ASA053
Wishart Variate Generator

ASA053 is a C 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 FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

asa053_test

WISHART, a C 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.

Source Code:

• asa053.h, the include file.
• i4_max.c, returns the maximum of two I4s.
• i4_min.c, returns the minimum of two I4's.
• r8_uniform_01.c, returns a unit pseudorandom R8.
• r8mat_print.c, prints an R8MAT.
• r8mat_print_some.c, prints some of an R8MAT.
• r8pp_print.c, prints an R8PP matrix.
• r8pp_print_some.c, prints some of an R8PP matrix.
• r8utp_print.c, prints an R8UTP matrix.
• r8utp_print_some.c, prints some of an R8UTP matrix.
• rnorm.c, returns two independent standard random normal deviates.
• timestamp.c, prints the current YMDHMS date as a time stamp.
• wshrt.c, returns a random Wishart variate.