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<html>
<head>
<title>
LINPACK_Z - Linear Algebra Library - Double Precision Complex
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
LINPACK_Z <br> Linear Algebra Library <br> Double Precision Complex
</h1>
<hr>
<p>
<b>LINPACK_Z</b>
is a FORTRAN90 library which
solves systems of linear
equations for a variety of matrix types and storage modes.
</p>
<p>
<b>LINPACK</b> has officially been superseded by the
<a href = "../../f_src/lapack/lapack.html">LAPACK</a> 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 <b>LINPACK</b> 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 <b>LINPACK</b> around.
</p>
<p>
Versions of <b>LINPACK</b> in various arithmetic precisions are available
through <a href = "http://www.netlib.org/">the NETLIB web site</a>.
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this web page
are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>LINPACK_Z</b> is available in
<a href = "../../cpp_src/linpack_z/linpack_z.html">a C++ version</a> and
<a href = "../../f77_src/linpack_z/linpack_z.html">a FORTRAN77 version</a> and
<a href = "../../f_src/linpack_z/linpack_z.html">a FORTRAN90 version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/blas1_z/blas1_z.html">
BLAS1_Z</a>,
a FORTRAN90 library which
contains basic linear algebra routines for vector-vector operations,
using double precision complex arithmetic.
</p>
<p>
<a href = "../../f_src/c8lib/c8lib.html">
C8LIB</a>,
a FORTRAN90 library which
implements certain elementary functions for double precision complex variables;
</p>
<p>
<a href = "../../f_src/complex_numbers/complex_numbers.html">
COMPLEX_NUMBERS</a>,
a FORTRAN90 program which
demonstrates some simple features involved in the use of
complex numbers in FORTRAN90 programming.
</p>
<p>
<a href = "../../f_src/lapack_examples/lapack_examples.html">
LAPACK_EXAMPLES</a>,
a FORTRAN90 program which
demonstrates the use of the LAPACK linear algebra library.
</p>
<p>
<a href = "../../f_src/linpack_bench/linpack_bench.html">
LINPACK_BENCH</a>,
a FORTRAN90 program which
is a benchmark which measures the time
taken by <b>LINPACK</b> to solve a particular linear system.
</p>
<p>
<a href = "../../f_src/linpack_c/linpack_c.html">
LINPACK_C</a>,
a FORTRAN90 library which
solves linear systems using single precision complex arithmetic;
</p>
<p>
<a href = "../../f_src/linpack_d/linpack_d.html">
LINPACK_D</a>,
a FORTRAN90 library which
solves linear systems using double precision real arithmetic;
</p>
<p>
<a href = "../../f_src/linpack_s/linpack_s.html">
LINPACK_S</a>,
a FORTRAN90 library which
solves linear systems using single precision real arithmetic;
</p>
<p>
<a href = "../../f_src/linplus/linplus.html">
LINPLUS</a>,
a FORTRAN90 library which
carries out some linear algebra
operations on matrices stored in formats not handled by <b>LINPACK</b>.
</p>
<p>
<a href = "../../f_src/nms/nms.html">
NMS</a>,
a FORTRAN90 library which
includes a wide variety of numerical software.
</p>
<p>
<a href = "../../f_src/slatec/slatec.html">
SLATEC</a>,
a FORTRAN90 library which
includes <b>LINPACK</b>.
</p>
<p>
<a href = "../../f_src/test_mat/test_mat.html">
TEST_MAT</a>,
a FORTRAN90 library which
defines test matrices, some of which have known determinants, eigenvalues
and eigenvectors, inverses and so on.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Jack Dongarra, Jim Bunch, Cleve Moler, Pete Stewart,<br>
LINPACK User's Guide,<br>
SIAM, 1979,<br>
ISBN13: 978-0-898711-72-1,<br>
LC: QA214.L56.
</li>
<li>
Charles Lawson, Richard Hanson, David Kincaid and Fred Krogh,<br>
Algorithm 539,
Basic Linear Algebra Subprograms for Fortran Usage,<br>
ACM Transactions on Mathematical Software,<br>
Volume 5, Number 3, September 1979, pages 308-323.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "linpack_z.f90">linpack_z.f90</a>,
the source code;
</li>
<li>
<a href = "linpack_z.sh">
linpack_z.sh</a>, commands to compile the source code
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "linpack_z_prb.f90">
linpack_z_prb.f90</a>, the sample calling program;
</li>
<li>
<a href = "linpack_z_prb.sh">
linpack_z_prb.sh</a>, commands to run the sample program;
</li>
<li>
<a href = "linpack_z_prb_output.txt">linpack_z_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>I_SWAP</b> swaps two integer values.
</li>
<li>
<b>Z_SWAP</b> swaps two complex values.
</li>
<li>
<b>Z_SWAP_CONJUGATE</b> swaps and conjugates two complex values.
</li>
<li>
<b>ZCHDC:</b> Cholesky decomposition of a Hermitian positive definite matrix.
