I was trying to use the random positive definite matrix generator implemented in sklearn (https://scikit-learn.org/stable/modules/generated/sklearn.datasets.make_spd_matrix.html). However, I noticed the documentation is very minimal, without any references on related research articles. I'm wondering if it generates a uniformly random covariance matrix to be used as a sampling method to generate a null distribution for covariances. I tried looking at the source code. But I didn't find any reasons or explanations explaining the method.

In other words, I wanted to know if the random symmetric positive definite matrix returned is uniformly sampled from the space of all positive definite matrices or not.

This is the idea I was interested in when I came across make_spd_matrix:

Kind regards,

Sina