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DefaultOptions.h

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    gmm_precond_ildlt.h 10.84 KiB
    // -*- c++ -*- (enables emacs c++ mode)
    //===========================================================================
    //
    // Copyright (C) 2003-2008 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 2.1 of the License,  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 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 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 General Public License.  This exception does not however
    // invalidate any other reasons why the executable file might be covered by
    // the GNU General Public License.
    //
    //===========================================================================
    
    // This file is a modified version of cholesky.h from ITL.
    // See http://osl.iu.edu/research/itl/
    // Following the corresponding Copyright notice.
    //===========================================================================
    //
    // Copyright (c) 1997-2001, The Trustees of Indiana University.
    // All rights reserved.
    // Redistribution and use in source and binary forms, with or without
    // modification, are permitted provided that the following conditions are met:
    //
    //    * Redistributions of source code must retain the above copyright
    //      notice, this list of conditions and the following disclaimer.
    //    * Redistributions in binary form must reproduce the above copyright
    //      notice, this list of conditions and the following disclaimer in the
    //      documentation and/or other materials provided with the distribution.
    //    * Neither the name of the University of California, Berkeley nor the
    //      names of its contributors may be used to endorse or promote products
    //      derived from this software without specific prior written permission.
    //
    // THIS SOFTWARE  IS  PROVIDED  BY  THE TRUSTEES  OF  INDIANA UNIVERSITY  AND
    // CONTRIBUTORS  ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES,  INCLUDING,
    // BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND  FITNESS
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    // OF INDIANA UNIVERSITY AND CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
    // INCIDENTAL, SPECIAL, EXEMPLARY,  OR CONSEQUENTIAL DAMAGES (INCLUDING,  BUT
    // NOT  LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
    // DATA,  OR PROFITS;  OR BUSINESS  INTERRUPTION)  HOWEVER  CAUSED AND ON ANY
    // THEORY  OF  LIABILITY,  WHETHER  IN  CONTRACT,  STRICT  LIABILITY, OR TORT
    // (INCLUDING  NEGLIGENCE  OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
    // THIS  SOFTWARE,  EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
    //
    //===========================================================================
    
    #ifndef GMM_PRECOND_ILDLT_H
    #define GMM_PRECOND_ILDLT_H
    
    /**@file gmm_precond_ildlt.h
       @author Andrew Lumsdaine <lums@osl.iu.edu>
       @author Lie-Quan Lee <llee@osl.iu.edu>
       @author Yves Renard <yves.renard@insa-lyon.fr>
       @date June 5, 2003.
       @brief Incomplete Level 0 ILDLT Preconditioner.
    */
    
    #include "gmm_precond.h"
    
    namespace gmm {
    
      /** Incomplete Level 0 LDLT Preconditioner.
          
      For use with symmetric real or hermitian complex sparse matrices.
    
      Notes: The idea under a concrete Preconditioner such as Incomplete
      Cholesky is to create a Preconditioner object to use in iterative
      methods.
    
    
      Y. Renard : Transformed in LDLT for stability reason.
      
      U=LT is stored in csr format. D is stored on the diagonal of U.
      */
      template <typename Matrix>
      class ildlt_precond {
    
      public :
        typedef typename linalg_traits<Matrix>::value_type value_type;
        typedef typename number_traits<value_type>::magnitude_type magnitude_type;
        typedef csr_matrix_ref<value_type *, size_type *, size_type *, 0> tm_type;
    
        tm_type U;
    
      protected :
        std::vector<value_type> Tri_val;
        std::vector<size_type> Tri_ind, Tri_ptr;
     
        template<typename M> void do_ildlt(const M& A, row_major);
        void do_ildlt(const Matrix& A, col_major);
    
      public:
    
