ConstrainedOptPack_MatrixVarReductImplicit.cpp

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#include "ConstrainedOptPack_MatrixVarReductImplicit.hpp"
#include "AbstractLinAlgPack_LinAlgOpPack.hpp"
#include "AbstractLinAlgPack_MatrixOpNonsing.hpp"
#include "AbstractLinAlgPack_MatrixOpOut.hpp"
#include "AbstractLinAlgPack_GenPermMatrixSlice.hpp"
#include "AbstractLinAlgPack_SpVectorClass.hpp"
#include "AbstractLinAlgPack_AssertOp.hpp"
#include "Teuchos_Workspace.hpp"
#include "Teuchos_Assert.hpp"

namespace {

//
// Implicit matrix-vector multiplication:
//
// y = b*y + a*op(inv(C)*N)*x
//
template<class V>
void imp_Vp_StMtV_implicit(
  AbstractLinAlgPack::VectorMutable               *y
  ,AbstractLinAlgPack::value_type                       a
  ,const AbstractLinAlgPack::MatrixOpNonsing    &C
  ,const AbstractLinAlgPack::MatrixOp               &N
  ,BLAS_Cpp::Transp                                     D_trans
  ,const V                                              &x
  ,DenseLinAlgPack::value_type                               b
  )
{
  using BLAS_Cpp::no_trans;
  using BLAS_Cpp::trans;
  namespace alap = AbstractLinAlgPack;
  using Teuchos::Workspace;
  Teuchos::WorkspaceStore* wss = Teuchos::get_default_workspace_store().get();

  const DenseLinAlgPack::size_type
    r   = C.rows(),
    dof = N.cols();

  // ToDo: Pass in workspace vectors to save some allocation time!

  if( D_trans == no_trans ) {
    // y = b*y
    alap::Vt_S(y,b);
    //
    // y += -a * inv(C) * ( N * x )
    //
    alap::VectorSpace::vec_mut_ptr_t
      t1 = N.space_cols().create_member(),
      t2 = C.space_rows().create_member();
    // t1 = N*x
    LinAlgOpPack::V_MtV( t1.get(), N, no_trans, x );
    // t2 = inv(C) * t1
    alap::V_InvMtV( t2.get(), C, no_trans, *t1 );
    // y += a*t2
    alap::Vp_StV( y, -a, *t2 );
  }
  else {
    //
    // y = b*y - a * N' * ( inv(C') * x )
    //
    alap::VectorSpace::vec_mut_ptr_t
      t1 = C.space_cols().create_member();
    // t1 = inv(C')*x
    alap::V_InvMtV( t1.get(), C, trans, x );
    // y = b*y - a*N'*t1
      alap::Vp_StMtV( y, -a,  N, trans, *t1, b );
  }
}

/*

//
// Generate a row of inv(C)*N if not already computed.
//
void imp_compute_InvCtN_row(
  DenseLinAlgPack::size_type                                                 r
  ,const ConstrainedOptPack::DecompositionSystemVarReduct      &decomp_sys
  ,DenseLinAlgPack::size_type                                                j
  ,DenseLinAlgPack::DVectorSlice                                              *e_j  // Set to all zeros on input and output!
  ,ConstrainedOptPack::MatrixVarReductImplicit::InvCtN_rows_t  *InvCtN_rows
  )
{
  typedef  DenseLinAlgPack::value_type  value_type;
  using DenseLinAlgPack::DVectorSlice;
  if( (*InvCtN_rows)[j-1] == NULL ) {
    // Generate row j of inv(C)*N
    value_type *vec = (*InvCtN_rows)[j-1] = new value_type[r]; // ToDo: We may want to allocate more vectors at once!
    DVectorSlice row_j(vec,r);
    // row_j = N'*inv(C')*e_j
    (*e_j)(j) = 1.0;
    imp_Vp_StMtV_implicit( &row_j, 1.0, decomp_sys, BLAS_Cpp::trans, *e_j, 0.0 );
    (*e_j)(j) = 0.0;
  }
}

