gmm_solver_cg.h

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// This file is a modified version of cg.h from ITL.
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/**@file gmm_solver_cg.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 Conjugate gradient iterative solver. 
*/
#ifndef GMM_SOLVER_CG_H__
#define GMM_SOLVER_CG_H__
 
#include "gmm_kernel.h"
#include "gmm_iter.h"
 
namespace gmm {
 
  /* ******************************************************************** */
  /*            conjugate gradient                                        */
  /* (preconditionned, with parametrable additional scalar product)       */
  /* ******************************************************************** */
 
  template <typename Matrix, typename Matps, typename Precond, 
            typename Vector1, typename Vector2>
  void cg(const Matrix& A, Vector1& x, const Vector2& b, const Matps& PS,
          const Precond &P, iteration &iter) {
 
    typedef typename temporary_dense_vector<Vector1>::vector_type temp_vector;
    typedef typename linalg_traits<Vector1>::value_type T;
 
    T rho, rho_1(0), a;
    temp_vector p(vect_size(x)), q(vect_size(x)), r(vect_size(x)),
      z(vect_size(x));
    iter.set_rhsnorm(gmm::sqrt(gmm::abs(vect_hp(PS, b, b))));
 
    if (iter.get_rhsnorm() == 0.0)
      clear(x);
    else {
      mult(A, scaled(x, T(-1)), b, r);
      mult(P, r, z);
      rho = vect_hp(PS, z, r);
      copy(z, p);
 
      while (!iter.finished_vect(r)) {
 
        if (!iter.first()) { 
          mult(P, r, z);
          rho = vect_hp(PS, z, r);
          add(z, scaled(p, rho / rho_1), p);
        }
        mult(A, p, q);
 
        a = rho / vect_hp(PS, q, p);    
        add(scaled(p, a), x);
        add(scaled(q, -a), r);
        rho_1 = rho;
 
        ++iter;
      }
    }
  }
 
  template <typename Matrix, typename Matps, typename Precond, 
            typename Vector1, typename Vector2>
  void cg(const Matrix& A, Vector1& x, const Vector2& b, const Matps& PS,
          const gmm::identity_matrix &, iteration &iter) {
 
    typedef typename temporary_dense_vector<Vector1>::vector_type temp_vector;
    typedef typename linalg_traits<Vector1>::value_type T;
 
    T rho, rho_1(0), a;
    temp_vector p(vect_size(x)), q(vect_size(x)), r(vect_size(x));
    iter.set_rhsnorm(gmm::sqrt(gmm::abs(vect_hp(PS, b, b))));
 
    if (iter.get_rhsnorm() == 0.0)
      clear(x);
    else {
      mult(A, scaled(x, T(-1)), b, r);
      rho = vect_hp(PS, r, r);
      copy(r, p);
 
      while (!iter.finished_vect(r)) {
 
        if (!iter.first()) { 
          rho = vect_hp(PS, r, r);
          add(r, scaled(p, rho / rho_1), p);
        }       
        mult(A, p, q);
        a = rho / vect_hp(PS, q, p);    
        add(scaled(p, a), x);
        add(scaled(q, -a), r);
        rho_1 = rho;
        ++iter;
      }
    }
  }
 
  template <typename Matrix, typename Matps, typename Precond, 
            typename Vector1, typename Vector2> inline 
  void cg(const Matrix& A, const Vector1& x, const Vector2& b, const Matps& PS,
         const Precond &P, iteration &iter)
  { cg(A, linalg_const_cast(x), b, PS, P, iter); }
 
  template <typename Matrix, typename Precond, 
            typename Vector1, typename Vector2> inline
  void cg(const Matrix& A, Vector1& x, const Vector2& b,
         const Precond &P, iteration &iter)
  { cg(A, x , b, identity_matrix(), P, iter); }
 
  template <typename Matrix, typename Precond, 
            typename Vector1, typename Vector2> inline
  void cg(const Matrix& A, const Vector1& x, const Vector2& b,
         const Precond &P, iteration &iter)
  { cg(A, x , b , identity_matrix(), P , iter); }
 
}
 
 
#endif //  GMM_SOLVER_CG_H__