tempest/resources/3rdparty/gmm-5.0/include/gmm/gmm_solver_bicgstab.h

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// This file is a modified version of bicgstab.h from ITL.
// See http://osl.iu.edu/research/itl/
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/**@file gmm_solver_bicgstab.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 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__