In this namespace the minimal wrappers for the BLAS and LAPACK functions are collected. More...

Functions
std::tuple< std::unique_ptr< double[]>, std::unique_ptr< double[]>, size_t >	cq (const double *const _A, const size_t _m, const size_t _n)
	: splits A = C*Q, with _C an rxm matrix (where r is the rank of _A) and _Q orthogonal. More...

std::tuple< std::unique_ptr< double[]>, std::unique_ptr< double[]>, size_t >	cq_destructive (double *const _A, const size_t _m, const size_t _n)
	: splits A = C*Q, with _C an rxm matrix (where r is the rank of _A) and _Q orthogonal. Destroys A. More...

double	dot_product (const double const _x, const size_t _n, const double const _y)
	: Computes the dot product = x^T*y More...

void	dyadic_vector_product (double _A, const size_t _m, const size_t _n, const double _alpha, const double const _x, const double *const _y)
	: Performs A = alphaxy^T More...

void	inplace_qr (double const _AtoQ, double const _R, const size_t _m, const size_t _n)
	: Performs (AtoQ,R) = QR(AtoQ) More...

void	inplace_rq (double const _R, double const _AtoQ, const size_t _m, const size_t _n)
	: Performs (R,AtoQ) = RQ(AtoQ) More...

void	inverse (double const _B, const double const _A, const size_t _m, const size_t _n)
	: Performs B = A^-1 More...

static bool	is_symmetric (const double *const _A, const size_t _n)

void	matrix_matrix_product (double const _C, const size_t _leftDim, const size_t _rightDim, const double _alpha, const double const _A, const size_t _lda, const bool _transposeA, const size_t _middleDim, const double *const _B, const size_t _ldb, const bool _transposeB)
	: Performs the Matrix-Matrix product C = alphaOP(A) OP(B) More...

static XERUS_force_inline void	matrix_matrix_product (double const _C, const size_t _leftDim, const size_t _rightDim, const double _alpha, const double const _A, const bool _transposeA, const size_t _middleDim, const double *const _B, const bool _transposeB)
	: Performs the Matrix-Matrix product C = alphaOP(A) OP(B) More...

void	matrix_vector_product (double const _x, const size_t _m, const double _alpha, const double const _A, const size_t _n, const bool _transposed, const double *const _y)
	: Perfroms x = alphaOP(A)y More...

double	one_norm (const double *const _x, const size_t _n)
	: Computes the one norm =\|\|x\|\|_1 More...

static bool	pos_neg_definite_diagonal (const double *const _A, const size_t _n)
	checks whether the diagonal of _A is all positive or all negative. returns false otherwise More...

std::tuple< std::unique_ptr< double[]>, std::unique_ptr< double[]>, size_t >	qc (const double *const _A, const size_t _m, const size_t _n)
	: splits A = Q*C, with _C an rxn matrix (where r is the rank of _A) and _Q orthogonal. More...

std::tuple< std::unique_ptr< double[]>, std::unique_ptr< double[]>, size_t >	qc_destructive (double *const _A, const size_t _m, const size_t _n)
	: splits A = Q*C, with _C an rxn matrix (where r is the rank of _A) and _Q orthogonal. Destroys A. More...

void	qr (double const _Q, double const _R, const double *const _A, const size_t _m, const size_t _n)
	: Performs (Q,R) = QR(A) More...

void	qr_destructive (double const _Q, double const _R, double *const _A, const size_t _m, const size_t _n)
	: Performs (Q,R) = QR(A), destroys A in the process More...

void	rq (double const _R, double const _Q, const double *const _A, const size_t _m, const size_t _n)
	: Performs (R,Q) = RQ(A) More...

void	rq_destructive (double const _R, double const _Q, double *const _A, const size_t _m, const size_t _n)
	: Performs (R,Q) = RQ(A), destroys A in the process More...

void	solve (double _x, const double _A, size_t _m, size_t _n, const double *_b, size_t _p)
	: Solves Ax = b for x More...

void	solve_least_squares (double const _x, const double const _A, const size_t _m, const size_t _n, const double *const _b, const size_t _p)
	: Solves min \|\|Ax - b\|\|_2 for x More...

void	solve_least_squares_destructive (double const _x, double const _A, const size_t _m, const size_t _n, double *const _b, const size_t _p)
	: Solves min \|\|Ax - b\|\|_2 for x More...

void	svd (double const _U, double const _S, double const _Vt, const double const _A, const size_t _m, const size_t _n)
	: Performs (U,S,V) = SVD(A) More...

void	svd_destructive (double const _U, double const _S, double const _Vt, double const _A, const size_t _m, const size_t _n)
	: Performs (U,S,V) = SVD(A). Destroys A. More...

double	two_norm (const double *const _x, const size_t _n)
	: Computes the two norm =\|\|x\|\|_2 More...

