	var tween,
+		collection = ( Animation.tweeners[ prop ] || [] ).concat( Animation.tweeners[ "*" ] ),
+		index = 0,
+		length = collection.length;
+	for ( ; index < length; index++ ) {
+		if ( ( tween = collection[ index ].call( animation, prop, value ) ) ) {
+
+			// We're done with this property
+			return tween;
+		}
+	}
+}
+
+function defaultPrefilter( elem, props, opts ) {
+	var prop, value, toggle, hooks, oldfire, propTween, restoreDisplay, display,
+		isBox = "width" in props || "height" in props,
+		anim = this,
+		orig = {},
+		style = elem.style,
+		hidden = elem.nodeType && isHiddenWithinTree( elem ),
+		dataShow = dataPriv.get( elem, "fxshow" );
+
+	// Queue-skipping animations hijack the fx hooks
+	if ( !opts.queue ) {
+		hooks = jQuery._queueHooks( elem, "fx" );
+		if ( hooks.unqueued == null ) {
+			hooks.unqueued = 0;
+			oldfire = hooks.empty.fire;
+			hooks.empty.fire = function() {
+				if ( !hooks.unqueued ) {
+					oldfire();
+				}
+			};
+		}
+		hooks.unqueued++;
+
+		anim.always( function() {
+
+			// Ensure the complete handler is called before this completes
+			anim.always( function() {
+				hooks.unqueued--;
+				if ( !jQuery.queue( elem, "fx" ).length ) {
+					hooks.empty.fire();
+				}
+			} );
+		} );
+	}
+
+	// Detect show/hide animations
+	for ( prop in props ) {
+		value = props[ prop ];
+		if ( rfxtypes.test( value ) ) {
+			delete props[ prop ];
+			toggle = toggle || value === "toggle";
+			if ( value === ( hidden ? "hide" : "show" ) ) {
+
+				// Pretend to be hidden if this is a "show" and
+				// there is still data from a stopped show/hide
+				if ( value === "show" && dataShow && dataShow[ prop ] !== undefined ) {
+					hidden = true;
+
+				// Ignore all other no-op show/hide data
+				} else {
+					continue;
+				}
+			}
+			orig[ prop ] = dataShow && dataShow[ prop ] || jQuery.style( elem, prop );
+		}
+	}
+
+	// Bail out if this is a no-op like .hide().hide()
+	propTween = !jQuery.isEmptyObject( props );
+	if ( !propTween && jQuery.isEmptyObject( orig ) ) {
+		return;
+	}
+
+	// Restrict "overflow" and "display" styles during box animations
+	if ( isBox && elem.nodeType === 1 ) {
+
+		// Support: IE <=9 - 11, Edge 12 - 15
+		// Record all 3 overflow attributes because IE does not infer the shorthand
+		// from identically-valued overflowX and overflowY and Edge just mirrors
+		// the overflowX value there.
+		opts.overflow = [ style.overflow, style.overflowX, style.overflowY ];
+
+		// Identify a display type, preferring old show/hide data over the CSS cascade
+		restoreDisplay = dataShow && dataShow.display;
+		if ( restoreDisplay == null ) {
+			restoreDisplay = dataPriv.get( elem, "display" );
+		}
+		display = jQuery.css( elem, "display" );
+		if ( display === "none" ) {
+			if ( restoreDisplay ) {
+				display = restoreDisplay;
+			} else {
+
+				// Get nonempty value(s) by temporarily forcing visibility
+				showHide( [ elem ], true );
+				restoreDisplay = elem.style.display || restoreDisplay;
+				display = jQuery.css( elem, "display" );
+				showHide( [ elem ] );
+			}
+		}
+
+		// Animate inline elements as inline-block
+		if ( display === "inline" || display === "inline-block" && restoreDisplay != null ) {
+			if ( jQuery.css( elem, "float" ) === "none" ) {
+
+				// Restore the original display value at the end of pure show/hide animations
+				if ( !propTween ) {
+					anim.done( function() {
+						style.display = restoreDisplay;
+					} );
+					if ( restoreDisplay == null ) {
+						display = style.display;
+						restoreDisplay = display === "none" ? "" : display;
+					}
+				}
+				style.display = "inline-block";
+			}
+		}
+	}
+
+	if ( opts.overflow ) {
+		style.overflow = "hidden";
+		anim.always( function() {
+			style.overflow = opts.overflow[ 0 ];
+			style.overflowX = opts.overflow[ 1 ];
+			style.overflowY = opts.overflow[ 2 ];
+		} );
+	}
+
+	// Implement show/hide animations
+	propTween = false;
+	for ( prop in orig ) {
+
+		// General show/hide setup for this element animation
+		if ( !propTween ) {
+			if ( dataShow ) {
+				if ( "hidden" in dataShow ) {
+					hidden = dataShow.hidden;
+				}
+			} else {
+				dataShow = dataPriv.access( elem, "fxshow", { display: restoreDisplay } );
+			}
+
+			// Store hidden/visible for toggle so `.stop().toggle()` "reverses"
+			if ( toggle ) {
+				dataShow.hidden = !hidden;
+			}
+
+			// Show elements before animating them
+			if ( hidden ) {
+				showHide( [ elem ], true );
+			}
+
+			/* eslint-disable no-loop-func */
+
+			anim.done( function() {
+
+				/* eslint-enable no-loop-func */
+
+				// The final step of a "hide" animation is actually hiding the element
+				if ( !hidden ) {
+					showHide( [ elem ] );
+				}
+				dataPriv.remove( elem, "fxshow" );
+				for ( prop in orig ) {
+					jQuery.style( elem, prop, orig[ prop ] );
+				}
+			} );
+		}
+
+		// Per-property setup
+		propTween = createTween( hidden ? dataShow[ prop ] : 0, prop, anim );
+		if ( !( prop in dataShow ) ) {
+			dataShow[ prop ] = propTween.start;
+			if ( hidden ) {
+				propTween.end = propTween.start;
+				propTween.start = 0;
+			}
+		}
+	}
+}
+
+function propFilter( props, specialEasing ) {
+	var index, name, easing, value, hooks;
+
+	// camelCase, specialEasing and expand cssHook pass
+	for ( index in props ) {
+		name = camelCase( index );
+		easing = specialEasing[ name ];
+		value = props[ index ];
+		if ( Array.isArray( value ) ) {
+			easing = value[ 1 ];
+			value = props[ index ] = value[ 0 ];
+		}
+
+		if ( index !== name ) {
+			props[ name ] = value;
+			delete props[ index ];
+		}
+
+		hooks = jQuery.cssHooks[ name ];
+		if ( hooks && "expand" in hooks ) {
+			value = hooks.expand( value );
+			delete props[ name ];
+
+			// Not quite $.extend, this won't overwrite existing keys.
+			// Reusing 'index' because we have the correct "name"
+			for ( index in value ) {
+				if ( !( index in props ) ) {
+					props[ index ] = value[ index ];
+					specialEasing[ index ] = easing;
+				}
+			}
+		} else {
+			specialEasing[ name ] = easing;
+		}
+	}
+}
+
+function Animation( elem, properties, options ) {
+	var result,
+		stopped,
+		index = 0,
+		length = Animation.prefilters.length,
+		deferred = jQuery.Deferred().always( function() {
+
+			// Don't match elem in the :animated selector
+			delete tick.elem;
+		} ),
+		tick = function() {
+			if ( stopped ) {
+				return false;
+			}
+			var currentTime = fxNow || createFxNow(),
+				remaining = Math.max( 0, animation.startTime + animation.duration - currentTime ),
+
+				// Support: Android 2.3 only
+				// Archaic crash bug won't allow us to use `1 - ( 0.5 || 0 )` (#12497)
+				temp = remaining / animation.duration || 0,
+				percent = 1 - temp,
+				index = 0,
+				length = animation.tweens.length;
+
+			for ( ; index < length; index++ ) {
+				animation.tweens[ index ].run( percent );
+			}
+
+			deferred.notifyWith( elem, [ animation, percent, remaining ] );
+
+			// If there's more to do, yield
+			if ( percent < 1 && length ) {
+				return remaining;
+			}
+
+			// If this was an empty animation, synthesize a final progress notification
+			if ( !length ) {
+				deferred.notifyWith( elem, [ animation, 1, 0 ] );
+			}
+
+			// Resolve the animation and report its conclusion
+			deferred.resolveWith( elem, [ animation ] );
+			return false;
+		},
+		animation = deferred.promise( {
+			elem: elem,
+			props: jQuery.extend( {}, properties ),
+			opts: jQuery.extend( true, {
+				specialEasing: {},
+				easing: jQuery.easing._default
+			}, options ),
+			originalProperties: properties,
+			originalOptions: options,
+			startTime: fxNow || createFxNow(),
+			duration: options.duration,
+			tweens: [],
+			createTween: function( prop, end ) {
+				var tween = jQuery.Tween( elem, animation.opts, prop, end,
+					animation.opts.specialEasing[ prop ] || animation.opts.easing );
+				animation.tweens.push( tween );
+				return tween;
+			},
+			stop: function( gotoEnd ) {
+				var index = 0,
+
+					// If we are going to the end, we want to run all the tweens
+					// otherwise we skip this part
+					length = gotoEnd ? animation.tweens.length : 0;
+				if ( stopped ) {
+					return this;
+				}
+				stopped = true;
+				for ( ; index < length; index++ ) {
+					animation.tweens[ index ].run( 1 );
+				}
+
+				// Resolve when we played the last frame; otherwise, reject
+				if ( gotoEnd ) {
+					deferred.notifyWith( elem, [ animation, 1, 0 ] );
+					deferred.resolveWith( elem, [ animation, gotoEnd ] );
+				} else {
+					deferred.rejectWith( elem, [ animation, gotoEnd ] );
+				}
+				return this;
+			}
+		} ),
+		props = animation.props;
+
+	propFilter( props, animation.opts.specialEasing );
+
+	for ( ; index < length; index++ ) {
+		result = Animation.prefilters[ index ].call( animation, elem, props, animation.opts );
+		if ( result ) {
+			if ( isFunction( result.stop ) ) {
+				jQuery._queueHooks( animation.elem, animation.opts.queue ).stop =
+					result.stop.bind( result );
+			}
+			return result;
+		}
+	}
+
+	jQuery.map( props, createTween, animation );
+
+	if ( isFunction( animation.opts.start ) ) {
+		animation.opts.start.call( elem, animation );
+	}
+
+	// Attach callbacks from options
+	animation
+		.progress( animation.opts.progress )
+		.done( animation.opts.done, animation.opts.complete )
+		.fail( animation.opts.fail )
+		.always( animation.opts.always );
+
+	jQuery.fx.timer(
+		jQuery.extend( tick, {
+			elem: elem,
+			anim: animation,
+			queue: animation.opts.queue
+		} )
+	);
+
+	return animation;
+}
+
+jQuery.Animation = jQuery.extend( Animation, {
+
+	tweeners: {
+		"*": [ function( prop, value ) {
+			var tween = this.createTween( prop, value );
+			adjustCSS( tween.elem, prop, rcssNum.exec( value ), tween );
+			return tween;
+		} ]
+	},
+
+	tweener: function( props, callback ) {
+		if ( isFunction( props ) ) {
+			callback = props;
+			props = [ "*" ];
+		} else {
+			props = props.match( rnothtmlwhite );
+		}
+
+		var prop,
+			index = 0,
+			length = props.length;
+
+		for ( ; index < length; index++ ) {
+			prop = props[ index ];
+			Animation.tweeners[ prop ] = Animation.tweeners[ prop ] || [];
+			Animation.tweeners[ prop ].unshift( callback );
+		}
+	},
+
+	prefilters: [ defaultPrefilter ],
+
+	prefilter: function( callback, prepend ) {
+		if ( prepend ) {
+			Animation.prefilters.unshift( callback );
+		} else {
+			Animation.prefilters.push( callback );
+		}
+	}
+} );
+
+jQuery.speed = function( speed, easing, fn ) {
+	var opt = speed && typeof speed === "object" ? jQuery.extend( {}, speed ) : {
+		complete: fn || !fn && easing ||
+			isFunction( speed ) && speed,
+		duration: speed,
+		easing: fn && easing || easing && !isFunction( easing ) && easing
+	};
+
+	// Go to the end state if fx are off
+	if ( jQuery.fx.off ) {
+		opt.duration = 0;
+
+	} else {
+		if ( typeof opt.duration !== "number" ) {
+			if ( opt.duration in jQuery.fx.speeds ) {
+				opt.duration = jQuery.fx.speeds[ opt.duration ];
+
+			} else {
+				opt.duration = jQuery.fx.speeds._default;
+			}
+		}
+	}
+
+	// Normalize opt.queue - true/undefined/null -> "fx"
+	if ( opt.queue == null || opt.queue === true ) {
+		opt.queue = "fx";
+	}
+
+	// Queueing
+	opt.old = opt.complete;
+
+	opt.complete = function() {
+		if ( isFunction( opt.old ) ) {
+			opt.old.call( this );
+		}
+
+		if ( opt.queue ) {
+			jQuery.dequeue( this, opt.queue );
+		}
+	};
+
+	return opt;
+};
+
+jQuery.fn.extend( {
+	fadeTo: function( speed, to, easing, callback ) {
+
+		// Show any hidden elements after setting opacity to 0
+		return this.filter( isHiddenWithinTree ).css( "opacity", 0 ).show()
+
+			// Animate to the value specified
+			.end().animate( { opacity: to }, speed, easing, callback );
+	},
+	animate: function( prop, speed, easing, callback ) {
+		var empty = jQuery.isEmptyObject( prop ),
+			optall = jQuery.speed( speed, easing, callback ),
+			doAnimation = function() {
+
+				// Operate on a copy of prop so per-property easing won't be lost
+				var anim = Animation( this, jQuery.extend( {}, prop ), optall );
+
+				// Empty animations, or finishing resolves immediately
+				if ( empty || dataPriv.get( this, "finish" ) ) {
+					anim.stop( true );
+				}
+			};
+
+		doAnimation.finish = doAnimation;
+
+		return empty || optall.queue === false ?
+			this.each( doAnimation ) :
+			this.queue( optall.queue, doAnimation );
+	},
+	stop: function( type, clearQueue, gotoEnd ) {
+		var stopQueue = function( hooks ) {
+			var stop = hooks.stop;
+			delete hooks.stop;
+			stop( gotoEnd );
+		};
+
+		if ( typeof type !== "string" ) {
+			gotoEnd = clearQueue;
+			clearQueue = type;
+			type = undefined;
+		}
+		if ( clearQueue ) {
+			this.queue( type || "fx", [] );
+		}
+
+		return this.each( function() {
+			var dequeue = true,
+				index = type != null && type + "queueHooks",
+				timers = jQuery.timers,
+				data = dataPriv.get( this );
+
+			if ( index ) {
+				if ( data[ index ] && data[ index ].stop ) {
+					stopQueue( data[ index ] );
+				}
+			} else {
+				for ( index in data ) {
+					if ( data[ index ] && data[ index ].stop && rrun.test( index ) ) {
+						stopQueue( data[ index ] );
+					}
+				}
+			}
+
+			for ( index = timers.length; index--; ) {
+				if ( timers[ index ].elem === this &&
+					( type == null || timers[ index ].queue === type ) ) {
+
+					timers[ index ].anim.stop( gotoEnd );
+					dequeue = false;
+					timers.splice( index, 1 );
+				}
+			}
+
+			// Start the next in the queue if the last step wasn't forced.
+			// Timers currently will call their complete callbacks, which
+			// will dequeue but only if they were gotoEnd.
+			if ( dequeue || !gotoEnd ) {
+				jQuery.dequeue( this, type );
+			}
+		} );
+	},
+	finish: function( type ) {
+		if ( type !== false ) {
+			type = type || "fx";
+		}
+		return this.each( function() {
+			var index,
+				data = dataPriv.get( this ),
+				queue = data[ type + "queue" ],
+				hooks = data[ type + "queueHooks" ],
+				timers = jQuery.timers,
+				length = queue ? queue.length : 0;
+
+			// Enable finishing flag on private data
+			data.finish = true;
+
+			// Empty the queue first
+			jQuery.queue( this, type, [] );
+
+			if ( hooks && hooks.stop ) {
+				hooks.stop.call( this, true );
+			}
+
+			// Look for any active animations, and finish them
+			for ( index = timers.length; index--; ) {
+				if ( timers[ index ].elem === this && timers[ index ].queue === type ) {
+					timers[ index ].anim.stop( true );
+					timers.splice( index, 1 );
+				}
+			}
+
+			// Look for any animations in the old queue and finish them
+			for ( index = 0; index < length; index++ ) {
+				if ( queue[ index ] && queue[ index ].finish ) {
+					queue[ index ].finish.call( this );
+				}
+			}
+
+			// Turn off finishing flag
+			delete data.finish;
+		} );
+	}
+} );
+
+jQuery.each( [ "toggle", "show", "hide" ], function( _i, name ) {
+	var cssFn = jQuery.fn[ name ];
+	jQuery.fn[ name ] = function( speed, easing, callback ) {
+		return speed == null || typeof speed === "boolean" ?
+			cssFn.apply( this, arguments ) :
+			this.animate( genFx( name, true ), speed, easing, callback );
+	};
+} );
+
+// Generate shortcuts for custom animations
+jQuery.each( {
+	slideDown: genFx( "show" ),
+	slideUp: genFx( "hide" ),
+	slideToggle: genFx( "toggle" ),
+	fadeIn: { opacity: "show" },
+	fadeOut: { opacity: "hide" },
+	fadeToggle: { opacity: "toggle" }
+}, function( name, props ) {
+	jQuery.fn[ name ] = function( speed, easing, callback ) {
+		return this.animate( props, speed, easing, callback );
+	};
+} );
+
+jQuery.timers = [];
+jQuery.fx.tick = function() {
+	var timer,
+		i = 0,
+		timers = jQuery.timers;
+
+	fxNow = Date.now();
+
+	for ( ; i < timers.length; i++ ) {
+		timer = timers[ i ];
+
+		// Run the timer and safely remove it when done (allowing for external removal)
+		if ( !timer() && timers[ i ] === timer ) {
+			timers.splice( i--, 1 );
+		}
+	}
+
+	if ( !timers.length ) {
+		jQuery.fx.stop();
+	}
+	fxNow = undefined;
+};
+
+jQuery.fx.timer = function( timer ) {
+	jQuery.timers.push( timer );
+	jQuery.fx.start();
+};
+
+jQuery.fx.interval = 13;
+jQuery.fx.start = function() {
+	if ( inProgress ) {
+		return;
+	}
+
+	inProgress = true;
+	schedule();
+};
+
+jQuery.fx.stop = function() {
+	inProgress = null;
+};
+
+jQuery.fx.speeds = {
+	slow: 600,
+	fast: 200,
+
+	// Default speed
+	_default: 400
+};
+
+
+// Based off of the plugin by Clint Helfers, with permission.
+// https://web.archive.org/web/20100324014747/http://blindsignals.com/index.php/2009/07/jquery-delay/
+jQuery.fn.delay = function( time, type ) {
+	time = jQuery.fx ? jQuery.fx.speeds[ time ] || time : time;
+	type = type || "fx";
+
+	return this.queue( type, function( next, hooks ) {
+		var timeout = window.setTimeout( next, time );
+		hooks.stop = function() {
+			window.clearTimeout( timeout );
+		};
+	} );
+};
+
+
+( function() {
+	var input = document.createElement( "input" ),
+		select = document.createElement( "select" ),
+		opt = select.appendChild( document.createElement( "option" ) );
+
+	input.type = "checkbox";
+
+	// Support: Android <=4.3 only
+	// Default value for a checkbox should be "on"
+	support.checkOn = input.value !== "";
+
+	// Support: IE <=11 only
+	// Must access selectedIndex to make default options select
+	support.optSelected = opt.selected;
+
+	// Support: IE <=11 only
+	// An input loses its value after becoming a radio
+	input = document.createElement( "input" );
+	input.value = "t";
+	input.type = "radio";
+	support.radioValue = input.value === "t";
+} )();
+
+
+var boolHook,
+	attrHandle = jQuery.expr.attrHandle;
+
+jQuery.fn.extend( {
+	attr: function( name, value ) {
+		return access( this, jQuery.attr, name, value, arguments.length > 1 );
+	},
+
+	removeAttr: function( name ) {
+		return this.each( function() {
+			jQuery.removeAttr( this, name );
+		} );
+	}
+} );
+
+jQuery.extend( {
+	attr: function( elem, name, value ) {
+		var ret, hooks,
+			nType = elem.nodeType;
+
+		// Don't get/set attributes on text, comment and attribute nodes
+		if ( nType === 3 || nType === 8 || nType === 2 ) {
+			return;
+		}
+
+		// Fallback to prop when attributes are not supported
+		if ( typeof elem.getAttribute === "undefined" ) {
+			return jQuery.prop( elem, name, value );
+		}
+
+		// Attribute hooks are determined by the lowercase version
+		// Grab necessary hook if one is defined
+		if ( nType !== 1 || !jQuery.isXMLDoc( elem ) ) {
+			hooks = jQuery.attrHooks[ name.toLowerCase() ] ||
+				( jQuery.expr.match.bool.test( name ) ? boolHook : undefined );
+		}
+
+		if ( value !== undefined ) {
+			if ( value === null ) {
+				jQuery.removeAttr( elem, name );
+				return;
+			}
+
+			if ( hooks && "set" in hooks &&
+				( ret = hooks.set( elem, value, name ) ) !== undefined ) {
+				return ret;
+			}
+
+			elem.setAttribute( name, value + "" );
+			return value;
+		}
+
+		if ( hooks && "get" in hooks && ( ret = hooks.get( elem, name ) ) !== null ) {
+			return ret;
+		}
+
+		ret = jQuery.find.attr( elem, name );
+
+		// Non-existent attributes return null, we normalize to undefined
+		return ret == null ? undefined : ret;
+	},
+
+	attrHooks: {
+		type: {
+			set: function( elem, value ) {
+				if ( !support.radioValue && value === "radio" &&
+					nodeName( elem, "input" ) ) {
+					var val = elem.value;
+					elem.setAttribute( "type", value );
+					if ( val ) {
+						elem.value = val;
+					}
+					return value;
+				}
+			}
+		}
+	},
+
+	removeAttr: function( elem, value ) {
+		var name,
+			i = 0,
+
+			// Attribute names can contain non-HTML whitespace characters
+			// https://html.spec.whatwg.org/multipage/syntax.html#attributes-2
+			attrNames = value && value.match( rnothtmlwhite );
+
+		if ( attrNames && elem.nodeType === 1 ) {
+			while ( ( name = attrNames[ i++ ] ) ) {
+				elem.removeAttribute( name );
+			}
+		}
+	}
+} );
+
+// Hooks for boolean attributes
+boolHook = {
+	set: function( elem, value, name ) {
+		if ( value === false ) {
+
+			// Remove boolean attributes when set to false
+			jQuery.removeAttr( elem, name );
+		} else {
+			elem.setAttribute( name, name );
+		}
+		return name;
+	}
+};
+
+jQuery.each( jQuery.expr.match.bool.source.match( /\w+/g ), function( _i, name ) {
+	var getter = attrHandle[ name ] || jQuery.find.attr;
+
+	attrHandle[ name ] = function( elem, name, isXML ) {
+		var ret, handle,
+			lowercaseName = name.toLowerCase();
+
+		if ( !isXML ) {
+
+			// Avoid an infinite loop by temporarily removing this function from the getter
+			handle = attrHandle[ lowercaseName ];
+			attrHandle[ lowercaseName ] = ret;
+			ret = getter( elem, name, isXML ) != null ?
+				lowercaseName :
+				null;
+			attrHandle[ lowercaseName ] = handle;
+		}
+		return ret;
+	};
+} );
+
+
+
+
+var rfocusable = /^(?:input|select|textarea|button)$/i,
+	rclickable = /^(?:a|area)$/i;
+
+jQuery.fn.extend( {
+	prop: function( name, value ) {
+		return access( this, jQuery.prop, name, value, arguments.length > 1 );
+	},
+
+	removeProp: function( name ) {
+		return this.each( function() {
+			delete this[ jQuery.propFix[ name ] || name ];
+		} );
+	}
+} );
+
+jQuery.extend( {
+	prop: function( elem, name, value ) {
+		var ret, hooks,
+			nType = elem.nodeType;
+
+		// Don't get/set properties on text, comment and attribute nodes
+		if ( nType === 3 || nType === 8 || nType === 2 ) {
+			return;
+		}
+
+		if ( nType !== 1 || !jQuery.isXMLDoc( elem ) ) {
+
+			// Fix name and attach hooks
+			name = jQuery.propFix[ name ] || name;
+			hooks = jQuery.propHooks[ name ];
+		}
+
+		if ( value !== undefined ) {
+			if ( hooks && "set" in hooks &&
+				( ret = hooks.set( elem, value, name ) ) !== undefined ) {
+				return ret;
+			}
+
+			return ( elem[ name ] = value );
+		}
+
+		if ( hooks && "get" in hooks && ( ret = hooks.get( elem, name ) ) !== null ) {
+			return ret;
+		}
+
+		return elem[ name ];
+	},
+
+	propHooks: {
+		tabIndex: {
+			get: function( elem ) {
+
+				// Support: IE <=9 - 11 only
+				// elem.tabIndex doesn't always return the
+				// correct value when it hasn't been explicitly set
+				// https://web.archive.org/web/20141116233347/http://fluidproject.org/blog/2008/01/09/getting-setting-and-removing-tabindex-values-with-javascript/
+				// Use proper attribute retrieval(#12072)
+				var tabindex = jQuery.find.attr( elem, "tabindex" );
+
+				if ( tabindex ) {
+					return parseInt( tabindex, 10 );
+				}
+
+				if (
+					rfocusable.test( elem.nodeName ) ||
+					rclickable.test( elem.nodeName ) &&
+					elem.href
+				) {
+					return 0;
+				}
+
+				return -1;
+			}
+		}
+	},
+
+	propFix: {
+		"for": "htmlFor",
+		"class": "className"
+	}
+} );
+
+// Support: IE <=11 only
+// Accessing the selectedIndex property
+// forces the browser to respect setting selected
+// on the option
+// The getter ensures a default option is selected
+// when in an optgroup
+// eslint rule "no-unused-expressions" is disabled for this code
+// since it considers such accessions noop
+if ( !support.optSelected ) {
+	jQuery.propHooks.selected = {
+		get: function( elem ) {
+
+			/* eslint no-unused-expressions: "off" */
+
+			var parent = elem.parentNode;
+			if ( parent && parent.parentNode ) {
+				parent.parentNode.selectedIndex;
+			}
+			return null;
+		},
+		set: function( elem ) {
+
+			/* eslint no-unused-expressions: "off" */
+
+			var parent = elem.parentNode;
+			if ( parent ) {
+				parent.selectedIndex;
+
+				if ( parent.parentNode ) {
+					parent.parentNode.selectedIndex;
+				}
+			}
+		}
+	};
+}
+
+jQuery.each( [
+	"tabIndex",
+	"readOnly",
+	"maxLength",
+	"cellSpacing",
+	"cellPadding",
+	"rowSpan",
+	"colSpan",
+	"useMap",
+	"frameBorder",
+	"contentEditable"
+], function() {
+	jQuery.propFix[ this.toLowerCase() ] = this;
+} );
+
+
+
+
+	// Strip and collapse whitespace according to HTML spec
+	// https://infra.spec.whatwg.org/#strip-and-collapse-ascii-whitespace
+	function stripAndCollapse( value ) {
+		var tokens = value.match( rnothtmlwhite ) || [];
+		return tokens.join( " " );
+	}
+
+
+function getClass( elem ) {
+	return elem.getAttribute && elem.getAttribute( "class" ) || "";
+}
+
+function classesToArray( value ) {
+	if ( Array.isArray( value ) ) {
+		return value;
+	}
+	if ( typeof value === "string" ) {
+		return value.match( rnothtmlwhite ) || [];
+	}
+	return [];
+}
+
+jQuery.fn.extend( {
+	addClass: function( value ) {
+		var classes, elem, cur, curValue, clazz, j, finalValue,
+			i = 0;
+
+		if ( isFunction( value ) ) {
+			return this.each( function( j ) {
+				jQuery( this ).addClass( value.call( this, j, getClass( this ) ) );
+			} );
+		}
+
+		classes = classesToArray( value );
+
+		if ( classes.length ) {
+			while ( ( elem = this[ i++ ] ) ) {
+				curValue = getClass( elem );
+				cur = elem.nodeType === 1 && ( " " + stripAndCollapse( curValue ) + " " );
+
+				if ( cur ) {
+					j = 0;
+					while ( ( clazz = classes[ j++ ] ) ) {
+						if ( cur.indexOf( " " + clazz + " " ) < 0 ) {
+							cur += clazz + " ";
+						}
+					}
+
+					// Only assign if different to avoid unneeded rendering.
+					finalValue = stripAndCollapse( cur );
+					if ( curValue !== finalValue ) {
+						elem.setAttribute( "class", finalValue );
+					}
+				}
+			}
+		}
+
+		return this;
+	},
+
+	removeClass: function( value ) {
+		var classes, elem, cur, curValue, clazz, j, finalValue,
+			i = 0;
+
+		if ( isFunction( value ) ) {
+			return this.each( function( j ) {
+				jQuery( this ).removeClass( value.call( this, j, getClass( this ) ) );
+			} );
+		}
+
+		if ( !arguments.length ) {
+			return this.attr( "class", "" );
+		}
+
+		classes = classesToArray( value );
+
+		if ( classes.length ) {
+			while ( ( elem = this[ i++ ] ) ) {
+				curValue = getClass( elem );
+
+				// This expression is here for better compressibility (see addClass)
+				cur = elem.nodeType === 1 && ( " " + stripAndCollapse( curValue ) + " " );
+
+				if ( cur ) {
+					j = 0;
+					while ( ( clazz = classes[ j++ ] ) ) {
+
+						// Remove *all* instances
+						while ( cur.indexOf( " " + clazz + " " ) > -1 ) {
+							cur = cur.replace( " " + clazz + " ", " " );
+						}
+					}
+
+					// Only assign if different to avoid unneeded rendering.
+					finalValue = stripAndCollapse( cur );
+					if ( curValue !== finalValue ) {
+						elem.setAttribute( "class", finalValue );
+					}
+				}
+			}
+		}
+
+		return this;
+	},
+
+	toggleClass: function( value, stateVal ) {
+		var type = typeof value,
+			isValidValue = type === "string" || Array.isArray( value );
+
+		if ( typeof stateVal === "boolean" && isValidValue ) {
+			return stateVal ? this.addClass( value ) : this.removeClass( value );
+		}
+
+		if ( isFunction( value ) ) {
+			return this.each( function( i ) {
+				jQuery( this ).toggleClass(
+					value.call( this, i, getClass( this ), stateVal ),
+					stateVal
+				);
+			} );
+		}
+
+		return this.each( function() {
+			var className, i, self, classNames;
+
+			if ( isValidValue ) {
+
+				// Toggle individual class names
+				i = 0;
+				self = jQuery( this );
+				classNames = classesToArray( value );
+
+				while ( ( className = classNames[ i++ ] ) ) {
+
+					// Check each className given, space separated list
+					if ( self.hasClass( className ) ) {
+						self.removeClass( className );
+					} else {
+						self.addClass( className );
+					}
+				}
+
+			// Toggle whole class name
+			} else if ( value === undefined || type === "boolean" ) {
+				className = getClass( this );
+				if ( className ) {
+
+					// Store className if set
+					dataPriv.set( this, "__className__", className );
+				}
+
+				// If the element has a class name or if we're passed `false`,
+				// then remove the whole classname (if there was one, the above saved it).
+				// Otherwise bring back whatever was previously saved (if anything),
+				// falling back to the empty string if nothing was stored.
+				if ( this.setAttribute ) {
+					this.setAttribute( "class",
+						className || value === false ?
+							"" :
+							dataPriv.get( this, "__className__" ) || ""
+					);
+				}
+			}
+		} );
+	},
+
+	hasClass: function( selector ) {
+		var className, elem,
+			i = 0;
+
+		className = " " + selector + " ";
+		while ( ( elem = this[ i++ ] ) ) {
+			if ( elem.nodeType === 1 &&
+				( " " + stripAndCollapse( getClass( elem ) ) + " " ).indexOf( className ) > -1 ) {
+				return true;
+			}
+		}
+
+		return false;
+	}
+} );
+
+
+
+
+var rreturn = /\r/g;
+
+jQuery.fn.extend( {
+	val: function( value ) {
+		var hooks, ret, valueIsFunction,
+			elem = this[ 0 ];
+
+		if ( !arguments.length ) {
+			if ( elem ) {
+				hooks = jQuery.valHooks[ elem.type ] ||
+					jQuery.valHooks[ elem.nodeName.toLowerCase() ];
+
+				if ( hooks &&
+					"get" in hooks &&
+					( ret = hooks.get( elem, "value" ) ) !== undefined
+				) {
+					return ret;
+				}
+
+				ret = elem.value;
+
+				// Handle most common string cases
+				if ( typeof ret === "string" ) {
+					return ret.replace( rreturn, "" );
+				}
+
+				// Handle cases where value is null/undef or number
+				return ret == null ? "" : ret;
+			}
+
+			return;
+		}
+
+		valueIsFunction = isFunction( value );
+
+		return this.each( function( i ) {
+			var val;
+
+			if ( this.nodeType !== 1 ) {
+				return;
+			}
+
+			if ( valueIsFunction ) {
+				val = value.call( this, i, jQuery( this ).val() );
+			} else {
+				val = value;
+			}
+
+			// Treat null/undefined as ""; convert numbers to string
+			if ( val == null ) {
+				val = "";
+
+			} else if ( typeof val === "number" ) {
+				val += "";
+
+			} else if ( Array.isArray( val ) ) {
+				val = jQuery.map( val, function( value ) {
+					return value == null ? "" : value + "";
+				} );
+			}
+
+			hooks = jQuery.valHooks[ this.type ] || jQuery.valHooks[ this.nodeName.toLowerCase() ];
+
+			// If set returns undefined, fall back to normal setting
+			if ( !hooks || !( "set" in hooks ) || hooks.set( this, val, "value" ) === undefined ) {
+				this.value = val;
+			}
+		} );
+	}
+} );
+
+jQuery.extend( {
+	valHooks: {
+		option: {
+			get: function( elem ) {
+
+				var val = jQuery.find.attr( elem, "value" );
+				return val != null ?
+					val :
+
+					// Support: IE <=10 - 11 only
+					// option.text throws exceptions (#14686, #14858)
+					// Strip and collapse whitespace
+					// https://html.spec.whatwg.org/#strip-and-collapse-whitespace
+					stripAndCollapse( jQuery.text( elem ) );
+			}
+		},
+		select: {
+			get: function( elem ) {
+				var value, option, i,
+					options = elem.options,
+					index = elem.selectedIndex,
+					one = elem.type === "select-one",
+					values = one ? null : [],
+					max = one ? index + 1 : options.length;
+
+				if ( index < 0 ) {
+					i = max;
+
+				} else {
+					i = one ? index : 0;
+				}
+
+				// Loop through all the selected options
+				for ( ; i < max; i++ ) {
+					option = options[ i ];
+
+					// Support: IE <=9 only
+					// IE8-9 doesn't update selected after form reset (#2551)
+					if ( ( option.selected || i === index ) &&
+
+							// Don't return options that are disabled or in a disabled optgroup
+							!option.disabled &&
+							( !option.parentNode.disabled ||
+								!nodeName( option.parentNode, "optgroup" ) ) ) {
+
+						// Get the specific value for the option
+						value = jQuery( option ).val();
+
+						// We don't need an array for one selects
+						if ( one ) {
+							return value;
+						}
+
+						// Multi-Selects return an array
+						values.push( value );
+					}
+				}
+
+				return values;
+			},
+
+			set: function( elem, value ) {
+				var optionSet, option,
+					options = elem.options,
+					values = jQuery.makeArray( value ),
+					i = options.length;
+
+				while ( i-- ) {
+					option = options[ i ];
+
+					/* eslint-disable no-cond-assign */
+
+					if ( option.selected =
+						jQuery.inArray( jQuery.valHooks.option.get( option ), values ) > -1
+					) {
+						optionSet = true;
+					}
+
+					/* eslint-enable no-cond-assign */
+				}
+
+				// Force browsers to behave consistently when non-matching value is set
+				if ( !optionSet ) {
+					elem.selectedIndex = -1;
+				}
+				return values;
+			}
+		}
+	}
+} );
+
+// Radios and checkboxes getter/setter
+jQuery.each( [ "radio", "checkbox" ], function() {
+	jQuery.valHooks[ this ] = {
+		set: function( elem, value ) {
+			if ( Array.isArray( value ) ) {
+				return ( elem.checked = jQuery.inArray( jQuery( elem ).val(), value ) > -1 );
+			}
+		}
+	};
+	if ( !support.checkOn ) {
+		jQuery.valHooks[ this ].get = function( elem ) {
+			return elem.getAttribute( "value" ) === null ? "on" : elem.value;
+		};
+	}
+} );
+
+
+
+
+// Return jQuery for attributes-only inclusion
+
+
+support.focusin = "onfocusin" in window;
+
+
+var rfocusMorph = /^(?:focusinfocus|focusoutblur)$/,
+	stopPropagationCallback = function( e ) {
+		e.stopPropagation();
+	};
+
+jQuery.extend( jQuery.event, {
+
+	trigger: function( event, data, elem, onlyHandlers ) {
+
+		var i, cur, tmp, bubbleType, ontype, handle, special, lastElement,
+			eventPath = [ elem || document ],
+			type = hasOwn.call( event, "type" ) ? event.type : event,
+			namespaces = hasOwn.call( event, "namespace" ) ? event.namespace.split( "." ) : [];
+
+		cur = lastElement = tmp = elem = elem || document;
+
+		// Don't do events on text and comment nodes
+		if ( elem.nodeType === 3 || elem.nodeType === 8 ) {
+			return;
+		}
+
+		// focus/blur morphs to focusin/out; ensure we're not firing them right now
+		if ( rfocusMorph.test( type + jQuery.event.triggered ) ) {
+			return;
+		}
+
+		if ( type.indexOf( "." ) > -1 ) {
+
+			// Namespaced trigger; create a regexp to match event type in handle()
+			namespaces = type.split( "." );
+			type = namespaces.shift();
+			namespaces.sort();
+		}
+		ontype = type.indexOf( ":" ) < 0 && "on" + type;
+
+		// Caller can pass in a jQuery.Event object, Object, or just an event type string
+		event = event[ jQuery.expando ] ?
+			event :
+			new jQuery.Event( type, typeof event === "object" && event );
+
+		// Trigger bitmask: & 1 for native handlers; & 2 for jQuery (always true)
+		event.isTrigger = onlyHandlers ? 2 : 3;
+		event.namespace = namespaces.join( "." );
+		event.rnamespace = event.namespace ?
+			new RegExp( "(^|\\.)" + namespaces.join( "\\.(?:.*\\.|)" ) + "(\\.|$)" ) :
+			null;
+
+		// Clean up the event in case it is being reused
+		event.result = undefined;
+		if ( !event.target ) {
+			event.target = elem;
+		}
+
+		// Clone any incoming data and prepend the event, creating the handler arg list
+		data = data == null ?
+			[ event ] :
+			jQuery.makeArray( data, [ event ] );
+
+		// Allow special events to draw outside the lines
+		special = jQuery.event.special[ type ] || {};
+		if ( !onlyHandlers && special.trigger && special.trigger.apply( elem, data ) === false ) {
+			return;
+		}
+
+		// Determine event propagation path in advance, per W3C events spec (#9951)
+		// Bubble up to document, then to window; watch for a global ownerDocument var (#9724)
+		if ( !onlyHandlers && !special.noBubble && !isWindow( elem ) ) {
+
+			bubbleType = special.delegateType || type;
+			if ( !rfocusMorph.test( bubbleType + type ) ) {
+				cur = cur.parentNode;
+			}
+			for ( ; cur; cur = cur.parentNode ) {
+				eventPath.push( cur );
+				tmp = cur;
+			}
+
+			// Only add window if we got to document (e.g., not plain obj or detached DOM)
+			if ( tmp === ( elem.ownerDocument || document ) ) {
+				eventPath.push( tmp.defaultView || tmp.parentWindow || window );
+			}
+		}
+
+		// Fire handlers on the event path
+		i = 0;
+		while ( ( cur = eventPath[ i++ ] ) && !event.isPropagationStopped() ) {
+			lastElement = cur;
+			event.type = i > 1 ?
+				bubbleType :
+				special.bindType || type;
+
+			// jQuery handler
+			handle = ( dataPriv.get( cur, "events" ) || Object.create( null ) )[ event.type ] &&
+				dataPriv.get( cur, "handle" );
+			if ( handle ) {
+				handle.apply( cur, data );
+			}
+
+			// Native handler
+			handle = ontype && cur[ ontype ];
+			if ( handle && handle.apply && acceptData( cur ) ) {
+				event.result = handle.apply( cur, data );
+				if ( event.result === false ) {
+					event.preventDefault();
+				}
+			}
+		}
+		event.type = type;
+
+		// If nobody prevented the default action, do it now
+		if ( !onlyHandlers && !event.isDefaultPrevented() ) {
+
+			if ( ( !special._default ||
+				special._default.apply( eventPath.pop(), data ) === false ) &&
+				acceptData( elem ) ) {
+
+				// Call a native DOM method on the target with the same name as the event.
+				// Don't do default actions on window, that's where global variables be (#6170)
+				if ( ontype && isFunction( elem[ type ] ) && !isWindow( elem ) ) {
+
+					// Don't re-trigger an onFOO event when we call its FOO() method
+					tmp = elem[ ontype ];
+
+					if ( tmp ) {
+						elem[ ontype ] = null;
+					}
+
+					// Prevent re-triggering of the same event, since we already bubbled it above
+					jQuery.event.triggered = type;
+
+					if ( event.isPropagationStopped() ) {
+						lastElement.addEventListener( type, stopPropagationCallback );
+					}
+
+					elem[ type ]();
+
+					if ( event.isPropagationStopped() ) {
+						lastElement.removeEventListener( type, stopPropagationCallback );
+					}
+
+					jQuery.event.triggered = undefined;
+
+					if ( tmp ) {
+						elem[ ontype ] = tmp;
+					}
+				}
+			}
+		}
+
+		return event.result;
+	},
+
+	// Piggyback on a donor event to simulate a different one
+	// Used only for `focus(in | out)` events
+	simulate: function( type, elem, event ) {
+		var e = jQuery.extend(
+			new jQuery.Event(),
+			event,
+			{
+				type: type,
+				isSimulated: true
+			}
+		);
+
+		jQuery.event.trigger( e, null, elem );
+	}
+
+} );
+
+jQuery.fn.extend( {
+
+	trigger: function( type, data ) {
+		return this.each( function() {
+			jQuery.event.trigger( type, data, this );
+		} );
+	},
+	triggerHandler: function( type, data ) {
+		var elem = this[ 0 ];
+		if ( elem ) {
+			return jQuery.event.trigger( type, data, elem, true );
+		}
+	}
+} );
+
+
+// Support: Firefox <=44
+// Firefox doesn't have focus(in | out) events
+// Related ticket - https://bugzilla.mozilla.org/show_bug.cgi?id=687787
+//
+// Support: Chrome <=48 - 49, Safari <=9.0 - 9.1
+// focus(in | out) events fire after focus & blur events,
+// which is spec violation - http://www.w3.org/TR/DOM-Level-3-Events/#events-focusevent-event-order
+// Related ticket - https://bugs.chromium.org/p/chromium/issues/detail?id=449857
+if ( !support.focusin ) {
+	jQuery.each( { focus: "focusin", blur: "focusout" }, function( orig, fix ) {
+
+		// Attach a single capturing handler on the document while someone wants focusin/focusout
+		var handler = function( event ) {
+			jQuery.event.simulate( fix, event.target, jQuery.event.fix( event ) );
+		};
+
+		jQuery.event.special[ fix ] = {
+			setup: function() {
+
+				// Handle: regular nodes (via `this.ownerDocument`), window
+				// (via `this.document`) & document (via `this`).
+				var doc = this.ownerDocument || this.document || this,
+					attaches = dataPriv.access( doc, fix );
+
+				if ( !attaches ) {
+					doc.addEventListener( orig, handler, true );
+				}
+				dataPriv.access( doc, fix, ( attaches || 0 ) + 1 );
+			},
+			teardown: function() {
+				var doc = this.ownerDocument || this.document || this,
+					attaches = dataPriv.access( doc, fix ) - 1;
+
+				if ( !attaches ) {
+					doc.removeEventListener( orig, handler, true );
+					dataPriv.remove( doc, fix );
+
+				} else {
+					dataPriv.access( doc, fix, attaches );
+				}
+			}
+		};
+	} );
+}
+var location = window.location;
+
+var nonce = { guid: Date.now() };
+
+var rquery = ( /\?/ );
+
+
+
+// Cross-browser xml parsing
+jQuery.parseXML = function( data ) {
+	var xml, parserErrorElem;
+	if ( !data || typeof data !== "string" ) {
+		return null;
+	}
+
+	// Support: IE 9 - 11 only
+	// IE throws on parseFromString with invalid input.
+	try {
+		xml = ( new window.DOMParser() ).parseFromString( data, "text/xml" );
+	} catch ( e ) {}
+
+	parserErrorElem = xml && xml.getElementsByTagName( "parsererror" )[ 0 ];
+	if ( !xml || parserErrorElem ) {
+		jQuery.error( "Invalid XML: " + (
+			parserErrorElem ?
+				jQuery.map( parserErrorElem.childNodes, function( el ) {
+					return el.textContent;
+				} ).join( "\n" ) :
+				data
+		) );
+	}
+	return xml;
+};
+
+
+var
+	rbracket = /\[\]$/,
+	rCRLF = /\r?\n/g,
+	rsubmitterTypes = /^(?:submit|button|image|reset|file)$/i,
+	rsubmittable = /^(?:input|select|textarea|keygen)/i;
+
+function buildParams( prefix, obj, traditional, add ) {
+	var name;
+
+	if ( Array.isArray( obj ) ) {
+
+		// Serialize array item.
+		jQuery.each( obj, function( i, v ) {
+			if ( traditional || rbracket.test( prefix ) ) {
+
+				// Treat each array item as a scalar.
+				add( prefix, v );
+
+			} else {
+
+				// Item is non-scalar (array or object), encode its numeric index.
+				buildParams(
+					prefix + "[" + ( typeof v === "object" && v != null ? i : "" ) + "]",
+					v,
+					traditional,
+					add
+				);
+			}
+		} );
+
+	} else if ( !traditional && toType( obj ) === "object" ) {
+
+		// Serialize object item.
+		for ( name in obj ) {
+			buildParams( prefix + "[" + name + "]", obj[ name ], traditional, add );
+		}
+
+	} else {
+
+		// Serialize scalar item.
+		add( prefix, obj );
+	}
+}
+
+// Serialize an array of form elements or a set of
+// key/values into a query string
+jQuery.param = function( a, traditional ) {
+	var prefix,
+		s = [],
+		add = function( key, valueOrFunction ) {
+
+			// If value is a function, invoke it and use its return value
+			var value = isFunction( valueOrFunction ) ?
+				valueOrFunction() :
+				valueOrFunction;
+
+			s[ s.length ] = encodeURIComponent( key ) + "=" +
+				encodeURIComponent( value == null ? "" : value );
+		};
+
+	if ( a == null ) {
+		return "";
+	}
+
+	// If an array was passed in, assume that it is an array of form elements.
+	if ( Array.isArray( a ) || ( a.jquery && !jQuery.isPlainObject( a ) ) ) {
+
+		// Serialize the form elements
+		jQuery.each( a, function() {
+			add( this.name, this.value );
+		} );
+
+	} else {
+
+		// If traditional, encode the "old" way (the way 1.3.2 or older
+		// did it), otherwise encode params recursively.
+		for ( prefix in a ) {
+			buildParams( prefix, a[ prefix ], traditional, add );
+		}
+	}
+
+	// Return the resulting serialization
+	return s.join( "&" );
+};
+
+jQuery.fn.extend( {
+	serialize: function() {
+		return jQuery.param( this.serializeArray() );
+	},
+	serializeArray: function() {
+		return this.map( function() {
+
+			// Can add propHook for "elements" to filter or add form elements
+			var elements = jQuery.prop( this, "elements" );
+			return elements ? jQuery.makeArray( elements ) : this;
+		} ).filter( function() {
+			var type = this.type;
+
+			// Use .is( ":disabled" ) so that fieldset[disabled] works
+			return this.name && !jQuery( this ).is( ":disabled" ) &&
+				rsubmittable.test( this.nodeName ) && !rsubmitterTypes.test( type ) &&
+				( this.checked || !rcheckableType.test( type ) );
+		} ).map( function( _i, elem ) {
+			var val = jQuery( this ).val();
+
+			if ( val == null ) {
+				return null;
+			}
+
+			if ( Array.isArray( val ) ) {
+				return jQuery.map( val, function( val ) {
+					return { name: elem.name, value: val.replace( rCRLF, "\r\n" ) };
+				} );
+			}
+
+			return { name: elem.name, value: val.replace( rCRLF, "\r\n" ) };
+		} ).get();
+	}
+} );
+
+
+var
+	r20 = /%20/g,
+	rhash = /#.*$/,
+	rantiCache = /([?&])_=[^&]*/,
+	rheaders = /^(.*?):[ \t]*([^\r\n]*)$/mg,
+
+	// #7653, #8125, #8152: local protocol detection
+	rlocalProtocol = /^(?:about|app|app-storage|.+-extension|file|res|widget):$/,
+	rnoContent = /^(?:GET|HEAD)$/,
+	rprotocol = /^\/\//,
+
+	/* Prefilters
+	 * 1) They are useful to introduce custom dataTypes (see ajax/jsonp.js for an example)
+	 * 2) These are called:
+	 *    - BEFORE asking for a transport
+	 *    - AFTER param serialization (s.data is a string if s.processData is true)
+	 * 3) key is the dataType
+	 * 4) the catchall symbol "*" can be used
+	 * 5) execution will start with transport dataType and THEN continue down to "*" if needed
+	 */
+	prefilters = {},
+
+	/* Transports bindings
+	 * 1) key is the dataType
+	 * 2) the catchall symbol "*" can be used
+	 * 3) selection will start with transport dataType and THEN go to "*" if needed
+	 */
+	transports = {},
+
+	// Avoid comment-prolog char sequence (#10098); must appease lint and evade compression
+	allTypes = "*/".concat( "*" ),
+
+	// Anchor tag for parsing the document origin
+	originAnchor = document.createElement( "a" );
+
+originAnchor.href = location.href;
+
+// Base "constructor" for jQuery.ajaxPrefilter and jQuery.ajaxTransport
+function addToPrefiltersOrTransports( structure ) {
+
+	// dataTypeExpression is optional and defaults to "*"
+	return function( dataTypeExpression, func ) {
+
+		if ( typeof dataTypeExpression !== "string" ) {
+			func = dataTypeExpression;
+			dataTypeExpression = "*";
+		}
+
+		var dataType,
+			i = 0,
+			dataTypes = dataTypeExpression.toLowerCase().match( rnothtmlwhite ) || [];
+
+		if ( isFunction( func ) ) {
+
+			// For each dataType in the dataTypeExpression
+			while ( ( dataType = dataTypes[ i++ ] ) ) {
+
+				// Prepend if requested
+				if ( dataType[ 0 ] === "+" ) {
+					dataType = dataType.slice( 1 ) || "*";
+					( structure[ dataType ] = structure[ dataType ] || [] ).unshift( func );
+
+				// Otherwise append
+				} else {
+					( structure[ dataType ] = structure[ dataType ] || [] ).push( func );
+				}
+			}
+		}
+	};
+}
+
+// Base inspection function for prefilters and transports
+function inspectPrefiltersOrTransports( structure, options, originalOptions, jqXHR ) {
+
+	var inspected = {},
+		seekingTransport = ( structure === transports );
+
+	function inspect( dataType ) {
+		var selected;
+		inspected[ dataType ] = true;
+		jQuery.each( structure[ dataType ] || [], function( _, prefilterOrFactory ) {
+			var dataTypeOrTransport = prefilterOrFactory( options, originalOptions, jqXHR );
+			if ( typeof dataTypeOrTransport === "string" &&
+				!seekingTransport && !inspected[ dataTypeOrTransport ] ) {
+
+				options.dataTypes.unshift( dataTypeOrTransport );
+				inspect( dataTypeOrTransport );
+				return false;
+			} else if ( seekingTransport ) {
+				return !( selected = dataTypeOrTransport );
+			}
+		} );
+		return selected;
+	}
+
+	return inspect( options.dataTypes[ 0 ] ) || !inspected[ "*" ] && inspect( "*" );
+}
+
+// A special extend for ajax options
+// that takes "flat" options (not to be deep extended)
+// Fixes #9887
+function ajaxExtend( target, src ) {
+	var key, deep,
+		flatOptions = jQuery.ajaxSettings.flatOptions || {};
+
+	for ( key in src ) {
+		if ( src[ key ] !== undefined ) {
+			( flatOptions[ key ] ? target : ( deep || ( deep = {} ) ) )[ key ] = src[ key ];
+		}
+	}
+	if ( deep ) {
+		jQuery.extend( true, target, deep );
+	}
+
+	return target;
+}
+
+/* Handles responses to an ajax request:
+ * - finds the right dataType (mediates between content-type and expected dataType)
+ * - returns the corresponding response
+ */
+function ajaxHandleResponses( s, jqXHR, responses ) {
+
+	var ct, type, finalDataType, firstDataType,
+		contents = s.contents,
+		dataTypes = s.dataTypes;
+
+	// Remove auto dataType and get content-type in the process
+	while ( dataTypes[ 0 ] === "*" ) {
+		dataTypes.shift();
+		if ( ct === undefined ) {
+			ct = s.mimeType || jqXHR.getResponseHeader( "Content-Type" );
+		}
+	}
+
+	// Check if we're dealing with a known content-type
+	if ( ct ) {
+		for ( type in contents ) {
+			if ( contents[ type ] && contents[ type ].test( ct ) ) {
+				dataTypes.unshift( type );
+				break;
+			}
+		}
+	}
+
+	// Check to see if we have a response for the expected dataType
+	if ( dataTypes[ 0 ] in responses ) {
+		finalDataType = dataTypes[ 0 ];
+	} else {
+
+		// Try convertible dataTypes
+		for ( type in responses ) {
+			if ( !dataTypes[ 0 ] || s.converters[ type + " " + dataTypes[ 0 ] ] ) {
+				finalDataType = type;
+				break;
+			}
+			if ( !firstDataType ) {
+				firstDataType = type;
+			}
+		}
+
+		// Or just use first one
+		finalDataType = finalDataType || firstDataType;
+	}
+
+	// If we found a dataType
+	// We add the dataType to the list if needed
+	// and return the corresponding response
+	if ( finalDataType ) {
+		if ( finalDataType !== dataTypes[ 0 ] ) {
+			dataTypes.unshift( finalDataType );
+		}
+		return responses[ finalDataType ];
+	}
+}
+
+/* Chain conversions given the request and the original response
+ * Also sets the responseXXX fields on the jqXHR instance
+ */
+function ajaxConvert( s, response, jqXHR, isSuccess ) {
+	var conv2, current, conv, tmp, prev,
+		converters = {},
+
+		// Work with a copy of dataTypes in case we need to modify it for conversion
+		dataTypes = s.dataTypes.slice();
+
+	// Create converters map with lowercased keys
+	if ( dataTypes[ 1 ] ) {
+		for ( conv in s.converters ) {
+			converters[ conv.toLowerCase() ] = s.converters[ conv ];
+		}
+	}
+
+	current = dataTypes.shift();
+
+	// Convert to each sequential dataType
+	while ( current ) {
+
+		if ( s.responseFields[ current ] ) {
+			jqXHR[ s.responseFields[ current ] ] = response;
+		}
+
+		// Apply the dataFilter if provided
+		if ( !prev && isSuccess && s.dataFilter ) {
+			response = s.dataFilter( response, s.dataType );
+		}
+
+		prev = current;
+		current = dataTypes.shift();
+
+		if ( current ) {
+
+			// There's only work to do if current dataType is non-auto
+			if ( current === "*" ) {
+
+				current = prev;
+
+			// Convert response if prev dataType is non-auto and differs from current
+			} else if ( prev !== "*" && prev !== current ) {
+
+				// Seek a direct converter
+				conv = converters[ prev + " " + current ] || converters[ "* " + current ];
+
+				// If none found, seek a pair
+				if ( !conv ) {
+					for ( conv2 in converters ) {
+
+						// If conv2 outputs current
+						tmp = conv2.split( " " );
+						if ( tmp[ 1 ] === current ) {
+
+							// If prev can be converted to accepted input
+							conv = converters[ prev + " " + tmp[ 0 ] ] ||
+								converters[ "* " + tmp[ 0 ] ];
+							if ( conv ) {
+
+								// Condense equivalence converters
+								if ( conv === true ) {
+									conv = converters[ conv2 ];
+
+								// Otherwise, insert the intermediate dataType
+								} else if ( converters[ conv2 ] !== true ) {
+									current = tmp[ 0 ];
+									dataTypes.unshift( tmp[ 1 ] );
+								}
+								break;
+							}
+						}
+					}
+				}
+
+				// Apply converter (if not an equivalence)
+				if ( conv !== true ) {
+
+					// Unless errors are allowed to bubble, catch and return them
+					if ( conv && s.throws ) {
+						response = conv( response );
+					} else {
+						try {
+							response = conv( response );
+						} catch ( e ) {
+							return {
+								state: "parsererror",
+								error: conv ? e : "No conversion from " + prev + " to " + current
+							};
+						}
+					}
+				}
+			}
+		}
+	}
+
+	return { state: "success", data: response };
+}
+
+jQuery.extend( {
+
+	// Counter for holding the number of active queries
+	active: 0,
+
+	// Last-Modified header cache for next request
+	lastModified: {},
+	etag: {},
+
+	ajaxSettings: {
+		url: location.href,
+		type: "GET",
+		isLocal: rlocalProtocol.test( location.protocol ),
+		global: true,
+		processData: true,
+		async: true,
+		contentType: "application/x-www-form-urlencoded; charset=UTF-8",
+
+		/*
+		timeout: 0,
+		data: null,
+		dataType: null,
+		username: null,
+		password: null,
+		cache: null,
+		throws: false,
+		traditional: false,
+		headers: {},
+		*/
+
+		accepts: {
+			"*": allTypes,
+			text: "text/plain",
+			html: "text/html",
+			xml: "application/xml, text/xml",
+			json: "application/json, text/javascript"
+		},
+
+		contents: {
+			xml: /\bxml\b/,
+			html: /\bhtml/,
+			json: /\bjson\b/
+		},
+
+		responseFields: {
+			xml: "responseXML",
+			text: "responseText",
+			json: "responseJSON"
+		},
+
+		// Data converters
+		// Keys separate source (or catchall "*") and destination types with a single space
+		converters: {
+
+			// Convert anything to text
+			"* text": String,
+
+			// Text to html (true = no transformation)
+			"text html": true,
+
+			// Evaluate text as a json expression
+			"text json": JSON.parse,
+
+			// Parse text as xml
+			"text xml": jQuery.parseXML
+		},
+
+		// For options that shouldn't be deep extended:
+		// you can add your own custom options here if
+		// and when you create one that shouldn't be
+		// deep extended (see ajaxExtend)
+		flatOptions: {
+			url: true,
+			context: true
+		}
+	},
+
+	// Creates a full fledged settings object into target
+	// with both ajaxSettings and settings fields.
