Beispiel #1
0
      /// \brief Verify the result of the "thin" QR factorization \f$A = QR\f$.
      ///
      /// This method returns a list of three magnitudes: 
      /// - \f$\| A - QR \|_F\f$
      /// - \f$\|I - Q^* Q\|_F\f$
      /// - \f$\|A\|_F\f$
      ///
      /// The notation $\f\| X \|\f$ denotes the Frobenius norm
      /// (square root of sum of squares) of a matrix \f$X\f$.
      /// Returning the Frobenius norm of \f$A\f$ allows you to scale
      /// or not scale the residual \f$\|A - QR\|\f$ as you prefer.
      virtual std::vector< magnitude_type >
      verify (const multivector_type& A,
	      const multivector_type& Q,
	      const Teuchos::SerialDenseMatrix< local_ordinal_type, scalar_type >& R)
      {
	using Teuchos::ArrayRCP;

	local_ordinal_type nrowsLocal_A, ncols_A, LDA;
	local_ordinal_type nrowsLocal_Q, ncols_Q, LDQ;
	fetchDims (A, nrowsLocal_A, ncols_A, LDA);
	fetchDims (Q, nrowsLocal_Q, ncols_Q, LDQ);
	if (nrowsLocal_A != nrowsLocal_Q)
	  throw std::runtime_error ("A and Q must have same number of rows");
	else if (ncols_A != ncols_Q)
	  throw std::runtime_error ("A and Q must have same number of columns");
	else if (ncols_A != R.numCols())
	  throw std::runtime_error ("A and R must have same number of columns");
	else if (R.numRows() < R.numCols())
	  throw std::runtime_error ("R must have no fewer rows than columns");

	// Const views suffice for verification
	ArrayRCP< const scalar_type > A_ptr = fetchConstView (A);
	ArrayRCP< const scalar_type > Q_ptr = fetchConstView (Q);
	return global_verify (nrowsLocal_A, ncols_A, A_ptr.get(), LDA,
			      Q_ptr.get(), LDQ, R.values(), R.stride(), 
			      pScalarMessenger_.get());
      }
Beispiel #2
0
void
Stokhos::SmolyakPseudoSpectralOperator<ordinal_type,value_type,point_compare_type>::
transformPCE2QP_smolyak(
  const value_type& alpha, 
  const Teuchos::SerialDenseMatrix<ordinal_type,value_type>& input,
  Teuchos::SerialDenseMatrix<ordinal_type,value_type>& result, 
  const value_type& beta,
  bool trans) const {
  Teuchos::SerialDenseMatrix<ordinal_type,value_type> op_input, op_result;
  result.scale(beta);

  for (ordinal_type i=0; i<operators.size(); i++) {
    Teuchos::RCP<operator_type> op = operators[i];
    if (trans) {
      op_input.reshape(input.numRows(), op->coeff_size());
      op_result.reshape(result.numRows(), op->point_size());
    }
    else {
      op_input.reshape(op->coeff_size(), input.numCols());
      op_result.reshape(op->point_size(), result.numCols());
    }
    
    gather(scatter_maps[i], input, trans, op_input);
    op->transformPCE2QP(smolyak_coeffs[i], op_input, op_result, 0.0, trans);
    scatter(gather_maps[i], op_result, trans, result);
  }
}
Beispiel #3
0
  // Update *this with alpha * A * B + beta * (*this). 
  void MvTimesMatAddMv (ScalarType alpha, const Anasazi::MultiVec<ScalarType> &A, 
                        const Teuchos::SerialDenseMatrix<int, ScalarType> &B, 
                        ScalarType beta)
  {
    
    assert (Length_ == A.GetVecLength());
    assert (B.numRows() == A.GetNumberVecs());
    assert (B.numCols() <= NumberVecs_);

    MyMultiVec* MyA;
    MyA = dynamic_cast<MyMultiVec*>(&const_cast<Anasazi::MultiVec<ScalarType> &>(A)); 
    assert(MyA!=NULL);

    if ((*this)[0] == (*MyA)[0]) {
      // If this == A, then need additional storage ...
      // This situation is a bit peculiar but it may be required by
      // certain algorithms.
      
