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

#include <BelosProjectedLeastSquaresSolver.hpp>

Public Types
typedef Scalar	scalar_type
	The template parameter of this class.

typedef Teuchos::ScalarTraits< Scalar >::magnitudeType	magnitude_type
	The type of the magnitude of a `scalar_type` value.

typedef Teuchos::SerialDenseMatrix< int, Scalar >	mat_type
	The type of a dense matrix (or vector) of `scalar_type`.

Public Member Functions
void	conjugateTranspose (mat_type &A_star, const mat_type &A) const
	A_star := (conjugate) transpose of A.

void	conjugateTransposeOfUpperTriangular (mat_type &L, const mat_type &R) const
	L := (conjugate) transpose of R (upper triangular).

void	zeroOutStrictLowerTriangle (mat_type &A) const
	Zero out everything below the diagonal of A.

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].

void	matScale (mat_type &A, const scalar_type &alpha) const
	A := alpha * A.

void	axpy (mat_type &Y, const scalar_type &alpha, const mat_type &X) const
	Y := Y + alpha * X.

void	matAdd (mat_type &A, const mat_type &B) const
	A := A + B.

void	matSub (mat_type &A, const mat_type &B) const
	A := A - B.

void	rightUpperTriSolve (mat_type &B, const mat_type &R) const
	In Matlab notation: B = B / R, where R is upper triangular.

void	matMatMult (const scalar_type &beta, mat_type &C, const scalar_type &alpha, const mat_type &A, const mat_type &B) const
	C := betaC + alphaA*B.

int	infNaNCount (const mat_type &A, const bool upperTriangular=false) const
	Return the number of Inf or NaN entries in the matrix A.

std::pair< bool, std::pair< magnitude_type, magnitude_type > >	isUpperTriangular (const mat_type &A) const
	Is the matrix A upper triangular / trapezoidal?

std::pair< bool, std::pair< magnitude_type, magnitude_type > >	isUpperHessenberg (const mat_type &A) const
	Is the matrix A upper Hessenberg?

void	ensureUpperTriangular (const mat_type &A, const char *const matrixName) const
	Throw an exception if A is not upper triangular / trapezoidal.

void	ensureUpperHessenberg (const mat_type &A, const char *const matrixName) const
	Throw an exception if A is not (strictly) upper Hessenberg.

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.

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.

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.

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 317 of file BelosProjectedLeastSquaresSolver.hpp.

Member Typedef Documentation

◆ scalar_type

template<class Scalar >

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

The template parameter of this class.

Definition at line 321 of file BelosProjectedLeastSquaresSolver.hpp.

◆ magnitude_type

template<class Scalar >

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

The type of the magnitude of a scalar_type value.

Definition at line 324 of file BelosProjectedLeastSquaresSolver.hpp.

◆ mat_type

template<class Scalar >

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

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

Definition at line 327 of file BelosProjectedLeastSquaresSolver.hpp.

Member Function Documentation

◆ conjugateTranspose()

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 338 of file BelosProjectedLeastSquaresSolver.hpp.

◆ conjugateTransposeOfUpperTriangular()

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 349 of file BelosProjectedLeastSquaresSolver.hpp.

◆ zeroOutStrictLowerTriangle()

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 362 of file BelosProjectedLeastSquaresSolver.hpp.

◆ partition()

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 382 of file BelosProjectedLeastSquaresSolver.hpp.

◆ matScale()

template<class Scalar >

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

inline

A := alpha * A.

Definition at line 403 of file BelosProjectedLeastSquaresSolver.hpp.

◆ axpy()

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 427 of file BelosProjectedLeastSquaresSolver.hpp.

◆ matAdd()

template<class Scalar >

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

inline

A := A + B.

Definition at line 447 of file BelosProjectedLeastSquaresSolver.hpp.

◆ matSub()

template<class Scalar >

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

inline

A := A - B.

Definition at line 474 of file BelosProjectedLeastSquaresSolver.hpp.

◆ rightUpperTriSolve()

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 504 of file BelosProjectedLeastSquaresSolver.hpp.

◆ matMatMult()

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 526 of file BelosProjectedLeastSquaresSolver.hpp.

◆ infNaNCount()

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 566 of file BelosProjectedLeastSquaresSolver.hpp.

◆ isUpperTriangular()

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 593 of file BelosProjectedLeastSquaresSolver.hpp.

◆ isUpperHessenberg()

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 626 of file BelosProjectedLeastSquaresSolver.hpp.

◆ ensureUpperTriangular()

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 659 of file BelosProjectedLeastSquaresSolver.hpp.

◆ ensureUpperHessenberg() [1/2]

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 680 of file BelosProjectedLeastSquaresSolver.hpp.

◆ ensureUpperHessenberg() [2/2]

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 710 of file BelosProjectedLeastSquaresSolver.hpp.

◆ ensureMinimumDimensions()

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 743 of file BelosProjectedLeastSquaresSolver.hpp.

◆ ensureEqualDimensions()

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 768 of file BelosProjectedLeastSquaresSolver.hpp.

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

BelosProjectedLeastSquaresSolver.hpp

Public Types

Public Member Functions

Detailed Description

Member Typedef Documentation

◆ scalar_type

◆ magnitude_type

◆ mat_type

Member Function Documentation

◆ conjugateTranspose()

◆ conjugateTransposeOfUpperTriangular()

◆ zeroOutStrictLowerTriangle()

◆ partition()

◆ matScale()

◆ axpy()

◆ matAdd()

◆ matSub()

◆ rightUpperTriSolve()

◆ matMatMult()

◆ infNaNCount()

◆ isUpperTriangular()

◆ isUpperHessenberg()

◆ ensureUpperTriangular()

◆ ensureUpperHessenberg() [1/2]

◆ ensureUpperHessenberg() [2/2]

◆ ensureMinimumDimensions()

◆ ensureEqualDimensions()