+	// If target is omitted, writes into ajaxSettings.
+	ajaxSetup: function( target, settings ) {
+		return settings ?
+
+			// Building a settings object
+			ajaxExtend( ajaxExtend( target, jQuery.ajaxSettings ), settings ) :
+
+			// Extending ajaxSettings
+			ajaxExtend( jQuery.ajaxSettings, target );
+	},
+
+	ajaxPrefilter: addToPrefiltersOrTransports( prefilters ),
+	ajaxTransport: addToPrefiltersOrTransports( transports ),
+
+	// Main method
+	ajax: function( url, options ) {
+
+		// If url is an object, simulate pre-1.5 signature
+		if ( typeof url === "object" ) {
+			options = url;
+			url = undefined;
+		}
+
+		// Force options to be an object
+		options = options || {};
+
+		var transport,
+
+			// URL without anti-cache param
+			cacheURL,
+
+			// Response headers
+			responseHeadersString,
+			responseHeaders,
+
+			// timeout handle
+			timeoutTimer,
+
+			// Url cleanup var
+			urlAnchor,
+
+			// Request state (becomes false upon send and true upon completion)
+			completed,
+
+			// To know if global events are to be dispatched
+			fireGlobals,
+
+			// Loop variable
+			i,
+
+			// uncached part of the url
+			uncached,
+
+			// Create the final options object
+			s = jQuery.ajaxSetup( {}, options ),
+
+			// Callbacks context
+			callbackContext = s.context || s,
+
+			// Context for global events is callbackContext if it is a DOM node or jQuery collection
+			globalEventContext = s.context &&
+				( callbackContext.nodeType || callbackContext.jquery ) ?
+				jQuery( callbackContext ) :
+				jQuery.event,
+
+			// Deferreds
+			deferred = jQuery.Deferred(),
+			completeDeferred = jQuery.Callbacks( "once memory" ),
+
+			// Status-dependent callbacks
+			statusCode = s.statusCode || {},
+
+			// Headers (they are sent all at once)
+			requestHeaders = {},
+			requestHeadersNames = {},
+
+			// Default abort message
+			strAbort = "canceled",
+
+			// Fake xhr
+			jqXHR = {
+				readyState: 0,
+
+				// Builds headers hashtable if needed
+				getResponseHeader: function( key ) {
+					var match;
+					if ( completed ) {
+						if ( !responseHeaders ) {
+							responseHeaders = {};
+							while ( ( match = rheaders.exec( responseHeadersString ) ) ) {
+								responseHeaders[ match[ 1 ].toLowerCase() + " " ] =
+									( responseHeaders[ match[ 1 ].toLowerCase() + " " ] || [] )
+										.concat( match[ 2 ] );
+							}
+						}
+						match = responseHeaders[ key.toLowerCase() + " " ];
+					}
+					return match == null ? null : match.join( ", " );
+				},
+
+				// Raw string
+				getAllResponseHeaders: function() {
+					return completed ? responseHeadersString : null;
+				},
+
+				// Caches the header
+				setRequestHeader: function( name, value ) {
+					if ( completed == null ) {
+						name = requestHeadersNames[ name.toLowerCase() ] =
+							requestHeadersNames[ name.toLowerCase() ] || name;
+						requestHeaders[ name ] = value;
+					}
+					return this;
+				},
+
+				// Overrides response content-type header
+				overrideMimeType: function( type ) {
+					if ( completed == null ) {
+						s.mimeType = type;
+					}
+					return this;
+				},
+
+				// Status-dependent callbacks
+				statusCode: function( map ) {
+					var code;
+					if ( map ) {
+						if ( completed ) {
+
+							// Execute the appropriate callbacks
+							jqXHR.always( map[ jqXHR.status ] );
+						} else {
+
+							// Lazy-add the new callbacks in a way that preserves old ones
+							for ( code in map ) {
+								statusCode[ code ] = [ statusCode[ code ], map[ code ] ];
+							}
+						}
+					}
+					return this;
+				},
+
+				// Cancel the request
+				abort: function( statusText ) {
+					var finalText = statusText || strAbort;
+					if ( transport ) {
+						transport.abort( finalText );
+					}
+					done( 0, finalText );
+					return this;
+				}
+			};
+
+		// Attach deferreds
+		deferred.promise( jqXHR );
+
+		// Add protocol if not provided (prefilters might expect it)
+		// Handle falsy url in the settings object (#10093: consistency with old signature)
+		// We also use the url parameter if available
+		s.url = ( ( url || s.url || location.href ) + "" )
+			.replace( rprotocol, location.protocol + "//" );
+
+		// Alias method option to type as per ticket #12004
+		s.type = options.method || options.type || s.method || s.type;
+
+		// Extract dataTypes list
+		s.dataTypes = ( s.dataType || "*" ).toLowerCase().match( rnothtmlwhite ) || [ "" ];
+
+		// A cross-domain request is in order when the origin doesn't match the current origin.
+		if ( s.crossDomain == null ) {
+			urlAnchor = document.createElement( "a" );
+
+			// Support: IE <=8 - 11, Edge 12 - 15
+			// IE throws exception on accessing the href property if url is malformed,
+			// e.g. http://example.com:80x/
+			try {
+				urlAnchor.href = s.url;
+
+				// Support: IE <=8 - 11 only
+				// Anchor's host property isn't correctly set when s.url is relative
+				urlAnchor.href = urlAnchor.href;
+				s.crossDomain = originAnchor.protocol + "//" + originAnchor.host !==
+					urlAnchor.protocol + "//" + urlAnchor.host;
+			} catch ( e ) {
+
+				// If there is an error parsing the URL, assume it is crossDomain,
+				// it can be rejected by the transport if it is invalid
+				s.crossDomain = true;
+			}
+		}
+
+		// Convert data if not already a string
+		if ( s.data && s.processData && typeof s.data !== "string" ) {
+			s.data = jQuery.param( s.data, s.traditional );
+		}
+
+		// Apply prefilters
+		inspectPrefiltersOrTransports( prefilters, s, options, jqXHR );
+
+		// If request was aborted inside a prefilter, stop there
+		if ( completed ) {
+			return jqXHR;
+		}
+
+		// We can fire global events as of now if asked to
+		// Don't fire events if jQuery.event is undefined in an AMD-usage scenario (#15118)
+		fireGlobals = jQuery.event && s.global;
+
+		// Watch for a new set of requests
+		if ( fireGlobals && jQuery.active++ === 0 ) {
+			jQuery.event.trigger( "ajaxStart" );
+		}
+
+		// Uppercase the type
+		s.type = s.type.toUpperCase();
+
+		// Determine if request has content
+		s.hasContent = !rnoContent.test( s.type );
+
+		// Save the URL in case we're toying with the If-Modified-Since
+		// and/or If-None-Match header later on
+		// Remove hash to simplify url manipulation
+		cacheURL = s.url.replace( rhash, "" );
+
+		// More options handling for requests with no content
+		if ( !s.hasContent ) {
+
+			// Remember the hash so we can put it back
+			uncached = s.url.slice( cacheURL.length );
+
+			// If data is available and should be processed, append data to url
+			if ( s.data && ( s.processData || typeof s.data === "string" ) ) {
+				cacheURL += ( rquery.test( cacheURL ) ? "&" : "?" ) + s.data;
+
+				// #9682: remove data so that it's not used in an eventual retry
+				delete s.data;
+			}
+
+			// Add or update anti-cache param if needed
+			if ( s.cache === false ) {
+				cacheURL = cacheURL.replace( rantiCache, "$1" );
+				uncached = ( rquery.test( cacheURL ) ? "&" : "?" ) + "_=" + ( nonce.guid++ ) +
+					uncached;
+			}
+
+			// Put hash and anti-cache on the URL that will be requested (gh-1732)
+			s.url = cacheURL + uncached;
+
+		// Change '%20' to '+' if this is encoded form body content (gh-2658)
+		} else if ( s.data && s.processData &&
+			( s.contentType || "" ).indexOf( "application/x-www-form-urlencoded" ) === 0 ) {
+			s.data = s.data.replace( r20, "+" );
+		}
+
+		// Set the If-Modified-Since and/or If-None-Match header, if in ifModified mode.
+		if ( s.ifModified ) {
+			if ( jQuery.lastModified[ cacheURL ] ) {
+				jqXHR.setRequestHeader( "If-Modified-Since", jQuery.lastModified[ cacheURL ] );
+			}
+			if ( jQuery.etag[ cacheURL ] ) {
+				jqXHR.setRequestHeader( "If-None-Match", jQuery.etag[ cacheURL ] );
+			}
+		}
+
+		// Set the correct header, if data is being sent
+		if ( s.data && s.hasContent && s.contentType !== false || options.contentType ) {
+			jqXHR.setRequestHeader( "Content-Type", s.contentType );
+		}
+
+		// Set the Accepts header for the server, depending on the dataType
+		jqXHR.setRequestHeader(
+			"Accept",
+			s.dataTypes[ 0 ] && s.accepts[ s.dataTypes[ 0 ] ] ?
+				s.accepts[ s.dataTypes[ 0 ] ] +
+					( s.dataTypes[ 0 ] !== "*" ? ", " + allTypes + "; q=0.01" : "" ) :
+				s.accepts[ "*" ]
+		);
+
+		// Check for headers option
+		for ( i in s.headers ) {
+			jqXHR.setRequestHeader( i, s.headers[ i ] );
+		}
+
+		// Allow custom headers/mimetypes and early abort
+		if ( s.beforeSend &&
+			( s.beforeSend.call( callbackContext, jqXHR, s ) === false || completed ) ) {
+
+			// Abort if not done already and return
+			return jqXHR.abort();
+		}
+
+		// Aborting is no longer a cancellation
+		strAbort = "abort";
+
+		// Install callbacks on deferreds
+		completeDeferred.add( s.complete );
+		jqXHR.done( s.success );
+		jqXHR.fail( s.error );
+
+		// Get transport
+		transport = inspectPrefiltersOrTransports( transports, s, options, jqXHR );
+
+		// If no transport, we auto-abort
+		if ( !transport ) {
+			done( -1, "No Transport" );
+		} else {
+			jqXHR.readyState = 1;
+
+			// Send global event
+			if ( fireGlobals ) {
+				globalEventContext.trigger( "ajaxSend", [ jqXHR, s ] );
+			}
+
+			// If request was aborted inside ajaxSend, stop there
+			if ( completed ) {
+				return jqXHR;
+			}
+
+			// Timeout
+			if ( s.async && s.timeout > 0 ) {
+				timeoutTimer = window.setTimeout( function() {
+					jqXHR.abort( "timeout" );
+				}, s.timeout );
+			}
+
+			try {
+				completed = false;
+				transport.send( requestHeaders, done );
+			} catch ( e ) {
+
+				// Rethrow post-completion exceptions
+				if ( completed ) {
+					throw e;
+				}
+
+				// Propagate others as results
+				done( -1, e );
+			}
+		}
+
+		// Callback for when everything is done
+		function done( status, nativeStatusText, responses, headers ) {
+			var isSuccess, success, error, response, modified,
+				statusText = nativeStatusText;
+
+			// Ignore repeat invocations
+			if ( completed ) {
+				return;
+			}
+
+			completed = true;
+
+			// Clear timeout if it exists
+			if ( timeoutTimer ) {
+				window.clearTimeout( timeoutTimer );
+			}
+
+			// Dereference transport for early garbage collection
+			// (no matter how long the jqXHR object will be used)
+			transport = undefined;
+
+			// Cache response headers
+			responseHeadersString = headers || "";
+
+			// Set readyState
+			jqXHR.readyState = status > 0 ? 4 : 0;
+
+			// Determine if successful
+			isSuccess = status >= 200 && status < 300 || status === 304;
+
+			// Get response data
+			if ( responses ) {
+				response = ajaxHandleResponses( s, jqXHR, responses );
+			}
+
+			// Use a noop converter for missing script but not if jsonp
+			if ( !isSuccess &&
+				jQuery.inArray( "script", s.dataTypes ) > -1 &&
+				jQuery.inArray( "json", s.dataTypes ) < 0 ) {
+				s.converters[ "text script" ] = function() {};
+			}
+
+			// Convert no matter what (that way responseXXX fields are always set)
+			response = ajaxConvert( s, response, jqXHR, isSuccess );
+
+			// If successful, handle type chaining
+			if ( isSuccess ) {
+
+				// Set the If-Modified-Since and/or If-None-Match header, if in ifModified mode.
+				if ( s.ifModified ) {
+					modified = jqXHR.getResponseHeader( "Last-Modified" );
+					if ( modified ) {
+						jQuery.lastModified[ cacheURL ] = modified;
+					}
+					modified = jqXHR.getResponseHeader( "etag" );
+					if ( modified ) {
+						jQuery.etag[ cacheURL ] = modified;
+					}
+				}
+
+				// if no content
+				if ( status === 204 || s.type === "HEAD" ) {
+					statusText = "nocontent";
+
+				// if not modified
+				} else if ( status === 304 ) {
+					statusText = "notmodified";
+
+				// If we have data, let's convert it
+				} else {
+					statusText = response.state;
+					success = response.data;
+					error = response.error;
+					isSuccess = !error;
+				}
+			} else {
+
+				// Extract error from statusText and normalize for non-aborts
+				error = statusText;
+				if ( status || !statusText ) {
+					statusText = "error";
+					if ( status < 0 ) {
+						status = 0;
+					}
+				}
+			}
+
+			// Set data for the fake xhr object
+			jqXHR.status = status;
+			jqXHR.statusText = ( nativeStatusText || statusText ) + "";
+
+			// Success/Error
+			if ( isSuccess ) {
+				deferred.resolveWith( callbackContext, [ success, statusText, jqXHR ] );
+			} else {
+				deferred.rejectWith( callbackContext, [ jqXHR, statusText, error ] );
+			}
+
+			// Status-dependent callbacks
+			jqXHR.statusCode( statusCode );
+			statusCode = undefined;
+
+			if ( fireGlobals ) {
+				globalEventContext.trigger( isSuccess ? "ajaxSuccess" : "ajaxError",
+					[ jqXHR, s, isSuccess ? success : error ] );
+			}
+
+			// Complete
+			completeDeferred.fireWith( callbackContext, [ jqXHR, statusText ] );
+
+			if ( fireGlobals ) {
+				globalEventContext.trigger( "ajaxComplete", [ jqXHR, s ] );
+
+				// Handle the global AJAX counter
+				if ( !( --jQuery.active ) ) {
+					jQuery.event.trigger( "ajaxStop" );
+				}
+			}
+		}
+
+		return jqXHR;
+	},
+
+	getJSON: function( url, data, callback ) {
+		return jQuery.get( url, data, callback, "json" );
+	},
+
+	getScript: function( url, callback ) {
+		return jQuery.get( url, undefined, callback, "script" );
+	}
+} );
+
+jQuery.each( [ "get", "post" ], function( _i, method ) {
+	jQuery[ method ] = function( url, data, callback, type ) {
+
+		// Shift arguments if data argument was omitted
+		if ( isFunction( data ) ) {
+			type = type || callback;
+			callback = data;
+			data = undefined;
+		}
+
+		// The url can be an options object (which then must have .url)
+		return jQuery.ajax( jQuery.extend( {
+			url: url,
+			type: method,
+			dataType: type,
+			data: data,
+			success: callback
+		}, jQuery.isPlainObject( url ) && url ) );
+	};
+} );
+
+jQuery.ajaxPrefilter( function( s ) {
+	var i;
+	for ( i in s.headers ) {
+		if ( i.toLowerCase() === "content-type" ) {
+			s.contentType = s.headers[ i ] || "";
+		}
+	}
+} );
+
+
+jQuery._evalUrl = function( url, options, doc ) {
+	return jQuery.ajax( {
+		url: url,
+
+		// Make this explicit, since user can override this through ajaxSetup (#11264)
+		type: "GET",
+		dataType: "script",
+		cache: true,
+		async: false,
+		global: false,
+
+		// Only evaluate the response if it is successful (gh-4126)
+		// dataFilter is not invoked for failure responses, so using it instead
+		// of the default converter is kludgy but it works.
+		converters: {
+			"text script": function() {}
+		},
+		dataFilter: function( response ) {
+			jQuery.globalEval( response, options, doc );
+		}
+	} );
+};
+
+
+jQuery.fn.extend( {
+	wrapAll: function( html ) {
+		var wrap;
+
+		if ( this[ 0 ] ) {
+			if ( isFunction( html ) ) {
+				html = html.call( this[ 0 ] );
+			}
+
+			// The elements to wrap the target around
+			wrap = jQuery( html, this[ 0 ].ownerDocument ).eq( 0 ).clone( true );
+
+			if ( this[ 0 ].parentNode ) {
+				wrap.insertBefore( this[ 0 ] );
+			}
+
+			wrap.map( function() {
+				var elem = this;
+
+				while ( elem.firstElementChild ) {
+					elem = elem.firstElementChild;
+				}
+
+				return elem;
+			} ).append( this );
+		}
+
+		return this;
+	},
+
+	wrapInner: function( html ) {
+		if ( isFunction( html ) ) {
+			return this.each( function( i ) {
+				jQuery( this ).wrapInner( html.call( this, i ) );
+			} );
+		}
+
+		return this.each( function() {
+			var self = jQuery( this ),
+				contents = self.contents();
+
+			if ( contents.length ) {
+				contents.wrapAll( html );
+
+			} else {
+				self.append( html );
+			}
+		} );
+	},
+
+	wrap: function( html ) {
+		var htmlIsFunction = isFunction( html );
+
+		return this.each( function( i ) {
+			jQuery( this ).wrapAll( htmlIsFunction ? html.call( this, i ) : html );
+		} );
+	},
+
+	unwrap: function( selector ) {
+		this.parent( selector ).not( "body" ).each( function() {
+			jQuery( this ).replaceWith( this.childNodes );
+		} );
+		return this;
+	}
+} );
+
+
+jQuery.expr.pseudos.hidden = function( elem ) {
+	return !jQuery.expr.pseudos.visible( elem );
+};
+jQuery.expr.pseudos.visible = function( elem ) {
+	return !!( elem.offsetWidth || elem.offsetHeight || elem.getClientRects().length );
+};
+
+
+
+
+jQuery.ajaxSettings.xhr = function() {
+	try {
+		return new window.XMLHttpRequest();
+	} catch ( e ) {}
+};
+
+var xhrSuccessStatus = {
+
+		// File protocol always yields status code 0, assume 200
+		0: 200,
+
+		// Support: IE <=9 only
+		// #1450: sometimes IE returns 1223 when it should be 204
+		1223: 204
+	},
+	xhrSupported = jQuery.ajaxSettings.xhr();
+
+support.cors = !!xhrSupported && ( "withCredentials" in xhrSupported );
+support.ajax = xhrSupported = !!xhrSupported;
+
+jQuery.ajaxTransport( function( options ) {
+	var callback, errorCallback;
+
+	// Cross domain only allowed if supported through XMLHttpRequest
+	if ( support.cors || xhrSupported && !options.crossDomain ) {
+		return {
+			send: function( headers, complete ) {
+				var i,
+					xhr = options.xhr();
+
+				xhr.open(
+					options.type,
+					options.url,
+					options.async,
+					options.username,
+					options.password
+				);
+
+				// Apply custom fields if provided
+				if ( options.xhrFields ) {
+					for ( i in options.xhrFields ) {
+						xhr[ i ] = options.xhrFields[ i ];
+					}
+				}
+
+				// Override mime type if needed
+				if ( options.mimeType && xhr.overrideMimeType ) {
+					xhr.overrideMimeType( options.mimeType );
+				}
+
+				// X-Requested-With header
+				// For cross-domain requests, seeing as conditions for a preflight are
+				// akin to a jigsaw puzzle, we simply never set it to be sure.
+				// (it can always be set on a per-request basis or even using ajaxSetup)
+				// For same-domain requests, won't change header if already provided.
+				if ( !options.crossDomain && !headers[ "X-Requested-With" ] ) {
+					headers[ "X-Requested-With" ] = "XMLHttpRequest";
+				}
+
+				// Set headers
+				for ( i in headers ) {
+					xhr.setRequestHeader( i, headers[ i ] );
+				}
+
+				// Callback
+				callback = function( type ) {
+					return function() {
+						if ( callback ) {
+							callback = errorCallback = xhr.onload =
+								xhr.onerror = xhr.onabort = xhr.ontimeout =
+									xhr.onreadystatechange = null;
+
+							if ( type === "abort" ) {
+								xhr.abort();
+							} else if ( type === "error" ) {
+
+								// Support: IE <=9 only
+								// On a manual native abort, IE9 throws
+								// errors on any property access that is not readyState
+								if ( typeof xhr.status !== "number" ) {
+									complete( 0, "error" );
+								} else {
+									complete(
+
+										// File: protocol always yields status 0; see #8605, #14207
+										xhr.status,
+										xhr.statusText
+									);
+								}
+							} else {
+								complete(
+									xhrSuccessStatus[ xhr.status ] || xhr.status,
+									xhr.statusText,
+
+									// Support: IE <=9 only
+									// IE9 has no XHR2 but throws on binary (trac-11426)
+									// For XHR2 non-text, let the caller handle it (gh-2498)
+									( xhr.responseType || "text" ) !== "text"  ||
+									typeof xhr.responseText !== "string" ?
+										{ binary: xhr.response } :
+										{ text: xhr.responseText },
+									xhr.getAllResponseHeaders()
+								);
+							}
+						}
+					};
+				};
+
+				// Listen to events
+				xhr.onload = callback();
+				errorCallback = xhr.onerror = xhr.ontimeout = callback( "error" );
+
+				// Support: IE 9 only
+				// Use onreadystatechange to replace onabort
+				// to handle uncaught aborts
+				if ( xhr.onabort !== undefined ) {
+					xhr.onabort = errorCallback;
+				} else {
+					xhr.onreadystatechange = function() {
+
+						// Check readyState before timeout as it changes
+						if ( xhr.readyState === 4 ) {
+
+							// Allow onerror to be called first,
+							// but that will not handle a native abort
+							// Also, save errorCallback to a variable
+							// as xhr.onerror cannot be accessed
+							window.setTimeout( function() {
+								if ( callback ) {
+									errorCallback();
+								}
+							} );
+						}
+					};
+				}
+
+				// Create the abort callback
+				callback = callback( "abort" );
+
+				try {
+
+					// Do send the request (this may raise an exception)
+					xhr.send( options.hasContent && options.data || null );
+				} catch ( e ) {
+
+					// #14683: Only rethrow if this hasn't been notified as an error yet
+					if ( callback ) {
+						throw e;
+					}
+				}
+			},
+
+			abort: function() {
+				if ( callback ) {
+					callback();
+				}
+			}
+		};
+	}
+} );
+
+
+
+
+// Prevent auto-execution of scripts when no explicit dataType was provided (See gh-2432)
+jQuery.ajaxPrefilter( function( s ) {
+	if ( s.crossDomain ) {
+		s.contents.script = false;
+	}
+} );
+
+// Install script dataType
+jQuery.ajaxSetup( {
+	accepts: {
+		script: "text/javascript, application/javascript, " +
+			"application/ecmascript, application/x-ecmascript"
+	},
+	contents: {
+		script: /\b(?:java|ecma)script\b/
+	},
+	converters: {
+		"text script": function( text ) {
+			jQuery.globalEval( text );
+			return text;
+		}
+	}
+} );
+
+// Handle cache's special case and crossDomain
+jQuery.ajaxPrefilter( "script", function( s ) {
+	if ( s.cache === undefined ) {
+		s.cache = false;
+	}
+	if ( s.crossDomain ) {
+		s.type = "GET";
+	}
+} );
+
+// Bind script tag hack transport
+jQuery.ajaxTransport( "script", function( s ) {
+
+	// This transport only deals with cross domain or forced-by-attrs requests
+	if ( s.crossDomain || s.scriptAttrs ) {
+		var script, callback;
+		return {
+			send: function( _, complete ) {
+				script = jQuery( "<script>" )
+					.attr( s.scriptAttrs || {} )
+					.prop( { charset: s.scriptCharset, src: s.url } )
+					.on( "load error", callback = function( evt ) {
+						script.remove();
+						callback = null;
+						if ( evt ) {
+							complete( evt.type === "error" ? 404 : 200, evt.type );
+						}
+					} );
+
+				// Use native DOM manipulation to avoid our domManip AJAX trickery
+				document.head.appendChild( script[ 0 ] );
+			},
+			abort: function() {
+				if ( callback ) {
+					callback();
+				}
+			}
+		};
+	}
+} );
+
+
+
+
+var oldCallbacks = [],
+	rjsonp = /(=)\?(?=&|$)|\?\?/;
+
+// Default jsonp settings
+jQuery.ajaxSetup( {
+	jsonp: "callback",
+	jsonpCallback: function() {
+		var callback = oldCallbacks.pop() || ( jQuery.expando + "_" + ( nonce.guid++ ) );
+		this[ callback ] = true;
+		return callback;
+	}
+} );
+
+// Detect, normalize options and install callbacks for jsonp requests
+jQuery.ajaxPrefilter( "json jsonp", function( s, originalSettings, jqXHR ) {
+
+	var callbackName, overwritten, responseContainer,
+		jsonProp = s.jsonp !== false && ( rjsonp.test( s.url ) ?
+			"url" :
+			typeof s.data === "string" &&
+				( s.contentType || "" )
+					.indexOf( "application/x-www-form-urlencoded" ) === 0 &&
+				rjsonp.test( s.data ) && "data"
+		);
+
+	// Handle iff the expected data type is "jsonp" or we have a parameter to set
+	if ( jsonProp || s.dataTypes[ 0 ] === "jsonp" ) {
+
+		// Get callback name, remembering preexisting value associated with it
+		callbackName = s.jsonpCallback = isFunction( s.jsonpCallback ) ?
+			s.jsonpCallback() :
+			s.jsonpCallback;
+
+		// Insert callback into url or form data
+		if ( jsonProp ) {
+			s[ jsonProp ] = s[ jsonProp ].replace( rjsonp, "$1" + callbackName );
+		} else if ( s.jsonp !== false ) {
+			s.url += ( rquery.test( s.url ) ? "&" : "?" ) + s.jsonp + "=" + callbackName;
+		}
+
+		// Use data converter to retrieve json after script execution
+		s.converters[ "script json" ] = function() {
+			if ( !responseContainer ) {
+				jQuery.error( callbackName + " was not called" );
+			}
+			return responseContainer[ 0 ];
+		};
+
+		// Force json dataType
+		s.dataTypes[ 0 ] = "json";
+
+		// Install callback
+		overwritten = window[ callbackName ];
+		window[ callbackName ] = function() {
+			responseContainer = arguments;
+		};
+
+		// Clean-up function (fires after converters)
+		jqXHR.always( function() {
+
+			// If previous value didn't exist - remove it
+			if ( overwritten === undefined ) {
+				jQuery( window ).removeProp( callbackName );
+
+			// Otherwise restore preexisting value
+			} else {
+				window[ callbackName ] = overwritten;
+			}
+
+			// Save back as free
+			if ( s[ callbackName ] ) {
+
+				// Make sure that re-using the options doesn't screw things around
+				s.jsonpCallback = originalSettings.jsonpCallback;
+
+				// Save the callback name for future use
+				oldCallbacks.push( callbackName );
+			}
+
+			// Call if it was a function and we have a response
+			if ( responseContainer && isFunction( overwritten ) ) {
+				overwritten( responseContainer[ 0 ] );
+			}
+
+			responseContainer = overwritten = undefined;
+		} );
+
+		// Delegate to script
+		return "script";
+	}
+} );
+
+
+
+
+// Support: Safari 8 only
+// In Safari 8 documents created via document.implementation.createHTMLDocument
+// collapse sibling forms: the second one becomes a child of the first one.
+// Because of that, this security measure has to be disabled in Safari 8.
+// https://bugs.webkit.org/show_bug.cgi?id=137337
+support.createHTMLDocument = ( function() {
+	var body = document.implementation.createHTMLDocument( "" ).body;
+	body.innerHTML = "<form></form><form></form>";
+	return body.childNodes.length === 2;
+} )();
+
+
+// Argument "data" should be string of html
+// context (optional): If specified, the fragment will be created in this context,
+// defaults to document
+// keepScripts (optional): If true, will include scripts passed in the html string
+jQuery.parseHTML = function( data, context, keepScripts ) {
+	if ( typeof data !== "string" ) {
+		return [];
+	}
+	if ( typeof context === "boolean" ) {
+		keepScripts = context;
+		context = false;
+	}
+
+	var base, parsed, scripts;
+
+	if ( !context ) {
+
+		// Stop scripts or inline event handlers from being executed immediately
+		// by using document.implementation
+		if ( support.createHTMLDocument ) {
+			context = document.implementation.createHTMLDocument( "" );
+
+			// Set the base href for the created document
+			// so any parsed elements with URLs
+			// are based on the document's URL (gh-2965)
+			base = context.createElement( "base" );
+			base.href = document.location.href;
+			context.head.appendChild( base );
+		} else {
+			context = document;
+		}
+	}
+
+	parsed = rsingleTag.exec( data );
+	scripts = !keepScripts && [];
+
+	// Single tag
+	if ( parsed ) {
+		return [ context.createElement( parsed[ 1 ] ) ];
+	}
+
+	parsed = buildFragment( [ data ], context, scripts );
+
+	if ( scripts && scripts.length ) {
+		jQuery( scripts ).remove();
+	}
+
+	return jQuery.merge( [], parsed.childNodes );
+};
+
+
+/**
+ * Load a url into a page
+ */
+jQuery.fn.load = function( url, params, callback ) {
+	var selector, type, response,
+		self = this,
+		off = url.indexOf( " " );
+
+	if ( off > -1 ) {
+		selector = stripAndCollapse( url.slice( off ) );
+		url = url.slice( 0, off );
+	}
+
+	// If it's a function
+	if ( isFunction( params ) ) {
+
+		// We assume that it's the callback
+		callback = params;
+		params = undefined;
+
+	// Otherwise, build a param string
+	} else if ( params && typeof params === "object" ) {
+		type = "POST";
+	}
+
+	// If we have elements to modify, make the request
+	if ( self.length > 0 ) {
+		jQuery.ajax( {
+			url: url,
+
+			// If "type" variable is undefined, then "GET" method will be used.
+			// Make value of this field explicit since
+			// user can override it through ajaxSetup method
+			type: type || "GET",
+			dataType: "html",
+			data: params
+		} ).done( function( responseText ) {
+
+			// Save response for use in complete callback
+			response = arguments;
+
+			self.html( selector ?
+
+				// If a selector was specified, locate the right elements in a dummy div
+				// Exclude scripts to avoid IE 'Permission Denied' errors
+				jQuery( "<div>" ).append( jQuery.parseHTML( responseText ) ).find( selector ) :
+
+				// Otherwise use the full result
+				responseText );
+
+		// If the request succeeds, this function gets "data", "status", "jqXHR"
+		// but they are ignored because response was set above.
+		// If it fails, this function gets "jqXHR", "status", "error"
+		} ).always( callback && function( jqXHR, status ) {
+			self.each( function() {
+				callback.apply( this, response || [ jqXHR.responseText, status, jqXHR ] );
+			} );
+		} );
+	}
+
+	return this;
+};
+
+
+
+
+jQuery.expr.pseudos.animated = function( elem ) {
+	return jQuery.grep( jQuery.timers, function( fn ) {
+		return elem === fn.elem;
+	} ).length;
+};
+
+
+
+
+jQuery.offset = {
+	setOffset: function( elem, options, i ) {
+		var curPosition, curLeft, curCSSTop, curTop, curOffset, curCSSLeft, calculatePosition,
+			position = jQuery.css( elem, "position" ),
+			curElem = jQuery( elem ),
+			props = {};
+
+		// Set position first, in-case top/left are set even on static elem
+		if ( position === "static" ) {
+			elem.style.position = "relative";
+		}
+
+		curOffset = curElem.offset();
+		curCSSTop = jQuery.css( elem, "top" );
+		curCSSLeft = jQuery.css( elem, "left" );
+		calculatePosition = ( position === "absolute" || position === "fixed" ) &&
+			( curCSSTop + curCSSLeft ).indexOf( "auto" ) > -1;
+
+		// Need to be able to calculate position if either
+		// top or left is auto and position is either absolute or fixed
+		if ( calculatePosition ) {
+			curPosition = curElem.position();
+			curTop = curPosition.top;
+			curLeft = curPosition.left;
+
+		} else {
+			curTop = parseFloat( curCSSTop ) || 0;
+			curLeft = parseFloat( curCSSLeft ) || 0;
+		}
+
+		if ( isFunction( options ) ) {
+
+			// Use jQuery.extend here to allow modification of coordinates argument (gh-1848)
+			options = options.call( elem, i, jQuery.extend( {}, curOffset ) );
+		}
+
+		if ( options.top != null ) {
+			props.top = ( options.top - curOffset.top ) + curTop;
+		}
+		if ( options.left != null ) {
+			props.left = ( options.left - curOffset.left ) + curLeft;
+		}
+
+		if ( "using" in options ) {
+			options.using.call( elem, props );
+
+		} else {
+			curElem.css( props );
+		}
+	}
+};
+
+jQuery.fn.extend( {
+
+	// offset() relates an element's border box to the document origin
+	offset: function( options ) {
+
+		// Preserve chaining for setter
+		if ( arguments.length ) {
+			return options === undefined ?
+				this :
+				this.each( function( i ) {
+					jQuery.offset.setOffset( this, options, i );
+				} );
+		}
+
+		var rect, win,
+			elem = this[ 0 ];
+
+		if ( !elem ) {
+			return;
+		}
+
+		// Return zeros for disconnected and hidden (display: none) elements (gh-2310)
+		// Support: IE <=11 only
+		// Running getBoundingClientRect on a
+		// disconnected node in IE throws an error
+		if ( !elem.getClientRects().length ) {
+			return { top: 0, left: 0 };
+		}
+
+		// Get document-relative position by adding viewport scroll to viewport-relative gBCR
+		rect = elem.getBoundingClientRect();
+		win = elem.ownerDocument.defaultView;
+		return {
+			top: rect.top + win.pageYOffset,
+			left: rect.left + win.pageXOffset
+		};
+	},
+
+	// position() relates an element's margin box to its offset parent's padding box
+	// This corresponds to the behavior of CSS absolute positioning
+	position: function() {
+		if ( !this[ 0 ] ) {
+			return;
+		}
+
+		var offsetParent, offset, doc,
+			elem = this[ 0 ],
+			parentOffset = { top: 0, left: 0 };
+
+		// position:fixed elements are offset from the viewport, which itself always has zero offset
+		if ( jQuery.css( elem, "position" ) === "fixed" ) {
+
+			// Assume position:fixed implies availability of getBoundingClientRect
+			offset = elem.getBoundingClientRect();
+
+		} else {
+			offset = this.offset();
+
+			// Account for the *real* offset parent, which can be the document or its root element
+			// when a statically positioned element is identified
+			doc = elem.ownerDocument;
+			offsetParent = elem.offsetParent || doc.documentElement;
+			while ( offsetParent &&
+				( offsetParent === doc.body || offsetParent === doc.documentElement ) &&
+				jQuery.css( offsetParent, "position" ) === "static" ) {
+
+				offsetParent = offsetParent.parentNode;
+			}
+			if ( offsetParent && offsetParent !== elem && offsetParent.nodeType === 1 ) {
+
+				// Incorporate borders into its offset, since they are outside its content origin
+				parentOffset = jQuery( offsetParent ).offset();
+				parentOffset.top += jQuery.css( offsetParent, "borderTopWidth", true );
+				parentOffset.left += jQuery.css( offsetParent, "borderLeftWidth", true );
+			}
+		}
+
+		// Subtract parent offsets and element margins
+		return {
+			top: offset.top - parentOffset.top - jQuery.css( elem, "marginTop", true ),
+			left: offset.left - parentOffset.left - jQuery.css( elem, "marginLeft", true )
+		};
+	},
+
+	// This method will return documentElement in the following cases:
+	// 1) For the element inside the iframe without offsetParent, this method will return
+	//    documentElement of the parent window
+	// 2) For the hidden or detached element
+	// 3) For body or html element, i.e. in case of the html node - it will return itself
+	//
+	// but those exceptions were never presented as a real life use-cases
+	// and might be considered as more preferable results.
+	//
+	// This logic, however, is not guaranteed and can change at any point in the future
+	offsetParent: function() {
+		return this.map( function() {
+			var offsetParent = this.offsetParent;
+
+			while ( offsetParent && jQuery.css( offsetParent, "position" ) === "static" ) {
+				offsetParent = offsetParent.offsetParent;
+			}
+
+			return offsetParent || documentElement;
+		} );
+	}
+} );
+
+// Create scrollLeft and scrollTop methods
+jQuery.each( { scrollLeft: "pageXOffset", scrollTop: "pageYOffset" }, function( method, prop ) {
+	var top = "pageYOffset" === prop;
+
+	jQuery.fn[ method ] = function( val ) {
+		return access( this, function( elem, method, val ) {
+
+			// Coalesce documents and windows
+			var win;
+			if ( isWindow( elem ) ) {
+				win = elem;
+			} else if ( elem.nodeType === 9 ) {
+				win = elem.defaultView;
+			}
+
+			if ( val === undefined ) {
+				return win ? win[ prop ] : elem[ method ];
+			}
+
+			if ( win ) {
+				win.scrollTo(
+					!top ? val : win.pageXOffset,
+					top ? val : win.pageYOffset
+				);
+
+			} else {
+				elem[ method ] = val;
+			}
+		}, method, val, arguments.length );
+	};
+} );
+
+// Support: Safari <=7 - 9.1, Chrome <=37 - 49
+// Add the top/left cssHooks using jQuery.fn.position
+// Webkit bug: https://bugs.webkit.org/show_bug.cgi?id=29084
+// Blink bug: https://bugs.chromium.org/p/chromium/issues/detail?id=589347
+// getComputedStyle returns percent when specified for top/left/bottom/right;
+// rather than make the css module depend on the offset module, just check for it here
+jQuery.each( [ "top", "left" ], function( _i, prop ) {
+	jQuery.cssHooks[ prop ] = addGetHookIf( support.pixelPosition,
+		function( elem, computed ) {
+			if ( computed ) {
+				computed = curCSS( elem, prop );
+
+				// If curCSS returns percentage, fallback to offset
+				return rnumnonpx.test( computed ) ?
+					jQuery( elem ).position()[ prop ] + "px" :
+					computed;
+			}
+		}
+	);
+} );
+
+
+// Create innerHeight, innerWidth, height, width, outerHeight and outerWidth methods
+jQuery.each( { Height: "height", Width: "width" }, function( name, type ) {
+	jQuery.each( {
+		padding: "inner" + name,
+		content: type,
+		"": "outer" + name
+	}, function( defaultExtra, funcName ) {
+
+		// Margin is only for outerHeight, outerWidth
+		jQuery.fn[ funcName ] = function( margin, value ) {
+			var chainable = arguments.length && ( defaultExtra || typeof margin !== "boolean" ),
+				extra = defaultExtra || ( margin === true || value === true ? "margin" : "border" );
+
+			return access( this, function( elem, type, value ) {
+				var doc;
+
+				if ( isWindow( elem ) ) {
+
+					// $( window ).outerWidth/Height return w/h including scrollbars (gh-1729)
+					return funcName.indexOf( "outer" ) === 0 ?
+						elem[ "inner" + name ] :
+						elem.document.documentElement[ "client" + name ];
+				}
+
+				// Get document width or height
+				if ( elem.nodeType === 9 ) {
+					doc = elem.documentElement;
+
+					// Either scroll[Width/Height] or offset[Width/Height] or client[Width/Height],
+					// whichever is greatest
+					return Math.max(
+						elem.body[ "scroll" + name ], doc[ "scroll" + name ],
+						elem.body[ "offset" + name ], doc[ "offset" + name ],
+						doc[ "client" + name ]
+					);
+				}
+
+				return value === undefined ?
+
+					// Get width or height on the element, requesting but not forcing parseFloat
+					jQuery.css( elem, type, extra ) :
+
+					// Set width or height on the element
+					jQuery.style( elem, type, value, extra );
+			}, type, chainable ? margin : undefined, chainable );
+		};
+	} );
+} );
+
+
+jQuery.each( [
+	"ajaxStart",
+	"ajaxStop",
+	"ajaxComplete",
+	"ajaxError",
+	"ajaxSuccess",
+	"ajaxSend"
+], function( _i, type ) {
+	jQuery.fn[ type ] = function( fn ) {
+		return this.on( type, fn );
+	};
+} );
+
+
+
+
+jQuery.fn.extend( {
+
+	bind: function( types, data, fn ) {
+		return this.on( types, null, data, fn );
+	},
+	unbind: function( types, fn ) {
+		return this.off( types, null, fn );
+	},
+
+	delegate: function( selector, types, data, fn ) {
+		return this.on( types, selector, data, fn );
+	},
+	undelegate: function( selector, types, fn ) {
+
+		// ( namespace ) or ( selector, types [, fn] )
+		return arguments.length === 1 ?
+			this.off( selector, "**" ) :
+			this.off( types, selector || "**", fn );
+	},
+
+	hover: function( fnOver, fnOut ) {
+		return this.mouseenter( fnOver ).mouseleave( fnOut || fnOver );
+	}
+} );
+
+jQuery.each(
+	( "blur focus focusin focusout resize scroll click dblclick " +
+	"mousedown mouseup mousemove mouseover mouseout mouseenter mouseleave " +
+	"change select submit keydown keypress keyup contextmenu" ).split( " " ),
+	function( _i, name ) {
+
+		// Handle event binding
+		jQuery.fn[ name ] = function( data, fn ) {
+			return arguments.length > 0 ?
+				this.on( name, null, data, fn ) :
+				this.trigger( name );
+		};
+	}
+);
+
+
+
+
+// Support: Android <=4.0 only
+// Make sure we trim BOM and NBSP
+var rtrim = /^[\s\uFEFF\xA0]+|[\s\uFEFF\xA0]+$/g;
+
+// Bind a function to a context, optionally partially applying any
+// arguments.
+// jQuery.proxy is deprecated to promote standards (specifically Function#bind)
+// However, it is not slated for removal any time soon
+jQuery.proxy = function( fn, context ) {
+	var tmp, args, proxy;
+
+	if ( typeof context === "string" ) {
+		tmp = fn[ context ];
+		context = fn;
+		fn = tmp;
+	}
+
+	// Quick check to determine if target is callable, in the spec
+	// this throws a TypeError, but we will just return undefined.
+	if ( !isFunction( fn ) ) {
+		return undefined;
+	}
+
+	// Simulated bind
+	args = slice.call( arguments, 2 );
+	proxy = function() {
+		return fn.apply( context || this, args.concat( slice.call( arguments ) ) );
+	};
+
+	// Set the guid of unique handler to the same of original handler, so it can be removed
+	proxy.guid = fn.guid = fn.guid || jQuery.guid++;
+
+	return proxy;
+};
+
+jQuery.holdReady = function( hold ) {
+	if ( hold ) {
+		jQuery.readyWait++;
+	} else {
+		jQuery.ready( true );
+	}
+};
+jQuery.isArray = Array.isArray;
+jQuery.parseJSON = JSON.parse;
+jQuery.nodeName = nodeName;
+jQuery.isFunction = isFunction;
+jQuery.isWindow = isWindow;
+jQuery.camelCase = camelCase;
+jQuery.type = toType;
+
+jQuery.now = Date.now;
+
+jQuery.isNumeric = function( obj ) {
+
+	// As of jQuery 3.0, isNumeric is limited to
+	// strings and numbers (primitives or objects)
+	// that can be coerced to finite numbers (gh-2662)
+	var type = jQuery.type( obj );
+	return ( type === "number" || type === "string" ) &&
+
+		// parseFloat NaNs numeric-cast false positives ("")
+		// ...but misinterprets leading-number strings, particularly hex literals ("0x...")
+		// subtraction forces infinities to NaN
+		!isNaN( obj - parseFloat( obj ) );
+};
+
+jQuery.trim = function( text ) {
+	return text == null ?
+		"" :
+		( text + "" ).replace( rtrim, "" );
+};
+
+
+
+// Register as a named AMD module, since jQuery can be concatenated with other
+// files that may use define, but not via a proper concatenation script that
+// understands anonymous AMD modules. A named AMD is safest and most robust
+// way to register. Lowercase jquery is used because AMD module names are
+// derived from file names, and jQuery is normally delivered in a lowercase
+// file name. Do this after creating the global so that if an AMD module wants
+// to call noConflict to hide this version of jQuery, it will work.
+
+// Note that for maximum portability, libraries that are not jQuery should
+// declare themselves as anonymous modules, and avoid setting a global if an
+// AMD loader is present. jQuery is a special case. For more information, see
+// https://github.com/jrburke/requirejs/wiki/Updating-existing-libraries#wiki-anon
+
+if ( typeof define === "function" && define.amd ) {
+	define( "jquery", [], function() {
+		return jQuery;
+	} );
+}
+
+
+
+
+var
+
+	// Map over jQuery in case of overwrite
+	_jQuery = window.jQuery,
+
+	// Map over the $ in case of overwrite
+	_$ = window.$;
+
+jQuery.noConflict = function( deep ) {
+	if ( window.$ === jQuery ) {
+		window.$ = _$;
+	}
+
+	if ( deep && window.jQuery === jQuery ) {
+		window.jQuery = _jQuery;
+	}
+
+	return jQuery;
+};
+
+// Expose jQuery and $ identifiers, even in AMD
+// (#7102#comment:10, https://github.com/jquery/jquery/pull/557)
+// and CommonJS for browser emulators (#13566)
+if ( typeof noGlobal === "undefined" ) {
+	window.jQuery = window.$ = jQuery;
+}
+
+
+
+
+return jQuery;
+} );
diff --git a/docs/source/_build/html/_static/jquery.js b/docs/source/_build/html/_static/jquery.js
new file mode 100644
index 0000000..c4c6022
--- /dev/null
+++ b/docs/source/_build/html/_static/jquery.js
@@ -0,0 +1,2 @@
+/*! jQuery v3.6.0 | (c) OpenJS Foundation and other contributors | jquery.org/license */
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@@ -0,0 +1,4 @@
+/**
+* @preserve HTML5 Shiv 3.7.3 | @afarkas @jdalton @jon_neal @rem | MIT/GPL2 Licensed
+*/
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+!function(n){var e={};function t(i){if(e[i])return e[i].exports;var o=e[i]={i:i,l:!1,exports:{}};return n[i].call(o.exports,o,o.exports,t),o.l=!0,o.exports}t.m=n,t.c=e,t.d=function(n,e,i){t.o(n,e)||Object.defineProperty(n,e,{enumerable:!0,get:i})},t.r=function(n){"undefined"!=typeof Symbol&&Symbol.toStringTag&&Object.defineProperty(n,Symbol.toStringTag,{value:"Module"}),Object.defineProperty(n,"__esModule",{value:!0})},t.t=function(n,e){if(1&e&&(n=t(n)),8&e)return n;if(4&e&&"object"==typeof n&&n&&n.__esModule)return n;var i=Object.create(null);if(t.r(i),Object.defineProperty(i,"default",{enumerable:!0,value:n}),2&e&&"string"!=typeof n)for(var o in n)t.d(i,o,function(e){return n[e]}.bind(null,o));return i},t.n=function(n){var e=n&&n.__esModule?function(){return n.default}:function(){return n};return t.d(e,"a",e),e},t.o=function(n,e){return Object.prototype.hasOwnProperty.call(n,e)},t.p="",t(t.s=0)}([function(n,e,t){t(1),n.exports=t(3)},function(n,e,t){(function(){var 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diff --git a/docs/source/_build/html/_static/language_data.js b/docs/source/_build/html/_static/language_data.js
new file mode 100644
index 0000000..2e22b06
--- /dev/null
+++ b/docs/source/_build/html/_static/language_data.js
@@ -0,0 +1,199 @@
+/*
+ * language_data.js
+ * ~~~~~~~~~~~~~~~~
+ *
+ * This script contains the language-specific data used by searchtools.js,
+ * namely the list of stopwords, stemmer, scorer and splitter.
+ *
+ * :copyright: Copyright 2007-2022 by the Sphinx team, see AUTHORS.
+ * :license: BSD, see LICENSE for details.
