computation/solver/iterative/BiCgStab.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_BICGSTAB_CXX

namespace Seldon
{


  template <class Titer, class Matrix1, class Vector1, class Preconditioner>
  int BiCgStab(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_2(0), alpha(0), beta, omega(0), sigma;
    Vector1 p(b), phat(b), s(b), shat(b), t(b), v(b), r(b), rtilde(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, rtilde);

    iter.SetNumberIteration(0);
    // Loop until the stopping criteria are satisfied
    while (! iter.Finished(r))
      {

        rho_1 = DotProdConj(rtilde, r);
        if (rho_1 == Complexe(0))
          {
            iter.Fail(1, "Bicgstab breakdown #1");
            break;
          }

        if (iter.First())
          Copy(r, p);
        else
          {
            if (omega == Complexe(0))
              {
                iter.Fail(2, "Bicgstab breakdown #2");
                break;
              }
            // p= r + beta*(p-omega*v)
            // beta = rho_i/rho_{i-1} * alpha/omega
            beta = (rho_1 / rho_2) * (alpha / omega);
            Add(-omega, v, p);
            Mlt(beta, p);
            Add(Complexe(1), r, p);
          }
        // preconditioning phat = M^{-1} p
        M.Solve(A, p, phat);

        // product matrix vector  v = A*phat
        Mlt(A, phat, v);

        // s=r-alpha*v  where alpha = rho_i / (v,rtilde)
        sigma = DotProdConj(rtilde, v);
        if (sigma == Complexe(0))
          {
            iter.Fail(3, "Bicgstab breakdown #3");
            break;
          }
        alpha = rho_1 / sigma;
        Copy(r, s);
        Add(-alpha, v, s);

        // we increment iter, bicgstab has two products matrix vector
        ++iter;
        if (iter.Finished(s))
          {
            // x=x+alpha*phat
            Add(alpha, phat, x);
            break;
          }

        // preconditioning shat = M^{-1} s
        M.Solve(A, s, shat);

        // product matrix vector t = A*shat
        Mlt(A, shat, t);

        omega = DotProdConj(t, s) / DotProdConj(t, t);

        // new iterate x=x+alpha*phat+omega*shat
        Add(alpha, phat, x);
        Add(omega, shat, x);

        // new residual r=s-omega*t
        Copy(s, r);
        Add(-omega, t, r);

        rho_2 = rho_1;

        ++iter;
      }

    return iter.ErrorCode();
  }

} // end namespace

#define SELDON_FILE_ITERATIVE_BICGSTAB_CXX
#endif