LINPACK_C
Linear Algebra Library
Single Precision Complex

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LINPACK has officially been superseded by the LAPACK library.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

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

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_c.C, the source code;
• linpack_c.H, the include file;
• linpack_c.csh, commands to compile the source code;

Examples and Tests:

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

List of Routines:

• CCHDC: Cholesky decomposition of a Hermitian positive definite matrix.
• CCHDD downdates an augmented Cholesky decomposition.
• CCHEX updates a Cholesky factorization.
• CCHUD updates an augmented Cholesky decomposition.
• CGBCO factors a complex band matrix and estimates its condition.
• CGBDI computes the determinant of a band matrix factored by CGBCO or CGBFA.
• CGBFA factors a complex band matrix by elimination.
• CGBSL solves a complex band system factored by CGBCO or CGBFA.
• CGECO factors a complex matrix and estimates its condition.
• CGEDI computes the determinant and inverse of a matrix.
• CGEFA factors a complex matrix by Gaussian elimination.
• CGESL solves a complex system factored by CGECO or CGEFA.
• CGTSL solves a complex general tridiagonal system.
• CHICO factors a complex hermitian matrix and estimates its condition.
• CHIDI computes the determinant and inverse of a matrix factored by CHIFA.
• CHIFA factors a complex hermitian matrix.
• CHISL solves a complex hermitian system factored by CHIFA.
• CHPCO factors a complex hermitian packed matrix and estimates its condition.
• CHPDI: determinant, inertia and inverse of a complex hermitian matrix.
• CHPFA factors a complex hermitian packed matrix.
• CHPSL solves a complex hermitian system factored by CHPFA.
• CPBCO factors a complex hermitian positive definite band matrix.
• CPBDI gets the determinant of a hermitian positive definite band matrix.
• CPBFA factors a complex hermitian positive definite band matrix.
• CPBSL solves a complex hermitian positive definite band system.
• CPOCO factors a complex hermitian positive definite matrix.
• CPODI: determinant, inverse of a complex hermitian positive definite matrix.
• CPOFA factors a complex hermitian positive definite matrix.
• CPOSL solves a complex hermitian positive definite system.
• CPPCO factors a complex hermitian positive definite matrix.
• CPPDI: determinant, inverse of a complex hermitian positive definite matrix.
• CPPFA factors a complex hermitian positive definite packed matrix.
• CPPSL solves a complex hermitian positive definite linear system.
• CPTSL solves a Hermitian positive definite tridiagonal linear system.
• CQRDC computes the QR factorization of an N by P complex matrix.
• CQRSL solves, transforms or projects systems factored by CQRDC.
• CSICO factors a complex symmetric matrix.
• CSIDI computes the determinant and inverse of a matrix factored by CSIFA.
• CSIFA factors a complex symmetric matrix.
• CSISL solves a complex symmetric system that was factored by CSIFA.
• CSPCO factors a complex symmetric matrix stored in packed form.
• CSPDI sets the determinant and inverse of a complex symmetric packed matrix.
• CSPFA factors a complex symmetric matrix stored in packed form.
• CSPSL solves a complex symmetric system factored by CSPFA.
• CSVDC applies the singular value decompostion to an N by P matrix.
• CTRCO estimates the condition of a complex triangular matrix.
• CTRDI computes the determinant and inverse of a complex triangular matrix.
• CTRSL solves triangular systems T*X=B or Hermitian(T)*X=B.
• R4_MAX returns the maximum of two R4's.
• SROTG constructs a float Givens plane rotation.

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