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Matrix data structures, linear solvers, least squares methods, eigenvalue, and singular value decompositions. For larger random dense matrices (above ~ 350 x 350) matrix-matrix multiplication C = A.B is about 50% faster than MTJ.

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/*
 * 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
 * Ax = b 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;
    }
}