Python: NxM array of samples drawn from NxM normal distributions

Question

I have two 2D arrays (or of higher dimension), one that defines averages (M) and one that defines standard deviations (S). Is there a python library (numpy, scipy, ...?) that allows me to generate an array (X) containing samples drawn from the corresponding distributions?

In other words: each entry x_ij is a sample that comes from the normal distribution defined by the corresponding mean m_ij and standard deviation s_ij.

Answer 1

Yes numpy can help here:

There is a np.random.normal function that accepts array-like inputs:

import numpy as np
means = np.arange(10) # [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
stddevs = np.ones(10) # [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]

samples = np.random.normal(means, stddevs)

array([-1.69515214, -0.20680708,  0.61345775,  2.98154162,  2.77888087,
        7.22203785,  5.29995343,  8.52766436,  9.70005434,  9.58381479])

even if they are multidimensional:

means = np.arange(10).reshape(2,5) # make it multidimensional with shape 2, 5
stddevs = np.ones(10).reshape(2,5)

samples = np.random.normal(means, stddevs)

array([[-0.76585438,  1.22226145,  2.85554809,  2.64009423,  4.67255324],
       [ 3.21658151,  4.59969355,  6.87946817,  9.14658687,  8.68465692]])

The second one has a shape of (2,5)

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In case you want only different means but the same standard deviation you can also only pass one array and one scalar and still get an array with the right shape:

means = np.arange(10)

samples = np.random.normal(means, 1)

array([ 0.54018686, -0.35737881,  2.08881115,  3.08742942,  4.4426366 ,
        3.6694955 ,  5.27515536,  8.68300816,  8.83893819,  7.71284217])