trsv: Triangular matrix-vector solve

\(x = op(A^{-1})\; b\) More...

Functions
template<typename TA , typename TX >
void	blas::trsv (blas::Layout layout, blas::Uplo uplo, blas::Op trans, blas::Diag diag, int64_t n, TA const *A, int64_t lda, TX *x, int64_t incx)
	Solve the triangular matrix-vector equation.
void	blas::trsv (blas::Layout layout, blas::Uplo uplo, blas::Op trans, blas::Diag diag, int64_t n, float const *A, int64_t lda, float *x, int64_t incx)
	CPU, float version.
void	blas::trsv (blas::Layout layout, blas::Uplo uplo, blas::Op trans, blas::Diag diag, int64_t n, double const *A, int64_t lda, double *x, int64_t incx)
	CPU, double version.
void	blas::trsv (blas::Layout layout, blas::Uplo uplo, blas::Op trans, blas::Diag diag, int64_t n, std::complex< float > const *A, int64_t lda, std::complex< float > *x, int64_t incx)
	CPU, complex<float> version.
void	blas::trsv (blas::Layout layout, blas::Uplo uplo, blas::Op trans, blas::Diag diag, int64_t n, std::complex< double > const *A, int64_t lda, std::complex< double > *x, int64_t incx)
	CPU, complex<double> version.

Detailed Description

\(x = op(A^{-1})\; b\)

Function Documentation

trsv()

template<typename TA , typename TX >

void blas::trsv	(	blas::Layout	layout,
		blas::Uplo	uplo,
		blas::Op	trans,
		blas::Diag	diag,
		int64_t	n,
		TA const *	A,
		int64_t	lda,
		TX *	x,
		int64_t	incx
	)

Solve the triangular matrix-vector equation.

\[ op(A) x = b, \]

where \(op(A)\) is one of \(op(A) = A\), \(op(A) = A^T\), or \(op(A) = A^H\), x and b are vectors, and A is an n-by-n, unit or non-unit, upper or lower triangular matrix.

No test for singularity or near-singularity is included in this routine. Such tests must be performed before calling this routine.

See also

LAPACK's latrs for a more numerically robust implementation.

Generic implementation for arbitrary data types.

Parameters

[in]	layout	Matrix storage, Layout::ColMajor or Layout::RowMajor.
[in]	uplo	What part of the matrix A is referenced, the opposite triangle being assumed to be zero. Uplo::Lower: A is lower triangular. Uplo::Upper: A is upper triangular.
[in]	trans	The equation to be solved: Op::NoTrans: \(A x = b\), Op::Trans: \(A^T x = b\), Op::ConjTrans: \(A^H x = b\).
[in]	diag	Whether A has a unit or non-unit diagonal: Diag::Unit: A is assumed to be unit triangular. The diagonal elements of A are not referenced. Diag::NonUnit: A is not assumed to be unit triangular.
[in]	n	Number of rows and columns of the matrix A. n >= 0.
[in]	A	The n-by-n matrix A, stored in an lda-by-n array [RowMajor: n-by-lda].
[in]	lda	Leading dimension of A. lda >= max(1, n).
[in,out]	x	The n-element vector x, in an array of length (n-1)*abs(incx) + 1.
[in]	incx	Stride between elements of x. incx must not be zero. If incx < 0, uses elements of x in reverse order: x(n-1), ..., x(0).