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<html>
<head>
<title>
TOEPLITZ - Solution of Toeplitz linear systems
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
TOEPLITZ <br> Solution of Toeplitz linear systems
</h1>
<hr>
<p>
<b>TOEPLITZ</b>
is a FORTRAN90 library which
solves a variety of Toeplitz and circulant linear systems.
</p>
<p>
The package can also handle circulant Toeplitz systems, and
some other more complicated but related forms.
</p>
<p>
The <b>TOEPLITZ</b> package was written in the early 1980's by
a joint working group of American and Soviet mathematicians.
</p>
<p>
The original, true, correct version of TOEPLITZ is available
in the TOEPLITZ subdirectory of
<a href = "http://www.netlib.org/">the NETLIB web site</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/blas1/blas1.html">
BLAS1</a>,
a FORTRAN90 library which
contains the level 1 Basic Linear
Algebra Subprograms.
</p>
<p>
<a href = "../../f_src/linpack/linpack.html">
LINPACK</a>,
a FORTRAN90 library which
carries out the factorization and solution
of linear systems of a variety of types.
</p>
<p>
<a href = "../../f_src/linplus/linplus.html">
LINPLUS</a>,
a FORTRAN90 library which
includes some routines for manipulating Toeplitz matrices.
</p>
<p>
<a href = "../../f_src/test_mat/test_mat.html">
TEST_MAT</a>,
a FORTRAN90 library which
includes some routines which define sample Toeplitz matrices.
</p>
<p>
<a href = "../../f_src/toeplitz_cholesky/toeplitz_cholesky.html">
TOEPLITZ_CHOLESKY</a>,
a FORTRAN90 library which
computes the Cholesky factorization of a nonnegative definite symmetric
Toeplitz matrix.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Oleg Arushanian, MK Samarin, Valentin Voevodin, Evgeny Tyrtyshnikov,
Burton Garbow, James Boyle, Wayne Cowell, Kenneth Dritz,<br>
The TOEPLITZ Package User's Guide,<br>
Argonne National Laboratory,<br>
ANL-83-16, 1983.
</li>
<li>
Jack Dongarra, Jim Bunch, Cleve Moler, Pete Stewart,<br>
LINPACK User's Guide,<br>
SIAM, 1979,<br>
ISBN13: 978-0-898711-72-1.
</li>
<li>
Charles Lawson, Richard Hanson, David Kincaid, Fred Krogh,<br>
Basic Linear Algebra Subprograms for Fortran Usage,<br>
Algorithm 539,<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 = "toeplitz.f90">toeplitz.f90</a>, the source code.
</li>
<li>
<a href = "toeplitz.sh">toeplitz.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "toeplitz_prb.f90">toeplitz_prb.f90</a>, a sample problem.
</li>
<li>
<a href = "toeplitz_prb.sh">toeplitz_prb.sh</a>,
commands to compile, link and run the sample problem.
</li>
<li>
<a href = "toeplitz_prb_output.txt">toeplitz_prb_output.txt</a>, sample problem
output.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>C4_ABS1</b> computes the L1 absolute value of a complex number.
</li>
<li>
<b>C4_SWAP</b> swaps two complex values.
</li>
<li>
<b>CAXPY</b> adds a constant times one vector to another.
</li>
<li>
<b>CBTO_SL</b> solves the complex block Toeplitz linear system A * X = B.
</li>
<li>
<b>CCCC_SL</b> solves the complex double column circulant system A * X = B.
</li>
<li>
<b>CCCG_SL</b> solves the complex CCG linear system A * X = B.
</li>
<li>
<b>CCC_SL</b> solves the complex column circulant system A * X = B.
</li>
<li>
<b>CCCT_SL</b> solves the complex CCT linear system A * X = B..
</li>
<li>
<b>CCG_SL</b> solves the complex CG linear system A * X = B.
</li>
<li>
<b>CCI_MXV</b> multiplies a complex circulant matrix times a vector.
</li>
<li>
<b>CCI_PRINT</b> prints a complex circulant matrix.
</li>
<li>
<b>CCI_PRINT_SOME</b> prints some of a complex circulant matrix.
</li>
<li>
<b>CCI_RANDOM</b> randomizes a complex circulant matrix.
</li>
<li>
<b>CCI_SL</b> solves the complex circulant system A * X = B.
</li>
<li>
<b>CCTG_SL</b> solves the complex CTG linear system A * X = B.
</li>
<li>
<b>CCT_SL</b> solves the complex CT linear system A * X = B.
</li>
<li>
<b>CDOTC</b> forms the dot product of two vectors, conjugating the first.
