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<html>
<head>
<title>
TEMPLATES - Iterative Solvers for Linear Systems
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
TEMPLATES <br> Iterative Solvers <br> for Linear Systems
</h1>
<hr>
<p>
<b>TEMPLATES</b>
is a FORTRAN90 library which
outlines the
most common iterative methods of solving a linear system.
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>TEMPLATES</b> is available in
<a href = "../../f77_src/templates/templates.html">a FORTRAN77 version</a> and
<a href = "../../f_src/templates/templates.html">a FORTRAN90 version</a> and
<a href = "../../m_src/templates/templates.html">a MATLAB version</a>
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/dlap/dlap.html">
DLAP</a>,
a FORTRAN90 library which
implements iterative methods for solving
linear systems.
</p>
<p>
<a href = "../../datasets/hbsmc/hbsmc.html">
HBSMC</a>,
a dataset directory which
contains large sparse matrices stored in the
Harwell-Boeing format.
</p>
<p>
<a href = "../../f_src/linpack/linpack.html">
LINPACK</a>,
a FORTRAN90 library which
carries out direct methods for solving linear systems.
</p>
<p>
<a href = "../../data/mm/mm.html">
MM</a>,
a data directory which
contains a description and
examples of the Matrix Market format for storing matrices.
</p>
<p>
<a href = "../../c_src/super_lu/super_lu.html">
SUPER_LU</a>,
a C program which
applies a fast direct solution method to
a sparse linear system.
</p>
<p>
<a href = "../../f_src/test_mat/test_mat.html">
TEST_MAT</a>,
a FORTRAN90 library
which defines test matrices.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Richard Barrett, Michael Berry, Tony Chan, James Demmel,
June Donato, Jack Dongarra, Victor Eijkhout, Roidan Pozo,
Charles Romine, Henk van der Vorst,<br>
Templates for the Solution of Linear Systems:<br>
Building Blocks for Iterative Methods,<br>
SIAM, 1994.
</li>
<li>
<a href = "http://www.netlib.org/templates/index.html">
http://www.netlib.org/templates/index.html</a> <br>
the TEMPLATES web site;
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "templates.f90">templates.f90</a>,
the source code.
</li>
<li>
<a href = "templates.sh">templates.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<b>JACOBI_GE_PRB</b> is a calling program that uses dense GE format
matrix storage, and the Jacobi iteration. Files you may
copy include:
<ul>
<li>
<a href = "jacobi_ge_prb.f90">jacobi_ge_prb.f90</a>,
the sample calling program.
</li>
<li>
<a href = "jacobi_ge_prb.sh">jacobi_ge_prb.sh</a>,
commands to compile, link and run the calling program.
</li>
<li>
<a href = "jacobi_ge_prb_output.txt">jacobi_ge_prb_output.txt</a>,
the output.
</li>
</ul>
</p>
<p>
<b>SOR_GE_PRB</b> is a calling program that uses dense GE format
matrix storage, and the Jacobi iteration. Files you may
copy include:
<ul>
<li>
<a href = "sor_ge_prb.f90">sor_ge_prb.f90</a>,
the sample calling program.
</li>
<li>
<a href = "sor_ge_prb.sh">sor_ge_prb.sh</a>,
commands to compile, link and run the calling program.
</li>
<li>
<a href = "sor_ge_prb_output.txt">sor_ge_prb_output.txt</a>,
the output.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>APPROXRES</b> approximates the residual using a Givens updating scheme.
</li>
<li>
<b>BICG</b> implements the BiConjugate Gradient method.
</li>
<li>
<b>BICG_REVCOM</b> is controlled by BICG using reverse communication.
</li>
<li>
<b>BICGSTAB</b> implements the BiConjugate Gradient Stabilized method.
</li>
<li>
<b>BICGSTAB_REVCOM</b> is controlled by BICGSTAB using reverse communication.
</li>
<li>
<b>CG</b> implements the Conjugate Gradient method.
</li>
<li>
<b>CG_REVCOM</b> is controlled by CG using reverse communication.
</li>
<li>
<b>CGS</b> implements the Conjugate Gradient Squared method.
</li>
<li>
<b>CGS_GE</b> implements the Conjugate Gradient Squared method for GE matrices.
</li>
<li>
<b>CGS_REVCOM</b> is controlled by CGS using reverse communication.
</li>
<li>
<b>CHEBY</b> implements the Chebyshev method.