+ *
+ */
+
+var stopwords = ["a", "and", "are", "as", "at", "be", "but", "by", "for", "if", "in", "into", "is", "it", "near", "no", "not", "of", "on", "or", "such", "that", "the", "their", "then", "there", "these", "they", "this", "to", "was", "will", "with"];
+
+
+/* Non-minified version is copied as a separate JS file, is available */
+
+/**
+ * Porter Stemmer
+ */
+var Stemmer = function() {
+
+  var step2list = {
+    ational: 'ate',
+    tional: 'tion',
+    enci: 'ence',
+    anci: 'ance',
+    izer: 'ize',
+    bli: 'ble',
+    alli: 'al',
+    entli: 'ent',
+    eli: 'e',
+    ousli: 'ous',
+    ization: 'ize',
+    ation: 'ate',
+    ator: 'ate',
+    alism: 'al',
+    iveness: 'ive',
+    fulness: 'ful',
+    ousness: 'ous',
+    aliti: 'al',
+    iviti: 'ive',
+    biliti: 'ble',
+    logi: 'log'
+  };
+
+  var step3list = {
+    icate: 'ic',
+    ative: '',
+    alize: 'al',
+    iciti: 'ic',
+    ical: 'ic',
+    ful: '',
+    ness: ''
+  };
+
+  var c = "[^aeiou]";          // consonant
+  var v = "[aeiouy]";          // vowel
+  var C = c + "[^aeiouy]*";    // consonant sequence
+  var V = v + "[aeiou]*";      // vowel sequence
+
+  var mgr0 = "^(" + C + ")?" + V + C;                      // [C]VC... is m>0
+  var meq1 = "^(" + C + ")?" + V + C + "(" + V + ")?$";    // [C]VC[V] is m=1
+  var mgr1 = "^(" + C + ")?" + V + C + V + C;              // [C]VCVC... is m>1
+  var s_v   = "^(" + C + ")?" + v;                         // vowel in stem
+
+  this.stemWord = function (w) {
+    var stem;
+    var suffix;
+    var firstch;
+    var origword = w;
+
+    if (w.length < 3)
+      return w;
+
+    var re;
+    var re2;
+    var re3;
+    var re4;
+
+    firstch = w.substr(0,1);
+    if (firstch == "y")
+      w = firstch.toUpperCase() + w.substr(1);
+
+    // Step 1a
+    re = /^(.+?)(ss|i)es$/;
+    re2 = /^(.+?)([^s])s$/;
+
+    if (re.test(w))
+      w = w.replace(re,"$1$2");
+    else if (re2.test(w))
+      w = w.replace(re2,"$1$2");
+
+    // Step 1b
+    re = /^(.+?)eed$/;
+    re2 = /^(.+?)(ed|ing)$/;
+    if (re.test(w)) {
+      var fp = re.exec(w);
+      re = new RegExp(mgr0);
+      if (re.test(fp[1])) {
+        re = /.$/;
+        w = w.replace(re,"");
+      }
+    }
+    else if (re2.test(w)) {
+      var fp = re2.exec(w);
+      stem = fp[1];
+      re2 = new RegExp(s_v);
+      if (re2.test(stem)) {
+        w = stem;
+        re2 = /(at|bl|iz)$/;
+        re3 = new RegExp("([^aeiouylsz])\\1$");
+        re4 = new RegExp("^" + C + v + "[^aeiouwxy]$");
+        if (re2.test(w))
+          w = w + "e";
+        else if (re3.test(w)) {
+          re = /.$/;
+          w = w.replace(re,"");
+        }
+        else if (re4.test(w))
+          w = w + "e";
+      }
+    }
+
+    // Step 1c
+    re = /^(.+?)y$/;
+    if (re.test(w)) {
+      var fp = re.exec(w);
+      stem = fp[1];
+      re = new RegExp(s_v);
+      if (re.test(stem))
+        w = stem + "i";
+    }
+
+    // Step 2
+    re = /^(.+?)(ational|tional|enci|anci|izer|bli|alli|entli|eli|ousli|ization|ation|ator|alism|iveness|fulness|ousness|aliti|iviti|biliti|logi)$/;
+    if (re.test(w)) {
+      var fp = re.exec(w);
+      stem = fp[1];
+      suffix = fp[2];
+      re = new RegExp(mgr0);
+      if (re.test(stem))
+        w = stem + step2list[suffix];
+    }
+
+    // Step 3
+    re = /^(.+?)(icate|ative|alize|iciti|ical|ful|ness)$/;
+    if (re.test(w)) {
+      var fp = re.exec(w);
+      stem = fp[1];
+      suffix = fp[2];
+      re = new RegExp(mgr0);
+      if (re.test(stem))
+        w = stem + step3list[suffix];
+    }
+
+    // Step 4
+    re = /^(.+?)(al|ance|ence|er|ic|able|ible|ant|ement|ment|ent|ou|ism|ate|iti|ous|ive|ize)$/;
+    re2 = /^(.+?)(s|t)(ion)$/;
+    if (re.test(w)) {
+      var fp = re.exec(w);
+      stem = fp[1];
+      re = new RegExp(mgr1);
+      if (re.test(stem))
+        w = stem;
+    }
+    else if (re2.test(w)) {
+      var fp = re2.exec(w);
+      stem = fp[1] + fp[2];
+      re2 = new RegExp(mgr1);
+      if (re2.test(stem))
+        w = stem;
+    }
+
+    // Step 5
+    re = /^(.+?)e$/;
+    if (re.test(w)) {
+      var fp = re.exec(w);
+      stem = fp[1];
+      re = new RegExp(mgr1);
+      re2 = new RegExp(meq1);
+      re3 = new RegExp("^" + C + v + "[^aeiouwxy]$");
+      if (re.test(stem) || (re2.test(stem) && !(re3.test(stem))))
+        w = stem;
+    }
+    re = /ll$/;
+    re2 = new RegExp(mgr1);
+    if (re.test(w) && re2.test(w)) {
+      re = /.$/;
+      w = w.replace(re,"");
+    }
+
+    // and turn initial Y back to y
+    if (firstch == "y")
+      w = firstch.toLowerCase() + w.substr(1);
+    return w;
+  }
+}
+
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--- /dev/null
+++ b/docs/source/_build/html/_static/pygments.css
@@ -0,0 +1,74 @@
+pre { line-height: 125%; }
+td.linenos .normal { color: inherit; background-color: transparent; padding-left: 5px; padding-right: 5px; }
+span.linenos { color: inherit; background-color: transparent; padding-left: 5px; padding-right: 5px; }
+td.linenos .special { color: #000000; background-color: #ffffc0; padding-left: 5px; padding-right: 5px; }
+span.linenos.special { color: #000000; background-color: #ffffc0; padding-left: 5px; padding-right: 5px; }
+.highlight .hll { background-color: #ffffcc }
+.highlight { background: #f8f8f8; }
+.highlight .c { color: #3D7B7B; font-style: italic } /* Comment */
+.highlight .err { border: 1px solid #FF0000 } /* Error */
+.highlight .k { color: #008000; font-weight: bold } /* Keyword */
+.highlight .o { color: #666666 } /* Operator */
+.highlight .ch { color: #3D7B7B; font-style: italic } /* Comment.Hashbang */
+.highlight .cm { color: #3D7B7B; font-style: italic } /* Comment.Multiline */
+.highlight .cp { color: #9C6500 } /* Comment.Preproc */
+.highlight .cpf { color: #3D7B7B; font-style: italic } /* Comment.PreprocFile */
+.highlight .c1 { color: #3D7B7B; font-style: italic } /* Comment.Single */
+.highlight .cs { color: #3D7B7B; font-style: italic } /* Comment.Special */
+.highlight .gd { color: #A00000 } /* Generic.Deleted */
+.highlight .ge { font-style: italic } /* Generic.Emph */
+.highlight .gr { color: #E40000 } /* Generic.Error */
+.highlight .gh { color: #000080; font-weight: bold } /* Generic.Heading */
+.highlight .gi { color: #008400 } /* Generic.Inserted */
+.highlight .go { color: #717171 } /* Generic.Output */
+.highlight .gp { color: #000080; font-weight: bold } /* Generic.Prompt */
+.highlight .gs { font-weight: bold } /* Generic.Strong */
+.highlight .gu { color: #800080; font-weight: bold } /* Generic.Subheading */
+.highlight .gt { color: #0044DD } /* Generic.Traceback */
+.highlight .kc { color: #008000; font-weight: bold } /* Keyword.Constant */
+.highlight .kd { color: #008000; font-weight: bold } /* Keyword.Declaration */
+.highlight .kn { color: #008000; font-weight: bold } /* Keyword.Namespace */
+.highlight .kp { color: #008000 } /* Keyword.Pseudo */
+.highlight .kr { color: #008000; font-weight: bold } /* Keyword.Reserved */
+.highlight .kt { color: #B00040 } /* Keyword.Type */
+.highlight .m { color: #666666 } /* Literal.Number */
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+.highlight .no { color: #880000 } /* Name.Constant */
+.highlight .nd { color: #AA22FF } /* Name.Decorator */
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+.highlight .ne { color: #CB3F38; font-weight: bold } /* Name.Exception */
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\ No newline at end of file
diff --git a/docs/source/_build/html/_static/searchtools.js b/docs/source/_build/html/_static/searchtools.js
new file mode 100644
index 0000000..e89e34d
--- /dev/null
+++ b/docs/source/_build/html/_static/searchtools.js
@@ -0,0 +1,566 @@
+/*
+ * searchtools.js
+ * ~~~~~~~~~~~~~~~~
+ *
+ * Sphinx JavaScript utilities for the full-text search.
+ *
+ * :copyright: Copyright 2007-2022 by the Sphinx team, see AUTHORS.
+ * :license: BSD, see LICENSE for details.
+ *
+ */
+"use strict";
+
+/**
+ * Simple result scoring code.
+ */
+if (typeof Scorer === "undefined") {
+  var Scorer = {
+    // Implement the following function to further tweak the score for each result
+    // The function takes a result array [docname, title, anchor, descr, score, filename]
+    // and returns the new score.
+    /*
+    score: result => {
+      const [docname, title, anchor, descr, score, filename] = result
+      return score
+    },
+    */
+
+    // query matches the full name of an object
+    objNameMatch: 11,
+    // or matches in the last dotted part of the object name
+    objPartialMatch: 6,
+    // Additive scores depending on the priority of the object
+    objPrio: {
+      0: 15, // used to be importantResults
+      1: 5, // used to be objectResults
+      2: -5, // used to be unimportantResults
+    },
+    //  Used when the priority is not in the mapping.
+    objPrioDefault: 0,
+
+    // query found in title
+    title: 15,
+    partialTitle: 7,
+    // query found in terms
+    term: 5,
+    partialTerm: 2,
+  };
+}
+
+const _removeChildren = (element) => {
+  while (element && element.lastChild) element.removeChild(element.lastChild);
+};
+
+/**
+ * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Regular_Expressions#escaping
+ */
+const _escapeRegExp = (string) =>
+  string.replace(/[.*+\-?^${}()|[\]\\]/g, "\\$&"); // $& means the whole matched string
+
+const _displayItem = (item, searchTerms) => {
+  const docBuilder = DOCUMENTATION_OPTIONS.BUILDER;
+  const docUrlRoot = DOCUMENTATION_OPTIONS.URL_ROOT;
+  const docFileSuffix = DOCUMENTATION_OPTIONS.FILE_SUFFIX;
+  const docLinkSuffix = DOCUMENTATION_OPTIONS.LINK_SUFFIX;
+  const showSearchSummary = DOCUMENTATION_OPTIONS.SHOW_SEARCH_SUMMARY;
+
+  const [docName, title, anchor, descr, score, _filename] = item;
+
+  let listItem = document.createElement("li");
+  let requestUrl;
+  let linkUrl;
+  if (docBuilder === "dirhtml") {
+    // dirhtml builder
+    let dirname = docName + "/";
+    if (dirname.match(/\/index\/$/))
+      dirname = dirname.substring(0, dirname.length - 6);
+    else if (dirname === "index/") dirname = "";
+    requestUrl = docUrlRoot + dirname;
+    linkUrl = requestUrl;
+  } else {
+    // normal html builders
+    requestUrl = docUrlRoot + docName + docFileSuffix;
+    linkUrl = docName + docLinkSuffix;
+  }
+  let linkEl = listItem.appendChild(document.createElement("a"));
+  linkEl.href = linkUrl + anchor;
+  linkEl.dataset.score = score;
+  linkEl.innerHTML = title;
+  if (descr)
+    listItem.appendChild(document.createElement("span")).innerHTML =
+      " (" + descr + ")";
+  else if (showSearchSummary)
+    fetch(requestUrl)
+      .then((responseData) => responseData.text())
+      .then((data) => {
+        if (data)
+          listItem.appendChild(
+            Search.makeSearchSummary(data, searchTerms)
+          );
+      });
+  Search.output.appendChild(listItem);
+};
+const _finishSearch = (resultCount) => {
+  Search.stopPulse();
+  Search.title.innerText = _("Search Results");
+  if (!resultCount)
+    Search.status.innerText = Documentation.gettext(
+      "Your search did not match any documents. Please make sure that all words are spelled correctly and that you've selected enough categories."
+    );
+  else
+    Search.status.innerText = _(
+      `Search finished, found ${resultCount} page(s) matching the search query.`
+    );
+};
+const _displayNextItem = (
+  results,
+  resultCount,
+  searchTerms
+) => {
+  // results left, load the summary and display it
+  // this is intended to be dynamic (don't sub resultsCount)
+  if (results.length) {
+    _displayItem(results.pop(), searchTerms);
+    setTimeout(
+      () => _displayNextItem(results, resultCount, searchTerms),
+      5
+    );
+  }
+  // search finished, update title and status message
+  else _finishSearch(resultCount);
+};
+
+/**
+ * Default splitQuery function. Can be overridden in ``sphinx.search`` with a
+ * custom function per language.
+ *
+ * The regular expression works by splitting the string on consecutive characters
+ * that are not Unicode letters, numbers, underscores, or emoji characters.
+ * This is the same as ``\W+`` in Python, preserving the surrogate pair area.
+ */
+if (typeof splitQuery === "undefined") {
+  var splitQuery = (query) => query
+      .split(/[^\p{Letter}\p{Number}_\p{Emoji_Presentation}]+/gu)
+      .filter(term => term)  // remove remaining empty strings
+}
+
+/**
+ * Search Module
+ */
+const Search = {
+  _index: null,
+  _queued_query: null,
+  _pulse_status: -1,
+
+  htmlToText: (htmlString) => {
+    const htmlElement = new DOMParser().parseFromString(htmlString, 'text/html');
+    htmlElement.querySelectorAll(".headerlink").forEach((el) => { el.remove() });
+    const docContent = htmlElement.querySelector('[role="main"]');
+    if (docContent !== undefined) return docContent.textContent;
+    console.warn(
+      "Content block not found. Sphinx search tries to obtain it via '[role=main]'. Could you check your theme or template."
+    );
+    return "";
+  },
+
+  init: () => {
+    const query = new URLSearchParams(window.location.search).get("q");
+    document
+      .querySelectorAll('input[name="q"]')
+      .forEach((el) => (el.value = query));
+    if (query) Search.performSearch(query);
+  },
+
+  loadIndex: (url) =>
+    (document.body.appendChild(document.createElement("script")).src = url),
+
+  setIndex: (index) => {
+    Search._index = index;
+    if (Search._queued_query !== null) {
+      const query = Search._queued_query;
+      Search._queued_query = null;
+      Search.query(query);
+    }
+  },
+
+  hasIndex: () => Search._index !== null,
+
+  deferQuery: (query) => (Search._queued_query = query),
+
+  stopPulse: () => (Search._pulse_status = -1),
+
+  startPulse: () => {
+    if (Search._pulse_status >= 0) return;
+
+    const pulse = () => {
+      Search._pulse_status = (Search._pulse_status + 1) % 4;
+      Search.dots.innerText = ".".repeat(Search._pulse_status);
+      if (Search._pulse_status >= 0) window.setTimeout(pulse, 500);
+    };
+    pulse();
+  },
+
+  /**
+   * perform a search for something (or wait until index is loaded)
+   */
+  performSearch: (query) => {
+    // create the required interface elements
+    const searchText = document.createElement("h2");
+    searchText.textContent = _("Searching");
+    const searchSummary = document.createElement("p");
+    searchSummary.classList.add("search-summary");
+    searchSummary.innerText = "";
+    const searchList = document.createElement("ul");
+    searchList.classList.add("search");
+
+    const out = document.getElementById("search-results");
+    Search.title = out.appendChild(searchText);
+    Search.dots = Search.title.appendChild(document.createElement("span"));
+    Search.status = out.appendChild(searchSummary);
+    Search.output = out.appendChild(searchList);
+
+    const searchProgress = document.getElementById("search-progress");
+    // Some themes don't use the search progress node
+    if (searchProgress) {
+      searchProgress.innerText = _("Preparing search...");
+    }
+    Search.startPulse();
+
+    // index already loaded, the browser was quick!
+    if (Search.hasIndex()) Search.query(query);
+    else Search.deferQuery(query);
+  },
+
+  /**
+   * execute search (requires search index to be loaded)
+   */
+  query: (query) => {
+    const filenames = Search._index.filenames;
+    const docNames = Search._index.docnames;
+    const titles = Search._index.titles;
+    const allTitles = Search._index.alltitles;
+    const indexEntries = Search._index.indexentries;
+
+    // stem the search terms and add them to the correct list
+    const stemmer = new Stemmer();
+    const searchTerms = new Set();
+    const excludedTerms = new Set();
+    const highlightTerms = new Set();
+    const objectTerms = new Set(splitQuery(query.toLowerCase().trim()));
+    splitQuery(query.trim()).forEach((queryTerm) => {
+      const queryTermLower = queryTerm.toLowerCase();
+
+      // maybe skip this "word"
+      // stopwords array is from language_data.js
+      if (
+        stopwords.indexOf(queryTermLower) !== -1 ||
+        queryTerm.match(/^\d+$/)
+      )
+        return;
+
+      // stem the word
+      let word = stemmer.stemWord(queryTermLower);
+      // select the correct list
+      if (word[0] === "-") excludedTerms.add(word.substr(1));
+      else {
+        searchTerms.add(word);
+        highlightTerms.add(queryTermLower);
+      }
+    });
+
+    if (SPHINX_HIGHLIGHT_ENABLED) {  // set in sphinx_highlight.js
+      localStorage.setItem("sphinx_highlight_terms", [...highlightTerms].join(" "))
+    }
+
+    // console.debug("SEARCH: searching for:");
+    // console.info("required: ", [...searchTerms]);
+    // console.info("excluded: ", [...excludedTerms]);
+
+    // array of [docname, title, anchor, descr, score, filename]
+    let results = [];
+    _removeChildren(document.getElementById("search-progress"));
+
+    const queryLower = query.toLowerCase();
+    for (const [title, foundTitles] of Object.entries(allTitles)) {
+      if (title.toLowerCase().includes(queryLower) && (queryLower.length >= title.length/2)) {
+        for (const [file, id] of foundTitles) {
+          let score = Math.round(100 * queryLower.length / title.length)
+          results.push([
+            docNames[file],
+            titles[file] !== title ? `${titles[file]} > ${title}` : title,
+            id !== null ? "#" + id : "",
+            null,
+            score,
+            filenames[file],
+          ]);
+        }
+      }
+    }
+
+    // search for explicit entries in index directives
+    for (const [entry, foundEntries] of Object.entries(indexEntries)) {
+      if (entry.includes(queryLower) && (queryLower.length >= entry.length/2)) {
+        for (const [file, id] of foundEntries) {
+          let score = Math.round(100 * queryLower.length / entry.length)
+          results.push([
+            docNames[file],
+            titles[file],
+            id ? "#" + id : "",
+            null,
+            score,
+            filenames[file],
+          ]);
+        }
+      }
+    }
+
+    // lookup as object
+    objectTerms.forEach((term) =>
+      results.push(...Search.performObjectSearch(term, objectTerms))
+    );
+
+    // lookup as search terms in fulltext
+    results.push(...Search.performTermsSearch(searchTerms, excludedTerms));
+
+    // let the scorer override scores with a custom scoring function
+    if (Scorer.score) results.forEach((item) => (item[4] = Scorer.score(item)));
+
+    // now sort the results by score (in opposite order of appearance, since the
+    // display function below uses pop() to retrieve items) and then
+    // alphabetically
+    results.sort((a, b) => {
+      const leftScore = a[4];
+      const rightScore = b[4];
+      if (leftScore === rightScore) {
+        // same score: sort alphabetically
+        const leftTitle = a[1].toLowerCase();
+        const rightTitle = b[1].toLowerCase();
+        if (leftTitle === rightTitle) return 0;
+        return leftTitle > rightTitle ? -1 : 1; // inverted is intentional
+      }
+      return leftScore > rightScore ? 1 : -1;
+    });
+
+    // remove duplicate search results
+    // note the reversing of results, so that in the case of duplicates, the highest-scoring entry is kept
+    let seen = new Set();
+    results = results.reverse().reduce((acc, result) => {
+      let resultStr = result.slice(0, 4).concat([result[5]]).map(v => String(v)).join(',');
+      if (!seen.has(resultStr)) {
+        acc.push(result);
+        seen.add(resultStr);
+      }
+      return acc;
+    }, []);
+
+    results = results.reverse();
+
+    // for debugging
+    //Search.lastresults = results.slice();  // a copy
+    // console.info("search results:", Search.lastresults);
+
+    // print the results
+    _displayNextItem(results, results.length, searchTerms);
+  },
+
+  /**
+   * search for object names
+   */
+  performObjectSearch: (object, objectTerms) => {
+    const filenames = Search._index.filenames;
+    const docNames = Search._index.docnames;
+    const objects = Search._index.objects;
+    const objNames = Search._index.objnames;
+    const titles = Search._index.titles;
+
+    const results = [];
+
+    const objectSearchCallback = (prefix, match) => {
+      const name = match[4]
+      const fullname = (prefix ? prefix + "." : "") + name;
+      const fullnameLower = fullname.toLowerCase();
+      if (fullnameLower.indexOf(object) < 0) return;
+
+      let score = 0;
+      const parts = fullnameLower.split(".");
+
+      // check for different match types: exact matches of full name or
+      // "last name" (i.e. last dotted part)
+      if (fullnameLower === object || parts.slice(-1)[0] === object)
+        score += Scorer.objNameMatch;
+      else if (parts.slice(-1)[0].indexOf(object) > -1)
+        score += Scorer.objPartialMatch; // matches in last name
+
+      const objName = objNames[match[1]][2];
+      const title = titles[match[0]];
+
+      // If more than one term searched for, we require other words to be
+      // found in the name/title/description
+      const otherTerms = new Set(objectTerms);
+      otherTerms.delete(object);
+      if (otherTerms.size > 0) {
+        const haystack = `${prefix} ${name} ${objName} ${title}`.toLowerCase();
+        if (
+          [...otherTerms].some((otherTerm) => haystack.indexOf(otherTerm) < 0)
+        )
+          return;
+      }
+
+      let anchor = match[3];
+      if (anchor === "") anchor = fullname;
+      else if (anchor === "-") anchor = objNames[match[1]][1] + "-" + fullname;
+
+      const descr = objName + _(", in ") + title;
+
+      // add custom score for some objects according to scorer
+      if (Scorer.objPrio.hasOwnProperty(match[2]))
+        score += Scorer.objPrio[match[2]];
+      else score += Scorer.objPrioDefault;
+
+      results.push([
+        docNames[match[0]],
+        fullname,
+        "#" + anchor,
+        descr,
+        score,
+        filenames[match[0]],
+      ]);
+    };
+    Object.keys(objects).forEach((prefix) =>
+      objects[prefix].forEach((array) =>
+        objectSearchCallback(prefix, array)
+      )
+    );
+    return results;
+  },
+
+  /**
+   * search for full-text terms in the index
+   */
+  performTermsSearch: (searchTerms, excludedTerms) => {
+    // prepare search
+    const terms = Search._index.terms;
+    const titleTerms = Search._index.titleterms;
+    const filenames = Search._index.filenames;
+    const docNames = Search._index.docnames;
+    const titles = Search._index.titles;
+
+    const scoreMap = new Map();
+    const fileMap = new Map();
+
+    // perform the search on the required terms
+    searchTerms.forEach((word) => {
+      const files = [];
+      const arr = [
+        { files: terms[word], score: Scorer.term },
+        { files: titleTerms[word], score: Scorer.title },
+      ];
+      // add support for partial matches
+      if (word.length > 2) {
+        const escapedWord = _escapeRegExp(word);
+        Object.keys(terms).forEach((term) => {
+          if (term.match(escapedWord) && !terms[word])
+            arr.push({ files: terms[term], score: Scorer.partialTerm });
+        });
+        Object.keys(titleTerms).forEach((term) => {
+          if (term.match(escapedWord) && !titleTerms[word])
+            arr.push({ files: titleTerms[word], score: Scorer.partialTitle });
+        });
+      }
+
+      // no match but word was a required one
+      if (arr.every((record) => record.files === undefined)) return;
+
+      // found search word in contents
+      arr.forEach((record) => {
+        if (record.files === undefined) return;
+
+        let recordFiles = record.files;
+        if (recordFiles.length === undefined) recordFiles = [recordFiles];
+        files.push(...recordFiles);
+
+        // set score for the word in each file
+        recordFiles.forEach((file) => {
+          if (!scoreMap.has(file)) scoreMap.set(file, {});
+          scoreMap.get(file)[word] = record.score;
+        });
+      });
+
+      // create the mapping
+      files.forEach((file) => {
+        if (fileMap.has(file) && fileMap.get(file).indexOf(word) === -1)
+          fileMap.get(file).push(word);
+        else fileMap.set(file, [word]);
+      });
+    });
+
+    // now check if the files don't contain excluded terms
+    const results = [];
+    for (const [file, wordList] of fileMap) {
+      // check if all requirements are matched
+
+      // as search terms with length < 3 are discarded
+      const filteredTermCount = [...searchTerms].filter(
+        (term) => term.length > 2
+      ).length;
+      if (
+        wordList.length !== searchTerms.size &&
+        wordList.length !== filteredTermCount
+      )
+        continue;
+
+      // ensure that none of the excluded terms is in the search result
+      if (
+        [...excludedTerms].some(
+          (term) =>
+            terms[term] === file ||
+            titleTerms[term] === file ||
+            (terms[term] || []).includes(file) ||
+            (titleTerms[term] || []).includes(file)
+        )
+      )
+        break;
+
+      // select one (max) score for the file.
+      const score = Math.max(...wordList.map((w) => scoreMap.get(file)[w]));
+      // add result to the result list
+      results.push([
+        docNames[file],
+        titles[file],
+        "",
+        null,
+        score,
+        filenames[file],
+      ]);
+    }
+    return results;
+  },
+
+  /**
+   * helper function to return a node containing the
+   * search summary for a given text. keywords is a list
+   * of stemmed words.
+   */
+  makeSearchSummary: (htmlText, keywords) => {
+    const text = Search.htmlToText(htmlText);
+    if (text === "") return null;
+
+    const textLower = text.toLowerCase();
+    const actualStartPosition = [...keywords]
+      .map((k) => textLower.indexOf(k.toLowerCase()))
+      .filter((i) => i > -1)
+      .slice(-1)[0];
+    const startWithContext = Math.max(actualStartPosition - 120, 0);
+
+    const top = startWithContext === 0 ? "" : "...";
+    const tail = startWithContext + 240 < text.length ? "..." : "";
+
+    let summary = document.createElement("p");
+    summary.classList.add("context");
+    summary.textContent = top + text.substr(startWithContext, 240).trim() + tail;
+
+    return summary;
+  },
+};
+
+_ready(Search.init);
diff --git a/docs/source/_build/html/_static/sg_gallery-binder.css b/docs/source/_build/html/_static/sg_gallery-binder.css
new file mode 100644
index 0000000..a33aa42
--- /dev/null
+++ b/docs/source/_build/html/_static/sg_gallery-binder.css
@@ -0,0 +1,6 @@
+/* CSS for binder integration */
+
+div.binder-badge {
+  margin: 1em auto;
+  vertical-align: middle;
+}
diff --git a/docs/source/_build/html/_static/sg_gallery-dataframe.css b/docs/source/_build/html/_static/sg_gallery-dataframe.css
new file mode 100644
index 0000000..25be730
--- /dev/null
+++ b/docs/source/_build/html/_static/sg_gallery-dataframe.css
@@ -0,0 +1,46 @@
+/* Pandas dataframe css */
+/* Taken from: https://github.com/spatialaudio/nbsphinx/blob/fb3ba670fc1ba5f54d4c487573dbc1b4ecf7e9ff/src/nbsphinx.py#L587-L619 */
+html[data-theme="light"] {
+  --sg-text-color: #000;
+  --sg-tr-odd-color: #f5f5f5;
+  --sg-tr-hover-color: rgba(66, 165, 245, 0.2);
+}
+html[data-theme="dark"] {
+  --sg-text-color: #fff;
+  --sg-tr-odd-color: #373737;
+  --sg-tr-hover-color: rgba(30, 81, 122, 0.2);
+}
+
+table.dataframe {
+  border: none !important;
+  border-collapse: collapse;
+  border-spacing: 0;
+  border-color: transparent;
+  color: var(--sg-text-color);
+  font-size: 12px;
+  table-layout: fixed;
+}
+table.dataframe thead {
+  border-bottom: 1px solid var(--sg-text-color);
+  vertical-align: bottom;
+}
+table.dataframe tr,
+table.dataframe th,
+table.dataframe td {
+  text-align: right;
+  vertical-align: middle;
+  padding: 0.5em 0.5em;
+  line-height: normal;
+  white-space: normal;
+  max-width: none;
+  border: none;
+}
+table.dataframe th {
+  font-weight: bold;
+}
+table.dataframe tbody tr:nth-child(odd) {
+  background: var(--sg-tr-odd-color);
+}
+table.dataframe tbody tr:hover {
+  background: var(--sg-tr-hover-color);
+}
diff --git a/docs/source/_build/html/_static/sg_gallery-rendered-html.css b/docs/source/_build/html/_static/sg_gallery-rendered-html.css
new file mode 100644
index 0000000..93dc2ff
--- /dev/null
+++ b/docs/source/_build/html/_static/sg_gallery-rendered-html.css
@@ -0,0 +1,224 @@
+/* Adapted from notebook/static/style/style.min.css */
+html[data-theme="light"] {
+  --sg-text-color: #000;
+  --sg-background-color: #ffffff;
+  --sg-code-background-color: #eff0f1;
+  --sg-tr-hover-color: rgba(66, 165, 245, 0.2);
+  --sg-tr-odd-color: #f5f5f5;
+}
+html[data-theme="dark"] {
+  --sg-text-color: #fff;
+  --sg-background-color: #121212;
+  --sg-code-background-color: #2f2f30;
+  --sg-tr-hover-color: rgba(66, 165, 245, 0.2);
+  --sg-tr-odd-color: #1f1f1f;
+}
+
+.rendered_html {
+  color: var(--sg-text-color);
+  /* any extras will just be numbers: */
+}
+.rendered_html em {
+  font-style: italic;
+}
+.rendered_html strong {
+  font-weight: bold;
+}
+.rendered_html u {
+  text-decoration: underline;
+}
+.rendered_html :link {
+  text-decoration: underline;
+}
+.rendered_html :visited {
+  text-decoration: underline;
+}
+.rendered_html h1 {
+  font-size: 185.7%;
+  margin: 1.08em 0 0 0;
+  font-weight: bold;
+  line-height: 1.0;
+}
+.rendered_html h2 {
+  font-size: 157.1%;
+  margin: 1.27em 0 0 0;
+  font-weight: bold;
+  line-height: 1.0;
+}
+.rendered_html h3 {
+  font-size: 128.6%;
+  margin: 1.55em 0 0 0;
+  font-weight: bold;
+  line-height: 1.0;
+}
+.rendered_html h4 {
+  font-size: 100%;
+  margin: 2em 0 0 0;
+  font-weight: bold;
+  line-height: 1.0;
+}
+.rendered_html h5 {
+  font-size: 100%;
+  margin: 2em 0 0 0;
+  font-weight: bold;
+  line-height: 1.0;
+  font-style: italic;
+}
+.rendered_html h6 {
+  font-size: 100%;
+  margin: 2em 0 0 0;
+  font-weight: bold;
+  line-height: 1.0;
+  font-style: italic;
+}
+.rendered_html h1:first-child {
+  margin-top: 0.538em;
+}
+.rendered_html h2:first-child {
+  margin-top: 0.636em;
+}
+.rendered_html h3:first-child {
+  margin-top: 0.777em;
+}
+.rendered_html h4:first-child {
+  margin-top: 1em;
+}
+.rendered_html h5:first-child {
+  margin-top: 1em;
+}
+.rendered_html h6:first-child {
+  margin-top: 1em;
+}
+.rendered_html ul:not(.list-inline),
+.rendered_html ol:not(.list-inline) {
+  padding-left: 2em;
+}
+.rendered_html ul {
+  list-style: disc;
+}
+.rendered_html ul ul {
+  list-style: square;
+  margin-top: 0;
+}
+.rendered_html ul ul ul {
+  list-style: circle;
+}
+.rendered_html ol {
+  list-style: decimal;
+}
+.rendered_html ol ol {
+  list-style: upper-alpha;
+  margin-top: 0;
+}
+.rendered_html ol ol ol {
+  list-style: lower-alpha;
+}
+.rendered_html ol ol ol ol {
+  list-style: lower-roman;
+}
+.rendered_html ol ol ol ol ol {
+  list-style: decimal;
+}
+.rendered_html * + ul {
+  margin-top: 1em;
+}
+.rendered_html * + ol {
+  margin-top: 1em;
+}
+.rendered_html hr {
+  color: var(--sg-text-color);
+  background-color: var(--sg-text-color);
+}
+.rendered_html pre {
+  margin: 1em 2em;
+  padding: 0px;
+  background-color: var(--sg-background-color);
+}
+.rendered_html code {
+  background-color: var(--sg-code-background-color);
+}
+.rendered_html p code {
+  padding: 1px 5px;
+}
+.rendered_html pre code {
+  background-color: var(--sg-background-color);
+}
+.rendered_html pre,
+.rendered_html code {
+  border: 0;
+  color: var(--sg-text-color);
+  font-size: 100%;
+}
+.rendered_html blockquote {
+  margin: 1em 2em;
+}
+.rendered_html table {
+  margin-left: auto;
+  margin-right: auto;
+  border: none;
+  border-collapse: collapse;
+  border-spacing: 0;
+  color: var(--sg-text-color);
+  font-size: 12px;
+  table-layout: fixed;
+}
+.rendered_html thead {
+  border-bottom: 1px solid var(--sg-text-color);
+  vertical-align: bottom;
+}
+.rendered_html tr,
+.rendered_html th,
+.rendered_html td {
+  text-align: right;
+  vertical-align: middle;
+  padding: 0.5em 0.5em;
+  line-height: normal;
+  white-space: normal;
+  max-width: none;
+  border: none;
+}
+.rendered_html th {
+  font-weight: bold;
+}
+.rendered_html tbody tr:nth-child(odd) {
+  background: var(--sg-tr-odd-color);
+}
+.rendered_html tbody tr:hover {
+  color: var(--sg-text-color);
+  background: var(--sg-tr-hover-color);
+}
+.rendered_html * + table {
+  margin-top: 1em;
+}
+.rendered_html p {
+  text-align: left;
+}
+.rendered_html * + p {
+  margin-top: 1em;
+}
+.rendered_html img {
+  display: block;
+  margin-left: auto;
+  margin-right: auto;
+}
+.rendered_html * + img {
+  margin-top: 1em;
+}
+.rendered_html img,
+.rendered_html svg {
+  max-width: 100%;
+  height: auto;
+}
+.rendered_html img.unconfined,
+.rendered_html svg.unconfined {
+  max-width: none;
+}
+.rendered_html .alert {
+  margin-bottom: initial;
+}
+.rendered_html * + .alert {
+  margin-top: 1em;
+}
+[dir="rtl"] .rendered_html p {
+  text-align: right;
+}
diff --git a/docs/source/_build/html/_static/sg_gallery.css b/docs/source/_build/html/_static/sg_gallery.css
new file mode 100644
index 0000000..7222783
--- /dev/null
+++ b/docs/source/_build/html/_static/sg_gallery.css
@@ -0,0 +1,342 @@
+/*
+Sphinx-Gallery has compatible CSS to fix default sphinx themes
+Tested for Sphinx 1.3.1 for all themes: default, alabaster, sphinxdoc,
+scrolls, agogo, traditional, nature, haiku, pyramid
+Tested for Read the Docs theme 0.1.7 */
+
+/* Define light colors */
+:root, html[data-theme="light"], body[data-theme="light"]{
+  --sg-tooltip-foreground: black;
+  --sg-tooltip-background: rgba(250, 250, 250, 0.9);
+  --sg-tooltip-border: #ccc transparent;
+  --sg-thumb-box-shadow-color: #6c757d40;
+  --sg-thumb-hover-border: #0069d9;
+  --sg-script-out: #888;
+  --sg-script-pre: #fafae2;
+  --sg-pytb-foreground: #000;
+  --sg-pytb-background: #ffe4e4;
+  --sg-pytb-border-color: #f66;
+  --sg-download-a-background-color: #ffc;
+  --sg-download-a-background-image: linear-gradient(to bottom, #ffc, #d5d57e);
+  --sg-download-a-border-color: 1px solid #c2c22d;
+  --sg-download-a-color: #000;
+  --sg-download-a-hover-background-color: #d5d57e;
+  --sg-download-a-hover-box-shadow-1: rgba(255, 255, 255, 0.1);
+  --sg-download-a-hover-box-shadow-2: rgba(0, 0, 0, 0.25);
+}
+@media(prefers-color-scheme: light) {
+  :root[data-theme="auto"], html[data-theme="auto"], body[data-theme="auto"] {
+    --sg-tooltip-foreground: black;
+    --sg-tooltip-background: rgba(250, 250, 250, 0.9);
+    --sg-tooltip-border: #ccc transparent;
+    --sg-thumb-box-shadow-color: #6c757d40;
+    --sg-thumb-hover-border: #0069d9;
+    --sg-script-out: #888;
+    --sg-script-pre: #fafae2;
+    --sg-pytb-foreground: #000;
+    --sg-pytb-background: #ffe4e4;
+    --sg-pytb-border-color: #f66;
+    --sg-download-a-background-color: #ffc;
+    --sg-download-a-background-image: linear-gradient(to bottom, #ffc, #d5d57e);
+    --sg-download-a-border-color: 1px solid #c2c22d;
+    --sg-download-a-color: #000;
+    --sg-download-a-hover-background-color: #d5d57e;
+    --sg-download-a-hover-box-shadow-1: rgba(255, 255, 255, 0.1);
+    --sg-download-a-hover-box-shadow-2: rgba(0, 0, 0, 0.25);
+  }
+}
+
+html[data-theme="dark"], body[data-theme="dark"] {
+  --sg-tooltip-foreground: white;
+  --sg-tooltip-background: rgba(10, 10, 10, 0.9);
+  --sg-tooltip-border: #333 transparent;
+  --sg-thumb-box-shadow-color: #79848d40;
+  --sg-thumb-hover-border: #003975;
+  --sg-script-out: rgb(179, 179, 179);
+  --sg-script-pre: #2e2e22;
+  --sg-pytb-foreground: #fff;
+  --sg-pytb-background: #1b1717;
+  --sg-pytb-border-color: #622;
+  --sg-download-a-background-color: #443;
+  --sg-download-a-background-image: linear-gradient(to bottom, #443, #221);
+  --sg-download-a-border-color: 1px solid #3a3a0d;
+  --sg-download-a-color: #fff;
+  --sg-download-a-hover-background-color: #616135;
+  --sg-download-a-hover-box-shadow-1: rgba(0, 0, 0, 0.1);
+  --sg-download-a-hover-box-shadow-2: rgba(255, 255, 255, 0.25);
+}
+@media(prefers-color-scheme: dark){
+  html[data-theme="auto"], body[data-theme="auto"] {
+    --sg-tooltip-foreground: white;
+    --sg-tooltip-background: rgba(10, 10, 10, 0.9);
+    --sg-tooltip-border: #333 transparent;
+    --sg-thumb-box-shadow-color: #79848d40;
+    --sg-thumb-hover-border: #003975;
+    --sg-script-out: rgb(179, 179, 179);
+    --sg-script-pre: #2e2e22;
+    --sg-pytb-foreground: #fff;
+    --sg-pytb-background: #1b1717;
+    --sg-pytb-border-color: #622;
+    --sg-download-a-background-color: #443;
+    --sg-download-a-background-image: linear-gradient(to bottom, #443, #221);
+    --sg-download-a-border-color: 1px solid #3a3a0d;
+    --sg-download-a-color: #fff;
+    --sg-download-a-hover-background-color: #616135;
+    --sg-download-a-hover-box-shadow-1: rgba(0, 0, 0, 0.1);
+    --sg-download-a-hover-box-shadow-2: rgba(255, 255, 255, 0.25);
+  }
+}
+
+.sphx-glr-thumbnails {
+  width: 100%;
+  margin: 0px 0px 20px 0px;
+
+  /* align thumbnails on a grid */
+  justify-content: space-between;
+  display: grid;
+  /* each grid column should be at least 160px (this will determine
+  the actual number of columns) and then take as much of the
+  remaining width as possible */
+  grid-template-columns: repeat(auto-fill, minmax(160px, 1fr));
+  gap: 15px;
+}
+.sphx-glr-thumbnails .toctree-wrapper {
+  /* hide empty toctree divs added to the DOM
+  by sphinx even though the toctree is hidden
+  (they would fill grid places with empty divs) */
+  display: none;
+}
+.sphx-glr-thumbcontainer {
+  background: transparent;
+  -moz-border-radius: 5px;
+  -webkit-border-radius: 5px;
+  border-radius: 5px;
+  box-shadow: 0 0 10px var(--sg-thumb-box-shadow-color);
+
+  /* useful to absolutely position link in div */
+  position: relative;
+
+  /* thumbnail width should include padding and borders
+  and take all available space */
+  box-sizing: border-box;
+  width: 100%;
+  padding: 10px;
+  border: 1px solid transparent;
+
+  /* align content in thumbnail */
+  display: flex;
+  flex-direction: column;
+  align-items: center;
+  gap: 7px;
+}
+.sphx-glr-thumbcontainer p {
+  position: absolute;
+  top: 0;
+  left: 0;
+}
+.sphx-glr-thumbcontainer p,
+.sphx-glr-thumbcontainer p a {
+  /* link should cover the whole thumbnail div */
+  width: 100%;
+  height: 100%;
+}
+.sphx-glr-thumbcontainer p a span {
+  /* text within link should be masked
+  (we are just interested in the href) */
+  display: none;
+}
+.sphx-glr-thumbcontainer:hover {
+  border: 1px solid;
+  border-color: var(--sg-thumb-hover-border);
+  cursor: pointer;
+}
+.sphx-glr-thumbcontainer a.internal {
+  bottom: 0;
+  display: block;
+  left: 0;
+  box-sizing: border-box;
+  padding: 150px 10px 0;
+  position: absolute;
+  right: 0;
+  top: 0;
+}
+/* Next one is to avoid Sphinx traditional theme to cover all the
+thumbnail with its default link Background color */
+.sphx-glr-thumbcontainer a.internal:hover {
+  background-color: transparent;
+}
+
+.sphx-glr-thumbcontainer p {
+  margin: 0 0 0.1em 0;
+}
+.sphx-glr-thumbcontainer .figure {
+  margin: 10px;
+  width: 160px;
+}
+.sphx-glr-thumbcontainer img {
+  display: inline;
+  max-height: 112px;
+  max-width: 160px;
+}
+.sphx-glr-thumbcontainer[tooltip]:hover:after {
+  background: var(--sg-tooltip-background);
+  -webkit-border-radius: 4px;
+  -moz-border-radius: 4px;
+  border-radius: 4px;
+  color: var(--sg-tooltip-foreground);
+  content: attr(tooltip);
+  padding: 10px;
+  z-index: 98;
+  width: 100%;
+  height: 100%;
+  position: absolute;
+  pointer-events: none;
+  top: 0;
+  box-sizing: border-box;
+  overflow: hidden;
+  backdrop-filter: blur(3px);
+}
+
+.sphx-glr-script-out {
+  color: var(--sg-script-out);
+  display: flex;
+  gap: 0.5em;
+}
+.sphx-glr-script-out::before {
+  content: "Out:";
+  /* These numbers come from the pre style in the pydata sphinx theme. This
+   * turns out to match perfectly on the rtd theme, but be a bit too low for
+   * the pydata sphinx theme. As I could not find a dimension to use that was
+   * scaled the same way, I just picked one option that worked pretty close for
+   * both. */
+  line-height: 1.4;
+  padding-top: 10px;
+}
+.sphx-glr-script-out .highlight {
+  background-color: transparent;
+  /* These options make the div expand... */
+  flex-grow: 1;
+  /* ... but also keep it from overflowing its flex container. */
+  overflow: auto;
+}
+.sphx-glr-script-out .highlight pre {
+  background-color: var(--sg-script-pre);
+  border: 0;
+  max-height: 30em;
+  overflow: auto;
+  padding-left: 1ex;
+  /* This margin is necessary in the pydata sphinx theme because pre has a box
+   * shadow which would be clipped by the overflow:auto in the parent div
+   * above. */
+  margin: 2px;
+  word-break: break-word;
+}
+.sphx-glr-script-out + p {
+  margin-top: 1.8em;
+}
+blockquote.sphx-glr-script-out {
+  margin-left: 0pt;
+}
+.sphx-glr-script-out.highlight-pytb .highlight pre {
+  color: var(--sg-pytb-foreground);
+  background-color: var(--sg-pytb-background);
+  border: 1px solid var(--sg-pytb-border-color);
+  margin-top: 10px;
+  padding: 7px;
+}
+
+div.sphx-glr-footer {
+  text-align: center;
+}
+
+div.sphx-glr-download {
+  margin: 1em auto;
+  vertical-align: middle;
+}
+
+div.sphx-glr-download a {
+  background-color: var(--sg-download-a-background-color);
+  background-image: var(--sg-download-a-background-image);
+  border-radius: 4px;
+  border: 1px solid var(--sg-download-a-border-color);
+  color: var(--sg-download-a-color);
+  display: inline-block;
+  font-weight: bold;
+  padding: 1ex;
+  text-align: center;
+}
+
+div.sphx-glr-download code.download {
+  display: inline-block;
+  white-space: normal;
+  word-break: normal;
+  overflow-wrap: break-word;
+  /* border and background are given by the enclosing 'a' */
+  border: none;
+  background: none;
+}
+
+div.sphx-glr-download a:hover {
+  box-shadow: inset 0 1px 0 var(--sg-download-a-hover-box-shadow-1), 0 1px 5px var(--sg-download-a-hover-box-shadow-2);
+  text-decoration: none;
+  background-image: none;
+  background-color: var(--sg-download-a-hover-background-color);
+}
+
+.sphx-glr-example-title:target::before {
+  display: block;
+  content: "";
+  margin-top: -50px;
+  height: 50px;
+  visibility: hidden;
+}
+
+ul.sphx-glr-horizontal {
+  list-style: none;
+  padding: 0;
+}
+ul.sphx-glr-horizontal li {
+  display: inline;
+}
+ul.sphx-glr-horizontal img {
+  height: auto !important;
+}
+
+.sphx-glr-single-img {
+  margin: auto;
+  display: block;
+  max-width: 100%;
+}
+
+.sphx-glr-multi-img {
+  max-width: 42%;
+  height: auto;
+}
+
+div.sphx-glr-animation {
+  margin: auto;
+  display: block;
+  max-width: 100%;
+}
+div.sphx-glr-animation .animation {
+  display: block;
+}
+
+p.sphx-glr-signature a.reference.external {
+  -moz-border-radius: 5px;
+  -webkit-border-radius: 5px;
+  border-radius: 5px;
+  padding: 3px;
+  font-size: 75%;
+  text-align: right;
+  margin-left: auto;
+  display: table;
+}
+
+.sphx-glr-clear {
+  clear: both;
+}
+
+a.sphx-glr-backref-instance {
+  text-decoration: none;
+}
diff --git a/docs/source/_build/html/_static/sphinx_highlight.js b/docs/source/_build/html/_static/sphinx_highlight.js
new file mode 100644
index 0000000..aae669d
--- /dev/null
+++ b/docs/source/_build/html/_static/sphinx_highlight.js
@@ -0,0 +1,144 @@
+/* Highlighting utilities for Sphinx HTML documentation. */
+"use strict";
+
+const SPHINX_HIGHLIGHT_ENABLED = true
+
+/**
+ * highlight a given string on a node by wrapping it in
+ * span elements with the given class name.
+ */
+const _highlight = (node, addItems, text, className) => {
+  if (node.nodeType === Node.TEXT_NODE) {
+    const val = node.nodeValue;
+    const parent = node.parentNode;
+    const pos = val.toLowerCase().indexOf(text);
+    if (
+      pos >= 0 &&
+      !parent.classList.contains(className) &&
+      !parent.classList.contains("nohighlight")
+    ) {
+      let span;
+
+      const closestNode = parent.closest("body, svg, foreignObject");
+      const isInSVG = closestNode && closestNode.matches("svg");
+      if (isInSVG) {
+        span = document.createElementNS("http://www.w3.org/2000/svg", "tspan");
+      } else {
+        span = document.createElement("span");
+        span.classList.add(className);
+      }
+
+      span.appendChild(document.createTextNode(val.substr(pos, text.length)));
+      parent.insertBefore(
+        span,
+        parent.insertBefore(
+          document.createTextNode(val.substr(pos + text.length)),
+          node.nextSibling
+        )
+      );
+      node.nodeValue = val.substr(0, pos);
+
+      if (isInSVG) {
+        const rect = document.createElementNS(
+          "http://www.w3.org/2000/svg",
+          "rect"
+        );
+        const bbox = parent.getBBox();
+        rect.x.baseVal.value = bbox.x;
+        rect.y.baseVal.value = bbox.y;
+        rect.width.baseVal.value = bbox.width;
+        rect.height.baseVal.value = bbox.height;
+        rect.setAttribute("class", className);
+        addItems.push({ parent: parent, target: rect });
+      }
+    }
+  } else if (node.matches && !node.matches("button, select, textarea")) {
+    node.childNodes.forEach((el) => _highlight(el, addItems, text, className));
+  }
+};
+const _highlightText = (thisNode, text, className) => {
+  let addItems = [];
+  _highlight(thisNode, addItems, text, className);
+  addItems.forEach((obj) =>
+    obj.parent.insertAdjacentElement("beforebegin", obj.target)
+  );
+};
+
+/**
+ * Small JavaScript module for the documentation.
+ */
+const SphinxHighlight = {
+
+  /**
+   * highlight the search words provided in localstorage in the text
+   */
+  highlightSearchWords: () => {
+    if (!SPHINX_HIGHLIGHT_ENABLED) return;  // bail if no highlight
+
+    // get and clear terms from localstorage
+    const url = new URL(window.location);
+    const highlight =
+        localStorage.getItem("sphinx_highlight_terms")
+        || url.searchParams.get("highlight")
+        || "";
+    localStorage.removeItem("sphinx_highlight_terms")
+    url.searchParams.delete("highlight");
+    window.history.replaceState({}, "", url);
+
+    // get individual terms from highlight string
+    const terms = highlight.toLowerCase().split(/\s+/).filter(x => x);
+    if (terms.length === 0) return; // nothing to do
+
+    // There should never be more than one element matching "div.body"
+    const divBody = document.querySelectorAll("div.body");
+    const body = divBody.length ? divBody[0] : document.querySelector("body");
+    window.setTimeout(() => {
+      terms.forEach((term) => _highlightText(body, term, "highlighted"));
+    }, 10);
+
+    const searchBox = document.getElementById("searchbox");
+    if (searchBox === null) return;
+    searchBox.appendChild(
+      document
+        .createRange()
+        .createContextualFragment(
+          '<p class="highlight-link">' +
+            '<a href="javascript:SphinxHighlight.hideSearchWords()">' +
+            _("Hide Search Matches") +
+            "</a></p>"
+        )
+    );
+  },
+
+  /**
+   * helper function to hide the search marks again
+   */
+  hideSearchWords: () => {
+    document
+      .querySelectorAll("#searchbox .highlight-link")
+      .forEach((el) => el.remove());
+    document
+      .querySelectorAll("span.highlighted")
+      .forEach((el) => el.classList.remove("highlighted"));
+    localStorage.removeItem("sphinx_highlight_terms")
+  },
+
+  initEscapeListener: () => {
+    // only install a listener if it is really needed
+    if (!DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS) return;
+
+    document.addEventListener("keydown", (event) => {
+      // bail for input elements
+      if (BLACKLISTED_KEY_CONTROL_ELEMENTS.has(document.activeElement.tagName)) return;
+      // bail with special keys
+      if (event.shiftKey || event.altKey || event.ctrlKey || event.metaKey) return;
+      if (DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS && (event.key === "Escape")) {
+        SphinxHighlight.hideSearchWords();
+        event.preventDefault();
+      }
+    });
+  },
+};
+
+_ready(SphinxHighlight.highlightSearchWords);
+_ready(SphinxHighlight.initEscapeListener);
diff --git a/docs/source/_build/html/_static/underscore-1.13.1.js b/docs/source/_build/html/_static/underscore-1.13.1.js
new file mode 100644
index 0000000..ffd77af
--- /dev/null
+++ b/docs/source/_build/html/_static/underscore-1.13.1.js
@@ -0,0 +1,2042 @@
+(function (global, factory) {
+  typeof exports === 'object' && typeof module !== 'undefined' ? module.exports = factory() :
+  typeof define === 'function' && define.amd ? define('underscore', factory) :
+  (global = typeof globalThis !== 'undefined' ? globalThis : global || self, (function () {
+    var current = global._;
+    var exports = global._ = factory();
+    exports.noConflict = function () { global._ = current; return exports; };
+  }()));
+}(this, (function () {
+  //     Underscore.js 1.13.1
+  //     https://underscorejs.org
+  //     (c) 2009-2021 Jeremy Ashkenas, Julian Gonggrijp, and DocumentCloud and Investigative Reporters & Editors
+  //     Underscore may be freely distributed under the MIT license.
+
+  // Current version.
+  var VERSION = '1.13.1';
+
+  // Establish the root object, `window` (`self`) in the browser, `global`
+  // on the server, or `this` in some virtual machines. We use `self`
+  // instead of `window` for `WebWorker` support.
