/* * Copyright (C) 2003-2006 Bjørn-Ove Heimsund * * This file is part of MTJ. * * This library is free software; you can redistribute it and/or modify it * under the terms of the GNU Lesser General Public License as published by the * Free Software Foundation; either version 2.1 of the License, or (at your * option) any later version. * * This library is distributed in the hope that it will be useful, but WITHOUT * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or * FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License * for more details. * * You should have received a copy of the GNU Lesser General Public License * along with this library; if not, write to the Free Software Foundation, * Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */ /* * Derived from public domain software at http://www.netlib.org/templates */ package no.uib.cipr.matrix.sparse; import no.uib.cipr.matrix.Matrix; import no.uib.cipr.matrix.NotConvergedException; import no.uib.cipr.matrix.Vector; /** * Conjugate Gradients squared solver. CGS solves the unsymmetric linear system * <code>Ax = b</code> using the Conjugate Gradient Squared method * * @author Templates */ public class CGS extends AbstractIterativeSolver { /** * Vectors for use in the iterative solution process */ private Vector p, q, u, phat, qhat, vhat, uhat, sum, r, rtilde; /** * Constructor for CGS. Uses the given vector as template for creating * scratch vectors. Typically, the solution or the right hand side vector * can be passed, and the template is not modified * * @param template * Vector to use as template for the work vectors needed in the * solution process */ public CGS(Vector template) { p = template.copy(); q = template.copy(); u = template.copy(); phat = template.copy(); qhat = template.copy(); vhat = template.copy(); uhat = template.copy(); sum = template.copy(); r = template.copy(); rtilde = template.copy(); } public Vector solve(Matrix A, Vector b, Vector x) throws IterativeSolverNotConvergedException { checkSizes(A, b, x); double rho_1 = 0, rho_2 = 0, alpha = 0, beta = 0; A.multAdd(-1, x, r.set(b)); rtilde.set(r); for (iter.setFirst(); !iter.converged(r, x); iter.next()) { rho_1 = rtilde.dot(r); if (rho_1 == 0) throw new IterativeSolverNotConvergedException( NotConvergedException.Reason.Breakdown, "rho", iter); if (iter.isFirst()) { u.set(r); p.set(u); } else { beta = rho_1 / rho_2; u.set(r).add(beta, q); sum.set(q).add(beta, p); p.set(u).add(beta, sum); } M.apply(p, phat); A.mult(phat, vhat); alpha = rho_1 / rtilde.dot(vhat); q.set(-alpha, vhat).add(u); M.apply(sum.set(u).add(q), uhat); x.add(alpha, uhat); A.mult(uhat, qhat); r.add(-alpha, qhat); rho_2 = rho_1; } return x; } }