      std::vector<ScalarType> tmp(NumberVecs_);

      for (int i = 0 ; i < Length_ ; ++i) {
        for (int v = 0; v < A.GetNumberVecs() ; ++v) {
          tmp[v] = (*MyA)(i, v);
        }

        for (int v = 0 ; v < B.numCols() ; ++v) {
          (*this)(i, v) *= beta; 
          ScalarType res = Teuchos::ScalarTraits<ScalarType>::zero();

          for (int j = 0 ; j < A.GetNumberVecs() ; ++j) {
            res +=  tmp[j] * B(j, v);
          }

          (*this)(i, v) += alpha * res;
        }
      }
    }
    else {
      for (int i = 0 ; i < Length_ ; ++i) {
        for (int v = 0 ; v < B.numCols() ; ++v) {
          (*this)(i, v) *= beta; 
          ScalarType res = 0.0;
          for (int j = 0 ; j < A.GetNumberVecs() ; ++j) {
            res +=  (*MyA)(i, j) * B(j, v);
          }

          (*this)(i, v) += alpha * res;
        }
      }
    }
  }
Beispiel #4
0
void
Stokhos::SmolyakPseudoSpectralOperator<ordinal_type,value_type,point_compare_type>::
apply_direct(
  const Teuchos::SerialDenseMatrix<ordinal_type,value_type>& A,
  const value_type& alpha, 
  const Teuchos::SerialDenseMatrix<ordinal_type,value_type>& input,
  Teuchos::SerialDenseMatrix<ordinal_type,value_type>& result, 
  const value_type& beta,
  bool trans) const {
  if (trans) {
    TEUCHOS_ASSERT(input.numCols() <= A.numCols());
    TEUCHOS_ASSERT(result.numCols() == A.numRows());
    TEUCHOS_ASSERT(result.numRows() == input.numRows());
    blas.GEMM(Teuchos::NO_TRANS, Teuchos::TRANS, input.numRows(), 
	      A.numRows(), input.numCols(), alpha, input.values(), 
	      input.stride(), A.values(), A.stride(), beta, 
	      result.values(), result.stride());
  }
  else {
    TEUCHOS_ASSERT(input.numRows() <= A.numCols());
    TEUCHOS_ASSERT(result.numRows() == A.numRows());
    TEUCHOS_ASSERT(result.numCols() == input.numCols());
    blas.GEMM(Teuchos::NO_TRANS, Teuchos::NO_TRANS, A.numRows(), 
	      input.numCols(), input.numRows(), alpha, A.values(), 
	      A.stride(), input.values(), input.stride(), beta, 
	      result.values(), result.stride());
  }
}
void assembleIRKState(
  const int stageIndex,
  const Teuchos::SerialDenseMatrix<int,Scalar> &A_in,
  const Scalar dt,
  const Thyra::VectorBase<Scalar> &x_base,
  const Thyra::ProductVectorBase<Scalar> &x_stage_bar,
  Teuchos::Ptr<Thyra::VectorBase<Scalar> > x_out_ptr
  )
{

  typedef ScalarTraits<Scalar> ST;

  const int numStages_in = A_in.numRows();
  TEUCHOS_ASSERT_IN_RANGE_UPPER_EXCLUSIVE( stageIndex, 0, numStages_in );
  TEUCHOS_ASSERT_EQUALITY( A_in.numRows(), numStages_in );
  TEUCHOS_ASSERT_EQUALITY( A_in.numCols(), numStages_in );
  TEUCHOS_ASSERT_EQUALITY( x_stage_bar.productSpace()->numBlocks(), numStages_in );
  Thyra::VectorBase<Scalar>& x_out = *x_out_ptr;

  V_V( outArg(x_out), x_base );
  for ( int j = 0; j < numStages_in; ++j ) {
    Vp_StV( outArg(x_out), dt * A_in(stageIndex,j), *x_stage_bar.getVectorBlock(j) );
  }

}
 void EpetraMultiVec::MvTimesMatAddMv ( double alpha, const MultiVec<double>& A, 
     const Teuchos::SerialDenseMatrix<int,double>& B, double beta ) 
 {
   Epetra_LocalMap LocalMap(B.numRows(), 0, Map().Comm());
   Epetra_MultiVector B_Pvec(View, LocalMap, B.values(), B.stride(), B.numCols());
   
