potrs: Cholesky forward and back solves

Functions
magma_int_t	magma_cpotrs_expert_gpu_work (magma_uplo_t uplo, magma_int_t n, magma_int_t nrhs, magmaFloatComplex_ptr dA, magma_int_t ldda, magmaFloatComplex_ptr dB, magma_int_t lddb, magma_int_t *info, void *host_work, magma_int_t *lwork_host, void *device_work, magma_int_t *lwork_device, magma_queue_t queue)
	CPOTRS solves a system of linear equations A*X = B with a Hermitian positive definite matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPOTRF.
magma_int_t	magma_cpotrs_gpu (magma_uplo_t uplo, magma_int_t n, magma_int_t nrhs, magmaFloatComplex_ptr dA, magma_int_t ldda, magmaFloatComplex_ptr dB, magma_int_t lddb, magma_int_t *info)
	CPOTRS solves a system of linear equations A*X = B with a Hermitian positive definite matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPOTRF.
magma_int_t	magma_dpotrs_expert_gpu_work (magma_uplo_t uplo, magma_int_t n, magma_int_t nrhs, magmaDouble_ptr dA, magma_int_t ldda, magmaDouble_ptr dB, magma_int_t lddb, magma_int_t *info, void *host_work, magma_int_t *lwork_host, void *device_work, magma_int_t *lwork_device, magma_queue_t queue)
	DPOTRS solves a system of linear equations A*X = B with a symmetric positive definite matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by DPOTRF.
magma_int_t	magma_dpotrs_gpu (magma_uplo_t uplo, magma_int_t n, magma_int_t nrhs, magmaDouble_ptr dA, magma_int_t ldda, magmaDouble_ptr dB, magma_int_t lddb, magma_int_t *info)
	DPOTRS solves a system of linear equations A*X = B with a symmetric positive definite matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by DPOTRF.
magma_int_t	magma_spotrs_expert_gpu_work (magma_uplo_t uplo, magma_int_t n, magma_int_t nrhs, magmaFloat_ptr dA, magma_int_t ldda, magmaFloat_ptr dB, magma_int_t lddb, magma_int_t *info, void *host_work, magma_int_t *lwork_host, void *device_work, magma_int_t *lwork_device, magma_queue_t queue)
	SPOTRS solves a system of linear equations A*X = B with a symmetric positive definite matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by SPOTRF.
magma_int_t	magma_spotrs_gpu (magma_uplo_t uplo, magma_int_t n, magma_int_t nrhs, magmaFloat_ptr dA, magma_int_t ldda, magmaFloat_ptr dB, magma_int_t lddb, magma_int_t *info)
	SPOTRS solves a system of linear equations A*X = B with a symmetric positive definite matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by SPOTRF.
magma_int_t	magma_zpotrs_expert_gpu_work (magma_uplo_t uplo, magma_int_t n, magma_int_t nrhs, magmaDoubleComplex_ptr dA, magma_int_t ldda, magmaDoubleComplex_ptr dB, magma_int_t lddb, magma_int_t *info, void *host_work, magma_int_t *lwork_host, void *device_work, magma_int_t *lwork_device, magma_queue_t queue)
	ZPOTRS solves a system of linear equations A*X = B with a Hermitian positive definite matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by ZPOTRF.
magma_int_t	magma_zpotrs_gpu (magma_uplo_t uplo, magma_int_t n, magma_int_t nrhs, magmaDoubleComplex_ptr dA, magma_int_t ldda, magmaDoubleComplex_ptr dB, magma_int_t lddb, magma_int_t *info)
	ZPOTRS solves a system of linear equations A*X = B with a Hermitian positive definite matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by ZPOTRF.

Detailed Description

Function Documentation

magma_cpotrs_expert_gpu_work()

magma_int_t magma_cpotrs_expert_gpu_work	(	magma_uplo_t	uplo,
		magma_int_t	n,
		magma_int_t	nrhs,
		magmaFloatComplex_ptr	dA,
		magma_int_t	ldda,
		magmaFloatComplex_ptr	dB,
		magma_int_t	lddb,
		magma_int_t *	info,
		void *	host_work,
		magma_int_t *	lwork_host,
		void *	device_work,
		magma_int_t *	lwork_device,
		magma_queue_t	queue )

CPOTRS solves a system of linear equations A*X = B with a Hermitian positive definite matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPOTRF.

