sy/hetrf: symmetric/Hermitian indefinite factorization (Aasen)

Functions
magma_int_t	magma_chetrf_aasen (magma_uplo_t uplo, magma_int_t cpu_panel, magma_int_t n, magmaFloatComplex *A, magma_int_t lda, magma_int_t *ipiv, magma_int_t *info)
	CHETRF_AASEN computes the factorization of a complex Hermitian matrix A based on a communication-avoiding variant of the Aasen's algorithm . More...
magma_int_t	magma_dsytrf_aasen (magma_uplo_t uplo, magma_int_t cpu_panel, magma_int_t n, double *A, magma_int_t lda, magma_int_t *ipiv, magma_int_t *info)
	DSYTRF_AASEN computes the factorization of a real symmetric matrix A based on a communication-avoiding variant of the Aasen's algorithm . More...
magma_int_t	magma_ssytrf_aasen (magma_uplo_t uplo, magma_int_t cpu_panel, magma_int_t n, float *A, magma_int_t lda, magma_int_t *ipiv, magma_int_t *info)
	SSYTRF_AASEN computes the factorization of a real symmetric matrix A based on a communication-avoiding variant of the Aasen's algorithm . More...
magma_int_t	magma_zhetrf_aasen (magma_uplo_t uplo, magma_int_t cpu_panel, magma_int_t n, magmaDoubleComplex *A, magma_int_t lda, magma_int_t *ipiv, magma_int_t *info)
	ZHETRF_AASEN computes the factorization of a complex Hermitian matrix A based on a communication-avoiding variant of the Aasen's algorithm . More...

Detailed Description

Function Documentation

magma_int_t magma_chetrf_aasen	(	magma_uplo_t	uplo,
		magma_int_t	cpu_panel,
		magma_int_t	n,
		magmaFloatComplex *	A,
		magma_int_t	lda,
		magma_int_t *	ipiv,
		magma_int_t *	info
	)

CHETRF_AASEN computes the factorization of a complex Hermitian matrix A based on a communication-avoiding variant of the Aasen's algorithm .

The form of the factorization is

A = U*D*U**H or A = L*D*L**H

where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is Hermitian and banded matrix of the band width equal to the block size.

Parameters

[in]	uplo	magma_uplo_t = MagmaUpper: Upper triangle of A is stored; = MagmaLower: Lower triangle of A is stored.
[in]	cpu_panel	INTEGER If cpu_panel =0, panel factorization is done on GPU.
[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, the banded matrix D and the triangular factor U or L.
[in]	lda	INTEGER The leading dimension of the array A. LDA >= max(1,N).
[out]	ipiv	INTEGER array, dimension (N) Details of the interchanges.
[out]	info	INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, D(i,i) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular, and division by zero will occur if it is used to solve a system of equations.

magma_int_t magma_dsytrf_aasen	(	magma_uplo_t	uplo,
		magma_int_t	cpu_panel,
		magma_int_t	n,
		double *	A,
		magma_int_t	lda,
		magma_int_t *	ipiv,
		magma_int_t *	info
	)

DSYTRF_AASEN computes the factorization of a real symmetric matrix A based on a communication-avoiding variant of the Aasen's algorithm .

The form of the factorization is

A = U*D*U**H or A = L*D*L**H

where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is symmetric and banded matrix of the band width equal to the block size.

Parameters

[in]	uplo	magma_uplo_t = MagmaUpper: Upper triangle of A is stored; = MagmaLower: Lower triangle of A is stored.
[in]	cpu_panel	INTEGER If cpu_panel =0, panel factorization is done on GPU.
[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, the banded matrix D and the triangular factor U or L.
[in]	lda	INTEGER The leading dimension of the array A. LDA >= max(1,N).
[out]	ipiv	INTEGER array, dimension (N) Details of the interchanges.
[out]	info	INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, D(i,i) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular, and division by zero will occur if it is used to solve a system of equations.

magma_int_t magma_ssytrf_aasen	(	magma_uplo_t	uplo,
		magma_int_t	cpu_panel,
		magma_int_t	n,
		float *	A,
		magma_int_t	lda,
		magma_int_t *	ipiv,
		magma_int_t *	info
	)

SSYTRF_AASEN computes the factorization of a real symmetric matrix A based on a communication-avoiding variant of the Aasen's algorithm .

The form of the factorization is

A = U*D*U**H or A = L*D*L**H

where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is symmetric and banded matrix of the band width equal to the block size.

Parameters

[in]	uplo	magma_uplo_t = MagmaUpper: Upper triangle of A is stored; = MagmaLower: Lower triangle of A is stored.
[in]	cpu_panel	INTEGER If cpu_panel =0, panel factorization is done on GPU.
[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, the banded matrix D and the triangular factor U or L.
[in]	lda	INTEGER The leading dimension of the array A. LDA >= max(1,N).
[out]	ipiv	INTEGER array, dimension (N) Details of the interchanges.
[out]	info	INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, D(i,i) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular, and division by zero will occur if it is used to solve a system of equations.

magma_int_t magma_zhetrf_aasen	(	magma_uplo_t	uplo,
		magma_int_t	cpu_panel,
		magma_int_t	n,
		magmaDoubleComplex *	A,
		magma_int_t	lda,
		magma_int_t *	ipiv,
		magma_int_t *	info
	)

ZHETRF_AASEN computes the factorization of a complex Hermitian matrix A based on a communication-avoiding variant of the Aasen's algorithm .

The form of the factorization is

A = U*D*U**H or A = L*D*L**H

where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is Hermitian and banded matrix of the band width equal to the block size.

Parameters

[in]	uplo	magma_uplo_t = MagmaUpper: Upper triangle of A is stored; = MagmaLower: Lower triangle of A is stored.
[in]	cpu_panel	INTEGER If cpu_panel =0, panel factorization is done on GPU.
[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, the banded matrix D and the triangular factor U or L.
[in]	lda	INTEGER The leading dimension of the array A. LDA >= max(1,N).
[out]	ipiv	INTEGER array, dimension (N) Details of the interchanges.
[out]	info	INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, D(i,i) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular, and division by zero will occur if it is used to solve a system of equations.