This is a package for generating latin hypercube samples with multi-dimensional uniformity.
To use, simply do:
>>> import lhsmdu >>> k = lhsmdu.sample(2, 20) # Latin Hypercube Sampling with multi-dimensional uniformity
This will generate a nested list with 2 variables, with 20 samples each.
To plot and see the difference between Monte Carlo and LHS-MDU sampling for a 2 dimensional system:
>>> l = lhsmdu.createRandomStandardUniformMatrix(2, 20) # Monte Carlo sampling >>> import matplotlib.pyplot as plt >>> fig = plt.figure() >>> ax = fig.gca() >>> ax.set_xticks(numpy.arange(0,1,0.1)) >>> ax.set_yticks(numpy.arange(0,1,0.1)) >>> plt.scatter(k[0], k[1], col="g", label="LHS-MDU") >>> plt.scatter(l[0], l[1], col="r", label="MC") >>> plt.grid() >>> plt.show()
You can use the strata generated by the algorithm to sample again, if you so desire. For this, you can do:
>>> m = lhsmdu.resample() >>> n = lhsmdu.resample() >>> o = lhsmdu.resample()
This will again generate the same number of samples as before, a nested list with 2 variables, with 20 samples each.
You can plot these together and see the sampling from the strata:
>>> fig = plt.figure() >>> ax = fig.gca() >>> ax.set_xticks(numpy.arange(0,1,0.1)) >>> ax.set_yticks(numpy.arange(0,1,0.1)) >>> plt.title("LHS-MDU") >>> plt.scatter(k[0], k[1], c="g", label="sample 1") >>> plt.scatter(m[0], m[1], c="r", label="resample 2") >>> plt.scatter(n[0], n[1], c="b", label="resample 3") >>> plt.scatter(o[0], o[1], c="y", label="resample 4") >>> plt.grid() >>> plt.show()
Alternatively, you can choose to get new strata each time, and see the sampling hence:
>>> p = lhsmdu.sample(2, 20) # Latin Hypercube Sampling with multi-dimensional uniformity >>> q = lhsmdu.sample(2, 20) # Latin Hypercube Sampling with multi-dimensional uniformity >>> r = lhsmdu.sample(2, 20) # Latin Hypercube Sampling with multi-dimensional uniformity >>> fig = plt.figure() >>> ax = fig.gca() >>> ax.set_xticks(numpy.arange(0,1,0.1)) >>> ax.set_yticks(numpy.arange(0,1,0.1)) >>> plt.title("LHS-MDU") >>> plt.scatter(k[0], k[1], c="g", label="sample 1") >>> plt.scatter(p[0], p[1], c="r", label="sample 2") >>> plt.scatter(q[0], q[1], c="b", label="sample 3") >>> plt.scatter(r[0], r[1], c="y", label="sample 4") >>> plt.grid() >>> plt.show()
After uniformly distributed samples have been generated from LHSMDU, you can convert these to samples from arbitrary distributions using inverse tranform sampling. In this, the CDF [0,1] of the distribution of interest is inverted, and then data points corresponding to the uniformly sampled points are picked up. To do this, you must have a rv_contiuous or rv_discrete distribution instance taken from scipy.stats. You can also use frozen distributions (after setting loc and scale parameters). Following is an example for normal distribution.:
>>> import scipy.stats.distributions as ssd >>> p = ssd.norm >>> new_samples = lhsmdu.inverseTransformSample(p, k[0]) >>> plt.hist(lhsmdu.inverseTransformSample(p, k[0])) >>> plt.show()