Belos::details::LocalDenseMatrixOps< Scalar > Class Template Reference

Low-level operations on non-distributed dense matrices. More...

#include <BelosProjectedLeastSquaresSolver.hpp>

Public Types
typedef Scalar	scalar_type
	The template parameter of this class. More...
typedef Teuchos::ScalarTraits < Scalar >::magnitudeType	magnitude_type
	The type of the magnitude of a scalar_type value. More...
typedef Teuchos::SerialDenseMatrix < int, Scalar >	mat_type
	The type of a dense matrix (or vector) of scalar_type. More...

Public Member Functions
void	conjugateTranspose (mat_type &A_star, const mat_type &A) const
	A_star := (conjugate) transpose of A. More...
void	conjugateTransposeOfUpperTriangular (mat_type &L, const mat_type &R) const
	L := (conjugate) transpose of R (upper triangular). More...
void	zeroOutStrictLowerTriangle (mat_type &A) const
	Zero out everything below the diagonal of A. More...
void	partition (Teuchos::RCP< mat_type > &A_11, Teuchos::RCP< mat_type > &A_21, Teuchos::RCP< mat_type > &A_12, Teuchos::RCP< mat_type > &A_22, mat_type &A, const int numRows1, const int numRows2, const int numCols1, const int numCols2)
	A -> [A_11, A_21, A_12, A_22]. More...
void	matScale (mat_type &A, const scalar_type &alpha) const
	A := alpha * A. More...
void	axpy (mat_type &Y, const scalar_type &alpha, const mat_type &X) const
	Y := Y + alpha * X. More...
void	matAdd (mat_type &A, const mat_type &B) const
	A := A + B. More...
void	matSub (mat_type &A, const mat_type &B) const
	A := A - B. More...
void	rightUpperTriSolve (mat_type &B, const mat_type &R) const
	In Matlab notation: B = B / R, where R is upper triangular. More...
void	matMatMult (const scalar_type &beta, mat_type &C, const scalar_type &alpha, const mat_type &A, const mat_type &B) const
	C := beta*C + alpha*A*B. More...
int	infNaNCount (const mat_type &A, const bool upperTriangular=false) const
	Return the number of Inf or NaN entries in the matrix A. More...
std::pair< bool, std::pair < magnitude_type, magnitude_type > >	isUpperTriangular (const mat_type &A) const
	Is the matrix A upper triangular / trapezoidal? More...
std::pair< bool, std::pair < magnitude_type, magnitude_type > >	isUpperHessenberg (const mat_type &A) const
	Is the matrix A upper Hessenberg? More...
void	ensureUpperTriangular (const mat_type &A, const char *const matrixName) const
	Throw an exception if A is not upper triangular / trapezoidal. More...
void	ensureUpperHessenberg (const mat_type &A, const char *const matrixName) const
	Throw an exception if A is not (strictly) upper Hessenberg. More...
void	ensureUpperHessenberg (const mat_type &A, const char *const matrixName, const magnitude_type relativeTolerance) const
	Throw an exception if A is not "approximately" upper Hessenberg. More...
void	ensureMinimumDimensions (const mat_type &A, const char *const matrixName, const int minNumRows, const int minNumCols) const
	Ensure that the matrix A is at least minNumRows by minNumCols. More...
void	ensureEqualDimensions (const mat_type &A, const char *const matrixName, const int numRows, const int numCols) const
	Ensure that the matrix A is exactly numRows by numCols. More...

Detailed Description

template<class Scalar>
class Belos::details::LocalDenseMatrixOps< Scalar >

Low-level operations on non-distributed dense matrices.

Author

Mark Hoemmen

This class provides a convenient wrapper around some BLAS operations, operating on non-distributed (hence "local") dense matrices.

Definition at line 349 of file BelosProjectedLeastSquaresSolver.hpp.

Member Typedef Documentation

template<class Scalar>

Belos::details::LocalDenseMatrixOps< Scalar >::scalar_type

The template parameter of this class.

Definition at line 353 of file BelosProjectedLeastSquaresSolver.hpp.

template<class Scalar>

Belos::details::LocalDenseMatrixOps< Scalar >::magnitude_type

The type of the magnitude of a scalar_type value.

Definition at line 356 of file BelosProjectedLeastSquaresSolver.hpp.

template<class Scalar>

Belos::details::LocalDenseMatrixOps< Scalar >::mat_type

The type of a dense matrix (or vector) of scalar_type.

