Cgne.cxx

// Copyright (C) 2003-2009 Marc Duruflé
//
// This file is part of the linear-algebra library Seldon,
// http://seldon.sourceforge.net/.
//
// Seldon is free software; you can redistribute it and/or modify it under the
// terms of the GNU Lesser General Public License as published by the Free
// Software Foundation; either version 2.1 of the License, or (at your option)
// any later version.
//
// Seldon is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for
// more details.
//
// You should have received a copy of the GNU Lesser General Public License
// along with Seldon. If not, see http://www.gnu.org/licenses/.
 
 
#ifndef SELDON_FILE_ITERATIVE_CGNE_CXX
 
namespace Seldon
{
 
 
#ifdef SELDON_WITH_VIRTUAL
  template<class T, class Vector1>
  int Cgne(const VirtualMatrix<T>& A, Vector1& x, const Vector1& b,
           Preconditioner_Base<T>& M,
           Iteration<typename ClassComplexType<T>::Treal>& iter)
#else
  template <class Titer, class Matrix1, class Vector1, class Preconditioner>
  int Cgne(const Matrix1& A, Vector1& x, const Vector1& b,
           Preconditioner& M, Iteration<Titer> & iter)
#endif
  {
    const int N = A.GetM();
    if (N <= 0)
      return 0;
 
    typedef typename Vector1::value_type Complexe;
    Complexe rho, rho_1, alpha, beta, delta;
    Vector1 p(b), q(b), r(b), z(b);
    Complexe zero, one;
    SetComplexZero(zero);
    SetComplexOne(one);
    rho = one; rho_1 = zero;
 
    // x should be equal to 0
    // see Cg to understand implementation
    // we solve A^t A x = A^t b
    // left-preconditioner is equal to M M^t
 
    // q = A^t (b - A x)
    if (!iter.IsInitGuess_Null())
      iter.MltAdd(-one, A, x, one, r);
    else
      x.Fill(zero);
    
    iter.Mlt(SeldonTrans, A, r, q);
    Copy(q, r);
    
    // we initialize iter
    int success_init = iter.Init(q);
    if (success_init != 0)
      return iter.ErrorCode();
    
    iter.SetNumberIteration(0);
    // Loop until the stopping criteria are satisfied
    while (! iter.Finished(r))
      {
        // Preconditioning
        M.TransSolve(A, r, q);
        M.Solve(A, q, z);
 
        rho = DotProd(r, z);
        if (rho == zero)
          {
            iter.Fail(1, "Cgne breakdown #1");
            break;
          }
 
        if (iter.First())
          Copy(z, p);
        else
          {
            beta = rho / rho_1;
            Mlt(beta, p);
            Add(one, z, p);
          }
        
        // instead of q = A*p, we compute q = A^t A *p
        iter.Mlt(A, p, q);
        iter.Mlt(SeldonTrans, A, q, z);
        
        delta = DotProd(p, z);
        if (delta == zero)
          {
            iter.Fail(2, "Cgne breakdown #2");
            break;
          }
        alpha = rho / delta;
 
        Add(alpha, p, x);
        Add(-alpha, z, r);
 
        rho_1 = rho;
 
        // two iterations, because of two multiplications with A
        ++iter;
        ++iter;
      }
 
    return iter.ErrorCode();
  }
 
 
} // end namespace
 
#define SELDON_FILE_ITERATIVE_CGNE_CXX
#endif