CG_RC
Conjugate Gradient Method with Reverse Communication

CG_RC is 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).

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

CG_RC is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

BACKTRACK_BINARY_RC, a C++ library which carries out a backtrack search for a set of binary decisions, using reverse communication (RC).

BISECTION_RC, a C++ library which seeks a solution to the equation F(X)=0 using bisection within a user-supplied change of sign interval [A,B]. The procedure is written using reverse communication (RC).

CG, 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.

JACOBI, a C++ library which implements the Jacobi iteration for solving symmetric positive definite systems of linear equations.

LINPLUS, a C++ library which carries out operations such as matrix-vector products, matrix factorization, direct and iterative linear solves for matrices in a variety of formats, including banded, border-banded, circulant, lower triangular, pentadiagonal, sparse, symmetric, toeplitz, tridiagonal, upper triangular and vandermonde formats.

MGMRES, a C++ library which applies the restarted GMRES algorithm to solve a sparse linear system.

SORT_RC, a C++ library which can sort a list of any kind of objects, using reverse communication (RC).

SUPERLU, C++ programs which illustrate how a C++ program can call the SUPERLU library, (which is written in C), which applies a fast direct solution method to solve sparse linear systems, by James Demmel, John Gilbert, and Xiaoye Li.

TEST_MAT, a C++ library which defines test matrices.

ZERO_RC, a C++ library which seeks solutions of a scalar nonlinear equation f(x) = 0, or a system of nonlinear equations, using reverse communication (RC).

Reference:

1. Richard Barrett, Michael Berry, Tony Chan, James Demmel, June Donato, Jack Dongarra, Victor Eijkhout, Roidan Pozo, Charles Romine, Henk van der Vorst,
   Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods,
   SIAM, 1994,
   ISBN: 0898714710,
   LC: QA297.8.T45.
2. Jonathan Shewchuk,
   An introduction to the conjugate gradient method without the agonizing pain,
   Edition 1.25, August 1994.

Source Code:

• cg_rc.cpp, the source code.
• cg_rc.hpp, the source code.
• cg_rc.sh, BASH commands to compile the source code.

Examples and Tests:

• cg_rc_prb.cpp, a sample calling program.
• cg_rc_prb.sh, BASH commands to compile and run the sample program.
• cg_rc_prb_output.txt, the output file.

List of Routines:

• CG_RC is a reverse communication conjugate gradient routine.
• R8VEC_UNIFORM_01_NEW returns a unit pseudorandom R8VEC.
• TIMESTAMP prints the current YMDHMS date as a time stamp.
• WATHEN returns the WATHEN matrix.
• WATHEN_ORDER returns the order of the WATHEN matrix.

You can go up one level to the C++ source codes.