TOMS423
Gaussian Elimination

TOMS423 is a FORTRAN77 library which implements ACM TOMS algorithm 423, for Gaussian elimination to factor a matrix and solve a related linear system.

While 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, most of the early algorithms are not available. This is one of them. I typed it in.

Usage:

call decomp(n,ndim,a,ip)

computes the LU factorization of an N by N matrix A, stored in an array with leading dimension NDIM. The vector IP returns pivot information.

call solve(n,ndim,a,b,ip)

solves a linear system A*X=B, after A has been factored by DECOMP. B contains the right hand side on input, and the solution on output.

Languages:

TOMS423 is available in a FORTRAN77 version.

Related Programs:

LAPACK_EXAMPLES, a FORTRAN77 program which demonstrates the use of the LAPACK linear algebra library.

LINPACK, a FORTRAN77 library which solves linear systems for a variety of matrix storage schemes, real or complex arithmetic, and single or double precision.

Author:

Cleve Moler

Reference:

1. Cleve Moler,
   Algorithm 423: Linear Equation Solver,
   Communications of the ACM,
   Volume 15, Number 4, April 1972, page 274.

Source Code:

• toms423.f, the source code.
• toms423.sh, commands to compile the source code.

Examples and Tests:

• toms423_prb.f, a sample calling program.
• toms423_prb.sh, commands to compile and run the sample program.
• toms423_prb_output.txt, the output from a run of the sample program.

List of Routines:

• DECOMP decomposes the matrix.
• SOLVE solves a linear system.

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