Matrix_tools.cpp

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#include <Matrix_tools.h>
#include <Matrice.h>
#include <Matrice_Base.h>
#include <Matrice_Nulle.h>
#include <Matrice_Diagonale.h>
#include <Matrice_Morse.h>
#include <Matrice_Morse_Sym.h>
#include <TRUSTTab.h>
#include <Array_tools.h>
 
#include <algorithm>
 
// conversion to morse format
void Matrix_tools::convert_to_morse_matrix( const Matrice_Base& in,
                                            Matrice_Morse&      out )
{
  Stencil stencil;
  StencilCoeffs coefficients;
 
  in.get_stencil_and_coefficients( stencil, coefficients );
 
  Matrix_tools::build_morse_matrix( in.nb_lignes( ),
                                    in.nb_colonnes( ),
                                    stencil,
                                    coefficients,
                                    out );
}
 
// conversion to morse format, storing initial location of coefficients pointers
void Matrix_tools::convert_to_morse_matrix_with_ptrs( const Matrice_Base& in,
                                                      Matrice_Morse&      out,
                                                      std::vector<const double *>& coeffs)
{
  Stencil stencil;
  StencilCoeffs coefficients;
 
  in.get_stencil_and_coeff_ptrs( stencil, coeffs);
 
  // Copy coefficients into StencilCoeffs
  coefficients.resize_array((int)coeffs.size());
  auto deref_fun = [](const double* src) { return *src; };
 
  std::transform(coeffs.begin(), coeffs.end(), coefficients.addr(), deref_fun);
 
  Matrix_tools::build_morse_matrix( in.nb_lignes( ),
                                    in.nb_colonnes( ),
                                    stencil,
                                    coefficients,
                                    out );
}
 
 
// conversion to symetric morse format
void Matrix_tools::convert_to_symmetric_morse_matrix( const Matrice_Base& in,
                                                      Matrice_Morse_Sym&  out )
{
  assert( in.nb_lignes( ) == in.nb_colonnes( ) );
 
  Stencil stencil;
  StencilCoeffs coefficients;
 
  in.get_symmetric_stencil_and_coefficients( stencil, coefficients );
 
  Matrix_tools::build_symmetric_morse_matrix( in.nb_lignes( ),
                                              stencil,
                                              coefficients,
                                              out );
}
 
// checking stencil
template <typename _TYPE_, typename _SIZE_>
bool Matrix_tools::is_normalized_stencil( const TRUSTTab<_TYPE_, _SIZE_>& stencil )
{
  const _SIZE_ size = stencil.dimension( 0 );
  for ( _SIZE_ i=1; i<size; ++i )
    {
      _TYPE_ delta1 = stencil( i-1, 0 ) - stencil( i, 0 );
      _TYPE_ delta2 = stencil( i-1, 1 ) - stencil( i, 1 );
      _TYPE_ delta  = ( delta1 == 0 ) ? delta2 : delta1;
 
      if ( delta >= 0 )
        return false;
    }
  return true;
}
 
// checking symmetric stencil
bool Matrix_tools::is_normalized_symmetric_stencil( const Stencil& stencil )
{
  if ( ! ( is_normalized_stencil( stencil ) ) )
    {
      Cerr << "non-normalized stencil" << finl;
      return false;
    }
 
  const int size = stencil.dimension( 0 );
  for ( int i=0; i<size; ++i )
    {
      int delta = stencil( i, 0 ) - stencil( i, 1 );
      if ( delta > 0 )
        {
          Cerr << "( " << i << " ) line index > column index : ( " << stencil( i, 0 ) << ", " << stencil( i, 1 ) << " )" << finl;
          return false;
        }
    }
 
  return true;
}
 
template <typename _SIZE_>
void Matrix_tools::fill_csr_arrays(const _SIZE_ nb_lines, const _SIZE_ nb_columns, const TRUSTTab<_SIZE_,_SIZE_>& stencil,
                                   TRUSTVect<_SIZE_,_SIZE_>& tab1, TRUSTVect<_SIZE_,_SIZE_>& tab2)
{
  assert( is_normalized_stencil( stencil ) );
 
  const _SIZE_ nb_coefficients = stencil.dimension( 0 );
 
