TOMS332
Jacobi Polynomials

TOMS332 is a FORTRAN77 library which implements ACM TOMS algorithm 332, for evaluating a Jacobi polynomial.

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.

Usage:

call jacobi ( degree, alfa, beta, x, f, fd, e, ed, flagf, flagfd )

where DEGREE is the degree of the polynomial, ALFA and BETA are the parameters of the polynomial, X is the point where the polynomial is to be evaluated, F and FD are the computed values of the polynomial and its derivative, E and ED are estimates for the error in the values of the polynomial and its derivative, FLAGF and FLAGFD are 0, 1 or 2 depending on whether the reported error estimates are relative, absolute, or zero.

Languages:

TOMS332 is available in a FORTRAN77 version.

Related Data and Programs:

POLPAK, a FORTRAN90 library which includes routines for evaluating Jacobi polynomials.

TEST_VALUES, a FORTRAN77 library which contains routines which return sample values of various functions, including the modified beta function, and the logarithm of the gamma function.

Reference:

1. Bruno Witte,
   Algorithm 332: Jacobi Polynomials,
   Communications of the ACM,
   Volume 11, Number 6, June 1968, page 436.
2. Ove Skovgaard,
   Remark on Algorithm 332,
   Communications of the ACM,
   Volume 18, Number 2, February 1975, pages 116-117.

Source Code:

• toms332.f, the source code.
• toms332.sh, commands to compile the source code.

Examples and Tests:

• toms332_prb.f, a sample calling program.
• toms332_prb.sh, commands to compile and run the sample program.
• toms332_prb_output.txt, the output file.

List of Routines:

• JACOBI evaluates a Jacobi polynomial.

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