potrs: Cholesky forward and back solves

Functions
int	plasma_cpotrs (plasma_enum_t uplo, int n, int nrhs, plasma_complex32_t *pA, int lda, plasma_complex32_t *pB, int ldb)
void	plasma_omp_cpotrs (plasma_enum_t uplo, plasma_desc_t A, plasma_desc_t B, plasma_sequence_t *sequence, plasma_request_t *request)
int	plasma_dpotrs (plasma_enum_t uplo, int n, int nrhs, double *pA, int lda, double *pB, int ldb)
void	plasma_omp_dpotrs (plasma_enum_t uplo, plasma_desc_t A, plasma_desc_t B, plasma_sequence_t *sequence, plasma_request_t *request)
int	plasma_spotrs (plasma_enum_t uplo, int n, int nrhs, float *pA, int lda, float *pB, int ldb)
void	plasma_omp_spotrs (plasma_enum_t uplo, plasma_desc_t A, plasma_desc_t B, plasma_sequence_t *sequence, plasma_request_t *request)
int	plasma_zpotrs (plasma_enum_t uplo, int n, int nrhs, plasma_complex64_t *pA, int lda, plasma_complex64_t *pB, int ldb)
void	plasma_omp_zpotrs (plasma_enum_t uplo, plasma_desc_t A, plasma_desc_t B, plasma_sequence_t *sequence, plasma_request_t *request)

Detailed Description

Function Documentation

int plasma_cpotrs	(	plasma_enum_t	uplo,
		int	n,
		int	nrhs,
		plasma_complex32_t *	pA,
		int	lda,
		plasma_complex32_t *	pB,
		int	ldb
	)

Solves a system of linear equations A * X = B with a Hermitian positive definite in the complex matrix A using the Cholesky factorization A = U^H*U or A = L*L^H computed by plasma_cpotrf.

Parameters

[in]	uplo	PlasmaUpper: Upper triangle of A is stored; PlasmaLower: Lower triangle of A is stored.
[in]	n	The order of the matrix A. n >= 0.
[in]	nrhs	The number of right hand sides, i.e., the number of columns of the matrix B. nrhs >= 0.
[in,out]	pA	The triangular factor U or L from the Cholesky factorization A = U^H*U or A = L*L^H, computed by plasma_cpotrf. Remark: If out-of-place layout translation is used, the matrix A can be considered as input, however if inplace layout translation is enabled, the content of A will be reordered for computation and restored before exiting the function.
[in]	lda	The leading dimension of the array A. lda >= max(1,n).
[in,out]	pB	On entry, the n-by-nrhs right hand side matrix B. On exit, if return value = 0, the n-by-nrhs solution matrix X.
[in]	ldb	The leading dimension of the array B. ldb >= max(1,n).

Return values

PlasmaSuccess	successful exit
<	0 if -i, the i-th argument had an illegal value

See also

plasma_omp_cpotrs

plasma_cpotrs

plasma_dpotrs

plasma_spotrs

plasma_cpotrf

void plasma_omp_cpotrs	(	plasma_enum_t	uplo,
		plasma_desc_t	A,
		plasma_desc_t	B,
		plasma_sequence_t *	sequence,
		plasma_request_t *	request
	)

Solves a system of linear equations using previously computed Cholesky factorization. Non-blocking tile version of plasma_cpotrs(). May return before the computation is finished. 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]	uplo	PlasmaUpper: Upper triangle of A is stored; PlasmaLower: Lower triangle of A is stored.
[in]	A	The triangular factor U or L from the Cholesky factorization A = U^H*U or A = L*L^H, computed by plasma_cpotrf.
[in,out]	B	On entry, the n-by-nrhs right hand side matrix B. On exit, if return value = 0, the n-by-nrhs solution matrix X.
[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_cpotrs

plasma_omp_cpotrs

plasma_omp_cpotrs

plasma_omp_dpotrs

plasma_omp_spotrs

plasma_omp_cpotrf

int plasma_dpotrs	(	plasma_enum_t	uplo,
		int	n,
		int	nrhs,
		double *	pA,
		int	lda,
		double *	pB,
		int	ldb
	)

Solves a system of linear equations A * X = B with a symmetric positive definite in the complex matrix A using the Cholesky factorization A = U^T*U or A = L*L^T computed by plasma_dpotrf.

Parameters

[in]	uplo	PlasmaUpper: Upper triangle of A is stored; PlasmaLower: Lower triangle of A is stored.
[in]	n	The order of the matrix A. n >= 0.
[in]	nrhs	The number of right hand sides, i.e., the number of columns of the matrix B. nrhs >= 0.
[in,out]	pA	The triangular factor U or L from the Cholesky factorization A = U^T*U or A = L*L^T, computed by plasma_dpotrf. Remark: If out-of-place layout translation is used, the matrix A can be considered as input, however if inplace layout translation is enabled, the content of A will be reordered for computation and restored before exiting the function.
[in]	lda	The leading dimension of the array A. lda >= max(1,n).
[in,out]	pB	On entry, the n-by-nrhs right hand side matrix B. On exit, if return value = 0, the n-by-nrhs solution matrix X.
[in]	ldb	The leading dimension of the array B. ldb >= max(1,n).