//
// Perform the matrix-vector multiplication:
// 
// y = b*y -a * op(P) * [inv(C) * N] * x
//
// by generating rows [inv(C)*N](j,:) for each nonzero entry op(P)(i,j).
//
template<class V>
void imp_Vp_StPtMtV_by_row(
  DenseLinAlgPack::DVectorSlice                                               *y
  ,DenseLinAlgPack::value_type                                               a
  ,const ConstrainedOptPack::GenPermMatrixSlice                &P
  ,BLAS_Cpp::Transp                                                     P_trans
  ,const ConstrainedOptPack::DecompositionSystemVarReduct      &decomp_sys
  ,const V                                                              &x
  ,DenseLinAlgPack::value_type                                               b
  ,ConstrainedOptPack::MatrixVarReductImplicit::InvCtN_rows_t *InvCtN_rows
  )
{
  using BLAS_Cpp::no_trans;
  using BLAS_Cpp::trans;
  using BLAS_Cpp::trans_not;
  using BLAS_Cpp::rows;
  using BLAS_Cpp::cols;
  using DenseLinAlgPack::dot;
  using DenseLinAlgPack::DVectorSlice;
  using AbstractLinAlgPack::dot;
  using AbstractLinAlgPack::Vp_StMtV;
  using AbstractLinAlgPack::GenPermMatrixSlice;
  using Teuchos::Workspace;
  Teuchos::WorkspaceStore* wss = Teuchos::get_default_workspace_store().get();
  
  const DenseLinAlgPack::size_type
    D_rows = decomp_sys.C().rows(),
    D_cols = decomp_sys.N().cols();
  // y = b*y
  if(b==0.0)       *y = 0.0;
  else if(b!=1.0)  DenseLinAlgPack::Vt_S(y,b);
  // Compute t = N'*inv(C')*e(j) then y(i) += -a*t'*x where op(P)(i,j) = 1.0
  Workspace<DenseLinAlgPack::value_type>   e_j_ws(wss,D_rows);
  DVectorSlice                              e_j(&e_j_ws[0],e_j_ws.size());
  e_j = 0.0;
  for( GenPermMatrixSlice::const_iterator itr = P.begin(); itr != P.end(); ++itr ) {
    const DenseLinAlgPack::size_type
      i = P_trans == no_trans ? itr->row_i() : itr->col_j(),
      j = P_trans == no_trans ? itr->col_j() : itr->row_i();
    // t = op(M') * e(j)
    imp_compute_InvCtN_row(D_rows,decomp_sys,j,&e_j,InvCtN_rows);
    DVectorSlice t((*InvCtN_rows)[j-1],D_cols);
    // y(i) += -a*t'*x
    (*y)(i) += (-a) * dot(t,x);
  }
}

*/

} // end namespace

namespace ConstrainedOptPack {

void MatrixVarReductImplicit::initialize(
  const mat_nonsing_ptr_t          &C
  ,const mat_ptr_t                 &N
  ,const mat_ptr_t                 &D_direct
  )
{
  namespace rcp = MemMngPack;
  // Validate the inputs
  TEUCHOS_TEST_FOR_EXCEPTION(
    C.get() == NULL, std::invalid_argument
    ,"MatrixVarReductImplicit::initialize(...): Error, "
    "C.get() must not be NULL" );
  TEUCHOS_TEST_FOR_EXCEPTION(
    N.get() == NULL, std::invalid_argument
    ,"MatrixVarReductImplicit::initialize(...): Error, "
    "N.get() must not be NULL" );
  if( D_direct.get() ) {
    const bool is_compatible_cols = D_direct->space_cols().is_compatible(C->space_cols());
    TEUCHOS_TEST_FOR_EXCEPTION(
      !is_compatible_cols, VectorSpace::IncompatibleVectorSpaces
      ,"MatrixVarReductImplicit::initialize(...): Error, "
      "D_direct->space_cols() is not compatible with C->space_cols()" );
    const bool is_compatible_rows = D_direct->space_rows().is_compatible(N->space_rows());
    TEUCHOS_TEST_FOR_EXCEPTION(
      !is_compatible_rows, VectorSpace::IncompatibleVectorSpaces
      ,"MatrixVarReductImplicit::initialize(...): Error, "
      "D_direct->space_rows() is not compatible with N->space_rows()" );
  }
  // Set the members
  C_        = C;
  N_        = N;
  D_direct_ = D_direct;
  if(!InvCtN_rows_set_list_.empty()) { // Free previously allocated vectors
    for( InvCtN_rows_set_list_t::iterator itr = InvCtN_rows_set_list_.begin();
       itr != InvCtN_rows_set_list_.end(); ++itr )
        {
      InvCtN_rows_[*itr] = Teuchos::null;
    }
    InvCtN_rows_set_list_.clear();
  }
}

void MatrixVarReductImplicit::set_uninitialized()
{
  namespace rcp = MemMngPack;
  C_        = Teuchos::null;
  N_        = Teuchos::null;
  D_direct_ = Teuchos::null;
}