  assert(tab1.size_array() == nb_lines+1);
  assert(tab2.size_array() == nb_coefficients);
 
  if ( nb_coefficients > 0 )
    {
      tab1 = 0 ;
      tab1[0] = 1;
      for (_SIZE_ i=0; i<nb_coefficients; ++i )
        {
          assert( stencil( i ,0 ) >= 0         );
          assert( stencil( i ,0 ) < nb_lines   );
          assert( stencil( i ,1 ) >= 0         );
          assert( stencil( i ,1 ) < nb_columns );
 
          tab1[stencil(i, 0) + 1] += 1;
          tab2[i] = stencil(i, 1) + 1;
        }
      for ( int i=0; i<nb_lines; ++i )
        tab1[i + 1] += tab1[i];
    }
}
 
// Explicit instanciation
template void Matrix_tools::fill_csr_arrays(const int nb_lines, const int nb_columns, const TRUSTTab<int,int>& stencil,
                                            TRUSTVect<int,int>& tab1, TRUSTVect<int,int>& tab2);
#if INT_is_64_ == 2
template void Matrix_tools::fill_csr_arrays(const trustIdType nb_lines, const trustIdType nb_columns, const TRUSTTab<trustIdType,trustIdType>& stencil,
                                            TRUSTVect<trustIdType,trustIdType>& tab1, TRUSTVect<trustIdType,trustIdType>& tab2);
#endif
 
// building morse matrices
void Matrix_tools::allocate_morse_matrix( const int nb_lines,
                                          const int nb_columns,
                                          const Stencil& stencil,
                                          Matrice_Morse& matrix ,
                                          const bool& attach_stencil_to_matrix )
{
  assert( is_normalized_stencil( stencil ) );
 
  const int nb_coefficients = stencil.dimension( 0 );
  matrix.dimensionner( nb_lines, nb_columns, nb_coefficients );
  {
    auto& tab1 = matrix.get_set_tab1();
    auto& tab2 = matrix.get_set_tab2();
    if ( nb_coefficients > 0 )
      {
        tab1 = 0;
        tab1[0] = 1;
        for ( int i=0; i<nb_coefficients; ++i )
          {
            tab1[stencil(i, 0) + 1] += 1;
            tab2[i] = stencil(i, 1) + 1;
          }
        for ( int i=0; i<nb_lines; ++i )
          tab1[i + 1] += tab1[i];
      }
  }
  if( attach_stencil_to_matrix )
    matrix.set_stencil( stencil );
}
 
void Matrix_tools::build_morse_matrix( const int     nb_lines,
                                       const int     nb_columns,
                                       const Stencil&      stencil,
                                       const StencilCoeffs& coefficients,
                                       Matrice_Morse&     matrix )
{
  // No : stencil do not rely on sorted columns
  //assert( is_normalized_stencil( stencil ) );
 
  const int nb_coefficients = stencil.dimension( 0 );
  assert( nb_coefficients == coefficients.size_array( ) );
 
  matrix.dimensionner( nb_lines,
                       nb_columns,
                       nb_coefficients );
 
  if ( nb_coefficients > 0 )
    {
      matrix.get_set_tab1() =0  ;
      matrix.get_set_tab1()( 0 ) = 1;
      for ( int i=0; i<nb_coefficients; ++i )
        {
          assert( stencil( i ,0 ) >= 0         );
          assert( stencil( i ,0 ) < nb_lines   );
          assert( stencil( i ,1 ) >= 0         );
          assert( stencil( i ,1 ) < nb_columns );
 
          matrix.get_set_tab1()( stencil( i, 0 ) + 1 ) += 1;
          matrix.get_set_tab2()( i ) = stencil( i, 1 ) + 1;
          matrix.get_set_coeff()( i ) = coefficients[ i ];
        }
      for ( int i=0; i<nb_lines; ++i )
        {
          matrix.get_set_tab1()( i + 1 ) += matrix.get_tab1()( i );
        }
    }
}
 
 
 
