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/// This file is part of Rheolef.
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/// Copyright (C) 2000-2009 Pierre Saramito <Pierre.Saramito@imag.fr>
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/// Rheolef is free software; you can redistribute it and/or modify
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/// it under the terms of the GNU General Public License as published by
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/// the Free Software Foundation; either version 2 of the License, or
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/// (at your option) any later version.
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/// Rheolef is distributed in the hope that it will be useful,
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/// but WITHOUT ANY WARRANTY; without even the implied warranty of
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/// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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/// GNU General Public License for more details.
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/// You should have received a copy of the GNU General Public License
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/// along with Rheolef; if not, write to the Free Software
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/// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
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/// =========================================================================
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NAME: cgs - cgs-conjugate gradient method
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"int cgs" ("const Matrix &A, Vector &x, const Vector &b",
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| const Preconditioner &M, int &max_iter, Real &tol);
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The simplest call to 'cgs' has the folling form:
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| int status = cgs(a, x, b, EYE, 100, 1e-7);
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'cgs' solves the unsymmetric linear system Ax = b
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using the conjugate gradient squared method.
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The return value indicates convergence within max_iter (input)
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iterations (0), or no convergence within max_iter iterations (1).
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Upon successful return, output arguments have the following values:
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"x" approximate solution to Ax = b
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"max_iter" the number of iterations performed before the tolerance was reached
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"tol" the residual after the final iteration
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"cg", "bicg", "bichstab", class "csr", class "vec"
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'cgs' is an iterative template routine.
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'cgs' follows the algorithm described on p. 26 in
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Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods,
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R. Barrett, M. Berry, T. F. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout,
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R. Pozo, C. Romine, H. Van der Vorst,
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SIAM, 1994, "ftp.netlib.org/templates/templates.ps".
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The present implementation is inspired from "IML++ 1.2" iterative method library,
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"http://math.nist.gov/iml++".
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| Pierre.Saramito@imag.fr
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LMC-IMAG, 38041 Grenoble cedex 9, France
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// ========== [ method implementation ] ====================================
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template < class Matrix, class Vector, class Preconditioner, class Real >
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cgs(const Matrix &A, Vector &x, const Vector &b,
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const Preconditioner &M, int &max_iter, Real &tol)
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Real rho_1, rho_2=0, alpha, beta;
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Vector p, phat, q, qhat, vhat, u, uhat;
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if ((resid = norm(r) / normb) <= tol) {
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for (int i = 1; i <= max_iter; i++) {
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rho_1 = dot(rtilde, r);
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if (rho_1 == Real(0)) {
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tol = norm(r) / normb;
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beta = rho_1 / rho_2;
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p = u + beta * (q + beta * p);
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alpha = rho_1 / dot(rtilde, vhat);
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q = u - alpha * vhat;
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uhat = M.solve(u + q);
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if ((resid = norm(r) / normb) < tol) {
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#endif // _SKIT_CGS_H
added
removed
skit/lib/cgs.h
