linpack_z

linpack_z, an Octave code which solves systems of linear equations for a variety of matrix types and storage modes, by Jack Dongarra, Jim Bunch, Cleve Moler, Pete Stewart. The matrix and vector data is presumed to be complex.

MATLAB already provides a wide set of linear equation solvers. This (partial) set of LINPACK routines is provided just for testing and comparison.

LINPACK has officially been superseded by the LAPACK library.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 information on this web page is distributed under the MIT license.

Languages:

linpack_z is available in a C++ version and a Fortran77 version and a Fortran90 version and a MATLAB version and an Octave version.

Related Data and Programs:

linpack_z_test

lapack_test, a FORTRAN90 code which demonstrates the use of the LAPACK linear algebra library.

linpack_d, an Octave code which solves linear systems using double precision real arithmetic;

test_matrix, an Octave code which contains a collection of test matrices.

Author:

Original FORTRAN77 version by Jack Dongarra, Jim Bunch, Cleve Moler, Pete Stewart. This 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:

• crand.m, returns a random complex scalar, vector, or matrix.
• drotg.m, computes a real Givens rotation.
• dzasum.m, takes the sum of the absolute values of a complex vector.
• dznrm2.m, computes the Euclidean norm of a complex vector.
• izamax.m, indexes the complex vector element of maximum absolute value.
• zabs1.m, returns the L1 norm of a complex number.
• zchdc.m, computes the Cholesky decomposition of a positive definite matrix;
• zchdd.m, downdates a Cholesky decomposition of a positive definite matrix;
• zchex.m, updates a Cholesky decomposition of a positive definite matrix;
• zchud.m, updates a Cholesky decomposition of a positive definite matrix;
• zdotc.m, computes the conjugated dot product of two vectors.
• zdrot.m, applies a complex Givens rotation.
• zgbco.m, factors a band matrix and estimates its condition.
• zgbdi.m, computes the determinant of a band matrix factored by ZGBCO or ZGBFA.
• zgbfa.m, factors a complex band matrix by elimination.
• zgbsl.m, solves a complex band system factored by ZGBCO or ZGBFA.
• zgeco.m, factors a complex matrix and estimates its condition.
• zgedi.m, computes the determinant and inverse of a matrix.
• zgefa.m, factors a complex matrix by Gaussian elimination.
• zgesl.m, solves a complex system factored by ZGECO or ZGEFA.
• zgtsl.m, solves a complex tridiagonal system.
• zhico.m, factors a Hermitian matrix and estimates its condition.
• zhidi.m, computes inverse, determinant and interia of a Hermitian matrix.
• zhifa.m, factors a Hermitian matrix by Gaussian elimination.
• zhisl.m, solves a linear system factored by ZHIFA or ZHICO.
• zhpco.m, factors a Hermitian packed matrix and estimates its condition.
• zhpdi.m, computes inverse, determinant and interia of a Hermitian packed matrix.
• zhpfa.m, factors a Hermitian packed matrix by Gaussian elimination.
• zhpsl.m, solves a linear system factored by ZHPFA or ZHPCO.
• zpbco.m, factors a Hermitian positive definite band matrix and estimates its condition.
• zpbdi.m, computes inverse, determinant and interia of a Hermitian positive definite band matrix.
• zpbfa.m, factors a Hermitian positive definite band matrix by Gaussian elimination.
• zpbsl.m, solves a linear system factored by ZPBFA or ZPBCO.
• zpoco.m, factors a Hermitian positive definite matrix and estimates its condition.
• zpodi.m, computes inverse, determinant and interia of a Hermitian positive definite matrix.
• zpofa.m, factors a Hermitian positive definite matrix by Gaussian elimination.
• zposl.m, solves a linear system factored by ZPOFA or ZPOCO.
• zppco.m, factors a Hermitian positive definite packed matrix and estimates its condition.
• zppdi.m, computes inverse, determinant and interia of a Hermitian positive definite packed matrix.
• zppfa.m, factors a Hermitian positive definite packed matrix by Gaussian elimination.
• zppsl.m, solves a linear system factored by ZPPFA or ZPPCO.
• zptsl.m, solves a Hermitian positive definite tridiagonal system.
• zqrdc.m, computes the QR decomposition of a general rectangular complex matrix.
• zqrdc_test.m
• zqrsl.m, uses the QR decomposition to solve linear systems and other tasks.
• zrotg.m, computes a complex Givens rotation.
• zsico.m, factors a complex symmetric indefinite matrix and estimates its condition.
• zsidi.m, computes inverse and determinant of a complex symmetric indefinite matrix.
• zsign1.m, is a complex transfer-of-sign function.
• zsign2.m, is a complex transfer-of-sign function.
• zsvdc.m, computes the singular value decomposition of a general complex matrix.
• ztrco.m, returns the condition of a complex triangular matrix.
• ztrdi.m, computes the inverse or determinant of a complex triangular matrix.
• ztrsl.m, solves a complex triangular linear system.