+  var root = typeof self == 'object' && self.self === self && self ||
+            typeof global == 'object' && global.global === global && global ||
+            Function('return this')() ||
+            {};
+
+  // Save bytes in the minified (but not gzipped) version:
+  var ArrayProto = Array.prototype, ObjProto = Object.prototype;
+  var SymbolProto = typeof Symbol !== 'undefined' ? Symbol.prototype : null;
+
+  // Create quick reference variables for speed access to core prototypes.
+  var push = ArrayProto.push,
+      slice = ArrayProto.slice,
+      toString = ObjProto.toString,
+      hasOwnProperty = ObjProto.hasOwnProperty;
+
+  // Modern feature detection.
+  var supportsArrayBuffer = typeof ArrayBuffer !== 'undefined',
+      supportsDataView = typeof DataView !== 'undefined';
+
+  // All **ECMAScript 5+** native function implementations that we hope to use
+  // are declared here.
+  var nativeIsArray = Array.isArray,
+      nativeKeys = Object.keys,
+      nativeCreate = Object.create,
+      nativeIsView = supportsArrayBuffer && ArrayBuffer.isView;
+
+  // Create references to these builtin functions because we override them.
+  var _isNaN = isNaN,
+      _isFinite = isFinite;
+
+  // Keys in IE < 9 that won't be iterated by `for key in ...` and thus missed.
+  var hasEnumBug = !{toString: null}.propertyIsEnumerable('toString');
+  var nonEnumerableProps = ['valueOf', 'isPrototypeOf', 'toString',
+    'propertyIsEnumerable', 'hasOwnProperty', 'toLocaleString'];
+
+  // The largest integer that can be represented exactly.
+  var MAX_ARRAY_INDEX = Math.pow(2, 53) - 1;
+
+  // Some functions take a variable number of arguments, or a few expected
+  // arguments at the beginning and then a variable number of values to operate
+  // on. This helper accumulates all remaining arguments past the function’s
+  // argument length (or an explicit `startIndex`), into an array that becomes
+  // the last argument. Similar to ES6’s "rest parameter".
+  function restArguments(func, startIndex) {
+    startIndex = startIndex == null ? func.length - 1 : +startIndex;
+    return function() {
+      var length = Math.max(arguments.length - startIndex, 0),
+          rest = Array(length),
+          index = 0;
+      for (; index < length; index++) {
+        rest[index] = arguments[index + startIndex];
+      }
+      switch (startIndex) {
+        case 0: return func.call(this, rest);
+        case 1: return func.call(this, arguments[0], rest);
+        case 2: return func.call(this, arguments[0], arguments[1], rest);
+      }
+      var args = Array(startIndex + 1);
+      for (index = 0; index < startIndex; index++) {
+        args[index] = arguments[index];
+      }
+      args[startIndex] = rest;
+      return func.apply(this, args);
+    };
+  }
+
+  // Is a given variable an object?
+  function isObject(obj) {
+    var type = typeof obj;
+    return type === 'function' || type === 'object' && !!obj;
+  }
+
+  // Is a given value equal to null?
+  function isNull(obj) {
+    return obj === null;
+  }
+
+  // Is a given variable undefined?
+  function isUndefined(obj) {
+    return obj === void 0;
+  }
+
+  // Is a given value a boolean?
+  function isBoolean(obj) {
+    return obj === true || obj === false || toString.call(obj) === '[object Boolean]';
+  }
+
+  // Is a given value a DOM element?
+  function isElement(obj) {
+    return !!(obj && obj.nodeType === 1);
+  }
+
+  // Internal function for creating a `toString`-based type tester.
+  function tagTester(name) {
+    var tag = '[object ' + name + ']';
+    return function(obj) {
+      return toString.call(obj) === tag;
+    };
+  }
+
+  var isString = tagTester('String');
+
+  var isNumber = tagTester('Number');
+
+  var isDate = tagTester('Date');
+
+  var isRegExp = tagTester('RegExp');
+
+  var isError = tagTester('Error');
+
+  var isSymbol = tagTester('Symbol');
+
+  var isArrayBuffer = tagTester('ArrayBuffer');
+
+  var isFunction = tagTester('Function');
+
+  // Optimize `isFunction` if appropriate. Work around some `typeof` bugs in old
+  // v8, IE 11 (#1621), Safari 8 (#1929), and PhantomJS (#2236).
+  var nodelist = root.document && root.document.childNodes;
+  if (typeof /./ != 'function' && typeof Int8Array != 'object' && typeof nodelist != 'function') {
+    isFunction = function(obj) {
+      return typeof obj == 'function' || false;
+    };
+  }
+
+  var isFunction$1 = isFunction;
+
+  var hasObjectTag = tagTester('Object');
+
+  // In IE 10 - Edge 13, `DataView` has string tag `'[object Object]'`.
+  // In IE 11, the most common among them, this problem also applies to
+  // `Map`, `WeakMap` and `Set`.
+  var hasStringTagBug = (
+        supportsDataView && hasObjectTag(new DataView(new ArrayBuffer(8)))
+      ),
+      isIE11 = (typeof Map !== 'undefined' && hasObjectTag(new Map));
+
+  var isDataView = tagTester('DataView');
+
+  // In IE 10 - Edge 13, we need a different heuristic
+  // to determine whether an object is a `DataView`.
+  function ie10IsDataView(obj) {
+    return obj != null && isFunction$1(obj.getInt8) && isArrayBuffer(obj.buffer);
+  }
+
+  var isDataView$1 = (hasStringTagBug ? ie10IsDataView : isDataView);
+
+  // Is a given value an array?
+  // Delegates to ECMA5's native `Array.isArray`.
+  var isArray = nativeIsArray || tagTester('Array');
+
+  // Internal function to check whether `key` is an own property name of `obj`.
+  function has$1(obj, key) {
+    return obj != null && hasOwnProperty.call(obj, key);
+  }
+
+  var isArguments = tagTester('Arguments');
+
+  // Define a fallback version of the method in browsers (ahem, IE < 9), where
+  // there isn't any inspectable "Arguments" type.
+  (function() {
+    if (!isArguments(arguments)) {
+      isArguments = function(obj) {
+        return has$1(obj, 'callee');
+      };
+    }
+  }());
+
+  var isArguments$1 = isArguments;
+
+  // Is a given object a finite number?
+  function isFinite$1(obj) {
+    return !isSymbol(obj) && _isFinite(obj) && !isNaN(parseFloat(obj));
+  }
+
+  // Is the given value `NaN`?
+  function isNaN$1(obj) {
+    return isNumber(obj) && _isNaN(obj);
+  }
+
+  // Predicate-generating function. Often useful outside of Underscore.
+  function constant(value) {
+    return function() {
+      return value;
+    };
+  }
+
+  // Common internal logic for `isArrayLike` and `isBufferLike`.
+  function createSizePropertyCheck(getSizeProperty) {
+    return function(collection) {
+      var sizeProperty = getSizeProperty(collection);
+      return typeof sizeProperty == 'number' && sizeProperty >= 0 && sizeProperty <= MAX_ARRAY_INDEX;
+    }
+  }
+
+  // Internal helper to generate a function to obtain property `key` from `obj`.
+  function shallowProperty(key) {
+    return function(obj) {
+      return obj == null ? void 0 : obj[key];
+    };
+  }
+
+  // Internal helper to obtain the `byteLength` property of an object.
+  var getByteLength = shallowProperty('byteLength');
+
+  // Internal helper to determine whether we should spend extensive checks against
+  // `ArrayBuffer` et al.
+  var isBufferLike = createSizePropertyCheck(getByteLength);
+
+  // Is a given value a typed array?
+  var typedArrayPattern = /\[object ((I|Ui)nt(8|16|32)|Float(32|64)|Uint8Clamped|Big(I|Ui)nt64)Array\]/;
+  function isTypedArray(obj) {
+    // `ArrayBuffer.isView` is the most future-proof, so use it when available.
+    // Otherwise, fall back on the above regular expression.
+    return nativeIsView ? (nativeIsView(obj) && !isDataView$1(obj)) :
+                  isBufferLike(obj) && typedArrayPattern.test(toString.call(obj));
+  }
+
+  var isTypedArray$1 = supportsArrayBuffer ? isTypedArray : constant(false);
+
+  // Internal helper to obtain the `length` property of an object.
+  var getLength = shallowProperty('length');
+
+  // Internal helper to create a simple lookup structure.
+  // `collectNonEnumProps` used to depend on `_.contains`, but this led to
+  // circular imports. `emulatedSet` is a one-off solution that only works for
+  // arrays of strings.
+  function emulatedSet(keys) {
+    var hash = {};
+    for (var l = keys.length, i = 0; i < l; ++i) hash[keys[i]] = true;
+    return {
+      contains: function(key) { return hash[key]; },
+      push: function(key) {
+        hash[key] = true;
+        return keys.push(key);
+      }
+    };
+  }
+
+  // Internal helper. Checks `keys` for the presence of keys in IE < 9 that won't
+  // be iterated by `for key in ...` and thus missed. Extends `keys` in place if
+  // needed.
+  function collectNonEnumProps(obj, keys) {
+    keys = emulatedSet(keys);
+    var nonEnumIdx = nonEnumerableProps.length;
+    var constructor = obj.constructor;
+    var proto = isFunction$1(constructor) && constructor.prototype || ObjProto;
+
+    // Constructor is a special case.
+    var prop = 'constructor';
+    if (has$1(obj, prop) && !keys.contains(prop)) keys.push(prop);
+
+    while (nonEnumIdx--) {
+      prop = nonEnumerableProps[nonEnumIdx];
+      if (prop in obj && obj[prop] !== proto[prop] && !keys.contains(prop)) {
+        keys.push(prop);
+      }
+    }
+  }
+
+  // Retrieve the names of an object's own properties.
+  // Delegates to **ECMAScript 5**'s native `Object.keys`.
+  function keys(obj) {
+    if (!isObject(obj)) return [];
+    if (nativeKeys) return nativeKeys(obj);
+    var keys = [];
+    for (var key in obj) if (has$1(obj, key)) keys.push(key);
+    // Ahem, IE < 9.
+    if (hasEnumBug) collectNonEnumProps(obj, keys);
+    return keys;
+  }
+
+  // Is a given array, string, or object empty?
+  // An "empty" object has no enumerable own-properties.
+  function isEmpty(obj) {
+    if (obj == null) return true;
+    // Skip the more expensive `toString`-based type checks if `obj` has no
+    // `.length`.
+    var length = getLength(obj);
+    if (typeof length == 'number' && (
+      isArray(obj) || isString(obj) || isArguments$1(obj)
+    )) return length === 0;
+    return getLength(keys(obj)) === 0;
+  }
+
+  // Returns whether an object has a given set of `key:value` pairs.
+  function isMatch(object, attrs) {
+    var _keys = keys(attrs), length = _keys.length;
+    if (object == null) return !length;
+    var obj = Object(object);
+    for (var i = 0; i < length; i++) {
+      var key = _keys[i];
+      if (attrs[key] !== obj[key] || !(key in obj)) return false;
+    }
+    return true;
+  }
+
+  // If Underscore is called as a function, it returns a wrapped object that can
+  // be used OO-style. This wrapper holds altered versions of all functions added
+  // through `_.mixin`. Wrapped objects may be chained.
+  function _$1(obj) {
+    if (obj instanceof _$1) return obj;
+    if (!(this instanceof _$1)) return new _$1(obj);
+    this._wrapped = obj;
+  }
+
+  _$1.VERSION = VERSION;
+
+  // Extracts the result from a wrapped and chained object.
+  _$1.prototype.value = function() {
+    return this._wrapped;
+  };
+
+  // Provide unwrapping proxies for some methods used in engine operations
+  // such as arithmetic and JSON stringification.
+  _$1.prototype.valueOf = _$1.prototype.toJSON = _$1.prototype.value;
+
+  _$1.prototype.toString = function() {
+    return String(this._wrapped);
+  };
+
+  // Internal function to wrap or shallow-copy an ArrayBuffer,
+  // typed array or DataView to a new view, reusing the buffer.
+  function toBufferView(bufferSource) {
+    return new Uint8Array(
+      bufferSource.buffer || bufferSource,
+      bufferSource.byteOffset || 0,
+      getByteLength(bufferSource)
+    );
+  }
+
+  // We use this string twice, so give it a name for minification.
+  var tagDataView = '[object DataView]';
+
+  // Internal recursive comparison function for `_.isEqual`.
+  function eq(a, b, aStack, bStack) {
+    // Identical objects are equal. `0 === -0`, but they aren't identical.
+    // See the [Harmony `egal` proposal](https://wiki.ecmascript.org/doku.php?id=harmony:egal).
+    if (a === b) return a !== 0 || 1 / a === 1 / b;
+    // `null` or `undefined` only equal to itself (strict comparison).
+    if (a == null || b == null) return false;
+    // `NaN`s are equivalent, but non-reflexive.
+    if (a !== a) return b !== b;
+    // Exhaust primitive checks
+    var type = typeof a;
+    if (type !== 'function' && type !== 'object' && typeof b != 'object') return false;
+    return deepEq(a, b, aStack, bStack);
+  }
+
+  // Internal recursive comparison function for `_.isEqual`.
+  function deepEq(a, b, aStack, bStack) {
+    // Unwrap any wrapped objects.
+    if (a instanceof _$1) a = a._wrapped;
+    if (b instanceof _$1) b = b._wrapped;
+    // Compare `[[Class]]` names.
+    var className = toString.call(a);
+    if (className !== toString.call(b)) return false;
+    // Work around a bug in IE 10 - Edge 13.
+    if (hasStringTagBug && className == '[object Object]' && isDataView$1(a)) {
+      if (!isDataView$1(b)) return false;
+      className = tagDataView;
+    }
+    switch (className) {
+      // These types are compared by value.
+      case '[object RegExp]':
+        // RegExps are coerced to strings for comparison (Note: '' + /a/i === '/a/i')
+      case '[object String]':
+        // Primitives and their corresponding object wrappers are equivalent; thus, `"5"` is
+        // equivalent to `new String("5")`.
+        return '' + a === '' + b;
+      case '[object Number]':
+        // `NaN`s are equivalent, but non-reflexive.
+        // Object(NaN) is equivalent to NaN.
+        if (+a !== +a) return +b !== +b;
+        // An `egal` comparison is performed for other numeric values.
+        return +a === 0 ? 1 / +a === 1 / b : +a === +b;
+      case '[object Date]':
+      case '[object Boolean]':
+        // Coerce dates and booleans to numeric primitive values. Dates are compared by their
+        // millisecond representations. Note that invalid dates with millisecond representations
+        // of `NaN` are not equivalent.
+        return +a === +b;
+      case '[object Symbol]':
+        return SymbolProto.valueOf.call(a) === SymbolProto.valueOf.call(b);
+      case '[object ArrayBuffer]':
+      case tagDataView:
+        // Coerce to typed array so we can fall through.
+        return deepEq(toBufferView(a), toBufferView(b), aStack, bStack);
+    }
+
+    var areArrays = className === '[object Array]';
+    if (!areArrays && isTypedArray$1(a)) {
+        var byteLength = getByteLength(a);
+        if (byteLength !== getByteLength(b)) return false;
+        if (a.buffer === b.buffer && a.byteOffset === b.byteOffset) return true;
+        areArrays = true;
+    }
+    if (!areArrays) {
+      if (typeof a != 'object' || typeof b != 'object') return false;
+
+      // Objects with different constructors are not equivalent, but `Object`s or `Array`s
+      // from different frames are.
+      var aCtor = a.constructor, bCtor = b.constructor;
+      if (aCtor !== bCtor && !(isFunction$1(aCtor) && aCtor instanceof aCtor &&
+                               isFunction$1(bCtor) && bCtor instanceof bCtor)
+                          && ('constructor' in a && 'constructor' in b)) {
+        return false;
+      }
+    }
+    // Assume equality for cyclic structures. The algorithm for detecting cyclic
+    // structures is adapted from ES 5.1 section 15.12.3, abstract operation `JO`.
+
+    // Initializing stack of traversed objects.
+    // It's done here since we only need them for objects and arrays comparison.
+    aStack = aStack || [];
+    bStack = bStack || [];
+    var length = aStack.length;
+    while (length--) {
+      // Linear search. Performance is inversely proportional to the number of
+      // unique nested structures.
+      if (aStack[length] === a) return bStack[length] === b;
+    }
+
+    // Add the first object to the stack of traversed objects.
+    aStack.push(a);
+    bStack.push(b);
+
+    // Recursively compare objects and arrays.
+    if (areArrays) {
+      // Compare array lengths to determine if a deep comparison is necessary.
+      length = a.length;
+      if (length !== b.length) return false;
+      // Deep compare the contents, ignoring non-numeric properties.
+      while (length--) {
+        if (!eq(a[length], b[length], aStack, bStack)) return false;
+      }
+    } else {
+      // Deep compare objects.
+      var _keys = keys(a), key;
+      length = _keys.length;
+      // Ensure that both objects contain the same number of properties before comparing deep equality.
+      if (keys(b).length !== length) return false;
+      while (length--) {
+        // Deep compare each member
+        key = _keys[length];
+        if (!(has$1(b, key) && eq(a[key], b[key], aStack, bStack))) return false;
+      }
+    }
+    // Remove the first object from the stack of traversed objects.
+    aStack.pop();
+    bStack.pop();
+    return true;
+  }
+
+  // Perform a deep comparison to check if two objects are equal.
+  function isEqual(a, b) {
+    return eq(a, b);
+  }
+
+  // Retrieve all the enumerable property names of an object.
+  function allKeys(obj) {
+    if (!isObject(obj)) return [];
+    var keys = [];
+    for (var key in obj) keys.push(key);
+    // Ahem, IE < 9.
+    if (hasEnumBug) collectNonEnumProps(obj, keys);
+    return keys;
+  }
+
+  // Since the regular `Object.prototype.toString` type tests don't work for
+  // some types in IE 11, we use a fingerprinting heuristic instead, based
+  // on the methods. It's not great, but it's the best we got.
+  // The fingerprint method lists are defined below.
+  function ie11fingerprint(methods) {
+    var length = getLength(methods);
+    return function(obj) {
+      if (obj == null) return false;
+      // `Map`, `WeakMap` and `Set` have no enumerable keys.
+      var keys = allKeys(obj);
+      if (getLength(keys)) return false;
+      for (var i = 0; i < length; i++) {
+        if (!isFunction$1(obj[methods[i]])) return false;
+      }
+      // If we are testing against `WeakMap`, we need to ensure that
+      // `obj` doesn't have a `forEach` method in order to distinguish
+      // it from a regular `Map`.
+      return methods !== weakMapMethods || !isFunction$1(obj[forEachName]);
+    };
+  }
+
+  // In the interest of compact minification, we write
+  // each string in the fingerprints only once.
+  var forEachName = 'forEach',
+      hasName = 'has',
+      commonInit = ['clear', 'delete'],
+      mapTail = ['get', hasName, 'set'];
+
+  // `Map`, `WeakMap` and `Set` each have slightly different
+  // combinations of the above sublists.
+  var mapMethods = commonInit.concat(forEachName, mapTail),
+      weakMapMethods = commonInit.concat(mapTail),
+      setMethods = ['add'].concat(commonInit, forEachName, hasName);
+
+  var isMap = isIE11 ? ie11fingerprint(mapMethods) : tagTester('Map');
+
+  var isWeakMap = isIE11 ? ie11fingerprint(weakMapMethods) : tagTester('WeakMap');
+
+  var isSet = isIE11 ? ie11fingerprint(setMethods) : tagTester('Set');
+
+  var isWeakSet = tagTester('WeakSet');
+
+  // Retrieve the values of an object's properties.
+  function values(obj) {
+    var _keys = keys(obj);
+    var length = _keys.length;
+    var values = Array(length);
+    for (var i = 0; i < length; i++) {
+      values[i] = obj[_keys[i]];
+    }
+    return values;
+  }
+
+  // Convert an object into a list of `[key, value]` pairs.
+  // The opposite of `_.object` with one argument.
+  function pairs(obj) {
+    var _keys = keys(obj);
+    var length = _keys.length;
+    var pairs = Array(length);
+    for (var i = 0; i < length; i++) {
+      pairs[i] = [_keys[i], obj[_keys[i]]];
+    }
+    return pairs;
+  }
+
+  // Invert the keys and values of an object. The values must be serializable.
+  function invert(obj) {
+    var result = {};
+    var _keys = keys(obj);
+    for (var i = 0, length = _keys.length; i < length; i++) {
+      result[obj[_keys[i]]] = _keys[i];
+    }
+    return result;
+  }
+
+  // Return a sorted list of the function names available on the object.
+  function functions(obj) {
+    var names = [];
+    for (var key in obj) {
+      if (isFunction$1(obj[key])) names.push(key);
+    }
+    return names.sort();
+  }
+
+  // An internal function for creating assigner functions.
+  function createAssigner(keysFunc, defaults) {
+    return function(obj) {
+      var length = arguments.length;
+      if (defaults) obj = Object(obj);
+      if (length < 2 || obj == null) return obj;
+      for (var index = 1; index < length; index++) {
+        var source = arguments[index],
+            keys = keysFunc(source),
+            l = keys.length;
+        for (var i = 0; i < l; i++) {
+          var key = keys[i];
+          if (!defaults || obj[key] === void 0) obj[key] = source[key];
+        }
+      }
+      return obj;
+    };
+  }
+
+  // Extend a given object with all the properties in passed-in object(s).
+  var extend = createAssigner(allKeys);
+
+  // Assigns a given object with all the own properties in the passed-in
+  // object(s).
+  // (https://developer.mozilla.org/docs/Web/JavaScript/Reference/Global_Objects/Object/assign)
+  var extendOwn = createAssigner(keys);
+
+  // Fill in a given object with default properties.
+  var defaults = createAssigner(allKeys, true);
+
+  // Create a naked function reference for surrogate-prototype-swapping.
+  function ctor() {
+    return function(){};
+  }
+
+  // An internal function for creating a new object that inherits from another.
+  function baseCreate(prototype) {
+    if (!isObject(prototype)) return {};
+    if (nativeCreate) return nativeCreate(prototype);
+    var Ctor = ctor();
+    Ctor.prototype = prototype;
+    var result = new Ctor;
+    Ctor.prototype = null;
+    return result;
+  }
+
+  // Creates an object that inherits from the given prototype object.
+  // If additional properties are provided then they will be added to the
+  // created object.
+  function create(prototype, props) {
+    var result = baseCreate(prototype);
+    if (props) extendOwn(result, props);
+    return result;
+  }
+
+  // Create a (shallow-cloned) duplicate of an object.
+  function clone(obj) {
+    if (!isObject(obj)) return obj;
+    return isArray(obj) ? obj.slice() : extend({}, obj);
+  }
+
+  // Invokes `interceptor` with the `obj` and then returns `obj`.
+  // The primary purpose of this method is to "tap into" a method chain, in
+  // order to perform operations on intermediate results within the chain.
+  function tap(obj, interceptor) {
+    interceptor(obj);
+    return obj;
+  }
+
+  // Normalize a (deep) property `path` to array.
+  // Like `_.iteratee`, this function can be customized.
+  function toPath$1(path) {
+    return isArray(path) ? path : [path];
+  }
+  _$1.toPath = toPath$1;
+
+  // Internal wrapper for `_.toPath` to enable minification.
+  // Similar to `cb` for `_.iteratee`.
+  function toPath(path) {
+    return _$1.toPath(path);
+  }
+
+  // Internal function to obtain a nested property in `obj` along `path`.
+  function deepGet(obj, path) {
+    var length = path.length;
+    for (var i = 0; i < length; i++) {
+      if (obj == null) return void 0;
+      obj = obj[path[i]];
+    }
+    return length ? obj : void 0;
+  }
+
+  // Get the value of the (deep) property on `path` from `object`.
+  // If any property in `path` does not exist or if the value is
+  // `undefined`, return `defaultValue` instead.
+  // The `path` is normalized through `_.toPath`.
+  function get(object, path, defaultValue) {
+    var value = deepGet(object, toPath(path));
+    return isUndefined(value) ? defaultValue : value;
+  }
+
+  // Shortcut function for checking if an object has a given property directly on
+  // itself (in other words, not on a prototype). Unlike the internal `has`
+  // function, this public version can also traverse nested properties.
+  function has(obj, path) {
+    path = toPath(path);
+    var length = path.length;
+    for (var i = 0; i < length; i++) {
+      var key = path[i];
+      if (!has$1(obj, key)) return false;
+      obj = obj[key];
+    }
+    return !!length;
+  }
+
+  // Keep the identity function around for default iteratees.
+  function identity(value) {
+    return value;
+  }
+
+  // Returns a predicate for checking whether an object has a given set of
+  // `key:value` pairs.
+  function matcher(attrs) {
+    attrs = extendOwn({}, attrs);
+    return function(obj) {
+      return isMatch(obj, attrs);
+    };
+  }
+
+  // Creates a function that, when passed an object, will traverse that object’s
+  // properties down the given `path`, specified as an array of keys or indices.
+  function property(path) {
+    path = toPath(path);
+    return function(obj) {
+      return deepGet(obj, path);
+    };
+  }
+
+  // Internal function that returns an efficient (for current engines) version
+  // of the passed-in callback, to be repeatedly applied in other Underscore
+  // functions.
+  function optimizeCb(func, context, argCount) {
+    if (context === void 0) return func;
+    switch (argCount == null ? 3 : argCount) {
+      case 1: return function(value) {
+        return func.call(context, value);
+      };
+      // The 2-argument case is omitted because we’re not using it.
+      case 3: return function(value, index, collection) {
+        return func.call(context, value, index, collection);
+      };
+      case 4: return function(accumulator, value, index, collection) {
+        return func.call(context, accumulator, value, index, collection);
+      };
+    }
+    return function() {
+      return func.apply(context, arguments);
+    };
+  }
+
+  // An internal function to generate callbacks that can be applied to each
+  // element in a collection, returning the desired result — either `_.identity`,
+  // an arbitrary callback, a property matcher, or a property accessor.
+  function baseIteratee(value, context, argCount) {
+    if (value == null) return identity;
+    if (isFunction$1(value)) return optimizeCb(value, context, argCount);
+    if (isObject(value) && !isArray(value)) return matcher(value);
+    return property(value);
+  }
+
+  // External wrapper for our callback generator. Users may customize
+  // `_.iteratee` if they want additional predicate/iteratee shorthand styles.
+  // This abstraction hides the internal-only `argCount` argument.
+  function iteratee(value, context) {
+    return baseIteratee(value, context, Infinity);
+  }
+  _$1.iteratee = iteratee;
+
+  // The function we call internally to generate a callback. It invokes
+  // `_.iteratee` if overridden, otherwise `baseIteratee`.
+  function cb(value, context, argCount) {
+    if (_$1.iteratee !== iteratee) return _$1.iteratee(value, context);
+    return baseIteratee(value, context, argCount);
+  }
+
+  // Returns the results of applying the `iteratee` to each element of `obj`.
+  // In contrast to `_.map` it returns an object.
+  function mapObject(obj, iteratee, context) {
+    iteratee = cb(iteratee, context);
+    var _keys = keys(obj),
+        length = _keys.length,
+        results = {};
+    for (var index = 0; index < length; index++) {
+      var currentKey = _keys[index];
+      results[currentKey] = iteratee(obj[currentKey], currentKey, obj);
+    }
+    return results;
+  }
+
+  // Predicate-generating function. Often useful outside of Underscore.
+  function noop(){}
+
+  // Generates a function for a given object that returns a given property.
+  function propertyOf(obj) {
+    if (obj == null) return noop;
+    return function(path) {
+      return get(obj, path);
+    };
+  }
+
+  // Run a function **n** times.
+  function times(n, iteratee, context) {
+    var accum = Array(Math.max(0, n));
+    iteratee = optimizeCb(iteratee, context, 1);
+    for (var i = 0; i < n; i++) accum[i] = iteratee(i);
+    return accum;
+  }
+
+  // Return a random integer between `min` and `max` (inclusive).
+  function random(min, max) {
+    if (max == null) {
+      max = min;
+      min = 0;
+    }
+    return min + Math.floor(Math.random() * (max - min + 1));
+  }
+
+  // A (possibly faster) way to get the current timestamp as an integer.
+  var now = Date.now || function() {
+    return new Date().getTime();
+  };
+
+  // Internal helper to generate functions for escaping and unescaping strings
+  // to/from HTML interpolation.
+  function createEscaper(map) {
+    var escaper = function(match) {
+      return map[match];
+    };
+    // Regexes for identifying a key that needs to be escaped.
+    var source = '(?:' + keys(map).join('|') + ')';
+    var testRegexp = RegExp(source);
+    var replaceRegexp = RegExp(source, 'g');
+    return function(string) {
+      string = string == null ? '' : '' + string;
+      return testRegexp.test(string) ? string.replace(replaceRegexp, escaper) : string;
+    };
+  }
+
+  // Internal list of HTML entities for escaping.
+  var escapeMap = {
+    '&': '&amp;',
+    '<': '&lt;',
+    '>': '&gt;',
+    '"': '&quot;',
+    "'": '&#x27;',
+    '`': '&#x60;'
+  };
+
+  // Function for escaping strings to HTML interpolation.
+  var _escape = createEscaper(escapeMap);
+
+  // Internal list of HTML entities for unescaping.
+  var unescapeMap = invert(escapeMap);
+
+  // Function for unescaping strings from HTML interpolation.
+  var _unescape = createEscaper(unescapeMap);
+
+  // By default, Underscore uses ERB-style template delimiters. Change the
+  // following template settings to use alternative delimiters.
+  var templateSettings = _$1.templateSettings = {
+    evaluate: /<%([\s\S]+?)%>/g,
+    interpolate: /<%=([\s\S]+?)%>/g,
+    escape: /<%-([\s\S]+?)%>/g
+  };
+
+  // When customizing `_.templateSettings`, if you don't want to define an
+  // interpolation, evaluation or escaping regex, we need one that is
+  // guaranteed not to match.
+  var noMatch = /(.)^/;
+
+  // Certain characters need to be escaped so that they can be put into a
+  // string literal.
+  var escapes = {
+    "'": "'",
+    '\\': '\\',
+    '\r': 'r',
+    '\n': 'n',
+    '\u2028': 'u2028',
+    '\u2029': 'u2029'
+  };
+
+  var escapeRegExp = /\\|'|\r|\n|\u2028|\u2029/g;
+
+  function escapeChar(match) {
+    return '\\' + escapes[match];
+  }
+
+  // In order to prevent third-party code injection through
+  // `_.templateSettings.variable`, we test it against the following regular
+  // expression. It is intentionally a bit more liberal than just matching valid
+  // identifiers, but still prevents possible loopholes through defaults or
+  // destructuring assignment.
+  var bareIdentifier = /^\s*(\w|\$)+\s*$/;
+
+  // JavaScript micro-templating, similar to John Resig's implementation.
+  // Underscore templating handles arbitrary delimiters, preserves whitespace,
+  // and correctly escapes quotes within interpolated code.
+  // NB: `oldSettings` only exists for backwards compatibility.
+  function template(text, settings, oldSettings) {
+    if (!settings && oldSettings) settings = oldSettings;
+    settings = defaults({}, settings, _$1.templateSettings);
+
+    // Combine delimiters into one regular expression via alternation.
+    var matcher = RegExp([
+      (settings.escape || noMatch).source,
+      (settings.interpolate || noMatch).source,
+      (settings.evaluate || noMatch).source
+    ].join('|') + '|$', 'g');
+
+    // Compile the template source, escaping string literals appropriately.
+    var index = 0;
+    var source = "__p+='";
+    text.replace(matcher, function(match, escape, interpolate, evaluate, offset) {
+      source += text.slice(index, offset).replace(escapeRegExp, escapeChar);
+      index = offset + match.length;
+
+      if (escape) {
+        source += "'+\n((__t=(" + escape + "))==null?'':_.escape(__t))+\n'";
+      } else if (interpolate) {
+        source += "'+\n((__t=(" + interpolate + "))==null?'':__t)+\n'";
+      } else if (evaluate) {
+        source += "';\n" + evaluate + "\n__p+='";
+      }
+
+      // Adobe VMs need the match returned to produce the correct offset.
+      return match;
+    });
+    source += "';\n";
+
+    var argument = settings.variable;
+    if (argument) {
+      // Insure against third-party code injection. (CVE-2021-23358)
+      if (!bareIdentifier.test(argument)) throw new Error(
+        'variable is not a bare identifier: ' + argument
+      );
+    } else {
+      // If a variable is not specified, place data values in local scope.
+      source = 'with(obj||{}){\n' + source + '}\n';
+      argument = 'obj';
+    }
+
+    source = "var __t,__p='',__j=Array.prototype.join," +
+      "print=function(){__p+=__j.call(arguments,'');};\n" +
+      source + 'return __p;\n';
+
+    var render;
+    try {
+      render = new Function(argument, '_', source);
+    } catch (e) {
+      e.source = source;
+      throw e;
+    }
+
+    var template = function(data) {
+      return render.call(this, data, _$1);
+    };
+
+    // Provide the compiled source as a convenience for precompilation.
+    template.source = 'function(' + argument + '){\n' + source + '}';
+
+    return template;
+  }
+
+  // Traverses the children of `obj` along `path`. If a child is a function, it
+  // is invoked with its parent as context. Returns the value of the final
+  // child, or `fallback` if any child is undefined.
+  function result(obj, path, fallback) {
+    path = toPath(path);
+    var length = path.length;
+    if (!length) {
+      return isFunction$1(fallback) ? fallback.call(obj) : fallback;
+    }
+    for (var i = 0; i < length; i++) {
+      var prop = obj == null ? void 0 : obj[path[i]];
+      if (prop === void 0) {
+        prop = fallback;
+        i = length; // Ensure we don't continue iterating.
+      }
+      obj = isFunction$1(prop) ? prop.call(obj) : prop;
+    }
+    return obj;
+  }
+
+  // Generate a unique integer id (unique within the entire client session).
+  // Useful for temporary DOM ids.
+  var idCounter = 0;
+  function uniqueId(prefix) {
+    var id = ++idCounter + '';
+    return prefix ? prefix + id : id;
+  }
+
+  // Start chaining a wrapped Underscore object.
+  function chain(obj) {
+    var instance = _$1(obj);
+    instance._chain = true;
+    return instance;
+  }
+
+  // Internal function to execute `sourceFunc` bound to `context` with optional
+  // `args`. Determines whether to execute a function as a constructor or as a
+  // normal function.
+  function executeBound(sourceFunc, boundFunc, context, callingContext, args) {
+    if (!(callingContext instanceof boundFunc)) return sourceFunc.apply(context, args);
+    var self = baseCreate(sourceFunc.prototype);
+    var result = sourceFunc.apply(self, args);
+    if (isObject(result)) return result;
+    return self;
+  }
+
+  // Partially apply a function by creating a version that has had some of its
+  // arguments pre-filled, without changing its dynamic `this` context. `_` acts
+  // as a placeholder by default, allowing any combination of arguments to be
+  // pre-filled. Set `_.partial.placeholder` for a custom placeholder argument.
+  var partial = restArguments(function(func, boundArgs) {
+    var placeholder = partial.placeholder;
+    var bound = function() {
+      var position = 0, length = boundArgs.length;
+      var args = Array(length);
+      for (var i = 0; i < length; i++) {
+        args[i] = boundArgs[i] === placeholder ? arguments[position++] : boundArgs[i];
+      }
+      while (position < arguments.length) args.push(arguments[position++]);
+      return executeBound(func, bound, this, this, args);
+    };
+    return bound;
+  });
+
+  partial.placeholder = _$1;
+
+  // Create a function bound to a given object (assigning `this`, and arguments,
+  // optionally).
+  var bind = restArguments(function(func, context, args) {
+    if (!isFunction$1(func)) throw new TypeError('Bind must be called on a function');
+    var bound = restArguments(function(callArgs) {
+      return executeBound(func, bound, context, this, args.concat(callArgs));
+    });
+    return bound;
+  });
+
+  // Internal helper for collection methods to determine whether a collection
+  // should be iterated as an array or as an object.
+  // Related: https://people.mozilla.org/~jorendorff/es6-draft.html#sec-tolength
+  // Avoids a very nasty iOS 8 JIT bug on ARM-64. #2094
+  var isArrayLike = createSizePropertyCheck(getLength);
+
+  // Internal implementation of a recursive `flatten` function.
+  function flatten$1(input, depth, strict, output) {
+    output = output || [];
+    if (!depth && depth !== 0) {
+      depth = Infinity;
+    } else if (depth <= 0) {
+      return output.concat(input);
+    }
+    var idx = output.length;
+    for (var i = 0, length = getLength(input); i < length; i++) {
+      var value = input[i];
+      if (isArrayLike(value) && (isArray(value) || isArguments$1(value))) {
+        // Flatten current level of array or arguments object.
+        if (depth > 1) {
+          flatten$1(value, depth - 1, strict, output);
+          idx = output.length;
+        } else {
+          var j = 0, len = value.length;
+          while (j < len) output[idx++] = value[j++];
+        }
+      } else if (!strict) {
+        output[idx++] = value;
+      }
+    }
+    return output;
+  }
+
+  // Bind a number of an object's methods to that object. Remaining arguments
+  // are the method names to be bound. Useful for ensuring that all callbacks
+  // defined on an object belong to it.
+  var bindAll = restArguments(function(obj, keys) {
+    keys = flatten$1(keys, false, false);
+    var index = keys.length;
+    if (index < 1) throw new Error('bindAll must be passed function names');
+    while (index--) {
+      var key = keys[index];
+      obj[key] = bind(obj[key], obj);
+    }
+    return obj;
+  });
+
+  // Memoize an expensive function by storing its results.
+  function memoize(func, hasher) {
+    var memoize = function(key) {
+      var cache = memoize.cache;
+      var address = '' + (hasher ? hasher.apply(this, arguments) : key);
+      if (!has$1(cache, address)) cache[address] = func.apply(this, arguments);
+      return cache[address];
+    };
+    memoize.cache = {};
+    return memoize;
+  }
+
+  // Delays a function for the given number of milliseconds, and then calls
+  // it with the arguments supplied.
+  var delay = restArguments(function(func, wait, args) {
+    return setTimeout(function() {
+      return func.apply(null, args);
+    }, wait);
+  });
+
+  // Defers a function, scheduling it to run after the current call stack has
+  // cleared.
+  var defer = partial(delay, _$1, 1);
+
+  // Returns a function, that, when invoked, will only be triggered at most once
+  // during a given window of time. Normally, the throttled function will run
+  // as much as it can, without ever going more than once per `wait` duration;
+  // but if you'd like to disable the execution on the leading edge, pass
+  // `{leading: false}`. To disable execution on the trailing edge, ditto.
+  function throttle(func, wait, options) {
+    var timeout, context, args, result;
+    var previous = 0;
+    if (!options) options = {};
+
+    var later = function() {
+      previous = options.leading === false ? 0 : now();
+      timeout = null;
+      result = func.apply(context, args);
+      if (!timeout) context = args = null;
+    };
+
+    var throttled = function() {
+      var _now = now();
+      if (!previous && options.leading === false) previous = _now;
+      var remaining = wait - (_now - previous);
+      context = this;
+      args = arguments;
+      if (remaining <= 0 || remaining > wait) {
+        if (timeout) {
+          clearTimeout(timeout);
+          timeout = null;
+        }
+        previous = _now;
+        result = func.apply(context, args);
+        if (!timeout) context = args = null;
+      } else if (!timeout && options.trailing !== false) {
+        timeout = setTimeout(later, remaining);
+      }
+      return result;
+    };
+
+    throttled.cancel = function() {
+      clearTimeout(timeout);
+      previous = 0;
+      timeout = context = args = null;
+    };
+
+    return throttled;
+  }
+
+  // When a sequence of calls of the returned function ends, the argument
+  // function is triggered. The end of a sequence is defined by the `wait`
+  // parameter. If `immediate` is passed, the argument function will be
+  // triggered at the beginning of the sequence instead of at the end.
+  function debounce(func, wait, immediate) {
+    var timeout, previous, args, result, context;
+
+    var later = function() {
+      var passed = now() - previous;
+      if (wait > passed) {
+        timeout = setTimeout(later, wait - passed);
+      } else {
+        timeout = null;
+        if (!immediate) result = func.apply(context, args);
+        // This check is needed because `func` can recursively invoke `debounced`.
+        if (!timeout) args = context = null;
+      }
+    };
+
+    var debounced = restArguments(function(_args) {
+      context = this;
+      args = _args;
+      previous = now();
+      if (!timeout) {
+        timeout = setTimeout(later, wait);
+        if (immediate) result = func.apply(context, args);
+      }
+      return result;
+    });
+
+    debounced.cancel = function() {
+      clearTimeout(timeout);
+      timeout = args = context = null;
+    };
+
+    return debounced;
+  }
+
+  // Returns the first function passed as an argument to the second,
+  // allowing you to adjust arguments, run code before and after, and
+  // conditionally execute the original function.
+  function wrap(func, wrapper) {
+    return partial(wrapper, func);
+  }
+
+  // Returns a negated version of the passed-in predicate.
+  function negate(predicate) {
+    return function() {
+      return !predicate.apply(this, arguments);
+    };
+  }
+
+  // Returns a function that is the composition of a list of functions, each
+  // consuming the return value of the function that follows.
+  function compose() {
+    var args = arguments;
+    var start = args.length - 1;
+    return function() {
+      var i = start;
+      var result = args[start].apply(this, arguments);
+      while (i--) result = args[i].call(this, result);
+      return result;
+    };
+  }
+
+  // Returns a function that will only be executed on and after the Nth call.
+  function after(times, func) {
+    return function() {
+      if (--times < 1) {
+        return func.apply(this, arguments);
+      }
+    };
+  }
+
+  // Returns a function that will only be executed up to (but not including) the
+  // Nth call.
+  function before(times, func) {
+    var memo;
+    return function() {
+      if (--times > 0) {
+        memo = func.apply(this, arguments);
+      }
+      if (times <= 1) func = null;
+      return memo;
+    };
+  }
+
+  // Returns a function that will be executed at most one time, no matter how
+  // often you call it. Useful for lazy initialization.
+  var once = partial(before, 2);
+
+  // Returns the first key on an object that passes a truth test.
+  function findKey(obj, predicate, context) {
+    predicate = cb(predicate, context);
+    var _keys = keys(obj), key;
+    for (var i = 0, length = _keys.length; i < length; i++) {
+      key = _keys[i];
+      if (predicate(obj[key], key, obj)) return key;
+    }
+  }
+
+  // Internal function to generate `_.findIndex` and `_.findLastIndex`.
+  function createPredicateIndexFinder(dir) {
+    return function(array, predicate, context) {
+      predicate = cb(predicate, context);
+      var length = getLength(array);
+      var index = dir > 0 ? 0 : length - 1;
+      for (; index >= 0 && index < length; index += dir) {
+        if (predicate(array[index], index, array)) return index;
+      }
+      return -1;
+    };
+  }
+
+  // Returns the first index on an array-like that passes a truth test.
+  var findIndex = createPredicateIndexFinder(1);
+
+  // Returns the last index on an array-like that passes a truth test.
+  var findLastIndex = createPredicateIndexFinder(-1);
+
+  // Use a comparator function to figure out the smallest index at which
+  // an object should be inserted so as to maintain order. Uses binary search.
+  function sortedIndex(array, obj, iteratee, context) {
+    iteratee = cb(iteratee, context, 1);
+    var value = iteratee(obj);
+    var low = 0, high = getLength(array);
+    while (low < high) {
+      var mid = Math.floor((low + high) / 2);
+      if (iteratee(array[mid]) < value) low = mid + 1; else high = mid;
+    }
+    return low;
+  }
+
+  // Internal function to generate the `_.indexOf` and `_.lastIndexOf` functions.
+  function createIndexFinder(dir, predicateFind, sortedIndex) {
+    return function(array, item, idx) {
+      var i = 0, length = getLength(array);
+      if (typeof idx == 'number') {
+        if (dir > 0) {
+          i = idx >= 0 ? idx : Math.max(idx + length, i);
+        } else {
+          length = idx >= 0 ? Math.min(idx + 1, length) : idx + length + 1;
+        }
+      } else if (sortedIndex && idx && length) {
+        idx = sortedIndex(array, item);
+        return array[idx] === item ? idx : -1;
+      }
+      if (item !== item) {
+        idx = predicateFind(slice.call(array, i, length), isNaN$1);
+        return idx >= 0 ? idx + i : -1;
+      }
+      for (idx = dir > 0 ? i : length - 1; idx >= 0 && idx < length; idx += dir) {
+        if (array[idx] === item) return idx;
+      }
+      return -1;
+    };
+  }
+
+  // Return the position of the first occurrence of an item in an array,
+  // or -1 if the item is not included in the array.
+  // If the array is large and already in sort order, pass `true`
+  // for **isSorted** to use binary search.
+  var indexOf = createIndexFinder(1, findIndex, sortedIndex);
+
+  // Return the position of the last occurrence of an item in an array,
+  // or -1 if the item is not included in the array.
+  var lastIndexOf = createIndexFinder(-1, findLastIndex);
+
+  // Return the first value which passes a truth test.
+  function find(obj, predicate, context) {
+    var keyFinder = isArrayLike(obj) ? findIndex : findKey;
+    var key = keyFinder(obj, predicate, context);
+    if (key !== void 0 && key !== -1) return obj[key];
+  }
+
+  // Convenience version of a common use case of `_.find`: getting the first
+  // object containing specific `key:value` pairs.
+  function findWhere(obj, attrs) {
+    return find(obj, matcher(attrs));
+  }
+
+  // The cornerstone for collection functions, an `each`
+  // implementation, aka `forEach`.
+  // Handles raw objects in addition to array-likes. Treats all
+  // sparse array-likes as if they were dense.
+  function each(obj, iteratee, context) {
+    iteratee = optimizeCb(iteratee, context);
+    var i, length;
+    if (isArrayLike(obj)) {
+      for (i = 0, length = obj.length; i < length; i++) {
+        iteratee(obj[i], i, obj);
+      }
+    } else {
+      var _keys = keys(obj);
+      for (i = 0, length = _keys.length; i < length; i++) {
+        iteratee(obj[_keys[i]], _keys[i], obj);
+      }
+    }
+    return obj;
+  }
+
+  // Return the results of applying the iteratee to each element.
+  function map(obj, iteratee, context) {
+    iteratee = cb(iteratee, context);
+    var _keys = !isArrayLike(obj) && keys(obj),
+        length = (_keys || obj).length,
+        results = Array(length);
+    for (var index = 0; index < length; index++) {
+      var currentKey = _keys ? _keys[index] : index;
+      results[index] = iteratee(obj[currentKey], currentKey, obj);
+    }
+    return results;
+  }
+
+  // Internal helper to create a reducing function, iterating left or right.
+  function createReduce(dir) {
+    // Wrap code that reassigns argument variables in a separate function than
+    // the one that accesses `arguments.length` to avoid a perf hit. (#1991)
+    var reducer = function(obj, iteratee, memo, initial) {
+      var _keys = !isArrayLike(obj) && keys(obj),
+          length = (_keys || obj).length,
+          index = dir > 0 ? 0 : length - 1;
+      if (!initial) {
+        memo = obj[_keys ? _keys[index] : index];
+        index += dir;
+      }
+      for (; index >= 0 && index < length; index += dir) {
+        var currentKey = _keys ? _keys[index] : index;
+        memo = iteratee(memo, obj[currentKey], currentKey, obj);
+      }
+      return memo;
+    };
+
+    return function(obj, iteratee, memo, context) {
+      var initial = arguments.length >= 3;
+      return reducer(obj, optimizeCb(iteratee, context, 4), memo, initial);
+    };
+  }
+
+  // **Reduce** builds up a single result from a list of values, aka `inject`,
+  // or `foldl`.
+  var reduce = createReduce(1);
+
+  // The right-associative version of reduce, also known as `foldr`.
+  var reduceRight = createReduce(-1);
+
+  // Return all the elements that pass a truth test.
+  function filter(obj, predicate, context) {
+    var results = [];
+    predicate = cb(predicate, context);
+    each(obj, function(value, index, list) {
+      if (predicate(value, index, list)) results.push(value);
+    });
+    return results;
+  }
+
+  // Return all the elements for which a truth test fails.
+  function reject(obj, predicate, context) {
+    return filter(obj, negate(cb(predicate)), context);
+  }
+
+  // Determine whether all of the elements pass a truth test.
+  function every(obj, predicate, context) {
+    predicate = cb(predicate, context);
+    var _keys = !isArrayLike(obj) && keys(obj),
+        length = (_keys || obj).length;
+    for (var index = 0; index < length; index++) {
+      var currentKey = _keys ? _keys[index] : index;
+      if (!predicate(obj[currentKey], currentKey, obj)) return false;
+    }
+    return true;
+  }
+
+  // Determine if at least one element in the object passes a truth test.
+  function some(obj, predicate, context) {
+    predicate = cb(predicate, context);
+    var _keys = !isArrayLike(obj) && keys(obj),
+        length = (_keys || obj).length;
+    for (var index = 0; index < length; index++) {
+      var currentKey = _keys ? _keys[index] : index;
+      if (predicate(obj[currentKey], currentKey, obj)) return true;
+    }
+    return false;
+  }
+
+  // Determine if the array or object contains a given item (using `===`).
+  function contains(obj, item, fromIndex, guard) {
+    if (!isArrayLike(obj)) obj = values(obj);
+    if (typeof fromIndex != 'number' || guard) fromIndex = 0;
+    return indexOf(obj, item, fromIndex) >= 0;
+  }
+
+  // Invoke a method (with arguments) on every item in a collection.
+  var invoke = restArguments(function(obj, path, args) {
+    var contextPath, func;
+    if (isFunction$1(path)) {
+      func = path;
+    } else {
+      path = toPath(path);
+      contextPath = path.slice(0, -1);
+      path = path[path.length - 1];
+    }
+    return map(obj, function(context) {
+      var method = func;
+      if (!method) {
+        if (contextPath && contextPath.length) {
+          context = deepGet(context, contextPath);
+        }
+        if (context == null) return void 0;
+        method = context[path];
+      }
+      return method == null ? method : method.apply(context, args);
+    });
+  });
+
+  // Convenience version of a common use case of `_.map`: fetching a property.
+  function pluck(obj, key) {
+    return map(obj, property(key));
+  }
+
+  // Convenience version of a common use case of `_.filter`: selecting only
+  // objects containing specific `key:value` pairs.
+  function where(obj, attrs) {
+    return filter(obj, matcher(attrs));
+  }
+
+  // Return the maximum element (or element-based computation).
+  function max(obj, iteratee, context) {
+    var result = -Infinity, lastComputed = -Infinity,
+        value, computed;
+    if (iteratee == null || typeof iteratee == 'number' && typeof obj[0] != 'object' && obj != null) {
+      obj = isArrayLike(obj) ? obj : values(obj);
+      for (var i = 0, length = obj.length; i < length; i++) {
+        value = obj[i];
+        if (value != null && value > result) {
+          result = value;
+        }
+      }
+    } else {
+      iteratee = cb(iteratee, context);
+      each(obj, function(v, index, list) {
+        computed = iteratee(v, index, list);
+        if (computed > lastComputed || computed === -Infinity && result === -Infinity) {
+          result = v;
+          lastComputed = computed;
+        }
+      });
+    }
+    return result;
+  }
+
+  // Return the minimum element (or element-based computation).
+  function min(obj, iteratee, context) {
+    var result = Infinity, lastComputed = Infinity,
+        value, computed;
+    if (iteratee == null || typeof iteratee == 'number' && typeof obj[0] != 'object' && obj != null) {
+      obj = isArrayLike(obj) ? obj : values(obj);
+      for (var i = 0, length = obj.length; i < length; i++) {
+        value = obj[i];
+        if (value != null && value < result) {
+          result = value;
+        }
+      }
+    } else {
+      iteratee = cb(iteratee, context);
+      each(obj, function(v, index, list) {
+        computed = iteratee(v, index, list);
+        if (computed < lastComputed || computed === Infinity && result === Infinity) {
+          result = v;
+          lastComputed = computed;
+        }
+      });
+    }
+    return result;
+  }
+
+  // Sample **n** random values from a collection using the modern version of the
+  // [Fisher-Yates shuffle](https://en.wikipedia.org/wiki/Fisher–Yates_shuffle).
+  // If **n** is not specified, returns a single random element.
+  // The internal `guard` argument allows it to work with `_.map`.
+  function sample(obj, n, guard) {
+    if (n == null || guard) {
+      if (!isArrayLike(obj)) obj = values(obj);
+      return obj[random(obj.length - 1)];
+    }
+    var sample = isArrayLike(obj) ? clone(obj) : values(obj);
+    var length = getLength(sample);
+    n = Math.max(Math.min(n, length), 0);
+    var last = length - 1;
+    for (var index = 0; index < n; index++) {
+      var rand = random(index, last);
+      var temp = sample[index];
+      sample[index] = sample[rand];
+      sample[rand] = temp;
+    }
+    return sample.slice(0, n);
+  }
+
+  // Shuffle a collection.
+  function shuffle(obj) {
+    return sample(obj, Infinity);
+  }
+
+  // Sort the object's values by a criterion produced by an iteratee.
+  function sortBy(obj, iteratee, context) {
+    var index = 0;
+    iteratee = cb(iteratee, context);
+    return pluck(map(obj, function(value, key, list) {
+      return {
+        value: value,
+        index: index++,
+        criteria: iteratee(value, key, list)
+      };
+    }).sort(function(left, right) {
+      var a = left.criteria;
+      var b = right.criteria;
+      if (a !== b) {
+        if (a > b || a === void 0) return 1;
+        if (a < b || b === void 0) return -1;
+      }
+      return left.index - right.index;
+    }), 'value');
+  }
+
+  // An internal function used for aggregate "group by" operations.
+  function group(behavior, partition) {
+    return function(obj, iteratee, context) {
+      var result = partition ? [[], []] : {};
+      iteratee = cb(iteratee, context);
+      each(obj, function(value, index) {
+        var key = iteratee(value, index, obj);
+        behavior(result, value, key);
+      });
+      return result;
+    };
+  }
+
+  // Groups the object's values by a criterion. Pass either a string attribute
+  // to group by, or a function that returns the criterion.
