LINPACK_S
Linear Algebra Library
Single Precision Real

LINPACK_S is a library of FORTRAN77 routines, using single precision real arithmetic, which can solve systems of linear equations for a variety of matrix types and storage modes.

LINPACK has officially been superseded by the LAPACK library. The LAPACK library uses more modern algorithms and code structure. However, the LAPACK library can be extraordinarily complex; what is done in a single LINPACK routine may correspond to 10 or 20 utility routines in LAPACK. This is fine if you treat LAPACK as a black box. But if you wish to learn how the algorithm works, or to adapt it, or to convert the code to another language, this is a real drawback. This is one reason I still keep a copy of LINPACK around.

Versions of LINPACK in various arithmetic precisions are available through the NETLIB web site.

Related Data and Programs:

BLAS1 is a FORTRAN77 library which contains a set of routines for vector operations, which have been incorporated into LINPACK.

LAPACK is a more modern linear algebra package, which has replaced LINPACK.

LINPACK_BENCH is a FORTRAN90 benchmark program which measures the time taken by LINPACK to solve a particular linear system.

LINPACK_C is a version of LINPACK for single precision complex arithmetic.

LINPACK_D is a version of LINPACK for double precision real arithmetic.

LINPACK_S is also available in a C++ version and a FORTRAN90 version and a MATLAB version.

LINPACK_Z is a version of LINPACK for double precision complex arithmetic.

LINPLUS is a FORTRAN90 library which carries out some linear algebra operations on matrices stored in formats not handled by LINPACK.

NMS is a FORTRAN90 library which includes LINPACK.

PETSC is a scientific library for use in parallel computation, which includes an implementation of the LINPACK routines.

SLATEC is a FORTRAN90 library which includes LINPACK.

TEST_MAT is a FORTRAN90 library which defines test matrices, some of which have known determinants, eigenvalues and eigenvectors, inverses and so on.

Reference:

1. Jack Dongarra, Jim Bunch, Cleve Moler, Pete Stewart,
   LINPACK User's Guide,
   SIAM, 1979,
   ISBN13: 978-0-898711-72-1,
   LC: QA214.L56.
2. Charles Lawson, Richard Hanson, David Kincaid and Fred Krogh,
   Algorithm 539, Basic Linear Algebra Subprograms for Fortran Usage,
   ACM Transactions on Mathematical Software,
   Volume 5, Number 3, September 1979, pages 308-323.

Source Code:

• linpack_s.f, the source code;
• linpack_s.csh, commands to compile the source code;

Examples and Tests:

• linpack_s_prb.f, the calling program for the single precision real routines;
• linpack_s_prb.csh, commands to run the calling program;
• linpack_s_prb_output.txt, the output file.

List of Routines:

• SCHDC computes the Cholesky decomposition of a positive definite matrix.
• SCHDD downdates an augmented Cholesky decomposition.
• SCHEX updates the Cholesky factorization of a positive definite matrix.
• SCHUD updates an augmented Cholesky decomposition.
• SGBCO factors a real band matrix and estimates its condition.
• SGBDI computes the determinant of a band matrix factored by SGBCO or SGBFA.
• SGBFA factors a real band matrix by elimination.
• SGBSL solves a real banded system factored by SGBCO or SGBFA.
• SGECO factors a real matrix and estimates its condition number.
• SGEDI computes the determinant and inverse of a matrix factored by SGECO or SGEFA.
• SGEFA factors a real matrix.
• SGESL solves a real general linear system A * X = B.
• SGTSL solves a general tridiagonal linear system.
• SPBCO factors a real symmetric positive definite banded matrix.
• SPBDI computes the determinant of a matrix factored by SPBCO or SPBFA.
• SPBFA factors a real symmetric positive definite matrix stored in band form.
• SPBSL solves a real symmetric positive definite band factored by SPBCO or SPBFA.
• SPOCO factors a real symmetric positive definite matrix and estimates its condition.
• SPODI computes the determinant and inverse of a certain matrix.
• SPOFA factors a real symmetric positive definite matrix.
• SPOSL solves a linear system factored by SPOCO or SPOFA.
• SPPCO factors a real symmetric positive definite matrix in packed form.
• SPPDI computes the determinant and inverse of a matrix factored by SPPCO or SPPFA.
• SPPFA factors a real symmetric positive definite matrix in packed form.
• SPPSL solves a real symmetric positive definite system factored by SPPCO or SPPFA.
• SPTSL solves a positive definite tridiagonal linear system.
• SQRDC computes the QR factorization of a real rectangular matrix.
• SQRSL computes transformations, projections, and least squares solutions.
• SSICO factors a real symmetric matrix and estimates its condition.
• SSIDI computes the determinant, inertia and inverse of a real symmetric matrix.
• SSIFA factors a real symmetric matrix.
• SSISL solves a real symmetric system factored by SSIFA.
• SSPCO factors a real symmetric matrix stored in packed form.
• SSPDI computes the determinant, inertia and inverse of a real symmetric matrix.
• SSPFA factors a real symmetric matrix stored in packed form.
• SSPSL solves the real symmetric system factored by SSPFA.
• SSVDC computes the singular value decomposition of a real rectangular matrix.
• STRCO estimates the condition of a real triangular matrix.
• STRDI computes the determinant and inverse of a real triangular matrix.
• STRSL solves triangular linear systems.

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