LINPACK_Z
Linear Algebra Library
Double Precision Complex

LINPACK_Z is a FORTRAN77 library which can solve 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LINPACK has officially been superseded by the LAPACK library.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_Z is available in a C++ version and a FORTRAN77 version and a FORTRAN90 version.

Related Data and Programs:

BLAS1_Z, a FORTRAN77 library which contains basic linear algebra routines for vector-vector operations, using double precision complex arithmetic.

COMPLEX_NUMBERS, a FORTRAN77 program which demonstrates some simple features involved in the use of complex numbers in FORTRAN77 programming.

LAPACK_EXAMPLES, a FORTRAN77 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 version of LINPACK for single precision complex arithmetic.

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

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

LINPLUS, a FORTRAN90 library to carry out some linear algebra operations on matrices stored in formats not handled by LINPACK.

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:

Jack Dongarra, Jim Bunch, Cleve Moler, Pete Stewart.

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_z.f, the source code;
• linpack_z.sh, commands to compile the source code;

Examples and Tests:

• linpack_z_prb.f, the calling program for the double precision complex routines;
• linpack_z_prb.sh, commands to run LINPACK_Z_PRB;
• linpack_z_prb_output.txt, the output file.

List of Routines:

• I_SWAP swaps two integer values.
• Z_SWAP swaps two complex values.
• Z_SWAP_CONJUGATE swaps and conjugates two complex values.
• ZCHDC: Cholesky decomposition of a Hermitian positive definite matrix.
• ZCHDD downdates an augmented Cholesky decomposition.
• ZCHEX updates a Cholesky factorization.
• ZCHUD updates an augmented Cholesky decomposition.
• ZGBCO factors a complex band matrix and estimates its condition.
• ZGBDI computes the determinant of a band matrix factored by ZGBCO or ZGBFA.
• ZGBFA factors a complex band matrix by elimination.
• ZGBSL solves a complex band system factored by ZGBCO or ZGBFA.
• ZGECO factors a complex matrix and estimates its condition.
• ZGEDI computes the determinant and inverse of a matrix.
• ZGEFA factors a complex matrix by Gaussian elimination.
• ZGESL solves a complex system factored by ZGECO or ZGEFA.
• ZGTSL solves a complex general tridiagonal system.
• ZHICO factors a complex hermitian matrix and estimates its condition.
• ZHIDI computes the determinant and inverse of a matrix factored by ZHIFA.
• ZHIFA factors a complex hermitian matrix.
• ZHISL solves a complex hermitian system factored by ZHIFA.
• ZHPCO factors a complex hermitian packed matrix and estimates its condition.
• ZHPDI: determinant, inertia and inverse of a complex hermitian matrix.
• ZHPFA factors a complex hermitian packed matrix.
• ZHPSL solves a complex hermitian system factored by ZHPFA.
• ZPBCO factors a complex hermitian positive definite band matrix.
• ZPBDI gets the determinant of a hermitian positive definite band matrix.
• ZPBFA factors a complex hermitian positive definite band matrix.
• ZPBSL solves a complex hermitian positive definite band system.
• ZPOCO factors a complex hermitian positive definite matrix.
• ZPODI: determinant, inverse of a complex hermitian positive definite matrix.
• ZPOFA factors a complex hermitian positive definite matrix.
• ZPOSL solves a complex hermitian positive definite system.
• ZPPCO factors a complex hermitian positive definite matrix.
• ZPPDI: determinant and inverse of a complex hermitian positive definite matrix.
• ZPPFA factors a complex hermitian positive definite packed matrix.
• ZPPSL solves a complex hermitian positive definite linear system.
• ZPTSL solves a Hermitian positive definite tridiagonal linear system.
• ZQRDC computes the QR factorization of an N by P complex matrix.
• ZQRSL solves, transforms or projects systems factored by ZQRDC.
• ZSICO factors a complex symmetric matrix.
• ZSIDI computes the determinant and inverse of a matrix factored by ZSIFA.
• ZSIFA factors a complex symmetric matrix.
• ZSISL solves a complex symmetric system that was factored by ZSIFA.
• ZSPCO factors a complex symmetric matrix stored in packed form.
• ZSPDI sets the determinant and inverse of a complex symmetric packed matrix.
• ZSPFA factors a complex symmetric matrix stored in packed form.
• ZSPSL solves a complex symmetric system factored by ZSPFA.
• ZSVDC applies the singular value decompostion to an N by P matrix.
• ZTRCO estimates the condition of a complex triangular matrix.
• ZTRDI computes the determinant and inverse of a complex triangular matrix.
• ZTRSL solves triangular systems T*X=B or Hermitian(T)*X=B.

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