trsm: Triangular solve matrix

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

Functions
int	plasma_ctrsm (plasma_enum_t side, plasma_enum_t uplo, plasma_enum_t transa, plasma_enum_t diag, int m, int n, plasma_complex32_t alpha, plasma_complex32_t *pA, int lda, plasma_complex32_t *pB, int ldb)
void	plasma_omp_ctrsm (plasma_enum_t side, plasma_enum_t uplo, plasma_enum_t transa, plasma_enum_t diag, plasma_complex32_t alpha, plasma_desc_t A, plasma_desc_t B, plasma_sequence_t *sequence, plasma_request_t *request)
int	plasma_dtrsm (plasma_enum_t side, plasma_enum_t uplo, plasma_enum_t transa, plasma_enum_t diag, int m, int n, double alpha, double *pA, int lda, double *pB, int ldb)
void	plasma_omp_dtrsm (plasma_enum_t side, plasma_enum_t uplo, plasma_enum_t transa, plasma_enum_t diag, double alpha, plasma_desc_t A, plasma_desc_t B, plasma_sequence_t *sequence, plasma_request_t *request)
int	plasma_strsm (plasma_enum_t side, plasma_enum_t uplo, plasma_enum_t transa, plasma_enum_t diag, int m, int n, float alpha, float *pA, int lda, float *pB, int ldb)
void	plasma_omp_strsm (plasma_enum_t side, plasma_enum_t uplo, plasma_enum_t transa, plasma_enum_t diag, float alpha, plasma_desc_t A, plasma_desc_t B, plasma_sequence_t *sequence, plasma_request_t *request)
int	plasma_ztrsm (plasma_enum_t side, plasma_enum_t uplo, plasma_enum_t transa, plasma_enum_t diag, int m, int n, plasma_complex64_t alpha, plasma_complex64_t *pA, int lda, plasma_complex64_t *pB, int ldb)
void	plasma_omp_ztrsm (plasma_enum_t side, plasma_enum_t uplo, plasma_enum_t transa, plasma_enum_t diag, plasma_complex64_t alpha, plasma_desc_t A, plasma_desc_t B, plasma_sequence_t *sequence, plasma_request_t *request)

Detailed Description

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

Function Documentation

int plasma_ctrsm	(	plasma_enum_t	side,
		plasma_enum_t	uplo,
		plasma_enum_t	transa,
		plasma_enum_t	diag,
		int	m,
		int	n,
		plasma_complex32_t	alpha,
		plasma_complex32_t *	pA,
		int	lda,
		plasma_complex32_t *	pB,
		int	ldb
	)

Solves one of the matrix equations

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

or

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

where op( A ) is one of:

\[ op( A ) = A, \]

\[ op( A ) = A^T, \]

\[ op( A ) = A^H, \]

alpha is a scalar, X and B are m-by-n matrices, and A is a unit or non-unit, upper or lower triangular matrix. The matrix X overwrites B.

Parameters

[in]	side	PlasmaLeft: op(A)*X = B, PlasmaRight: X*op(A) = B.
[in]	uplo	PlasmaUpper: A is upper triangular, PlasmaLower: A is lower triangular.
[in]	transa	PlasmaNoTrans: A is not transposed, PlasmaTrans: A is transposed, PlasmaConjTrans: A is conjugate transposed.
[in]	diag	PlasmaNonUnit: A has non-unit diagonal, PlasmaUnit: A has unit diagonal.
[in]	m	The number of rows of the matrix B. m >= 0.
[in]	n	The number of columns of the matrix B. n >= 0.
[in]	alpha	The scalar alpha.
[in]	pA	The k-by-k triangular matrix, where k = m if side = PlasmaLeft, and k = n if side = PlasmaRight. If uplo = PlasmaUpper, the leading k-by-k upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. If uplo = PlasmaLower, the leading k-by-k lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. If diag = PlasmaUnit, the diagonal elements of A are also not referenced and are assumed to be 1.
[in]	lda	The leading dimension of the array A. lda >= max(1,k).
[in,out]	pB	On entry, the m-by-n right hand side matrix B. On exit, if return value = 0, the m-by-n solution matrix X.
[in]	ldb	The leading dimension of the array B. ldb >= max(1,m).