// building symmetric morse matrices
void Matrix_tools::allocate_symmetric_morse_matrix( const int     order,
                                                    const Stencil&      stencil,
                                                    Matrice_Morse_Sym& matrix )
{
  assert( is_normalized_symmetric_stencil( stencil ) );
 
  const int nb_coefficients = stencil.dimension( 0 );
 
  matrix.dimensionner( order,
                       order,
                       nb_coefficients );
 
  if ( nb_coefficients > 0 )
    {
      matrix.get_set_tab1()= 0 ;
      matrix.get_set_tab1()( 0 ) = 1;
      for ( int i=0; i<nb_coefficients; ++i )
        {
          assert( stencil( i ,0 ) >= 0               );
          assert( stencil( i ,0 ) < order            );
          assert( stencil( i ,1 ) >= 0               );
          assert( stencil( i ,1 ) < order            );
          assert( stencil( i, 0 ) <= stencil( i, 1 ) );
 
          matrix.get_set_tab1()( stencil( i, 0 ) + 1 ) += 1;
          matrix.get_set_tab2()( i ) = stencil( i, 1 ) + 1;
        }
      for ( int i=0; i<order; ++i )
        {
          matrix.get_set_tab1()( i + 1 ) += matrix.get_tab1()( i );
        }
    }
  matrix.set_symmetric( 1 );
}
 
 
void Matrix_tools::build_symmetric_morse_matrix( const int     order,
                                                 const Stencil&      stencil,
                                                 const StencilCoeffs& coefficients,
                                                 Matrice_Morse_Sym& matrix )
{
  // No : stencil do not rely on sorted columns
  // assert( is_normalized_symmetric_stencil( stencil ) );
 
  const int nb_coefficients = stencil.dimension( 0 );
  assert( nb_coefficients == coefficients.size_array( ) );
 
  matrix.dimensionner( order,
                       order,
                       nb_coefficients );
 
  if ( nb_coefficients > 0 )
    {
      matrix.get_set_tab1() = 0 ;
      matrix.get_set_tab1()( 0 ) = 1;
      for ( int i=0; i<nb_coefficients; ++i )
        {
          assert( stencil( i ,0 ) >= 0               );
          assert( stencil( i ,0 ) < order            );
          assert( stencil( i ,1 ) >= 0               );
          assert( stencil( i ,1 ) < order            );
          assert( stencil( i, 0 ) <= stencil( i, 1 ) );
 
          matrix.get_set_tab1()( stencil( i, 0 ) + 1 ) += 1;
          matrix.get_set_tab2()( i )  = stencil( i, 1 ) + 1;
          matrix.get_set_coeff()( i ) = coefficients[ i ];
        }
      for ( int i=0; i<order; ++i )
        {
          matrix.get_set_tab1()( i + 1 ) += matrix.get_tab1()( i );
        }
    }
  matrix.set_symmetric( 1 );
}
 
 
// allocation for scaled addition
void Matrix_tools::allocate_for_scaled_addition( const Matrice& A,
                                                 const Matrice& B,
                                                 Matrice&       C )
{
  assert( A.valeur( ).nb_lignes( )   == B.valeur( ).nb_lignes( )   );
  assert( A.valeur( ).nb_colonnes( ) == B.valeur( ).nb_colonnes( ) );
 
  Stencil A_stencil;
  A.valeur( ).get_stencil( A_stencil );
  const int A_size = (int)A_stencil.dimension( 0 );
 
  Stencil B_stencil;
  B.valeur( ).get_stencil( B_stencil );
  const int B_size = (int)B_stencil.dimension( 0 );
 
  int size = A_size + B_size;
  Stencil stencil;
 
  stencil.resize( size, 2 );
 
  for ( int i=0; i<A_size; ++i )
    {
      stencil( i , 0 ) = A_stencil( i, 0 );
      stencil( i , 1 ) = A_stencil( i, 1 ) ;
    }
 
  for ( int i=0; i<B_size; ++i )
    {
      stencil( i+A_size , 0 ) = B_stencil( i, 0 );
      stencil( i+A_size , 1 ) = B_stencil( i, 1 ) ;
    }
 
  tableau_trier_retirer_doublons( stencil );
 
