CG
Conjugate Gradient Solver for Linear Systems
CG
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.
Licensing:
The computer code and data files made available on this
web page are distributed under
the GNU LGPL license.
Languages:
CG is available in
a C version and
a C++ version and
a FORTRAN77 version and
a FORTRAN90 version and
a MATLAB version and
a Python version.
Related Data and Programs:
CG_RC,
a C library which
implements the conjugate gradient method for solving
a positive definite sparse linear system A*x=b,
using reverse communication.
SPARSE_DISPLAY,
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 builtin
MATLAB "spy" command.
WATHEN,
a C library which
compares storage schemes (full, banded, sparse triplet) and
solution strategies (Linpack full, Linpack banded, conjugate gradient)
for linear systems involving the Wathen matrix, which can arise when
solving a problem using the finite element method (FEM).
Reference:

Frank Beckman,
The Solution of Linear Equations by the Conjugate Gradient Method,
in Mathematical Methods for Digital Computers,
edited by John Ralston, Herbert Wilf,
Wiley, 1967,
ISBN: 0471706892,
LC: QA76.5.R3.

Jonathan Shewchuk,
An introduction to the conjugate gradient method without the
agonizing pain,
Edition 1.25, August 1994.
Source Code:

cg.c, the source code.

cg.h, the include file.
Examples and Tests:
List of Routines:

I4_MIN returns the smaller of two I4's.

ORTH_RANDOM returns the ORTH_RANDOM matrix.

PDS_RANDOM returns the PDS_RANDOM matrix.

R8_NORMAL_01 samples the standard normal probability distribution.

R8_SIGN returns the sign of an R8.

R8_UNIFORM_01 returns a unit pseudorandom R8.

R83_CG uses the conjugate gradient method on an R83 system.

R83_DIF2 returns the DIF2 matrix in R83 format.

R83_MV multiplies a R83 matrix times a vector.

R83_RESID computes the residual R = BA*X for R83 matrices.

R83S_CG uses the conjugate gradient method on an R83S system.

R83S_DIF2 returns the DIF2 matrix in R83S format.

R83S_MV multiplies a R83S matrix times a vector.

R83S_RESID computes the residual R = BA*X for R83S matrices.

R83T_CG uses the conjugate gradient method on an R83T system.

R83T_DIF2 returns the DIF2 matrix in R83T format.

R83T_MV multiplies a R83T matrix times a vector.

R83T_RESID computes the residual R = BA*X for R83T matrices.

R8GE_CG uses the conjugate gradient method on an R8GE system.

R8GE_DIF2 returns the DIF2 matrix in R8GE format.

R8GE_MV multiplies an R8GE matrix by an R8VEC.

R8GE_RESID computes the residual R = BA*X for R8GE matrices.

R8MAT_COPY copies one R8MAT to another.

R8MAT_HOUSE_AXH computes A*H where H is a compact Householder matrix.

R8MAT_IDENTITY_NEW sets the square matrix A to the identity.

R8MAT_PRINT prints an R8MAT.

R8MAT_PRINT_SOME prints some of an R8MAT.

R8PBU_CG uses the conjugate gradient method on a R8PBU system.

R8PBU_DIF2 returns the DIF2 matrix in R8PBU format.

R8PBU_MV multiplies a R8PBU matrix times a vector.

R8PBU_RESID computes the residual R = BA*X for R8PBU matrices.

R8SD_CG uses the conjugate gradient method on a R8SD linear system.

R8SD_DIF2 returns the DIF2 matrix in R8SD format.

R8SD_MV multiplies a R8SD matrix times a vector.

R8SD_RESID computes the residual R = BA*X for R8SD matrices.

R8SP_CG uses the conjugate gradient method on a R8SP linear system.

R8SP_DIF2 returns the DIF2 matrix in R8SP format.

R8SP_MV multiplies a R8SP matrix times a vector.

R8SP_RESID computes the residual R = BA*X for R8SP matrices.

R8VEC_COPY copies an R8VEC.

R8VEC_DIFF_NORM returns the L2 norm of the difference of R8VEC's.

R8VEC_DOT_PRODUCT computes the dot product of a pair of R8VEC's.

R8VEC_HOUSE_COLUMN defines a Householder premultiplier that "packs" a column.

R8VEC_NORM returns the L2 norm of an R8VEC.

R8VEC_PRINT prints an R8VEC.

R8VEC_UNIFORM_01_NEW returns a unit pseudorandom R8VEC.

R8VEC_ZERO_NEW creates and zeroes an R8VEC.

TIMESTAMP prints the current YMDHMS date as a time stamp.
You can go up one level to
the C source codes.
Last revised on 09 July 2014.