ASA053
Wishart Variate Generator

ASA053 is a FORTRAN77 library which returns samples from the Wishart distribution.

As far as I can tell, there are two mistakes in the printed text of the algorithm; one involves incorrectly determining the number of degrees of freedom for the ChiSquared distribution; the other omits an absolute value sign when inverting the Wilson-Hilferty formula, so that square roots of negative values are occasionally requested. These mistakes have been corrected here.

Source code for many Applied Statistics Algorithms is available through STATLIB.

Licensing:

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

Languages:

ASA053 is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

WISHART, a FORTRAN77 library which produces sample matrices from the Wishart or Bartlett distributions, useful for sampling random covariance matrices.

Reference:

1. Stanley Sawyer,
   Wishart Distributions and Inverse-Wishart Sampling,
   Washington University,
   30 April 2007, 12 pages.
2. William Smith, Ronald Hocking,
   Algorithm AS 53, Wishart Variate Generator,
   Applied Statistics,
   Volume 21, Number 3, pages 341-345, 1972.

Original Source Code:

• asa053_original.f, the original text of the source code. Note that the line "DF = N - I + 1" is believed (by me) to be incorrect, and is replaced in the present version by "DF = NP - I + 1".

Source Code:

• asa053.f, the source code.
• asa053.sh, BASH commands to compile the source code.

Examples and Tests:

• asa053_prb.f, a sample calling program.
• asa053_prb.sh, BASH commands to compile and run the sample program.
• asa053_prb_output.txt, the output file.

List of Routines:

• WSHRT returns a random Wishart variate.
• RNORM returns two independent standard random normal deviates.
• R8_UNIFORM_01 returns a pseudorandom R8 scaled to [0,1].
• R8PP_PRINT prints an R8PP matrix.
• R8PP_PRINT_SOME prints some of an R8PP matrix.
• TIMESTAMP prints out the current YMDHMS date as a timestamp.

You can go up one level to the FORTRAN77 source codes.