        size_type nrows(void) const { return mat_nrows(U); }
        size_type ncols(void) const { return mat_ncols(U); }
        value_type &D(size_type i) { return Tri_val[Tri_ptr[i]]; }
        const value_type &D(size_type i) const { return Tri_val[Tri_ptr[i]]; }
        ildlt_precond(void) {}
        void build_with(const Matrix& A) {
          Tri_ptr.resize(mat_nrows(A)+1);
          do_ildlt(A, typename principal_orientation_type<typename
    		  linalg_traits<Matrix>::sub_orientation>::potype());
        }
        ildlt_precond(const Matrix& A)  { build_with(A); }
        size_type memsize() const { 
          return sizeof(*this) + 
    	Tri_val.size() * sizeof(value_type) + 
    	(Tri_ind.size()+Tri_ptr.size()) * sizeof(size_type); 
        }
      };
    
      template <typename Matrix> template<typename M>
      void ildlt_precond<Matrix>::do_ildlt(const M& A, row_major) {
        typedef typename linalg_traits<Matrix>::storage_type store_type;
        typedef value_type T;
        typedef typename number_traits<T>::magnitude_type R;
        
        size_type Tri_loc = 0, n = mat_nrows(A), d, g, h, i, j, k;
        if (n == 0) return;
        T z, zz;
        Tri_ptr[0] = 0;
        R prec = default_tol(R());
        R max_pivot = gmm::abs(A(0,0)) * prec;
        
        for (int count = 0; count < 2; ++count) {
          if (count) { Tri_val.resize(Tri_loc); Tri_ind.resize(Tri_loc); }
          for (Tri_loc = 0, i = 0; i < n; ++i) {
    	typedef typename linalg_traits<M>::const_sub_row_type row_type;
    	row_type row = mat_const_row(A, i);
            typename linalg_traits<row_type>::const_iterator
    	  it = vect_const_begin(row), ite = vect_const_end(row);
    
    	if (count) { Tri_val[Tri_loc] = T(0); Tri_ind[Tri_loc] = i; }
    	++Tri_loc; // diagonal element
    
    	for (k = 0; it != ite; ++it, ++k) {
    	  j = index_of_it(it, k, store_type());
    	  if (i == j) {
    	    if (count) Tri_val[Tri_loc-1] = *it; 
    	  }
    	  else if (j > i) {
    	    if (count) { Tri_val[Tri_loc] = *it; Tri_ind[Tri_loc]=j; }
    	    ++Tri_loc;
    	  }
    	}
    	Tri_ptr[i+1] = Tri_loc;
          }
        }
        
        if (A(0,0) == T(0)) {
          Tri_val[Tri_ptr[0]] = T(1);
          GMM_WARNING2("pivot 0 is too small");
        }
        
        for (k = 0; k < n; k++) {
          d = Tri_ptr[k];
          z = T(gmm::real(Tri_val[d])); Tri_val[d] = z;
          if (gmm::abs(z) <= max_pivot) {
    	Tri_val[d] = z = T(1);
    	GMM_WARNING2("pivot " << k << " is too small [" << gmm::abs(z) << "]");
          }
          max_pivot = std::max(max_pivot, std::min(gmm::abs(z) * prec, R(1)));
          
          for (i = d + 1; i < Tri_ptr[k+1]; ++i) Tri_val[i] /= z;
          for (i = d + 1; i < Tri_ptr[k+1]; ++i) {
    	zz = gmm::conj(Tri_val[i] * z);
    	h = Tri_ind[i];
    	g = i;
    	
    	for (j = Tri_ptr[h] ; j < Tri_ptr[h+1]; ++j)
    	  for ( ; g < Tri_ptr[k+1] && Tri_ind[g] <= Tri_ind[j]; ++g)
    	    if (Tri_ind[g] == Tri_ind[j])
    	      Tri_val[j] -= zz * Tri_val[g];
          }
        }
        U = tm_type(&(Tri_val[0]), &(Tri_ind[0]), &(Tri_ptr[0]),
    			n, mat_ncols(A));
      }
      
      template <typename Matrix>
      void ildlt_precond<Matrix>::do_ildlt(const Matrix& A, col_major)
      { do_ildlt(gmm::conjugated(A), row_major()); }
    
