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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;

/**
 * BiCG stabilized solver. BiCGstab solves the unsymmetric linear system
 * Ax = b using the Preconditioned BiConjugate Gradient Stabilized
 * method
 * 
 * @author Templates
 */
public class BiCGstab extends AbstractIterativeSolver {

    /**
     * Vectors for use in the iterative solution process
     */
    private Vector p, s, phat, shat, t, v, temp, r, rtilde;

    /**
     * Constructor for BiCGstab. 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 BiCGstab(Vector template) {
        p = template.copy();
        s = template.copy();
        phat = template.copy();
        shat = template.copy();
        t = template.copy();
        v = template.copy();
        temp = 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 = 1, rho_2 = 1, alpha = 1, beta = 1, omega = 1;

        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 (omega == 0)
                throw new IterativeSolverNotConvergedException(
                        NotConvergedException.Reason.Breakdown, "omega", iter);

            if (iter.isFirst())
                p.set(r);
            else {
                beta = (rho_1 / rho_2) * (alpha / omega);

                // temp = p - omega * v
                temp.set(-omega, v).add(p);

                // p = r + beta * temp = r + beta * (p - omega * v)
                p.set(r).add(beta, temp);
            }

            M.apply(p, phat);
            A.mult(phat, v);
            alpha = rho_1 / rtilde.dot(v);
            s.set(r).add(-alpha, v);

            x.add(alpha, phat);
            if (iter.converged(s, x))
                return x;

            M.apply(s, shat);
            A.mult(shat, t);
            omega = t.dot(s) / t.dot(t);
            x.add(omega, shat);
            r.set(s).add(-omega, t);

            rho_2 = rho_1;
        }

        return x;
    }
}