AbstractLinAlgPack_MatrixSymDiagSparse.cpp

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#include <assert.h>

#include <fstream>    // For debugging only
#include <limits>

#include "AbstractLinAlgPack_MatrixSymDiagSparse.hpp"
#include "AbstractLinAlgPack_SpVectorClass.hpp"
#include "AbstractLinAlgPack_EtaVector.hpp"
#include "AbstractLinAlgPack_AssertOp.hpp"
#include "AbstractLinAlgPack_SpVectorOut.hpp"
#include "DenseLinAlgPack_DVectorClass.hpp"
#include "DenseLinAlgPack_DMatrixAssign.hpp"
#include "DenseLinAlgPack_DMatrixClass.hpp"
#include "DenseLinAlgPack_DMatrixOp.hpp"
#include "DenseLinAlgPack_assert_print_nan_inf.hpp"
#include "DenseLinAlgPack_LinAlgOpPack.hpp"
#include "Teuchos_Assert.hpp"

namespace {
template< class T >
inline
T my_min( const T& v1, const T& v2 ) { return v1 < v2 ? v1 : v2; }
} // end namespace

namespace AbstractLinAlgPack {

MatrixSymDiagSparse::MatrixSymDiagSparse()
  : num_updates_at_once_(0) // Flag that it is to be determined internally.
{}

// Overridden from MatrixBase

size_type MatrixSymDiagSparse::rows() const
{
  return diag().dim();
}

// Overridden from MatrixOp

std::ostream& MatrixSymDiagSparse::output(std::ostream& out) const
{
  out << "*** Sparse diagonal matrix ***\n"
    << "diag =\n" << diag();
  return out;
}

// Overridden from MatrixOpSerial

void MatrixSymDiagSparse::Vp_StMtV(DVectorSlice* vs_lhs, value_type alpha
  , BLAS_Cpp::Transp trans_rhs1, const DVectorSlice& vs_rhs2, value_type beta) const
{
  const SpVectorSlice &diag = this->diag();

  size_type n = diag.dim();

  // Assert that the dimensions of the aruments match up and if not
  // then throw an excption.
  DenseLinAlgPack::Vp_MtV_assert_sizes( vs_lhs->dim(), n, n, trans_rhs1, vs_rhs2.dim() );

  // y = b*y + a * op(A) * x
  //
  // A is symmetric and diagonal A = diag(diag) so:
  //
  // y(j) = b*y(j) + a * diag(j) * x(j), for j = 1...n

  for( SpVectorSlice::const_iterator d_itr = diag.begin(); d_itr != diag.end(); ++d_itr )
  {
    const size_type i = d_itr->index(); 
    (*vs_lhs)(i) = beta * (*vs_lhs)(i) + alpha * d_itr->value() * vs_rhs2(i);
  }
}

// Overridden from MatrixSymOpSerial

void MatrixSymDiagSparse::Mp_StMtMtM(
  DMatrixSliceSym* B, value_type alpha
  ,EMatRhsPlaceHolder dummy_place_holder
  ,const MatrixOpSerial& A, BLAS_Cpp::Transp A_trans
  ,value_type b
  ) const
{
  using BLAS_Cpp::rows;
  using BLAS_Cpp::cols;
  using BLAS_Cpp::trans_not;

  using DenseLinAlgPack::nonconst_tri_ele;
  using DenseLinAlgPack::assign;
  using DenseLinAlgPack::syrk;
  using DenseLinAlgPack::assert_print_nan_inf;

  using LinAlgOpPack::V_MtV;

  typedef EtaVector eta;

  // Assert the size matching of M * op(A)
  DenseLinAlgPack::MtV_assert_sizes(
      this->rows(), this->cols(), BLAS_Cpp::no_trans
    , rows( A.rows(), A.cols(), A_trans ) );

  // Assert size matchin of B = (op(A') * M * op(A))
  DenseLinAlgPack::Vp_V_assert_sizes(
      B->cols(), cols( A.rows(), A.cols(), A_trans ) );

  //
  // B = a * op(A') * M * op(A)
  //
  //   = a * op(A') * M^(1/2) * M^(1/2) * op(A)
  //
  //   = a * E * E'
  //
  // E = M^(1/2) * op(A)
  //
  //     [ .                                                 ] [ .              ]
  //     [   sqrt(M(j(1)))                                   ] [ op(A)(j(1),:)  ]
  //     [                .                                  ] [ .              ]
  //   = [                  sqrt(M(j(i))                     ] [ op(A)(j(i),:)  ]
  //     [                              .                    ] [ .              ]
  //     [                                sqrt(M(j(nz))      ] [ op(A)(j(nz),:) ]
  //     [                                               .   ] [ .              ]
  //
  //
  //     [ .        ]
  //     [ d(j(1))' ]
  //     [ .        ]
  //   = [ d(j(i))' ]
  //     [ .        ]
  //     [ d(j(1))' ]
  //     [ .        ]
  //
  //     where: d(j(i)) = sqrt(M(j(i)) * op(A')(:,j(i))    <: R^m 
  //                    = sqrt(M(j(i)) * op(A') * e(j(i))  <: R^m
  //
  //  Above M^(1/2) only has nz nonzero elements sqrt(M(j(i)), i = 1..nz and only
  //  the corresponding rows of op(A)(j(i),:), i = 1..nz are shown.  A may in fact
  //  dense matrix but the columns are extracted through op(A)*eta(j(i)), i=1..nz.
  //
  //  The above product B = a * E * E' is a set of nz rank-1 updates and can be written
  //  in the form:
  //
  //  B = sum( a * d(j(i)) * d(j(i))', i = 1..nz )
  //
  //  Since it is more efficient to perform several rank-1 updates at a time we will
  //  perform them in blocks.
  //
  //  B = B + D(k) * D(k)', k = 1 .. num_blocks
  //
  //      where:
  //         num_blocks = nz / num_updates_at_once + 1 (integer division)
  //         D(k) = [ d(j(i1)) ... d(j(i2)) ]
  //         i1 = (k-1) * num_updates_at_once + 1
  //         i2 = i1 + num_updates_at_once - 1
  
