computation/solver/iterative/QCgs.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_QCGS_CXX

namespace Seldon
{


  template <class Titer, class Matrix1, class Vector1, class Preconditioner>
  int QCgs(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, mu,nu,alpha,beta,sigma,delta;
    Vector1 p(b), q(b), r(b), rtilde(b), u(b),
      phat(b), r_qcgs(b), x_qcgs(b), v(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);
    rho_1 = Complexe(1);
    q.Zero(); p.Zero();
    Copy(r, r_qcgs); Copy(x, x_qcgs);
    Matrix<Complexe, Symmetric, RowSymPacked> bt_b(2,2),bt_b_m1(2,2);
    Vector<Complexe> bt_rn(2);

    iter.SetNumberIteration(0);
    // Loop until the stopping criteria are reached
    while (! iter.Finished(r_qcgs))
      {
        rho_2 = DotProd(rtilde, r);

        if (rho_1 == Complexe(0))
          {
            iter.Fail(1, "QCgs breakdown #1");
            break;
          }
        beta = rho_2/rho_1;

        // u = r + beta*q
        // p = beta*(beta*p +q) + u  where beta = rho_i/rho_{i-1}
        Copy(r, u);
        Add(beta, q, u);
        Mlt(beta, p);
        Add(Complexe(1), q, p);
        Mlt(beta, p);
        Add(Complexe(1), u, p);

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

        // product matrix vector vhat = A*phat
        Mlt(A, phat, v); ++iter;
        sigma = DotProd(rtilde, v);
        if (sigma == Complexe(0))
          {
            iter.Fail(2, "Qcgs breakdown #2");
            break;
          }
        // q = u-alpha*v  where alpha = rho_i/(rtilde,v)
        alpha = rho_2 /sigma;
        Copy(u, q);
        Add(-alpha, v, q);

        // u = u +q
        Add(Complexe(1), q, u);
        // x = x + alpha u
        Add(alpha, u, x);
        // preconditioning phat = M^{-1} u
        M.Solve(A, u, phat);
        // product matrix vector q = A*phat
        Mlt(A, phat, u);

        // r = r - alpha u
        Add(-alpha, u, r);
        // u = r_qcgs - r_n
        Copy(r_qcgs, u);
        Add(-Complexe(1), r, u);
        bt_b(0,0) = DotProd(u,u);
        bt_b(1,1) = DotProd(v,v);
        bt_b(1,0) = DotProd(u,v);

        // we compute inverse of bt_b
        delta = bt_b(0,0)*bt_b(1,1) - bt_b(1,0)*bt_b(0,1);
        if (delta == Complexe(0))
          {
            iter.Fail(3, "Qcgs breakdown #3");
            break;
          }
        bt_b_m1(0,0) = bt_b(1,1)/delta;
        bt_b_m1(1,1) = bt_b(0,0)/delta;
        bt_b_m1(1,0) = -bt_b(1,0)/delta;

        bt_rn(0) = -DotProd(u, r); bt_rn(1) = -DotProd(v, r);
        mu = bt_b_m1(0,0)*bt_rn(0)+bt_b_m1(0,1)*bt_rn(1);
        nu = bt_b_m1(1,0)*bt_rn(0)+bt_b_m1(1,1)*bt_rn(1);

        // smoothing step
        // r_qcgs = r + mu (r_qcgs - r) + nu v
        Copy(r, r_qcgs); Add(mu, u, r_qcgs);
        Add(nu, v, r_qcgs);
        // x_qcgs = x + mu (x_qcgs - x) - nu p
        Mlt(mu,x_qcgs);
        Add(Complexe(1)-mu, x, x_qcgs);
        Add(-nu, p, x_qcgs);

        rho_1 = rho_2;

        ++iter;
      }

    M.Solve(A, x_qcgs, x);
    return iter.ErrorCode();
  }

} // end namespace

#define SELDON_FILE_ITERATIVE_QCGS_CXX
#endif