computation/solver/iterative/Lsqr.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_LSQR_CXX

namespace Seldon
{


  template <class Titer, class Matrix1, class Vector1, class Preconditioner>
  int Lsqr(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, rho_bar, phi, phi_bar, theta, c, s, tmp;
    Titer beta, alpha, rnorm;
    Vector1 v(b), v1(b), u(b), u1(b), w(b);

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

    Copy(b, u);
    if (!iter.IsInitGuess_Null())
      MltAdd(Complexe(-1), A, x, Complexe(1), u);
    else
      x.Zero();

    rnorm = Norm2(u);

    Copy(b, u);
    beta = Norm2(u);
    tmp = 1.0/beta; Mlt(tmp, u);
    // matrix vector product
    Mlt(SeldonTrans,A, u, v);
    alpha = Norm2(v);
    tmp = 1.0/alpha; Mlt(tmp, v);

    Copy(v,w); x.Zero();

    phi_bar = beta; rho_bar = alpha;

    iter.SetNumberIteration(0);
    // Loop until the stopping criteria are satisfied
    while (! iter.Finished(rnorm))
      {
        // matrix vector product u1 = A*v
        Mlt(A, v, u1);
        // u1 = u1 - alpha*u
        Add(-alpha, u, u1);
        beta = Norm2(u1);
        if (beta == Complexe(0) )
          {
            iter.Fail(1, "Lsqr breakdown #1");
            break;
          }
        tmp = 1.0/beta; Mlt(tmp, u1);

        // matrix vector  product v1 = A^t u1
        Mlt(SeldonTrans, A, u1, v1);
        // v1 = v1 - beta*v
        Add(-beta, v, v1);
        alpha = Norm2(v1);
        if (alpha == Complexe(0) )
          {
            iter.Fail(2, "Lsqr breakdown #2");
            break;
          }
        tmp = 1.0/alpha; Mlt(tmp, v1);

        rho = sqrt(rho_bar*rho_bar+beta*beta);
        if (rho == Complexe(0) )
          {
            iter.Fail(3, "Lsqr breakdown #3");
            break;
          }

        c       = rho_bar/rho;
        s       = beta / rho;
        theta   = s*alpha;
        rho_bar = -c * alpha;
        phi     = c * phi_bar;
        phi_bar = s * phi_bar;

        // x = x + (phi/rho) w
        tmp = phi/rho;
        Add(tmp, w, x);
        // w = v1 - (theta/rho) w
        tmp  = -theta/rho;
        Mlt(tmp,w); Add(Complexe(1), v1, w);

        rnorm = abs(phi_bar);

        Swap(u1,u); Swap(v1,v);

        ++iter;
        ++iter;
      }

    return iter.ErrorCode();
  }

} // end namespace

#define SELDON_FILE_ITERATIVE_LSQR_CXX
#endif