Detailed Description

In this namespace the minimal wrappers for the BLAS and LAPACK functions are collected.

As an end user of xerus it should never be nessecary to call any of these functions, unless a seriously low level implementation of a critical part of an algorithm is required.

Function Documentation

◆ cq()

std::tuple< std::unique_ptr< double[]>, std::unique_ptr< double[]>, size_t > xerus::blasWrapper::cq	(	const double *const	_A,
		const size_t	_m,
		const size_t	_n
	)

: splits A = C*Q, with _C an rxm matrix (where r is the rank of _A) and _Q orthogonal.

Definition at line 308 of file blasLapackWrapper.cpp.

◆ cq_destructive()

std::tuple< std::unique_ptr< double[]>, std::unique_ptr< double[]>, size_t > xerus::blasWrapper::cq_destructive	(	double *const	_A,
		const size_t	_m,
		const size_t	_n
	)

: splits A = C*Q, with _C an rxm matrix (where r is the rank of _A) and _Q orthogonal. Destroys A.

Definition at line 317 of file blasLapackWrapper.cpp.

◆ dot_product()

double xerus::blasWrapper::dot_product	(	const double *const	_x,
		const size_t	_n,
		const double *const	_y
	)

: Computes the dot product = x^T*y

Definition at line 100 of file blasLapackWrapper.cpp.

◆ dyadic_vector_product()

void xerus::blasWrapper::dyadic_vector_product	(	double *	_A,
		const size_t	_m,
		const size_t	_n,
		const double	_alpha,
		const double *const	_x,
		const double *const	_y
	)

: Performs A = alpha*x*y^T

Definition at line 132 of file blasLapackWrapper.cpp.

◆ inplace_qr()

void xerus::blasWrapper::inplace_qr	(	double *const	_AtoQ,
		double *const	_R,
		const size_t	_m,
		const size_t	_n
	)

: Performs (AtoQ,R) = QR(AtoQ)

Definition at line 383 of file blasLapackWrapper.cpp.

◆ inplace_rq()

void xerus::blasWrapper::inplace_rq	(	double *const	_R,
		double *const	_AtoQ,
		const size_t	_m,
		const size_t	_n
	)

: Performs (R,AtoQ) = RQ(AtoQ)

Definition at line 450 of file blasLapackWrapper.cpp.

◆ inverse()

void xerus::blasWrapper::inverse	(	double *const	_B,
		const double *const	_A,
		const size_t	_m,
		const size_t	_n
	)

: Performs B = A^-1

◆ is_symmetric()

static bool xerus::blasWrapper::is_symmetric	(	const double *const	_A,
		const size_t	_n
	)

static

Definition at line 501 of file blasLapackWrapper.cpp.

◆ matrix_matrix_product() [1/2]

void xerus::blasWrapper::matrix_matrix_product	(	double *const	_C,
		const size_t	_leftDim,
		const size_t	_rightDim,
		const double	_alpha,
		const double *const	_A,
		const size_t	_lda,
		const bool	_transposeA,
		const size_t	_middleDim,
		const double *const	_B,
		const size_t	_ldb,
		const bool	_transposeB
	)

: Performs the Matrix-Matrix product C = alpha*OP(A) * OP(B)

Performs the Matrix-Matrix product c = a * b.

Definition at line 149 of file blasLapackWrapper.cpp.

◆ matrix_matrix_product() [2/2]

static XERUS_force_inline void xerus::blasWrapper::matrix_matrix_product	(	double *const	_C,
		const size_t	_leftDim,
		const size_t	_rightDim,
		const double	_alpha,
		const double *const	_A,
		const bool	_transposeA,
		const size_t	_middleDim,
		const double *const	_B,
		const bool	_transposeB
	)

static

: Performs the Matrix-Matrix product C = alpha*OP(A) * OP(B)

Definition at line 74 of file blasLapackWrapper.h.

◆ matrix_vector_product()

void xerus::blasWrapper::matrix_vector_product	(	double *const	_x,
		const size_t	_m,
		const double	_alpha,
		const double *const	_A,
		const size_t	_n,
		const bool	_transposed,
		const double *const	_y
	)

: Perfroms x = alpha*OP(A)*y

Definition at line 115 of file blasLapackWrapper.cpp.

◆ one_norm()

double xerus::blasWrapper::one_norm	(	const double *const	_x,
		const size_t	_n
	)

: Computes the one norm =||x||_1

Definition at line 76 of file blasLapackWrapper.cpp.

◆ pos_neg_definite_diagonal()

static bool xerus::blasWrapper::pos_neg_definite_diagonal	(	const double *const	_A,
		const size_t	_n
	)

static

checks whether the diagonal of _A is all positive or all negative. returns false otherwise

Definition at line 519 of file blasLapackWrapper.cpp.

