gmm_solver_bicgstab.h

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// This file is a modified version of bicgstab.h from ITL.
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/**@file gmm_solver_bicgstab.h
   @author Andrew Lumsdaine <[email protected]>
   @author Lie-Quan Lee <[email protected]>
   @author  Yves Renard <[email protected]>
   @date October 13, 2002.
   @brief BiCGStab iterative solver.
*/
 
#ifndef GMM_SOLVER_BICGSTAB_H__
#define GMM_SOLVER_BICGSTAB_H__
 
#include "gmm_kernel.h"
#include "gmm_iter.h"
 
namespace gmm {
 
  /* ******************************************************************** */
  /*            BiConjugate Gradient Stabilized                           */
  /* (preconditionned, with parametrable scalar product)                  */
  /* ******************************************************************** */
 
  template <typename Matrix, typename Vector, typename VectorB,
            typename Preconditioner>
  void bicgstab(const Matrix& A, Vector& x, const VectorB& b,
               const Preconditioner& M, iteration &iter) {
 
    typedef typename linalg_traits<Vector>::value_type T;
    typedef typename number_traits<T>::magnitude_type R;
    typedef typename temporary_dense_vector<Vector>::vector_type temp_vector;
    
    T rho_1, rho_2(0), alpha(0), beta, omega(0);
    temp_vector p(vect_size(x)), phat(vect_size(x)), s(vect_size(x)),
      shat(vect_size(x)), 
      t(vect_size(x)), v(vect_size(x)), r(vect_size(x)), rtilde(vect_size(x));
    
    gmm::mult(A, gmm::scaled(x, -T(1)), b, r);    
    gmm::copy(r, rtilde);
    R norm_r = gmm::vect_norm2(r);
    iter.set_rhsnorm(gmm::vect_norm2(b));
 
    if (iter.get_rhsnorm() == 0.0) { clear(x); return; }
    
    while (!iter.finished(norm_r)) {
      
      rho_1 = gmm::vect_sp(rtilde, r);
      if (rho_1 == T(0)) {
        if (iter.get_maxiter() == size_type(-1)) 
          { GMM_ASSERT1(false, "Bicgstab failed to converge"); }
        else { GMM_WARNING1("Bicgstab failed to converge"); return; }
      }
      
      if (iter.first())
        gmm::copy(r, p);
      else {
        if (omega == T(0)) {
          if (iter.get_maxiter() == size_type(-1))
            { GMM_ASSERT1(false, "Bicgstab failed to converge"); }
          else { GMM_WARNING1("Bicgstab failed to converge"); return; }
        }
        
        beta = (rho_1 / rho_2) * (alpha / omega);
        
        gmm::add(gmm::scaled(v, -omega), p);
        gmm::add(r, gmm::scaled(p, beta), p);      
      }
      gmm::mult(M, p, phat);
      gmm::mult(A, phat, v);    
      alpha = rho_1 / gmm::vect_sp(v, rtilde);
      gmm::add(r, gmm::scaled(v, -alpha), s);
      
      if (iter.finished_vect(s)) 
        { gmm::add(gmm::scaled(phat, alpha), x); break; }
      
      gmm::mult(M, s, shat);    
      gmm::mult(A, shat, t);
      omega = gmm::vect_sp(t, s) / gmm::vect_norm2_sqr(t);
      
      gmm::add(gmm::scaled(phat, alpha), x); 
      gmm::add(gmm::scaled(shat, omega), x);
      gmm::add(s, gmm::scaled(t, -omega), r); 
      norm_r = gmm::vect_norm2(r);
      rho_2 = rho_1;
      
      ++iter;
    }
  }
  
  template <typename Matrix, typename Vector, typename VectorB,
            typename Preconditioner>
  void bicgstab(const Matrix& A, const Vector& x, const VectorB& b,
               const Preconditioner& M, iteration &iter)
  { bicgstab(A, linalg_const_cast(x), b, M, iter); }
  
}
 
 
#endif //  GMM_SOLVER_BICGSTAB_H__