LINPACK_D
Linear Algebra Library
Double Precision Real

LINPACK_D is a library of C++ 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LINPACK has officially been superseded by the LAPACK library.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 the BLAS Level 1 library of routines for vector operations, which are incorporated into LINPACK.

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

LINPACK_BENCH is a 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 FORTRAN77 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 C++ routines similar to LINPACK, but for some more unusual matrix formats.

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 library of FORTRAN90 routines defining matrices with known inverses, determinants, eigenvalues 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_d.C, the source code for the double precision real library;
• linpack_d.H, the include file for the double precision real library;
• linpack_d.csh, commands to compile the source code for the double precision real library;

Examples and Tests:

• linpack_d_prb.C, the calling program for the double precision real library;
• linpack_d_prb.csh, commands to run the calling program;
• linpack_d_prb.out, the sample output.

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

You can go up one level to the C++ source codes.