potrf: Cholesky factorization

Functions
int	plasma_cpotrf (plasma_enum_t uplo, int n, plasma_complex32_t *pA, int lda)
void	plasma_omp_cpotrf (plasma_enum_t uplo, plasma_desc_t A, plasma_sequence_t *sequence, plasma_request_t *request)
int	plasma_dpotrf (plasma_enum_t uplo, int n, double *pA, int lda)
void	plasma_omp_dpotrf (plasma_enum_t uplo, plasma_desc_t A, plasma_sequence_t *sequence, plasma_request_t *request)
int	plasma_spotrf (plasma_enum_t uplo, int n, float *pA, int lda)
void	plasma_omp_spotrf (plasma_enum_t uplo, plasma_desc_t A, plasma_sequence_t *sequence, plasma_request_t *request)
int	plasma_zpotrf (plasma_enum_t uplo, int n, plasma_complex64_t *pA, int lda)
void	plasma_omp_zpotrf (plasma_enum_t uplo, plasma_desc_t A, plasma_sequence_t *sequence, plasma_request_t *request)

Detailed Description

Function Documentation

int plasma_cpotrf	(	plasma_enum_t	uplo,
		int	n,
		plasma_complex32_t *	pA,
		int	lda
	)

Performs the Cholesky factorization of a Hermitian positive definite matrix A. The factorization has the form

\[ A = L \times L^H, \]

or

\[ A = U^H \times U, \]

where U is an upper triangular matrix and L is a lower triangular matrix.

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,out]	pA	On entry, the Hermitian positive definite matrix A. If uplo = PlasmaUpper, the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If uplo = PlasmaLower, the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, if return value = 0, the factor U or L from the Cholesky factorization A = U^H*U or A = L*L^H.
[in]	lda	The leading dimension of the array A. lda >= max(1,n).

Return values

PlasmaSuccess	successful exit
<	0 if -i, the i-th argument had an illegal value
>	0 if i, the leading minor of order i of A is not positive definite, so the factorization could not be completed, and the solution has not been computed.

See also

plasma_omp_cpotrf

plasma_cpotrf

plasma_dpotrf

plasma_spotrf

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

Performs the Cholesky factorization of a Hermitian positive definite matrix. Non-blocking tile version of plasma_cpotrf(). 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	On entry, the Hermitian positive definite matrix A. If uplo = PlasmaUpper, the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If uplo = PlasmaLower, the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, if return value = 0, the factor U or L from the Cholesky factorization A = U^H*U or A = L*L^H.
[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_cpotrf

plasma_omp_cpotrf

plasma_omp_cpotrf

plasma_omp_dpotrf

plasma_omp_spotrf

int plasma_dpotrf	(	plasma_enum_t	uplo,
		int	n,
		double *	pA,
		int	lda
	)

Performs the Cholesky factorization of a symmetric positive definite matrix A. The factorization has the form

\[ A = L \times L^T, \]

or

\[ A = U^T \times U, \]

where U is an upper triangular matrix and L is a lower triangular matrix.

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,out]	pA	On entry, the symmetric positive definite matrix A. If uplo = PlasmaUpper, the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If uplo = PlasmaLower, the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, if return value = 0, the factor U or L from the Cholesky factorization A = U^T*U or A = L*L^T.
[in]	lda	The leading dimension of the array A. lda >= max(1,n).

Return values

PlasmaSuccess	successful exit
<	0 if -i, the i-th argument had an illegal value
>	0 if i, the leading minor of order i of A is not positive definite, so the factorization could not be completed, and the solution has not been computed.

See also

plasma_omp_dpotrf

plasma_cpotrf

plasma_dpotrf

plasma_spotrf

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

Performs the Cholesky factorization of a symmetric positive definite matrix. Non-blocking tile version of plasma_dpotrf(). 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	On entry, the symmetric positive definite matrix A. If uplo = PlasmaUpper, the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If uplo = PlasmaLower, the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, if return value = 0, the factor U or L from the Cholesky factorization A = U^T*U or A = L*L^T.
[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_dpotrf

plasma_omp_dpotrf

plasma_omp_cpotrf

plasma_omp_dpotrf

plasma_omp_spotrf

int plasma_spotrf	(	plasma_enum_t	uplo,
		int	n,
		float *	pA,
		int	lda
	)

Performs the Cholesky factorization of a symmetric positive definite matrix A. The factorization has the form

\[ A = L \times L^T, \]

or

\[ A = U^T \times U, \]

where U is an upper triangular matrix and L is a lower triangular matrix.

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,out]	pA	On entry, the symmetric positive definite matrix A. If uplo = PlasmaUpper, the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If uplo = PlasmaLower, the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, if return value = 0, the factor U or L from the Cholesky factorization A = U^T*U or A = L*L^T.
[in]	lda	The leading dimension of the array A. lda >= max(1,n).

Return values

PlasmaSuccess	successful exit
<	0 if -i, the i-th argument had an illegal value
>	0 if i, the leading minor of order i of A is not positive definite, so the factorization could not be completed, and the solution has not been computed.

See also

plasma_omp_spotrf

plasma_cpotrf

plasma_dpotrf

plasma_spotrf

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

Performs the Cholesky factorization of a symmetric positive definite matrix. Non-blocking tile version of plasma_spotrf(). 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	On entry, the symmetric positive definite matrix A. If uplo = PlasmaUpper, the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If uplo = PlasmaLower, the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, if return value = 0, the factor U or L from the Cholesky factorization A = U^T*U or A = L*L^T.
[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_spotrf

plasma_omp_spotrf

plasma_omp_cpotrf

plasma_omp_dpotrf

plasma_omp_spotrf

int plasma_zpotrf	(	plasma_enum_t	uplo,
		int	n,
		plasma_complex64_t *	pA,
		int	lda
	)

Performs the Cholesky factorization of a Hermitian positive definite matrix A. The factorization has the form

\[ A = L \times L^H, \]

or

\[ A = U^H \times U, \]

where U is an upper triangular matrix and L is a lower triangular matrix.

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,out]	pA	On entry, the Hermitian positive definite matrix A. If uplo = PlasmaUpper, the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If uplo = PlasmaLower, the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, if return value = 0, the factor U or L from the Cholesky factorization A = U^H*U or A = L*L^H.
[in]	lda	The leading dimension of the array A. lda >= max(1,n).

Return values

PlasmaSuccess	successful exit
<	0 if -i, the i-th argument had an illegal value
>	0 if i, the leading minor of order i of A is not positive definite, so the factorization could not be completed, and the solution has not been computed.

See also

plasma_omp_zpotrf

plasma_cpotrf

plasma_dpotrf

plasma_spotrf

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

Performs the Cholesky factorization of a Hermitian positive definite matrix. Non-blocking tile version of plasma_zpotrf(). 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	On entry, the Hermitian positive definite matrix A. If uplo = PlasmaUpper, the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If uplo = PlasmaLower, the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, if return value = 0, the factor U or L from the Cholesky factorization A = U^H*U or A = L*L^H.
[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_zpotrf

plasma_omp_zpotrf

plasma_omp_cpotrf

plasma_omp_dpotrf

plasma_omp_spotrf