◆ qc()

std::tuple< std::unique_ptr< double[]>, std::unique_ptr< double[]>, size_t > xerus::blasWrapper::qc	(	const double *const	_A,
		const size_t	_m,
		const size_t	_n
	)

: splits A = Q*C, with _C an rxn matrix (where r is the rank of _A) and _Q orthogonal.

Definition at line 235 of file blasLapackWrapper.cpp.

◆ qc_destructive()

std::tuple< std::unique_ptr< double[]>, std::unique_ptr< double[]>, size_t > xerus::blasWrapper::qc_destructive	(	double *const	_A,
		const size_t	_m,
		const size_t	_n
	)

: splits A = Q*C, with _C an rxn matrix (where r is the rank of _A) and _Q orthogonal. Destroys A.

Definition at line 243 of file blasLapackWrapper.cpp.

◆ qr()

void xerus::blasWrapper::qr	(	double *const	_Q,
		double *const	_R,
		const double *const	_A,
		const size_t	_m,
		const size_t	_n
	)

: Performs (Q,R) = QR(A)

Definition at line 374 of file blasLapackWrapper.cpp.

◆ qr_destructive()

void xerus::blasWrapper::qr_destructive	(	double *const	_Q,
		double *const	_R,
		double *const	_A,
		const size_t	_m,
		const size_t	_n
	)

: Performs (Q,R) = QR(A), destroys A in the process

Definition at line 388 of file blasLapackWrapper.cpp.

◆ rq()

void xerus::blasWrapper::rq	(	double *const	_R,
		double *const	_Q,
		const double *const	_A,
		const size_t	_m,
		const size_t	_n
	)

: Performs (R,Q) = RQ(A)

Definition at line 441 of file blasLapackWrapper.cpp.

◆ rq_destructive()

void xerus::blasWrapper::rq_destructive	(	double *const	_R,
		double *const	_Q,
		double *const	_A,
		const size_t	_m,
		const size_t	_n
	)

: Performs (R,Q) = RQ(A), destroys A in the process

Definition at line 455 of file blasLapackWrapper.cpp.

◆ solve()

void xerus::blasWrapper::solve	(	double *const	_x,
		const double *const	_A,
		const size_t	_m,
		const size_t	_n,
		const double *const	_b,
		const size_t	_nrhs
	)

: Solves Ax = b for x

Solves Ax = b for x order of checks and solvers inspired by matlabs mldivide https://de.mathworks.com/help/matlab/ref/mldivide.html

Definition at line 542 of file blasLapackWrapper.cpp.

◆ solve_least_squares()

void xerus::blasWrapper::solve_least_squares	(	double *const	_x,
		const double *const	_A,
		const size_t	_m,
		const size_t	_n,
		const double *const	_b,
		const size_t	_p
	)

: Solves min ||Ax - b||_2 for x

Definition at line 654 of file blasLapackWrapper.cpp.

◆ solve_least_squares_destructive()

void xerus::blasWrapper::solve_least_squares_destructive	(	double *const	_x,
		double *const	_A,
		const size_t	_m,
		const size_t	_n,
		double *const	_b,
		const size_t	_p
	)

: Solves min ||Ax - b||_2 for x

Definition at line 665 of file blasLapackWrapper.cpp.

◆ svd()

void xerus::blasWrapper::svd	(	double *const	_U,
		double *const	_S,
		double *const	_Vt,
		const double *const	_A,
		const size_t	_m,
		const size_t	_n
	)

: Performs (U,S,V) = SVD(A)

Definition at line 201 of file blasLapackWrapper.cpp.

◆ svd_destructive()

void xerus::blasWrapper::svd_destructive	(	double *const	_U,
		double *const	_S,
		double *const	_Vt,
		double *const	_A,
		const size_t	_m,
		const size_t	_n
	)

: Performs (U,S,V) = SVD(A). Destroys A.

Definition at line 210 of file blasLapackWrapper.cpp.

◆ two_norm()

double xerus::blasWrapper::two_norm	(	const double *const	_x,
		const size_t	_n
	)

: Computes the two norm =||x||_2

Definition at line 88 of file blasLapackWrapper.cpp.

Functions

Detailed Description

Function Documentation

◆ cq()

◆ cq_destructive()

◆ dot_product()

◆ dyadic_vector_product()

◆ inplace_qr()

◆ inplace_rq()

◆ inverse()

◆ is_symmetric()

◆ matrix_matrix_product() [1/2]

◆ matrix_matrix_product() [2/2]

◆ matrix_vector_product()

◆ one_norm()

◆ pos_neg_definite_diagonal()

◆ qc()

◆ qc_destructive()

◆ qr()

◆ qr_destructive()

◆ rq()

◆ rq_destructive()

◆ solve()

◆ solve_least_squares()

◆ solve_least_squares_destructive()

◆ svd()

◆ svd_destructive()

◆ two_norm()