// 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_QMRSYM_CXX

namespace Seldon
{
  
  //! Solves linear system using Symmetric Quasi-Minimal Residual (SQMR)
  /*!
    Solves the symmetric linear system Ax = b using the
    Quasi-Minimal Residual method.
    
    See: R. W. Freund and N. M. Nachtigal, A quasi-minimal residual method for
    non-Hermitian linear systems, Numerical Math., 60(1991), pp. 315-339
    
    \param[in] A  Complex Symmetric Matrix
    \param[in,out] x  Vector on input it is the initial guess
    on output it is the solution
    \param[in] b  Right hand side of the linear system
    \param[in] M Left preconditioner
    \param[in] iter Iteration parameters
  */
  template <class Titer, class Matrix1, class Vector1, class Preconditioner>
  int QmrSym(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 delta, ep(0), beta;
    Titer  rho, rho_1;
    Complexe theta_1, gamma_1;
    Complexe theta(0), gamma(1), eta(-1);
    
    Vector1 r(b), y(b);
    Vector1 v(b), p_tld(b);
    Vector1 p(b), d(b), s(b);
    
    // we initialize iter
    int success_init = iter.Init(b);
    if (success_init != 0)
      return iter.ErrorCode();
    
    // r = b - Ax
    Copy(b, r);
    if (!iter.IsInitGuess_Null())
      MltAdd(Complexe(-1), A, x, Complexe(1), r);
    else
      x.Zero();
    
    Copy(r, v);
    
    M.Solve(A, v, y);
    rho = Norm2(y);
    
    iter.SetNumberIteration(0);
    // Loop until the stopping criteria are reached
    while (! iter.Finished(r))
      {
        
        if (rho == Titer(0))
          {
            iter.Fail(1, "Qmr breakdown #1");
            break;
          }
                  
        // v = v / rho
        // y = y / rho
        Mlt(Complexe(1./rho), v);
        Mlt(Complexe(1./rho), y);
        
        delta = DotProd(v, y);
        if (delta == Complexe(0))
          {
            iter.Fail(3, "Qmr breakdown #2");
            break;
          }
        
        if (iter.First())
          Copy(y, p);
        else
          {
            // p = y - (rho delta / ep) p
            Mlt(Complexe(-(rho  * delta / ep)), p);
            Add(Complexe(1), y, p);
          }
        
        // product matrix vector p_tld = A*p
        Mlt(A, p, p_tld);
        
        ep = DotProd(p, p_tld);
        if (ep == Complexe(0))
          {
            iter.Fail(4, "Qmr breakdown #3");
            break;
          }
        
        beta = ep / delta;
        if (beta == Complexe(0))
          {
            iter.Fail(5, "Qmr breakdown #4");
            break;
          }
          
        // v = -beta v + p_tld
        Mlt(Complexe(-beta), v); Add(Complexe(1), p_tld, v);
        M.Solve(A, v, y);
        
        rho_1 = rho;
        rho = Norm2(y);
        
        gamma_1 = gamma;
        theta_1 = theta;
                
        theta = rho / (gamma_1 * beta);
        gamma = Complexe(1) / sqrt(1.0 + theta * theta);
        
        if (gamma == Titer(0))
          {
            iter.Fail(6, "Qmr breakdown #5");
            break;
          }
        
        eta = -eta * rho_1 * gamma * gamma / (beta * gamma_1 * gamma_1);
        
        if (iter.First())
          {
            Copy(p, d);
            Mlt(eta, d);
            Copy(p_tld, s);
            Mlt(eta, s);
          }
        else
          {
            Complexe tmp = (theta_1 * theta_1 * gamma * gamma);
            Mlt(tmp, d);
            Add(eta, p, d);
            Mlt(tmp, s);
            Add(eta, p_tld, s);
          }
        Add(Complexe(1), d, x);
        Add(-Complexe(1), s, r);
        
        ++iter;
      }
    
    return iter.ErrorCode();
  }
  
} // end namespace

#define SELDON_FILE_ITERATIVE_QMRSYM_CXX
#endif