   EpetraMultiVec *A_vec = dynamic_cast<EpetraMultiVec *>(&const_cast<MultiVec<double> &>(A)); 
   TEUCHOS_TEST_FOR_EXCEPTION( A_vec==NULL,  std::invalid_argument, "Anasazi::EpetraMultiVec::SetBlocks() cast of MultiVec<double> to EpetraMultiVec failed.");
   
   TEUCHOS_TEST_FOR_EXCEPTION( 
       Multiply( 'N', 'N', alpha, *A_vec, B_Pvec, beta ) != 0,
       EpetraMultiVecFailure, "Anasazi::EpetraMultiVec::MvTimesMatAddMv() call to Epetra_MultiVec::Multiply() returned a nonzero value.");
 }
void EpetraMultiVec::MvTransMv ( const double alpha, const MultiVec<double>& A,
				 Teuchos::SerialDenseMatrix<int,double>& B) const
{    
  EpetraMultiVec *A_vec = dynamic_cast<EpetraMultiVec *>(&const_cast<MultiVec<double> &>(A));
  
  if (A_vec) {
    Epetra_LocalMap LocalMap(B.numRows(), 0, Map().Comm());
    Epetra_MultiVector B_Pvec(View, LocalMap, B.values(), B.stride(), B.numCols());
    
    int info = B_Pvec.Multiply( 'T', 'N', alpha, *A_vec, *this, 0.0 );
    TEST_FOR_EXCEPTION(info!=0, EpetraMultiVecFailure, 
		       "Belos::EpetraMultiVec::MvTransMv call to Multiply() returned a nonzero value.");
  }
}
        // Generic BLAS level 3 matrix multiplication
        // \f$\text{this}\leftarrow \alpha A B+\beta\text{this}\f$   
        void gemm(const Real alpha,
                  const MV& A,
                  const Teuchos::SerialDenseMatrix<int,Real> &B,
                  const Real beta) {

           // Scale this by beta
            this->scale(beta);

            for(int i=0;i<B.numRows();++i) {
                for(int j=0;j<B.numCols();++j) {
                    mvec_[j]->axpy(alpha*B(i,j),*A.getVector(i));  
                }
            }
        } 
void EpetraMultiVec::MvTimesMatAddMv ( const double alpha, const MultiVec<double>& A, 
				       const Teuchos::SerialDenseMatrix<int,double>& B, const double beta ) 
{
  Epetra_LocalMap LocalMap(B.numRows(), 0, Map().Comm());
  Epetra_MultiVector B_Pvec(View, LocalMap, B.values(), B.stride(), B.numCols());
  
  EpetraMultiVec *A_vec = dynamic_cast<EpetraMultiVec *>(&const_cast<MultiVec<double> &>(A)); 
  TEST_FOR_EXCEPTION(A_vec==NULL, EpetraMultiVecFailure,
                     "Belos::EpetraMultiVec::MvTimesMatAddMv cast from Belos::MultiVec<> to Belos::EpetraMultiVec failed.");
  
  int info = Multiply( 'N', 'N', alpha, *A_vec, B_Pvec, beta );
  TEST_FOR_EXCEPTION(info!=0, EpetraMultiVecFailure, 
		     "Belos::EpetraMultiVec::MvTimesMatAddMv call to Multiply() returned a nonzero value.");

}
Beispiel #10
0
void
Stokhos::SmolyakPseudoSpectralOperator<ordinal_type,value_type,point_compare_type>::
scatter(
  const Teuchos::Array<ordinal_type>& map, 
  const Teuchos::SerialDenseMatrix<ordinal_type,value_type>& input, 
  bool trans, 
  Teuchos::SerialDenseMatrix<ordinal_type,value_type>& result) const {
  if (trans) {
    for (ordinal_type j=0; j<map.size(); j++)
      for (ordinal_type i=0; i<input.numRows(); i++)
	result(i,map[j]) += input(i,j);
  }
  else {
    for (ordinal_type j=0; j<input.numCols(); j++)
      for (ordinal_type i=0; i<map.size(); i++)
	result(map[i],j) += input(i,j);
  }
}
  void EpetraMultiVec::MvTransMv ( double alpha, const MultiVec<double>& A,
                                   Teuchos::SerialDenseMatrix<int,double>& B
#ifdef HAVE_ANASAZI_EXPERIMENTAL
                                   , ConjType conj
#endif
                                  ) const
  {    
    EpetraMultiVec *A_vec = dynamic_cast<EpetraMultiVec *>(&const_cast<MultiVec<double> &>(A));
    
    if (A_vec) {
      Epetra_LocalMap LocalMap(B.numRows(), 0, Map().Comm());
      Epetra_MultiVector B_Pvec(View, LocalMap, B.values(), B.stride(), B.numCols());
      