  C.typer( "Matrice_Morse" );
  Matrice_Morse& C_ = ref_cast( Matrice_Morse, C.valeur( ) );
 
  allocate_morse_matrix( A.valeur( ).nb_lignes( ),
                         A.valeur( ).nb_colonnes( ),
                         stencil,
                         C_ );
}
 
void Matrix_tools::allocate_for_symmetric_scaled_addition( const Matrice& A,
                                                           const Matrice& B,
                                                           Matrice&       C )
{
  assert( A.valeur( ).nb_lignes( )   == A.valeur( ).nb_lignes( )   );
  assert( A.valeur( ).nb_lignes( )   == B.valeur( ).nb_lignes( )   );
  assert( A.valeur( ).nb_colonnes( ) == B.valeur( ).nb_colonnes( ) );
 
  Stencil A_stencil;
  A.valeur( ).get_symmetric_stencil( A_stencil );
  const int A_size = (int)A_stencil.dimension( 0 );
 
  Stencil B_stencil;
  B.valeur( ).get_symmetric_stencil( B_stencil );
  const int B_size = (int)B_stencil.dimension( 0 );
 
  int size = A_size + B_size;
  Stencil stencil;
 
  stencil.resize( size, 2 );
 
  for ( int i=0; i<A_size; ++i )
    {
      stencil( i , 0 ) = A_stencil( i, 0 );
      stencil( i , 1 ) = A_stencil( i, 1 ) ;
    }
 
  for ( int i=0; i<B_size; ++i )
    {
      stencil( i+A_size , 0 ) = B_stencil( i, 0 );
      stencil( i+A_size , 1 ) = B_stencil( i, 1 ) ;
    }
 
  tableau_trier_retirer_doublons( stencil );
 
  C.typer( "Matrice_Morse_Sym" );
  Matrice_Morse_Sym& C_ = ref_cast( Matrice_Morse_Sym, C.valeur( ) );
 
  allocate_symmetric_morse_matrix( A.valeur( ).nb_lignes( ),
                                   stencil,
                                   C_ );
}
 
 
// scaled addition
void Matrix_tools::add_scaled_matrices( const Matrice& A,
                                        const double alpha,
                                        const Matrice& B,
                                        const double beta,
                                        Matrice&       C )
{
  assert( sub_type( Matrice_Morse, C.valeur( ) ) );
  Matrice_Morse& C_ = ref_cast( Matrice_Morse, C.valeur( ) );
 
  assert( C_.check_sorted_morse_matrix_structure( ) );
 
  Stencil A_stencil;
  StencilCoeffs A_coefficients;
  A.valeur( ).get_stencil_and_coefficients( A_stencil,
                                            A_coefficients );
 
  Stencil B_stencil;
  StencilCoeffs B_coefficients;
  B.valeur( ).get_stencil_and_coefficients( B_stencil,
                                            B_coefficients );
 
  int A_k = 0;
  int B_k = 0;
 
  C_.get_set_coeff() = 0.0 ;
 
  const int nb_lines = C_.nb_lignes( );
  for ( int i=0; i<nb_lines; ++i )
    {
      auto k0   = C_.get_tab1()( i ) - 1;
      auto k1   = C_.get_tab1()( i + 1 ) - 1;
 
      for ( auto k=k0; k<k1; ++k )
        {
          int j = C_.get_tab2()( k ) - 1;
 
          if ( ( A_k < A_stencil.dimension( 0 ) ) && ( A_stencil( A_k, 0 ) == i ) && ( A_stencil( A_k, 1 ) == j ) )
            {
              C_.get_set_coeff()( k ) += alpha * A_coefficients[ A_k ];
              ++A_k;
            }
 
          if ( ( B_k < B_stencil.dimension( 0 ) ) && ( B_stencil( B_k, 0 ) == i ) && ( B_stencil( B_k, 1 ) == j ) )
            {
              C_.get_set_coeff()( k ) += beta * B_coefficients[ B_k ];
              ++B_k;
            }
        }
    }
 
  assert( A_k == A_coefficients.size_array( ) );
  assert( B_k == B_coefficients.size_array( ) );
}
 
void Matrix_tools::add_symmetric_scaled_matrices( const Matrice& A,
                                                  const double alpha,
                                                  const Matrice& B,
                                                  const double beta,
                                                  Matrice&       C )
{
  assert( sub_type( Matrice_Morse_Sym, C.valeur( ) ) );
  Matrice_Morse_Sym& C_ = ref_cast( Matrice_Morse_Sym, C.valeur( ) );
 
  assert( C_.check_sorted_symmetric_morse_matrix_structure( ) );
 
