trsm: Triangular solve matrix

\(C = op(A)^{-1} B \) or \(C = B \;op(A)^{-1}\) where \(A\) is triangular More...

Functions
template<typename TA , typename TB >
void	blas::trsm (blas::Layout layout, blas::Side side, blas::Uplo uplo, blas::Op trans, blas::Diag diag, int64_t m, int64_t n, blas::scalar_type< TA, TB > alpha, TA const *A, int64_t lda, TB *B, int64_t ldb)
	Solve the triangular matrix-vector equation.
void	blas::batch::trsm (blas::Layout layout, std::vector< blas::Side > const &side, std::vector< blas::Uplo > const &uplo, std::vector< blas::Op > const &trans, std::vector< blas::Diag > const &diag, std::vector< int64_t > const &m, std::vector< int64_t > const &n, std::vector< float > const &alpha, std::vector< float * > const &Aarray, std::vector< int64_t > const &lda, std::vector< float * > const &Barray, std::vector< int64_t > const &ldb, size_t batch_size, std::vector< int64_t > &info)
	CPU, variable-size batched, float version.
void	blas::batch::trsm (blas::Layout layout, std::vector< blas::Side > const &side, std::vector< blas::Uplo > const &uplo, std::vector< blas::Op > const &trans, std::vector< blas::Diag > const &diag, std::vector< int64_t > const &m, std::vector< int64_t > const &n, std::vector< double > const &alpha, std::vector< double * > const &Aarray, std::vector< int64_t > const &lda, std::vector< double * > const &Barray, std::vector< int64_t > const &ldb, size_t batch_size, std::vector< int64_t > &info)
	CPU, variable-size batched, double version.
void	blas::batch::trsm (blas::Layout layout, std::vector< blas::Side > const &side, std::vector< blas::Uplo > const &uplo, std::vector< blas::Op > const &trans, std::vector< blas::Diag > const &diag, std::vector< int64_t > const &m, std::vector< int64_t > const &n, std::vector< std::complex< float > > const &alpha, std::vector< std::complex< float > * > const &Aarray, std::vector< int64_t > const &lda, std::vector< std::complex< float > * > const &Barray, std::vector< int64_t > const &ldb, size_t batch_size, std::vector< int64_t > &info)
	CPU, variable-size batched, complex<float> version.
void	blas::batch::trsm (blas::Layout layout, std::vector< blas::Side > const &side, std::vector< blas::Uplo > const &uplo, std::vector< blas::Op > const &trans, std::vector< blas::Diag > const &diag, std::vector< int64_t > const &m, std::vector< int64_t > const &n, std::vector< std::complex< double > > const &alpha, std::vector< std::complex< double > * > const &Aarray, std::vector< int64_t > const &lda, std::vector< std::complex< double > * > const &Barray, std::vector< int64_t > const &ldb, size_t batch_size, std::vector< int64_t > &info)
	CPU, variable-size batched, complex<double> version.
void	blas::batch::trsm (blas::Layout layout, std::vector< blas::Side > const &side, std::vector< blas::Uplo > const &uplo, std::vector< blas::Op > const &trans, std::vector< blas::Diag > const &diag, std::vector< int64_t > const &m, std::vector< int64_t > const &n, std::vector< float > const &alpha, std::vector< float * > const &Aarray, std::vector< int64_t > const &lda, std::vector< float * > const &Barray, std::vector< int64_t > const &ldb, size_t batch_size, std::vector< int64_t > &info, blas::Queue &queue)
	GPU device, variable-size batched, float version.
void	blas::batch::trsm (blas::Layout layout, std::vector< blas::Side > const &side, std::vector< blas::Uplo > const &uplo, std::vector< blas::Op > const &trans, std::vector< blas::Diag > const &diag, std::vector< int64_t > const &m, std::vector< int64_t > const &n, std::vector< double > const &alpha, std::vector< double * > const &Aarray, std::vector< int64_t > const &lda, std::vector< double * > const &Barray, std::vector< int64_t > const &ldb, size_t batch_size, std::vector< int64_t > &info, blas::Queue &queue)
	GPU device, variable-size batched, double version.
void	blas::batch::trsm (blas::Layout layout, std::vector< blas::Side > const &side, std::vector< blas::Uplo > const &uplo, std::vector< blas::Op > const &trans, std::vector< blas::Diag > const &diag, std::vector< int64_t > const &m, std::vector< int64_t > const &n, std::vector< std::complex< float > > const &alpha, std::vector< std::complex< float > * > const &Aarray, std::vector< int64_t > const &lda, std::vector< std::complex< float > * > const &Barray, std::vector< int64_t > const &ldb, size_t batch_size, std::vector< int64_t > &info, blas::Queue &queue)
	GPU device, variable-size batched, complex<float> version.
void	blas::batch::trsm (blas::Layout layout, std::vector< blas::Side > const &side, std::vector< blas::Uplo > const &uplo, std::vector< blas::Op > const &trans, std::vector< blas::Diag > const &diag, std::vector< int64_t > const &m, std::vector< int64_t > const &n, std::vector< std::complex< double > > const &alpha, std::vector< std::complex< double > * > const &Aarray, std::vector< int64_t > const &lda, std::vector< std::complex< double > * > const &Barray, std::vector< int64_t > const &ldb, size_t batch_size, std::vector< int64_t > &info, blas::Queue &queue)
	GPU device, variable-size batched, complex<double> version.
void	blas::trsm (blas::Layout layout, blas::Side side, blas::Uplo uplo, blas::Op trans, blas::Diag diag, int64_t m, int64_t n, float alpha, float const *A, int64_t lda, float *B, int64_t ldb, blas::Queue &queue)
	GPU device, float version.
void	blas::trsm (blas::Layout layout, blas::Side side, blas::Uplo uplo, blas::Op trans, blas::Diag diag, int64_t m, int64_t n, double alpha, double const *A, int64_t lda, double *B, int64_t ldb, blas::Queue &queue)
	GPU device, double version.
void	blas::trsm (blas::Layout layout, blas::Side side, blas::Uplo uplo, blas::Op trans, blas::Diag diag, int64_t m, int64_t n, std::complex< float > alpha, std::complex< float > const *A, int64_t lda, std::complex< float > *B, int64_t ldb, blas::Queue &queue)
	GPU device, complex<float> version.
void	blas::trsm (blas::Layout layout, blas::Side side, blas::Uplo uplo, blas::Op trans, blas::Diag diag, int64_t m, int64_t n, std::complex< double > alpha, std::complex< double > const *A, int64_t lda, std::complex< double > *B, int64_t ldb, blas::Queue &queue)
	GPU device, complex<double> version.
void	blas::trsm (blas::Layout layout, blas::Side side, blas::Uplo uplo, blas::Op trans, blas::Diag diag, int64_t m, int64_t n, float alpha, float const *A, int64_t lda, float *B, int64_t ldb)
	CPU, float version.
void	blas::trsm (blas::Layout layout, blas::Side side, blas::Uplo uplo, blas::Op trans, blas::Diag diag, int64_t m, int64_t n, double alpha, double const *A, int64_t lda, double *B, int64_t ldb)
	CPU, double version.
void	blas::trsm (blas::Layout layout, blas::Side side, blas::Uplo uplo, blas::Op trans, blas::Diag diag, int64_t m, int64_t n, std::complex< float > alpha, std::complex< float > const *A, int64_t lda, std::complex< float > *B, int64_t ldb)
	CPU, complex<float> version.
void	blas::trsm (blas::Layout layout, blas::Side side, blas::Uplo uplo, blas::Op trans, blas::Diag diag, int64_t m, int64_t n, std::complex< double > alpha, std::complex< double > const *A, int64_t lda, std::complex< double > *B, int64_t ldb)
	CPU, complex<double> version.