This is an expert API, exposing more controls to the user

Parameters

[in]	uplo	magma_uplo_t = MagmaUpper: Upper triangle of A is stored; = MagmaLower: Lower triangle of A is stored.
[in]	n	INTEGER The order of the matrix A. N >= 0.
[in]	nrhs	INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
[in]	dA	COMPLEX array on the GPU, dimension (LDDA,N) The triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H, as computed by CPOTRF.
[in]	ldda	INTEGER The leading dimension of the array A. LDDA >= max(1,N).
[in,out]	dB	COMPLEX array on the GPU, dimension (LDDB,NRHS) On entry, the right hand side matrix B. On exit, the solution matrix X.
[in]	lddb	INTEGER The leading dimension of the array B. LDDB >= max(1,N).
[out]	info	INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value
[in,out]	host_work	Workspace, allocated on host (CPU) memory. For faster CPU-GPU communication, user can allocate it as pinned memory using magma_malloc_pinned()
[in,out]	lwork_host	INTEGER pointer The size of the workspace (host_work) in bytes lwork_host[0] < 0: a workspace query is assumed, the routine calculates the required amount of workspace and returns it in lwork_host. The workspace itself is not referenced, and no computation is performed.

• lwork[0] >= 0: the routine assumes that the user has provided a workspace with the size in lwork_host.

Parameters

[in,out]	device_work	Workspace, allocated on device (GPU) memory.
[in,out]	lwork_device	INTEGER pointer The size of the workspace (device_work) in bytes lwork_device[0] < 0: a workspace query is assumed, the routine calculates the required amount of workspace and returns it in lwork_device. The workspace itself is not referenced, and no computation is performed. lwork_device[0] >= 0: the routine assumes that the user has provided a workspace with the size in lwork_device.
[in]	queue	magma_queue_t created/destroyed by the user

magma_cpotrs_gpu()

magma_int_t magma_cpotrs_gpu	(	magma_uplo_t	uplo,
		magma_int_t	n,
		magma_int_t	nrhs,
		magmaFloatComplex_ptr	dA,
		magma_int_t	ldda,
		magmaFloatComplex_ptr	dB,
		magma_int_t	lddb,
		magma_int_t *	info )

CPOTRS solves a system of linear equations A*X = B with a Hermitian positive definite matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPOTRF.

Parameters

[in]	uplo	magma_uplo_t = MagmaUpper: Upper triangle of A is stored; = MagmaLower: Lower triangle of A is stored.
[in]	n	INTEGER The order of the matrix A. N >= 0.
[in]	nrhs	INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
[in]	dA	COMPLEX array on the GPU, dimension (LDDA,N) The triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H, as computed by CPOTRF.
[in]	ldda	INTEGER The leading dimension of the array A. LDDA >= max(1,N).
[in,out]	dB	COMPLEX array on the GPU, dimension (LDDB,NRHS) On entry, the right hand side matrix B. On exit, the solution matrix X.
[in]	lddb	INTEGER The leading dimension of the array B. LDDB >= max(1,N).
[out]	info	INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value

magma_dpotrs_expert_gpu_work()

magma_int_t magma_dpotrs_expert_gpu_work	(	magma_uplo_t	uplo,
		magma_int_t	n,
		magma_int_t	nrhs,
		magmaDouble_ptr	dA,
		magma_int_t	ldda,
		magmaDouble_ptr	dB,
		magma_int_t	lddb,
		magma_int_t *	info,
		void *	host_work,
		magma_int_t *	lwork_host,
		void *	device_work,
		magma_int_t *	lwork_device,
		magma_queue_t	queue )

DPOTRS solves a system of linear equations A*X = B with a symmetric positive definite matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by DPOTRF.

This is an expert API, exposing more controls to the user

Parameters

[in]	uplo	magma_uplo_t = MagmaUpper: Upper triangle of A is stored; = MagmaLower: Lower triangle of A is stored.
[in]	n	INTEGER The order of the matrix A. N >= 0.
[in]	nrhs	INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
[in]	dA	DOUBLE PRECISION array on the GPU, dimension (LDDA,N) The triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H, as computed by DPOTRF.
[in]	ldda	INTEGER The leading dimension of the array A. LDDA >= max(1,N).
[in,out]	dB	DOUBLE PRECISION array on the GPU, dimension (LDDB,NRHS) On entry, the right hand side matrix B. On exit, the solution matrix X.
[in]	lddb	INTEGER The leading dimension of the array B. LDDB >= max(1,N).
[out]	info	INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value
[in,out]	host_work	Workspace, allocated on host (CPU) memory. For faster CPU-GPU communication, user can allocate it as pinned memory using magma_malloc_pinned()
[in,out]	lwork_host	INTEGER pointer The size of the workspace (host_work) in bytes lwork_host[0] < 0: a workspace query is assumed, the routine calculates the required amount of workspace and returns it in lwork_host. The workspace itself is not referenced, and no computation is performed.