+  var groupBy = group(function(result, value, key) {
+    if (has$1(result, key)) result[key].push(value); else result[key] = [value];
+  });
+
+  // Indexes the object's values by a criterion, similar to `_.groupBy`, but for
+  // when you know that your index values will be unique.
+  var indexBy = group(function(result, value, key) {
+    result[key] = value;
+  });
+
+  // Counts instances of an object that group by a certain criterion. Pass
+  // either a string attribute to count by, or a function that returns the
+  // criterion.
+  var countBy = group(function(result, value, key) {
+    if (has$1(result, key)) result[key]++; else result[key] = 1;
+  });
+
+  // Split a collection into two arrays: one whose elements all pass the given
+  // truth test, and one whose elements all do not pass the truth test.
+  var partition = group(function(result, value, pass) {
+    result[pass ? 0 : 1].push(value);
+  }, true);
+
+  // Safely create a real, live array from anything iterable.
+  var reStrSymbol = /[^\ud800-\udfff]|[\ud800-\udbff][\udc00-\udfff]|[\ud800-\udfff]/g;
+  function toArray(obj) {
+    if (!obj) return [];
+    if (isArray(obj)) return slice.call(obj);
+    if (isString(obj)) {
+      // Keep surrogate pair characters together.
+      return obj.match(reStrSymbol);
+    }
+    if (isArrayLike(obj)) return map(obj, identity);
+    return values(obj);
+  }
+
+  // Return the number of elements in a collection.
+  function size(obj) {
+    if (obj == null) return 0;
+    return isArrayLike(obj) ? obj.length : keys(obj).length;
+  }
+
+  // Internal `_.pick` helper function to determine whether `key` is an enumerable
+  // property name of `obj`.
+  function keyInObj(value, key, obj) {
+    return key in obj;
+  }
+
+  // Return a copy of the object only containing the allowed properties.
+  var pick = restArguments(function(obj, keys) {
+    var result = {}, iteratee = keys[0];
+    if (obj == null) return result;
+    if (isFunction$1(iteratee)) {
+      if (keys.length > 1) iteratee = optimizeCb(iteratee, keys[1]);
+      keys = allKeys(obj);
+    } else {
+      iteratee = keyInObj;
+      keys = flatten$1(keys, false, false);
+      obj = Object(obj);
+    }
+    for (var i = 0, length = keys.length; i < length; i++) {
+      var key = keys[i];
+      var value = obj[key];
+      if (iteratee(value, key, obj)) result[key] = value;
+    }
+    return result;
+  });
+
+  // Return a copy of the object without the disallowed properties.
+  var omit = restArguments(function(obj, keys) {
+    var iteratee = keys[0], context;
+    if (isFunction$1(iteratee)) {
+      iteratee = negate(iteratee);
+      if (keys.length > 1) context = keys[1];
+    } else {
+      keys = map(flatten$1(keys, false, false), String);
+      iteratee = function(value, key) {
+        return !contains(keys, key);
+      };
+    }
+    return pick(obj, iteratee, context);
+  });
+
+  // Returns everything but the last entry of the array. Especially useful on
+  // the arguments object. Passing **n** will return all the values in
+  // the array, excluding the last N.
+  function initial(array, n, guard) {
+    return slice.call(array, 0, Math.max(0, array.length - (n == null || guard ? 1 : n)));
+  }
+
+  // Get the first element of an array. Passing **n** will return the first N
+  // values in the array. The **guard** check allows it to work with `_.map`.
+  function first(array, n, guard) {
+    if (array == null || array.length < 1) return n == null || guard ? void 0 : [];
+    if (n == null || guard) return array[0];
+    return initial(array, array.length - n);
+  }
+
+  // Returns everything but the first entry of the `array`. Especially useful on
+  // the `arguments` object. Passing an **n** will return the rest N values in the
+  // `array`.
+  function rest(array, n, guard) {
+    return slice.call(array, n == null || guard ? 1 : n);
+  }
+
+  // Get the last element of an array. Passing **n** will return the last N
+  // values in the array.
+  function last(array, n, guard) {
+    if (array == null || array.length < 1) return n == null || guard ? void 0 : [];
+    if (n == null || guard) return array[array.length - 1];
+    return rest(array, Math.max(0, array.length - n));
+  }
+
+  // Trim out all falsy values from an array.
+  function compact(array) {
+    return filter(array, Boolean);
+  }
+
+  // Flatten out an array, either recursively (by default), or up to `depth`.
+  // Passing `true` or `false` as `depth` means `1` or `Infinity`, respectively.
+  function flatten(array, depth) {
+    return flatten$1(array, depth, false);
+  }
+
+  // Take the difference between one array and a number of other arrays.
+  // Only the elements present in just the first array will remain.
+  var difference = restArguments(function(array, rest) {
+    rest = flatten$1(rest, true, true);
+    return filter(array, function(value){
+      return !contains(rest, value);
+    });
+  });
+
+  // Return a version of the array that does not contain the specified value(s).
+  var without = restArguments(function(array, otherArrays) {
+    return difference(array, otherArrays);
+  });
+
+  // Produce a duplicate-free version of the array. If the array has already
+  // been sorted, you have the option of using a faster algorithm.
+  // The faster algorithm will not work with an iteratee if the iteratee
+  // is not a one-to-one function, so providing an iteratee will disable
+  // the faster algorithm.
+  function uniq(array, isSorted, iteratee, context) {
+    if (!isBoolean(isSorted)) {
+      context = iteratee;
+      iteratee = isSorted;
+      isSorted = false;
+    }
+    if (iteratee != null) iteratee = cb(iteratee, context);
+    var result = [];
+    var seen = [];
+    for (var i = 0, length = getLength(array); i < length; i++) {
+      var value = array[i],
+          computed = iteratee ? iteratee(value, i, array) : value;
+      if (isSorted && !iteratee) {
+        if (!i || seen !== computed) result.push(value);
+        seen = computed;
+      } else if (iteratee) {
+        if (!contains(seen, computed)) {
+          seen.push(computed);
+          result.push(value);
+        }
+      } else if (!contains(result, value)) {
+        result.push(value);
+      }
+    }
+    return result;
+  }
+
+  // Produce an array that contains the union: each distinct element from all of
+  // the passed-in arrays.
+  var union = restArguments(function(arrays) {
+    return uniq(flatten$1(arrays, true, true));
+  });
+
+  // Produce an array that contains every item shared between all the
+  // passed-in arrays.
+  function intersection(array) {
+    var result = [];
+    var argsLength = arguments.length;
+    for (var i = 0, length = getLength(array); i < length; i++) {
+      var item = array[i];
+      if (contains(result, item)) continue;
+      var j;
+      for (j = 1; j < argsLength; j++) {
+        if (!contains(arguments[j], item)) break;
+      }
+      if (j === argsLength) result.push(item);
+    }
+    return result;
+  }
+
+  // Complement of zip. Unzip accepts an array of arrays and groups
+  // each array's elements on shared indices.
+  function unzip(array) {
+    var length = array && max(array, getLength).length || 0;
+    var result = Array(length);
+
+    for (var index = 0; index < length; index++) {
+      result[index] = pluck(array, index);
+    }
+    return result;
+  }
+
+  // Zip together multiple lists into a single array -- elements that share
+  // an index go together.
+  var zip = restArguments(unzip);
+
+  // Converts lists into objects. Pass either a single array of `[key, value]`
+  // pairs, or two parallel arrays of the same length -- one of keys, and one of
+  // the corresponding values. Passing by pairs is the reverse of `_.pairs`.
+  function object(list, values) {
+    var result = {};
+    for (var i = 0, length = getLength(list); i < length; i++) {
+      if (values) {
+        result[list[i]] = values[i];
+      } else {
+        result[list[i][0]] = list[i][1];
+      }
+    }
+    return result;
+  }
+
+  // Generate an integer Array containing an arithmetic progression. A port of
+  // the native Python `range()` function. See
+  // [the Python documentation](https://docs.python.org/library/functions.html#range).
+  function range(start, stop, step) {
+    if (stop == null) {
+      stop = start || 0;
+      start = 0;
+    }
+    if (!step) {
+      step = stop < start ? -1 : 1;
+    }
+
+    var length = Math.max(Math.ceil((stop - start) / step), 0);
+    var range = Array(length);
+
+    for (var idx = 0; idx < length; idx++, start += step) {
+      range[idx] = start;
+    }
+
+    return range;
+  }
+
+  // Chunk a single array into multiple arrays, each containing `count` or fewer
+  // items.
+  function chunk(array, count) {
+    if (count == null || count < 1) return [];
+    var result = [];
+    var i = 0, length = array.length;
+    while (i < length) {
+      result.push(slice.call(array, i, i += count));
+    }
+    return result;
+  }
+
+  // Helper function to continue chaining intermediate results.
+  function chainResult(instance, obj) {
+    return instance._chain ? _$1(obj).chain() : obj;
+  }
+
+  // Add your own custom functions to the Underscore object.
+  function mixin(obj) {
+    each(functions(obj), function(name) {
+      var func = _$1[name] = obj[name];
+      _$1.prototype[name] = function() {
+        var args = [this._wrapped];
+        push.apply(args, arguments);
+        return chainResult(this, func.apply(_$1, args));
+      };
+    });
+    return _$1;
+  }
+
+  // Add all mutator `Array` functions to the wrapper.
+  each(['pop', 'push', 'reverse', 'shift', 'sort', 'splice', 'unshift'], function(name) {
+    var method = ArrayProto[name];
+    _$1.prototype[name] = function() {
+      var obj = this._wrapped;
+      if (obj != null) {
+        method.apply(obj, arguments);
+        if ((name === 'shift' || name === 'splice') && obj.length === 0) {
+          delete obj[0];
+        }
+      }
+      return chainResult(this, obj);
+    };
+  });
+
+  // Add all accessor `Array` functions to the wrapper.
+  each(['concat', 'join', 'slice'], function(name) {
+    var method = ArrayProto[name];
+    _$1.prototype[name] = function() {
+      var obj = this._wrapped;
+      if (obj != null) obj = method.apply(obj, arguments);
+      return chainResult(this, obj);
+    };
+  });
+
+  // Named Exports
+
+  var allExports = {
+    __proto__: null,
+    VERSION: VERSION,
+    restArguments: restArguments,
+    isObject: isObject,
+    isNull: isNull,
+    isUndefined: isUndefined,
+    isBoolean: isBoolean,
+    isElement: isElement,
+    isString: isString,
+    isNumber: isNumber,
+    isDate: isDate,
+    isRegExp: isRegExp,
+    isError: isError,
+    isSymbol: isSymbol,
+    isArrayBuffer: isArrayBuffer,
+    isDataView: isDataView$1,
+    isArray: isArray,
+    isFunction: isFunction$1,
+    isArguments: isArguments$1,
+    isFinite: isFinite$1,
+    isNaN: isNaN$1,
+    isTypedArray: isTypedArray$1,
+    isEmpty: isEmpty,
+    isMatch: isMatch,
+    isEqual: isEqual,
+    isMap: isMap,
+    isWeakMap: isWeakMap,
+    isSet: isSet,
+    isWeakSet: isWeakSet,
+    keys: keys,
+    allKeys: allKeys,
+    values: values,
+    pairs: pairs,
+    invert: invert,
+    functions: functions,
+    methods: functions,
+    extend: extend,
+    extendOwn: extendOwn,
+    assign: extendOwn,
+    defaults: defaults,
+    create: create,
+    clone: clone,
+    tap: tap,
+    get: get,
+    has: has,
+    mapObject: mapObject,
+    identity: identity,
+    constant: constant,
+    noop: noop,
+    toPath: toPath$1,
+    property: property,
+    propertyOf: propertyOf,
+    matcher: matcher,
+    matches: matcher,
+    times: times,
+    random: random,
+    now: now,
+    escape: _escape,
+    unescape: _unescape,
+    templateSettings: templateSettings,
+    template: template,
+    result: result,
+    uniqueId: uniqueId,
+    chain: chain,
+    iteratee: iteratee,
+    partial: partial,
+    bind: bind,
+    bindAll: bindAll,
+    memoize: memoize,
+    delay: delay,
+    defer: defer,
+    throttle: throttle,
+    debounce: debounce,
+    wrap: wrap,
+    negate: negate,
+    compose: compose,
+    after: after,
+    before: before,
+    once: once,
+    findKey: findKey,
+    findIndex: findIndex,
+    findLastIndex: findLastIndex,
+    sortedIndex: sortedIndex,
+    indexOf: indexOf,
+    lastIndexOf: lastIndexOf,
+    find: find,
+    detect: find,
+    findWhere: findWhere,
+    each: each,
+    forEach: each,
+    map: map,
+    collect: map,
+    reduce: reduce,
+    foldl: reduce,
+    inject: reduce,
+    reduceRight: reduceRight,
+    foldr: reduceRight,
+    filter: filter,
+    select: filter,
+    reject: reject,
+    every: every,
+    all: every,
+    some: some,
+    any: some,
+    contains: contains,
+    includes: contains,
+    include: contains,
+    invoke: invoke,
+    pluck: pluck,
+    where: where,
+    max: max,
+    min: min,
+    shuffle: shuffle,
+    sample: sample,
+    sortBy: sortBy,
+    groupBy: groupBy,
+    indexBy: indexBy,
+    countBy: countBy,
+    partition: partition,
+    toArray: toArray,
+    size: size,
+    pick: pick,
+    omit: omit,
+    first: first,
+    head: first,
+    take: first,
+    initial: initial,
+    last: last,
+    rest: rest,
+    tail: rest,
+    drop: rest,
+    compact: compact,
+    flatten: flatten,
+    without: without,
+    uniq: uniq,
+    unique: uniq,
+    union: union,
+    intersection: intersection,
+    difference: difference,
+    unzip: unzip,
+    transpose: unzip,
+    zip: zip,
+    object: object,
+    range: range,
+    chunk: chunk,
+    mixin: mixin,
+    'default': _$1
+  };
+
+  // Default Export
+
+  // Add all of the Underscore functions to the wrapper object.
+  var _ = mixin(allExports);
+  // Legacy Node.js API.
+  _._ = _;
+
+  return _;
+
+})));
+//# sourceMappingURL=underscore-umd.js.map
diff --git a/docs/source/_build/html/_static/underscore.js b/docs/source/_build/html/_static/underscore.js
new file mode 100644
index 0000000..cf177d4
--- /dev/null
+++ b/docs/source/_build/html/_static/underscore.js
@@ -0,0 +1,6 @@
+!function(n,r){"object"==typeof exports&&"undefined"!=typeof module?module.exports=r():"function"==typeof define&&define.amd?define("underscore",r):(n="undefined"!=typeof globalThis?globalThis:n||self,function(){var t=n._,e=n._=r();e.noConflict=function(){return n._=t,e}}())}(this,(function(){
+//     Underscore.js 1.13.1
+//     https://underscorejs.org
+//     (c) 2009-2021 Jeremy Ashkenas, Julian Gonggrijp, and DocumentCloud and Investigative Reporters & Editors
+//     Underscore may be freely distributed under the MIT license.
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+<section id="v0-1-2">
+<h2>v0.1.2<a class="headerlink" href="#v0-1-2" title="Permalink to this heading"></a></h2>
+<ul class="simple">
+<li><p>Elaborate on installation. Use pip from conda-forge channel to install <cite>PSimPy</cite></p></li>
+<li><p>Add info about how tests can be run</p></li>
+</ul>
+</section>
+<section id="v0-1-1">
+<h2>v0.1.1<a class="headerlink" href="#v0-1-1" title="Permalink to this heading"></a></h2>
+<ul class="simple">
+<li><p>Add info about installation</p></li>
+<li><p>Change np.float128 to float to avoid issues in windows system</p></li>
+<li><p>Update metadata</p></li>
+</ul>
+</section>
+<section id="v0-1-0">
+<h2>v0.1.0<a class="headerlink" href="#v0-1-0" title="Permalink to this heading"></a></h2>
+<ul class="simple">
+<li><p>First release</p></li>
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+<li class="toctree-l2 current"><a class="current reference internal" href="#">Emulator</a><ul>
+<li class="toctree-l3"><a class="reference internal" href="robustgasp.html"> RobustGaSP</a></li>
+</ul>
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+<li class="toctree-l2"><a class="reference internal" href="../inference/index.html">Inference</a></li>
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+             
+  <section id="emulator">
+<h1>Emulator<a class="headerlink" href="#emulator" title="Permalink to this heading"></a></h1>
+<p>This module hosts functionality for emulation methods.</p>
+<p>Emulation, also known as surrogate modeling or meta-modeling, is a type of
+method which is used to build cheap-to-evaluate emulators (surrogate models) to
+approximate expensive-to-evaluate simulators. It can greatly reduce
+computational costs of tasks in which a computationally intensive simulator
+needs to be run multiple times, such as a global sensitivity anlaysis,
+uncertainty quantification, or parameter calibration.</p>
+<p>Currently implemented classes in this module are:</p>
+<ul class="simple">
+<li><p><a class="reference internal" href="robustgasp.html#psimpy.emulator.robustgasp.ScalarGaSP" title="psimpy.emulator.robustgasp.ScalarGaSP"><code class="xref py py-class docutils literal notranslate"><span class="pre">ScalarGaSP</span></code></a>: Gaussian process emulation for simulators which return a
+scalar value as output.</p></li>
+<li><p><a class="reference internal" href="robustgasp.html#psimpy.emulator.robustgasp.PPGaSP" title="psimpy.emulator.robustgasp.PPGaSP"><code class="xref py py-class docutils literal notranslate"><span class="pre">PPGaSP</span></code></a>: Gaussian process emulation for simulators which return
+multiple values as output.</p></li>
+</ul>
+<div class="toctree-wrapper compound">
+</div>
+</section>
+
+
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+          </div>
+          <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer">
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+<html class="writer-html5" lang="en" >
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+<li class="toctree-l1"><a class="reference internal" href="../quickstart.html">Getting Started</a></li>
+<li class="toctree-l1 current"><a class="reference internal" href="../api.html">API &amp; Theory</a><ul class="current">
+<li class="toctree-l2 current"><a class="reference internal" href="index.html">Emulator</a><ul class="current">
+<li class="toctree-l3 current"><a class="current reference internal" href="#"> RobustGaSP</a><ul>
+<li class="toctree-l4"><a class="reference internal" href="#theory-recap-of-gp-emulation">Theory recap of GP emulation</a></li>
+<li class="toctree-l4"><a class="reference internal" href="#scalargasp-class">ScalarGaSP Class</a></li>
+<li class="toctree-l4"><a class="reference internal" href="#ppgasp-class">PPGaSP Class</a></li>
+</ul>
+</li>
+</ul>
+</li>
+<li class="toctree-l2"><a class="reference internal" href="../inference/index.html">Inference</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../sampler/index.html">Sampler</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../sensitivity/index.html">Sensitivity</a></li>
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+<li class="toctree-l1"><a class="reference internal" href="../refs.html">References</a></li>
+</ul>
+
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+          <li class="breadcrumb-item"><a href="index.html">Emulator</a></li>
+      <li class="breadcrumb-item active">RobustGaSP</li>
+      <li class="wy-breadcrumbs-aside">
+            <a href="../_sources/emulator/robustgasp.rst.txt" rel="nofollow"> View page source</a>
+      </li>
+  </ul>
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+</div>
+          <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article">
+           <div itemprop="articleBody">
+             
+  <section id="robustgasp">
+<h1>RobustGaSP<a class="headerlink" href="#robustgasp" title="Permalink to this heading"></a></h1>
+<p><cite>RobustGaSP</cite>, standing for <cite>Robust Gaussian Stochastic Process Emulation</cite>, is a
+<cite>R</cite> package developed by <span id="id1">Gu <em>et al.</em> [<a class="reference internal" href="../refs.html#id6" title="Meng Yang Gu, Jesus Palomo, and James O. Berger. Robustgasp: robust Gaussian stochastic process emulation in R. The R Journal, 11(1):112–136, 2019. doi:10.32614/RJ-2019-011.">2019</a>]</span>. It implements robust methods to
+estimate the unknown parameters which can greatly improve predictive performance
+of the built emulator. In addition, it implements the <cite>PP GaSP</cite> (parallel partial
+Gaussian stochastic process) emulator for simulators which return multiple values
+as output, see <span id="id2">Gu and Berger [<a class="reference internal" href="../refs.html#id4" title="Meng Yang Gu and James O. Berger. Parallel partial Gaussian process emulation for computer models with massive output. Annals of Applied Statistics, 10(3):1317–1347, 2016. doi:10.1214/16-AOAS934.">2016</a>]</span> for more detail.</p>
+<p>In <code class="xref py py-mod docutils literal notranslate"><span class="pre">PSimPy.emulator.robustgasp</span></code>, we have implemented class
+<a class="reference internal" href="#psimpy.emulator.robustgasp.ScalarGaSP" title="psimpy.emulator.robustgasp.ScalarGaSP"><code class="xref py py-class docutils literal notranslate"><span class="pre">ScalarGaSP</span></code></a> and  class <a class="reference internal" href="#psimpy.emulator.robustgasp.PPGaSP" title="psimpy.emulator.robustgasp.PPGaSP"><code class="xref py py-class docutils literal notranslate"><span class="pre">PPGaSP</span></code></a> based on <cite>RobustGaSP</cite> and
+<cite>rpy2</cite>, which allows us to use <cite>RobustGaSP</cite> directly from within <cite>Python</cite>.</p>
+<section id="theory-recap-of-gp-emulation">
+<h2>Theory recap of GP emulation<a class="headerlink" href="#theory-recap-of-gp-emulation" title="Permalink to this heading"></a></h2>
+<p>A simulator represents a mapping from an input space to an output space.
+Gaussian process emulation treats a computationally expensive simulator as an
+unknown function from a Bayesian perspective: the prior belief of the simulator,
+namely a Gaussian process, is updated based on a modest number of simulation runs,
+leading to a posterior which can be evaluated much faster than the simulator and
+can then be used for computationally demanding analyses <span id="id3">[<a class="reference internal" href="../refs.html#id14" title="H. Zhao, F. Amann, and J. Kowalski. Emulator-based global sensitivity analysis for flow-like landslide run-out models. Landslides, ():, 2021. doi:https://doi.org/10.1007/s10346-021-01690-w.">Zhao <em>et al.</em>, 2021</a>]</span>. A recap
+of Gaussian process emulation is provided below, which is adapted from <cite>Chapter 3</cite>
+of <span id="id4">Zhao [<a class="reference internal" href="../refs.html#id15" title="Hu Zhao. Gaussian processes for sensitivity analysis, Bayesian inference, and uncertainty quantification in landslide research. PhD thesis, RWTH Aachen University, 2021. doi:10.18154/RWTH-2021-11693.">2021</a>]</span>.</p>
+<section id="gp-prior">
+<h3>GP prior<a class="headerlink" href="#gp-prior" title="Permalink to this heading"></a></h3>
+<p>Let <span class="math notranslate nohighlight">\(f(\cdot)\)</span> denote a simulator that one wants to approximate. It
+defines a mapping from a <span class="math notranslate nohighlight">\(p\)</span>-dimensional input
+<span class="math notranslate nohighlight">\(\mathbf{x}=(x_1,\ldots,x_p)^T \in \mathcal{X} \subset{\mathbb{R}^p}\)</span>
+to a scalar output <span class="math notranslate nohighlight">\(y \in \mathbb{R}\)</span>.</p>
+<p>From the Bayesian perspective, the prior belief of the simulator is modeled by
+a Gaussian process, namely</p>
+<div class="math notranslate nohighlight" id="equation-gp">
+<span class="eqno">(1)<a class="headerlink" href="#equation-gp" title="Permalink to this equation"></a></span>\[f(\cdot) \sim \mathcal{GP}(m(\cdot), C(\cdot,\cdot)).\]</div>
+<p>The Gaussian process is fully specified by its mean function <span class="math notranslate nohighlight">\(m(\cdot)\)</span>
+and covariance function <span class="math notranslate nohighlight">\(C(\cdot,\cdot)\)</span>. The mean function is usually
+modeled by parametric regression</p>
+<div class="math notranslate nohighlight" id="equation-gpmean">
+<span class="eqno">(2)<a class="headerlink" href="#equation-gpmean" title="Permalink to this equation"></a></span>\[m(\mathbf{x})=\mathbf{h}^T(\mathbf{x}) \boldsymbol{\beta}=\sum_{t=1}^{q} h_{t}(\mathbf{x}) \beta_{t},\]</div>
+<p>with <span class="math notranslate nohighlight">\(q\)</span>-dimensional vectors
+<span class="math notranslate nohighlight">\(\mathbf{h}(\mathbf{x})=\left(h_{1}(\mathbf{x}), h_{2}(\mathbf{x}), \ldots, h_{q}(\mathbf{x})\right)^T\)</span>
+and <span class="math notranslate nohighlight">\(\boldsymbol{\beta}=\left(\beta_{1}, \beta_{2}, \ldots, \beta_{q}\right)^T\)</span>
+denoting the chosen basis functions and unknown regression parameters respectively.
+The basis functions are commonly chosen as constant <span class="math notranslate nohighlight">\(\mathbf{h}(\mathbf{x})=1\)</span>
+or some prescribed polynomials like <span class="math notranslate nohighlight">\(\mathbf{h}(\mathbf{x})=(1,x_1,\ldots,x_p)^T\)</span>.</p>
+<p>The covariance function is often assumed to be stationary and typically has a
+separable form of</p>
+<div class="math notranslate nohighlight" id="equation-gpcovariance">
+<span class="eqno">(3)<a class="headerlink" href="#equation-gpcovariance" title="Permalink to this equation"></a></span>\[C\left(\mathbf{x}_{i}, \mathbf{x}_{j}\right)=\sigma^2 c\left(\mathbf{x}_{i}, \mathbf{x}_{j}\right)=\sigma^2 \prod_{l=1}^{p} c_{l}\left(x_{i l}, x_{j l}\right),\]</div>
+<p>where <span class="math notranslate nohighlight">\(c\left(\mathbf{x}_{i}, \mathbf{x}_{j}\right)\)</span> is the correlation
+function, and <span class="math notranslate nohighlight">\(c_{l}\left(x_{i l}, x_{j l}\right)\)</span> corresponds to the
+correlation between the <span class="math notranslate nohighlight">\(l\)</span>-th component of <span class="math notranslate nohighlight">\(\mathbf{x}_i\)</span> and
+the counterpart of <span class="math notranslate nohighlight">\(\mathbf{x}_j\)</span>. Various correlation functions can be
+chosen for <span class="math notranslate nohighlight">\(c_{l}\left(x_{i l}, x_{j l}\right)\)</span>. In what follows a specific
+correlation function from the Matern family is chosen to illustrate the theory.
+It should be noted that it can be replaced by any other correlation function
+without loss of generality.</p>
+<div class="math notranslate nohighlight" id="equation-gpcorrelation">
+<span class="eqno">(4)<a class="headerlink" href="#equation-gpcorrelation" title="Permalink to this equation"></a></span>\[c_{l}\left(x_{i l}, x_{j l}\right) = \left(1+\frac{\sqrt{5}||x_{il}-x_{jl}||}{\psi_l}+\frac{5||x_{il}-x_{jl}||^2}{3\psi_{l}^{2}} \right) \exp{\left(-\frac{\sqrt{5}||x_{il}-x_{jl}||}{\psi_l}\right)},\]</div>
+<p>where <span class="math notranslate nohighlight">\(\psi_l\)</span> is the correlation length parameter in the <span class="math notranslate nohighlight">\(l\)</span>-th
+dimension. The unknowns in the covariance function
+<span class="math notranslate nohighlight">\(C\left(\mathbf{x}_{i}, \mathbf{x}_{j}\right)\)</span> are the variance
+<span class="math notranslate nohighlight">\(\sigma^2\)</span> and the <span class="math notranslate nohighlight">\(p\)</span> correlation length parameters
+<span class="math notranslate nohighlight">\(\boldsymbol{\psi}=(\psi_1,\ldots,\psi_p)^T\)</span>.</p>
+</section>
+<section id="gp-posterior">
+<h3>GP posterior<a class="headerlink" href="#gp-posterior" title="Permalink to this heading"></a></h3>
+<p>Equations <a class="reference internal" href="#equation-gp">(1)</a> to <a class="reference internal" href="#equation-gpcorrelation">(4)</a> encode prior knowledge of the simulator
+<span class="math notranslate nohighlight">\(f(\cdot)\)</span>. From the Bayesian viewpoint, this prior knowledge can be updated
+to a posterior based on a limited number of training data. Training data here refer
+to <span class="math notranslate nohighlight">\(n^{tr}\)</span> pairs of input-output data of <span class="math notranslate nohighlight">\(f(\cdot)\)</span>.</p>
+<p>Let <span class="math notranslate nohighlight">\(\mathbf{x}^{tr}:=\{\mathbf{x}_i\}_{i=1}^{n^{tr}}\)</span> and
+<span class="math notranslate nohighlight">\(\mathbf{y}^{tr}:=\{f(\mathbf{x}_i)\}_{i=1}^{n^{tr}}\)</span> denote the training
+inputs and outputs respectively. Since any finite number of random variables
+from a Gaussian process are jointly Gaussian distributed, the joint distribution
+of the <span class="math notranslate nohighlight">\(n^{tr}\)</span> outputs <span class="math notranslate nohighlight">\(\mathbf{y}^{tr}\)</span> follow a
+<span class="math notranslate nohighlight">\(n^{tr}\)</span>-dimensional Gaussian distribution</p>
+<div class="math notranslate nohighlight" id="equation-gplikelihood1">
+<span class="eqno">(5)<a class="headerlink" href="#equation-gplikelihood1" title="Permalink to this equation"></a></span>\[p(\mathbf{y}^{tr} | \boldsymbol{\beta}, \sigma^{2}, \boldsymbol{\psi})  \sim \mathcal{N}_{n^{tr}}\left(\mathbf{H}\boldsymbol{\beta}, \sigma^{2} \mathbf{R}\right),\]</div>
+<p>where <span class="math notranslate nohighlight">\(\mathbf{H}=\left[\mathbf{h}(\mathbf{x}_{1}), \ldots, \mathbf{h}(\mathbf{x}_{n^{tr}}) \right]^T\)</span>
+is the <span class="math notranslate nohighlight">\(n^{tr} \times q\)</span> basis design matrix and <span class="math notranslate nohighlight">\(\mathbf{R}\)</span> is the
+<span class="math notranslate nohighlight">\(n^{tr} \times n^{tr}\)</span> correlation matrix with <span class="math notranslate nohighlight">\((i,j)\)</span> element
+<span class="math notranslate nohighlight">\(c(\mathbf{x}_{i}, \mathbf{x}_{j})\)</span>. Equation <a class="reference internal" href="#equation-gplikelihood1">(5)</a> is known
+as the likelihood function.</p>
+<p>Similarly, the joint distribution of the function output <span class="math notranslate nohighlight">\(y^*\)</span> at any
+untried input <span class="math notranslate nohighlight">\(\mathbf{x}^*\)</span> and <span class="math notranslate nohighlight">\(\mathbf{y}^{tr}\)</span> follows a
+<span class="math notranslate nohighlight">\((n^{tr}+1)\)</span>-dimensional Gaussian distribution</p>
+<div class="math notranslate nohighlight" id="equation-jointystarytr">
+<span class="eqno">(6)<a class="headerlink" href="#equation-jointystarytr" title="Permalink to this equation"></a></span>\[\begin{split}p(y^*, \mathbf{y}^{tr} \mid \boldsymbol{\beta}, \sigma^{2}, \boldsymbol{\psi}) \sim \mathcal{N}_{n^{tr}+1}\left(\left[\begin{array}{c}
+\mathbf{h}^T\left(\mathbf{x}^*\right) \\
+\mathbf{H}
+\end{array}\right] \boldsymbol{\beta}, \sigma^{2}\left[\begin{array}{cc}
+c\left(\mathbf{x}^*, \mathbf{x}^*\right) &amp; \mathbf{r}^T\left(\mathbf{x}^*\right) \\
+\mathbf{r}\left(\mathbf{x}^*\right) &amp; \mathbf{R}
+\end{array}\right]\right)\end{split}\]</div>
+<p>where <span class="math notranslate nohighlight">\(\mathbf{r}(\mathbf{x}^*)=\left(c(\mathbf{x}^*, \mathbf{x}_{1}), \ldots, c(\mathbf{x}^*, \mathbf{x}_{n^{tr}}) \right)^T\)</span>.
+According to the property of the multivariate Gaussian distribution, the conditional
+distribution of <span class="math notranslate nohighlight">\(y^*\)</span> conditioned on <span class="math notranslate nohighlight">\(\mathbf{y}^{tr}\)</span> is again a
+Gaussian distribution, namely</p>
+<div class="math notranslate nohighlight" id="equation-conditionalgaussian">
+<span class="eqno">(7)<a class="headerlink" href="#equation-conditionalgaussian" title="Permalink to this equation"></a></span>\[p(y^* | \mathbf{y}^{tr}, \boldsymbol{\beta}, \sigma^{2}, \boldsymbol{\psi}) \sim  \mathcal{N}
+\left(m', \sigma^2 c' \right),\label{eq:conditionalGaussian}\]</div>
+<div class="math notranslate nohighlight" id="equation-conditionalgaussianm">
+<span class="eqno">(8)<a class="headerlink" href="#equation-conditionalgaussianm" title="Permalink to this equation"></a></span>\[m'=\mathbf{h}^T(\mathbf{x}^*) \boldsymbol{\beta} + \mathbf{r}^T(\mathbf{x}^*) \mathbf{R}^{-1} (\mathbf{y}^{tr}-\mathbf{H}\boldsymbol{\beta})\]</div>
+<div class="math notranslate nohighlight" id="equation-conditionalgaussianc">
+<span class="eqno">(9)<a class="headerlink" href="#equation-conditionalgaussianc" title="Permalink to this equation"></a></span>\[c'=c(\mathbf{x}^*, \mathbf{x}^*) - \mathbf{r}^T(\mathbf{x}^*) \mathbf{R}^{-1} \mathbf{r}(\mathbf{x}^*).\]</div>
+<p>Equations <a class="reference internal" href="#equation-conditionalgaussian">(7)</a> to <a class="reference internal" href="#equation-conditionalgaussianc">(9)</a> can be easily
+extended to any dimensionality since the joint distribution of the function
+outputs at any number of untried inputs and <span class="math notranslate nohighlight">\(\mathbf{y}^{tr}\)</span> also follows
+a multivariate Gaussian distribution. Equations <a class="reference internal" href="#equation-conditionalgaussian">(7)</a> to
+<a class="reference internal" href="#equation-conditionalgaussianc">(9)</a> therefore essentially define the posterior which is an
+updated Gaussian process, given the unknown regression parameters
+<span class="math notranslate nohighlight">\(\boldsymbol{\beta}\)</span>, variance <span class="math notranslate nohighlight">\(\sigma^2\)</span>, and correlation length
+parameters <span class="math notranslate nohighlight">\(\boldsymbol{\psi}\)</span>.</p>
+<p>For any new input <span class="math notranslate nohighlight">\(\mathbf{x}^*\)</span>, the output <span class="math notranslate nohighlight">\(y^*\)</span> can be almost
+instantaneously predicted, given by the mean <span class="math notranslate nohighlight">\(m'\)</span>, namely equation
+<a class="reference internal" href="#equation-conditionalgaussianm">(8)</a>. Moreover, the uncertainty associated with the prediction
+can be estimated by for example the variance <span class="math notranslate nohighlight">\(\sigma^2c'\)</span>. Depending on how
+the unknown parameters (<span class="math notranslate nohighlight">\(\boldsymbol{\beta}\)</span>, <span class="math notranslate nohighlight">\(\sigma^2\)</span>, and <span class="math notranslate nohighlight">\(\boldsymbol{\psi}\)</span>)
+are learned based on the training data, the posterior can have various forms, see
+<cite>Section 3.3</cite> of <span id="id5">Zhao [<a class="reference internal" href="../refs.html#id15" title="Hu Zhao. Gaussian processes for sensitivity analysis, Bayesian inference, and uncertainty quantification in landslide research. PhD thesis, RWTH Aachen University, 2021. doi:10.18154/RWTH-2021-11693.">2021</a>]</span>.</p>
+</section>
+<section id="sample-from-gp">
+<h3>Sample from GP<a class="headerlink" href="#sample-from-gp" title="Permalink to this heading"></a></h3>
+<p>A Gaussian process, either the prior or the posterior, defines a distribution over
+functions. Once its mean function <span class="math notranslate nohighlight">\(m(\cdot)\)</span> and covariance function
+<span class="math notranslate nohighlight">\(C(\cdot,\cdot)\)</span> are specified, the Gaussian process can be evaluated at a
+finite number <span class="math notranslate nohighlight">\(s\)</span> of input points <span class="math notranslate nohighlight">\(\{\mathbf{x}_i\}_{i=1}^{s}\)</span>.
+The joint distribution of <span class="math notranslate nohighlight">\(\{y_i=f(\mathbf{x}_i)\}_{i=1}^{s}\)</span> follows a
+<span class="math notranslate nohighlight">\(s\)</span>-variate Gaussian distribution. A sample of the <span class="math notranslate nohighlight">\(s\)</span>-variate Gaussian
+distribution, denoted as <span class="math notranslate nohighlight">\(\tilde{\mathbf{y}}:=(\tilde{y}_1,\ldots,\tilde{y}_s)^T\)</span>,
+can be viewed as a sample of the Gaussian process (evaluated at a finite number of points).
+To generate <span class="math notranslate nohighlight">\(\tilde{\mathbf{y}}\)</span>, the <span class="math notranslate nohighlight">\(s \times s\)</span> covariance matrix
+<span class="math notranslate nohighlight">\(\boldsymbol{\Sigma}\)</span> needs to be decomposed into the product of a lower triangular
+matrix <span class="math notranslate nohighlight">\(\mathbf{L}\)</span> and its conjugate transpose <span class="math notranslate nohighlight">\(\mathbf{L}^T\)</span> using the Cholesky
+decomposition</p>
+<div class="math notranslate nohighlight" id="equation-choleskydecomposition">
+<span class="eqno">(10)<a class="headerlink" href="#equation-choleskydecomposition" title="Permalink to this equation"></a></span>\[\begin{split}\boldsymbol{\Sigma}=\left(\begin{array}{cccc}
+C\left(\mathbf{x}_{1}, \mathbf{x}_{1}\right) &amp; C\left(\mathbf{x}_{1}, \mathbf{x}_{2}\right) &amp; \ldots &amp; C\left(\mathbf{x}_{1}, \mathbf{x}_{s}\right) \\
+C\left(\mathbf{x}_{2}, \mathbf{x}_{1}\right) &amp; C\left(\mathbf{x}_{2}, \mathbf{x}_{2}\right) &amp; \ldots &amp; C\left(\mathbf{x}_{2}, \mathbf{x}_{s}\right) \\
+\vdots &amp; \vdots &amp; \ddots &amp; \vdots \\
+C\left(\mathbf{x}_{s}, \mathbf{x}_{1}\right) &amp; \ldots &amp; \ldots &amp; C\left(\mathbf{x}_{s}, \mathbf{x}_{s}\right)
+\end{array}\right)=\mathbf{L}\mathbf{L}^T.\end{split}\]</div>
+<p>Then a sample <span class="math notranslate nohighlight">\(\tilde{\mathbf{y}}\)</span> can be obtained as follows:</p>
+<div class="math notranslate nohighlight" id="equation-gpsample">
+<span class="eqno">(11)<a class="headerlink" href="#equation-gpsample" title="Permalink to this equation"></a></span>\[\tilde{\mathbf{y}} = (m(\mathbf{x}_i),\ldots,m(\mathbf{x}_s))^T + \mathbf{L}\mathbf{w},\]</div>
+<p>where <span class="math notranslate nohighlight">\(\mathbf{w}:=(w_1,\dots,w_s)^T\)</span> denotes a <span class="math notranslate nohighlight">\(s\)</span>-dimensional random vector
+consisting of <span class="math notranslate nohighlight">\(s\)</span> independent standard normal random variables <span class="math notranslate nohighlight">\(w_i,i \in \{1,\ldots,s\}\)</span>.</p>
+</section>
+</section>
+<section id="scalargasp-class">
+<h2>ScalarGaSP Class<a class="headerlink" href="#scalargasp-class" title="Permalink to this heading"></a></h2>
+<p>Class <a class="reference internal" href="#psimpy.emulator.robustgasp.ScalarGaSP" title="psimpy.emulator.robustgasp.ScalarGaSP"><code class="xref py py-class docutils literal notranslate"><span class="pre">ScalarGaSP</span></code></a> provides Gaussian process emulation for simulators
+which return a scalar value as output, namely <span class="math notranslate nohighlight">\(y \in \mathbb{R}\)</span>. Please
+refer to <span id="id6">Gu <em>et al.</em> [<a class="reference internal" href="../refs.html#id5" title="Meng Yang Gu, Xiao Jing Wang, and James O. Berger. Robust Gaussian stochastic process emulation. Annals of Statistics, 46(6A):3038–3066, 2018. doi:10.1214/17-AOS1648.">2018</a>]</span> for the detailed theory.</p>
+<p>It is imported by:</p>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">psimpy.emulator.robustgasp</span> <span class="kn">import</span> <span class="n">ScalarGaSP</span>
+</pre></div>
+</div>
+<section id="methods">
+<h3>Methods<a class="headerlink" href="#methods" title="Permalink to this heading"></a></h3>
+<dl class="py class">
+<dt class="sig sig-object py" id="psimpy.emulator.robustgasp.ScalarGaSP">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">ScalarGaSP</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ndim</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">zero_mean</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'No'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">nugget</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">nugget_est</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">range_par</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">NA</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">method</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'post_mode'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">prior_choice</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'ref_approx'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">a</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.2</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">b</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">kernel_type</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'matern_5_2'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">isotropic</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">optimization</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'lbfgs'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">alpha</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">lower_bound</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">max_eval</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">num_initial_values</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">2</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/psimpy/emulator/robustgasp.html#ScalarGaSP"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#psimpy.emulator.robustgasp.ScalarGaSP" title="Permalink to this definition"></a></dt>
+<dd><p>Set up basic parameters of the emulator.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters</dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>ndim</strong> (<em>int</em>) – Input parameter dimension.</p></li>
+<li><p><strong>zero_mean</strong> (<em>str</em><em>, </em><em>optional</em>) – If <cite>‘Yes’</cite>, the mean is set to zero. If <cite>‘No’</cite>, the mean is
+specified by <code class="docutils literal notranslate"><span class="pre">trend</span></code>. Default is <cite>‘No’</cite>.</p></li>
+<li><p><strong>nugget</strong> (<em>float</em><em>, </em><em>optional</em>) – Nugget variance ratio.
+If <span class="math notranslate nohighlight">\(0\)</span>, there is no nugget or the nugget is estimated.
+If not <span class="math notranslate nohighlight">\(0\)</span>, it means a fixed nugget. Default is <span class="math notranslate nohighlight">\(0\)</span>.</p></li>
+<li><p><strong>nugget_est</strong> (<em>bool</em><em>, </em><em>optional</em>) – <cite>True</cite> means <code class="docutils literal notranslate"><span class="pre">nugget</span></code> should be estimated.
+<cite>False</cite> means <code class="docutils literal notranslate"><span class="pre">nugget</span></code> is fixed or not estimated.
+Default is <cite>False</cite>.</p></li>
+<li><p><strong>range_par</strong> (<em>numpy array</em><em>, </em><em>optional</em>) – Range parameters. One dimension <code class="xref py py-class docutils literal notranslate"><span class="pre">numpy.ndarray</span></code> of length
+<code class="docutils literal notranslate"><span class="pre">ndim</span></code>. If given, range parameters are set to the given values
+rather than estimated based on training data.
+By default <cite>NA</cite>, meaning that range parameters are estimated based
+on training data.</p></li>
+<li><p><strong>method</strong> (<em>str</em><em>, </em><em>optional</em>) – Method used for parameter estimation.
+<cite>‘post_mode’</cite>: marginal posterior mode estimation, resulted emulator
+is a Student’s t-process.
+<cite>‘mmle’</cite>: maximum marginal likelihood estimation, resulted emulator
+is a Student’s t-process.
+<cite>‘mle’</cite>: maximum likelihood estimation, resulted emulator is a
+Gaussian process.
+Default is <cite>‘post_mode’</cite>.</p></li>
+<li><p><strong>prior_choice</strong> (<em>str</em><em>, </em><em>optional</em>) – <cite>‘ref_xi’</cite>, <cite>‘ref_gamma’</cite>, or <cite>‘ref_approx’</cite>.
+Default is <cite>‘ref_approx’</cite>.</p></li>
+<li><p><strong>a</strong> (<em>float</em><em>, </em><em>optional</em>) – Prior parameters in the jointly robust prior. Default <span class="math notranslate nohighlight">\(0.2\)</span>.</p></li>
+<li><p><strong>b</strong> (<em>float</em><em>, </em><em>optional</em>) – Prior parameters in the jointly robust prior.
+Default value is <span class="math notranslate nohighlight">\(ntrain^{-1/ndim}(a+ndim)\)</span>, where <code class="docutils literal notranslate"><span class="pre">ntrain</span></code>
+is the number of training input points and <code class="docutils literal notranslate"><span class="pre">ndim</span></code> is input
+parameter dimension.</p></li>
+<li><p><strong>kernel_type</strong> (<em>str</em><em>, </em><em>optional</em>) – <cite>‘matern_3_2’</cite>: Matern correlation with roughness parameter <span class="math notranslate nohighlight">\(3/2\)</span>.
+<cite>‘matern_5_2’</cite>: Matern correlation with roughness parameter <span class="math notranslate nohighlight">\(5/2\)</span>.
+<cite>‘pow_exp’</cite>: power exponential correlation with roughness parameter
+<code class="docutils literal notranslate"><span class="pre">alpha</span></code>.
+Default is <cite>‘matern_5_2’</cite>.</p></li>
+<li><p><strong>isotropic</strong> (<em>bool</em><em>, </em><em>optional</em>) – <cite>True</cite>: isotropic kernel. <cite>False</cite>: separable kernel.
+Default is <cite>False</cite>.</p></li>
+<li><p><strong>optimization</strong> (<em>str</em><em>, </em><em>optional</em>) – Optimization method for kernel parameters.
+<cite>‘lbfgs’</cite>: low storage version of the Broyden-Fletcher-Goldarb-Shanno
+method.
+<cite>‘nelder-mead’</cite>: Nelder and Mead method.
+<cite>‘brent’</cite>: Brent method for one-dimensional problems.</p></li>
+<li><p><strong>alpha</strong> (<em>numpy array</em><em>, </em><em>optional</em>) – Roughness parameters in the <cite>‘pow_exp’</cite> correlation functions. One
+dimension <code class="xref py py-class docutils literal notranslate"><span class="pre">numpy.ndarray</span></code> of length <code class="docutils literal notranslate"><span class="pre">ndim</span></code>.
+Default is a one dimension array with each entry being <span class="math notranslate nohighlight">\(1.9\)</span>.</p></li>
+<li><p><strong>lower_bound</strong> (<em>bool</em>) – <cite>True</cite>: the default lower bounds of the inverse range parameters are
+used to constrain the optimization.
+<cite>False</cite>: the optimization is unconstrained.
+Default is <cite>True</cite>.</p></li>
+<li><p><strong>max_eval</strong> (<em>int</em><em>, </em><em>optional</em>) – Maximum number of steps to estimate the range and nugget parameters.
+Default is <span class="math notranslate nohighlight">\(max(30,20+5*ndim)\)</span>.</p></li>
+<li><p><strong>num_initial_values</strong> (<em>int</em><em>, </em><em>optional</em>) – Number of initial values of the kernel parameters in optimization.
+Default is <span class="math notranslate nohighlight">\(2\)</span>.</p></li>
+</ul>
+</dd>
+</dl>
+<dl class="py method">
+<dt class="sig sig-object py" id="psimpy.emulator.robustgasp.ScalarGaSP.train">
+<span class="sig-name descname"><span class="pre">train</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">design</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">response</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">trend</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/psimpy/emulator/robustgasp.html#ScalarGaSP.train"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#psimpy.emulator.robustgasp.ScalarGaSP.train" title="Permalink to this definition"></a></dt>
+<dd><p>Train a scalar GP given training data.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters</dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>design</strong> (<em>numpy array</em>) – Training input points. Shape <code class="code docutils literal notranslate"><span class="pre">(ntrain,</span> <span class="pre">ndim)</span></code>.
+<code class="docutils literal notranslate"><span class="pre">ntrain</span></code> is the number of training points, <code class="docutils literal notranslate"><span class="pre">ndim</span></code> is the input
+dimension. If <span class="math notranslate nohighlight">\(ndim=1\)</span>, both <code class="code docutils literal notranslate"><span class="pre">(ntrain,</span> <span class="pre">1)</span></code> and
+<code class="code docutils literal notranslate"><span class="pre">(ntrain,)</span></code> <code class="xref py py-class docutils literal notranslate"><span class="pre">numpy.ndarray</span></code> are valid.</p></li>
+<li><p><strong>response</strong> (<em>numpy array</em>) – Training output points. Shape <code class="code docutils literal notranslate"><span class="pre">(ntrain,</span> <span class="pre">1)</span></code> or
+<code class="code docutils literal notranslate"><span class="pre">(ntrain,)</span></code>.</p></li>
+<li><p><strong>trend</strong> (<em>numpy array</em><em>, </em><em>optional</em>) – Basis function matrix. Shape <code class="code docutils literal notranslate"><span class="pre">(ntrain,</span> <span class="pre">q)</span></code>.
+If <cite>None</cite>, a <code class="code docutils literal notranslate"><span class="pre">(ntrain,</span> <span class="pre">1)</span></code> matrix of ones is used.
+If <span class="math notranslate nohighlight">\(q=1\)</span>, both <code class="code docutils literal notranslate"><span class="pre">(ntrain,</span> <span class="pre">1)</span></code> and <code class="code docutils literal notranslate"><span class="pre">(ntrain,)</span></code>
+<code class="xref py py-class docutils literal notranslate"><span class="pre">numpy.ndarray</span></code> are valid.</p></li>
+</ul>
+</dd>
+<dt class="field-even">Return type</dt>
+<dd class="field-even"><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="psimpy.emulator.robustgasp.ScalarGaSP.predict">
+<span class="sig-name descname"><span class="pre">predict</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">testing_input</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">testing_trend</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/psimpy/emulator/robustgasp.html#ScalarGaSP.predict"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#psimpy.emulator.robustgasp.ScalarGaSP.predict" title="Permalink to this definition"></a></dt>
+<dd><p>Make prediction using the trained scalar GP emulator.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters</dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>testing_input</strong> (<em>numpy array</em>) – Input points at which to make prediction. Shape <code class="code docutils literal notranslate"><span class="pre">(ntest,</span> <span class="pre">ndim)</span></code>.
+<code class="docutils literal notranslate"><span class="pre">ntest</span></code> is the number of input points and <code class="docutils literal notranslate"><span class="pre">ndim</span></code> is the
+input dimension. If <span class="math notranslate nohighlight">\(ndim=1\)</span>, both <code class="code docutils literal notranslate"><span class="pre">(ntest,</span> <span class="pre">1)</span></code> and
+<code class="code docutils literal notranslate"><span class="pre">(ntest,)</span></code> <code class="xref py py-class docutils literal notranslate"><span class="pre">numpy.ndarray</span></code> are valid.</p></li>
+<li><p><strong>testing_trend</strong> (<em>numpy array</em><em>, </em><em>optional</em>) – Basis function matrix corresponds to <code class="docutils literal notranslate"><span class="pre">testing_input</span></code>.
+Shape <code class="code docutils literal notranslate"><span class="pre">(ntest,</span> <span class="pre">q)</span></code>. By default <code class="code docutils literal notranslate"><span class="pre">(ntest,</span> <span class="pre">1)</span></code> matrix of ones.
+If <span class="math notranslate nohighlight">\(q=1\)</span>, both <code class="code docutils literal notranslate"><span class="pre">(ntest,</span> <span class="pre">1)</span></code> and <code class="code docutils literal notranslate"><span class="pre">(ntest,)</span></code>
+<code class="xref py py-class docutils literal notranslate"><span class="pre">numpy.ndarray</span></code> are valid.</p></li>
+</ul>
+</dd>
+<dt class="field-even">Returns</dt>
+<dd class="field-even"><p><strong>predictions</strong> – Emulator-prediction at <code class="docutils literal notranslate"><span class="pre">testing_input</span></code>. Shape <code class="code docutils literal notranslate"><span class="pre">(ntest,</span> <span class="pre">4)</span></code>.
+<cite>predictions[:, 0]</cite> - mean,
+<cite>predictions[:, 1]</cite> - low95,
+<cite>predictions[:, 2]</cite> - upper95,
+<cite>predictions[:, 3]</cite> - sd</p>
+</dd>
+<dt class="field-odd">Return type</dt>
+<dd class="field-odd"><p>numpy array</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="psimpy.emulator.robustgasp.ScalarGaSP.sample">
+<span class="sig-name descname"><span class="pre">sample</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">testing_input</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">nsamples</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">testing_trend</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/psimpy/emulator/robustgasp.html#ScalarGaSP.sample"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#psimpy.emulator.robustgasp.ScalarGaSP.sample" title="Permalink to this definition"></a></dt>
+<dd><p>Draw samples using the trained scalar GP emulator.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters</dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>testing_input</strong> (<em>numpy array</em>) – Input points at which to draw samples. Shape <code class="code docutils literal notranslate"><span class="pre">(ntest,</span> <span class="pre">ndim)</span></code>.