  Stencil A_stencil;
  StencilCoeffs A_coefficients;
  A.valeur( ).get_symmetric_stencil_and_coefficients( A_stencil,
                                                      A_coefficients );
 
  Stencil B_stencil;
  StencilCoeffs B_coefficients;
  B.valeur( ).get_symmetric_stencil_and_coefficients( B_stencil,
                                                      B_coefficients );
 
  int A_k = 0;
  int B_k = 0;
 
  C_.get_set_coeff() = 0.0 ;
 
  const int nb_lines = C_.nb_lignes( );
  for ( int i=0; i<nb_lines; ++i )
    {
      auto k0   = C_.get_tab1()( i ) - 1;
      auto k1   = C_.get_tab1()( i + 1 ) - 1;
 
      for ( auto k=k0; k<k1; ++k )
        {
          int j = C_.get_tab2()( k ) - 1;
 
          if ( ( A_k < A_stencil.dimension( 0 ) ) && ( A_stencil( A_k, 0 ) == i ) && ( A_stencil( A_k, 1 ) == j ) )
            {
              C_.get_set_coeff()( k ) += alpha * A_coefficients[ A_k ];
              ++A_k;
            }
 
          if ( ( B_k < B_stencil.dimension( 0 ) ) && ( B_stencil( B_k, 0 ) == i ) && ( B_stencil( B_k, 1 ) == j ) )
            {
              C_.get_set_coeff()( k ) += beta * B_coefficients[ B_k ];
              ++B_k;
            }
        }
    }
 
  assert( A_k == A_coefficients.size_array( ) );
  assert( B_k == B_coefficients.size_array( ) );
}
 
// stencil analysis
bool Matrix_tools::is_null_stencil( const Stencil& stencil )
{
  return ( stencil.dimension( 0 ) == 0 );
}
 
bool Matrix_tools::is_diagonal_stencil( const int nb_lines,
                                        const int nb_columns,
                                        const Stencil& stencil )
{
  if ( nb_lines != nb_columns )
    {
      return false;
    }
 
  const int size = stencil.dimension( 0 );
 
  if ( size == 0 )
    {
      return false;
    }
 
  for ( int i=0; i<size; ++i )
    {
      if ( stencil( i, 0 ) != stencil( i, 1 ) )
        {
          return false;
        }
 
      if ( stencil( i, 0 ) >= nb_lines )
        {
          return false;
        }
 
      if ( stencil( i, 1 ) >= nb_columns )
        {
          return false;
        }
    }
 
  return true;
}
 
void Matrix_tools::allocate_from_stencil( const int nb_lines,
                                          const int nb_columns,
                                          const Stencil& stencil,
                                          Matrice&      matrix ,
                                          const bool&   attach_stencil_to_matrix)
{
  if ( is_null_stencil( stencil ) )
    {
      matrix.typer( "Matrice_Nulle" );
      Matrice_Nulle& matrix_ = ref_cast( Matrice_Nulle, matrix.valeur( ) );
      matrix_.dimensionner( nb_lines, nb_columns );
    }
  else if ( is_diagonal_stencil( nb_lines,
                                 nb_columns,
                                 stencil ) )
    {
      matrix.typer( "Matrice_Diagonale" );
      Matrice_Diagonale& matrix_ = ref_cast( Matrice_Diagonale, matrix.valeur( ) );
      matrix_.dimensionner( nb_lines );
      if( attach_stencil_to_matrix )
        {
          matrix_.set_stencil( stencil );
        }
    }
  else
    {
      matrix.typer( "Matrice_Morse" );
      Matrice_Morse& matrix_ = ref_cast( Matrice_Morse, matrix.valeur( ) );
      allocate_morse_matrix( nb_lines,
                             nb_columns,
                             stencil,
                             matrix_,
                             attach_stencil_to_matrix );
    }
}
 
// extending a matrix's stencil
void Matrix_tools::extend_matrix_stencil( const Stencil& stencil,
                                          Matrice&      matrix ,
                                          const bool&   attach_stencil_to_matrix )
{
  if ( ! ( is_null_stencil( stencil ) ) )
    {
      const int nb_lines   = matrix.valeur( ).nb_lignes( );
      const int nb_columns = matrix.valeur( ).nb_colonnes( );
 
