computation/solver/iterative/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
{


  template <class Titer, class Matrix1, class Vector1, class Preconditioner>
  int Cgne(Matrix1& A, Vector1& x, const Vector1& b,
           Preconditioner& M, Iteration<Titer> & iter)
  {
    const int N = A.GetM();
    if (N <= 0)
      return 0;

    typedef typename Vector1::value_type Complexe;
    Complexe rho(1), rho_1(0), alpha, beta, delta;
    Vector1 p(b), q(b), r(b), z(b);
    Titer dp;

    // 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
    Mlt(SeldonTrans, A, b, q);
    // we initialize iter
    int success_init = iter.Init(q);
    if (success_init != 0)
      return iter.ErrorCode();

    if (!iter.IsInitGuess_Null())
      {
        // r = A^t b - A^t A x
        Mlt(A, x, p);
        Mlt(SeldonTrans, A, p, r); Mlt(Complexe(-1), r);
        Add(Complexe(1), q, r);
      }
    else
      {
        Copy(q, r);
        x.Zero();
      }

    dp = Norm2(q);
    iter.SetNumberIteration(0);
    // Loop until the stopping criteria are satisfied
    while (! iter.Finished(dp))
      {
        // Preconditioning
        M.TransSolve(A, r, q);
        M.Solve(A, q, z);

        rho = DotProd(r,z);
        if (rho == Complexe(0))
          {
            iter.Fail(1, "Cgne breakdown #1");
            break;
          }

        if (iter.First())
          Copy(z, p);
        else
          {
            beta = rho / rho_1;
            Mlt(beta, p);
            Add(Complexe(1), z, p);
          }

        // instead of q = A*p, we compute q = A^t A *p
        Mlt(A, p, q);
        Mlt(SeldonTrans, A, q, z);

        delta = DotProd(p, z);
        if (delta == Complexe(0))
          {
            iter.Fail(2, "Cgne breakdown #2");
            break;
          }
        alpha = rho / delta;

        Add(alpha, p, x);
        Add(-alpha, z, r);

        rho_1 = rho;
        dp = Norm2(r);

        // two iterations, because of two multiplications with A
        ++iter;
        ++iter;
      }

    return iter.ErrorCode();
  }


} // end namespace

#define SELDON_FILE_ITERATIVE_CGNE_CXX
#endif