ASA103
The Digamma or Psi Function

ASA103 is a Python 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.

Licensing:

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

Languages:

ASA103 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:

FN, a Python 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.

POLPAK, a Python library which evaluates a variety of mathematical functions, including Chebyshev, Gegenbauer, Hermite, Jacobi, Laguerre, Legendre polynomials, and the Collatz sequence.

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

Author:

Original FORTRAN77 version by Jose Bernardo; Python 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:

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

Examples and Tests:

• asa103_test.py, calls all the tests.
• asa103_test.sh, runs all the tests.
• asa103_test.txt, the output file.

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