Detailed Description

\(C = op(A)^{-1} B \) or \(C = B \;op(A)^{-1}\) where \(A\) is triangular

Function Documentation

trsm()

template<typename TA , typename TB >

void blas::trsm	(	blas::Layout	layout,
		blas::Side	side,
		blas::Uplo	uplo,
		blas::Op	trans,
		blas::Diag	diag,
		int64_t	m,
		int64_t	n,
		blas::scalar_type< TA, TB >	alpha,
		TA const *	A,
		int64_t	lda,
		TB *	B,
		int64_t	ldb
	)

Solve the triangular matrix-vector equation.

\[ op(A) X = \alpha B, \]

or

\[ X op(A) = \alpha B, \]

where \(op(A)\) is one of \(op(A) = A\), \(op(A) = A^T\), or \(op(A) = A^H\), X and B are m-by-n matrices, and A is an m-by-m or 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

latrs for a more numerically robust implementation.

Generic implementation for arbitrary data types.

Parameters

[in]	layout	Matrix storage, Layout::ColMajor or Layout::RowMajor.
[in]	side	Whether \(op(A)\) is on the left or right of X: Side::Left: \(op(A) X = B\). Side::Right: \(X op(A) = B\).
[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 form of \(op(A)\): Op::NoTrans: \(op(A) = A\). Op::Trans: \(op(A) = A^T\). Op::ConjTrans: \(op(A) = A^H\).
[in]	diag	Whether A has a unit or non-unit diagonal: Diag::Unit: A is assumed to be unit triangular. Diag::NonUnit: A is not assumed to be unit triangular.
[in]	m	Number of rows of matrices B and X. m >= 0.
[in]	n	Number of columns of matrices B and X. n >= 0.
[in]	alpha	Scalar alpha. If alpha is zero, A is not accessed.
[in]	A	If side = Left: the m-by-m matrix A, stored in an lda-by-m array [RowMajor: m-by-lda]. If side = Right: the n-by-n matrix A, stored in an lda-by-n array [RowMajor: n-by-lda].
[in]	lda	Leading dimension of A. If side = left: lda >= max(1, m). If side = right: lda >= max(1, n).
[in,out]	B	On entry, the m-by-n matrix B, stored in an ldb-by-n array [RowMajor: m-by-ldb]. On exit, overwritten by the solution matrix X.
[in]	ldb	Leading dimension of B. ldb >= max(1, m) [RowMajor: ldb >= max(1, n)].