sy/hetrf: symmetric/Hermitian indefinite factorization - no pivoting

Functions
magma_int_t	magma_chetrf_nopiv (magma_uplo_t uplo, magma_int_t n, magmaFloatComplex *A, magma_int_t lda, magma_int_t *info)
	CHETRF_nopiv computes the LDLt factorization of a complex Hermitian matrix A.
magma_int_t	magma_chetrf_nopiv_gpu (magma_uplo_t uplo, magma_int_t n, magmaFloatComplex_ptr dA, magma_int_t ldda, magma_int_t *info)
	CHETRF_nopiv_gpu computes the LDLt factorization of a complex Hermitian matrix A.
magma_int_t	magma_dsytrf_nopiv (magma_uplo_t uplo, magma_int_t n, double *A, magma_int_t lda, magma_int_t *info)
	DSYTRF_nopiv computes the LDLt factorization of a real symmetric matrix A.
magma_int_t	magma_dsytrf_nopiv_gpu (magma_uplo_t uplo, magma_int_t n, magmaDouble_ptr dA, magma_int_t ldda, magma_int_t *info)
	DSYTRF_nopiv_gpu computes the LDLt factorization of a real symmetric matrix A.
magma_int_t	magma_ssytrf_nopiv (magma_uplo_t uplo, magma_int_t n, float *A, magma_int_t lda, magma_int_t *info)
	SSYTRF_nopiv computes the LDLt factorization of a real symmetric matrix A.
magma_int_t	magma_ssytrf_nopiv_gpu (magma_uplo_t uplo, magma_int_t n, magmaFloat_ptr dA, magma_int_t ldda, magma_int_t *info)
	SSYTRF_nopiv_gpu computes the LDLt factorization of a real symmetric matrix A.
magma_int_t	magma_zhetrf_nopiv (magma_uplo_t uplo, magma_int_t n, magmaDoubleComplex *A, magma_int_t lda, magma_int_t *info)
	ZHETRF_nopiv computes the LDLt factorization of a complex Hermitian matrix A.
magma_int_t	magma_zhetrf_nopiv_gpu (magma_uplo_t uplo, magma_int_t n, magmaDoubleComplex_ptr dA, magma_int_t ldda, magma_int_t *info)
	ZHETRF_nopiv_gpu computes the LDLt factorization of a complex Hermitian matrix A.

Detailed Description

Function Documentation

magma_chetrf_nopiv()

magma_int_t magma_chetrf_nopiv	(	magma_uplo_t	uplo,
		magma_int_t	n,
		magmaFloatComplex *	A,
		magma_int_t	lda,
		magma_int_t *	info )

CHETRF_nopiv computes the LDLt factorization of a complex Hermitian matrix A.

This version does not require work space on the GPU passed as input. GPU memory is allocated in the routine.

The factorization has the form A = U^H * D * U, if UPLO = MagmaUpper, or A = L * D * L^H, if UPLO = MagmaLower, where U is an upper triangular matrix, L is lower triangular, and D is a diagonal matrix.

This is the block version of the algorithm, calling Level 3 BLAS.

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,out]	A	COMPLEX array, dimension (LDA,N) On entry, the Hermitian matrix A. If UPLO = MagmaUpper, 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 = MagmaLower, 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 INFO = 0, the factor U or L from the Cholesky factorization A = U^H D U or A = L D L^H. Higher performance is achieved if A is in pinned memory.
[in]	lda	INTEGER The leading dimension of the array A. LDA >= max(1,N).
[out]	info	INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value if INFO = -6, the GPU memory allocation failed > 0: if INFO = i, the leading minor of order i is not positive definite, and the factorization could not be completed.

magma_chetrf_nopiv_gpu()

magma_int_t magma_chetrf_nopiv_gpu	(	magma_uplo_t	uplo,
		magma_int_t	n,
		magmaFloatComplex_ptr	dA,
		magma_int_t	ldda,
		magma_int_t *	info )

CHETRF_nopiv_gpu computes the LDLt factorization of a complex Hermitian matrix A.

The factorization has the form A = U^H * D * U, if UPLO = MagmaUpper, or A = L * D * L^H, if UPLO = MagmaLower, where U is an upper triangular matrix, L is lower triangular, and D is a diagonal matrix.

