SYSV

Computes the solution to symmetric linear systems. More...

Collaboration diagram for SYSV:

Functions
template<std::floating_point Float>
auto	tatooine::lapack::sysv (uplo u, int N, int NRHS, Float *A, int LDA, int *IPIV, Float *B, int LDB, Float *WORK, int LWORK) -> int
template<std::floating_point Float>
auto	tatooine::lapack::sysv (uplo u, int N, int NRHS, Float *A, int LDA, int *IPIV, Float *B, int LDB) -> int
template<std::floating_point Float, size_t N>
auto	tatooine::lapack::sysv (tensor< Float, N, N > &A, tensor< Float, N > &b, uplo const u)
template<std::floating_point Float>
auto	tatooine::lapack::sysv (tensor< Float > &A, tensor< Float > &B, uplo const u)

Detailed Description

Computes the solution to symmetric linear systems.

Computes the solution to a system of linear equations \(\mA\mX = \mB\), where \(\mA\) is an \(n\times n\) symmetric matrix and \(\mX\) and \(\mB\) are \(n\times m\) matrices.

The diagonal pivoting method is used to factor \(\mA\) as \(\mA = \mU \mD \mU^\top\) if uplo = Upper, or \(\mA = \mL \mD \mL^\top\) if uplo = Lower, where \(\mU\) (or \(\mL\)) is a product of permutation and unit upper (lower) triangular matrices, and \(\mD\) is symmetric and block diagonal with \(1\times 1\) and \(2\times 2\) diagonal blocks. The factored form of \(\mA\) is then used to solve the system of equations T.

• LAPACK documentation

Function Documentation

sysv() [1/4]

template<std::floating_point Float>

auto tatooine::lapack::sysv	(	tensor< Float > &	A,
		tensor< Float > &	B,
		uplo const	u
	)

sysv() [2/4]

template<std::floating_point Float, size_t N>

auto tatooine::lapack::sysv	(	tensor< Float, N, N > &	A,
		tensor< Float, N > &	b,
		uplo const	u
	)

sysv() [3/4]

template<std::floating_point Float>

auto tatooine::lapack::sysv	(	uplo	u,
		int	N,
		int	NRHS,
		Float *	A,
		int	LDA,
		int *	IPIV,
		Float *	B,
		int	LDB
	)		-> int

sysv() [4/4]

template<std::floating_point Float>

auto tatooine::lapack::sysv	(	uplo	u,
		int	N,
		int	NRHS,
		Float *	A,
		int	LDA,
		int *	IPIV,
		Float *	B,
		int	LDB,
		Float *	WORK,
		int	LWORK
	)		-> int