    TEUCHOS_TEST_FOR_EXCEPTION( 
        B_Pvec.Multiply( 'T', 'N', alpha, *A_vec, *this, 0.0 ) != 0,
        EpetraMultiVecFailure, "Anasazi::EpetraMultiVec::MvTransMv() call to Epetra_MultiVec::Multiply() returned a nonzero value.");
    }
  }
Beispiel #12
0
  // Compute a dense matrix B through the matrix-matrix multiply alpha * A^H * (*this). 
  void MvTransMv (ScalarType alpha, const Anasazi::MultiVec<ScalarType>& A, 
                  Teuchos::SerialDenseMatrix< int, ScalarType >& B
#ifdef HAVE_ANASAZI_EXPERIMENTAL
                  , Anasazi::ConjType conj
#endif
                 ) const
  {
    MyMultiVec* MyA;
    MyA = dynamic_cast<MyMultiVec*>(&const_cast<Anasazi::MultiVec<ScalarType> &>(A)); 
    assert (MyA != 0);
    
    assert (A.GetVecLength() == Length_);
    assert (NumberVecs_ <= B.numCols());
    assert (A.GetNumberVecs() <= B.numRows());
    
#ifdef HAVE_ANASAZI_EXPERIMENTAL
    if (conj == Anasazi::CONJ) {
#endif
      for (int v = 0 ; v < A.GetNumberVecs() ; ++v) {
        for (int w = 0 ; w < NumberVecs_ ; ++w) {
          ScalarType value = 0.0;
          for (int i = 0 ; i < Length_ ; ++i) {
            value += Teuchos::ScalarTraits<ScalarType>::conjugate((*MyA)(i, v)) * (*this)(i, w);
          }
          B(v, w) = alpha * value;
        }
      }
#ifdef HAVE_ANASAZI_EXPERIMENTAL
    } else {
      for (int v = 0 ; v < A.GetNumberVecs() ; ++v) {
        for (int w = 0 ; w < NumberVecs_ ; ++w) {
          ScalarType value = 0.0;
          for (int i = 0 ; i < Length_ ; ++i) {
            value += (*MyA)(i, v) * (*this)(i, w);
          }
          B(v, w) = alpha * value;
        }
      }
    }
#endif
  }
Beispiel #13
0
  // Compute a dense matrix B through the matrix-matrix multiply alpha * A^H * (*this).
  void MvTransMv (const ScalarType alpha, const Belos::MultiVec<ScalarType>& A,
                  Teuchos::SerialDenseMatrix< int, ScalarType >& B) const
  {
    MyMultiVec* MyA;
    MyA = dynamic_cast<MyMultiVec*>(&const_cast<Belos::MultiVec<ScalarType> &>(A));
    TEUCHOS_ASSERT(MyA != NULL);

    assert (A.GetGlobalLength() == Length_);
    assert (NumberVecs_ <= B.numCols());
    assert (A.GetNumberVecs() <= B.numRows());

      for (int v = 0 ; v < A.GetNumberVecs() ; ++v) {
        for (int w = 0 ; w < NumberVecs_ ; ++w) {
          ScalarType value = 0.0;
          for (int i = 0 ; i < Length_ ; ++i) {
            value += Teuchos::ScalarTraits<ScalarType>::conjugate((*MyA)(i, v)) * (*this)(i, w);
          }
          B(v, w) = alpha * value;
        }
      }
  }
Beispiel #14
0
  /*! \brief Update \c mv with \f$ \alpha A B + \beta mv \f$.
   */
  static void MvTimesMatAddMv( const double alpha, const  _MV & A, 
    const Teuchos::SerialDenseMatrix<int,double>& B, 
    const double beta,  _MV & mv )
    {
//      Out::os() << "MvTimesMatAddMv()" << endl;
      int n = B.numCols();
//      Out::os() << "B.numCols()=" << n << endl;

