wishart_matrix, a Python code which produces sample matrices from the Wishart or Bartlett distributions, useful for sampling random covariance matrices.

The Wishart distribution is a probability distribution for random nonnegative-definite NxN matrices that can be used to select random covariance matrices.

The objects of the distribution are NxN matrices which are the sum of DF rank-one matrices X*X' constructed from N-vectors X, where the vectors X have zero mean and covariance SIGMA. This implies that the expected value of a Wishart matrix is DF * SIGMA.

A simplified version of the Wishart distribution assumes that SIGMA is the identity matrix. We will call this the "unit Wishart distribution".

Because any Wishart matrix W is symmetric nonnegative definite, there is an upper triangular factor T so that W = T' * T. There is a corresponding Bartlett distribution of the matrices T, so that one can alternatively sample the Bartlett distribution by sampling the Bartlett distribution for T, and then forming W.


The computer code and data files made available on this web page are distributed under the MIT license.


wishart_matrix is available in a C version and a C++ version and a Fortran77 version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.

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Source Code:

Last revised on 31 December 2023.