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<html>
<head>
<title>
CG - Conjugate Gradient Solver for Linear Systems
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
CG <br> Conjugate Gradient Solver for Linear Systems
</h1>
<hr>
<p>
<b>CG</b>
is a MATLAB library which
implements a simple version of the conjugate gradient (CG) method
for solving a system of linear equations of the form A*x=b,
suitable for situations in which the matrix A is positive definite
(only real, positive eigenvalues) and symmetric.
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files 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>CG</b> is available in
<a href = "../../c_src/cg/cg.html">a C version</a> and
<a href = "../../cpp_src/cg/cg.html">a C++ version</a> and
<a href = "../../f77_src/cg/cg.html">a FORTRAN77 version</a> and
<a href = "../../f_src/cg/cg.html">a FORTRAN90 version</a> and
<a href = "../../m_src/cg/cg.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../m_src/cg_rc/cg_rc.html">
CG_RC</a>,
a MATLAB library which
implements the conjugate gradient method for solving
a positive definite sparse linear system A*x=b,
using reverse communication.
</p>
<p>
<a href = "../../m_src/linplus/linplus.html">
LINPLUS</a>,
a MATLAB library which
carries out operations such as matrix-vector products,
matrix factorization, linear solvers including Gauss-elimination,
Jacobi iteration, Gauss-Seidel iteration, Conjugate Gradient (CG),
for matrices in a variety of formats, including banded, border-banded,
circulant, lower triangular, pentadiagonal, sparse, symmetric,
toeplitz, tridiagonal, upper triangular and vandermonde formats.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Frank Beckman,<br>
The Solution of Linear Equations by the Conjugate Gradient Method,<br>
in Mathematical Methods for Digital Computers,<br>
edited by John Ralston, Herbert Wilf,<br>
Wiley, 1967,<br>
ISBN: 0471706892,<br>
LC: QA76.5.R3.
</li>
<li>
Jonathan Shewchuk,<br>
An introduction to the conjugate gradient method without the
agonizing pain,
Edition 1.25, August 1994.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "orth_random.m">orth_random.m</a>,
returns the ORTH_RANDOM matrix.
</li>
<li>
<a href = "pds_random.m">pds_random.m</a>,
returns the PDS_RANDOM matrix.
</li>
<li>
<a href = "r8_sign.m">r8_sign.m</a>,
returns the sign of an R8.
</li>
<li>
<a href = "r8_normal.m">r8_normal.m</a>,
returns a unit pseudonormal R8.
</li>
<li>
<a href = "r8_uniform_01.m">r8_uniform_01.m</a>,
returns a unit pseudorandom R8.
</li>
<li>
<a href = "r83_cg.m">r83_cg.m</a>,
uses the conjugate gradient method on an R83 system.
</li>
<li>
<a href = "r83_dif2.m">r83_dif2.m</a>,
returns the DIF2 matrix in R83 format.
</li>
<li>
<a href = "r83_mv.m">r83_mv.m</a>,
multiplies an R83 matrix times an R8VEC.
</li>
<li>
<a href = "r83_resid.m">r83_resid.m</a>,
computes the residual R = B-A*X for R83 matrices.
</li>
<li>
<a href = "r83s_cg.m">r83s_cg.m</a>,
uses the conjugate gradient method on an R83S system.
</li>
<li>
<a href = "r83s_dif2.m">r83s_dif2.m</a>,
returns the DIF2 matrix in R83S format.
</li>
<li>
<a href = "r83s_mv.m">r83s_mv.m</a>,
multiplies an R83S matrix times an R8VEC.
</li>
<li>
<a href = "r83s_resid.m">r83s_resid.m</a>,
computes the residual R = B-A*X for R83S matrices.
</li>
<li>
<a href = "r83t_cg.m">r83t_cg.m</a>,
uses the conjugate gradient method on an R83T system.
</li>
<li>
<a href = "r83t_dif2.m">r83t_dif2.m</a>,
returns the DIF2 matrix in R83T format.
</li>
<li>
<a href = "r83t_mv.m">r83t_mv.m</a>,
multiplies an R83T matrix times an R8VEC.
</li>
<li>
<a href = "r83t_resid.m">r83t_resid.m</a>,
computes the residual R = B-A*X for R83T matrices.
</li>
<li>
<a href = "r8ge_cg.m">r8ge_cg.m</a>,
uses the conjugate gradient method on an R8GE system.
