computation/solver/iterative/BiCgcr.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_BICGCR_CXX

namespace Seldon
{


  template <class Titer, class Matrix1, class Vector1, class Preconditioner>
  int BiCgcr(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, mu, alpha, beta, tau;
    Vector1 v(b), w(b), s(b), z(b), p(b), a(b);
    v.Zero(); w.Zero(); s.Zero(); z.Zero();  p.Zero(); a.Zero();

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

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

    iter.SetNumberIteration(0);
    // s = M*v   p = s
    M.Solve(A, v, s); Copy(s, p);
    // a = A*p   w = M*a
    Mlt(A, p, a); M.Solve(A, a, w);
    // we made one product matrix vector
    ++iter;

    while (! iter.Finished(v))
      {
        rho = DotProd(w, v);
        mu = DotProd(w, a);

        // new iterate x = x + alpha*p0  where alpha = (r1,r0)/(p1,p1)
        if (mu == Complexe(0))
          {
            iter.Fail(1, "Bicgcr breakdown #1");
            break;
          }
        alpha = rho/mu;
        Add(alpha, p, x);

        // new residual r0 = r0 - alpha * p1
        // r1 = r1 - alpha*p2
        Add(-alpha, a, v);
        Add(-alpha, w, s);

        Mlt(A, s, z);
        tau = DotProd(w, z);

        if (tau == Complexe(0))
          {
            iter.Fail(2, "Bicgcr breakdown #2");
            break;
          }

        beta = tau/mu;

        Mlt(Complexe(-beta), p);
        Add(Complexe(1), s, p);
        Mlt(Complexe(-beta), a);
        Add(Complexe(1), z, a);

        M.Solve(A, a, w);

        ++iter;
      }

    return iter.ErrorCode();
  }

} // end namespace

#define SELDON_FILE_ITERATIVE_BICGCR_CXX
#endif