TOMS571
The Von Mises and Fisher Directional Distributions

TOMS571 is a FORTRAN77 library which implements ACM TOMS algorithm 571, containing routines to determine the concentration parameter from the average modulus of a set of sample vectors, and vice versa, for both the von Mises (circular) and Fisher (spherical) distributions of directions.

The text of many ACM TOMS algorithms is available online through ACM: http://www.acm.org/pubs/calgo or NETLIB: http://www.netlib.org/toms/index.html.

Languages:

TOMS571 is available in a FORTRAN77 version.

Related Data and Programs:

PROB, a FORTRAN90 library which contains routines to sample the von Mises and Fisher distributions.

Reference:

1. Geoffrey Hill,
   Algorithm 571, Statistics for von Mises's and Fisher's Distributions of Directions, I1(x)/I0(x), I1.5(x)/I0.5(x), and Their Inverses,
   ACM Transactions on Mathematical Software,
   Volume 7, Number 2, June 1981, pages 233-238.

Source Code:

• toms571.f, the source code.
• toms571.sh, commands to compile the source code.

Examples and Tests:

• toms571_prb.f, a sample calling program.
• toms571_prb.sh, commands to compile and run the sample program.
• toms571_prb_output.txt, the output file.

List of Routines:

• BESRA2 returns the Bessel function ratio I1(V) / I0(V).
• BESRAT returns the Bessel function ratio I1(V) / I0(V).
• R4_CAPPA3 estimates KAPPA from the sample mean, for the Fisher distribution.
• R4_PRECIS returns the number of matching decimal digits.
• R4_SPHERR computes the expected sample mean for the Fisher distribution.
• R8_CAPPA3 estimates KAPPA from the sample mean, for the Fisher distribution.
• R8_PRECIS returns the number of matching decimal digits.
• R8_SPHERR computes the expected sample mean for the Fisher distribution.
• TIMESTAMP prints out the current YMDHMS date as a timestamp.
• VKAPPA estimates KAPPA from the sample mean, for the von Mises distribution.

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