Return values

PlasmaSuccess

successful exit

See also

plasma_omp_ctrsm

plasma_ctrsm

plasma_dtrsm

plasma_strsm

void plasma_omp_ctrsm	(	plasma_enum_t	side,
		plasma_enum_t	uplo,
		plasma_enum_t	transa,
		plasma_enum_t	diag,
		plasma_complex32_t	alpha,
		plasma_desc_t	A,
		plasma_desc_t	B,
		plasma_sequence_t *	sequence,
		plasma_request_t *	request
	)

Computes triangular solve. Non-blocking tile version of plasma_ctrsm(). Operates on matrices stored by tiles. All matrices are passed through descriptors. All dimensions are taken from the descriptors. Allows for pipelining of operations at runtime.

Parameters

[in]	side	PlasmaLeft: op(A)*X = B, PlasmaRight: X*op(A) = B.
[in]	uplo	PlasmaUpper: A is upper triangular, PlasmaLower: A is lower triangular.
[in]	transa	PlasmaNoTrans: A is not transposed, PlasmaTrans: A is transposed, PlasmaConjTrans: A is conjugate transposed.
[in]	diag	PlasmaNonUnit: A has non-unit diagonal, PlasmaUnit: A has unit diagonal.
[in]	alpha	The scalar alpha.
[in]	A	Descriptor of matrix A.
[in]	B	Descriptor of matrix B.
[in]	sequence	Identifies the sequence of function calls that this call belongs to (for completion checks and exception handling purposes). Check the sequence->status for errors.
[out]	request	Identifies this function call (for exception handling purposes).

Return values

void	Errors are returned by setting sequence->status and request->status to error values. The sequence->status and request->status should never be set to PlasmaSuccess (the initial values) since another async call may be setting a failure value at the same time.

See also

plasma_ctrsm

plasma_omp_ctrsm

plasma_omp_dtrsm

plasma_omp_strsm

int plasma_dtrsm	(	plasma_enum_t	side,
		plasma_enum_t	uplo,
		plasma_enum_t	transa,
		plasma_enum_t	diag,
		int	m,
		int	n,
		double	alpha,
		double *	pA,
		int	lda,
		double *	pB,
		int	ldb
	)

Solves one of the matrix equations

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

or

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

where op( A ) is one of:

\[ op( A ) = A, \]

\[ op( A ) = A^T, \]

\[ op( A ) = A^T, \]

alpha is a scalar, X and B are m-by-n matrices, and A is a unit or non-unit, upper or lower triangular matrix. The matrix X overwrites B.

Parameters

[in]	side	PlasmaLeft: op(A)*X = B, PlasmaRight: X*op(A) = B.
[in]	uplo	PlasmaUpper: A is upper triangular, PlasmaLower: A is lower triangular.
[in]	transa	PlasmaNoTrans: A is not transposed, PlasmaTrans: A is transposed, PlasmaConjTrans: A is conjugate transposed.
[in]	diag	PlasmaNonUnit: A has non-unit diagonal, PlasmaUnit: A has unit diagonal.
[in]	m	The number of rows of the matrix B. m >= 0.
[in]	n	The number of columns of the matrix B. n >= 0.
[in]	alpha	The scalar alpha.
[in]	pA	The k-by-k triangular matrix, where k = m if side = PlasmaLeft, and k = n if side = PlasmaRight. If uplo = PlasmaUpper, the leading k-by-k upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. If uplo = PlasmaLower, the leading k-by-k lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. If diag = PlasmaUnit, the diagonal elements of A are also not referenced and are assumed to be 1.
[in]	lda	The leading dimension of the array A. lda >= max(1,k).
[in,out]	pB	On entry, the m-by-n right hand side matrix B. On exit, if return value = 0, the m-by-n solution matrix X.
[in]	ldb	The leading dimension of the array B. ldb >= max(1,m).

Return values

PlasmaSuccess

successful exit

See also

plasma_omp_dtrsm

plasma_ctrsm

plasma_dtrsm

plasma_strsm

void plasma_omp_dtrsm	(	plasma_enum_t	side,
		plasma_enum_t	uplo,
		plasma_enum_t	transa,
		plasma_enum_t	diag,
		double	alpha,
		plasma_desc_t	A,
		plasma_desc_t	B,
		plasma_sequence_t *	sequence,
		plasma_request_t *	request
	)

Computes triangular solve. Non-blocking tile version of plasma_dtrsm(). Operates on matrices stored by tiles. All matrices are passed through descriptors. All dimensions are taken from the descriptors. Allows for pipelining of operations at runtime.