</li>
<li>
<b>CGEFA</b> factors a complex matrix by gaussian elimination.
</li>
<li>
<b>CGESL</b> solves the complex general system A * X = B.
</li>
<li>
<b>CSALW</b> Fourier transforms the rows of a complex rectangular matrix.
</li>
<li>
<b>CSCAL</b> scales a complex vector by a constant.
</li>
<li>
<b>CSSCAL</b> scales a complex vector by a real constant.
</li>
<li>
<b>CTG_SL</b> solves a linear system involving a complex TG matrix.
</li>
<li>
<b>CTG_SL1</b> solves a CTG linear system.
</li>
<li>
<b>CTO_MXV</b> multiplies a complex Toeplitz matrix times a vector.
</li>
<li>
<b>CTO_PRINT</b> prints a complex Toeplitz matrix.
</li>
<li>
<b>CTO_PRINT_SOME</b> prints some of a complex Toeplitz matrix.
</li>
<li>
<b>CTO_RANDOM</b> randomizes a complex Toeplitz matrix.
</li>
<li>
<b>CTO_SL</b> solves the complex Toeplitz system A * X = B.
</li>
<li>
<b>CTO_VXM</b> multiplies a vector times a complex Toeplitz matrix.
</li>
<li>
<b>CTRDI</b> computes the determinant and inverse of a complex triangular matrix.
</li>
<li>
<b>CVEC_INDICATOR</b> sets a complex vector to the indicator vector.
</li>
<li>
<b>CVEC_PRINT</b> prints a complex vector, with an optional title.
</li>
<li>
<b>CVEC_PRINT_SOME</b> prints some of a complex vector.
</li>
<li>
<b>CVEC_RANDOM</b> returns a random complex vector in a given range.
</li>
<li>
<b>ICAMAX</b> finds the index of element having maximum absolute value.
</li>
<li>
<b>ISAMAX</b> finds the index of the vector element of maximum absolute value.
</li>
<li>
<b>R4_RANDOM</b> returns a random real in a given range.
</li>
<li>
<b>R4VEC_INDICATOR</b> sets a real vector to the indicator vector.
</li>
<li>
<b>R4VEC_PRINT</b> prints a real vector.
</li>
<li>
<b>R4VEC_PRINT_SOME</b> prints "some" of a real vector.
</li>
<li>
<b>R4VEC_RANDOM</b> returns a random real vector in a given range.
</li>
<li>
<b>SAMAX</b> returns the maximum absolute value of the entries in a vector.
</li>
<li>
<b>SAXPY</b> adds a constant times one vector to another.
</li>
<li>
<b>SBTO_MXV</b> computes the real block Toeplitz matrix product A * X = B.
</li>
<li>
<b>SBTO_PRINT</b> prints a block Toeplitz matrix.
</li>
<li>
<b>SBTO_PRINT_SOME</b> prints some of a block Toeplitz matrix.
</li>
<li>
<b>SBTO_SL</b> solves the real block Toeplitz linear system A * X = B.
</li>
<li>
<b>SBTO_TO_SGE</b> converts a block Toeplitz matrix to a Linpack General matrix.
</li>
<li>
<b>SBTO_VXM</b> computes the real block Toeplitz matrix product X * A = B.
</li>
<li>
<b>SCC_QR</b> computes the QR factorization of a real M by L column circulant matrix.
</li>
<li>
<b>SCNRM2</b> computes the unitary norm of a complex vector.
</li>
<li>
<b>SDOT</b> forms the dot product of two vectors.
</li>
<li>
<b>SGEFA</b> factors a real matrix.
</li>
<li>
<b>SGESL</b> solves a real general linear system A * X = B.
</li>
<li>
<b>SNRM2</b> computes the Euclidean norm of a vector.
</li>
<li>
<b>SSCAL</b> scales a vector by a constant.
</li>
<li>
<b>STO_MXV</b> multiplies a Toeplitz matrix times a vector.
</li>
<li>
<b>STO_PRINT</b> prints a Toeplitz matrix.
</li>
<li>
<b>STO_PRINT_SOME</b> prints some of a Toeplitz matrix.
</li>
<li>
<b>STO_RANDOM</b> randomizes a Toeplitz matrix.
</li>
<li>
<b>STO_SL</b> solves the real Toeplitz system A * X = B.
</li>
<li>
<b>STO_VXM</b> multiplies a vector times a Toeplitz matrix.
</li>
<li>
<b>STRDI</b> computes the determinant and inverse of a real triangular matrix.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</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 13 November 2006.
</i>
<!-- John Burkardt -->
</body>
</html>