• lwork[0] >= 0: the routine assumes that the user has provided a workspace with the size in lwork_host.

Parameters

[in,out]	device_work	Workspace, allocated on device (GPU) memory.
[in,out]	lwork_device	INTEGER pointer The size of the workspace (device_work) in bytes lwork_device[0] < 0: a workspace query is assumed, the routine calculates the required amount of workspace and returns it in lwork_device. The workspace itself is not referenced, and no computation is performed. lwork_device[0] >= 0: the routine assumes that the user has provided a workspace with the size in lwork_device.
[in]	queue	magma_queue_t created/destroyed by the user

magma_dpotrs_gpu()

magma_int_t magma_dpotrs_gpu	(	magma_uplo_t	uplo,
		magma_int_t	n,
		magma_int_t	nrhs,
		magmaDouble_ptr	dA,
		magma_int_t	ldda,
		magmaDouble_ptr	dB,
		magma_int_t	lddb,
		magma_int_t *	info )

DPOTRS solves a system of linear equations A*X = B with a symmetric positive definite matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by DPOTRF.

Parameters

[in]	uplo	magma_uplo_t = MagmaUpper: Upper triangle of A is stored; = MagmaLower: Lower triangle of A is stored.
[in]	n	INTEGER The order of the matrix A. N >= 0.
[in]	nrhs	INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
[in]	dA	DOUBLE PRECISION array on the GPU, dimension (LDDA,N) The triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H, as computed by DPOTRF.
[in]	ldda	INTEGER The leading dimension of the array A. LDDA >= max(1,N).
[in,out]	dB	DOUBLE PRECISION array on the GPU, dimension (LDDB,NRHS) On entry, the right hand side matrix B. On exit, the solution matrix X.
[in]	lddb	INTEGER The leading dimension of the array B. LDDB >= max(1,N).
[out]	info	INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value

magma_spotrs_expert_gpu_work()

magma_int_t magma_spotrs_expert_gpu_work	(	magma_uplo_t	uplo,
		magma_int_t	n,
		magma_int_t	nrhs,
		magmaFloat_ptr	dA,
		magma_int_t	ldda,
		magmaFloat_ptr	dB,
		magma_int_t	lddb,
		magma_int_t *	info,
		void *	host_work,
		magma_int_t *	lwork_host,
		void *	device_work,
		magma_int_t *	lwork_device,
		magma_queue_t	queue )

SPOTRS solves a system of linear equations A*X = B with a symmetric positive definite matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by SPOTRF.

This is an expert API, exposing more controls to the user

Parameters

[in]	uplo	magma_uplo_t = MagmaUpper: Upper triangle of A is stored; = MagmaLower: Lower triangle of A is stored.
[in]	n	INTEGER The order of the matrix A. N >= 0.
[in]	nrhs	INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
[in]	dA	REAL array on the GPU, dimension (LDDA,N) The triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H, as computed by SPOTRF.
[in]	ldda	INTEGER The leading dimension of the array A. LDDA >= max(1,N).
[in,out]	dB	REAL array on the GPU, dimension (LDDB,NRHS) On entry, the right hand side matrix B. On exit, the solution matrix X.
[in]	lddb	INTEGER The leading dimension of the array B. LDDB >= max(1,N).
[out]	info	INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value
[in,out]	host_work	Workspace, allocated on host (CPU) memory. For faster CPU-GPU communication, user can allocate it as pinned memory using magma_malloc_pinned()
[in,out]	lwork_host	INTEGER pointer The size of the workspace (host_work) in bytes lwork_host[0] < 0: a workspace query is assumed, the routine calculates the required amount of workspace and returns it in lwork_host. The workspace itself is not referenced, and no computation is performed.

• lwork[0] >= 0: the routine assumes that the user has provided a workspace with the size in lwork_host.

Parameters

[in,out]	device_work	Workspace, allocated on device (GPU) memory.
[in,out]	lwork_device	INTEGER pointer The size of the workspace (device_work) in bytes lwork_device[0] < 0: a workspace query is assumed, the routine calculates the required amount of workspace and returns it in lwork_device. The workspace itself is not referenced, and no computation is performed. lwork_device[0] >= 0: the routine assumes that the user has provided a workspace with the size in lwork_device.
[in]	queue	magma_queue_t created/destroyed by the user

magma_spotrs_gpu()

magma_int_t magma_spotrs_gpu	(	magma_uplo_t	uplo,
		magma_int_t	n,
		magma_int_t	nrhs,
		magmaFloat_ptr	dA,
		magma_int_t	ldda,
		magmaFloat_ptr	dB,
		magma_int_t	lddb,
		magma_int_t *	info )

SPOTRS solves a system of linear equations A*X = B with a symmetric positive definite matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by SPOTRF.

