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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.
/*
* 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;
import no.uib.cipr.matrix.Vector.Norm;
/**
* Quasi-Minimal Residual method. QMR solves the unsymmetric linear system
* Ax = b using the Quasi-Minimal Residual method. QMR uses two
* preconditioners, and by default these are the same preconditioner.
*
* @author Templates
*/
public class QMR extends AbstractIterativeSolver {
/**
* Left preconditioner
*/
private Preconditioner M1;
/**
* Right preconditioner
*/
private Preconditioner M2;
/**
* Vectors for use in the iterative solution process
*/
private Vector r, y, z, v, w, p, q, d, s, v_tld, w_tld, y_tld, z_tld,
p_tld;
/**
* Constructor for QMR. 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 QMR(Vector template) {
M1 = M;
M2 = M;
r = template.copy();
y = template.copy();
z = template.copy();
v = template.copy();
w = template.copy();
p = template.copy();
q = template.copy();
d = template.copy();
s = template.copy();
v_tld = template.copy();
w_tld = template.copy();
y_tld = template.copy();
z_tld = template.copy();
p_tld = template.copy();
}
/**
* Constructor for QMR. 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. Allows setting different
* right and left preconditioners.
*
* @param template
* Vector to use as template for the work vectors needed in the
* solution process
* @param M1
* Left preconditioner
* @param M2
* Right preconditioner
*/
public QMR(Vector template, Preconditioner M1, Preconditioner M2) {
this.M1 = M1;
this.M2 = M2;
r = template.copy();
y = template.copy();
z = template.copy();
v = template.copy();
w = template.copy();
p = template.copy();
q = template.copy();
d = template.copy();
s = template.copy();
v_tld = template.copy();
w_tld = template.copy();
y_tld = template.copy();
z_tld = template.copy();
p_tld = template.copy();
}
public Vector solve(Matrix A, Vector b, Vector x)
throws IterativeSolverNotConvergedException {
checkSizes(A, b, x);
double rho = 0, rho_1 = 0, xi = 0, gamma = 1., gamma_1 = 0, theta = 0, theta_1 = 0, eta = -1., delta = 0, ep = 0, beta = 0;
A.multAdd(-1, x, r.set(b));
v_tld.set(r);
M1.apply(v_tld, y);
rho = y.norm(Norm.Two);
w_tld.set(r);
M2.transApply(w_tld, z);
xi = z.norm(Norm.Two);
for (iter.setFirst(); !iter.converged(r, x); iter.next()) {
if (rho == 0)
throw new IterativeSolverNotConvergedException(
NotConvergedException.Reason.Breakdown, "rho", iter);
if (xi == 0)
throw new IterativeSolverNotConvergedException(
NotConvergedException.Reason.Breakdown, "xi", iter);
v.set(1 / rho, v_tld);
y.scale(1 / rho);
w.set(1 / xi, w_tld);
z.scale(1 / xi);
delta = z.dot(y);
if (delta == 0)
throw new IterativeSolverNotConvergedException(
NotConvergedException.Reason.Breakdown, "delta", iter);
M2.apply(y, y_tld);
M1.transApply(z, z_tld);
if (iter.isFirst()) {
p.set(y_tld);
q.set(z_tld);
} else {
p.scale(-xi * delta / ep).add(y_tld);
q.scale(-rho * delta / ep).add(z_tld);
}
A.mult(p, p_tld);
ep = q.dot(p_tld);
if (ep == 0)
throw new IterativeSolverNotConvergedException(
NotConvergedException.Reason.Breakdown, "ep", iter);
beta = ep / delta;
if (beta == 0)
throw new IterativeSolverNotConvergedException(
NotConvergedException.Reason.Breakdown, "beta", iter);
v_tld.set(-beta, v).add(p_tld);
M1.apply(v_tld, y);
rho_1 = rho;
rho = y.norm(Norm.Two);
A.transMultAdd(q, w_tld.set(-beta, w));
M2.transApply(w_tld, z);
xi = z.norm(Norm.Two);
gamma_1 = gamma;
theta_1 = theta;
theta = rho / (gamma_1 * beta);
gamma = 1 / Math.sqrt(1 + theta * theta);
if (gamma == 0)
throw new IterativeSolverNotConvergedException(
NotConvergedException.Reason.Breakdown, "gamma", iter);
eta = -eta * rho_1 * gamma * gamma / (beta * gamma_1 * gamma_1);
if (iter.isFirst()) {
d.set(eta, p);
s.set(eta, p_tld);
} else {
double val = theta_1 * theta_1 * gamma * gamma;
d.scale(val).add(eta, p);
s.scale(val).add(eta, p_tld);
}
x.add(d);
r.add(-1, s);
}
return x;
}
@Override
public void setPreconditioner(Preconditioner M) {
super.setPreconditioner(M);
M1 = M;
M2 = M;
}
}
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