LINPACK_C
Linear Algebra Library
Single Precision Complex

LINPACK_C is a FORTRAN90 library which solves systems of linear equations for a variety of matrix types and storage modes, by Jack Dongarra, Jim Bunch, Cleve Moler, Pete Stewart.

LINPACK has officially been superseded by the LAPACK library.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.

Languages:

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

Related Data and Programs:

BLAS1_C, a FORTRAN90 library which contains basic linear algebra routines for vector-vector operations, using single precision complex arithmetic.

C4LIB, a FORTRAN90 library which implements certain elementary functions for single precision complex variables;

COMPLEX_NUMBERS, a FORTRAN90 program which demonstrates some simple features involved in the use of complex numbers in FORTRAN90 programming.

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

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

LINPACK_D, a FORTRAN90 library which is a version of LINPACK for double precision real arithmetic.

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

LINPACK_S, a FORTRAN90 library which is a version of LINPACK for single precision real arithmetic.

LINPACK_Z, a FORTRAN90 library which is a version of LINPACK for double precision complex arithmetic.

NMS, a FORTRAN90 library which includes LINPACK.

SLATEC, a FORTRAN90 library which includes LINPACK.

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

Author:

Original FORTRAN77 version by Jack Dongarra, Jim Bunch, Cleve Moler, Pete Stewart. FORTRAN90 version by John Burkardt.

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.f90, the source code;

Examples and Tests:

• linpack_c_test.f90, the calling program;
• linpack_c_test.txt, the output file.

List of Routines:

• C4_SWAP swaps two C4's.
• C4_SWAP_CONJUGATE swaps and conjugates two C4's.
• CCHDC computes the Cholesky decomposition of a 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 computes the determinant, inertia and inverse
• 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 and 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 positive definite tridiagonal linear system.
• CQRDC computes the QR factorization of an N by P complex matrix.
• CQRSL applies the output of cqrdc to compute coordinate
• CSICO factors a complex symmetric matrix by elimination with
• 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 is a subroutine to reduce a complex nxp matrix x by
• 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.

You can go up one level to the FORTRAN90 source codes.