gmm_solver_qmr.h

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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