      Stencil full_stencil;
      matrix.valeur( ).get_stencil( full_stencil );
 
      const int size = stencil.dimension( 0 );
 
      const int old_size = full_stencil.size( ) / 2 ;
 
      full_stencil.resize( old_size + size, 2);
 
      for ( int i=0; i<size; ++i )
        {
          full_stencil( old_size + i , 0 ) = stencil( i, 0 );
          full_stencil( old_size + i , 1 ) = stencil( i, 1 );
        }
 
      tableau_trier_retirer_doublons( full_stencil );
 
      allocate_from_stencil( nb_lines,
                             nb_columns,
                             full_stencil,
                             matrix ,
                             attach_stencil_to_matrix );
    }
}
 
 
 
void Matrix_tools::matdiag_mult_matmorse( const DoubleTab& diag,
                                          Matrice_Morse& mat,
                                          const bool& inverse )
{
  const int nb_lignes = mat.nb_lignes( );
  const auto& tab1 = mat.get_tab1( );
  const auto& tab2 = mat.get_tab2( );
  auto nnz_tot = 0;
  for( int i=0; i<nb_lignes; i++ )
    {
      const int nnz_i = (int)(tab1[ i+1 ] - tab1[ i ]); // nnz sur la ligne i
      for(int k=0; k<nnz_i; k++)
        {
          const int j = tab2[nnz_tot + k] - 1 ; // indice de la colonne
          double& coefficient = mat.coef( i, j );
          if( inverse )
            coefficient *= 1./diag[ i ] ;
          else
            coefficient *= diag[ i ] ;
        }
      nnz_tot += nnz_i;
    }
}
 
void Matrix_tools::matmorse_mult_matdiag( const DoubleTab& diag,
                                          Matrice_Morse& mat,
                                          const bool& inverse )
{
  const int nb_lignes = mat.nb_lignes( );
  const auto& tab1 = mat.get_tab1( );
  const auto& tab2 = mat.get_tab2( );
  auto nnz_tot = 0;
  for( int i=0; i<nb_lignes; i++ )
    {
      const int nnz_i = (int)(tab1[ i+1 ] - tab1[ i ]); // nnz sur la ligne i
      for(int k=0; k<nnz_i; k++)
        {
          const int j = tab2[nnz_tot + k] - 1 ; // indice de la colonne
          double& coefficient = mat.coef( i, j );
          if( inverse )
            coefficient *= 1./diag[ j ] ;
          else
            coefficient *= diag[ j ] ;
        }
      nnz_tot += nnz_i;
    }
}
 
 
void Matrix_tools::uniform_matdiag_mult_matmorse( const double diag,
                                                  Matrice_Morse& mat,
                                                  const bool& inverse )
{
  const int nb_lignes = mat.nb_lignes( );
  const auto& tab1 = mat.get_tab1( );
  const auto& tab2 = mat.get_tab2( );
  auto nnz_tot = 0;
  for( int i=0; i<nb_lignes; i++ )
    {
      const int nnz_i = (int)(tab1[ i+1 ] - tab1[ i ]); // nnz sur la ligne i
      for(int k=0; k<nnz_i; k++)
        {
          const int j = tab2[nnz_tot + k] - 1 ; // indice de la colonne
          double& coefficient = mat.coef( i, j );
          if( inverse )
            coefficient *= 1./diag ;
          else
            coefficient *= diag ;
        }
      nnz_tot += nnz_i;
    }
}
 
void Matrix_tools::matmorse_mult_uniform_matdiag( const double diag,
                                                  Matrice_Morse& mat,
                                                  const bool& inverse )
{
  uniform_matdiag_mult_matmorse( diag, mat, inverse );
}
 
void Matrix_tools::extend_matrix(Matrice_Morse& mat, int nl, int nc)
{
 
  auto& tab1 = mat.get_set_tab1();
  auto old_tab1 = tab1;
  tab1.reset(), tab1.resize(nl + 1);
  for (int i = 0; i <= nl; i++) tab1(i) = old_tab1(std::min(i, old_tab1.size_array() - 1));
  mat.set_nb_columns(nc); //plus facile
}