+<code class="docutils literal notranslate"><span class="pre">ntest</span></code> is the number of input points and <code class="docutils literal notranslate"><span class="pre">ndim</span></code> is the input
+dimension. If <span class="math notranslate nohighlight">\(ndim=1\)</span>, both <code class="code docutils literal notranslate"><span class="pre">(ntest,</span> <span class="pre">1)</span></code> and
+<code class="code docutils literal notranslate"><span class="pre">(ntest,)</span></code> <code class="xref py py-class docutils literal notranslate"><span class="pre">numpy.ndarray</span></code> are valid.</p></li>
+<li><p><strong>nsamples</strong> (<em>int</em><em>, </em><em>optional</em>) – Number of samples to be drawn.</p></li>
+<li><p><strong>testing_trend</strong> (<em>numpy array</em><em>, </em><em>optional</em>) – Basis function matrix corresponds to <code class="docutils literal notranslate"><span class="pre">testing_input</span></code>.
+Shape <code class="code docutils literal notranslate"><span class="pre">(ntest,</span> <span class="pre">q)</span></code>. By default <code class="code docutils literal notranslate"><span class="pre">(ntest,</span> <span class="pre">1)</span></code> matrix of ones.
+If <span class="math notranslate nohighlight">\(q=1\)</span>, both <code class="code docutils literal notranslate"><span class="pre">(ntest,</span> <span class="pre">1)</span></code> and <code class="code docutils literal notranslate"><span class="pre">(ntest,)</span></code>
+<code class="xref py py-class docutils literal notranslate"><span class="pre">numpy.ndarray</span></code> are valid.</p></li>
+</ul>
+</dd>
+<dt class="field-even">Returns</dt>
+<dd class="field-even"><p><strong>samples</strong> – Shape <code class="code docutils literal notranslate"><span class="pre">(ntest,</span> <span class="pre">nsamples)</span></code>. Each column contains one realization
+of the trained emulator at <code class="docutils literal notranslate"><span class="pre">testing_input</span></code>.</p>
+</dd>
+<dt class="field-odd">Return type</dt>
+<dd class="field-odd"><p>numpy array</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="psimpy.emulator.robustgasp.ScalarGaSP.loo_validate">
+<span class="sig-name descname"><span class="pre">loo_validate</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="../_modules/psimpy/emulator/robustgasp.html#ScalarGaSP.loo_validate"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#psimpy.emulator.robustgasp.ScalarGaSP.loo_validate" title="Permalink to this definition"></a></dt>
+<dd><p>Validate trained scalar GP emulator using leave-one-out-cross-validation.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Returns</dt>
+<dd class="field-odd"><p><strong>validation</strong> – Shape <code class="code docutils literal notranslate"><span class="pre">(n,</span> <span class="pre">2)</span></code>.
+validation[:, 0] - leave one out fitted values,
+validation[:, 1] - stand deviation of each prediction</p>
+</dd>
+<dt class="field-even">Return type</dt>
+<dd class="field-even"><p>numpy array</p>
+</dd>
+</dl>
+</dd></dl>
+
+</dd></dl>
+
+</section>
+</section>
+<section id="ppgasp-class">
+<h2>PPGaSP Class<a class="headerlink" href="#ppgasp-class" title="Permalink to this heading"></a></h2>
+<p>Class <a class="reference internal" href="#psimpy.emulator.robustgasp.PPGaSP" title="psimpy.emulator.robustgasp.PPGaSP"><code class="xref py py-class docutils literal notranslate"><span class="pre">PPGaSP</span></code></a> provides Gaussian process emulation for simulators
+which return multiple values as output, namely <span class="math notranslate nohighlight">\(y \in \mathbb{R}^k, k&gt;1\)</span>.
+Please refer to <span id="id7">Gu and Berger [<a class="reference internal" href="../refs.html#id4" title="Meng Yang Gu and James O. Berger. Parallel partial Gaussian process emulation for computer models with massive output. Annals of Applied Statistics, 10(3):1317–1347, 2016. doi:10.1214/16-AOAS934.">2016</a>]</span> for the detailed theory.</p>
+<p>It is imported by:</p>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">psimpy.emulator.robustgasp</span> <span class="kn">import</span> <span class="n">PPGaSP</span>
+</pre></div>
+</div>
+<section id="id8">
+<h3>Methods<a class="headerlink" href="#id8" title="Permalink to this heading"></a></h3>
+<dl class="py class">
+<dt class="sig sig-object py" id="psimpy.emulator.robustgasp.PPGaSP">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">PPGaSP</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ndim</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">zero_mean</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'No'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">nugget</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">nugget_est</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">range_par</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">NA</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">method</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'post_mode'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">prior_choice</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'ref_approx'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">a</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.2</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">b</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">kernel_type</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'matern_5_2'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">isotropic</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">optimization</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'lbfgs'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">alpha</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">lower_bound</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">max_eval</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">num_initial_values</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">2</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/psimpy/emulator/robustgasp.html#PPGaSP"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#psimpy.emulator.robustgasp.PPGaSP" title="Permalink to this definition"></a></dt>
+<dd><p>Set up basic parameters of the emulator.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters</dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>ndim</strong> (<em>int</em>) – Input parameter dimension.</p></li>
+<li><p><strong>zero_mean</strong> (<em>str</em><em>, </em><em>optional</em>) – If <cite>‘Yes’</cite>, the mean is set to zero. If <cite>‘No’</cite>, the mean is
+specified by <code class="docutils literal notranslate"><span class="pre">trend</span></code>. Default is <cite>‘No’</cite>.</p></li>
+<li><p><strong>nugget</strong> (<em>float</em><em>, </em><em>optional</em>) – Nugget variance ratio.
+If <span class="math notranslate nohighlight">\(0\)</span>, there is no nugget or the nugget is estimated.
+If not <span class="math notranslate nohighlight">\(0\)</span>, it means a fixed nugget. Default is <span class="math notranslate nohighlight">\(0\)</span>.</p></li>
+<li><p><strong>nugget_est</strong> (<em>bool</em><em>, </em><em>optional</em>) – <cite>True</cite> means <code class="docutils literal notranslate"><span class="pre">nugget</span></code> should be estimated.
+<cite>False</cite> means <code class="docutils literal notranslate"><span class="pre">nugget</span></code> is fixed or not estimated.
+Default is <cite>False</cite>.</p></li>
+<li><p><strong>range_par</strong> (<em>numpy array</em><em>, </em><em>optional</em>) – Range parameters. One dimension <code class="xref py py-class docutils literal notranslate"><span class="pre">numpy.ndarray</span></code> of length
+<code class="docutils literal notranslate"><span class="pre">ndim</span></code>. If given, range parameters are set to the given values
+rather than estimated based on training data.
+By default <cite>NA</cite>, meaning that range parameters are estimated based
+on training data.</p></li>
+<li><p><strong>method</strong> (<em>str</em><em>, </em><em>optional</em>) – Method used for parameter estimation.
+<cite>‘post_mode’</cite>: marginal posterior mode estimation, resulted emulator
+is a Student’s t-process.
+<cite>‘mmle’</cite>: maximum marginal likelihood estimation, resulted emulator
+is a Student’s t-process.
+<cite>‘mle’</cite>: maximum likelihood estimation, resulted emulator is a
+Gaussian process.
+Default is <cite>‘post_mode’</cite>.</p></li>
+<li><p><strong>prior_choice</strong> (<em>str</em><em>, </em><em>optional</em>) – <cite>‘ref_xi’</cite>, <cite>‘ref_gamma’</cite>, or <cite>‘ref_approx’</cite>.
+Default is <cite>‘ref_approx’</cite>.</p></li>
+<li><p><strong>a</strong> (<em>float</em><em>, </em><em>optional</em>) – Prior parameters in the jointly robust prior. Default <span class="math notranslate nohighlight">\(0.2\)</span>.</p></li>
+<li><p><strong>b</strong> (<em>float</em><em>, </em><em>optional</em>) – Prior parameters in the jointly robust prior.
+Default value is <span class="math notranslate nohighlight">\(ntrain^{-1/ndim}(a+ndim)\)</span>, where <code class="docutils literal notranslate"><span class="pre">ntrain</span></code>
+is the number of training input points and <code class="docutils literal notranslate"><span class="pre">ndim</span></code> is input
+parameter dimension.</p></li>
+<li><p><strong>kernel_type</strong> (<em>str</em><em>, </em><em>optional</em>) – <cite>‘matern_3_2’</cite>: Matern correlation with roughness parameter <span class="math notranslate nohighlight">\(3/2\)</span>.
+<cite>‘matern_5_2’</cite>: Matern correlation with roughness parameter <span class="math notranslate nohighlight">\(5/2\)</span>.
+<cite>‘pow_exp’</cite>: power exponential correlation with roughness parameter
+<code class="docutils literal notranslate"><span class="pre">alpha</span></code>.
+Default is <cite>‘matern_5_2’</cite>.</p></li>
+<li><p><strong>isotropic</strong> (<em>bool</em><em>, </em><em>optional</em>) – <cite>True</cite>: isotropic kernel. <cite>False</cite>: separable kernel.
+Default is <cite>False</cite>.</p></li>
+<li><p><strong>optimization</strong> (<em>str</em><em>, </em><em>optional</em>) – Optimization method for kernel parameters.
+<cite>‘lbfgs’</cite>: low storage version of the Broyden-Fletcher-Goldarb-Shanno
+method.
+<cite>‘nelder-mead’</cite>: Nelder and Mead method.
+<cite>‘brent’</cite>: Brent method for one-dimensional problems.</p></li>
+<li><p><strong>alpha</strong> (<em>numpy array</em><em>, </em><em>optional</em>) – Roughness parameters in the <cite>‘pow_exp’</cite> correlation functions. One
+dimension <code class="xref py py-class docutils literal notranslate"><span class="pre">numpy.ndarray</span></code> of length <code class="docutils literal notranslate"><span class="pre">ndim</span></code>.
+Default is a one dimension array with each entry being <span class="math notranslate nohighlight">\(1.9\)</span>.</p></li>
+<li><p><strong>lower_bound</strong> (<em>bool</em>) – <cite>True</cite>: the default lower bounds of the inverse range parameters are
+used to constrain the optimization.
+<cite>False</cite>: the optimization is unconstrained.
+Default is <cite>True</cite>.</p></li>
+<li><p><strong>max_eval</strong> (<em>int</em><em>, </em><em>optional</em>) – Maximum number of steps to estimate the range and nugget parameters.
+Default is <span class="math notranslate nohighlight">\(max(30,20+5*ndim)\)</span>.</p></li>
+<li><p><strong>num_initial_values</strong> (<em>int</em><em>, </em><em>optional</em>) – Number of initial values of the kernel parameters in optimization.
+Default is <span class="math notranslate nohighlight">\(2\)</span>.</p></li>
+</ul>
+</dd>
+</dl>
+<dl class="py method">
+<dt class="sig sig-object py" id="psimpy.emulator.robustgasp.PPGaSP.train">
+<span class="sig-name descname"><span class="pre">train</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">design</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">response</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">trend</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/psimpy/emulator/robustgasp.html#PPGaSP.train"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#psimpy.emulator.robustgasp.PPGaSP.train" title="Permalink to this definition"></a></dt>
+<dd><p>Train a parallel partial GP given training data.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters</dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>design</strong> (<em>numpy array</em>) – Training input points. Shape <code class="code docutils literal notranslate"><span class="pre">(ntrain,</span> <span class="pre">ndim)</span></code>.
+<code class="docutils literal notranslate"><span class="pre">ntrain</span></code> is the number of training points, <code class="docutils literal notranslate"><span class="pre">ndim</span></code> is the input
+dimension. If <span class="math notranslate nohighlight">\(ndim=1\)</span>, both <code class="code docutils literal notranslate"><span class="pre">(ndim,</span> <span class="pre">1)</span></code> and
+<code class="code docutils literal notranslate"><span class="pre">(ndim,)</span></code> <code class="xref py py-class docutils literal notranslate"><span class="pre">numpy.ndarray</span></code> are valid.</p></li>
+<li><p><strong>response</strong> (<em>numpy array</em>) – Training output points. Shape <code class="code docutils literal notranslate"><span class="pre">(ntrain,</span> <span class="pre">nresponse)</span></code>,
+<span class="math notranslate nohighlight">\(nresponse&gt;1\)</span>.</p></li>
+<li><p><strong>trend</strong> (<em>numpy array</em><em>, </em><em>optional</em>) – Basis function matrix. Shape <code class="code docutils literal notranslate"><span class="pre">(ntrain,</span> <span class="pre">q)</span></code>.
+If <cite>None</cite>, a <code class="code docutils literal notranslate"><span class="pre">(ntrain,</span> <span class="pre">1)</span></code> matrix of ones is used.
+If <span class="math notranslate nohighlight">\(q=1\)</span>, both <code class="code docutils literal notranslate"><span class="pre">(ntrain,</span> <span class="pre">1)</span></code> and <code class="code docutils literal notranslate"><span class="pre">(ntrain,)</span></code>
+<code class="xref py py-class docutils literal notranslate"><span class="pre">numpy.ndarray</span></code> are valid.</p></li>
+</ul>
+</dd>
+<dt class="field-even">Return type</dt>
+<dd class="field-even"><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="psimpy.emulator.robustgasp.PPGaSP.predict">
+<span class="sig-name descname"><span class="pre">predict</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">testing_input</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">testing_trend</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/psimpy/emulator/robustgasp.html#PPGaSP.predict"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#psimpy.emulator.robustgasp.PPGaSP.predict" title="Permalink to this definition"></a></dt>
+<dd><p>Make prediction using the trained parallel partial GP emulator.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters</dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>testing_input</strong> (<em>numpy array</em>) – Input points at which to make prediction. Shape <code class="code docutils literal notranslate"><span class="pre">(ntest,</span> <span class="pre">ndim)</span></code>.
+<code class="docutils literal notranslate"><span class="pre">ntest</span></code> is the number of input points and <code class="docutils literal notranslate"><span class="pre">ndim</span></code> is the input
+dimension. If <span class="math notranslate nohighlight">\(ndim=1\)</span>, both <code class="code docutils literal notranslate"><span class="pre">(ntest,</span> <span class="pre">1)</span></code> and
+<code class="code docutils literal notranslate"><span class="pre">(ntest,)</span></code> <code class="xref py py-class docutils literal notranslate"><span class="pre">numpy.ndarray</span></code> are valid.</p></li>
+<li><p><strong>testing_trend</strong> (<em>numpy array</em><em>, </em><em>optional</em>) – Basis function matrix corresponds to <code class="docutils literal notranslate"><span class="pre">testing_input</span></code>.
+Shape <code class="code docutils literal notranslate"><span class="pre">(ntest,</span> <span class="pre">q)</span></code>. By default <code class="code docutils literal notranslate"><span class="pre">(ntest,</span> <span class="pre">1)</span></code> matrix of ones.
+If <span class="math notranslate nohighlight">\(q=1\)</span>, both <code class="code docutils literal notranslate"><span class="pre">(ntest,</span> <span class="pre">1)</span></code> and <code class="code docutils literal notranslate"><span class="pre">(ntest,)</span></code>
+<code class="xref py py-class docutils literal notranslate"><span class="pre">numpy.ndarray</span></code> are valid.</p></li>
+</ul>
+</dd>
+<dt class="field-even">Returns</dt>
+<dd class="field-even"><p><strong>predictions</strong> – Emulator-prediction at <code class="docutils literal notranslate"><span class="pre">testing_input</span></code>.
+Shape <code class="code docutils literal notranslate"><span class="pre">(ntest,</span> <span class="pre">nresponse,</span> <span class="pre">4)</span></code>.
+<cite>predictions[:, :, 0]</cite> - mean,
+<cite>predictions[:, :, 1]</cite> - low95,
+<cite>predictions[:, :, 2]</cite> - upper95,
+<cite>predictions[:, :, 3]</cite> - sd</p>
+</dd>
+<dt class="field-odd">Return type</dt>
+<dd class="field-odd"><p>numpy array</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="psimpy.emulator.robustgasp.PPGaSP.sample">
+<span class="sig-name descname"><span class="pre">sample</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">testing_input</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">nsamples</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">testing_trend</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/psimpy/emulator/robustgasp.html#PPGaSP.sample"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#psimpy.emulator.robustgasp.PPGaSP.sample" title="Permalink to this definition"></a></dt>
+<dd><p>Draw samples using the trained parallel partial GaSP emulator.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters</dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>testing_input</strong> (<em>numpy array</em>) – Input point at which to draw samples. Shape <code class="code docutils literal notranslate"><span class="pre">(ntest,</span> <span class="pre">ndim)</span></code>.
+<code class="docutils literal notranslate"><span class="pre">ntest</span></code> is the number of input points and <code class="docutils literal notranslate"><span class="pre">ndim</span></code> is the input
+dimension. If <span class="math notranslate nohighlight">\(ndim=1\)</span>, both <code class="code docutils literal notranslate"><span class="pre">(ntest,</span> <span class="pre">1)</span></code> and
+<code class="code docutils literal notranslate"><span class="pre">(ntest,)</span></code> <code class="xref py py-class docutils literal notranslate"><span class="pre">numpy.ndarray</span></code> are valid.</p></li>
+<li><p><strong>nsamples</strong> (<em>int</em><em>, </em><em>optional</em>) – Number of samples to be drawn.</p></li>
+<li><p><strong>testing_trend</strong> (<em>numpy array</em><em>, </em><em>optional</em>) – Basis function matrix corresponds to <code class="docutils literal notranslate"><span class="pre">testing_input</span></code>.
+Shape <code class="code docutils literal notranslate"><span class="pre">(ntest,</span> <span class="pre">q)</span></code>. By default <code class="code docutils literal notranslate"><span class="pre">(ntest,</span> <span class="pre">1)</span></code> matrix of ones.
+If <span class="math notranslate nohighlight">\(q=1\)</span>, both <code class="code docutils literal notranslate"><span class="pre">(ntest,</span> <span class="pre">1)</span></code> and <code class="code docutils literal notranslate"><span class="pre">(ntest,)</span></code>
+<code class="xref py py-class docutils literal notranslate"><span class="pre">numpy.ndarray</span></code> are valid.</p></li>
+</ul>
+</dd>
+<dt class="field-even">Returns</dt>
+<dd class="field-even"><p><strong>samples</strong> – Shape <code class="code docutils literal notranslate"><span class="pre">(ntest,</span> <span class="pre">nresponse,</span> <span class="pre">nsamples)</span></code>.
+<cite>samples[:, :, i]</cite> corresponds to i-th realization of the trained
+emulator at <code class="docutils literal notranslate"><span class="pre">testing_input</span></code>, i=1, …, <code class="docutils literal notranslate"><span class="pre">nsamples</span></code>.</p>
+</dd>
+<dt class="field-odd">Return type</dt>
+<dd class="field-odd"><p>numpy array</p>
+</dd>
+</dl>
+</dd></dl>
+
+</dd></dl>
+
+</section>
+</section>
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+
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+<h1>Example Gallery<a class="headerlink" href="#example-gallery" title="Permalink to this heading"></a></h1>
+<div class="toctree-wrapper compound">
+<ul>
+<li class="toctree-l1"><a class="reference internal" href="auto_examples/emulator/index.html">Emulator</a></li>
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+          <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer">
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+<html class="writer-html5" lang="en" >
+<head>
+  <meta charset="utf-8" />
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+           <div itemprop="articleBody">
+             
+
+<h1 id="index">Index</h1>
+
+<div class="genindex-jumpbox">
+ <a href="#A"><strong>A</strong></a>
+ | <a href="#E"><strong>E</strong></a>
+ | <a href="#G"><strong>G</strong></a>
+ | <a href="#I"><strong>I</strong></a>
+ | <a href="#L"><strong>L</strong></a>
+ | <a href="#M"><strong>M</strong></a>
+ | <a href="#O"><strong>O</strong></a>
+ | <a href="#P"><strong>P</strong></a>
+ | <a href="#R"><strong>R</strong></a>
+ | <a href="#S"><strong>S</strong></a>
+ | <a href="#T"><strong>T</strong></a>
+ | <a href="#V"><strong>V</strong></a>
+ 
+</div>
+<h2 id="A">A</h2>
+<table style="width: 100%" class="indextable genindextable"><tr>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="inference/active_learning.html#psimpy.inference.active_learning.ActiveLearning">ActiveLearning (class in psimpy.inference.active_learning)</a>
+</li>
+  </ul></td>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="inference/active_learning.html#psimpy.inference.active_learning.ActiveLearning.approx_ln_pxl">approx_ln_pxl() (ActiveLearning method)</a>
+</li>
+  </ul></td>
+</tr></table>
+
+<h2 id="E">E</h2>
+<table style="width: 100%" class="indextable genindextable"><tr>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="simulator/ravaflow24.html#psimpy.simulator.ravaflow24.Ravaflow24Mixture.extract_impact_area">extract_impact_area() (Ravaflow24Mixture method)</a>
+</li>
+  </ul></td>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="simulator/ravaflow24.html#psimpy.simulator.ravaflow24.Ravaflow24Mixture.extract_qoi_max">extract_qoi_max() (Ravaflow24Mixture method)</a>
+</li>
+      <li><a href="simulator/ravaflow24.html#psimpy.simulator.ravaflow24.Ravaflow24Mixture.extract_qoi_max_loc">extract_qoi_max_loc() (Ravaflow24Mixture method)</a>
+</li>
+  </ul></td>
+</tr></table>
+
+<h2 id="G">G</h2>
+<table style="width: 100%" class="indextable genindextable"><tr>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="inference/bayes_inference.html#psimpy.inference.bayes_inference.GridEstimation">GridEstimation (class in psimpy.inference.bayes_inference)</a>
+</li>
+  </ul></td>
+</tr></table>
+
+<h2 id="I">I</h2>
+<table style="width: 100%" class="indextable genindextable"><tr>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="inference/active_learning.html#psimpy.inference.active_learning.ActiveLearning.initial_simulation">initial_simulation() (ActiveLearning method)</a>
+</li>
+  </ul></td>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="inference/active_learning.html#psimpy.inference.active_learning.ActiveLearning.iterative_emulation">iterative_emulation() (ActiveLearning method)</a>
+</li>
+  </ul></td>
+</tr></table>
+
+<h2 id="L">L</h2>
+<table style="width: 100%" class="indextable genindextable"><tr>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="sampler/latin.html#psimpy.sampler.latin.LHS">LHS (class in psimpy.sampler.latin)</a>
+</li>
+  </ul></td>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="emulator/robustgasp.html#psimpy.emulator.robustgasp.ScalarGaSP.loo_validate">loo_validate() (ScalarGaSP method)</a>
+</li>
+  </ul></td>
+</tr></table>
+
+<h2 id="M">M</h2>
+<table style="width: 100%" class="indextable genindextable"><tr>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="simulator/mass_point_model.html#psimpy.simulator.mass_point_model.MassPointModel">MassPointModel (class in psimpy.simulator.mass_point_model)</a>
+</li>
+  </ul></td>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="sampler/metropolis_hastings.html#psimpy.sampler.metropolis_hastings.MetropolisHastings">MetropolisHastings (class in psimpy.sampler.metropolis_hastings)</a>
+</li>
+      <li><a href="inference/bayes_inference.html#psimpy.inference.bayes_inference.MetropolisHastingsEstimation">MetropolisHastingsEstimation (class in psimpy.inference.bayes_inference)</a>
+</li>
+  </ul></td>
+</tr></table>
+
+<h2 id="O">O</h2>
+<table style="width: 100%" class="indextable genindextable"><tr>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="simulator/run_simulator.html#psimpy.simulator.run_simulator.RunSimulator.outputs">outputs (RunSimulator attribute)</a>
+</li>
+  </ul></td>
+</tr></table>
+
+<h2 id="P">P</h2>
+<table style="width: 100%" class="indextable genindextable"><tr>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="simulator/run_simulator.html#psimpy.simulator.run_simulator.RunSimulator.parallel_run">parallel_run() (RunSimulator method)</a>
+</li>
+      <li><a href="emulator/robustgasp.html#psimpy.emulator.robustgasp.PPGaSP">PPGaSP (class in psimpy.emulator.robustgasp)</a>
+</li>
+  </ul></td>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="emulator/robustgasp.html#psimpy.emulator.robustgasp.PPGaSP.predict">predict() (PPGaSP method)</a>
+
+      <ul>
+        <li><a href="emulator/robustgasp.html#psimpy.emulator.robustgasp.ScalarGaSP.predict">(ScalarGaSP method)</a>
+</li>
+      </ul></li>
+      <li><a href="simulator/ravaflow24.html#psimpy.simulator.ravaflow24.Ravaflow24Mixture.preprocess">preprocess() (Ravaflow24Mixture method)</a>
+</li>
+  </ul></td>
+</tr></table>
+
+<h2 id="R">R</h2>
+<table style="width: 100%" class="indextable genindextable"><tr>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="simulator/ravaflow24.html#psimpy.simulator.ravaflow24.Ravaflow24Mixture">Ravaflow24Mixture (class in psimpy.simulator.ravaflow24)</a>
+</li>
+      <li><a href="inference/bayes_inference.html#psimpy.inference.bayes_inference.GridEstimation.run">run() (GridEstimation method)</a>
+
+      <ul>
+        <li><a href="simulator/mass_point_model.html#psimpy.simulator.mass_point_model.MassPointModel.run">(MassPointModel method)</a>
+</li>
+        <li><a href="inference/bayes_inference.html#psimpy.inference.bayes_inference.MetropolisHastingsEstimation.run">(MetropolisHastingsEstimation method)</a>
+</li>
+        <li><a href="simulator/ravaflow24.html#psimpy.simulator.ravaflow24.Ravaflow24Mixture.run">(Ravaflow24Mixture method)</a>
+</li>
+        <li><a href="sensitivity/sobol.html#psimpy.sensitivity.sobol.SobolAnalyze.run">(SobolAnalyze method)</a>
+</li>
+      </ul></li>
+  </ul></td>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="simulator/run_simulator.html#psimpy.simulator.run_simulator.RunSimulator">RunSimulator (class in psimpy.simulator.run_simulator)</a>
+</li>
+  </ul></td>
+</tr></table>
+
+<h2 id="S">S</h2>
+<table style="width: 100%" class="indextable genindextable"><tr>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="sampler/saltelli.html#psimpy.sampler.saltelli.Saltelli">Saltelli (class in psimpy.sampler.saltelli)</a>
+</li>
+      <li><a href="sampler/latin.html#psimpy.sampler.latin.LHS.sample">sample() (LHS method)</a>
+
+      <ul>
+        <li><a href="sampler/metropolis_hastings.html#psimpy.sampler.metropolis_hastings.MetropolisHastings.sample">(MetropolisHastings method)</a>
+</li>
+        <li><a href="emulator/robustgasp.html#psimpy.emulator.robustgasp.PPGaSP.sample">(PPGaSP method)</a>
+</li>
+        <li><a href="sampler/saltelli.html#psimpy.sampler.saltelli.Saltelli.sample">(Saltelli method)</a>
+</li>
+        <li><a href="emulator/robustgasp.html#psimpy.emulator.robustgasp.ScalarGaSP.sample">(ScalarGaSP method)</a>
+</li>
+      </ul></li>
+  </ul></td>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="emulator/robustgasp.html#psimpy.emulator.robustgasp.ScalarGaSP">ScalarGaSP (class in psimpy.emulator.robustgasp)</a>
+</li>
+      <li><a href="simulator/run_simulator.html#psimpy.simulator.run_simulator.RunSimulator.serial_run">serial_run() (RunSimulator method)</a>
+</li>
+      <li><a href="sensitivity/sobol.html#psimpy.sensitivity.sobol.SobolAnalyze">SobolAnalyze (class in psimpy.sensitivity.sobol)</a>
+</li>
+  </ul></td>
+</tr></table>
+
+<h2 id="T">T</h2>
+<table style="width: 100%" class="indextable genindextable"><tr>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="emulator/robustgasp.html#psimpy.emulator.robustgasp.PPGaSP.train">train() (PPGaSP method)</a>
+
+      <ul>
+        <li><a href="emulator/robustgasp.html#psimpy.emulator.robustgasp.ScalarGaSP.train">(ScalarGaSP method)</a>
+</li>
+      </ul></li>
+  </ul></td>
+</tr></table>
+
+<h2 id="V">V</h2>
+<table style="width: 100%" class="indextable genindextable"><tr>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="simulator/run_simulator.html#psimpy.simulator.run_simulator.RunSimulator.var_samples">var_samples (RunSimulator attribute)</a>
+</li>
+  </ul></td>
+</tr></table>
+
+
+
+           </div>
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+<dl class="field-list simple">
+<dt class="field-odd">Release</dt>
+<dd class="field-odd"><p>0.1.2</p>
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+<dd class="field-even"><p>Apr 22, 2023</p>
+</dd>
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+<li class="toctree-l1"><a class="reference internal" href="api.html">API &amp; Theory</a><ul>
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+<li class="toctree-l2"><a class="reference internal" href="sampler/index.html">Sampler</a></li>
+<li class="toctree-l2"><a class="reference internal" href="sensitivity/index.html">Sensitivity</a></li>
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diff --git a/docs/source/_build/html/inference/active_learning.html b/docs/source/_build/html/inference/active_learning.html
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+<html class="writer-html5" lang="en" >
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+<li class="toctree-l2 current"><a class="reference internal" href="index.html">Inference</a><ul class="current">
+<li class="toctree-l3 current"><a class="current reference internal" href="#"> Active Learning</a><ul>
+<li class="toctree-l4"><a class="reference internal" href="#activelearning-class">ActiveLearning Class</a></li>
+</ul>
+</li>
+<li class="toctree-l3"><a class="reference internal" href="bayes_inference.html"> Bayes Inference</a></li>
+</ul>
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+             
+  <section id="active-learning">
+<h1>Active Learning<a class="headerlink" href="#active-learning" title="Permalink to this heading"></a></h1>
+<p>Active learning is a machine learning technique that involves selecting the most
+informative data points for the purpose of training an emulator. The idea behind
+active learning is to reduce the amount of training data required for a machine
+learning model to achieve a certain level of accuracy. This is achieved by iteratively
+choosing a new data point that is expected to be the most informative.</p>
+<p>In this module, the <a class="reference internal" href="#psimpy.inference.active_learning.ActiveLearning" title="psimpy.inference.active_learning.ActiveLearning"><code class="xref py py-class docutils literal notranslate"><span class="pre">ActiveLearning</span></code></a> class is implemented to actively build a
+Gaussian process emulator for the natural logarithm of the unnormalized posterior in
+Bayesian inference. It is supposed to facilitate efficient parameter calibration of
+computationally expensive simulators. For detailed theories, please refer to
+<span id="id1">Wang and Li [<a class="reference internal" href="../refs.html#id13" title="Hong Qiao Wang and Jing Lai Li. Adaptive Gaussian process approximation for Bayesian inference with expensive likelihood functions. Neural Computation, 30(11):3072–3094, 2018. doi:10.1162/neco_a_01127.">2018</a>]</span>, <span id="id2">Kandasamy <em>et al.</em> [<a class="reference internal" href="../refs.html#id8" title="Kirthevasan Kandasamy, Jeff Schneider, and Barnabás Póczos. Query efficient posterior estimation in scientific experiments via Bayesian active learning. Artificial Intelligence, 243:45–56, 2017. doi:https://doi.org/10.1016/j.artint.2016.11.002.">2017</a>]</span>, and <span id="id3">Zhao and Kowalski [<a class="reference internal" href="../refs.html#id16" title="Hu Zhao and Julia Kowalski. Bayesian active learning for parameter calibration of landslide run-out models. Landslides, 19():2033–2045, 2022. doi:https://doi.org/10.1007/s10346-022-01857-z.">2022</a>]</span>.</p>
+<section id="activelearning-class">
+<h2>ActiveLearning Class<a class="headerlink" href="#activelearning-class" title="Permalink to this heading"></a></h2>
+<p>The <a class="reference internal" href="#psimpy.inference.active_learning.ActiveLearning" title="psimpy.inference.active_learning.ActiveLearning"><code class="xref py py-class docutils literal notranslate"><span class="pre">ActiveLearning</span></code></a> class is imported by:</p>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">psimpy.inference.active_learning</span> <span class="kn">import</span> <span class="n">ActiveLearning</span>
+</pre></div>
+</div>
+<section id="methods">
+<h3>Methods<a class="headerlink" href="#methods" title="Permalink to this heading"></a></h3>
+<dl class="py class">
+<dt class="sig sig-object py" id="psimpy.inference.active_learning.ActiveLearning">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">ActiveLearning</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ndim</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">bounds</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">data</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">run_sim_obj</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">prior</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">likelihood</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">lhs_sampler</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">scalar_gasp</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">scalar_gasp_trend='constant'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">indicator='entropy'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">optimizer=&lt;function</span> <span class="pre">brute&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">args_prior=None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">kwgs_prior=None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">args_likelihood=None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">kwgs_likelihood=None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">args_optimizer=None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">kwgs_optimizer=None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/psimpy/inference/active_learning.html#ActiveLearning"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#psimpy.inference.active_learning.ActiveLearning" title="Permalink to this definition"></a></dt>
+<dd><p>Contruct a scalar GP emulator for natural logarithm  of the product of
+prior and likelihood (i.e. unnormalized posterior), via active learning.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters</dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>ndim</strong> (<em>int</em>) – Dimension of parameter <code class="docutils literal notranslate"><span class="pre">x</span></code>.</p></li>
+<li><p><strong>bounds</strong> (<em>numpy array</em>) – Upper and lower boundaries of each parameter. Shape <code class="code docutils literal notranslate"><span class="pre">(ndim,</span> <span class="pre">2)</span></code>.
+<cite>bounds[:, 0]</cite> corresponds to lower boundaries of each parameter and
+<cite>bounds[:, 1]</cite> to upper boundaries of each parameter.</p></li>
+<li><p><strong>data</strong> (<em>numpy array</em>) – Observed data for parameter calibration.</p></li>
+<li><p><strong>run_sim_obj</strong> (instance of class <a class="reference internal" href="../simulator/run_simulator.html#psimpy.simulator.run_simulator.RunSimulator" title="psimpy.simulator.run_simulator.RunSimulator"><code class="xref py py-class docutils literal notranslate"><span class="pre">RunSimulator</span></code></a>) – It has an attribute <code class="xref py py-attr docutils literal notranslate"><span class="pre">simulator</span></code> and two methods to run
+<code class="xref py py-attr docutils literal notranslate"><span class="pre">simulator</span></code>, namely <a class="reference internal" href="../simulator/run_simulator.html#psimpy.simulator.run_simulator.RunSimulator.serial_run" title="psimpy.simulator.run_simulator.RunSimulator.serial_run"><code class="xref py py-meth docutils literal notranslate"><span class="pre">serial_run()</span></code></a> and
+<a class="reference internal" href="../simulator/run_simulator.html#psimpy.simulator.run_simulator.RunSimulator.parallel_run" title="psimpy.simulator.run_simulator.RunSimulator.parallel_run"><code class="xref py py-meth docutils literal notranslate"><span class="pre">parallel_run()</span></code></a>. For each simulation, <code class="xref py py-attr docutils literal notranslate"><span class="pre">simulator</span></code>
+must return outputs <code class="docutils literal notranslate"><span class="pre">y</span></code> as a numpy array.</p></li>
+<li><p><strong>prior</strong> (<em>Callable</em>) – Prior probability density function.
+Call with <code class="code docutils literal notranslate"><span class="pre">prior(x,</span> <span class="pre">*args_prior,</span> <span class="pre">**kwgs_prior)</span></code> and return
+the value of prior probability density at <code class="docutils literal notranslate"><span class="pre">x</span></code>.</p></li>
+<li><p><strong>likelihood</strong> (<em>Callable</em>) – Likelihood function constructed based on <code class="docutils literal notranslate"><span class="pre">data</span></code> and simulation
+outputs <code class="docutils literal notranslate"><span class="pre">y</span></code> evaluated at <code class="docutils literal notranslate"><span class="pre">x</span></code>. Call with
+<code class="code docutils literal notranslate"><span class="pre">likelihood(y,</span> <span class="pre">data,</span> <span class="pre">*args_likelihood,</span> <span class="pre">**kwgs_likelihood)</span></code>
+and return the likelihood value at <code class="docutils literal notranslate"><span class="pre">x</span></code>.</p></li>
+<li><p><strong>lhs_sampler</strong> (instance of class <a class="reference internal" href="../sampler/latin.html#psimpy.sampler.latin.LHS" title="psimpy.sampler.latin.LHS"><code class="xref py py-class docutils literal notranslate"><span class="pre">LHS</span></code></a>) – Latin hypercube sampler used to draw initial samples of <code class="docutils literal notranslate"><span class="pre">x</span></code>.
+These initial samples are used to run initial simulations and build
+initial emulator.</p></li>
+<li><p><strong>scalar_gasp</strong> (instance of class <a class="reference internal" href="../emulator/robustgasp.html#psimpy.emulator.robustgasp.ScalarGaSP" title="psimpy.emulator.robustgasp.ScalarGaSP"><code class="xref py py-class docutils literal notranslate"><span class="pre">ScalarGaSP</span></code></a>) – An object which sets up the emulator structure. Providing training
+data, the emulator can be trained and used to make predictions.</p></li>
+<li><p><strong>scalar_gasp_trend</strong> (<em>str</em><em> or </em><em>Callable</em><em>, </em><em>optional</em>) – Mean function of <code class="docutils literal notranslate"><span class="pre">scalar_gasp</span></code> emulator, which is used to
+determine the <code class="docutils literal notranslate"><span class="pre">trend</span></code> or <code class="docutils literal notranslate"><span class="pre">testing_trend</span></code> at given <code class="docutils literal notranslate"><span class="pre">design</span></code> or
+<code class="docutils literal notranslate"><span class="pre">testing_input</span></code>.
+<cite>‘zero’</cite> - trend is set to zero.
+<cite>‘constant’</cite> - trend is set to a constant.
+<cite>‘linear’</cite> - trend is linear to design or testing_input.
+Callable - a function takes design or testing_input as parameter
+and returns the trend.
+Default is <cite>‘constant’</cite>.</p></li>
+<li><p><strong>indicator</strong> (<em>str</em><em>, </em><em>optional</em>) – Indicator of uncertainty. <cite>‘entropy’</cite> or <cite>‘variance’</cite>. Default is
+<cite>‘entropy’</cite>.</p></li>
+<li><p><strong>optimizer</strong> (<em>Callable</em><em>, </em><em>optional</em>) – A function which finds the input point <code class="docutils literal notranslate"><span class="pre">x</span></code> that minimizes the
+uncertainty <code class="docutils literal notranslate"><span class="pre">indicator</span></code> at each iteration step.
+Call with <code class="code docutils literal notranslate"><span class="pre">optimizer(func,</span> <span class="pre">*args_optimizer,</span> <span class="pre">**kwgs_optimizer)</span></code>.
+The objective function <code class="docutils literal notranslate"><span class="pre">func</span></code> is defined by the class method
+<code class="xref py py-meth docutils literal notranslate"><span class="pre">_uncertainty_indicator()</span></code> which have only one argument <code class="docutils literal notranslate"><span class="pre">x</span></code>.
+The <code class="docutils literal notranslate"><span class="pre">optimizer</span></code> should return either the solution array, or a
+<code class="xref py py-class docutils literal notranslate"><span class="pre">scipy.optimize.OptimizeResult</span></code> object which has the attribute
+<code class="xref py py-attr docutils literal notranslate"><span class="pre">x</span></code> denoting the solution array.
+By default is set to <code class="xref py py-func docutils literal notranslate"><span class="pre">scipy.optimize.brute()</span></code>.</p></li>
+<li><p><strong>args_prior</strong> (<em>list</em><em>, </em><em>optional</em>) – Positional arguments for <code class="docutils literal notranslate"><span class="pre">prior</span></code>.</p></li>
+<li><p><strong>kwgs_prior</strong> (<em>dict</em><em>, </em><em>optional</em>) – Keyword arguments for <code class="docutils literal notranslate"><span class="pre">prior</span></code>.</p></li>
+<li><p><strong>args_likelihood</strong> (<em>list</em><em>, </em><em>optional</em>) – Positional arguments for <code class="docutils literal notranslate"><span class="pre">likelihood</span></code>.</p></li>
+<li><p><strong>kwgs_likelihood</strong> (<em>dict</em><em>, </em><em>optional</em>) – Keyword arguments for <code class="docutils literal notranslate"><span class="pre">likelihood</span></code>.</p></li>
+<li><p><strong>args_optimizer</strong> (<em>list</em><em>, </em><em>optional</em>) – Positional arguments for <code class="docutils literal notranslate"><span class="pre">optimizer</span></code>.</p></li>
+<li><p><strong>kwgs_optimizer</strong> (<em>dict</em><em>, </em><em>optional</em>) – Keyword arguments for <code class="docutils literal notranslate"><span class="pre">optimizer</span></code>.</p></li>
+</ul>
+</dd>
+</dl>
+<dl class="py method">
+<dt class="sig sig-object py" id="psimpy.inference.active_learning.ActiveLearning.initial_simulation">
+<span class="sig-name descname"><span class="pre">initial_simulation</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">n0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">prefixes</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mode</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'serial'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">max_workers</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/psimpy/inference/active_learning.html#ActiveLearning.initial_simulation"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#psimpy.inference.active_learning.ActiveLearning.initial_simulation" title="Permalink to this definition"></a></dt>
+<dd><p>Run <code class="docutils literal notranslate"><span class="pre">n0</span></code> initial simulations.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters</dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>n0</strong> (<em>int</em>) – Number of initial simulation runs.</p></li>
+<li><p><strong>prefixes</strong> (<em>list</em><em> of </em><em>str</em><em>, </em><em>optional</em>) – Consist of <code class="docutils literal notranslate"><span class="pre">n0</span></code> strings. Each is used to name corresponding
+simulation output file(s).
+If <cite>None</cite>, <cite>‘sim0’</cite>, <cite>‘sim1’</cite>, … are used.</p></li>
+<li><p><strong>mode</strong> (<em>str</em><em>, </em><em>optional</em>) – <cite>‘parallel’</cite> or <cite>‘serial’</cite>. Run <cite>n0</cite> simulations in parallel or
+in serial.</p></li>
+<li><p><strong>max_workers</strong> (<em>int</em><em>, </em><em>optional</em>) – Controls the maximum number of tasks running in parallel.
+Default is the number of CPUs on the host.</p></li>
+</ul>
+</dd>
+<dt class="field-even">Return type</dt>
+<dd class="field-even"><p><code class="xref py py-class docutils literal notranslate"><span class="pre">tuple</span></code>[<code class="xref py py-class docutils literal notranslate"><span class="pre">ndarray</span></code>, <code class="xref py py-class docutils literal notranslate"><span class="pre">ndarray</span></code>]</p>
+</dd>
+<dt class="field-odd">Returns</dt>
+<dd class="field-odd"><p><ul class="simple">
+<li><p><strong>init_var_samples</strong> (<em>numpy array</em>) – Variable input samples for <code class="docutils literal notranslate"><span class="pre">n0</span></code> initial simulations.
+Shape of <code class="code docutils literal notranslate"><span class="pre">(n0,</span> <span class="pre">ndim)</span></code>.</p></li>
+<li><p><strong>init_sim_outputs</strong> (<em>numpy array</em>) – Outputs of <code class="docutils literal notranslate"><span class="pre">n0</span></code> intial simulations.
+<code class="code docutils literal notranslate"><span class="pre">init_sim_outputs.shape[0]</span></code> is <code class="docutils literal notranslate"><span class="pre">n0</span></code>.</p></li>
+</ul>
+</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="psimpy.inference.active_learning.ActiveLearning.iterative_emulation">
+<span class="sig-name descname"><span class="pre">iterative_emulation</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ninit</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">init_var_samples</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">init_sim_outputs</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">niter</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">iter_prefixes</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/psimpy/inference/active_learning.html#ActiveLearning.iterative_emulation"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#psimpy.inference.active_learning.ActiveLearning.iterative_emulation" title="Permalink to this definition"></a></dt>
+<dd><p>Sequentially pick <code class="docutils literal notranslate"><span class="pre">niter</span></code> new input points based on <code class="docutils literal notranslate"><span class="pre">ninit</span></code>
+simulations.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters</dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>niter</strong> (<em>int</em>) – Number of interative simulaitons.</p></li>
+<li><p><strong>ninit</strong> (<em>int</em>) – Number of initial simulations.</p></li>
+<li><p><strong>init_var_samples</strong> (<em>numpy array</em>) – Variable input samples for <code class="docutils literal notranslate"><span class="pre">ninit</span></code> simulations.
+Shape of <code class="code docutils literal notranslate"><span class="pre">(ninit,</span> <span class="pre">ndim)</span></code>.</p></li>
+<li><p><strong>init_sim_outputs</strong> (<em>numpy array</em>) – Outputs of <code class="docutils literal notranslate"><span class="pre">ninit</span></code> simulations.
+<code class="code docutils literal notranslate"><span class="pre">init_sim_outputs.shape[0]</span></code> is <code class="docutils literal notranslate"><span class="pre">ninit</span></code>.</p></li>
+<li><p><strong>iter_prefixes</strong> (<em>list</em><em> of </em><em>str</em><em>, </em><em>optional</em>) – Consist of <code class="docutils literal notranslate"><span class="pre">niter</span></code> strings. Each is used to name
+corresponding iterative simulation output file(s).
+If <cite>None</cite>, <cite>‘iter_sim0’</cite>, <cite>‘iter_sim1’</cite>, … are used.</p></li>
+</ul>
+</dd>
+<dt class="field-even">Return type</dt>
+<dd class="field-even"><p><code class="xref py py-class docutils literal notranslate"><span class="pre">tuple</span></code>[<code class="xref py py-class docutils literal notranslate"><span class="pre">ndarray</span></code>, <code class="xref py py-class docutils literal notranslate"><span class="pre">ndarray</span></code>, <code class="xref py py-class docutils literal notranslate"><span class="pre">ndarray</span></code>]</p>
+</dd>
+<dt class="field-odd">Returns</dt>
+<dd class="field-odd"><p><ul class="simple">
+<li><p><strong>var_samples</strong> (<em>numpy array</em>) – Variable input samples of <code class="docutils literal notranslate"><span class="pre">ninit</span></code> simulations and <code class="docutils literal notranslate"><span class="pre">niter</span></code>
+iterative simulations. Shape of <code class="code docutils literal notranslate"><span class="pre">(ninit+niter,</span> <span class="pre">ndim)</span></code>.</p></li>
+<li><p><strong>sim_outputs</strong> (<em>numpy array</em>) – Outputs of <code class="docutils literal notranslate"><span class="pre">ninit</span></code> and <code class="docutils literal notranslate"><span class="pre">niter</span></code> simulations.
+<code class="code docutils literal notranslate"><span class="pre">sim_outputs.shape[0]</span></code> is <span class="math notranslate nohighlight">\(ninit+niter\)</span>.</p></li>
+<li><p><strong>ln_pxl_values</strong> (<em>numpy array</em>) – Natural logarithm values of the product of prior and likelihood
+at <code class="docutils literal notranslate"><span class="pre">ninit</span></code> and <code class="docutils literal notranslate"><span class="pre">niter</span></code> simulations.
+Shape of <code class="code docutils literal notranslate"><span class="pre">(ninit+niter,)</span></code>.</p></li>
+</ul>
+</p>
+</dd>
+</dl>
+<p class="rubric">Notes</p>
+<p>If a duplicated iteration point is returned by the <code class="docutils literal notranslate"><span class="pre">optimizer</span></code>, the
+iteration will be stopped right away. In that case, the first dimension
+of returned <code class="docutils literal notranslate"><span class="pre">var_samples</span></code>, <code class="docutils literal notranslate"><span class="pre">sim_outputs</span></code>, <code class="docutils literal notranslate"><span class="pre">ln_pxl_values</span></code> is smaller
+than <span class="math notranslate nohighlight">\(ninit+niter\)</span>.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="psimpy.inference.active_learning.ActiveLearning.approx_ln_pxl">
+<span class="sig-name descname"><span class="pre">approx_ln_pxl</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/psimpy/inference/active_learning.html#ActiveLearning.approx_ln_pxl"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#psimpy.inference.active_learning.ActiveLearning.approx_ln_pxl" title="Permalink to this definition"></a></dt>
+<dd><p>Approximate <cite>ln_pxl</cite> value at <code class="docutils literal notranslate"><span class="pre">x</span></code> based on the trained emulator.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters</dt>
+<dd class="field-odd"><p><strong>x</strong> (<em>numpy array</em>) – One variable sample at which <cite>ln_pxl</cite> is to be approximated. Shape of
+<code class="code docutils literal notranslate"><span class="pre">(ndim,)</span></code>.</p>
+</dd>
+<dt class="field-even">Return type</dt>
+<dd class="field-even"><p>A float value which is the emulator-predicted <cite>ln_pxl</cite> value at <code class="docutils literal notranslate"><span class="pre">x</span></code>.</p>
+</dd>
+</dl>
+</dd></dl>
+
+</dd></dl>
+
+</section>
+</section>
+</section>
+
+
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+<li class="toctree-l3 current"><a class="current reference internal" href="#"> Bayes Inference</a><ul>
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+  <section id="bayes-inference">
+<h1>Bayes Inference<a class="headerlink" href="#bayes-inference" title="Permalink to this heading"></a></h1>
+<p>Bayesian inference is a statistical method for making probabilistic inference about
+unknown parameters based on observed data and prior knowledge. The update from
+prior knowledge to posterior in light of observed data is based on Bayes’ theorem:</p>
+<div class="math notranslate nohighlight" id="equation-bayes">
+<span class="eqno">(1)<a class="headerlink" href="#equation-bayes" title="Permalink to this equation"></a></span>\[p(\mathbf{x} \mid \mathbf{d}) = \frac{L(\mathbf{x} \mid \mathbf{d}) p(\mathbf{x})}
+{\int L(\mathbf{x} \mid \mathbf{d}) p(\mathbf{x}) d \mathbf{x}}\]</div>
+<p>where <span class="math notranslate nohighlight">\(\mathbf{x}\)</span> represents the collection of unknown parameters and
+<span class="math notranslate nohighlight">\(\mathbf{d}\)</span> represents the collection of observed data. The prior probability
+distribution, <span class="math notranslate nohighlight">\(p(\mathbf{x})\)</span>, represents the degree of belief in the parameters before
+any data is observed. The likelihood function, <span class="math notranslate nohighlight">\(L(\mathbf{x} \mid \mathbf{d})\)</span>, represents
+the probability of observing the data given the parameters. The posterior distribution,
+<span class="math notranslate nohighlight">\(p(\mathbf{x} \mid \mathbf{d})\)</span>, is obtained by multiplying the prior probability
+distribution by the likelihood function and then normalizing the result. Bayesian inference
+allows for incorporating subjective prior beliefs, which can be updated as new data becomes available.</p>
+<p>For many real world problems, it is hardly possible to analytically compute the posterior due to
+the complexity of the denominator in equation <a class="reference internal" href="#equation-bayes">(1)</a>, namely the nomalizing constant. In this
+module, two numerical approximations are implemented: grid estimation and Metropolis Hastings
+estimation.</p>
+<p>In grid estimation, the denominator in equation <a class="reference internal" href="#equation-bayes">(1)</a> is approximated by numerical integration
+on a regular grid and the posterior value at each grid point is computed, as shown in equation
+<a class="reference internal" href="#equation-grid-estimation">(2)</a>. The number of grid points increases dramatically with the increase of the number
+of unknown parameters. Grid estimation is therefore limited to low-dimensional problems.</p>
+<div class="math notranslate nohighlight" id="equation-grid-estimation">
+<span class="eqno">(2)<a class="headerlink" href="#equation-grid-estimation" title="Permalink to this equation"></a></span>\[p(\mathbf{x} \mid \mathbf{d}) \approx \frac{L(\mathbf{x} \mid \mathbf{d}) p(\mathbf{x})}
+{\sum_{i=1}^N L\left(\mathbf{x}_i \mid \mathbf{d}\right) p\left(\mathbf{x}_i\right) \Delta \mathbf{x}_i}\]</div>
+<p>Metropolis Hastings estimation directly draw samples from the unnormalized posterior distribution, namely
+the numerator of equation <a class="reference internal" href="#equation-bayes">(1)</a>. The samples are then used to estimate properties of the posterior
+distribution, like the mean and variance, or to estimate the posterior distribution.</p>
+<section id="gridestimation-class">
+<h2>GridEstimation Class<a class="headerlink" href="#gridestimation-class" title="Permalink to this heading"></a></h2>
+<p>The <a class="reference internal" href="#psimpy.inference.bayes_inference.GridEstimation" title="psimpy.inference.bayes_inference.GridEstimation"><code class="xref py py-class docutils literal notranslate"><span class="pre">GridEstimation</span></code></a> class is imported by:</p>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">psimpy.inference.bayes_inference</span> <span class="kn">import</span> <span class="n">GridEstimation</span>
+</pre></div>
+</div>
+<section id="methods">
+<h3>Methods<a class="headerlink" href="#methods" title="Permalink to this heading"></a></h3>
+<dl class="py class">
+<dt class="sig sig-object py" id="psimpy.inference.bayes_inference.GridEstimation">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">GridEstimation</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ndim</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">bounds</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">prior</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">likelihood</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">ln_prior</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">ln_likelihood</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">ln_pxl</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">args_prior</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">kwgs_prior</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">args_likelihood</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">kwgs_likelihood</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">args_ln_pxl</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">kwgs_ln_pxl</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/psimpy/inference/bayes_inference.html#GridEstimation"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#psimpy.inference.bayes_inference.GridEstimation" title="Permalink to this definition"></a></dt>
+<dd><p>Set up basic input for Bayesian inference.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters</dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>ndim</strong> (<em>int</em>) – Dimension of parameter <code class="docutils literal notranslate"><span class="pre">x</span></code>.</p></li>
+<li><p><strong>bounds</strong> (<em>numpy array</em>) – Upper and lower boundaries of each parameter.
+Shape <code class="code docutils literal notranslate"><span class="pre">(ndim,</span> <span class="pre">2)</span></code>.
+<cite>bounds[:, 0]</cite> corresponds to lower boundaries of each parameter and
+<cite>bounds[:, 1]</cite> to upper boundaries of each parameter.</p></li>
+<li><p><strong>prior</strong> (<em>Callable</em>) – Prior probability density function.
+Call with <code class="code docutils literal notranslate"><span class="pre">prior(x,</span> <span class="pre">*args_prior,</span> <span class="pre">**kwgs_prior)</span></code>.
