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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 C++ 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 = "../../cpp_src/cg_rc/cg_rc.html">
CG_RC</a>,
a C++ library which
implements the conjugate gradient (CG) method for solving
a positive definite sparse linear system A*x=b,
using reverse communication (RC).
</p>
<p>
<a href = "../../cpp_src/linplus/linplus.html">
LINPLUS</a>,
a C++ 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>
<p>
<a href = "../../cpp_src/sparse_display/sparse_display.html">
SPARSE_DISPLAY</a>,
a C++ library which
can read information defining a matrix of numbers and display
the sparsity pattern or location of the nonzero elements using
gnuplot. This operation is already available in the built-in
MATLAB "spy" command.
</p>
<p>
<a href = "../../cpp_src/wathen/wathen.html">
WATHEN</a>,
a C++ library which
compares storage schemes (full, banded, sparse triplet) and
solution strategies (Linpack full, Linpack banded,
conjugate gradient (CG)) for linear systems involving the Wathen matrix,
which can arise when solving a problem using the
finite element method (FEM).
</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 = "cg.cpp">cg.cpp</a>, the source code.
</li>
<li>
<a href = "cg.hpp">cg.hpp</a>, the include file.
</li>
<li>
<a href = "cg.sh">cg.sh</a>,
BASH commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "cg_prb.cpp">cg_prb.cpp</a>
a sample calling program.
</li>
<li>
<a href = "cg_prb.sh">cg_prb.sh</a>,
BASH commands to compile and run the sample program.
</li>
<li>
<a href = "cg_prb_output.txt">cg_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>I4_MIN</b> returns the minimum of two I4's.
</li>
<li>
<b>ORTH_RANDOM</b> returns the ORTH_RANDOM matrix.
</li>
<li>
<b>PDS_RANDOM</b> returns the PDS_RANDOM matrix.
</li>
<li>
<b>R8_NORMAL_01</b> samples the standard normal probability distribution.
</li>
<li>
<b>R8_SIGN</b> returns the sign of an R8.
</li>
<li>
<b>R8_UNIFORM_01</b> returns a unit pseudorandom R8.
</li>
<li>
<b>R83_CG</b> uses the conjugate gradient method on an R83 system.
</li>
<li>
<b>R83_DIF2</b> returns the DIF2 matrix in R83 format.
</li>
<li>
<b>R83_MV</b> multiplies a R83 matrix times a vector.
</li>
<li>
<b>R83_RESID</b> computes the residual R = B-A*X for R83 matrices.
</li>
<li>
<b>R83S_CG</b> uses the conjugate gradient method on an R83S system.
</li>
<li>
<b>R83S_DIF2</b> returns the DIF2 matrix in R83S format.
</li>
<li>
<b>R83S_MV</b> multiplies a R83S matrix times a vector.
</li>
<li>
<b>R83S_RESID</b> computes the residual R = B-A*X for R83S matrices.
</li>
<li>
<b>R83T_CG</b> uses the conjugate gradient method on an R83T system.
</li>
<li>
<b>R83T_DIF2</b> returns the DIF2 matrix in R83T format.
</li>
<li>
<b>R83T_MV</b> multiplies a R83T matrix times a vector.
</li>
<li>
<b>R83T_RESID</b> computes the residual R = B-A*X for R83T matrices.
</li>
<li>
<b>R8GE_CG</b> uses the conjugate gradient method on an R8GE system.
</li>
<li>
<b>R8GE_DIF2</b> returns the DIF2 matrix in R8GE format.
</li>
<li>
<b>R8GE_MV</b> multiplies an R8GE matrix by an R8VEC.
</li>
<li>
<b>R8GE_RESID</b> computes the residual R = B-A*X for R8GE matrices.
</li>
<li>
<b>R8MAT_COPY</b> copies one R8MAT to another.
</li>
<li>
<b>R8MAT_HOUSE_AXH</b> computes A*H where H is a compact Householder matrix.
</li>
<li>
<b>R8MAT_IDENTITY_NEW</b> returns an identity matrix.
</li>
<li>
<b>R8MAT_PRINT</b> prints an R8MAT.
</li>
<li>
<b>R8MAT_PRINT_SOME</b> prints some of an R8MAT.
</li>
<li>
<b>R8MAT_ZERO_NEW</b> returns a new zeroed R8MAT.
</li>
<li>
<b>R8PBU_CG</b> uses the conjugate gradient method on a R8PBU system.
</li>
<li>
<b>R8PBU_DIF2</b> returns the DIF2 matrix in R8PBU format.
</li>
<li>
<b>R8PBU_MV</b> multiplies a R8PBU matrix times a vector.
</li>
<li>
<b>R8PBU_RESID</b> computes the residual R = B-A*X for R8PBU matrices.
</li>
<li>
<b>R8SD_CG</b> uses the conjugate gradient method on a R8SD linear system.
</li>
<li>
<b>R8SD_DIF2</b> returns the DIF2 matrix in R8SD format.
</li>
<li>
<b>R8SD_MV</b> multiplies a R8SD matrix times a vector.
</li>
<li>
<b>R8SD_RESID</b> computes the residual R = B-A*X for R8SD matrices.
</li>
<li>
<b>R8SP_CG</b> uses the conjugate gradient method on a R8SP linear system.
</li>
<li>
<b>R8SP_DIF2</b> returns the DIF2 matrix in R8SP format.
</li>
<li>
<b>R8SP_MV</b> multiplies a R8SP matrix times a vector.
</li>
<li>
<b>R8SP_RESID</b> computes the residual R = B-A*X for R8SP matrices.
</li>
<li>
<b>R8VEC_COPY</b> copies an R8VEC.
</li>
<li>
<b>R8VEC_DIFF_NORM</b> returns the L2 norm of the difference of R8VEC's.
</li>
<li>
<b>R8VEC_DOT_PRODUCT</b> computes the dot product of a pair of R8VEC's.
</li>
<li>
<b>R8VEC_HOUSE_COLUMN</b> defines a Householder premultiplier that "packs" a column.
</li>
<li>
<b>R8VEC_NORM</b> returns the L2 norm of an R8VEC.
</li>
<li>
<b>R8VEC_PRINT</b> prints an R8VEC.
</li>
<li>
<b>R8VEC_UNIFORM_01_NEW</b> returns a new unit pseudorandom R8VEC.
</li>
<li>
<b>R8VEC_ZERO_NEW</b> creates and zeroes an R8VEC.
</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 = "../cpp_src.html">
the C++ source codes</a>.
</p>
<hr>
<i>
Last revised on 09 July 2014.
</i>
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