MAGMA  2.3.0
Matrix Algebra for GPU and Multicore Architectures
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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]uplomagma_uplo_t
  • = MagmaUpper: Upper triangle of A is stored;
  • = MagmaLower: Lower triangle of A is stored.
[in]cpu_panelINTEGER If cpu_panel =0, panel factorization is done on GPU.
[in]nINTEGER The order of the matrix A. N >= 0.
[in,out]ACOMPLEX 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]ldaINTEGER The leading dimension of the array A. LDA >= max(1,N).
[out]ipivINTEGER array, dimension (N) Details of the interchanges.
[out]infoINTEGER
  • = 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]uplomagma_uplo_t
  • = MagmaUpper: Upper triangle of A is stored;
  • = MagmaLower: Lower triangle of A is stored.
[in]cpu_panelINTEGER If cpu_panel =0, panel factorization is done on GPU.
[in]nINTEGER The order of the matrix A. N >= 0.
[in,out]ADOUBLE 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]ldaINTEGER The leading dimension of the array A. LDA >= max(1,N).
[out]ipivINTEGER array, dimension (N) Details of the interchanges.
[out]infoINTEGER
  • = 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]uplomagma_uplo_t
  • = MagmaUpper: Upper triangle of A is stored;
  • = MagmaLower: Lower triangle of A is stored.
[in]cpu_panelINTEGER If cpu_panel =0, panel factorization is done on GPU.
[in]nINTEGER The order of the matrix A. N >= 0.
[in,out]AREAL 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]ldaINTEGER The leading dimension of the array A. LDA >= max(1,N).
[out]ipivINTEGER array, dimension (N) Details of the interchanges.
[out]infoINTEGER
  • = 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]uplomagma_uplo_t
  • = MagmaUpper: Upper triangle of A is stored;
  • = MagmaLower: Lower triangle of A is stored.
[in]cpu_panelINTEGER If cpu_panel =0, panel factorization is done on GPU.
[in]nINTEGER The order of the matrix A. N >= 0.
[in,out]ACOMPLEX*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]ldaINTEGER The leading dimension of the array A. LDA >= max(1,N).
[out]ipivINTEGER array, dimension (N) Details of the interchanges.
[out]infoINTEGER
  • = 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.