LINPACK_S
Linear Algebra Library
Single Precision Real

LINPACK_S is a FORTRAN90 library which solves 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LINPACK has officially been superseded by the LAPACK library.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.

Licensing:

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

Language:

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

Related Data and Programs:

BLAS1_S, a FORTRAN90 library which contains basic linear algebra routines for vector-vector operations, using single precision real arithmetic.

LAPACK_EXAMPLES, a FORTRAN90 program which demonstrates the use of the LAPACK linear algebra library.

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

LINPACK_C, a FORTRAN90 library which solves linear systems using single precision complex arithmetic;

LINPACK_D, a FORTRAN90 library which solves linear systems using double precision real arithmetic;

LINPACK_Q, a FORTRAN90 library which implements a few of the LINPACK library of linear solvers, using quadruple precision.

LINPACK_Z, a FORTRAN90 library which solves linear systems using double precision complex arithmetic;

NMS, a FORTRAN90 library which includes LINPACK.

SLATEC, a FORTRAN90 library which collects together a number of standard numerical libraries.

SVD_DEMO, a FORTRAN90 program which demonstrates the singular value decomposition for a simple example.

TEST_MAT, 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, 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.f90, the source code;

Examples and Tests:

• linpack_s_test.f90, the calling program;
• linpack_s_test.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 general 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 SPD band system 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 FORTRAN90 source codes.