Create a matrix like a transtision matrix How i can create random matrix with sum of values by column = 1 in python ?

CodePudding user response：

(EDIT: added output)

I suggest completing this in two steps:

1. Create a random matrix

2. Normalize each column

1. Create random matrix

Let's say you want a 3 by 3 random transition matrix:

M = np.random.rand(3, 3)

Each of M's entries will have a random value between 0 and 1.

Normalize M's columns

By dividing each column by the column sum will achieve what you want. This can be done in several ways, but I prefer to create an array r whose elements is the column sum of M:

r = M.sum(axis=0)

Then, divide M by r:

transition_matrix = M / r

Example output

>>> import numpy as np

>>> M = np.random.rand(3,3 )
>>> r = M.sum(axis=0)
>>> transition_matrix = M / r

>>> M
array([[0.74145687, 0.68389986, 0.37008102],
       [0.81869654, 0.0394523 , 0.94880781],
       [0.93057194, 0.48279246, 0.15581823]])
>>> r
array([2.49072535, 1.20614462, 1.47470706])
>>> transition_matrix
array([[0.29768713, 0.56701315, 0.25095223],
       [0.32869804, 0.03270943, 0.64338731],
       [0.37361483, 0.40027743, 0.10566046]])
>>> transition_matrix.sum(axis=0)
array([1., 1., 1.])

CodePudding user response：

You could use KNOWN distribution where each sample would have (by default) summed to one, e.g. Dirichlet distribution.

After that code is basically one liner, Python 3.8, Windows 10 x64

import numpy as np

N = 3

# set alphas array, 1s by default
a = np.empty(N)
a.fill(1.0)

mtx = np.random.dirichlet(a, N).transpose()

print(mtx)

and it will print something like

[[0.56634637 0.04568052 0.79105779]
 [0.42542107 0.81892862 0.02465906]
 [0.00823256 0.13539087 0.18428315]]