ASA103
The Digamma or Psi Function

ASA103 is a FORTRAN77 library which evaluates the digamma or psi function, by Jose Bernardo.

ASA103 is Applied Statistics Algorithm 103. Source code for many Applied Statistics Algorithms is available through STATLIB.

Languages:

ASA103 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:

ASA121, a FORTRAN77 library which evaluates the trigamma function.

FN, a FORTRAN77 library which approximates elementary and special functions using Chebyshev polynomials; functions include Airy, Bessel I, Bessel J, Bessel K, Bessel Y, beta, confluent hypergeometric, cosine integral, Dawson's integral, digamma (psi), error, exponential integral, gamma, hyperbolic cosine integral, hyperbolic sine integral, incomplete gamma, log gamma, logarithmic integral, Pochhammer, psi, sine integral, Spence; by Wayne Fullerton.

SPECFUN, a FORTRAN77 library which computes special functions, including the Psi or Digamma function.

TEST_VALUES, a FORTRAN77 library which contains sample values for a number of distributions.

TOMS708, a FORTRAN77 library which includes routines to evaluate the digamma function.

Author:

Original FORTRAN77 version by Jose Bernardo; This FORTRAN77 version by John Burkardt.

Reference:

1. Jose Bernardo,
   Algorithm AS 103: Psi ( Digamma ) Function,
   Applied Statistics,
   Volume 25, Number 3, 1976, pages 315-317.

Source Code:

• asa103.f, the source code.
• asa103.sh, commands to compile the source code.

Examples and Tests:

• asa103_prb.f, a sample calling program.
• asa103_prb.sh, commands to compile and run the sample program.
• asa103_prb_output.txt, the output file.

List of Routines:

• DIGAMA calculates DIGAMMA ( X ) = d ( LOG ( GAMMA ( X ) ) ) / dX
• PSI_VALUES returns some values of the Psi or Digamma function for testing.
• TIMESTAMP prints out the current YMDHMS date as a timestamp.

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