  const SpVectorSlice
    &diag = this->diag();

  const size_type
    n = this->rows(),
    m = cols(A.rows(),A.cols(),A_trans);

  // Get the actual number of updates to use per rank-(num_updates) update
  const size_type
    num_updates
      = my_min( num_updates_at_once()
              ? num_updates_at_once()
              : 20  // There may be a better default value for this?
            , diag.nz()
            );

  // Get the number of blocks of rank-(num_updates) updates
  size_type
    num_blocks = diag.nz() / num_updates;
  if( diag.nz() % num_updates > 0 )
    num_blocks++;

  // Initialize B = b*B
  if( b != 1.0 )
    assign( &nonconst_tri_ele( B->gms(), B->uplo() ), 0.0 );

  // Perform the rank-(num_updates) updates
  DMatrix D(m,num_updates);
  for( size_type k = 1; k <= num_blocks; ++k ) {
    const size_type
      i1 = (k-1) * num_updates + 1,
      i2 = my_min( diag.nz(), i1 + num_updates - 1 );
    // Generate the colunns of D(k)
    SpVectorSlice::const_iterator
      m_itr = diag.begin() + (i1-1);
    for( size_type l = 1; l <= i2-i1+1; ++l, ++m_itr ) {
      TEUCHOS_TEST_FOR_EXCEPT( !(  m_itr < diag.end()  ) );
      TEUCHOS_TEST_FOR_EXCEPT( !(  m_itr->value() >= 0.0  ) );
      V_MtV( &D.col(l), A, trans_not(A_trans)
        , eta( m_itr->index(), n, std::sqrt(m_itr->value()) )() );
    }
    const DMatrixSlice
      D_update = D(1,m,1,i2-i1+1);


//    // For debugging only
//    std::ofstream ofile("MatrixSymDiagonalSparse_Error.out");
//    assert_print_nan_inf( D_update, "D", true, &ofile );
    // Perform the rank-(num_updates) update
    syrk( BLAS_Cpp::no_trans, alpha, D_update, 1.0, B );
  }
}

// Overridden from MatrixConvertToSparse

index_type
MatrixSymDiagSparse::num_nonzeros(
  EExtractRegion        extract_region
  ,EElementUniqueness   element_uniqueness
  ) const
{
  return diag().nz();
}

void MatrixSymDiagSparse::coor_extract_nonzeros(
  EExtractRegion                extract_region
  ,EElementUniqueness           element_uniqueness
  ,const index_type             len_Aval
  ,value_type                   Aval[]
  ,const index_type             len_Aij
  ,index_type                   Arow[]
  ,index_type                   Acol[]
  ,const index_type             row_offset
  ,const index_type             col_offset
  ) const
{
  const SpVectorSlice
    &diag = this->diag();

  TEUCHOS_TEST_FOR_EXCEPTION(
    (len_Aval != 0 ? len_Aval != diag.nz() : Aval != NULL)
    ,std::invalid_argument
    ,"MatrixSymDiagSparse::coor_extract_nonzeros(...): Error!" );
  TEUCHOS_TEST_FOR_EXCEPTION(
    (len_Aij != 0 ? len_Aij != diag.nz() : (Acol != NULL || Acol != NULL) )
    ,std::invalid_argument
    ,"MatrixSymDiagSparse::coor_extract_nonzeros(...): Error!" );

  if( len_Aval > 0 ) {
    SpVectorSlice::const_iterator
      itr;
    FortranTypes::f_dbl_prec
      *l_Aval;
    for( itr = diag.begin(), l_Aval = Aval; itr != diag.end(); ++itr ) {
      *l_Aval++ = itr->value();
    }     
  }
  if( len_Aij > 0 ) {
    SpVectorSlice::const_iterator
      itr;
    index_type
      *l_Arow, *l_Acol;
    for( itr = diag.begin(), l_Arow = Arow, l_Acol = Acol; itr != diag.end(); ++itr ) {
      const index_type
        ij = itr->index() + diag.offset();
      *l_Arow++ = ij + row_offset;
      *l_Acol++ = ij + col_offset;
    }     
  }
}

} // end namespace AbstractLinAlgPack