// Overridden from MatrixBase

size_type MatrixVarReductImplicit::rows() const
{
  return C_.get() ? C_->rows() : 0;
}

size_type MatrixVarReductImplicit::cols() const
{
  return N_.get() ? N_->cols() : 0;
}

// Overridden from MatrixOp

const VectorSpace& MatrixVarReductImplicit::space_cols() const
{
  assert_initialized();
  return C_->space_cols();
}

const VectorSpace& MatrixVarReductImplicit::space_rows() const
{
  assert_initialized();
  return N_->space_rows();
}

MatrixOp& MatrixVarReductImplicit::operator=(const MatrixOp& M)
{
  assert_initialized();
  TEUCHOS_TEST_FOR_EXCEPT(true); // ToDo: Finish!
  return *this;
}

std::ostream& MatrixVarReductImplicit::output(std::ostream& o) const
{
  o << "This is a " << this->rows() << " x " << this->cols()
    << " variable reduction matrix D = -inv(C)*N where C and N are:\n"
    << "C =\n" << *C_
    << "N =\n" << *N_;
  return o;
}

void MatrixVarReductImplicit::Vp_StMtV(
  VectorMutable* y, value_type a
  ,BLAS_Cpp::Transp D_trans
  ,const Vector& x, value_type b
  ) const
{
  assert_initialized();
  AbstractLinAlgPack::Vp_MtV_assert_compatibility(y,*this,D_trans,x);
  imp_Vp_StMtV_implicit( y, a, *C_, *N_, D_trans, x, b );
}

void MatrixVarReductImplicit::Vp_StMtV(
  VectorMutable* y, value_type a
  ,BLAS_Cpp::Transp D_trans
  ,const SpVectorSlice& x, value_type b
  ) const
{
  using BLAS_Cpp::rows;
  using BLAS_Cpp::cols;
  using Teuchos::Workspace;
  Teuchos::WorkspaceStore* wss = Teuchos::get_default_workspace_store().get();

  assert_initialized();
  AbstractLinAlgPack::Vp_MtV_assert_compatibility(y,*this,D_trans,x);
  imp_Vp_StMtV_implicit( y, a, *C_, *N_, D_trans, x, b );
/*
  const size_type
    D_rows = this->rows(), D_cols = this->cols(),
    opD_rows = rows(D_rows,D_cols,D_trans), opD_cols = cols(D_rows,D_cols,D_trans);
  DenseLinAlgPack::Vp_MtV_assert_sizes(y->size(),D_rows,D_cols,D_trans,x.size());
  if( use_dense_mat_vec_ && D_dense_.rows() > 0 ) {
    LinAlgOpPack::Vp_StMtV( y, a, D_dense_, D_trans, x, b );
  }
  else {
    if( x.nz() == x.size() ) {  // This is B.S.  Should use MatrixWithOpFactorized object for C!
      DVectorSlice dx = AbstractLinAlgPack::dense_view(x);
      imp_Vp_StMtV_implicit( y, -a, *decomp_sys_, D_trans, dx, b );
    }
    else if( D_trans == BLAS_Cpp::trans && x.nz() < D_cols ) {
      //
      // y = b*y + (-a)*[N'*inv(C')]*x
      //
      // We can do something crafty here.  We can generate columns of N'*inv(C')
      // and then perform y += -a*[N'*inv(C')](:,j)*x(j) for nonzero x(j)
      //
      Workspace<DenseLinAlgPack::value_type>   e_j_ws(wss,D_rows);
      DVectorSlice                              e_j(&e_j_ws[0],e_j_ws.size());
      e_j = 0.0;
      // y = b*y
      if(b==0.0)       *y = 0.0;
      else if(b!=1.0)  Vt_S(y,b);
      // y += -a*[N'*inv(C')](:,j)*x(j), for j <: { j | x(j) != 0.0 }
      const SpVectorSlice::difference_type o = x.offset();
      for( SpVectorSlice::const_iterator itr = x.begin(); itr != x.end(); ++itr ) {
        const size_type j = itr->indice() + o;
        imp_compute_InvCtN_row(D_rows,*decomp_sys_,j,&e_j,&InvCtN_rows_);
        DenseLinAlgPack::Vp_StV( y, -a * itr->value(), DVectorSlice(InvCtN_rows_[j-1],D_cols) );
      }
    }
    else {   // This is B.S.  Should use MatrixWithOpFactorized object for C!
      DVector dx;
      LinAlgOpPack::assign( &dx, x );
      imp_Vp_StMtV_implicit( y, -a, *decomp_sys_, D_trans, dx(), b );
    }
  }
*/
  // ToDo: Consider implementing the above specialized implementation!
}