</li>
<li>
<b>ZCHDD</b> downdates an augmented Cholesky decomposition.
</li>
<li>
<b>ZCHEX</b> updates a Cholesky factorization.
</li>
<li>
<b>ZCHUD</b> updates an augmented Cholesky decomposition.
</li>
<li>
<b>ZGBCO</b> factors a complex band matrix and estimates its condition.
</li>
<li>
<b>ZGBDI</b> computes the determinant of a band matrix factored by ZGBCO or ZGBFA.
</li>
<li>
<b>ZGBFA</b> factors a complex band matrix by elimination.
</li>
<li>
<b>ZGBSL</b> solves a complex band system factored by ZGBCO or ZGBFA.
</li>
<li>
<b>ZGECO</b> factors a complex matrix and estimates its condition.
</li>
<li>
<b>ZGEDI</b> computes the determinant and inverse of a matrix.
</li>
<li>
<b>ZGEFA</b> factors a complex matrix by Gaussian elimination.
</li>
<li>
<b>ZGESL</b> solves a complex system factored by ZGECO or ZGEFA.
</li>
<li>
<b>ZGTSL</b> solves a complex general tridiagonal system.
</li>
<li>
<b>ZHICO</b> factors a complex hermitian matrix and estimates its condition.
</li>
<li>
<b>ZHIDI</b> computes the determinant and inverse of a matrix factored by ZHIFA.
</li>
<li>
<b>ZHIFA</b> factors a complex hermitian matrix.
</li>
<li>
<b>ZHISL</b> solves a complex hermitian system factored by ZHIFA.
</li>
<li>
<b>ZHPCO</b> factors a complex hermitian packed matrix and estimates its condition.
</li>
<li>
<b>ZHPDI:</b> determinant, inertia and inverse of a complex hermitian matrix.
</li>
<li>
<b>ZHPFA</b> factors a complex hermitian packed matrix.
</li>
<li>
<b>ZHPSL</b> solves a complex hermitian system factored by ZHPFA.
</li>
<li>
<b>ZPBCO</b> factors a complex hermitian positive definite band matrix.
</li>
<li>
<b>ZPBDI</b> gets the determinant of a hermitian positive definite band matrix.
</li>
<li>
<b>ZPBFA</b> factors a complex hermitian positive definite band matrix.
</li>
<li>
<b>ZPBSL</b> solves a complex hermitian positive definite band system.
</li>
<li>
<b>ZPOCO</b> factors a complex hermitian positive definite matrix.
</li>
<li>
<b>ZPODI:</b> determinant, inverse of a complex hermitian positive definite matrix.
</li>
<li>
<b>ZPOFA</b> factors a complex hermitian positive definite matrix.
</li>
<li>
<b>ZPOSL</b> solves a complex hermitian positive definite system.
</li>
<li>
<b>ZPPCO</b> factors a complex hermitian positive definite matrix.
</li>
<li>
<b>ZPPDI:</b> determinant and inverse of a complex hermitian positive definite matrix.
</li>
<li>
<b>ZPPFA</b> factors a complex hermitian positive definite packed matrix.
</li>
<li>
<b>ZPPSL</b> solves a complex hermitian positive definite linear system.
</li>
<li>
<b>ZPTSL</b> solves a Hermitian positive definite tridiagonal linear system.
</li>
<li>
<b>ZQRDC</b> computes the QR factorization of an N by P complex matrix.
</li>
<li>
<b>ZQRSL</b> solves, transforms or projects systems factored by ZQRDC.
</li>
<li>
<b>ZSICO</b> factors a complex symmetric matrix.
</li>
<li>
<b>ZSIDI</b> computes the determinant and inverse of a matrix factored by ZSIFA.
</li>
<li>
<b>ZSIFA</b> factors a complex symmetric matrix.
</li>
<li>
<b>ZSISL</b> solves a complex symmetric system that was factored by ZSIFA.
</li>
<li>
<b>ZSPCO</b> factors a complex symmetric matrix stored in packed form.
</li>
<li>
<b>ZSPDI</b> sets the determinant and inverse of a complex symmetric packed matrix.
</li>
<li>
<b>ZSPFA</b> factors a complex symmetric matrix stored in packed form.
</li>
<li>
<b>ZSPSL</b> solves a complex symmetric system factored by ZSPFA.
</li>
<li>
<b>ZSVDC</b> applies the singular value decompostion to an N by P matrix.
</li>
<li>
<b>ZTRCO</b> estimates the condition of a complex triangular matrix.
</li>
<li>
<b>ZTRDI</b> computes the determinant and inverse of a complex triangular matrix.
</li>
<li>
<b>ZTRSL</b> solves triangular systems T*X=B or Hermitian(T)*X=B.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../f_src.html">
the FORTRAN90 source codes</a>.
</p>
<hr>
<i>
Last revised on 24 June 2009.
</i>
<!-- John Burkardt -->
</body>
</html>