Return values

PlasmaSuccess	successful exit
<	0 if -i, the i-th argument had an illegal value

See also

plasma_omp_dpotrs

plasma_cpotrs

plasma_dpotrs

plasma_spotrs

plasma_dpotrf

void plasma_omp_dpotrs	(	plasma_enum_t	uplo,
		plasma_desc_t	A,
		plasma_desc_t	B,
		plasma_sequence_t *	sequence,
		plasma_request_t *	request
	)

Solves a system of linear equations using previously computed Cholesky factorization. Non-blocking tile version of plasma_dpotrs(). May return before the computation is finished. 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]	uplo	PlasmaUpper: Upper triangle of A is stored; PlasmaLower: Lower triangle of A is stored.
[in]	A	The triangular factor U or L from the Cholesky factorization A = U^T*U or A = L*L^T, computed by plasma_dpotrf.
[in,out]	B	On entry, the n-by-nrhs right hand side matrix B. On exit, if return value = 0, the n-by-nrhs solution matrix X.
[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_dpotrs

plasma_omp_dpotrs

plasma_omp_cpotrs

plasma_omp_dpotrs

plasma_omp_spotrs

plasma_omp_dpotrf

int plasma_spotrs	(	plasma_enum_t	uplo,
		int	n,
		int	nrhs,
		float *	pA,
		int	lda,
		float *	pB,
		int	ldb
	)

Solves a system of linear equations A * X = B with a symmetric positive definite in the complex matrix A using the Cholesky factorization A = U^T*U or A = L*L^T computed by plasma_spotrf.

Parameters

[in]	uplo	PlasmaUpper: Upper triangle of A is stored; PlasmaLower: Lower triangle of A is stored.
[in]	n	The order of the matrix A. n >= 0.
[in]	nrhs	The number of right hand sides, i.e., the number of columns of the matrix B. nrhs >= 0.
[in,out]	pA	The triangular factor U or L from the Cholesky factorization A = U^T*U or A = L*L^T, computed by plasma_spotrf. Remark: If out-of-place layout translation is used, the matrix A can be considered as input, however if inplace layout translation is enabled, the content of A will be reordered for computation and restored before exiting the function.
[in]	lda	The leading dimension of the array A. lda >= max(1,n).
[in,out]	pB	On entry, the n-by-nrhs right hand side matrix B. On exit, if return value = 0, the n-by-nrhs solution matrix X.
[in]	ldb	The leading dimension of the array B. ldb >= max(1,n).

Return values

PlasmaSuccess	successful exit
<	0 if -i, the i-th argument had an illegal value

See also

plasma_omp_spotrs

plasma_cpotrs

plasma_dpotrs

plasma_spotrs

plasma_spotrf

void plasma_omp_spotrs	(	plasma_enum_t	uplo,
		plasma_desc_t	A,
		plasma_desc_t	B,
		plasma_sequence_t *	sequence,
		plasma_request_t *	request
	)

Solves a system of linear equations using previously computed Cholesky factorization. Non-blocking tile version of plasma_spotrs(). May return before the computation is finished. 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]	uplo	PlasmaUpper: Upper triangle of A is stored; PlasmaLower: Lower triangle of A is stored.
[in]	A	The triangular factor U or L from the Cholesky factorization A = U^T*U or A = L*L^T, computed by plasma_spotrf.
[in,out]	B	On entry, the n-by-nrhs right hand side matrix B. On exit, if return value = 0, the n-by-nrhs solution matrix X.
[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_spotrs

plasma_omp_spotrs

plasma_omp_cpotrs

plasma_omp_dpotrs

plasma_omp_spotrs

plasma_omp_spotrf

int plasma_zpotrs	(	plasma_enum_t	uplo,
		int	n,
		int	nrhs,
		plasma_complex64_t *	pA,
		int	lda,
		plasma_complex64_t *	pB,
		int	ldb
	)

Solves a system of linear equations A * X = B with a Hermitian positive definite in the complex matrix A using the Cholesky factorization A = U^H*U or A = L*L^H computed by plasma_zpotrf.

Parameters

[in]	uplo	PlasmaUpper: Upper triangle of A is stored; PlasmaLower: Lower triangle of A is stored.
[in]	n	The order of the matrix A. n >= 0.
[in]	nrhs	The number of right hand sides, i.e., the number of columns of the matrix B. nrhs >= 0.
[in,out]	pA	The triangular factor U or L from the Cholesky factorization A = U^H*U or A = L*L^H, computed by plasma_zpotrf. Remark: If out-of-place layout translation is used, the matrix A can be considered as input, however if inplace layout translation is enabled, the content of A will be reordered for computation and restored before exiting the function.
[in]	lda	The leading dimension of the array A. lda >= max(1,n).
[in,out]	pB	On entry, the n-by-nrhs right hand side matrix B. On exit, if return value = 0, the n-by-nrhs solution matrix X.
[in]	ldb	The leading dimension of the array B. ldb >= max(1,n).

Return values

PlasmaSuccess	successful exit
<	0 if -i, the i-th argument had an illegal value

See also

plasma_omp_zpotrs

plasma_cpotrs

plasma_dpotrs

plasma_spotrs

plasma_zpotrf

void plasma_omp_zpotrs	(	plasma_enum_t	uplo,
		plasma_desc_t	A,
		plasma_desc_t	B,
		plasma_sequence_t *	sequence,
		plasma_request_t *	request
	)

Solves a system of linear equations using previously computed Cholesky factorization. Non-blocking tile version of plasma_zpotrs(). May return before the computation is finished. 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]	uplo	PlasmaUpper: Upper triangle of A is stored; PlasmaLower: Lower triangle of A is stored.
[in]	A	The triangular factor U or L from the Cholesky factorization A = U^H*U or A = L*L^H, computed by plasma_zpotrf.
[in,out]	B	On entry, the n-by-nrhs right hand side matrix B. On exit, if return value = 0, the n-by-nrhs solution matrix X.
[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_zpotrs

plasma_omp_zpotrs

plasma_omp_cpotrs

plasma_omp_dpotrs

plasma_omp_spotrs

plasma_omp_zpotrf