Creating a 2d numpy array with certain constraints

Question

I would like to create a 2 dimensional numpy array M of size n,n (a square matrix M that is) with the following constraints:

The sum of each row equals to one
The elements of each row are all between 0 and 1
The value of row i that dominates is located at entry M[i,i].

For example, for a square matrix it would be something like M = np.array([[0.88,0.12],[0.13,0.87]])

(Bonus) Ideally I want the entries of each row to follow some Gaussian like distribution whose peak, for row i, is located at element M[i,i].

In this SO thread a similar question is asked. However, playing with the responses there I was not able to find a way to do it. This is a search problem, and I do understand it might be formulated as an optimization problem. However, I am wondering if these constraints can satisfied without the need of some specialized solver.

s0meparry · Accepted Answer · 2022-06-02 17:05:30Z

1

For 1) and 2):

M = np.random.rand(n,n)
x = M / M.sum(1, keepdims=True)

edited Jun 2, 2022 at 17:05

answered Jun 2, 2022 at 17:04

s0meparry

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Marion Over a year ago

Thanks, this is easy, indeed. However, the 3d one is the tricky one (the "Bonus" should go to the fourth point).

Mechanic Pig · Accepted Answer · 2022-06-03 04:41:07Z

0

I subtract the number of columns from the number of rows per coordinate, and then use them to calculate the value of the Gaussian function, and finally multiply it by a random array and normalize it.

It may not be so random, but it has a high probability of meeting your requirements:

>>> size = 4
>>> ii, jj = np.indices((size, size))
>>> gaussian = np.exp(-((ii - jj) ** 2) / 2)
>>> result = np.random.normal(1, .1, gaussian.shape) * gaussian
>>> result /= result.sum(1, keepdims=True)
>>> result
array([[0.47556382, 0.38041462, 0.11953135, 0.02449021],
       [0.24805318, 0.4126681 , 0.26168636, 0.07759236],
       [0.10350016, 0.26245839, 0.37168771, 0.26235374],
       [0.02027633, 0.11892695, 0.31971733, 0.54107939]])

edited Jun 3, 2022 at 4:41

answered Jun 2, 2022 at 18:06

Mechanic Pig

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