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        "author": "Sahil Moza",
        "author_email": "sahil.moza@gmail.com",
        "bugtrack_url": null,
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        "description": "LHS-MDU\n--------\n\nBasics\n======\nThis is a package for generating latin hypercube samples with multi-dimensional uniformity.\n\nTo use, simply do::\n\n    >>> import lhsmdu \n    >>> k = lhsmdu.sample(2, 20) # Latin Hypercube Sampling with multi-dimensional uniformity \n\nThis will generate a nested list with 2 variables, with 20 samples each.\n\nTo plot and see the difference between Monte Carlo and LHS-MDU sampling for a 2 dimensional system::\n\n    >>> l = lhsmdu.createRandomStandardUniformMatrix(2, 20) # Monte Carlo sampling \n    >>> import matplotlib.pyplot as plt \n    >>> fig = plt.figure() \n    >>> ax = fig.gca()\n    >>> ax.set_xticks(numpy.arange(0,1,0.1))\n    >>> ax.set_yticks(numpy.arange(0,1,0.1))\n    >>> plt.scatter(k[0], k[1], col=\"g\", label=\"LHS-MDU\") \n    >>> plt.scatter(l[0], l[1], col=\"r\", label=\"MC\") \n    >>> plt.grid()\n    >>> plt.show() \n\nYou can use the strata generated by the algorithm to sample again, if you so desire. For this, you can do::\n\n    >>> m = lhsmdu.resample()\n    >>> n = lhsmdu.resample()\n    >>> o = lhsmdu.resample()\n\nThis will again generate the same number of samples as before, a nested list with 2 variables, with 20 samples each.\n\nYou can plot these together and see the sampling from the strata::\n\n    >>> fig = plt.figure() \n    >>> ax = fig.gca()\n    >>> ax.set_xticks(numpy.arange(0,1,0.1))\n    >>> ax.set_yticks(numpy.arange(0,1,0.1))\n    >>> plt.title(\"LHS-MDU\") \n    >>> plt.scatter(k[0], k[1], c=\"g\", label=\"sample 1\") \n    >>> plt.scatter(m[0], m[1], c=\"r\", label=\"resample 2\") \n    >>> plt.scatter(n[0], n[1], c=\"b\", label=\"resample 3\") \n    >>> plt.scatter(o[0], o[1], c=\"y\", label=\"resample 4\") \n    >>> plt.grid()\n    >>> plt.show() \n\nAlternatively, you can choose to get new strata each time, and see the sampling hence::\n\n    >>> p = lhsmdu.sample(2, 20) # Latin Hypercube Sampling with multi-dimensional uniformity \n    >>> q = lhsmdu.sample(2, 20) # Latin Hypercube Sampling with multi-dimensional uniformity \n    >>> r = lhsmdu.sample(2, 20) # Latin Hypercube Sampling with multi-dimensional uniformity \n    >>> fig = plt.figure() \n    >>> ax = fig.gca()\n    >>> ax.set_xticks(numpy.arange(0,1,0.1))\n    >>> ax.set_yticks(numpy.arange(0,1,0.1))\n    >>> plt.title(\"LHS-MDU\") \n    >>> plt.scatter(k[0], k[1], c=\"g\", label=\"sample 1\") \n    >>> plt.scatter(p[0], p[1], c=\"r\", label=\"sample 2\") \n    >>> plt.scatter(q[0], q[1], c=\"b\", label=\"sample 3\") \n    >>> plt.scatter(r[0], r[1], c=\"y\", label=\"sample 4\") \n    >>> plt.grid()\n    >>> plt.show() \n\n===========================================================================================\n\nSampling from arbitrary CDFs\n=======================\n\nAfter 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.::\n\n    >>> import scipy.stats.distributions as ssd\n    >>> p = ssd.norm\n    >>> new_samples = lhsmdu.inverseTransformSample(p, k[0])\n    >>> plt.hist(lhsmdu.inverseTransformSample(p, k[0]))\n    >>> plt.show()\n\n\n\n\n",
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        "license": "MIT",
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        "name": "lhsmdu",
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        "summary": "This is an implementation of Latin Hypercube Sampling with Multi-Dimensional Uniformity (LHS-MDU) from Deutsch and Deutsch, \"Latin hypercube sampling with multidimensional uniformity.",
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