This is the block version of the algorithm, calling Level 3 BLAS.

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,out]	dA	COMPLEX array on the GPU, dimension (LDDA,N) On entry, the Hermitian matrix A. If UPLO = MagmaUpper, 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 = MagmaLower, 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 INFO = 0, the factor U or L from the Cholesky factorization A = U^H D U or A = L D L^H. Higher performance is achieved if A is in pinned memory, e.g. allocated using cudaMallocHost.
[in]	ldda	INTEGER The leading dimension of the array A. LDDA >= max(1,N).
[out]	info	INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value if INFO = -6, the GPU memory allocation failed > 0: if INFO = i, the leading minor of order i is not positive definite, and the factorization could not be completed.

magma_dsytrf_nopiv()

magma_int_t magma_dsytrf_nopiv	(	magma_uplo_t	uplo,
		magma_int_t	n,
		double *	A,
		magma_int_t	lda,
		magma_int_t *	info )

DSYTRF_nopiv computes the LDLt factorization of a real symmetric matrix A.

This version does not require work space on the GPU passed as input. GPU memory is allocated in the routine.

The factorization has the form A = U^H * D * U, if UPLO = MagmaUpper, or A = L * D * L^H, if UPLO = MagmaLower, where U is an upper triangular matrix, L is lower triangular, and D is a diagonal matrix.

This is the block version of the algorithm, calling Level 3 BLAS.

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,out]	A	DOUBLE PRECISION array, dimension (LDA,N) On entry, the symmetric matrix A. If UPLO = MagmaUpper, 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 = MagmaLower, 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 INFO = 0, the factor U or L from the Cholesky factorization A = U^H D U or A = L D L^H. Higher performance is achieved if A is in pinned memory.
[in]	lda	INTEGER The leading dimension of the array A. LDA >= max(1,N).
[out]	info	INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value if INFO = -6, the GPU memory allocation failed > 0: if INFO = i, the leading minor of order i is not positive definite, and the factorization could not be completed.

magma_dsytrf_nopiv_gpu()

magma_int_t magma_dsytrf_nopiv_gpu	(	magma_uplo_t	uplo,
		magma_int_t	n,
		magmaDouble_ptr	dA,
		magma_int_t	ldda,
		magma_int_t *	info )

DSYTRF_nopiv_gpu computes the LDLt factorization of a real symmetric matrix A.

The factorization has the form A = U^H * D * U, if UPLO = MagmaUpper, or A = L * D * L^H, if UPLO = MagmaLower, where U is an upper triangular matrix, L is lower triangular, and D is a diagonal matrix.

This is the block version of the algorithm, calling Level 3 BLAS.

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,out]	dA	DOUBLE PRECISION array on the GPU, dimension (LDDA,N) On entry, the symmetric matrix A. If UPLO = MagmaUpper, 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 = MagmaLower, 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 INFO = 0, the factor U or L from the Cholesky factorization A = U^H D U or A = L D L^H. Higher performance is achieved if A is in pinned memory, e.g. allocated using cudaMallocHost.
[in]	ldda	INTEGER The leading dimension of the array A. LDDA >= max(1,N).
[out]	info	INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value if INFO = -6, the GPU memory allocation failed > 0: if INFO = i, the leading minor of order i is not positive definite, and the factorization could not be completed.

magma_ssytrf_nopiv()

magma_int_t magma_ssytrf_nopiv	(	magma_uplo_t	uplo,
		magma_int_t	n,
		float *	A,
		magma_int_t	lda,
		magma_int_t *	info )

SSYTRF_nopiv computes the LDLt factorization of a real symmetric matrix A.

This version does not require work space on the GPU passed as input. GPU memory is allocated in the routine.

The factorization has the form A = U^H * D * U, if UPLO = MagmaUpper, or A = L * D * L^H, if UPLO = MagmaLower, where U is an upper triangular matrix, L is lower triangular, and D is a diagonal matrix.

This is the block version of the algorithm, calling Level 3 BLAS.

