metaforce/gmm/gmm_solver_constrained_cg.h

/* -*- c++ -*- (enables emacs c++ mode) */
/*===========================================================================

 Copyright (C) 2002-2017 Yves Renard

 This file is a part of GetFEM++

 GetFEM++  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 3 of the License,  or
 (at your option) any later version along with the GCC Runtime Library
 Exception either version 3.1 or (at your option) any later version.
 This program  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 and GCC Runtime Library Exception for more details.
 You  should  have received a copy of the GNU Lesser General Public License
 along  with  this program;  if not, write to the Free Software Foundation,
 Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301, USA.

 As a special exception, you  may use  this file  as it is a part of a free
 software  library  without  restriction.  Specifically,  if   other  files
 instantiate  templates  or  use macros or inline functions from this file,
 or  you compile this  file  and  link  it  with other files  to produce an
 executable, this file  does  not  by itself cause the resulting executable
 to be covered  by the GNU Lesser General Public License.  This   exception
 does not  however  invalidate  any  other  reasons why the executable file
 might be covered by the GNU Lesser General Public License.

===========================================================================*/

/**@file gmm_solver_constrained_cg.h
   @author  Yves Renard <Yves.Renard@insa-lyon.fr>
   @date October 13, 2002.
   @brief Constrained conjugate gradient. */
//  preconditionning does not work

#ifndef GMM_SOLVER_CCG_H__
#define GMM_SOLVER_CCG_H__

#include "gmm_kernel.h"
#include "gmm_iter.h"

namespace gmm {

  template <typename CMatrix, typename CINVMatrix, typename Matps,
	    typename VectorX>
  void pseudo_inverse(const CMatrix &C, CINVMatrix &CINV,
		      const Matps& /* PS */, VectorX&) {
    // compute the pseudo inverse of the non-square matrix C such
    // CINV = inv(C * trans(C)) * C.
    // based on a conjugate gradient method.
    
    // optimisable : copie de la ligne, precalcul de C * trans(C).
    
    typedef VectorX TmpVec;
    typedef typename linalg_traits<VectorX>::value_type value_type;
    
    size_type nr = mat_nrows(C), nc = mat_ncols(C);
    
    TmpVec d(nr), e(nr), l(nc), p(nr), q(nr), r(nr);
    value_type rho, rho_1, alpha;
    clear(d);
    clear(CINV);
    
    for (size_type i = 0; i < nr; ++i) {
      d[i] = 1.0; rho = 1.0;
      clear(e);
      copy(d, r);
      copy(d, p);
      
      while (rho >= 1E-38) { /* conjugate gradient to compute e             */
	                     /* which is the i nd row of inv(C * trans(C))  */
	mult(gmm::transposed(C), p, l);
	mult(C, l, q);	  
	alpha = rho / vect_sp(p, q);
	add(scaled(p, alpha), e);  
	add(scaled(q, -alpha), r); 
	rho_1 = rho;
	rho = vect_sp(r, r);
	add(r, scaled(p, rho / rho_1), p);
      }
      
      mult(transposed(C), e, l); /* l is the i nd row of CINV     */
      // cout << "l = " << l << endl;
      clean(l, 1E-15);
      copy(l, mat_row(CINV, i));
      
      d[i] = 0.0;
    }
  }
  
  /** Compute the minimum of @f$ 1/2((Ax).x) - bx @f$ under the contraint @f$ Cx <= f @f$ */
  template < typename Matrix,  typename CMatrix, typename Matps,
	     typename VectorX, typename VectorB, typename VectorF,
	     typename Preconditioner >
  void constrained_cg(const Matrix& A, const CMatrix& C, VectorX& x,
		      const VectorB& b, const VectorF& f,const Matps& PS,
		      const Preconditioner& M, iteration &iter) {
    typedef typename temporary_dense_vector<VectorX>::vector_type TmpVec;
    typedef typename temporary_vector<CMatrix>::vector_type TmpCVec;
    typedef row_matrix<TmpCVec> TmpCmat;
    
    typedef typename linalg_traits<VectorX>::value_type value_type;
    value_type rho = 1.0, rho_1, lambda, gamma;
    TmpVec p(vect_size(x)), q(vect_size(x)), q2(vect_size(x)),
      r(vect_size(x)), old_z(vect_size(x)), z(vect_size(x)),
      memox(vect_size(x));
    std::vector<bool> satured(mat_nrows(C));
    clear(p);
    iter.set_rhsnorm(sqrt(vect_sp(PS, b, b)));
    if (iter.get_rhsnorm() == 0.0) iter.set_rhsnorm(1.0);
   
    TmpCmat CINV(mat_nrows(C), mat_ncols(C));
    pseudo_inverse(C, CINV, PS, x);
    
    while(true) {
      // computation of residu
      copy(z, old_z);
      copy(x, memox);
      mult(A, scaled(x, -1.0), b, r);
      mult(M, r, z); // preconditionner not coherent
      bool transition = false;
      for (size_type i = 0; i < mat_nrows(C); ++i) {
	value_type al = vect_sp(mat_row(C, i), x) - f[i];
	if (al >= -1.0E-15) {
	  if (!satured[i]) { satured[i] = true; transition = true; }
	  value_type bb = vect_sp(mat_row(CINV, i), z);
	  if (bb > 0.0) add(scaled(mat_row(C, i), -bb), z);
	}
	else
	  satured[i] = false;
      }
    
      // descent direction
      rho_1 = rho; rho = vect_sp(PS, r, z); // ...
      
      if (iter.finished(rho)) break;
      
      if (iter.get_noisy() > 0 && transition) std::cout << "transition\n";
      if (transition || iter.first()) gamma = 0.0;
      else gamma = std::max(0.0, (rho - vect_sp(PS, old_z, z) ) / rho_1);
      // std::cout << "gamma = " << gamma << endl;
      // itl::add(r, itl::scaled(p, gamma), p);
      add(z, scaled(p, gamma), p); // ...
      
      ++iter;
      // one dimensionnal optimization
      mult(A, p, q);
      lambda = rho / vect_sp(PS, q, p);
      for (size_type i = 0; i < mat_nrows(C); ++i)
	if (!satured[i]) {
	  value_type bb = vect_sp(mat_row(C, i), p) - f[i];
	  if (bb > 0.0)
	    lambda = std::min(lambda, (f[i]-vect_sp(mat_row(C, i), x)) / bb);
	}
      add(x, scaled(p, lambda), x);
      add(memox, scaled(x, -1.0), memox);
      
    }
  }
  
}

#endif //  GMM_SOLVER_CCG_H__