</li>
<li>
<b>CHEBY_REVCOM</b> is controlled by CHEBY using reverse communication.
</li>
<li>
<b>DIF</b> returns the second difference matrix.
</li>
<li>
<b>ELEM_VEC</b> constructs the I-th elementary vector E, scaled by ALPHA.
</li>
<li>
<b>GETBREAK</b> is supposed to allow the user to set certain tolerances.
</li>
<li>
<b>GETEIG_GE</b> computes the eigenvalues of the iteration matrix for the GE format.
</li>
<li>
<b>GIVENS_APPLY</b> applies a sequence of Givens rotations to a column of H.
</li>
<li>
<b>GIVENS_SET</b> computes Givens rotation parameters.
</li>
<li>
<b>GMRES</b> implements the Generalized Minimal Residual method.
</li>
<li>
<b>GMRES_REVCOM</b> is controlled by GMRES using reverse communication.
</li>
<li>
<b>JACOBI_GE</b> implements the Jacobi method for a matrix in GE format.
</li>
<li>
<b>JACOBI_REVCOM</b> is controlled by JACOBI using reverse communication.
</li>
<li>
<b>JACOBI_SPLIT_GE</b> splits a GE matrix for the Jacobi algorithm.
</li>
<li>
<b>JACOBI_RECON_GE</b> reconstitutes a split GE matrix for the Jacobi algorithm.
</li>
<li>
<b>MATVEC_GE</b> computes Z := ALPHA * A * X + BETA * Y for a GE matrix.
</li>
<li>
<b>MATVEC_GB</b> computes Z := ALPHA * A * X + BETA * Y for a GB matrix.
</li>
<li>
<b>MVGE</b> is a version of the MATVEC routine which assumes that the
</li>
<li>
<b>ORTHOH</b> constructs the I-th column of the upper Hessenberg matrix H
</li>
<li>
<b>PSOLVE</b> calls the appropriate preconditioner solver.
</li>
<li>
<b>PSOLVE_JACOBI</b> ??
</li>
<li>
<b>PSOLVE_JACOBI_TRANS</b> solves the linear system Mx = b where matrix M is diagonal.
</li>
<li>
<b>PSOLVE_NONE</b> is for the unpreconditioned version, i.e. just does
</li>
<li>
<b>PSOLVE_NONE_TRANS</b> is for the unpreconditioned version, i.e. just does
</li>
<li>
<b>PSOLVE_Q</b> is a solver for QMR which requires left preconditioning
</li>
<li>
<b>PSOLVE_T</b> calls the appropriate solver.
</li>
<li>
<b>PSOLVE_T_Q</b> is a solver for QMR which requires right preconditioning.
</li>
<li>
<b>QMR</b> implements the Quasi-Minimal Residual method.
</li>
<li>
<b>QMR_REVCOM</b> is controlled by QMR using reverse communication.
</li>
<li>
<b>RESID_GE</b> computes the residual A*X-B when A is stored in GE format.
</li>
<li>
<b>ROTVEC</b> applies a Givens rotation to a vector (X,Y).
</li>
<li>
<b>R4VEC_PRINT_SOME</b> prints "some" of an R4VEC.
</li>
<li>
<b>SAMAX</b> returns the maximum absolute value of the entries in a vector.
</li>
<li>
<b>SGB_TO_SGE</b> converts a general band matrix to general matrix format.
</li>
<li>
<b>SGE_CHECK</b> checks the dimensions of a general matrix.
</li>
<li>
<b>SLT_SL</b> solves a lower triangular system.
</li>
<li>
<b>SNRM2</b> computes the Euclidean norm of a vector.
</li>
<li>
<b>SOR_GE</b> implements the Successive Over-Relaxation method for a GE matrix.
</li>
<li>
<b>SOR_REVCOM</b> is controlled by SOR using reverse communication.
</li>
<li>
<b>SOR_SPLIT_GE</b> splits a GE matrix for the SOR algorithm.
</li>
<li>
<b>SOR_RECON_GE</b> reconstructs the matrix A and right hand side B after splitting.
</li>
<li>
<b>STOPB</b> computes the stopping criterion on B.
</li>
<li>
<b>STOPX</b> computes the stopping criterion on X.
</li>
<li>
<b>SUT_MXV</b> computes A * x, where A is an upper triangular matrix.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
<li>
<b>UPDATE</b> ??
</li>
<li>
<b>VECGEN</b> generates a vector of all ones, zeros, or the row sum
</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>