Definition at line 359 of file BelosProjectedLeastSquaresSolver.hpp.

Member Function Documentation

template<class Scalar>

void Belos::details::LocalDenseMatrixOps< Scalar >::conjugateTranspose ( mat_type &  A_star, const mat_type &  A  ) const

inline

A_star := (conjugate) transpose of A.

Definition at line 370 of file BelosProjectedLeastSquaresSolver.hpp.

template<class Scalar>

void Belos::details::LocalDenseMatrixOps< Scalar >::conjugateTransposeOfUpperTriangular ( mat_type &  L, const mat_type &  R  ) const

inline

L := (conjugate) transpose of R (upper triangular).

Definition at line 381 of file BelosProjectedLeastSquaresSolver.hpp.

template<class Scalar>

void Belos::details::LocalDenseMatrixOps< Scalar >::zeroOutStrictLowerTriangle ( mat_type &  A ) const

inline

Zero out everything below the diagonal of A.

Definition at line 394 of file BelosProjectedLeastSquaresSolver.hpp.

template<class Scalar>

void Belos::details::LocalDenseMatrixOps< Scalar >::partition ( Teuchos::RCP< mat_type > &  A_11, Teuchos::RCP< mat_type > &  A_21, Teuchos::RCP< mat_type > &  A_12, Teuchos::RCP< mat_type > &  A_22, mat_type &  A, const int  numRows1, const int  numRows2, const int  numCols1, const int  numCols2  )

inline

A -> [A_11, A_21, A_12, A_22].

The first four arguments are the output arguments. They are views of their respective submatrices of A.

Note

SerialDenseMatrix's operator= and copy constructor both always copy the matrix deeply, so I can't make the output arguments "mat_type&".

Definition at line 414 of file BelosProjectedLeastSquaresSolver.hpp.

template<class Scalar>

void Belos::details::LocalDenseMatrixOps< Scalar >::matScale ( mat_type &  A, const scalar_type &  alpha  ) const

inline

A := alpha * A.

Definition at line 435 of file BelosProjectedLeastSquaresSolver.hpp.

template<class Scalar>

void Belos::details::LocalDenseMatrixOps< Scalar >::axpy ( mat_type &  Y, const scalar_type &  alpha, const mat_type &  X  ) const

inline

Y := Y + alpha * X.

"AXPY" stands for "alpha times X plus y," and is the traditional abbreviation for this operation.

Definition at line 459 of file BelosProjectedLeastSquaresSolver.hpp.

template<class Scalar>

void Belos::details::LocalDenseMatrixOps< Scalar >::matAdd ( mat_type &  A, const mat_type &  B  ) const

inline

A := A + B.

Definition at line 479 of file BelosProjectedLeastSquaresSolver.hpp.

template<class Scalar>

void Belos::details::LocalDenseMatrixOps< Scalar >::matSub ( mat_type &  A, const mat_type &  B  ) const

inline

A := A - B.

Definition at line 506 of file BelosProjectedLeastSquaresSolver.hpp.

template<class Scalar>

void Belos::details::LocalDenseMatrixOps< Scalar >::rightUpperTriSolve ( mat_type &  B, const mat_type &  R  ) const

inline

In Matlab notation: B = B / R, where R is upper triangular.

This method only looks at the upper left R.numCols() by R.numCols() part of R.

Definition at line 536 of file BelosProjectedLeastSquaresSolver.hpp.

template<class Scalar>

void Belos::details::LocalDenseMatrixOps< Scalar >::matMatMult ( const scalar_type &  beta, mat_type &  C, const scalar_type &  alpha, const mat_type &  A, const mat_type &  B  ) const

inline

C := beta*C + alpha*A*B.

This method is a thin wrapper around the BLAS' _GEMM routine. The matrix C is NOT allowed to alias the matrices A or B. This method makes no effort to check for aliasing.

Definition at line 558 of file BelosProjectedLeastSquaresSolver.hpp.

template<class Scalar>

int Belos::details::LocalDenseMatrixOps< Scalar >::infNaNCount ( const mat_type &  A, const bool  upperTriangular = false  ) const

inline

Return the number of Inf or NaN entries in the matrix A.

Parameters

A	[in] The matrix to check.
upperTriangular	[in] If true, only check the upper triangle / trapezoid of A. Otherwise, check all entries of A.