</li>
<li>
<a href = "r8ge_dif2.m">r8ge_dif2.m</a>,
returns the DIF2 matrix in R8GE format.
</li>
<li>
<a href = "r8ge_mv.m">r8ge_mv.m</a>,
multiplies an R8GE matrix by an R8VEC.
</li>
<li>
<a href = "r8ge_resid.m">r8ge_resid.m</a>,
computes the residual R = B-A*X for R8GE matrices.
</li>
<li>
<a href = "r8mat_house_axh.m">r8mat_house_axh.m</a>,
computes A*H where H is a compact Householder matrix.
</li>
<li>
<a href = "r8mat_print.m">r8mat_print.m</a>,
prints an R8MAT.
</li>
<li>
<a href = "r8mat_print_some.m">r8mat_print_some.m</a>,
prints some of an R8MAT.
</li>
<li>
<a href = "r8pbu_cg.m">r8pbu_cg.m</a>,
uses the conjugate gradient method on an R8PBU system.
</li>
<li>
<a href = "r8pbu_dif2.m">r8pbu_dif2.m</a>,
returns the DIF2 matrix in R8PBU format.
</li>
<li>
<a href = "r8pbu_mv.m">r8pbu_mv.m</a>,
multiplies an R8PBU matrix by an R8VEC.
</li>
<li>
<a href = "r8pbu_resid.m">r8pbu_resid.m</a>,
computes the residual R = B-A*X for R8PBU matrices.
</li>
<li>
<a href = "r8sd_cg.m">r8sd_cg.m</a>,
uses the conjugate gradient method on an R8SD linear system.
</li>
<li>
<a href = "r8sd_dif2.m">r8sd_dif2.m</a>,
returns the DIF2 matrix in R8SD format.
</li>
<li>
<a href = "r8sd_mv.m">r8sd_mv.m</a>,
multiplies an R8SD matrix by an R8VEC.
</li>
<li>
<a href = "r8sd_resid.m">r8sd_resid.m</a>,
computes the residual R = B-A*X for R8SD matrices.
</li>
<li>
<a href = "r8sp_cg.m">r8sp_cg.m</a>,
uses the conjugate gradient method on an R8SP system.
</li>
<li>
<a href = "r8sp_dif2.m">r8sp_dif2.m</a>,
returns the DIF2 matrix in R8SP format.
</li>
<li>
<a href = "r8sp_mv.m">r8sp_mv.m</a>,
multiplies an R8SP matrix by an R8VEC.
</li>
<li>
<a href = "r8sp_resid.m">r8sp_resid.m</a>,
computes the residual R = B-A*X for R8SP matrices.
</li>
<li>
<a href = "r8vec_diff_norm.m">r8vec_diff_norm.m</a>,
returns the L2 norm of the difference of R8VEC's.
</li>
<li>
<a href = "r8vec_house_column.m">r8vec_house_column.m</a>,
defines a Householder premultiplier that "packs" a column.
</li>
<li>
<a href = "r8vec_norm.m">r8vec_norm.m</a>,
returns the L2 norm of an R8VEC.
</li>
<li>
<a href = "r8vec_print.m">r8vec_print.m</a>,
prints an R8VEC.
</li>
<li>
<a href = "r8vec_uniform_01.m">r8vec_uniform_01.m</a>,
returns a unit pseudorandom R8VEC.
</li>
<li>
<a href = "timestamp.m">timestamp.m</a>,
prints the current YMDHMS date as a time stamp.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "cg_test.m">cg_test.m</a>,
a sample calling program.
</li>
<li>
<a href = "cg_test_output.txt">cg_test_output.txt</a>,
the output file.
</li>
<li>
<a href = "cg_test01.m">cg_test01.m</a>,
tests R8GE_CG.
</li>
<li>
<a href = "cg_test02.m">cg_test02.m</a>,
tests R83_CG.
</li>
<li>
<a href = "cg_test023.m">cg_test023.m</a>,
tests R83S_CG.
</li>
<li>
<a href = "cg_test025.m">cg_test025.m</a>,
tests R83T_CG.
</li>
<li>
<a href = "cg_test03.m">cg_test03.m</a>,
tests R8PBU_CG.
</li>
<li>
<a href = "cg_test04.m">cg_test04.m</a>,
tests R8SD_CG.
</li>
<li>
<a href = "cg_test05.m">cg_test05.m</a>,
tests R8SP_CG.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../m_src.html">
the MATLAB source codes</a>.
</p>
<hr>
<i>
Last revised on 09 July 2014.
</i>
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