Parameters

[in]	uplo	magma_uplo_t = MagmaUpper: Upper triangle of A is stored; = MagmaLower: Lower triangle of A is stored.
[in]	n	INTEGER The order of the matrix A. N >= 0.
[in]	nrhs	INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
[in]	dA	REAL array on the GPU, dimension (LDDA,N) The triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H, as computed by SPOTRF.
[in]	ldda	INTEGER The leading dimension of the array A. LDDA >= max(1,N).
[in,out]	dB	REAL array on the GPU, dimension (LDDB,NRHS) On entry, the right hand side matrix B. On exit, the solution matrix X.
[in]	lddb	INTEGER The leading dimension of the array B. LDDB >= max(1,N).
[out]	info	INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value

magma_zpotrs_expert_gpu_work()

magma_int_t magma_zpotrs_expert_gpu_work	(	magma_uplo_t	uplo,
		magma_int_t	n,
		magma_int_t	nrhs,
		magmaDoubleComplex_ptr	dA,
		magma_int_t	ldda,
		magmaDoubleComplex_ptr	dB,
		magma_int_t	lddb,
		magma_int_t *	info,
		void *	host_work,
		magma_int_t *	lwork_host,
		void *	device_work,
		magma_int_t *	lwork_device,
		magma_queue_t	queue )

ZPOTRS solves a system of linear equations A*X = B with a Hermitian positive definite matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by ZPOTRF.

This is an expert API, exposing more controls to the user

Parameters

[in]	uplo	magma_uplo_t = MagmaUpper: Upper triangle of A is stored; = MagmaLower: Lower triangle of A is stored.
[in]	n	INTEGER The order of the matrix A. N >= 0.
[in]	nrhs	INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
[in]	dA	COMPLEX_16 array on the GPU, dimension (LDDA,N) The triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H, as computed by ZPOTRF.
[in]	ldda	INTEGER The leading dimension of the array A. LDDA >= max(1,N).
[in,out]	dB	COMPLEX_16 array on the GPU, dimension (LDDB,NRHS) On entry, the right hand side matrix B. On exit, the solution matrix X.
[in]	lddb	INTEGER The leading dimension of the array B. LDDB >= max(1,N).
[out]	info	INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value
[in,out]	host_work	Workspace, allocated on host (CPU) memory. For faster CPU-GPU communication, user can allocate it as pinned memory using magma_malloc_pinned()
[in,out]	lwork_host	INTEGER pointer The size of the workspace (host_work) in bytes lwork_host[0] < 0: a workspace query is assumed, the routine calculates the required amount of workspace and returns it in lwork_host. The workspace itself is not referenced, and no computation is performed.

• lwork[0] >= 0: the routine assumes that the user has provided a workspace with the size in lwork_host.

Parameters

[in,out]	device_work	Workspace, allocated on device (GPU) memory.
[in,out]	lwork_device	INTEGER pointer The size of the workspace (device_work) in bytes lwork_device[0] < 0: a workspace query is assumed, the routine calculates the required amount of workspace and returns it in lwork_device. The workspace itself is not referenced, and no computation is performed. lwork_device[0] >= 0: the routine assumes that the user has provided a workspace with the size in lwork_device.
[in]	queue	magma_queue_t created/destroyed by the user

magma_zpotrs_gpu()

magma_int_t magma_zpotrs_gpu	(	magma_uplo_t	uplo,
		magma_int_t	n,
		magma_int_t	nrhs,
		magmaDoubleComplex_ptr	dA,
		magma_int_t	ldda,
		magmaDoubleComplex_ptr	dB,
		magma_int_t	lddb,
		magma_int_t *	info )

ZPOTRS solves a system of linear equations A*X = B with a Hermitian positive definite matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by ZPOTRF.

Parameters

[in]	uplo	magma_uplo_t = MagmaUpper: Upper triangle of A is stored; = MagmaLower: Lower triangle of A is stored.
[in]	n	INTEGER The order of the matrix A. N >= 0.
[in]	nrhs	INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
[in]	dA	COMPLEX_16 array on the GPU, dimension (LDDA,N) The triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H, as computed by ZPOTRF.
[in]	ldda	INTEGER The leading dimension of the array A. LDDA >= max(1,N).
[in,out]	dB	COMPLEX_16 array on the GPU, dimension (LDDB,NRHS) On entry, the right hand side matrix B. On exit, the solution matrix X.
[in]	lddb	INTEGER The leading dimension of the array B. LDDB >= max(1,N).
[out]	info	INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value