docs: add example of Latin hypercube sampling

docs/examples/sampler/plot_latin.py

+"""
+
+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')
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