      template <typename Matrix, typename V1, typename V2> inline
      void mult(const ildlt_precond<Matrix>& P, const V1 &v1, V2 &v2) {
        gmm::copy(v1, v2);
        gmm::lower_tri_solve(gmm::conjugated(P.U), v2, true);
        for (size_type i = 0; i < mat_nrows(P.U); ++i) v2[i] /= P.D(i);
        gmm::upper_tri_solve(P.U, v2, true);
      }
    
      template <typename Matrix, typename V1, typename V2> inline
      void transposed_mult(const ildlt_precond<Matrix>& P,const V1 &v1,V2 &v2)
      { mult(P, v1, v2); }
    
      template <typename Matrix, typename V1, typename V2> inline
      void left_mult(const ildlt_precond<Matrix>& P, const V1 &v1, V2 &v2) {
        copy(v1, v2);
        gmm::lower_tri_solve(gmm::conjugated(P.U), v2, true);
        for (size_type i = 0; i < mat_nrows(P.U); ++i) v2[i] /= P.D(i);
      }
    
      template <typename Matrix, typename V1, typename V2> inline
      void right_mult(const ildlt_precond<Matrix>& P, const V1 &v1, V2 &v2)
      { copy(v1, v2); gmm::upper_tri_solve(P.U, v2, true);  }
    
      template <typename Matrix, typename V1, typename V2> inline
      void transposed_left_mult(const ildlt_precond<Matrix>& P, const V1 &v1,
    			    V2 &v2) {
        copy(v1, v2);
        gmm::upper_tri_solve(P.U, v2, true);
        for (size_type i = 0; i < mat_nrows(P.U); ++i) v2[i] /= P.D(i);
      }
    
      template <typename Matrix, typename V1, typename V2> inline
      void transposed_right_mult(const ildlt_precond<Matrix>& P, const V1 &v1,
    			     V2 &v2)
      { copy(v1, v2); gmm::lower_tri_solve(gmm::conjugated(P.U), v2, true); }
    
    
    
      // for compatibility with old versions
    
      template <typename Matrix>
      struct cholesky_precond : public ildlt_precond<Matrix> {
        cholesky_precond(const Matrix& A) : ildlt_precond<Matrix>(A) {}
        cholesky_precond(void) {}
      } IS_DEPRECATED;
    
      template <typename Matrix, typename V1, typename V2> inline
      void mult(const cholesky_precond<Matrix>& P, const V1 &v1, V2 &v2) {
        gmm::copy(v1, v2);
        gmm::lower_tri_solve(gmm::conjugated(P.U), v2, true);
        for (size_type i = 0; i < mat_nrows(P.U); ++i) v2[i] /= P.D(i);
        gmm::upper_tri_solve(P.U, v2, true);
      }
    
      template <typename Matrix, typename V1, typename V2> inline
      void transposed_mult(const cholesky_precond<Matrix>& P,const V1 &v1,V2 &v2)
      { mult(P, v1, v2); }
    
      template <typename Matrix, typename V1, typename V2> inline
      void left_mult(const cholesky_precond<Matrix>& P, const V1 &v1, V2 &v2) {
        copy(v1, v2);
        gmm::lower_tri_solve(gmm::conjugated(P.U), v2, true);
        for (size_type i = 0; i < mat_nrows(P.U); ++i) v2[i] /= P.D(i);
      }
    
      template <typename Matrix, typename V1, typename V2> inline
      void right_mult(const cholesky_precond<Matrix>& P, const V1 &v1, V2 &v2)
      { copy(v1, v2); gmm::upper_tri_solve(P.U, v2, true);  }
    
      template <typename Matrix, typename V1, typename V2> inline
      void transposed_left_mult(const cholesky_precond<Matrix>& P, const V1 &v1,
    			    V2 &v2) {
        copy(v1, v2);
        gmm::upper_tri_solve(P.U, v2, true);
        for (size_type i = 0; i < mat_nrows(P.U); ++i) v2[i] /= P.D(i);
      }
    
      template <typename Matrix, typename V1, typename V2> inline
      void transposed_right_mult(const cholesky_precond<Matrix>& P, const V1 &v1,
    			     V2 &v2)
      { copy(v1, v2); gmm::lower_tri_solve(gmm::conjugated(P.U), v2, true); }
      
    }
    
    #endif