+Return the prior probability density value at <code class="docutils literal notranslate"><span class="pre">x</span></code>, where <code class="docutils literal notranslate"><span class="pre">x</span></code> is
+a one dimension <code class="xref py py-class docutils literal notranslate"><span class="pre">numpy.ndarray</span></code> of shape <code class="code docutils literal notranslate"><span class="pre">(ndim,)</span></code>.</p></li>
+<li><p><strong>likelihood</strong> (<em>Callable</em>) – Likelihood function.
+Call with <code class="code docutils literal notranslate"><span class="pre">likelihood(x,</span> <span class="pre">*args_likelihood,</span> <span class="pre">**kwgs_likelihood)</span></code>.
+Return the likelihood value at <code class="docutils literal notranslate"><span class="pre">x</span></code>.</p></li>
+<li><p><strong>ln_prior</strong> (<em>Callable</em>) – Natural logarithm of prior probability density function.
+Call with <code class="code docutils literal notranslate"><span class="pre">ln_prior(x,</span> <span class="pre">*args_prior,</span> <span class="pre">**kwgs_prior)</span></code>.
+Return the value of natural logarithm of prior probability density
+at <code class="docutils literal notranslate"><span class="pre">x</span></code>.</p></li>
+<li><p><strong>ln_likelihood</strong> (<em>Callable</em>) – Natural logarithm of likelihood function.
+Call with <code class="code docutils literal notranslate"><span class="pre">ln_likelihood(x,</span> <span class="pre">*args_likelihood,</span> <span class="pre">**kwgs_likelihood)</span></code>.
+Return the value of natural logarithm of likelihood at <code class="docutils literal notranslate"><span class="pre">x</span></code>.</p></li>
+<li><p><strong>ln_pxl</strong> (<em>Callable</em>) – Natural logarithm of the product of prior and likelihood.
+Call with <code class="code docutils literal notranslate"><span class="pre">ln_pxl(x,</span> <span class="pre">*args_ln_pxl,</span> <span class="pre">**kwgs_ln_pxl)</span></code>.
+Return the value of natural logarithm of the product of prior and
+likelihood at <code class="docutils literal notranslate"><span class="pre">x</span></code>.</p></li>
+<li><p><strong>args_prior</strong> (<em>list</em><em>, </em><em>optional</em>) – Positional arguments for <code class="docutils literal notranslate"><span class="pre">prior</span></code> or <code class="docutils literal notranslate"><span class="pre">ln_prior</span></code>.</p></li>
+<li><p><strong>kwgs_prior</strong> (<em>dict</em><em>, </em><em>optional</em>) – Keyword arguments for <code class="docutils literal notranslate"><span class="pre">prior</span></code> or <code class="docutils literal notranslate"><span class="pre">ln_prior</span></code>.</p></li>
+<li><p><strong>args_likelihood</strong> (<em>list</em><em>, </em><em>optional</em>) – Positional arguments for <code class="docutils literal notranslate"><span class="pre">likelihood</span></code> or <code class="docutils literal notranslate"><span class="pre">ln_likelihood</span></code>.</p></li>
+<li><p><strong>kwgs_likelihood</strong> (<em>dict</em><em>, </em><em>optional</em>) – Keyword arguments for <code class="docutils literal notranslate"><span class="pre">likelihood</span></code> or <code class="docutils literal notranslate"><span class="pre">ln_likelihood</span></code>.</p></li>
+<li><p><strong>args_ln_pxl</strong> (<em>list</em><em>, </em><em>optional</em>) – Positional arguments for <code class="docutils literal notranslate"><span class="pre">ln_pxl</span></code>.</p></li>
+<li><p><strong>kwgs_ln_pxl</strong> (<em>dict</em><em>, </em><em>optional</em>) – Keyword arguments for <code class="docutils literal notranslate"><span class="pre">ln_pxl</span></code>.</p></li>
+</ul>
+</dd>
+</dl>
+<dl class="py method">
+<dt class="sig sig-object py" id="psimpy.inference.bayes_inference.GridEstimation.run">
+<span class="sig-name descname"><span class="pre">run</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">nbins</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/psimpy/inference/bayes_inference.html#GridEstimation.run"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#psimpy.inference.bayes_inference.GridEstimation.run" title="Permalink to this definition"></a></dt>
+<dd><p>Use Grid approximation to estimate the posterior.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters</dt>
+<dd class="field-odd"><p><strong>nbins</strong> (<em>int</em><em> or </em><em>list</em><em> of </em><em>ints</em>) – Number of bins for each parameter.
+If <cite>int</cite>, the same value is used for each parameter.
+If <cite>list of int</cite>, it should be of length <code class="docutils literal notranslate"><span class="pre">ndim</span></code>.</p>
+</dd>
+<dt class="field-even">Return type</dt>
+<dd class="field-even"><p><code class="xref py py-class docutils literal notranslate"><span class="pre">tuple</span></code>[<code class="xref py py-class docutils literal notranslate"><span class="pre">ndarray</span></code>, <code class="xref py py-class docutils literal notranslate"><span class="pre">list</span></code>[<code class="xref py py-class docutils literal notranslate"><span class="pre">ndarray</span></code>]]</p>
+</dd>
+<dt class="field-odd">Returns</dt>
+<dd class="field-odd"><p><ul class="simple">
+<li><p><strong>posterior</strong> (<em>numpy array</em>) – Estimated posterior probability density values at grid points.
+Shape of <code class="code docutils literal notranslate"><span class="pre">(nbins[0],</span> <span class="pre">nbins[1],</span> <span class="pre">...,</span> <span class="pre">nbins[ndim])</span></code>.</p></li>
+<li><p><strong>x_ndim</strong> (<em>list of numpy array</em>) – Contain <code class="docutils literal notranslate"><span class="pre">ndim</span></code> 1d <code class="xref py py-class docutils literal notranslate"><span class="pre">numpy.ndarray</span></code> <cite>x1</cite>, <cite>x2</cite>, … Each <cite>xi</cite>
+is a 1d array of length <code class="docutils literal notranslate"><span class="pre">nbins[i]</span></code>, representing the 1d coordinate
+array along the i-th axis.</p></li>
+</ul>
+</p>
+</dd>
+</dl>
+</dd></dl>
+
+</dd></dl>
+
+</section>
+</section>
+<section id="metropolishastingsestimation-class">
+<h2>MetropolisHastingsEstimation Class<a class="headerlink" href="#metropolishastingsestimation-class" title="Permalink to this heading"></a></h2>
+<p>The <a class="reference internal" href="#psimpy.inference.bayes_inference.MetropolisHastingsEstimation" title="psimpy.inference.bayes_inference.MetropolisHastingsEstimation"><code class="xref py py-class docutils literal notranslate"><span class="pre">MetropolisHastingsEstimation</span></code></a> class is imported by:</p>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">psimpy.inference.bayes_inference</span> <span class="kn">import</span> <span class="n">MetropolisHastingsEstimation</span>
+</pre></div>
+</div>
+<section id="id1">
+<h3>Methods<a class="headerlink" href="#id1" title="Permalink to this heading"></a></h3>
+<dl class="py class">
+<dt class="sig sig-object py" id="psimpy.inference.bayes_inference.MetropolisHastingsEstimation">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">MetropolisHastingsEstimation</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ndim</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">bounds</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">prior</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">likelihood</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">ln_prior</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">ln_likelihood</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">ln_pxl</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">args_prior</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">kwgs_prior</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">args_likelihood</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">kwgs_likelihood</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">args_ln_pxl</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">kwgs_ln_pxl</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/psimpy/inference/bayes_inference.html#MetropolisHastingsEstimation"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#psimpy.inference.bayes_inference.MetropolisHastingsEstimation" title="Permalink to this definition"></a></dt>
+<dd><p>Set up basic input for Bayesian inference.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters</dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>ndim</strong> (<em>int</em>) – Dimension of parameter <code class="docutils literal notranslate"><span class="pre">x</span></code>.</p></li>
+<li><p><strong>bounds</strong> (<em>numpy array</em>) – Upper and lower boundaries of each parameter.
+Shape <code class="code docutils literal notranslate"><span class="pre">(ndim,</span> <span class="pre">2)</span></code>.
+<cite>bounds[:, 0]</cite> corresponds to lower boundaries of each parameter and
+<cite>bounds[:, 1]</cite> to upper boundaries of each parameter.</p></li>
+<li><p><strong>prior</strong> (<em>Callable</em>) – Prior probability density function.
+Call with <code class="code docutils literal notranslate"><span class="pre">prior(x,</span> <span class="pre">*args_prior,</span> <span class="pre">**kwgs_prior)</span></code>.
+Return the prior probability density value at <code class="docutils literal notranslate"><span class="pre">x</span></code>, where <code class="docutils literal notranslate"><span class="pre">x</span></code> is
+a one dimension <code class="xref py py-class docutils literal notranslate"><span class="pre">numpy.ndarray</span></code> of shape <code class="code docutils literal notranslate"><span class="pre">(ndim,)</span></code>.</p></li>
+<li><p><strong>likelihood</strong> (<em>Callable</em>) – Likelihood function.
+Call with <code class="code docutils literal notranslate"><span class="pre">likelihood(x,</span> <span class="pre">*args_likelihood,</span> <span class="pre">**kwgs_likelihood)</span></code>.
+Return the likelihood value at <code class="docutils literal notranslate"><span class="pre">x</span></code>.</p></li>
+<li><p><strong>ln_prior</strong> (<em>Callable</em>) – Natural logarithm of prior probability density function.
+Call with <code class="code docutils literal notranslate"><span class="pre">ln_prior(x,</span> <span class="pre">*args_prior,</span> <span class="pre">**kwgs_prior)</span></code>.
+Return the value of natural logarithm of prior probability density
+at <code class="docutils literal notranslate"><span class="pre">x</span></code>.</p></li>
+<li><p><strong>ln_likelihood</strong> (<em>Callable</em>) – Natural logarithm of likelihood function.
+Call with <code class="code docutils literal notranslate"><span class="pre">ln_likelihood(x,</span> <span class="pre">*args_likelihood,</span> <span class="pre">**kwgs_likelihood)</span></code>.
+Return the value of natural logarithm of likelihood at <code class="docutils literal notranslate"><span class="pre">x</span></code>.</p></li>
+<li><p><strong>ln_pxl</strong> (<em>Callable</em>) – Natural logarithm of the product of prior and likelihood.
+Call with <code class="code docutils literal notranslate"><span class="pre">ln_pxl(x,</span> <span class="pre">*args_ln_pxl,</span> <span class="pre">**kwgs_ln_pxl)</span></code>.
+Return the value of natural logarithm of the product of prior and
+likelihood at <code class="docutils literal notranslate"><span class="pre">x</span></code>.</p></li>
+<li><p><strong>args_prior</strong> (<em>list</em><em>, </em><em>optional</em>) – Positional arguments for <code class="docutils literal notranslate"><span class="pre">prior</span></code> or <code class="docutils literal notranslate"><span class="pre">ln_prior</span></code>.</p></li>
+<li><p><strong>kwgs_prior</strong> (<em>dict</em><em>, </em><em>optional</em>) – Keyword arguments for <code class="docutils literal notranslate"><span class="pre">prior</span></code> or <code class="docutils literal notranslate"><span class="pre">ln_prior</span></code>.</p></li>
+<li><p><strong>args_likelihood</strong> (<em>list</em><em>, </em><em>optional</em>) – Positional arguments for <code class="docutils literal notranslate"><span class="pre">likelihood</span></code> or <code class="docutils literal notranslate"><span class="pre">ln_likelihood</span></code>.</p></li>
+<li><p><strong>kwgs_likelihood</strong> (<em>dict</em><em>, </em><em>optional</em>) – Keyword arguments for <code class="docutils literal notranslate"><span class="pre">likelihood</span></code> or <code class="docutils literal notranslate"><span class="pre">ln_likelihood</span></code>.</p></li>
+<li><p><strong>args_ln_pxl</strong> (<em>list</em><em>, </em><em>optional</em>) – Positional arguments for <code class="docutils literal notranslate"><span class="pre">ln_pxl</span></code>.</p></li>
+<li><p><strong>kwgs_ln_pxl</strong> (<em>dict</em><em>, </em><em>optional</em>) – Keyword arguments for <code class="docutils literal notranslate"><span class="pre">ln_pxl</span></code>.</p></li>
+</ul>
+</dd>
+</dl>
+<dl class="py method">
+<dt class="sig sig-object py" id="psimpy.inference.bayes_inference.MetropolisHastingsEstimation.run">
+<span class="sig-name descname"><span class="pre">run</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">nsamples</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mh_sampler</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/psimpy/inference/bayes_inference.html#MetropolisHastingsEstimation.run"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#psimpy.inference.bayes_inference.MetropolisHastingsEstimation.run" title="Permalink to this definition"></a></dt>
+<dd><p>Use Metropolis Hastings sampling to draw samples from the posterior.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters</dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>nsamples</strong> (<em>int</em>) – Number of samples to be drawn.</p></li>
+<li><p><strong>mh_sampler</strong> (instance of <a class="reference internal" href="../sampler/metropolis_hastings.html#psimpy.sampler.metropolis_hastings.MetropolisHastings" title="psimpy.sampler.metropolis_hastings.MetropolisHastings"><code class="xref py py-class docutils literal notranslate"><span class="pre">MetropolisHastings</span></code></a>) – Metropolis Hastings sampler.</p></li>
+</ul>
+</dd>
+<dt class="field-even">Return type</dt>
+<dd class="field-even"><p><code class="xref py py-class docutils literal notranslate"><span class="pre">tuple</span></code>[<code class="xref py py-class docutils literal notranslate"><span class="pre">ndarray</span></code>, <code class="xref py py-class docutils literal notranslate"><span class="pre">ndarray</span></code>]</p>
+</dd>
+<dt class="field-odd">Returns</dt>
+<dd class="field-odd"><p><ul class="simple">
+<li><p><strong>mh_samples</strong> (<em>numpy array</em>) – Samples drawn from the posterior. Shape of <code class="code docutils literal notranslate"><span class="pre">(nsamples,</span> <span class="pre">ndim)</span></code>.</p></li>
+<li><p><strong>mh_accept</strong> (<em>numpy array</em>) – Shape of <code class="code docutils literal notranslate"><span class="pre">(nsamples,)</span></code>. Each element indicates whether the
+corresponding sample is the proposed new state (value 1) or the old
+state (value 0). <code class="code docutils literal notranslate"><span class="pre">np.mean(mh_accept)</span></code> thus gives the overall
+acceptance ratio.</p></li>
+</ul>
+</p>
+</dd>
+</dl>
+</dd></dl>
+
+</dd></dl>
+
+</section>
+</section>
+</section>
+
+
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+             
+  <section id="inference">
+<h1>Inference<a class="headerlink" href="#inference" title="Permalink to this heading"></a></h1>
+<p>This module hosts functionality for inference methods.</p>
+<p>Currently implemented classes are:</p>
+<ul class="simple">
+<li><p><a class="reference internal" href="active_learning.html#psimpy.inference.active_learning.ActiveLearning" title="psimpy.inference.active_learning.ActiveLearning"><code class="xref py py-class docutils literal notranslate"><span class="pre">ActiveLearning</span></code></a>: Construct a Gaussian process emulator for an unnormalized posterior.</p></li>
+<li><p><a class="reference internal" href="bayes_inference.html#psimpy.inference.bayes_inference.GridEstimation" title="psimpy.inference.bayes_inference.GridEstimation"><code class="xref py py-class docutils literal notranslate"><span class="pre">GridEstimation</span></code></a>: Estimate a posterior distribution by grid estimation.</p></li>
+<li><p><a class="reference internal" href="bayes_inference.html#psimpy.inference.bayes_inference.MetropolisHastingsEstimation" title="psimpy.inference.bayes_inference.MetropolisHastingsEstimation"><code class="xref py py-class docutils literal notranslate"><span class="pre">MetropolisHastingsEstimation</span></code></a>: Estimate a posterior by Metropolis Hastings estimation.</p></li>
+</ul>
+<div class="toctree-wrapper compound">
+</div>
+</section>
+
+
+           </div>
+          </div>
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+<li class="toctree-l2"><a class="reference internal" href="#overview">Overview</a></li>
+<li class="toctree-l2"><a class="reference internal" href="#installation">Installation</a></li>
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+             
+  <section id="getting-started">
+<h1>Getting Started<a class="headerlink" href="#getting-started" title="Permalink to this heading"></a></h1>
+<section id="overview">
+<h2>Overview<a class="headerlink" href="#overview" title="Permalink to this heading"></a></h2>
+<p>PSimPy (Predictive and probabilistic simulation with Python) implements
+a Gaussian process emulation-based framework that enables systematically and
+efficiently performing uncertainty-related analyses of physics-based
+models, which are often computationlly expensive. Examples are variance-based
+global sensitvity analysis, uncertainty quantification, and parameter
+calibration.</p>
+</section>
+<section id="installation">
+<h2>Installation<a class="headerlink" href="#installation" title="Permalink to this heading"></a></h2>
+<p><code class="xref py py-mod docutils literal notranslate"><span class="pre">PSimPy</span></code> is a pure Python package. All Python-related dependencies are
+automatically taken care of. It should be noted that some modules rely on or use
+non-Python package and software. More specifically, the emulator module
+<code class="xref py py-mod docutils literal notranslate"><span class="pre">robustgasp.py</span></code> relies on the R package
+<a class="reference external" href="https://cran.r-project.org/web/packages/RobustGaSP/">RobustGaSP</a>;
+the simulator module <code class="xref py py-mod docutils literal notranslate"><span class="pre">ravaflow24.py</span></code> relies on the open source software
+<a class="reference external" href="https://www.landslidemodels.org/r.avaflow/">r.avaflow 2.4</a>.</p>
+<p>If the simulator module <code class="xref py py-mod docutils literal notranslate"><span class="pre">ravaflow24.py</span></code> is desired, you may follow the
+official <a class="reference external" href="https://www.landslidemodels.org/r.avaflow/manual.php">r.avaflow User manual</a>
+to install it. The installation of the R package <cite>RobustGaSP</cite> is covered in
+following steps.</p>
+<p>We recommond you to install <code class="xref py py-mod docutils literal notranslate"><span class="pre">PSimPy</span></code> in a virtual environment such as a
+<cite>conda</cite> environment. You may want to first install <cite>Anaconda</cite> or <cite>Miniconda</cite> if you
+haven’t. The steps afterwards are as follows.</p>
+<ol class="arabic">
+<li><p>Create a conda environment with Python 3.9:</p>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">conda</span> <span class="n">create</span> <span class="o">--</span><span class="n">name</span> <span class="n">your_env_name</span> <span class="n">python</span><span class="o">=</span><span class="mf">3.9</span>
+</pre></div>
+</div>
+</li>
+<li><p>Install <cite>R</cite> if you don’t have it on your machine (if you have <cite>R</cite>, you can
+skip this step; alternatively, you can still follow this step to install <cite>R</cite> in
+the conda environment):</p>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">conda</span> <span class="n">activate</span> <span class="n">your_env_name</span>
+<span class="n">conda</span> <span class="n">install</span> <span class="o">-</span><span class="n">c</span> <span class="n">conda</span><span class="o">-</span><span class="n">forge</span> <span class="n">r</span><span class="o">-</span><span class="n">base</span><span class="o">=</span><span class="mf">3.6</span>
+</pre></div>
+</div>
+</li>
+<li><p>Install the R package <cite>RobustGaSP</cite> in the R terminal:</p>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">R</span>
+<span class="n">install</span><span class="o">.</span><span class="n">packages</span><span class="p">(</span><span class="s2">&quot;RobustGaSP&quot;</span><span class="p">,</span><span class="n">repos</span><span class="o">=</span><span class="s2">&quot;https://cran.r-project.org&quot;</span><span class="p">,</span><span class="n">version</span><span class="o">=</span><span class="s2">&quot;0.6.4&quot;</span><span class="p">)</span>
+</pre></div>
+</div>
+<p>Try if it is successfully installed by:</p>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">library</span><span class="p">(</span><span class="s2">&quot;RobustGaSP&quot;</span><span class="p">)</span>
+</pre></div>
+</div>
+</li>
+<li><p>Configure the environment variable <cite>R_HOME</cite> so that <cite>rpy2</cite> knows where to find
+<cite>R</cite> packages. You can find your <cite>R_HOME</cite> by typing the following command in the
+R terminal:</p>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">R</span><span class="o">.</span><span class="n">home</span><span class="p">()</span>
+<span class="n">q</span><span class="p">()</span>
+</pre></div>
+</div>
+<p>It is a path like “…/lib/R”. Set the environment variable <cite>R_HOME</cite> in your
+conda environment by:</p>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">conda</span> <span class="n">env</span> <span class="n">config</span> <span class="nb">vars</span> <span class="nb">set</span> <span class="n">R_HOME</span><span class="o">=</span><span class="n">your_R_HOME</span>
+</pre></div>
+</div>
+<p>Afterwards reactivate your conda environment to make the change take effect by:</p>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">conda</span> <span class="n">deactivate</span>
+<span class="n">conda</span> <span class="n">activate</span> <span class="n">your_env_name</span>
+</pre></div>
+</div>
+</li>
+<li><p>Install <code class="xref py py-mod docutils literal notranslate"><span class="pre">PSimPy</span></code> using <cite>pip</cite> in your conda environment by:</p>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">conda</span> <span class="n">install</span> <span class="o">-</span><span class="n">c</span> <span class="n">conda</span><span class="o">-</span><span class="n">forge</span> <span class="n">pip</span>
+<span class="n">pip</span> <span class="n">install</span> <span class="n">psimpy</span>
+</pre></div>
+</div>
+</li>
+</ol>
+<p>Now you should have <code class="xref py py-mod docutils literal notranslate"><span class="pre">PSimPy</span></code> and its dependencies successfully installed
+in your conda environment. You can use it in the Python terminal or in your
+Python IDE.</p>
+<p>If you would like to use it with Jupyter Notebook (iPython Notebook), there is
+one extra step needed to set your conda environment on your Notebook:</p>
+<ol class="arabic" start="6">
+<li><p>Install <cite>ipykernel</cite> and install a kernel that points to your conda environment
+by:</p>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">conda</span> <span class="n">install</span> <span class="o">-</span><span class="n">c</span> <span class="n">conda</span><span class="o">-</span><span class="n">forge</span> <span class="n">ipykernel</span>
+<span class="n">python</span> <span class="o">-</span><span class="n">m</span> <span class="n">ipykernel</span> <span class="n">install</span> <span class="o">--</span><span class="n">user</span> <span class="o">--</span><span class="n">name</span><span class="o">=</span><span class="n">your_env_name</span>
+</pre></div>
+</div>
+</li>
+</ol>
+<p>Now you can start your Notebook, change the kernel to your conda environment, and
+use <code class="xref py py-mod docutils literal notranslate"><span class="pre">PSimPy</span></code>.</p>
+</section>
+</section>
+
+
+           </div>
+          </div>
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+            <a href="_sources/refs.rst.txt" rel="nofollow"> View page source</a>
+      </li>
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+          <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article">
+           <div itemprop="articleBody">
+             
+  <section id="references">
+<h1>References<a class="headerlink" href="#references" title="Permalink to this heading"></a></h1>
+<div class="docutils container" id="id1">
+<dl class="citation">
+<dt class="label" id="id6"><span class="brackets">1</span></dt>
+<dd><p>Meng Yang Gu, Jesus Palomo, and James O. Berger. Robustgasp: robust Gaussian stochastic process emulation in R. <em>The R Journal</em>, 11(1):112–136, 2019. <a class="reference external" href="https://doi.org/10.32614/RJ-2019-011">doi:10.32614/RJ-2019-011</a>.</p>
+</dd>
+<dt class="label" id="id4"><span class="brackets">2</span></dt>
+<dd><p>Meng Yang Gu and James O. Berger. Parallel partial Gaussian process emulation for computer models with massive output. <em>Annals of Applied Statistics</em>, 10(3):1317–1347, 2016. <a class="reference external" href="https://doi.org/10.1214/16-AOAS934">doi:10.1214/16-AOAS934</a>.</p>
+</dd>
+<dt class="label" id="id14"><span class="brackets">3</span></dt>
+<dd><p>H. Zhao, F. Amann, and J. Kowalski. Emulator-based global sensitivity analysis for flow-like landslide run-out models. <em>Landslides</em>, ():, 2021. <a class="reference external" href="https://doi.org/https://doi.org/10.1007/s10346-021-01690-w">doi:https://doi.org/10.1007/s10346-021-01690-w</a>.</p>
+</dd>
+<dt class="label" id="id15"><span class="brackets">4</span></dt>
+<dd><p>Hu Zhao. <em>Gaussian processes for sensitivity analysis, Bayesian inference, and uncertainty quantification in landslide research</em>. PhD thesis, RWTH Aachen University, 2021. <a class="reference external" href="https://doi.org/10.18154/RWTH-2021-11693">doi:10.18154/RWTH-2021-11693</a>.</p>
+</dd>
+<dt class="label" id="id5"><span class="brackets">5</span></dt>
+<dd><p>Meng Yang Gu, Xiao Jing Wang, and James O. Berger. Robust Gaussian stochastic process emulation. <em>Annals of Statistics</em>, 46(6A):3038–3066, 2018. <a class="reference external" href="https://doi.org/10.1214/17-AOS1648">doi:10.1214/17-AOS1648</a>.</p>
+</dd>
+<dt class="label" id="id13"><span class="brackets">6</span></dt>
+<dd><p>Hong Qiao Wang and Jing Lai Li. Adaptive Gaussian process approximation for Bayesian inference with expensive likelihood functions. <em>Neural Computation</em>, 30(11):3072–3094, 2018. <a class="reference external" href="https://doi.org/10.1162/neco_a_01127">doi:10.1162/neco_a_01127</a>.</p>
+</dd>
+<dt class="label" id="id8"><span class="brackets">7</span></dt>
+<dd><p>Kirthevasan Kandasamy, Jeff Schneider, and Barnabás Póczos. Query efficient posterior estimation in scientific experiments via Bayesian active learning. <em>Artificial Intelligence</em>, 243:45–56, 2017. <a class="reference external" href="https://doi.org/https://doi.org/10.1016/j.artint.2016.11.002">doi:https://doi.org/10.1016/j.artint.2016.11.002</a>.</p>
+</dd>
+<dt class="label" id="id16"><span class="brackets">8</span></dt>
+<dd><p>Hu Zhao and Julia Kowalski. Bayesian active learning for parameter calibration of landslide run-out models. <em>Landslides</em>, 19():2033–2045, 2022. <a class="reference external" href="https://doi.org/https://doi.org/10.1007/s10346-022-01857-z">doi:https://doi.org/10.1007/s10346-022-01857-z</a>.</p>
+</dd>
+<dt class="label" id="id11"><span class="brackets">9</span></dt>
+<dd><p>Andrea Saltelli. Making best use of model evaluations to compute sensitivity indices. <em>Computer Physics Communications</em>, 145(2):280–297, 2002. <a class="reference external" href="https://doi.org/https://doi.org/10.1016/S0010-4655(02)00280-1">doi:https://doi.org/10.1016/S0010-4655(02)00280-1</a>.</p>
+</dd>
+<dt class="label" id="id12"><span class="brackets">10</span></dt>
+<dd><p>Andrea Saltelli, Paola Annoni, Ivano Azzini, Francesca Campolongo, Marco Ratto, and Stefano Tarantola. Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index. <em>Computer Physics Communications</em>, 181(2):259–270, 2010. <a class="reference external" href="https://doi.org/https://doi.org/10.1016/j.cpc.2009.09.018">doi:https://doi.org/10.1016/j.cpc.2009.09.018</a>.</p>
+</dd>
+<dt class="label" id="id7"><span class="brackets">11</span></dt>
+<dd><p>Jon Herman and Will Usher. SALib: an open-source Python library for sensitivity analysis. <em>The Journal of Open Source Software</em>, 2017. <a class="reference external" href="https://doi.org/10.21105/joss.00097">doi:10.21105/joss.00097</a>.</p>
+</dd>
+<dt class="label" id="id3"><span class="brackets">12</span></dt>
+<dd><p>Jan-Thomas Fischer, Julia Kowalski, and Shiva P. Pudasaini. Topographic curvature effects in applied avalanche modeling. <em>Cold Regions Science and Technology</em>, 74-75:21–30, 2012. <a class="reference external" href="https://doi.org/https://doi.org/10.1016/j.coldregions.2012.01.005">doi:https://doi.org/10.1016/j.coldregions.2012.01.005</a>.</p>
+</dd>
+<dt class="label" id="id10"><span class="brackets">13</span></dt>
+<dd><p>M. Mergili, J. T. Fischer, J. Krenn, and S. P. Pudasaini. R.avaflow v1, an advanced open-source computational framework for the propagation and interaction of two-phase mass flows. <em>Geoscientific Model Development</em>, 10(2):553–569, 2017. <a class="reference external" href="https://doi.org/10.5194/gmd-10-553-2017">doi:10.5194/gmd-10-553-2017</a>.</p>
+</dd>
+<dt class="label" id="id2"><span class="brackets">14</span></dt>
+<dd><p>M. Christen, J. Kowalski, and P. Bartelt. RAMMS: numerical simulation of dense snow avalanches in three-dimensional terrain. <em>Cold Regions Science and Technology</em>, 63(1):1–14, 2010. <a class="reference external" href="https://doi.org/https://doi.org/10.1016/j.coldregions.2010.04.005">doi:https://doi.org/10.1016/j.coldregions.2010.04.005</a>.</p>
+</dd>
+<dt class="label" id="id9"><span class="brackets">15</span></dt>
+<dd><p>Loic Le Gratiet, Claire Cannamela, and Bertrand Iooss. A Bayesian approach for global sensitivity analysis of (multifidelity) computer codes. <em>SIAM/ASA Journal on Uncertainty Quantification</em>, 2(1):336–363, 2014. <a class="reference external" href="https://doi.org/10.1137/130926869">doi:10.1137/130926869</a>.</p>
+</dd>
+</dl>
+</div>
+</section>
+
+
+           </div>
+          </div>
+          <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer">
+        <a href="changelog.html" class="btn btn-neutral float-left" title="Changes" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a>
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+    <p>&#169; Copyright 2023, Hu Zhao.</p>
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+  <section id="sampler">
+<h1>Sampler<a class="headerlink" href="#sampler" title="Permalink to this heading"></a></h1>
+<p>This module hosts functionality for sampling methods.</p>
+<p>Currently implemented classes are:</p>
+<ul class="simple">
+<li><p><a class="reference internal" href="latin.html#psimpy.sampler.latin.LHS" title="psimpy.sampler.latin.LHS"><code class="xref py py-class docutils literal notranslate"><span class="pre">LHS</span></code></a>: Latin hypercube sampling.</p></li>
+<li><p><a class="reference internal" href="metropolis_hastings.html#psimpy.sampler.metropolis_hastings.MetropolisHastings" title="psimpy.sampler.metropolis_hastings.MetropolisHastings"><code class="xref py py-class docutils literal notranslate"><span class="pre">MetropolisHastings</span></code></a>: Metropolis Hastings sampling.</p></li>
+<li><p><a class="reference internal" href="saltelli.html#psimpy.sampler.saltelli.Saltelli" title="psimpy.sampler.saltelli.Saltelli"><code class="xref py py-class docutils literal notranslate"><span class="pre">Saltelli</span></code></a>: Saltelli’s version of Sobol’ sampling.</p></li>
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+<li class="toctree-l2 current"><a class="reference internal" href="index.html">Sampler</a><ul class="current">
+<li class="toctree-l3 current"><a class="current reference internal" href="#"> Latin Hypercube</a><ul>
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+             
+  <section id="latin-hypercube-sampling">
+<h1>Latin Hypercube Sampling<a class="headerlink" href="#latin-hypercube-sampling" title="Permalink to this heading"></a></h1>
+<p>Latin hypercube sampling is one type of space-filling sampling method. It is often
+used to draw input points for emulator training. The following figure gives a
+three-dimensional example.</p>
+<a class="reference internal image-reference" href="../_images/latin_hypercube_sampling_sketch.png"><img alt="an illustration of Latin hypercube sampling" class="align-center" src="../_images/latin_hypercube_sampling_sketch.png" style="width: 800px;" /></a>
+<p>Three random variables <span class="math notranslate nohighlight">\(X\)</span>, <span class="math notranslate nohighlight">\(Y\)</span>, and <span class="math notranslate nohighlight">\(Z\)</span> consist of
+a three-dimensional space. If we want to draw <span class="math notranslate nohighlight">\(6\)</span> samples from this space
+using Latin hypercube sampling, we first divide the range of each variable into
+<span class="math notranslate nohighlight">\(6\)</span> equally probable intervals as shown on the left. In each interval,
+we pick a value for the corresponding variable. Then we shuffle the picked values
+of each variable (e.g. <span class="math notranslate nohighlight">\(x_1\)</span> to <span class="math notranslate nohighlight">\(x_6\)</span>) as shown in the middle. Last,
+each combination gives us one sample of the three variables as shown on the right.
+It should be noted that each sample excludes any other samples from the intervals
+that it locates in. This can be straightforwardly extended to draw <span class="math notranslate nohighlight">\(M\)</span> samples
+from <span class="math notranslate nohighlight">\(N\)</span>-dimensional space consisting of <span class="math notranslate nohighlight">\(N\)</span> random variables.</p>
+<section id="lhs-class">
+<h2>LHS Class<a class="headerlink" href="#lhs-class" title="Permalink to this heading"></a></h2>
+<p>The <a class="reference internal" href="#psimpy.sampler.latin.LHS" title="psimpy.sampler.latin.LHS"><code class="xref py py-class docutils literal notranslate"><span class="pre">LHS</span></code></a> class is imported by:</p>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">psimpy.sampler.latin</span> <span class="kn">import</span> <span class="n">LHS</span>
+</pre></div>
+</div>
+<section id="methods">
+<h3>Methods<a class="headerlink" href="#methods" title="Permalink to this heading"></a></h3>
+<dl class="py class">
+<dt class="sig sig-object py" id="psimpy.sampler.latin.LHS">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">LHS</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ndim</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">bounds</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">seed</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">criterion</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'random'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">iteration</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/psimpy/sampler/latin.html#LHS"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#psimpy.sampler.latin.LHS" title="Permalink to this definition"></a></dt>
+<dd><p>Latin hypercube sampling.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters</dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>ndim</strong> (<em>int</em>) – Dimension of parameters.</p></li>
+<li><p><strong>bounds</strong> (<em>numpy array</em>) – Upper and lower boundaries of each parameter. Shape <code class="code docutils literal notranslate"><span class="pre">(ndim,</span> <span class="pre">2)</span></code>.
+<cite>bounds[:, 0]</cite> corresponds to lower boundaries of each parameter and
+<cite>bounds[:, 1]</cite> to upper boundaries of each parameter.</p></li>
+<li><p><strong>seed</strong> (<em>int</em><em>, </em><em>optional</em>) – Seed to initialize the pseudo-random number generator.</p></li>
+<li><p><strong>criterion</strong> (<em>str</em><em>, </em><em>optional</em>) – Criterion for generating Latin hypercube samples.
+<cite>‘random’</cite> - randomly locate samples in each bin.
+<cite>‘center’</cite> - locate samples in bin centers.
+<cite>‘maximin’</cite> - locate samples in each bin by maximizing their minimum
+distance.
+Default is <cite>‘random’</cite>.</p></li>
+<li><p><strong>iteration</strong> (<em>int</em><em>, </em><em>optional</em>) – Number of iterations if <code class="code docutils literal notranslate"><span class="pre">criterion='maximin'</span></code>.</p></li>
+</ul>
+</dd>
+</dl>
+<dl class="py method">
+<dt class="sig sig-object py" id="psimpy.sampler.latin.LHS.sample">
+<span class="sig-name descname"><span class="pre">sample</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">nsamples</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/psimpy/sampler/latin.html#LHS.sample"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#psimpy.sampler.latin.LHS.sample" title="Permalink to this definition"></a></dt>
+<dd><p>Draw Latin hypercube samples.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters</dt>
+<dd class="field-odd"><p><strong>nsamples</strong> (<em>int</em>) – Number of samples to be drawn.</p>
+</dd>
+<dt class="field-even">Returns</dt>
+<dd class="field-even"><p><strong>lhs_samples</strong> – Latin hypercube samples. Shape <code class="code docutils literal notranslate"><span class="pre">(nsamples,</span> <span class="pre">ndim)</span></code>.</p>
+</dd>
+<dt class="field-odd">Return type</dt>
+<dd class="field-odd"><p>numpy array</p>
+</dd>
+</dl>
+</dd></dl>
+
+</dd></dl>
+
+<div class="admonition warning">
+<p class="admonition-title">Warning</p>
+<p>The <a class="reference internal" href="#psimpy.sampler.latin.LHS" title="psimpy.sampler.latin.LHS"><code class="xref py py-class docutils literal notranslate"><span class="pre">LHS</span></code></a> class considers each random variable being uniformly
+distributed in its range. If this is not the case, one needs to transform picked
+samples accordingly.</p>
+</div>
+</section>
+</section>
+</section>
+
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+  <section id="metropolis-hastings-sampling">
+<h1>Metropolis Hastings Sampling<a class="headerlink" href="#metropolis-hastings-sampling" title="Permalink to this heading"></a></h1>
+<p>Metropolis Hastings sampling is a widely used Markov Chain Monte Carlo (MCMC)
+algorithm for generating a sequence of samples from a target probability
+distribution where direct sampling is difficult. The samples can be used to
+estimate properties of the target distribution, like its mean, variance, and higher
+moments. The samples can also be used to approximate the target distribution,
+for example via a histogram. The algorithm works by constructing a Markov chain
+with a stationary distribution equal to the target distribution.</p>
+<p>Steps of the algorithm are as follows:</p>
+<blockquote>
+<div><ol class="arabic simple">
+<li><p>Choose an initial state for the Markov chain, usually from the target distribution.</p></li>
+<li><p>At each iteration, propose a new state by sampling from a proposal distribution.</p></li>
+<li><p>Calculate the acceptance probability.</p></li>
+<li><p>Accept or reject the proposed state based on the acceptance probability.</p></li>
+<li><p>Repeat steps 2-4 for a large number of iterations to obtain a sequence of samples.</p></li>
+<li><p>Apply “burn-in” and “thining”.</p></li>
+</ol>
+</div></blockquote>
+<p>Final samples from the Markov chain can then be used to estimate the target
+distribution or its properties.</p>
+<section id="metropolishastings-class">
+<h2>MetropolisHastings Class<a class="headerlink" href="#metropolishastings-class" title="Permalink to this heading"></a></h2>
+<p>The <a class="reference internal" href="#psimpy.sampler.metropolis_hastings.MetropolisHastings" title="psimpy.sampler.metropolis_hastings.MetropolisHastings"><code class="xref py py-class docutils literal notranslate"><span class="pre">MetropolisHastings</span></code></a> class is imported by:</p>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">psimpy.sampler.metropolis_hastings</span> <span class="kn">import</span> <span class="n">MetropolisHastings</span>
+</pre></div>
+</div>
+<section id="methods">
+<h3>Methods<a class="headerlink" href="#methods" title="Permalink to this heading"></a></h3>
+<dl class="py class">
+<dt class="sig sig-object py" id="psimpy.sampler.metropolis_hastings.MetropolisHastings">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">MetropolisHastings</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ndim</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">init_state</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">f_sample</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">target</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">ln_target</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">bounds</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">f_density</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">symmetric</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">nburn</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">nthin</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">seed</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">args_target</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">kwgs_target</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">args_f_sample</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">kwgs_f_sample</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">args_f_density</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">kwgs_f_density</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/psimpy/sampler/metropolis_hastings.html#MetropolisHastings"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#psimpy.sampler.metropolis_hastings.MetropolisHastings" title="Permalink to this definition"></a></dt>
+<dd><p>Metropolis Hastings sampling.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters</dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>ndim</strong> (<em>int</em>) – Dimension of parameter <code class="docutils literal notranslate"><span class="pre">x</span></code>.</p></li>
+<li><p><strong>init_state</strong> (<em>numpy array</em>) – Contains <code class="docutils literal notranslate"><span class="pre">ndim</span></code> numeric values representing the starting point of
+the Metropolis hastings chain. Shape <code class="code docutils literal notranslate"><span class="pre">(ndim,)</span></code>.</p></li>
+<li><p><strong>f_sample</strong> (<em>Callable</em>) – A function which proposes a new state <code class="docutils literal notranslate"><span class="pre">x'</span></code> given a current state
+<code class="docutils literal notranslate"><span class="pre">x</span></code>. Call with <code class="code docutils literal notranslate"><span class="pre">f_sample(x,</span> <span class="pre">*args_f_sample,</span> <span class="pre">**kwgs_f_sample)</span></code>.
+Return the proposed state <code class="docutils literal notranslate"><span class="pre">x'</span></code> as a <code class="xref py py-class docutils literal notranslate"><span class="pre">numpy.ndarray</span></code> of
+shape <code class="code docutils literal notranslate"><span class="pre">(ndim,)</span></code>. If <span class="math notranslate nohighlight">\(ndim=1\)</span>, <code class="docutils literal notranslate"><span class="pre">f_sample</span></code> may also
+return a scalar value.</p></li>
+<li><p><strong>target</strong> (<em>Callable</em><em>, </em><em>optional</em>) – Target probability density function, up to a normalizing constant.
+Call with <code class="code docutils literal notranslate"><span class="pre">target(x,</span> <span class="pre">*args_target,</span> <span class="pre">**kwgs_target)</span></code>.
+Return the probability density value at <code class="docutils literal notranslate"><span class="pre">x</span></code>.
+If <code class="docutils literal notranslate"><span class="pre">target</span></code> is not given, <code class="docutils literal notranslate"><span class="pre">ln_target</span></code> must be provided.</p></li>
+<li><p><strong>ln_target</strong> (<em>Callable</em><em>, </em><em>optional</em>) – Natural logarithm of target probability density function.
+Call with <code class="code docutils literal notranslate"><span class="pre">ln_target(x,</span> <span class="pre">*args_target,</span> <span class="pre">**kwgs_target)</span></code>.
+Return the value of natural logarithm of target probability density
+value at <code class="docutils literal notranslate"><span class="pre">x</span></code>.
+If <code class="docutils literal notranslate"><span class="pre">ln_target</span></code> is not given, <code class="docutils literal notranslate"><span class="pre">target</span></code> must be provided.</p></li>
+<li><p><strong>bounds</strong> (<em>numpy array</em><em>, </em><em>optional</em>) – Upper and lower boundaries of each parameter. Shape <code class="code docutils literal notranslate"><span class="pre">(ndim,</span> <span class="pre">2)</span></code>.
+<cite>bounds[:, 0]</cite> corresponds to lower boundaries of each parameter and
+<cite>bounds[:, 1]</cite> to upper boundaries of each parameter.</p></li>
+<li><p><strong>f_density</strong> (<em>Callable</em><em>, </em><em>optional</em>) – Call with <code class="code docutils literal notranslate"><span class="pre">f_density(x1,</span> <span class="pre">x2,</span> <span class="pre">*args_f_density,</span> <span class="pre">**kwgs_f_density)</span></code>.
+Return the probability density at state <code class="docutils literal notranslate"><span class="pre">x1</span></code> given state <code class="docutils literal notranslate"><span class="pre">x2</span></code>.
+It must be provided if <code class="docutils literal notranslate"><span class="pre">symmetric</span></code> is set to <cite>False</cite>.</p></li>
+<li><p><strong>symmetric</strong> (<em>bool</em><em>, </em><em>optional</em>) – Whether <code class="docutils literal notranslate"><span class="pre">f_density</span></code> is symmetric or asymmetric.</p></li>
+<li><p><strong>nburn</strong> (<em>int</em><em>, </em><em>optional</em>) – Number of burnin. Default no burnin.</p></li>
+<li><p><strong>nthin</strong> (<em>int</em><em>, </em><em>optional</em>) – Number of thining to reduce dependency. Default no thining.</p></li>
+<li><p><strong>seed</strong> (<em>int</em><em>, </em><em>optional</em>) – Seed to initialize the pseudo-random number generator.
+Default <cite>None</cite>.</p></li>
+<li><p><strong>args_target</strong> (<em>list</em><em>, </em><em>optional</em>) – Positional arguments for <code class="docutils literal notranslate"><span class="pre">target</span></code> or <code class="docutils literal notranslate"><span class="pre">ln_target</span></code>.</p></li>
+<li><p><strong>kwgs_target</strong> (<em>dict</em><em>, </em><em>optional</em>) – Keyword arguments for <code class="docutils literal notranslate"><span class="pre">target</span></code> or <code class="docutils literal notranslate"><span class="pre">ln_target</span></code>.</p></li>
+<li><p><strong>args_f_sample</strong> (<em>list</em><em>, </em><em>optional</em>) – Positional arguments for <code class="docutils literal notranslate"><span class="pre">f_sample</span></code>.</p></li>
+<li><p><strong>kwgs_f_sample</strong> (<em>dict</em><em>, </em><em>optional</em>) – Keyword arguments for <code class="docutils literal notranslate"><span class="pre">f_sample</span></code>.</p></li>
+<li><p><strong>args_f_density</strong> (<em>list</em><em>, </em><em>optional</em>) – Positional arguments for <code class="docutils literal notranslate"><span class="pre">f_density</span></code>.</p></li>
+<li><p><strong>kwgs_f_density</strong> (<em>dict</em><em>, </em><em>optional</em>) – Keyword arguments for <code class="docutils literal notranslate"><span class="pre">f_density</span></code>.</p></li>
+</ul>
+</dd>
+</dl>
+<dl class="py method">
+<dt class="sig sig-object py" id="psimpy.sampler.metropolis_hastings.MetropolisHastings.sample">
+<span class="sig-name descname"><span class="pre">sample</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">nsamples</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/psimpy/sampler/metropolis_hastings.html#MetropolisHastings.sample"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#psimpy.sampler.metropolis_hastings.MetropolisHastings.sample" title="Permalink to this definition"></a></dt>
+<dd><p>Draw samples.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters</dt>
+<dd class="field-odd"><p><strong>nsamples</strong> (<em>int</em>) – Number of samples to be drawn.</p>
+</dd>
+<dt class="field-even">Return type</dt>
+<dd class="field-even"><p><code class="xref py py-class docutils literal notranslate"><span class="pre">tuple</span></code>[<code class="xref py py-class docutils literal notranslate"><span class="pre">ndarray</span></code>, <code class="xref py py-class docutils literal notranslate"><span class="pre">ndarray</span></code>]</p>
+</dd>
+<dt class="field-odd">Returns</dt>
+<dd class="field-odd"><p><ul class="simple">
+<li><p><strong>mh_samples</strong> (<em>numpy array</em>) – Samples drawn from <code class="docutils literal notranslate"><span class="pre">target</span></code>. Shape <code class="code docutils literal notranslate"><span class="pre">(nsamples,</span> <span class="pre">ndim)</span></code>.</p></li>
+<li><p><strong>mh_accept</strong> (<em>numpy array</em>) – Shape of <code class="code docutils literal notranslate"><span class="pre">(nsamples,)</span></code>. Each element indicates whether the
+corresponding sample is the proposed new state (value 1) or the old
+state (value 0). <code class="code docutils literal notranslate"><span class="pre">np.mean(mh_accept)</span></code> thus gives the overall
+acceptance ratio.</p></li>
+</ul>
+</p>
+</dd>
+</dl>
+</dd></dl>
+
+</dd></dl>
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+  <section id="saltelli-sampling">
+<h1>Saltelli Sampling<a class="headerlink" href="#saltelli-sampling" title="Permalink to this heading"></a></h1>
+<p>Saltelli sampling is a method to draw samples for the purpose of Sobol’
+sensitvity analysis (variance-based sensitivity analysis). Detailed description
+of the theory can be found in <span id="id1">Saltelli [<a class="reference internal" href="../refs.html#id11" title="Andrea Saltelli. Making best use of model evaluations to compute sensitivity indices. Computer Physics Communications, 145(2):280–297, 2002. doi:https://doi.org/10.1016/S0010-4655(02)00280-1.">2002</a>]</span> and <span id="id2">Saltelli <em>et al.</em> [<a class="reference internal" href="../refs.html#id12" title="Andrea Saltelli, Paola Annoni, Ivano Azzini, Francesca Campolongo, Marco Ratto, and Stefano Tarantola. Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index. Computer Physics Communications, 181(2):259–270, 2010. doi:https://doi.org/10.1016/j.cpc.2009.09.018.">2010</a>]</span>.
+The <a class="reference internal" href="#psimpy.sampler.saltelli.Saltelli" title="psimpy.sampler.saltelli.Saltelli"><code class="xref py py-class docutils literal notranslate"><span class="pre">Saltelli</span></code></a> class relies on the Python package <cite>SALib</cite> <span id="id3">[<a class="reference internal" href="../refs.html#id7" title="Jon Herman and Will Usher. SALib: an open-source Python library for sensitivity analysis. The Journal of Open Source Software, 2017. doi:10.21105/joss.00097.">Herman and Usher, 2017</a>]</span>.</p>
+<section id="saltelli-class">
+<h2>Saltelli Class<a class="headerlink" href="#saltelli-class" title="Permalink to this heading"></a></h2>
+<p>The <a class="reference internal" href="#psimpy.sampler.saltelli.Saltelli" title="psimpy.sampler.saltelli.Saltelli"><code class="xref py py-class docutils literal notranslate"><span class="pre">Saltelli</span></code></a> class is imported by:</p>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">psimpy.sampler.saltelli</span> <span class="kn">import</span> <span class="n">Saltelli</span>
+</pre></div>
+</div>
+<section id="methods">
+<h3>Methods<a class="headerlink" href="#methods" title="Permalink to this heading"></a></h3>
+<dl class="py class">
+<dt class="sig sig-object py" id="psimpy.sampler.saltelli.Saltelli">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">Saltelli</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ndim</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">bounds</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">calc_second_order</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">skip_values</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/psimpy/sampler/saltelli.html#Saltelli"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#psimpy.sampler.saltelli.Saltelli" title="Permalink to this definition"></a></dt>
+<dd><p>Saltelli’s version of Sobol’ sampling.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters</dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>ndim</strong> (<em>int</em>) – Dimension of parameters.</p></li>
+<li><p><strong>bounds</strong> (<em>numpy array</em><em>, </em><em>optional</em>) – Upper and lower boundaries of each parameter. Shape <code class="code docutils literal notranslate"><span class="pre">(ndim,</span> <span class="pre">2)</span></code>.
+<cite>bounds[:, 0]</cite> corresponds to lower boundaries of each parameter and
+<cite>bounds[:, 1]</cite> to upper boundaries of each parameter.</p></li>
+<li><p><strong>calc_second_order</strong> (<em>bool</em><em>, </em><em>optional</em>) – If <cite>True</cite>, calculate second-order Sobol’ indices.
+If <cite>False</cite>, second-order Sobol’ indices are not computed.</p></li>
+<li><p><strong>skip_values</strong> (<em>int</em><em>, </em><em>optional</em>) – Number of points to skip in the Sobol’ sequence. It should be
+ideally a value of base <span class="math notranslate nohighlight">\(2\)</span>.</p></li>
+</ul>
+</dd>
+</dl>
+<dl class="py method">
+<dt class="sig sig-object py" id="psimpy.sampler.saltelli.Saltelli.sample">
+<span class="sig-name descname"><span class="pre">sample</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">nbase</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/psimpy/sampler/saltelli.html#Saltelli.sample"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#psimpy.sampler.saltelli.Saltelli.sample" title="Permalink to this definition"></a></dt>
+<dd><p>Draw samples using Saltelli’s extension of the Sobol’ sequence.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters</dt>
+<dd class="field-odd"><p><strong>nbase</strong> (<em>int</em>) – Number of base samples. Correspond to the parameter <code class="docutils literal notranslate"><span class="pre">N</span></code> of
+<code class="xref py py-func docutils literal notranslate"><span class="pre">SALib.sample.saltelli.sample()</span></code>.</p>
+</dd>
+<dt class="field-even">Returns</dt>
+<dd class="field-even"><p><strong>samples</strong> – Shape of <code class="code docutils literal notranslate"><span class="pre">(nbase*(2*ndim+2),</span> <span class="pre">ndim)</span></code> if <code class="docutils literal notranslate"><span class="pre">calc_second_order</span></code>
+is <cite>True</cite>. Shape of <code class="code docutils literal notranslate"><span class="pre">(nbase*(ndim+2),</span> <span class="pre">ndim)</span></code> if
+<code class="docutils literal notranslate"><span class="pre">calc_second_order</span></code> is <cite>False</cite>.</p>
+</dd>
+<dt class="field-odd">Return type</dt>
+<dd class="field-odd"><p>numpy array</p>
+</dd>
+</dl>
+</dd></dl>
+
+</dd></dl>
+
+</section>
+</section>
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+  <section id="sensitivity">
+<h1>Sensitivity<a class="headerlink" href="#sensitivity" title="Permalink to this heading"></a></h1>
+<p>This module hosts functionality for sensitivity analysis methods.</p>
+<p>Currently implemented classes are:</p>
+<ul class="simple">
+<li><p><a class="reference internal" href="sobol.html#psimpy.sensitivity.sobol.SobolAnalyze" title="psimpy.sensitivity.sobol.SobolAnalyze"><code class="xref py py-class docutils literal notranslate"><span class="pre">SobolAnalyze</span></code></a>: Compute Sobol’ sensitivity indices.</p></li>
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+<li class="toctree-l3 current"><a class="current reference internal" href="#"> Sobol Analyze</a><ul>
+<li class="toctree-l4"><a class="reference internal" href="#sobolanalyze-class">SobolAnalyze Class</a></li>
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+  <section id="sobol-sensitivity-analysis">
+<h1>Sobol’ Sensitivity Analysis<a class="headerlink" href="#sobol-sensitivity-analysis" title="Permalink to this heading"></a></h1>
+<p>This module is used to compute Sobol’ indices given model (e.g. simulator or emulator)
+outputs evaluated at chosen Saltelli samples (see the <a class="reference internal" href="../sampler/saltelli.html#psimpy.sampler.saltelli.Saltelli" title="psimpy.sampler.saltelli.Saltelli"><code class="xref py py-class docutils literal notranslate"><span class="pre">Saltelli</span></code></a> class).
