LHSMDU
Installation
You can install lhsmdu using pip:
$ pip install lhsmdu
Alternatively, you can clone on github and then install the package locally:
$ git clone https://github.com/sahilm89/lhsmdu $ cd lhsmdu $ python setup.py install user # for this user only.
or:
$ pip install git+https://github.com/sahilm89/lhsmdu user
Basics
This is a package for generating latin hypercube samples with multidimensional uniformity.
To use, simply do:
>>> import lhsmdu >>> k = lhsmdu.sample(2, 20) # Latin Hypercube Sampling with multidimensional uniformity
This will generate a nested list with 2 variables, with 20 samples each.
To plot and see the difference between Monte Carlo and LHSMDU sampling for a 2 dimensional system:
>>> l = lhsmdu.createRandomStandardUniformMatrix(2, 20) # Monte Carlo sampling >>> k = lhsmdu.sample(2, 20) # Latin Hypercube Sampling with multidimensional uniformity >>> k = np.array(k) >>> l = np.array(l) >>> 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], color="g", label="LHSMDU") >>> plt.scatter(l[0], l[1], color="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::

>>> m = np.array(m) >>> n = np.array(n) >>> o = np.array(o)
>>> 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("LHSMDU") >>> 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 multidimensional uniformity >>> q = lhsmdu.sample(2, 20) # Latin Hypercube Sampling with multidimensional uniformity >>> r = lhsmdu.sample(2, 20) # Latin Hypercube Sampling with multidimensional uniformity >>> p = np.array(p) >>> q = np.array(q) >>> r = np.array(r) >>> 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("LHSMDU") >>> 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()
Changing the random seed
You will notice that the strata generated are the same each time you run the program again. This is because the random seed is a global constant set to a default value by design, so that simulations can be replicated. In order to change this behavior, you can set a new random seed using the following code:
>>> randSeed = 11 # random number of choice >>> lhsmdu.setRandomSeed(randSeed) # Latin Hypercube Sampling with multidimensional uniformity >>> lhsmdu.sample(2, 20) # Latin Hypercube Sampling with multidimensional uniformity
Alternatively, you can also set the seed by using sample with a new seed:
>>> lhsmdu.sample(2, 20, randomSeed=randSeed) # Latin Hypercube Sampling with multidimensional uniformity
To change the random seed in every run, you can set on top of the program:
>>> lhsmdu.setRandomSeed(None)
Sampling from arbitrary CDFs
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(new_samples[0]) >>> plt.show()
Citing this repository
To cite, please cite both the original paper from Deutsch and Deutsch: http://dx.doi.org/10.1016%2Fj.jspi.2011.09.016. and the repository: https://doi.org/10.5281/zenodo.2578781