Definition at line 598 of file BelosProjectedLeastSquaresSolver.hpp.

template<class Scalar>

std::pair<bool, std::pair<magnitude_type, magnitude_type> > Belos::details::LocalDenseMatrixOps< Scalar >::isUpperTriangular ( const mat_type &  A ) const

inline

Is the matrix A upper triangular / trapezoidal?

Returns

(is upper triangular?, (squared Frobenius norm of strict lower triangle, squared Frobenius norm of the whole matrix))

Definition at line 625 of file BelosProjectedLeastSquaresSolver.hpp.

template<class Scalar>

std::pair<bool, std::pair<magnitude_type, magnitude_type> > Belos::details::LocalDenseMatrixOps< Scalar >::isUpperHessenberg ( const mat_type &  A ) const

inline

Is the matrix A upper Hessenberg?

Returns

(is upper Hessenberg?, (squared Frobenius norm of the part of A that should be zero if A is upper Hessenberg, squared Frobenius norm of the whole matrix))

Definition at line 658 of file BelosProjectedLeastSquaresSolver.hpp.

template<class Scalar>

void Belos::details::LocalDenseMatrixOps< Scalar >::ensureUpperTriangular ( const mat_type &  A, const char *const  matrixName  ) const

inline

Throw an exception if A is not upper triangular / trapezoidal.

Parameters

A	[in] The matrix to test.
matrixName	[in] Name of the matrix. Used only to make the exception message more informative.

Definition at line 691 of file BelosProjectedLeastSquaresSolver.hpp.

template<class Scalar>

void Belos::details::LocalDenseMatrixOps< Scalar >::ensureUpperHessenberg ( const mat_type &  A, const char *const  matrixName  ) const

inline

Throw an exception if A is not (strictly) upper Hessenberg.

Parameters

A	[in] The matrix to test.
matrixName	[in] Name of the matrix. Used only to make the exception message more informative.

Definition at line 712 of file BelosProjectedLeastSquaresSolver.hpp.

template<class Scalar>

void Belos::details::LocalDenseMatrixOps< Scalar >::ensureUpperHessenberg ( const mat_type &  A, const char *const  matrixName, const magnitude_type  relativeTolerance  ) const

inline

Throw an exception if A is not "approximately" upper Hessenberg.

"Approximately" in this case means that the Frobenius norm of the part of A that should be zero, divided by the Frobenius norm of all of A, is less than or equal to the given relative tolerance.

Parameters

A	[in] The matrix to test.
matrixName	[in] Name of the matrix. Used only to make the exception message more informative.
relativeTolerance	[in] Amount by which we allow the norm of the part of A that should be zero to deviate from zero, relative to the norm of A.

Definition at line 742 of file BelosProjectedLeastSquaresSolver.hpp.

template<class Scalar>

void Belos::details::LocalDenseMatrixOps< Scalar >::ensureMinimumDimensions ( const mat_type &  A, const char *const  matrixName, const int  minNumRows, const int  minNumCols  ) const

inline

Ensure that the matrix A is at least minNumRows by minNumCols.

If A has fewer rows than minNumRows, or fewer columns than minNumCols, this method throws an informative exception.

Parameters

A	[in] The matrix whose dimensions to check.
matrixName	[in] Name of the matrix; used to make the exception message more informative.
minNumRows	[in] Minimum number of rows allowed in A.
minNumCols	[in] Minimum number of columns allowed in A.

Definition at line 775 of file BelosProjectedLeastSquaresSolver.hpp.

template<class Scalar>

void Belos::details::LocalDenseMatrixOps< Scalar >::ensureEqualDimensions ( const mat_type &  A, const char *const  matrixName, const int  numRows, const int  numCols  ) const

inline

Ensure that the matrix A is exactly numRows by numCols.

If A has a different number of rows than numRows, or a different number of columns than numCols, this method throws an informative exception.

Parameters

A	[in] The matrix whose dimensions to check.
matrixName	[in] Name of the matrix; used to make the exception message more informative.
numRows	[in] Number of rows that A must have.
numCols	[in] Number of columns that A must have.

Definition at line 800 of file BelosProjectedLeastSquaresSolver.hpp.

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The documentation for this class was generated from the following file:

• BelosProjectedLeastSquaresSolver.hpp