+Detailed description of the theory can be found in <span id="id1">Saltelli [<a class="reference internal" href="../refs.html#id11" title="Andrea Saltelli. Making best use of model evaluations to compute sensitivity indices. Computer Physics Communications, 145(2):280–297, 2002. doi:https://doi.org/10.1016/S0010-4655(02)00280-1.">2002</a>]</span> and <span id="id2">Saltelli <em>et al.</em> [<a class="reference internal" href="../refs.html#id12" title="Andrea Saltelli, Paola Annoni, Ivano Azzini, Francesca Campolongo, Marco Ratto, and Stefano Tarantola. Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index. Computer Physics Communications, 181(2):259–270, 2010. doi:https://doi.org/10.1016/j.cpc.2009.09.018.">2010</a>]</span>.
+The <a class="reference internal" href="#psimpy.sensitivity.sobol.SobolAnalyze" title="psimpy.sensitivity.sobol.SobolAnalyze"><code class="xref py py-class docutils literal notranslate"><span class="pre">SobolAnalyze</span></code></a> class relies on the Python package <cite>SALib</cite> <span id="id3">[<a class="reference internal" href="../refs.html#id7" title="Jon Herman and Will Usher. SALib: an open-source Python library for sensitivity analysis. The Journal of Open Source Software, 2017. doi:10.21105/joss.00097.">Herman and Usher, 2017</a>]</span>.</p>
+<section id="sobolanalyze-class">
+<h2>SobolAnalyze Class<a class="headerlink" href="#sobolanalyze-class" title="Permalink to this heading"></a></h2>
+<p>The <a class="reference internal" href="#psimpy.sensitivity.sobol.SobolAnalyze" title="psimpy.sensitivity.sobol.SobolAnalyze"><code class="xref py py-class docutils literal notranslate"><span class="pre">SobolAnalyze</span></code></a> class is imported by:</p>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">psimpy.sensitivity.sobol</span> <span class="kn">import</span> <span class="n">SobolAnalyze</span>
+</pre></div>
+</div>
+<section id="methods">
+<h3>Methods<a class="headerlink" href="#methods" title="Permalink to this heading"></a></h3>
+<dl class="py class">
+<dt class="sig sig-object py" id="psimpy.sensitivity.sobol.SobolAnalyze">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">SobolAnalyze</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ndim</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">Y</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">calc_second_order</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">nresamples</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">100</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">conf_level</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.95</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">seed</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/psimpy/sensitivity/sobol.html#SobolAnalyze"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#psimpy.sensitivity.sobol.SobolAnalyze" title="Permalink to this definition"></a></dt>
+<dd><p>Sobol’ sensitivity analysis.
+This class is built based on <code class="xref py py-func docutils literal notranslate"><span class="pre">SALib.analyze.sobol()</span></code>.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters</dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>ndim</strong> (<em>int</em>) – Dimension of parameter <code class="docutils literal notranslate"><span class="pre">x</span></code>.</p></li>
+<li><p><strong>Y</strong> (<em>numpy array</em>) – Model outputs evaluated at varaible input points drawn by Saltelli
+sampling. Shape of <code class="code docutils literal notranslate"><span class="pre">(nsaltelli,</span> <span class="pre">nrealizations)</span></code>. <code class="docutils literal notranslate"><span class="pre">nsaltelli</span></code>
+is the number of Saltelli sample points, and <code class="docutils literal notranslate"><span class="pre">nrealizations</span></code> is
+the number of  realizations of model output at one input point.
+More specially: <span class="math notranslate nohighlight">\(nrealizations=1\)</span> for a deterministic model
+which returns a scalar output at one input point,
+and <span class="math notranslate nohighlight">\(nrealizations&gt;1\)</span> for a stochastic model which returns
+multiple realizations of a scalar output at one input point (such
+as a Gaussian process model).
+If <span class="math notranslate nohighlight">\(nrealizations=1\)</span>, an array of shape <code class="code docutils literal notranslate"><span class="pre">(nsaltelli,)</span></code>
+is also valid.</p></li>
+<li><p><strong>calc_second_order</strong> (<em>bool</em><em>, </em><em>optional</em>) – If <cite>True</cite>, calculate secord order Sobol’ indices.</p></li>
+<li><p><strong>nresamples</strong> (<em>int</em><em>, </em><em>optional</em>) – Size of bootstrap sampling.</p></li>
+<li><p><strong>conf_level</strong> (<em>float</em><em>, </em><em>optional</em>) – Confidence interval level. Must be a value within the range
+<span class="math notranslate nohighlight">\((0,1)\)</span>.</p></li>
+<li><p><strong>seed</strong> (<em>int</em><em>, </em><em>optional</em>) – Seed to initialize the pseudo-random number generator.</p></li>
+</ul>
+</dd>
+</dl>
+<dl class="py method">
+<dt class="sig sig-object py" id="psimpy.sensitivity.sobol.SobolAnalyze.run">
+<span class="sig-name descname"><span class="pre">run</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">mode</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">max_workers</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/psimpy/sensitivity/sobol.html#SobolAnalyze.run"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#psimpy.sensitivity.sobol.SobolAnalyze.run" title="Permalink to this definition"></a></dt>
+<dd><p>Perform Sobol’ analysis.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters</dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>mode</strong> (<em>str</em><em>, </em><em>optional</em>) – <cite>‘parallel’</cite> or <cite>‘serial’</cite>. Run sobol’ analysis for each colomn of
+<code class="docutils literal notranslate"><span class="pre">Y</span></code> in parallel or in serial. Only relevant when
+<span class="math notranslate nohighlight">\(nrealizations&gt;1\)</span>.</p></li>
+<li><p><strong>max_workers</strong> (<em>int</em><em>, </em><em>optional</em>) – The maximum number of tasks running in parallel.
+Default is the number of CPUs on the host.
+Only relevant when <span class="math notranslate nohighlight">\(nrealizations&gt;1\)</span>.</p></li>
+</ul>
+</dd>
+<dt class="field-even">Returns</dt>
+<dd class="field-even"><p><strong>S_res</strong> – Sobol’ sensitivity indices.
+<cite>S_res[‘S1’]</cite> - <code class="xref py py-class docutils literal notranslate"><span class="pre">numpy.ndarray</span></code> of shape <code class="code docutils literal notranslate"><span class="pre">(ndim,</span> <span class="pre">3)</span></code>,
+first-order Sobol’ index, its std, and conf_level for each parameter.
+<cite>S_res[‘ST’]</cite> - <code class="xref py py-class docutils literal notranslate"><span class="pre">numpy.ndarray</span></code> of shape <code class="code docutils literal notranslate"><span class="pre">(ndim,</span> <span class="pre">3)</span></code>,
+total-effect Sobol’ index, its std, and conf_level for each parameter.
+<cite>S_res[‘S2’]</cite> - <code class="xref py py-class docutils literal notranslate"><span class="pre">numpy.ndarray</span></code> of shape
+<code class="code docutils literal notranslate"><span class="pre">(ndim*(ndim-1)/2,</span> <span class="pre">3)</span></code>, second-order Sobol’ index, its std,
+and conf_level for each pair of parameters.
+<cite>S_res[‘S2’]</cite> is only available if <code class="docutils literal notranslate"><span class="pre">calc_second_order</span></code> is True.</p>
+</dd>
+<dt class="field-odd">Return type</dt>
+<dd class="field-odd"><p>dict</p>
+</dd>
+</dl>
+</dd></dl>
+
+</dd></dl>
+
+</section>
+</section>
+</section>
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+  <section id="simulator">
+<h1>Simulator<a class="headerlink" href="#simulator" title="Permalink to this heading"></a></h1>
+<p>Computer simulations are widely used to study real-world systems in many fields.
+Such a simulation model, so-called <cite>simulator</cite>, essentially defines a mapping from
+an input space <span class="math notranslate nohighlight">\(\mathcal{X}\)</span> to an output space <span class="math notranslate nohighlight">\(\mathcal{Y}\)</span>.
+More specifically, given a simulator <span class="math notranslate nohighlight">\(\mathbf{y}=\mathbf{f}(\mathbf{x})\)</span>,
+it maps a <span class="math notranslate nohighlight">\(p\)</span>-dimensional input <span class="math notranslate nohighlight">\(\mathbf{x} \in \mathcal{X} \subset{\mathbb{R}^p}\)</span>
+to a <span class="math notranslate nohighlight">\(k\)</span>-dimensional output <span class="math notranslate nohighlight">\(\mathbf{y} \in \mathcal{Y} \subset{\mathbb{R}^k}\)</span>.
+The mapping <span class="math notranslate nohighlight">\(\mathbf{f}\)</span> can vary from simple linear equations which can be analytically
+solved to complex partial differential equations which requires numerical schemes such as
+finite element methods.</p>
+<p>This module hosts simulators and functionality for running simulators. Currently
+implemented classes are:</p>
+<ul class="simple">
+<li><p><a class="reference internal" href="run_simulator.html#psimpy.simulator.run_simulator.RunSimulator" title="psimpy.simulator.run_simulator.RunSimulator"><code class="xref py py-class docutils literal notranslate"><span class="pre">RunSimulator</span></code></a>: Serial and parallel execution of simulators.</p></li>
+<li><p><a class="reference internal" href="mass_point_model.html#psimpy.simulator.mass_point_model.MassPointModel" title="psimpy.simulator.mass_point_model.MassPointModel"><code class="xref py py-class docutils literal notranslate"><span class="pre">MassPointModel</span></code></a>: Mass point model for landslide run-out simulation.</p></li>
+<li><p><a class="reference internal" href="ravaflow24.html#psimpy.simulator.ravaflow24.Ravaflow24Mixture" title="psimpy.simulator.ravaflow24.Ravaflow24Mixture"><code class="xref py py-class docutils literal notranslate"><span class="pre">Ravaflow24Mixture</span></code></a>: Voellmy-type shallow flow model for landslide run-out simulation.</p></li>
+</ul>
+<div class="toctree-wrapper compound">
+</div>
+<div class="admonition note">
+<p class="admonition-title">Note</p>
+<p><a class="reference internal" href="mass_point_model.html#psimpy.simulator.mass_point_model.MassPointModel" title="psimpy.simulator.mass_point_model.MassPointModel"><code class="xref py py-class docutils literal notranslate"><span class="pre">MassPointModel</span></code></a> and <a class="reference internal" href="ravaflow24.html#psimpy.simulator.ravaflow24.Ravaflow24Mixture" title="psimpy.simulator.ravaflow24.Ravaflow24Mixture"><code class="xref py py-class docutils literal notranslate"><span class="pre">Ravaflow24Mixture</span></code></a> are only relevant if
+the user wants to perform run-out simulation. <a class="reference internal" href="mass_point_model.html#psimpy.simulator.mass_point_model.MassPointModel" title="psimpy.simulator.mass_point_model.MassPointModel"><code class="xref py py-class docutils literal notranslate"><span class="pre">MassPointModel</span></code></a> is purely
+Python-based and can be used right away. <a class="reference internal" href="ravaflow24.html#psimpy.simulator.ravaflow24.Ravaflow24Mixture" title="psimpy.simulator.ravaflow24.Ravaflow24Mixture"><code class="xref py py-class docutils literal notranslate"><span class="pre">Ravaflow24Mixture</span></code></a> depends on
+<a class="reference external" href="https://www.landslidemodels.org/r.avaflow/">r.avaflow 2.4</a>, which needs to be
+installed by the user.</p>
+</div>
+</section>
+
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+<li class="toctree-l3"><a class="reference internal" href="run_simulator.html"> Run Simulator</a></li>
+<li class="toctree-l3 current"><a class="current reference internal" href="#"> Mass Point Model</a><ul>
+<li class="toctree-l4"><a class="reference internal" href="#theory-of-mass-point-model">Theory of mass point model</a></li>
+<li class="toctree-l4"><a class="reference internal" href="#masspointmodel-class">MassPointModel Class</a></li>
+</ul>
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+  <section id="mass-point-model">
+<h1>Mass Point Model<a class="headerlink" href="#mass-point-model" title="Permalink to this heading"></a></h1>
+<section id="theory-of-mass-point-model">
+<h2>Theory of mass point model<a class="headerlink" href="#theory-of-mass-point-model" title="Permalink to this heading"></a></h2>
+<p>A <cite>mass point model</cite> is an extremely simplified model to simulate mass movement
+on a given topography. It assumes that the flow mass is condensed to a single point.</p>
+<p>Let <span class="math notranslate nohighlight">\(Z(x,y)\)</span> define a topography in a Cartesian
+coordinate system <span class="math notranslate nohighlight">\(\{x, y, z\}\)</span>. It induces a local non-orthogonal
+coordinate system <span class="math notranslate nohighlight">\(\{T_x, T_y, T_n\}\)</span>, where <span class="math notranslate nohighlight">\(T_x\)</span> and <span class="math notranslate nohighlight">\(T_y\)</span>
+denote surface tangent directions and <span class="math notranslate nohighlight">\(T_n\)</span> denote surface normal direction
+<span class="math notranslate nohighlight">\(T_n\)</span>, as shown by the following figure <span id="id1">[<a class="reference internal" href="../refs.html#id15" title="Hu Zhao. Gaussian processes for sensitivity analysis, Bayesian inference, and uncertainty quantification in landslide research. PhD thesis, RWTH Aachen University, 2021. doi:10.18154/RWTH-2021-11693.">Zhao, 2021</a>]</span></p>
+<a class="reference internal image-reference" href="../_images/coordinate_system.png"><img alt="a surface-induced coordinate system" class="align-center" src="../_images/coordinate_system.png" style="width: 300px;" /></a>
+<p>The govening equations describing the movement of a masspoint on the surface are
+given by</p>
+<div class="math notranslate nohighlight" id="equation-dxdt">
+<span class="eqno">(1)<a class="headerlink" href="#equation-dxdt" title="Permalink to this equation"></a></span>\[\frac{d x}{d t} = U_{T_x} \frac{1}{\sqrt{1+\left(\partial_x Z(x, y)\right)^2}}\]</div>
+<div class="math notranslate nohighlight" id="equation-dydt">
+<span class="eqno">(2)<a class="headerlink" href="#equation-dydt" title="Permalink to this equation"></a></span>\[\frac{d y}{d t} = U_{T_y} \frac{1}{\sqrt{1+\left(\partial_y Z(x, y)\right)^2}}\]</div>
+<div class="math notranslate nohighlight" id="equation-dutxdt">
+<span class="eqno">(3)<a class="headerlink" href="#equation-dutxdt" title="Permalink to this equation"></a></span>\[\frac{d U_{T_x}}{d t}=g_{T_x} - \frac{U_{T_x}}{\|\boldsymbol{U}\|}
+\cdot \left(\mu\left(g_N+\boldsymbol{U}^T \boldsymbol{K} \boldsymbol{U}\right) +
+\frac{g}{\xi}\|\boldsymbol{U}\|^2\right)\]</div>
+<div class="math notranslate nohighlight" id="equation-dutydt">
+<span class="eqno">(4)<a class="headerlink" href="#equation-dutydt" title="Permalink to this equation"></a></span>\[\frac{d U_{T_y}}{d t} = g_{T_y} - \frac{U_{T_y}}{\|\boldsymbol{U}\|}
+\cdot\left(\mu\left(g_N+\boldsymbol{U}^T \boldsymbol{K} \boldsymbol{U}\right) +
+\frac{g}{\xi}\|\boldsymbol{U}\|^2\right)\]</div>
+<p>where <span class="math notranslate nohighlight">\(\mu\)</span> and <span class="math notranslate nohighlight">\(\xi\)</span> are dry-Coulomb and turbulent friction coefficient
+respectively (Voellmy friction model is used here). <span class="math notranslate nohighlight">\(\mathbf{K}\)</span> is the
+curvature tensor <span id="id2">[<a class="reference internal" href="../refs.html#id3" title="Jan-Thomas Fischer, Julia Kowalski, and Shiva P. Pudasaini. Topographic curvature effects in applied avalanche modeling. Cold Regions Science and Technology, 74-75:21–30, 2012. doi:https://doi.org/10.1016/j.coldregions.2012.01.005.">Fischer <em>et al.</em>, 2012</a>]</span>. <span class="math notranslate nohighlight">\(\mathbf{U}\)</span> represents the masspoint’s
+velocity. <span class="math notranslate nohighlight">\(U_{T_x}\)</span> and <span class="math notranslate nohighlight">\(U_{T_y}\)</span> are the velocity components along <span class="math notranslate nohighlight">\(T_x\)</span>
+and <span class="math notranslate nohighlight">\(T_y\)</span> direction respectively.</p>
+<p>Equations <a class="reference internal" href="#equation-dxdt">(1)</a> to <a class="reference internal" href="#equation-dutydt">(4)</a> can be rewritten in the vector format as</p>
+<div class="math notranslate nohighlight" id="equation-dalphadt">
+<span class="eqno">(5)<a class="headerlink" href="#equation-dalphadt" title="Permalink to this equation"></a></span>\[\frac{d \boldsymbol{\alpha}}{d t}=\boldsymbol{f}(t, \boldsymbol{\alpha})\]</div>
+<div class="math notranslate nohighlight" id="equation-alpha">
+<span class="eqno">(6)<a class="headerlink" href="#equation-alpha" title="Permalink to this equation"></a></span>\[\begin{split}\boldsymbol{\alpha}=\left[\begin{array}{c}
+x(t) \\
+y(t) \\
+U_{T_x}(t) \\
+U_{T_y}(t)
+\end{array}\right]\end{split}\]</div>
+<div class="math notranslate nohighlight" id="equation-vector-f">
+<span class="eqno">(7)<a class="headerlink" href="#equation-vector-f" title="Permalink to this equation"></a></span>\[\begin{split}\boldsymbol{f}=\left[\begin{array}{c}
+U_{T_x} \frac{1}{\sqrt{1+\left(\partial_x Z(x, y)^2\right.}} \\
+U_{T_y} \frac{1}{\sqrt{1+\left(\partial_y Z(x, y)^2\right.}} \\
+g_{T_x}-\frac{U_{T_x}}{\|\boldsymbol{U}\|} \cdot\left(\mu\left(g_N+\boldsymbol{U}^T
+\boldsymbol{K} \boldsymbol{U}\right)+\frac{g}{\xi}\|\boldsymbol{U}\|^2\right) \\
+g_{T_y}-\frac{U_{T_y}}{\|\boldsymbol{U}\|} \cdot\left(\mu\left(g_N+\boldsymbol{U}^T
+\boldsymbol{K} \boldsymbol{U}\right)+\frac{g}{\xi}\|\boldsymbol{U}\|^2\right)
+\end{array}\right]\end{split}\]</div>
+<p>Equation <a class="reference internal" href="#equation-dalphadt">(5)</a> defines an initial value problem. Given initial
+<span class="math notranslate nohighlight">\(\boldsymbol{\alpha}_0\)</span>, the system can be solved forward in time using
+numerical schemes such as the runge-kutta method. Class <a class="reference internal" href="#psimpy.simulator.mass_point_model.MassPointModel" title="psimpy.simulator.mass_point_model.MassPointModel"><code class="xref py py-class docutils literal notranslate"><span class="pre">MassPointModel</span></code></a>
+utilizes the explicit runge-kutta method <code class="docutils literal notranslate"><span class="pre">dopri5</span></code> provided by
+<code class="xref py py-class docutils literal notranslate"><span class="pre">scipy.integrate.ode</span></code>.</p>
+</section>
+<section id="masspointmodel-class">
+<h2>MassPointModel Class<a class="headerlink" href="#masspointmodel-class" title="Permalink to this heading"></a></h2>
+<p>The <a class="reference internal" href="#psimpy.simulator.mass_point_model.MassPointModel" title="psimpy.simulator.mass_point_model.MassPointModel"><code class="xref py py-class docutils literal notranslate"><span class="pre">MassPointModel</span></code></a> class is imported by:</p>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">psimpy.simulator.mass_point_model</span> <span class="kn">import</span> <span class="n">MassPointModel</span>
+</pre></div>
+</div>
+<section id="methods">
+<h3>Methods<a class="headerlink" href="#methods" title="Permalink to this heading"></a></h3>
+<dl class="py class">
+<dt class="sig sig-object py" id="psimpy.simulator.mass_point_model.MassPointModel">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">MassPointModel</span></span><a class="reference internal" href="../_modules/psimpy/simulator/mass_point_model.html#MassPointModel"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#psimpy.simulator.mass_point_model.MassPointModel" title="Permalink to this definition"></a></dt>
+<dd><p>Simulate the movement of a masspoint on a topography.</p>
+<dl class="py method">
+<dt class="sig sig-object py" id="psimpy.simulator.mass_point_model.MassPointModel.run">
+<span class="sig-name descname"><span class="pre">run</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">elevation</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">coulomb_friction</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">turbulent_friction</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">x0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">ux0</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">uy0</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">dt</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">tend</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">300</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">t0</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">g</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">9.8</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">atol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1e-06</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">rtol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1e-06</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">curvature</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/psimpy/simulator/mass_point_model.html#MassPointModel.run"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#psimpy.simulator.mass_point_model.MassPointModel.run" title="Permalink to this definition"></a></dt>
+<dd><p>Solve the mass point model using <code class="xref py py-class docutils literal notranslate"><span class="pre">scipy.integrate.ode</span></code> solver
+given required input data.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters</dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>elevation</strong> (<em>str</em>) – Name of the elevation raster file, in ESRI ascii format, including
+the path.</p></li>
+<li><p><strong>coulomb_friction</strong> (<em>float</em>) – Dry Coulomb friction coefficient.</p></li>
+<li><p><strong>turbulent_friction</strong> (<em>float</em><em> or </em><em>int</em>) – Turbulent friction coefficient, in <span class="math notranslate nohighlight">\(m/s^2\)</span>.</p></li>
+<li><p><strong>x0</strong> (<em>float</em><em> or </em><em>int</em>) – <cite>x</cite> coordinate of initial position.</p></li>
+<li><p><strong>y0</strong> (<em>float</em><em> or </em><em>int</em>) – <cite>y</cite> coordinate of initial position.</p></li>
+<li><p><strong>ux0</strong> (<em>float</em><em> or </em><em>int</em>) – Initial velocity in <cite>x</cite> direction.</p></li>
+<li><p><strong>uy0</strong> (<em>float</em><em> or </em><em>int</em>) – Initial velocity in <cite>y</cite> direction.</p></li>
+<li><p><strong>dt</strong> (<em>float</em><em> or </em><em>int</em>) – Time step in seconds.</p></li>
+<li><p><strong>tend</strong> (<em>float</em><em> or </em><em>int</em>) – End time in seconds.</p></li>
+<li><p><strong>t0</strong> (<em>float</em><em> or </em><em>int</em>) – Initial time.</p></li>
+<li><p><strong>g</strong> (<em>float</em><em> or </em><em>int</em>) – Gravity acceleration, in <span class="math notranslate nohighlight">\(m/s^2\)</span>.</p></li>
+<li><p><strong>atol</strong> (<em>float</em>) – Absolute tolerance for solution.</p></li>
+<li><p><strong>rtol</strong> (<em>float</em>) – Relative tolerance for solution.</p></li>
+<li><p><strong>curvature</strong> (<em>bool</em>) – If <cite>True</cite>, take the curvature effect into account.</p></li>
+</ul>
+</dd>
+<dt class="field-even">Returns</dt>
+<dd class="field-even"><p><strong>output</strong> – Time history of the mass point’s location and velocity.
+2d <code class="xref py py-class docutils literal notranslate"><span class="pre">numpy.ndarray</span></code>. Each row corresponds to a time step and
+each column corresponds to a quantity. In total <span class="math notranslate nohighlight">\(6\)</span> columns,
+namely <code class="code docutils literal notranslate"><span class="pre">output.shape[1]=6</span></code>. More specifically:
+<code class="code docutils literal notranslate"><span class="pre">output[:,0]</span></code> are the time steps,
+<code class="code docutils literal notranslate"><span class="pre">output[:,1]</span></code> are the <cite>x</cite> coordinates,
+<code class="code docutils literal notranslate"><span class="pre">output[:,2]</span></code> are the <cite>y</cite> coordinates,
+<code class="code docutils literal notranslate"><span class="pre">output[:,3]</span></code> are velocity values in <cite>x</cite> direction,
+<code class="code docutils literal notranslate"><span class="pre">output[:,4]</span></code> are velocity values in <cite>y</cite> direction,
+<code class="code docutils literal notranslate"><span class="pre">output[:,5]</span></code> are total velocity values.</p>
+</dd>
+<dt class="field-odd">Return type</dt>
+<dd class="field-odd"><p>numpy array</p>
+</dd>
+</dl>
+</dd></dl>
+
+</dd></dl>
+
+</section>
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+  <section id="ravaflow24-mixture-model">
+<h1>Ravaflow24 Mixture Model<a class="headerlink" href="#ravaflow24-mixture-model" title="Permalink to this heading"></a></h1>
+<p><cite>r.avaflow 2.4</cite> is a GIS-supported open source software for mass flow modeling.
+It is developed by <span id="id1">Mergili <em>et al.</em> [<a class="reference internal" href="../refs.html#id10" title="M. Mergili, J. T. Fischer, J. Krenn, and S. P. Pudasaini. R.avaflow v1, an advanced open-source computational framework for the propagation and interaction of two-phase mass flows. Geoscientific Model Development, 10(2):553–569, 2017. doi:10.5194/gmd-10-553-2017.">2017</a>]</span>. For more information see its official
+user manual <a class="reference external" href="https://www.landslidemodels.org/r.avaflow/">here</a>.</p>
+<p>In <code class="xref py py-mod docutils literal notranslate"><span class="pre">PSimPy.simulator.ravaflow24</span></code>, we have implemented class
+<a class="reference internal" href="#psimpy.simulator.ravaflow24.Ravaflow24Mixture" title="psimpy.simulator.ravaflow24.Ravaflow24Mixture"><code class="xref py py-class docutils literal notranslate"><span class="pre">Ravaflow24Mixture</span></code></a>. It provides an Python interface to directly run
+the <cite>Voellmy-tpye shallow flow model</cite> of <cite>r.avaflow 2.4</cite> from within Python.
+For detailed theory of <cite>Voellmy-tpye shallow flow model</cite>, one can refer to
+<span id="id2">Christen <em>et al.</em> [<a class="reference internal" href="../refs.html#id2" title="M. Christen, J. Kowalski, and P. Bartelt. RAMMS: numerical simulation of dense snow avalanches in three-dimensional terrain. Cold Regions Science and Technology, 63(1):1–14, 2010. doi:https://doi.org/10.1016/j.coldregions.2010.04.005.">2010</a>]</span> and <span id="id3">Fischer <em>et al.</em> [<a class="reference internal" href="../refs.html#id3" title="Jan-Thomas Fischer, Julia Kowalski, and Shiva P. Pudasaini. Topographic curvature effects in applied avalanche modeling. Cold Regions Science and Technology, 74-75:21–30, 2012. doi:https://doi.org/10.1016/j.coldregions.2012.01.005.">2012</a>]</span>.</p>
+<section id="ravaflow24mixture-class">
+<h2>Ravaflow24Mixture Class<a class="headerlink" href="#ravaflow24mixture-class" title="Permalink to this heading"></a></h2>
+<p>The <a class="reference internal" href="#psimpy.simulator.ravaflow24.Ravaflow24Mixture" title="psimpy.simulator.ravaflow24.Ravaflow24Mixture"><code class="xref py py-class docutils literal notranslate"><span class="pre">Ravaflow24Mixture</span></code></a> class is imported by:</p>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">psimpy.simulator.ravaflow24</span> <span class="kn">import</span> <span class="n">Ravaflow24Mixture</span>
+</pre></div>
+</div>
+<section id="methods">
+<h3>Methods<a class="headerlink" href="#methods" title="Permalink to this heading"></a></h3>
+<dl class="py class">
+<dt class="sig sig-object py" id="psimpy.simulator.ravaflow24.Ravaflow24Mixture">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">Ravaflow24Mixture</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">dir_sim</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">time_step</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">10</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">time_end</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">300</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">cfl</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.4</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">time_step_length</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.001</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">conversion_control</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'0'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">curvature_control</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'1'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">surface_control</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'0'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">entrainment_control</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'0'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">shear_velocity_coef</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.05</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">basal_friction_diff</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">stopping_control</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'0'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">stopping_threshold</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">friction_control</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'0'</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/psimpy/simulator/ravaflow24.html#Ravaflow24Mixture"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#psimpy.simulator.ravaflow24.Ravaflow24Mixture" title="Permalink to this definition"></a></dt>
+<dd><p><cite>r.avaflow 2.4 Mixture model</cite> (Voellmy-type shallow flow model).</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters</dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>dir_sim</strong> (<em>str</em>) – Directory to save output files generated by <cite>r.avaflow</cite>.</p></li>
+<li><p><strong>time_step</strong> (<em>float</em><em> or </em><em>int</em>) – Time step for simulation, in seconds.</p></li>
+<li><p><strong>time_end</strong> (<em>float</em><em> or </em><em>int</em>) – End time for simulation, in seconds.</p></li>
+<li><p><strong>cfl</strong> (<em>float</em>) – CFL criterion, a value being equal or smaller than 0.5.</p></li>
+<li><p><strong>time_step_length</strong> (<em>float</em>) – If <code class="docutils literal notranslate"><span class="pre">cfl</span></code> is not applicable, <code class="docutils literal notranslate"><span class="pre">time_step_length</span></code> is used.
+In seconds. Recommended range is around <span class="math notranslate nohighlight">\(0.1\)</span> to <span class="math notranslate nohighlight">\(0.5\)</span>.</p></li>
+<li><p><strong>conversion_control</strong> (<em>str</em>) – <cite>‘0’</cite>: no conversion of flow heights to flow depths.
+<cite>‘1’</cite>: conversion is applied.</p></li>
+<li><p><strong>curvature_control</strong> (<em>str</em>) – <cite>‘0’</cite>: curvature is neglected.
+<cite>‘1’</cite>: curvature is considered in the decelerating source terms.
+<cite>‘2’</cite>: curvature is considered in all relevant terms.</p></li>
+<li><p><strong>surface_control</strong> (<em>str</em>) – <cite>‘0’</cite>: no balancing of forces.
+<cite>‘1’</cite>: apply balancing of forces.</p></li>
+<li><p><strong>entrainment_control</strong> (<em>str</em>) – <cite>‘0’</cite>: no entrainment.
+<cite>‘1’</cite>: the entrainment coefficient is multiplied with flow momentum.
+<cite>‘2’</cite>: simplified entrainment and deposition model is used.
+<cite>‘3’</cite>: combination of <cite>‘1’</cite> for entrainmnet and <cite>‘2’</cite> for deposition.
+<cite>‘4’</cite>: acceleration-deceleration entrainment and deposition model.</p></li>
+<li><p><strong>shear_velocity_coef</strong> (<em>float</em>) – Only used with <code class="docutils literal notranslate"><span class="pre">entrainment_control</span></code> being <cite>‘2’</cite> or <cite>‘3’</cite>, range
+<span class="math notranslate nohighlight">\([0,1]\)</span>.</p></li>
+<li><p><strong>basal_friction_diff</strong> (<em>float</em>) – Difference between the basal friction angles of the basal surface
+and the flow, in degrees. Only used with <code class="docutils literal notranslate"><span class="pre">entrainment_control</span></code>
+being <cite>‘2’</cite> or <cite>‘3’</cite>.</p></li>
+<li><p><strong>stopping_control</strong> (<em>str</em>) – <cite>‘0’</cite>: no stopping control is used.
+<cite>‘1’</cite>: stop if the flow kinetic energy is equal or smaller than a
+given threshold.
+<cite>‘2’</cite>: stop if the flow momentum is equal or smaller than a given
+threshold.
+<cite>‘3’</cite>: stop if the dynamic flow pressure of all raster cells is
+euqal or smaller than a given threshold.</p></li>
+<li><p><strong>stopping_threshold</strong> (<em>float</em>) – Threshold value for <code class="docutils literal notranslate"><span class="pre">stopping_control</span></code>.
+If <code class="docutils literal notranslate"><span class="pre">stopping_control</span></code> is <cite>‘1’</cite> or <cite>‘2’</cite>, <code class="docutils literal notranslate"><span class="pre">stopping_threshold</span></code>
+has to be given as the maximum value reached during the flow.
+If <code class="docutils literal notranslate"><span class="pre">stopping_control</span></code> is <cite>‘3’</cite>, the pressure threshold has to be
+specified.</p></li>
+<li><p><strong>friction_control</strong> (<em>str</em><em>, </em><em>optional</em>) – <cite>‘0’</cite>: no dynamic adaptation of friction parameters.
+<cite>‘1’</cite>: dynamic adaptation of friction parameters (ignored for the
+mixture model).</p></li>
+</ul>
+</dd>
+</dl>
+<dl class="py method">
+<dt class="sig sig-object py" id="psimpy.simulator.ravaflow24.Ravaflow24Mixture.preprocess">
+<span class="sig-name descname"><span class="pre">preprocess</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">prefix</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">elevation</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">hrelease</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">cellsize</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">20</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">hrelease_ratio</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1.0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">internal_friction</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">35</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">basal_friction</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">20</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">turbulent_friction</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">3</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">entrainment_coef</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">-7.0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">EPSG</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/psimpy/simulator/ravaflow24.html#Ravaflow24Mixture.preprocess"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#psimpy.simulator.ravaflow24.Ravaflow24Mixture.preprocess" title="Permalink to this definition"></a></dt>
+<dd><p>Preprocess simulation input data simulation.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters</dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>prefix</strong> (<em>str</em>) – Prefix required by <cite>r.avaflow</cite> to name output files.</p></li>
+<li><p><strong>elevation</strong> (<em>str</em>) – Name of elevation raster file (including its path).
+The file format should be supported by <cite>GDAL</cite>.
+Its unit is in meters.</p></li>
+<li><p><strong>hrelease</strong> (<em>str</em>) – Name of release height raster file (including its path).
+The file format should be supported by <cite>GDAL</cite>.
+Its unit is in meters.</p></li>
+<li><p><strong>cellsize</strong> (<em>float</em><em> or </em><em>int</em><em>, </em><em>optional</em>) – Cell size in meters to be used for simulation.</p></li>
+<li><p><strong>hrelease_ratio</strong> (<em>float</em><em>, </em><em>optional</em>) – A positive value to multiple <code class="docutils literal notranslate"><span class="pre">hrelease</span></code> in order to control
+the release volume.</p></li>
+<li><p><strong>internal_friction</strong> (<em>float</em><em> or </em><em>int</em><em>, </em><em>optional</em>) – Internal friction angle, in degrees, range <span class="math notranslate nohighlight">\([0,90)\)</span>.</p></li>
+<li><p><strong>basal_friction</strong> (<em>float</em><em> or </em><em>int</em><em>, </em><em>optional</em>) – Basal friction angle, in degrees, range <span class="math notranslate nohighlight">\([0,90)\)</span>.</p></li>
+<li><p><strong>turbulent_friction</strong> (<em>float</em><em> or </em><em>int</em><em>, </em><em>optional</em>) – Logarithm with base <span class="math notranslate nohighlight">\(10\)</span> of the turbulent friction, in
+<span class="math notranslate nohighlight">\(m/s^2\)</span>.</p></li>
+<li><p><strong>entrainment_coef</strong> (<em>float</em><em>, </em><em>optional</em>) – Logarithm with base <span class="math notranslate nohighlight">\(10\)</span> of the entrainment coefficient,
+except for <span class="math notranslate nohighlight">\(0\)</span> meaning no entrainment.</p></li>
+<li><p><strong>EPSG</strong> (<em>str</em><em>, </em><em>optional</em>) – <cite>EPSG</cite> (European Petroleum Survey Group) code to create
+<a class="reference external" href="https://grass.osgeo.org/grass82/manuals/grass_database.html">GRASS Location</a>.
+If <cite>None</cite>, <code class="docutils literal notranslate"><span class="pre">elevation</span></code> must be a georeferenced file which has
+metadata to create the <cite>GRASS Location</cite>.</p></li>
+</ul>
+</dd>
+<dt class="field-even">Return type</dt>
+<dd class="field-even"><p><code class="xref py py-class docutils literal notranslate"><span class="pre">tuple</span></code>[<code class="xref py py-class docutils literal notranslate"><span class="pre">str</span></code>, <code class="xref py py-class docutils literal notranslate"><span class="pre">str</span></code>]</p>
+</dd>
+<dt class="field-odd">Returns</dt>
+<dd class="field-odd"><p><ul class="simple">
+<li><p><strong>grass_location</strong> (<em>str</em>) – Name of the <cite>GRASS Location</cite> (including path).</p></li>
+<li><p><strong>sh_file</strong> (<em>str</em>) – Name of the shell file (including path), which will be called by
+<a class="reference external" href="https://grass.osgeo.org/">GRASS</a> to run the simulation.</p></li>
+</ul>
+</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="psimpy.simulator.ravaflow24.Ravaflow24Mixture.run">
+<span class="sig-name descname"><span class="pre">run</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">grass_location</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sh_file</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/psimpy/simulator/ravaflow24.html#Ravaflow24Mixture.run"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#psimpy.simulator.ravaflow24.Ravaflow24Mixture.run" title="Permalink to this definition"></a></dt>
+<dd><p>Run simulation.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters</dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>grass_location</strong> (<em>str</em>) – Name of the <cite>GRASS Location</cite> (including path).</p></li>
+<li><p><strong>sh_file</strong> (<em>str</em>) – Name of the shell file (including path).</p></li>
+</ul>
+</dd>
+<dt class="field-even">Return type</dt>
+<dd class="field-even"><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="psimpy.simulator.ravaflow24.Ravaflow24Mixture.extract_impact_area">
+<span class="sig-name descname"><span class="pre">extract_impact_area</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">prefix</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">qoi</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'h'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">threshold</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.5</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/psimpy/simulator/ravaflow24.html#Ravaflow24Mixture.extract_impact_area"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#psimpy.simulator.ravaflow24.Ravaflow24Mixture.extract_impact_area" title="Permalink to this definition"></a></dt>
+<dd><p>Extract impact area defined by a given quantity of interest and its
+threshold.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters</dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>prefix</strong> (<em>str</em>) – Prefix used by <cite>r.avaflow</cite> to name output files.</p></li>
+<li><p><strong>qoi</strong> (<em>str</em>) – Quantity of interest to determine the impact area.
+<cite>‘h’</cite>: maximum flow height, in meters.
+<cite>‘v’</cite>: maximum flow velocity, in <span class="math notranslate nohighlight">\(m/s\)</span>.
+<cite>‘p’</cite>: maximum flow pressure, in <span class="math notranslate nohighlight">\(Pa\)</span>.
+<cite>‘t’</cite>: maximum flow kinetic energy, in <span class="math notranslate nohighlight">\(J\)</span>.</p></li>
+<li><p><strong>threshold</strong> (<em>float</em><em> or </em><em>int</em>) – Threshold of <code class="docutils literal notranslate"><span class="pre">qoi</span></code> to determine impact area. Areas where <code class="docutils literal notranslate"><span class="pre">qoi</span></code>
+is larger than <code class="docutils literal notranslate"><span class="pre">threshold</span></code> are regarded as impar area.</p></li>
+</ul>
+</dd>
+<dt class="field-even">Returns</dt>
+<dd class="field-even"><p><strong>impact_area</strong> – A scalar value representing the overall impact area.</p>
+</dd>
+<dt class="field-odd">Return type</dt>
+<dd class="field-odd"><p>float</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="psimpy.simulator.ravaflow24.Ravaflow24Mixture.extract_qoi_max">
+<span class="sig-name descname"><span class="pre">extract_qoi_max</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">prefix</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">qoi</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">aggregate</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/psimpy/simulator/ravaflow24.html#Ravaflow24Mixture.extract_qoi_max"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#psimpy.simulator.ravaflow24.Ravaflow24Mixture.extract_qoi_max" title="Permalink to this definition"></a></dt>
+<dd><p>Extract the maximum value(s) of a quantity of interest.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters</dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>prefix</strong> (<em>str</em>) – Prefix used by <cite>r.avaflow</cite> to name output files.</p></li>
+<li><p><strong>qoi</strong> (<em>str</em>) – Quantity of interest.
+<cite>‘h’</cite>: maximum flow height, in meters.
+<cite>‘v’</cite>: maximum flow velocity, in <span class="math notranslate nohighlight">\(m/s\)</span>.
+<cite>‘p’</cite>: maximum flow pressure, in <span class="math notranslate nohighlight">\(Pa\)</span>.
+<cite>‘t’</cite>: maximum flow kinetic energy, in <span class="math notranslate nohighlight">\(J\)</span>.</p></li>
+<li><p><strong>aggregate</strong> (<em>bool</em>) – If <cite>True</cite>, returns the overall maximum value over all spatio-tempo
+grids. If <cite>False</cite>, returns the maximum values over all time steps at
+each spatio location, namely a raster of maximum values.</p></li>
+</ul>
+</dd>
+<dt class="field-even">Returns</dt>
+<dd class="field-even"><p><strong>qoi_max</strong> – Maximum value(s) of <code class="docutils literal notranslate"><span class="pre">qoi</span></code> in one simulation.</p>
+</dd>
+<dt class="field-odd">Return type</dt>
+<dd class="field-odd"><p>float or numpy array</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="psimpy.simulator.ravaflow24.Ravaflow24Mixture.extract_qoi_max_loc">
+<span class="sig-name descname"><span class="pre">extract_qoi_max_loc</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">prefix</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">loc</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">qoi</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/psimpy/simulator/ravaflow24.html#Ravaflow24Mixture.extract_qoi_max_loc"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#psimpy.simulator.ravaflow24.Ravaflow24Mixture.extract_qoi_max_loc" title="Permalink to this definition"></a></dt>
+<dd><p>Extract maximum value(s) of a quantity of interest at specific
+location(s).</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters</dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>prefix</strong> (<em>str</em>) – Prefix used by <cite>r.avaflow</cite> to name output files.</p></li>
+<li><p><strong>loc</strong> (<em>numpy array</em>) – Coordinates of interested locations. Shape <code class="code docutils literal notranslate"><span class="pre">(nloc,</span> <span class="pre">2)</span></code>, where
+<code class="docutils literal notranslate"><span class="pre">nloc</span></code> is the number of interested locations.
+<code class="code docutils literal notranslate"><span class="pre">loc[:,0]</span></code> corresponds to <cite>x</cite> coordinates and
+<code class="code docutils literal notranslate"><span class="pre">loc[:,1]</span></code> to <cite>y</cite> coordinates.</p></li>
+<li><p><strong>qoi</strong> (<em>str</em>) – Quantity of interest.
+<cite>‘h’</cite>: maximum flow height, in meters.
+<cite>‘v’</cite>: maximum flow velocity, in <span class="math notranslate nohighlight">\(m/s\)</span>.
+<cite>‘p’</cite>: maximum flow pressure, in <span class="math notranslate nohighlight">\(Pa\)</span>.
+<cite>‘t’</cite>: maximum flow kinetic energy, in <span class="math notranslate nohighlight">\(J\)</span>.</p></li>
+</ul>
+</dd>
+<dt class="field-even">Returns</dt>
+<dd class="field-even"><p><strong>qoi_max_loc</strong> – Consist of maximum value(s) of <code class="docutils literal notranslate"><span class="pre">qoi</span></code> at each location.
+Shape of <code class="code docutils literal notranslate"><span class="pre">(nloc,)</span></code>.</p>
+</dd>
+<dt class="field-odd">Return type</dt>
+<dd class="field-odd"><p>numpy array</p>
+</dd>
+</dl>
+</dd></dl>
+
+</dd></dl>
+
+</section>
+</section>
+</section>
+
+
+           </div>
+          </div>
+          <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer">
+        <a href="mass_point_model.html" class="btn btn-neutral float-left" title="Mass Point Model" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a>
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+<!DOCTYPE html>
+<html class="writer-html5" lang="en" >
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+<li class="toctree-l2 current"><a class="reference internal" href="index.html">Simulator</a><ul class="current">
+<li class="toctree-l3 current"><a class="current reference internal" href="#"> Run Simulator</a><ul>
+<li class="toctree-l4"><a class="reference internal" href="#runsimulator-class">RunSimulator Class</a></li>
+</ul>
+</li>
+<li class="toctree-l3"><a class="reference internal" href="mass_point_model.html"> Mass Point Model</a></li>
+<li class="toctree-l3"><a class="reference internal" href="ravaflow24.html"> Ravaflow Mixture Model</a></li>
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+           <div itemprop="articleBody">
+             
+  <section id="run-simulator">
+<h1>Run Simulator<a class="headerlink" href="#run-simulator" title="Permalink to this heading"></a></h1>
+<p>A <cite>simulator</cite> which describes certain real-world system is often subject to
+uncertainties. Uncertainty-related analyses require running the <cite>simulator</cite>
+multiple times at different variable input points. Class <a class="reference internal" href="#psimpy.simulator.run_simulator.RunSimulator" title="psimpy.simulator.run_simulator.RunSimulator"><code class="xref py py-class docutils literal notranslate"><span class="pre">RunSimulator</span></code></a>
+implemented in this module provides functionality to sequentially or parallelly
+execute <cite>simulator</cite> at a number of varaible input points.</p>
+<p>The user needs to define their <cite>simulator</cite>, implement an interface (essentially
+a Python function) to call the <cite>simulator</cite> from within Python and return output
+of interest, and inform <a class="reference internal" href="#psimpy.simulator.run_simulator.RunSimulator" title="psimpy.simulator.run_simulator.RunSimulator"><code class="xref py py-class docutils literal notranslate"><span class="pre">RunSimulator</span></code></a> the signature of the interface.</p>
+<section id="runsimulator-class">
+<h2>RunSimulator Class<a class="headerlink" href="#runsimulator-class" title="Permalink to this heading"></a></h2>
+<p>The <a class="reference internal" href="#psimpy.simulator.run_simulator.RunSimulator" title="psimpy.simulator.run_simulator.RunSimulator"><code class="xref py py-class docutils literal notranslate"><span class="pre">RunSimulator</span></code></a> class is imported by:</p>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">psimpy.simulator.run_simulator</span> <span class="kn">import</span> <span class="n">RunSimulator</span>
+</pre></div>
+</div>
+<section id="methods">
+<h3>Methods<a class="headerlink" href="#methods" title="Permalink to this heading"></a></h3>
+<dl class="py class">
+<dt class="sig sig-object py" id="psimpy.simulator.run_simulator.RunSimulator">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">RunSimulator</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">simulator</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">var_inp_parameter</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">fix_inp</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">o_parameter</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">dir_out</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">save_out</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/psimpy/simulator/run_simulator.html#RunSimulator"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#psimpy.simulator.run_simulator.RunSimulator" title="Permalink to this definition"></a></dt>
+<dd><p>Serial or parallel execution of a given simulator.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters</dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>simulator</strong> (<em>Callable</em>) – A Python function defining the simulator. Its parameters are defined
+in three parts:
+<code class="docutils literal notranslate"><span class="pre">var_inp_parameter</span></code> defines variable parameters;
+<code class="docutils literal notranslate"><span class="pre">fix_inp</span></code> defines fixed parameters (<code class="docutils literal notranslate"><span class="pre">fix_inp.keys()</span></code>) and their
+values (<code class="docutils literal notranslate"><span class="pre">fix_inp.values()</span></code>);
+<code class="docutils literal notranslate"><span class="pre">o_parameter</span></code> defines an additional variable which is used to
+name files saved onto the disk within the function body of
+<code class="docutils literal notranslate"><span class="pre">simulator</span></code>.
+The simulator should return outputs of interest as
+<code class="xref py py-class docutils literal notranslate"><span class="pre">numpy.ndarray</span></code>.</p></li>
+<li><p><strong>var_inp_parameter</strong> (<em>list</em><em> of </em><em>str</em>) – A list consists of all variable input parameters of <code class="docutils literal notranslate"><span class="pre">simulator</span></code>.</p></li>
+<li><p><strong>fix_inp</strong> (<em>dict</em><em>, </em><em>optional</em>) – A dictionary consists of key-value pairs of all fixed input of the
+<code class="docutils literal notranslate"><span class="pre">simulator</span></code>.</p></li>
+<li><p><strong>o_parameter</strong> (<em>str</em><em>, </em><em>optional</em>) – Keyword parameter of <code class="docutils literal notranslate"><span class="pre">simulator</span></code> which is used to name internally
+saved files (if defined). It is only relevant if the function body
+of <code class="docutils literal notranslate"><span class="pre">simulator</span></code> saves data onto the disk.</p></li>
+<li><p><strong>dir_out</strong> (<em>str</em><em>, </em><em>optional</em>) – Directory to save outputs of interest returned by <code class="docutils literal notranslate"><span class="pre">simulator</span></code>.</p></li>
+<li><p><strong>save_out</strong> (<em>bool</em><em>, </em><em>optional</em>) – Whether to save returned values of <code class="docutils literal notranslate"><span class="pre">simulator</span></code>. If <cite>True</cite>,
+<code class="docutils literal notranslate"><span class="pre">dir_out</span></code> must be given.</p></li>
+</ul>
+</dd>
+</dl>
+<dl class="py method">
+<dt class="sig sig-object py" id="psimpy.simulator.run_simulator.RunSimulator.serial_run">
+<span class="sig-name descname"><span class="pre">serial_run</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">var_samples</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">prefixes</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">append</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/psimpy/simulator/run_simulator.html#RunSimulator.serial_run"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#psimpy.simulator.run_simulator.RunSimulator.serial_run" title="Permalink to this definition"></a></dt>
+<dd><p>Perform serial execution of <code class="docutils literal notranslate"><span class="pre">simulator</span></code> at a set of <code class="docutils literal notranslate"><span class="pre">var_samples</span></code>.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters</dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>var_samples</strong> (<em>numpy array</em>) – Samples of variable input parameters. The first axis
+(<code class="code docutils literal notranslate"><span class="pre">var_samples.shape[0]</span></code>) corresponds to the number of samples.
+The second axis (<code class="code docutils literal notranslate"><span class="pre">var_samples.shape[1]</span></code>) corresponds to the
+number of variable input parameters.</p></li>
+<li><p><strong>prefixes</strong> (<em>list</em><em> of </em><em>str</em><em>, </em><em>optional</em>) – Contains <code class="code docutils literal notranslate"><span class="pre">len(var_samples)</span></code> prefixes. Each of them is used to
+name corresponding simulation output file.</p></li>
+<li><p><strong>append</strong> (<em>bool</em><em>, </em><em>optional</em>) – If <cite>True</cite>, append <code class="docutils literal notranslate"><span class="pre">var_samples</span></code> to existing samples and
+correspondingly append simulation outputs.</p></li>
+</ul>
+</dd>
+<dt class="field-even">Return type</dt>
+<dd class="field-even"><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="psimpy.simulator.run_simulator.RunSimulator.parallel_run">
+<span class="sig-name descname"><span class="pre">parallel_run</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">var_samples</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">prefixes</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">append</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">max_workers</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/psimpy/simulator/run_simulator.html#RunSimulator.parallel_run"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#psimpy.simulator.run_simulator.RunSimulator.parallel_run" title="Permalink to this definition"></a></dt>
+<dd><p>Perform parallel execution of <code class="docutils literal notranslate"><span class="pre">simulator</span></code> at a set of <code class="docutils literal notranslate"><span class="pre">var_samples</span></code>.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters</dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>var_samples</strong> (<em>numpy array</em>) – Samples of variable input parameters. The first axis
+(<code class="code docutils literal notranslate"><span class="pre">var_samples.shape[0]</span></code>) corresponds to the number of samples.
+The second axis (<code class="code docutils literal notranslate"><span class="pre">var_samples.shape[1]</span></code>) corresponds to the
+number of variable input parameters.</p></li>
+<li><p><strong>prefixes</strong> (<em>list</em><em> of </em><em>str</em><em>, </em><em>optional</em>) – Contains <code class="code docutils literal notranslate"><span class="pre">len(var_samples)</span></code> prefixes. Each of them is used to
+name corresponding simulation output file.</p></li>
+<li><p><strong>append</strong> (<em>bool</em><em>, </em><em>optional</em>) – If <cite>True</cite>, append <code class="docutils literal notranslate"><span class="pre">var_samples</span></code> to existing samples and
+correspondingly append simulation outputs.</p></li>
+<li><p><strong>max_workers</strong> (<em>int</em><em>, </em><em>optional</em>) – Controls the maximum number of tasks running in parallel.
+Default is the number of CPUs on the host.</p></li>
+</ul>
+</dd>
+<dt class="field-even">Return type</dt>
+<dd class="field-even"><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></p>
+</dd>
+</dl>
+</dd></dl>
+
+</dd></dl>
+
+</section>
+<section id="attributes">
+<h3>Attributes<a class="headerlink" href="#attributes" title="Permalink to this heading"></a></h3>
+<dl class="py attribute">
+<dt class="sig sig-object py" id="psimpy.simulator.run_simulator.RunSimulator.var_samples">
+<span class="sig-prename descclassname"><span class="pre">RunSimulator.</span></span><span class="sig-name descname"><span class="pre">var_samples</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="pre">ndarray</span></em><a class="headerlink" href="#psimpy.simulator.run_simulator.RunSimulator.var_samples" title="Permalink to this definition"></a></dt>
+<dd><p>Samples of variable input parameters.</p>
+</dd></dl>
+
+<dl class="py attribute">
+<dt class="sig sig-object py" id="psimpy.simulator.run_simulator.RunSimulator.outputs">
+<span class="sig-prename descclassname"><span class="pre">RunSimulator.</span></span><span class="sig-name descname"><span class="pre">outputs</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="pre">list</span></em><a class="headerlink" href="#psimpy.simulator.run_simulator.RunSimulator.outputs" title="Permalink to this definition"></a></dt>
+<dd><p>Simulation outputs.</p>
+</dd></dl>
+
+</section>
+</section>
+</section>
+
+
+           </div>
+          </div>
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+    <p>&#169; Copyright 2023, Hu Zhao.</p>
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