Parameters

[in]	side	PlasmaLeft: op(A)*X = B, PlasmaRight: X*op(A) = B.
[in]	uplo	PlasmaUpper: A is upper triangular, PlasmaLower: A is lower triangular.
[in]	transa	PlasmaNoTrans: A is not transposed, PlasmaTrans: A is transposed, PlasmaConjTrans: A is conjugate transposed.
[in]	diag	PlasmaNonUnit: A has non-unit diagonal, PlasmaUnit: A has unit diagonal.
[in]	alpha	The scalar alpha.
[in]	A	Descriptor of matrix A.
[in]	B	Descriptor of matrix B.
[in]	sequence	Identifies the sequence of function calls that this call belongs to (for completion checks and exception handling purposes). Check the sequence->status for errors.
[out]	request	Identifies this function call (for exception handling purposes).

Return values

void	Errors are returned by setting sequence->status and request->status to error values. The sequence->status and request->status should never be set to PlasmaSuccess (the initial values) since another async call may be setting a failure value at the same time.

See also

plasma_dtrsm

plasma_omp_ctrsm

plasma_omp_dtrsm

plasma_omp_strsm

int plasma_strsm	(	plasma_enum_t	side,
		plasma_enum_t	uplo,
		plasma_enum_t	transa,
		plasma_enum_t	diag,
		int	m,
		int	n,
		float	alpha,
		float *	pA,
		int	lda,
		float *	pB,
		int	ldb
	)

Solves one of the matrix equations

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

or

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

where op( A ) is one of:

\[ op( A ) = A, \]

\[ op( A ) = A^T, \]

\[ op( A ) = A^T, \]

alpha is a scalar, X and B are m-by-n matrices, and A is a unit or non-unit, upper or lower triangular matrix. The matrix X overwrites B.

Parameters

[in]	side	PlasmaLeft: op(A)*X = B, PlasmaRight: X*op(A) = B.
[in]	uplo	PlasmaUpper: A is upper triangular, PlasmaLower: A is lower triangular.
[in]	transa	PlasmaNoTrans: A is not transposed, PlasmaTrans: A is transposed, PlasmaConjTrans: A is conjugate transposed.
[in]	diag	PlasmaNonUnit: A has non-unit diagonal, PlasmaUnit: A has unit diagonal.
[in]	m	The number of rows of the matrix B. m >= 0.
[in]	n	The number of columns of the matrix B. n >= 0.
[in]	alpha	The scalar alpha.
[in]	pA	The k-by-k triangular matrix, where k = m if side = PlasmaLeft, and k = n if side = PlasmaRight. If uplo = PlasmaUpper, the leading k-by-k upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. If uplo = PlasmaLower, the leading k-by-k lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. If diag = PlasmaUnit, the diagonal elements of A are also not referenced and are assumed to be 1.
[in]	lda	The leading dimension of the array A. lda >= max(1,k).
[in,out]	pB	On entry, the m-by-n right hand side matrix B. On exit, if return value = 0, the m-by-n solution matrix X.
[in]	ldb	The leading dimension of the array B. ldb >= max(1,m).

Return values

PlasmaSuccess

successful exit

See also

plasma_omp_strsm

plasma_ctrsm

plasma_dtrsm

plasma_strsm

void plasma_omp_strsm	(	plasma_enum_t	side,
		plasma_enum_t	uplo,
		plasma_enum_t	transa,
		plasma_enum_t	diag,
		float	alpha,
		plasma_desc_t	A,
		plasma_desc_t	B,
		plasma_sequence_t *	sequence,
		plasma_request_t *	request
	)

Computes triangular solve. Non-blocking tile version of plasma_strsm(). Operates on matrices stored by tiles. All matrices are passed through descriptors. All dimensions are taken from the descriptors. Allows for pipelining of operations at runtime.

Parameters

[in]	side	PlasmaLeft: op(A)*X = B, PlasmaRight: X*op(A) = B.
[in]	uplo	PlasmaUpper: A is upper triangular, PlasmaLower: A is lower triangular.
[in]	transa	PlasmaNoTrans: A is not transposed, PlasmaTrans: A is transposed, PlasmaConjTrans: A is conjugate transposed.
[in]	diag	PlasmaNonUnit: A has non-unit diagonal, PlasmaUnit: A has unit diagonal.
[in]	alpha	The scalar alpha.
[in]	A	Descriptor of matrix A.
[in]	B	Descriptor of matrix B.
[in]	sequence	Identifies the sequence of function calls that this call belongs to (for completion checks and exception handling purposes). Check the sequence->status for errors.
[out]	request	Identifies this function call (for exception handling purposes).