      TEST_FOR_EXCEPT(mv.size() != n);

      for (int j=0; j<mv.size(); j++)
      {
        Vector<double> tmp;
        if (beta==one())
        {
          tmp = mv[j].copy();
        }
        else if (beta==zero())
        {
          tmp = mv[j].copy();
          tmp.setToConstant(zero());
        }
        else
        {
          tmp = beta * mv[j];
        }
        if (alpha != zero())
        {
          for (int i=0; i<A.size(); i++)
          {
            tmp = tmp + alpha*B(i,j)*A[i];
          }
        }
        mv[j].acceptCopyOf(tmp);
      }
    }
  void EpetraOpMultiVec::MvTransMv ( double alpha, const MultiVec<double>& A,
                                   Teuchos::SerialDenseMatrix<int,double>& B
#ifdef HAVE_ANASAZI_EXPERIMENTAL
                                   , ConjType conj
#endif
                                  ) const
  {    
    EpetraOpMultiVec *A_vec = dynamic_cast<EpetraOpMultiVec *>(&const_cast<MultiVec<double> &>(A));
    
    if (A_vec) {
      Epetra_LocalMap LocalMap(B.numRows(), 0, Epetra_MV->Map().Comm());
      Epetra_MultiVector B_Pvec(Epetra_DataAccess::View, LocalMap, B.values(), B.stride(), B.numCols());
     
      int info = Epetra_OP->Apply( *Epetra_MV, *Epetra_MV_Temp );
      TEUCHOS_TEST_FOR_EXCEPTION( info != 0, EpetraSpecializedMultiVecFailure, 
        "Anasazi::EpetraOpMultiVec::MvTransMv(): Error returned from Epetra_Operator::Apply()" );

      TEUCHOS_TEST_FOR_EXCEPTION( 
        B_Pvec.Multiply( 'T', 'N', alpha, *(A_vec->GetEpetraMultiVector()), *Epetra_MV_Temp, 0.0 ) != 0,
        EpetraSpecializedMultiVecFailure, "Anasazi::EpetraOpMultiVec::MvTransMv() call to Epetra_MultiVector::Multiply() returned a nonzero value.");
    }
  }
Beispiel #16
0
    void
    factorExplicit (Kokkos::MultiVector<Scalar, NodeType>& A,
		    Kokkos::MultiVector<Scalar, NodeType>& Q,
		    Teuchos::SerialDenseMatrix<LocalOrdinal, Scalar>& R,
		    const bool contiguousCacheBlocks,
		    const bool forceNonnegativeDiagonal=false)
    {
      using Teuchos::asSafe;
      typedef Kokkos::MultiVector<Scalar, NodeType> KMV;

      // Tsqr currently likes LocalOrdinal ordinals, but
      // Kokkos::MultiVector has size_t ordinals.  Do conversions
      // here.  
      //
      // Teuchos::asSafe() can do safe conversion (e.g., checking for
      // overflow when casting to a narrower integer type), if a
      // custom specialization is defined for
      // Teuchos::ValueTypeConversionTraits<size_t, LocalOrdinal>.
      // Otherwise, this has the same (potentially) unsafe effect as
      // static_cast<LocalOrdinal>(...) would have.
      const LocalOrdinal A_numRows = asSafe<LocalOrdinal> (A.getNumRows());
      const LocalOrdinal A_numCols = asSafe<LocalOrdinal> (A.getNumCols());
      const LocalOrdinal A_stride = asSafe<LocalOrdinal> (A.getStride());
      const LocalOrdinal Q_numRows = asSafe<LocalOrdinal> (Q.getNumRows());
      const LocalOrdinal Q_numCols = asSafe<LocalOrdinal> (Q.getNumCols());
      const LocalOrdinal Q_stride = asSafe<LocalOrdinal> (Q.getStride());

