Metadata-Version: 2.1
Name: lhsmdu
Version: 1.1
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.
Home-page: http://github.com/sahilm89/lhsmdu
Author: Sahil Moza
Author-email: sahil.moza@gmail.com
License: MIT
Description: LHS-MDU
        --------
        
        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 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()
        
        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.3929531
        
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