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,out]	A	REAL array, dimension (LDA,N) On entry, the symmetric matrix A. If UPLO = MagmaUpper, 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 = MagmaLower, 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 INFO = 0, the factor U or L from the Cholesky factorization A = U^H D U or A = L D L^H. Higher performance is achieved if A is in pinned memory.
[in]	lda	INTEGER The leading dimension of the array A. LDA >= max(1,N).
[out]	info	INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value if INFO = -6, the GPU memory allocation failed > 0: if INFO = i, the leading minor of order i is not positive definite, and the factorization could not be completed.

magma_ssytrf_nopiv_gpu()

magma_int_t magma_ssytrf_nopiv_gpu	(	magma_uplo_t	uplo,
		magma_int_t	n,
		magmaFloat_ptr	dA,
		magma_int_t	ldda,
		magma_int_t *	info )

SSYTRF_nopiv_gpu computes the LDLt factorization of a real symmetric matrix A.

The factorization has the form A = U^H * D * U, if UPLO = MagmaUpper, or A = L * D * L^H, if UPLO = MagmaLower, where U is an upper triangular matrix, L is lower triangular, and D is a diagonal matrix.

This is the block version of the algorithm, calling Level 3 BLAS.

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,out]	dA	REAL array on the GPU, dimension (LDDA,N) On entry, the symmetric matrix A. If UPLO = MagmaUpper, 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 = MagmaLower, 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 INFO = 0, the factor U or L from the Cholesky factorization A = U^H D U or A = L D L^H. Higher performance is achieved if A is in pinned memory, e.g. allocated using cudaMallocHost.
[in]	ldda	INTEGER The leading dimension of the array A. LDDA >= max(1,N).
[out]	info	INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value if INFO = -6, the GPU memory allocation failed > 0: if INFO = i, the leading minor of order i is not positive definite, and the factorization could not be completed.

magma_zhetrf_nopiv()

magma_int_t magma_zhetrf_nopiv	(	magma_uplo_t	uplo,
		magma_int_t	n,
		magmaDoubleComplex *	A,
		magma_int_t	lda,
		magma_int_t *	info )

ZHETRF_nopiv computes the LDLt factorization of a complex Hermitian matrix A.

This version does not require work space on the GPU passed as input. GPU memory is allocated in the routine.

The factorization has the form A = U^H * D * U, if UPLO = MagmaUpper, or A = L * D * L^H, if UPLO = MagmaLower, where U is an upper triangular matrix, L is lower triangular, and D is a diagonal matrix.

This is the block version of the algorithm, calling Level 3 BLAS.

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,out]	A	COMPLEX_16 array, dimension (LDA,N) On entry, the Hermitian matrix A. If UPLO = MagmaUpper, 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 = MagmaLower, 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 INFO = 0, the factor U or L from the Cholesky factorization A = U^H D U or A = L D L^H. Higher performance is achieved if A is in pinned memory.
[in]	lda	INTEGER The leading dimension of the array A. LDA >= max(1,N).
[out]	info	INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value if INFO = -6, the GPU memory allocation failed > 0: if INFO = i, the leading minor of order i is not positive definite, and the factorization could not be completed.

magma_zhetrf_nopiv_gpu()

magma_int_t magma_zhetrf_nopiv_gpu	(	magma_uplo_t	uplo,
		magma_int_t	n,
		magmaDoubleComplex_ptr	dA,
		magma_int_t	ldda,
		magma_int_t *	info )

ZHETRF_nopiv_gpu computes the LDLt factorization of a complex Hermitian matrix A.

The factorization has the form A = U^H * D * U, if UPLO = MagmaUpper, or A = L * D * L^H, if UPLO = MagmaLower, where U is an upper triangular matrix, L is lower triangular, and D is a diagonal matrix.

This is the block version of the algorithm, calling Level 3 BLAS.

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,out]	dA	COMPLEX_16 array on the GPU, dimension (LDDA,N) On entry, the Hermitian matrix A. If UPLO = MagmaUpper, 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 = MagmaLower, 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 INFO = 0, the factor U or L from the Cholesky factorization A = U^H D U or A = L D L^H. Higher performance is achieved if A is in pinned memory, e.g. allocated using cudaMallocHost.
[in]	ldda	INTEGER The leading dimension of the array A. LDDA >= max(1,N).
[out]	info	INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value if INFO = -6, the GPU memory allocation failed > 0: if INFO = i, the leading minor of order i is not positive definite, and the factorization could not be completed.