Return values

void	Errors are returned by setting sequence->status and request->status to error values. The sequence->status and request->status should never be set to PlasmaSuccess (the initial values) since another async call may be setting a failure value at the same time.

See also

plasma_strsm

plasma_omp_ctrsm

plasma_omp_dtrsm

plasma_omp_strsm

int plasma_ztrsm	(	plasma_enum_t	side,
		plasma_enum_t	uplo,
		plasma_enum_t	transa,
		plasma_enum_t	diag,
		int	m,
		int	n,
		plasma_complex64_t	alpha,
		plasma_complex64_t *	pA,
		int	lda,
		plasma_complex64_t *	pB,
		int	ldb
	)

Solves one of the matrix equations

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

or

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

where op( A ) is one of:

\[ op( A ) = A, \]

\[ op( A ) = A^T, \]

\[ op( A ) = A^H, \]

alpha is a scalar, X and B are m-by-n matrices, and A is a unit or non-unit, upper or lower triangular matrix. The matrix X overwrites B.

Parameters

[in]	side	PlasmaLeft: op(A)*X = B, PlasmaRight: X*op(A) = B.
[in]	uplo	PlasmaUpper: A is upper triangular, PlasmaLower: A is lower triangular.
[in]	transa	PlasmaNoTrans: A is not transposed, PlasmaTrans: A is transposed, PlasmaConjTrans: A is conjugate transposed.
[in]	diag	PlasmaNonUnit: A has non-unit diagonal, PlasmaUnit: A has unit diagonal.
[in]	m	The number of rows of the matrix B. m >= 0.
[in]	n	The number of columns of the matrix B. n >= 0.
[in]	alpha	The scalar alpha.
[in]	pA	The k-by-k triangular matrix, where k = m if side = PlasmaLeft, and k = n if side = PlasmaRight. If uplo = PlasmaUpper, the leading k-by-k upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. If uplo = PlasmaLower, the leading k-by-k lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. If diag = PlasmaUnit, the diagonal elements of A are also not referenced and are assumed to be 1.
[in]	lda	The leading dimension of the array A. lda >= max(1,k).
[in,out]	pB	On entry, the m-by-n right hand side matrix B. On exit, if return value = 0, the m-by-n solution matrix X.
[in]	ldb	The leading dimension of the array B. ldb >= max(1,m).

Return values

PlasmaSuccess

successful exit

See also

plasma_omp_ztrsm

plasma_ctrsm

plasma_dtrsm

plasma_strsm

void plasma_omp_ztrsm	(	plasma_enum_t	side,
		plasma_enum_t	uplo,
		plasma_enum_t	transa,
		plasma_enum_t	diag,
		plasma_complex64_t	alpha,
		plasma_desc_t	A,
		plasma_desc_t	B,
		plasma_sequence_t *	sequence,
		plasma_request_t *	request
	)

Computes triangular solve. Non-blocking tile version of plasma_ztrsm(). Operates on matrices stored by tiles. All matrices are passed through descriptors. All dimensions are taken from the descriptors. Allows for pipelining of operations at runtime.

Parameters

[in]	side	PlasmaLeft: op(A)*X = B, PlasmaRight: X*op(A) = B.
[in]	uplo	PlasmaUpper: A is upper triangular, PlasmaLower: A is lower triangular.
[in]	transa	PlasmaNoTrans: A is not transposed, PlasmaTrans: A is transposed, PlasmaConjTrans: A is conjugate transposed.
[in]	diag	PlasmaNonUnit: A has non-unit diagonal, PlasmaUnit: A has unit diagonal.
[in]	alpha	The scalar alpha.
[in]	A	Descriptor of matrix A.
[in]	B	Descriptor of matrix B.
[in]	sequence	Identifies the sequence of function calls that this call belongs to (for completion checks and exception handling purposes). Check the sequence->status for errors.
[out]	request	Identifies this function call (for exception handling purposes).

Return values

void	Errors are returned by setting sequence->status and request->status to error values. The sequence->status and request->status should never be set to PlasmaSuccess (the initial values) since another async call may be setting a failure value at the same time.

See also

plasma_ztrsm

plasma_omp_ctrsm

plasma_omp_dtrsm

plasma_omp_strsm