/usr/include/gmm/gmm_solver_qmr.h is in libgmm-dev 4.0.0-0ubuntu1.
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//===========================================================================
//
// Copyright (C) 1997-2008 Yves Renard
//
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//===========================================================================
// This file is a modified version of qmr.h from ITL.
// See http://osl.iu.edu/research/itl/
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/**@file gmm_solver_qmr.h
@author Andrew Lumsdaine <lums@osl.iu.edu>
@author Lie-Quan Lee <llee@osl.iu.edu>
@author Yves Renard <Yves.Renard@insa-lyon.fr>
@date October 13, 2002.
@brief Quasi-Minimal Residual iterative solver.
*/
#ifndef GMM_QMR_H
#define GMM_QMR_H
#include "gmm_kernel.h"
#include "gmm_iter.h"
namespace gmm {
/** Quasi-Minimal Residual.
This routine solves the unsymmetric linear system Ax = b using
the Quasi-Minimal Residual method.
See: R. W. Freund and N. M. Nachtigal, A quasi-minimal residual
method for non-Hermitian linear systems, Numerical Math.,
60(1991), pp. 315-339
Preconditioner - Incomplete LU, Incomplete LU with threshold,
SSOR or identity_preconditioner.
*/
template <typename Matrix, typename Vector, typename VectorB,
typename Precond1>
void qmr(const Matrix &A, Vector &x, const VectorB &b, const Precond1 &M1,
iteration& iter) {
typedef typename linalg_traits<Vector>::value_type T;
typedef typename number_traits<T>::magnitude_type R;
T delta(0), ep(0), beta(0), theta_1(0), gamma_1(0);
T theta(0), gamma(1), eta(-1);
R rho_1(0), rho, xi;
typedef typename temporary_vector<Vector>::vector_type TmpVec;
size_type nn = vect_size(x);
TmpVec r(nn), v_tld(nn), y(nn), w_tld(nn), z(nn), v(nn), w(nn);
TmpVec y_tld(nn), z_tld(nn), p(nn), q(nn), p_tld(nn), d(nn), s(nn);
iter.set_rhsnorm(double(gmm::vect_norm2(b)));
if (iter.get_rhsnorm() == 0.0) { clear(x); return; }
gmm::mult(A, gmm::scaled(x, T(-1)), b, r);
gmm::copy(r, v_tld);
gmm::left_mult(M1, v_tld, y);
rho = gmm::vect_norm2(y);
gmm::copy(r, w_tld);
gmm::transposed_right_mult(M1, w_tld, z);
xi = gmm::vect_norm2(z);
while (! iter.finished_vect(r)) {
if (rho == R(0) || xi == R(0)) {
if (iter.get_maxiter() == size_type(-1))
{ GMM_ASSERT1(false, "QMR failed to converge"); }
else { GMM_WARNING1("QMR failed to converge"); return; }
}
gmm::copy(gmm::scaled(v_tld, T(R(1)/rho)), v);
gmm::scale(y, T(R(1)/rho));
gmm::copy(gmm::scaled(w_tld, T(R(1)/xi)), w);
gmm::scale(z, T(R(1)/xi));
delta = gmm::vect_sp(z, y);
if (delta == T(0)) {
if (iter.get_maxiter() == size_type(-1))
{ GMM_ASSERT1(false, "QMR failed to converge"); }
else { GMM_WARNING1("QMR failed to converge"); return; }
}
gmm::right_mult(M1, y, y_tld);
gmm::transposed_left_mult(M1, z, z_tld);
if (iter.first()) {
gmm::copy(y_tld, p);
gmm::copy(z_tld, q);
} else {
gmm::add(y_tld, gmm::scaled(p, -(T(xi * delta) / ep)), p);
gmm::add(z_tld, gmm::scaled(q, -(T(rho * delta) / ep)), q);
}
gmm::mult(A, p, p_tld);
ep = gmm::vect_sp(q, p_tld);
if (ep == T(0)) {
if (iter.get_maxiter() == size_type(-1))
{ GMM_ASSERT1(false, "QMR failed to converge"); }
else { GMM_WARNING1("QMR failed to converge"); return; }
}
beta = ep / delta;
if (beta == T(0)) {
if (iter.get_maxiter() == size_type(-1))
{ GMM_ASSERT1(false, "QMR failed to converge"); }
else { GMM_WARNING1("QMR failed to converge"); return; }
}
gmm::add(p_tld, gmm::scaled(v, -beta), v_tld);
gmm::left_mult(M1, v_tld, y);
rho_1 = rho;
rho = gmm::vect_norm2(y);
gmm::mult(gmm::transposed(A), q, w_tld);
gmm::add(w_tld, gmm::scaled(w, -beta), w_tld);
gmm::transposed_right_mult(M1, w_tld, z);
xi = gmm::vect_norm2(z);
gamma_1 = gamma;
theta_1 = theta;
theta = rho / (gamma_1 * beta);
gamma = T(1) / gmm::sqrt(T(1) + gmm::sqr(theta));
if (gamma == T(0)) {
if (iter.get_maxiter() == size_type(-1))
{ GMM_ASSERT1(false, "QMR failed to converge"); }
else { GMM_WARNING1("QMR failed to converge"); return; }
}
eta = -eta * T(rho_1) * gmm::sqr(gamma) / (beta * gmm::sqr(gamma_1));
if (iter.first()) {
gmm::copy(gmm::scaled(p, eta), d);
gmm::copy(gmm::scaled(p_tld, eta), s);
} else {
T tmp = gmm::sqr(theta_1 * gamma);
gmm::add(gmm::scaled(p, eta), gmm::scaled(d, tmp), d);
gmm::add(gmm::scaled(p_tld, eta), gmm::scaled(s, tmp), s);
}
gmm::add(d, x);
gmm::add(gmm::scaled(s, T(-1)), r);
++iter;
}
}
}
#endif
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