MinRes.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_MINRES_CXX
 
namespace Seldon
{
 
 
#ifdef SELDON_WITH_VIRTUAL
  template<class T, class Vector1>
  int MinRes(const VirtualMatrix<T>& A, Vector1& x, const Vector1& b,
             Preconditioner_Base<T>& M,
             Iteration<typename ClassComplexType<T>::Treal>& iter)
#else
  template <class Titer, class Matrix1, class Vector1, class Preconditioner>
  int MinRes(const Matrix1& A, Vector1& x, const Vector1& b,
             Preconditioner& M, Iteration<Titer> & iter)
#endif
  {
    const int N = A.GetM();
    if (N <= 0)
      return 0;
 
    typedef typename Vector1::value_type Complexe;
    Vector1 u_old(b), u(b), r(b), v_old(b), v(b),
      w_old(b), w(b), z(b), w_oold(b);
 
    Complexe dp, beta, ibeta, beta_old, alpha, eta, ceta;
    Complexe cold, coold, c, soold, sold, s, rho0, rho1, rho2, rho3;
    Complexe zero, one;
    SetComplexZero(zero);
    SetComplexOne(one);
 
    int success_init = iter.Init(b);
    if (success_init != 0)
      return iter.ErrorCode();
 
    Copy(b,r);
    // r = b - A x
    if (!iter.IsInitGuess_Null())
      iter.MltAdd(-one, A, x, one, r);
    else
      x.Fill(zero);
 
    u_old.Fill(zero); v_old.Fill(zero);
    w_old.Fill(zero); w.Fill(zero); w_oold.Fill(zero);
    
    // preconditioning
    M.Solve(A, r, z);
    dp = DotProd(r, z);
    dp = sqrt(dp); beta = dp; eta = beta;
    Copy(r, v); Copy(z, u);
 
    ibeta = one / beta;
    Mlt(ibeta, v); Mlt(ibeta, u);
 
    c = one; s = zero; cold = one; sold = zero;
    typedef typename ClassComplexType<Complexe>::Treal Treal;
    Treal np = Norm2(b);
 
    iter.SetNumberIteration(0);
    // Loop until the stopping criteria are satisfied
    while (!iter.Finished(np))
      {
        // matrix-vector product r = A*u
        iter.Mlt(A, u, r);
        alpha = DotProd(r, u);
        // preconditioning
        M.Solve(A, r, z);
 
        //  r = r - alpha v
        //  z = z - alpha u
        Add(-alpha, v, r);
        Add(-alpha, u, z);
        //  r = r - beta v_old
        //  z = z - beta u_old
        Add(-beta, v_old, r);
        Add(-beta, u_old, z);
 
        beta_old = beta;
 
        dp = DotProd(r, z);
        beta = sqrt(dp);
 
        // QR factorization
        coold = cold; cold = c; soold = sold; sold = s;
 
        rho0 = cold * alpha - coold * sold * beta_old;
        rho1 = sqrt(rho0*rho0 + beta*beta);
        rho2 = sold * alpha + coold * cold * beta_old;
        rho3 = soold * beta_old;
 
        // Givens rotation
        if (rho1 == zero)
          {
            iter.Fail(1, "Minres breakdown #1");
            break;
          }
        c = rho0 / rho1;
        s = beta / rho1;
 
        // update
        Copy(w_old, w_oold); Copy(w, w_old);
        Copy(u, w);
 
        Add(-rho2, w_old, w);
        Add(-rho3, w_oold, w);
        Mlt(one/rho1, w);
 
        ceta = c*eta;
        Add(ceta, w, x);
        eta = -s*eta;
 
        Copy(v, v_old); Copy(u, u_old);
        Copy(r, v); Copy(z, u);
        if (beta == zero)
          {
            iter.Fail(2, "MinRes breakdown #2");
            break;
          }
        ibeta = one/beta;
        Mlt(ibeta, v); Mlt(ibeta, u);
 
        // residual norm
        np *= abs(s);
        ++ iter;
      }
    return iter.ErrorCode();
  }
 
} // end namespace
 
#define SELDON_FILE_ITERATIVE_MINRES_CXX
#endif