LINPACK_D
Linear Algebra Library
Double Precision Real

LINPACK_D is a library of FORTRAN77 routines, using double 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LINPACK has officially been superseded by the LAPACK library.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 also available in a C++ version and a FORTRAN90 version and a MATLAB version.

LINPACK_S is a version of LINPACK for single precision real arithmetic.

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

LINPLUS is a set of FORTRAN90 routines to carry 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 of routines which define 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_d.f, the source codes;
• linpack_d.csh, commands to compile the source code;

Examples and Tests:

• linpack_d_prb.f, the calling program for the double precision real routines;
• linpack_d_prb.csh, commands to run LINPACK_D_PRB;
• linpack_d_prb_output.txt, the output file.

List of Routines:

• DCHDC computes the Cholesky decomposition of a positive definite matrix.
• DCHDD downdates an augmented Cholesky decomposition.
• DCHEX updates the Cholesky factorization of a positive definite matrix.
• DCHUD updates an augmented Cholesky decomposition.
• DGBCO factors a double precision band matrix and estimates its condition.
• DGBDI computes the determinant of a band matrix factored by DGBCO or DGBFA.
• DGBFA factors a double precision band matrix by elimination.
• DGBSL solves a double precision banded system factored by DGBCO or DGBFA.
• DGECO factors a double precision matrix and estimates its condition number.
• DGEDI computes the determinant and inverse of a matrix factored by DGECO or DGEFA.
• DGEFA factors a double precision matrix.
• DGESL solves a double precision general linear system A * X = B.
• DGTSL solves a general tridiagonal linear system.
• DPBCO factors a double precision symmetric positive definite banded matrix.
• DPBDI computes the determinant of a matrix factored by DPBCO or DPBFA.
• DPBFA factors a double precision symmetric positive definite matrix stored in band form.
• DPBSL solves a double precision symmetric positive definite band factored by DPBCO or DPBFA.
• DPOCO factors a double precision symmetric positive definite matrix and estimates its condition.
• DPODI computes the determinant and inverse of a certain matrix.
• DPOFA factors a double precision symmetric positive definite matrix.
• DPOSL solves a linear system factored by DPOCO or DPOFA.
• DPPCO factors a double precision symmetric positive definite matrix in packed form.
• DPPDI computes the determinant and inverse of a matrix factored by DPPCO or DPPFA.
• DPPFA factors a double precision symmetric positive definite matrix in packed form.
• DPPSL solves a double precision symmetric positive definite system factored by DPPCO or DPPFA.
• DPTSL solves a positive definite tridiagonal linear system.
• DQRDC computes the QR factorization of a double precision rectangular matrix.
• DQRSL computes transformations, projections, and least squares solutions.
• DSICO factors a double precision symmetric matrix and estimates its condition.
• DSIDI computes the determinant, inertia and inverse of a double precision symmetric matrix.
• DSIFA factors a double precision symmetric matrix.
• DSISL solves a double precision symmetric system factored by DSIFA.
• DSPCO factors a double precision symmetric matrix stored in packed form.
• DSPDI computes the determinant, inertia and inverse of a double precision symmetric matrix.
• DSPFA factors a double precision symmetric matrix stored in packed form.
• DSPSL solves the double precision symmetric system factored by DSPFA.
• DSVDC computes the singular value decomposition of a double precision rectangular matrix.
• DTRCO estimates the condition of a double precision triangular matrix.
• DTRDI computes the determinant and inverse of a double precision triangular matrix.
• DTRSL solves triangular linear systems.

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