void MatrixVarReductImplicit::Vp_StPtMtV(
  VectorMutable* y, value_type a
  ,const GenPermMatrixSlice& P, BLAS_Cpp::Transp P_trans
  ,BLAS_Cpp::Transp D_trans
  ,const Vector& x, value_type b
  ) const
{
  using BLAS_Cpp::rows;
  using BLAS_Cpp::cols;
  assert_initialized();
/*
  const size_type
    D_rows = this->rows(), D_cols = this->cols(),
    opD_rows = rows(D_rows,D_cols,D_trans), opD_cols = cols(D_rows,D_cols,D_trans);
  DenseLinAlgPack::Vp_MtV_assert_sizes(y->size(),P.rows(),P.cols(),P_trans,opD_rows);
  DenseLinAlgPack::Vp_MtV_assert_sizes(cols(P.rows(),P.cols(),P_trans),D_rows,D_cols,D_trans,x.size());
  if( D_dense_.rows() > 0 ) {
    AbstractLinAlgPack::dense_Vp_StPtMtV(y,a,P,P_trans,D_dense_,D_trans,x,b);
  }
  else if( P.nz() > D_cols || D_trans == BLAS_Cpp::trans ) {
    // Just use the default implementation
    MatrixOp::Vp_StPtMtV(y,a,P,P_trans,D_trans,x,b);
  }
  else {
    imp_Vp_StPtMtV_by_row(y,a,P,P_trans,*decomp_sys_,x,b,&InvCtN_rows_);
  }
*/
  MatrixOp::Vp_StPtMtV(y,a,P,P_trans,D_trans,x,b); // ToDo:Update specialized implementation above!
}

void MatrixVarReductImplicit::Vp_StPtMtV(
  VectorMutable* y, value_type a
  ,const GenPermMatrixSlice& P, BLAS_Cpp::Transp P_trans
  ,BLAS_Cpp::Transp D_trans
  ,const SpVectorSlice& x, value_type b
  ) const
{
  using BLAS_Cpp::rows;
  using BLAS_Cpp::cols;
  assert_initialized();
/*
  const size_type
    D_rows = this->rows(), D_cols = this->cols(),
    opD_rows = rows(D_rows,D_cols,D_trans), opD_cols = cols(D_rows,D_cols,D_trans);
  DenseLinAlgPack::Vp_MtV_assert_sizes(y->size(),P.rows(),P.cols(),P_trans,opD_rows);
  DenseLinAlgPack::Vp_MtV_assert_sizes(cols(P.rows(),P.cols(),P_trans),D_rows,D_cols,D_trans,x.size());
  if( D_dense_.rows() > 0 ) {
    AbstractLinAlgPack::dense_Vp_StPtMtV(y,a,P,P_trans,D_dense_,D_trans,x,b);
  }
  else if( P.nz() > D_cols || D_trans == BLAS_Cpp::trans ) {
    // Just use the default implementation
    MatrixOp::Vp_StPtMtV(y,a,P,P_trans,D_trans,x,b);
  }
  else {
    imp_Vp_StPtMtV_by_row(y,a,P,P_trans,*decomp_sys_,x,b,&InvCtN_rows_);
  }
*/
  MatrixOp::Vp_StPtMtV(y,a,P,P_trans,D_trans,x,b); // ToDo:Update specialized implementation above!
}

// Private member functions

void MatrixVarReductImplicit::assert_initialized() const
{
  TEUCHOS_TEST_FOR_EXCEPTION(
    C_.get() == NULL, std::logic_error
    ,"MatrixVarReductImplicit::assert_initialized(): Error, "
    "initialize(...) has not been called yet!" );
}

} // end namespace ConstrainedOptPack