      // Sanity checks for matrix dimensions
      if (A_numRows < A_numCols) {
	std::ostringstream os;
	os << "In Tsqr::factorExplicit: input matrix A has " << A_numRows 
	   << " local rows, and " << A_numCols << " columns.  The input "
	  "matrix must have at least as many rows on each processor as "
	  "there are columns.";
	throw std::invalid_argument(os.str());
      } else if (A_numRows != Q_numRows) {
	std::ostringstream os;
	os << "In Tsqr::factorExplicit: input matrix A and output matrix Q "
	  "must have the same number of rows.  A has " << A_numRows << " rows"
	  " and Q has " << Q_numRows << " rows.";
	throw std::invalid_argument(os.str());
      } else if (R.numRows() < R.numCols()) {
	std::ostringstream os;
	os << "In Tsqr::factorExplicit: output matrix R must have at least "
	  "as many rows as columns.  R has " << R.numRows() << " rows and "
	   << R.numCols() << " columns.";
	throw std::invalid_argument(os.str());
      } else if (A_numCols != R.numCols()) {
	std::ostringstream os;
	os << "In Tsqr::factorExplicit: input matrix A and output matrix R "
	  "must have the same number of columns.  A has " << A_numCols 
	   << " columns and R has " << R.numCols() << " columns.";
	throw std::invalid_argument(os.str());
      }

      // Check for quick exit, based on matrix dimensions
      if (Q_numCols == 0)
	return;

      // Hold on to nonconst views of A and Q.  This will make TSQR
      // correct (if perhaps inefficient) for all possible Kokkos Node
      // types, even GPU nodes.
      Teuchos::ArrayRCP<scalar_type> A_ptr = A.getValuesNonConst();
      Teuchos::ArrayRCP<scalar_type> Q_ptr = Q.getValuesNonConst();

      R.putScalar (STS::zero());
      NodeOutput nodeResults = 
	nodeTsqr_->factor (A_numRows, A_numCols, A_ptr.getRawPtr(), A_stride,
			   R.values(), R.stride(), contiguousCacheBlocks);
      // FIXME (mfh 19 Oct 2010) Replace actions on raw pointer with
      // actions on the Kokkos::MultiVector or at least the ArrayRCP.
      nodeTsqr_->fill_with_zeros (Q_numRows, Q_numCols, 
				  Q_ptr.getRawPtr(), Q_stride,
				  contiguousCacheBlocks);
      matview_type Q_rawView (Q_numRows, Q_numCols, 
			      Q_ptr.getRawPtr(), Q_stride);
      matview_type Q_top_block = 
	nodeTsqr_->top_block (Q_rawView, contiguousCacheBlocks);
      if (Q_top_block.nrows() < R.numCols()) {
	std::ostringstream os;
	os << "The top block of Q has too few rows.  This means that the "
	   << "the intranode TSQR implementation has a bug in its top_block"
	   << "() method.  The top block should have at least " << R.numCols()
	   << " rows, but instead has only " << Q_top_block.ncols() 
	   << " rows.";
	throw std::logic_error (os.str());
      }
      {
	matview_type Q_top (R.numCols(), Q_numCols, Q_top_block.get(), 
			    Q_top_block.lda());
	matview_type R_view (R.numRows(), R.numCols(), R.values(), R.stride());
	distTsqr_->factorExplicit (R_view, Q_top, forceNonnegativeDiagonal);
      }
      nodeTsqr_->apply (ApplyType::NoTranspose, 
			A_numRows, A_numCols, A_ptr.getRawPtr(), A_stride,
			nodeResults, Q_numCols, Q_ptr.getRawPtr(), Q_stride,
			contiguousCacheBlocks);

      // If necessary, force the R factor to have a nonnegative diagonal.
      if (forceNonnegativeDiagonal && 
	  ! QR_produces_R_factor_with_nonnegative_diagonal()) {
	details::NonnegDiagForcer<LocalOrdinal, Scalar, STS::isComplex> forcer;
	matview_type Q_mine (Q_numRows, Q_numCols, Q_ptr.getRawPtr(), Q_stride);
	matview_type R_mine (R.numRows(), R.numCols(), R.values(), R.stride());
	forcer.force (Q_mine, R_mine);
      }

      // "Commit" the changes to the multivector.
      A_ptr = Teuchos::null;
      Q_ptr = Teuchos::null;
    }