computation/solver/iterative/BiCg.cxx

// Copyright (C) 2003-2009 Marc Duruflé
// Copyright (C) 2001-2009 Vivien Mallet
//
// 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_BICG_CXX

namespace Seldon
{


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

    typedef typename Vector1::value_type Complexe;
    Complexe rho_1, rho_2(0), alpha, beta, delta;

    Vector1 r(b), z(b), p(b), q(b);
    Vector1 r_tilde(b), z_tilde(b), p_tilde(b), q_tilde(b);

    // we initialize iter
    int success_init = iter.Init(b);
    if (success_init != 0)
      return iter.ErrorCode();

    // we compute the residual r = b - Ax
    Copy(b, r);
    if (!iter.IsInitGuess_Null())
      MltAdd(Complexe(-1), A, x, Complexe(1), r);
    else
      x.Zero();

    Copy(r, r_tilde);

    iter.SetNumberIteration(0);
    // Loop until the stopping criteria are reached
    while (! iter.Finished(r))
      {
        // preconditioning z = M^{-1} r and z_tilde = M^{-t} r_tilde
        M.Solve(A, r, z);
        M.TransSolve(A, r_tilde, z_tilde);
        // rho_1 = (z,r_tilde)
        rho_1 = DotProd(z, r_tilde);

        if (rho_1 == Complexe(0))
          {
            iter.Fail(1, "Bicg breakdown #1");
            break;
          }

        if (iter.First())
          {
            Copy(z, p);
            Copy(z_tilde, p_tilde);
          }
        else
          {
            // p=beta*p+z  where beta = rho_i/rho_{i-1}
            // p_tilde=beta*p_tilde+z_tilde
            beta = rho_1 / rho_2;
            Mlt(beta, p);
            Add(Complexe(1), z, p);
            Mlt(beta, p_tilde);
            Add(Complexe(1), z_tilde, p_tilde);
          }

        // we do the product matrix vector and transpose matrix vector
        // q = A*p    q_tilde = A^t p_tilde
        Mlt(A, p, q);
        ++iter;
        Mlt(SeldonTrans, A, p_tilde, q_tilde);

        delta = DotProd(p_tilde, q);
        if (delta == Complexe(0))
          {
            iter.Fail(2, "Bicg breakdown #2");
            break;
          }

        alpha = rho_1 / delta;

        // the new iterate x=x+alpha*p and residual r=r-alpha*q
        // where alpha = rho_i/delta
        Add(alpha, p, x);
        Add(-alpha, q, r);
        Add(-alpha, q_tilde, r_tilde);

        rho_2 = rho_1;

        ++iter;
      }

    return iter.ErrorCode();
  }

}

#define SELDON_FILE_ITERATIVE_BICG_CXX
#endif