LINPACK_Z
Linear Algebra Library
Double Precision Complex

LINPACK_Z is a library of C++ routines, using double 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LINPACK has officially been superseded by the LAPACK library.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 a version of LINPACK for single precision complex arithmetic.

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 also available in a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

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_z.C, the source code;
• linpack_z.H, the include file;
• linpack_z.csh, commands to compile the source code;

Examples and Tests:

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

List of Routines:

• D_MAX returns the maximum of two single precision real values.
• DROTG constructs a Givens plane rotation.
• 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, 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 C++ source codes.