You can install lhsmdu using pip:
$ pip install lhsmduAlternatively, 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 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
>>> k = lhsmdu.sample(2, 20) # Latin Hypercube Sampling with multi-dimensional 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="LHS-MDU")
>>> 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("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
>>> 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("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() 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 multi-dimensional uniformity
>>> lhsmdu.sample(2, 20) # Latin Hypercube Sampling with multi-dimensional 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 multi-dimensional 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()To cite, please cite both the repository using DOI https://dx.doi.org/10.5281/zenodo.2578780 and the original paper from Deutsch and Deutsch: http://dx.doi.org/10.1016%2Fj.jspi.2011.09.016.