Hermitian single-complex precision
[Symmetric indefinite solve]

Functions

magma_int_t magma_clahef_gpu (magma_uplo_t uplo, magma_int_t n, magma_int_t nb, magma_int_t *kb, magmaFloatComplex *hA, magma_int_t lda, magmaFloatComplex_ptr dA, magma_int_t ldda, magma_int_t *ipiv, magmaFloatComplex_ptr dW, magma_int_t lddw, magma_queue_t queues[], magma_event_t event[], magma_int_t *info)
 CLAHEF computes a partial factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method.

Function Documentation

magma_int_t magma_clahef_gpu ( magma_uplo_t  uplo,
magma_int_t  n,
magma_int_t  nb,
magma_int_t *  kb,
magmaFloatComplex *  hA,
magma_int_t  lda,
magmaFloatComplex_ptr  dA,
magma_int_t  ldda,
magma_int_t *  ipiv,
magmaFloatComplex_ptr  dW,
magma_int_t  lddw,
magma_queue_t  queues[],
magma_event_t  event[],
magma_int_t *  info 
)

CLAHEF computes a partial factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method.

The partial factorization has the form:

A = ( I U12 ) ( A11 0 ) ( I 0 ) if UPLO = 'U', or: ( 0 U22 ) ( 0 D ) ( U12' U22' )

A = ( L11 0 ) ( D 0 ) ( L11' L21' ) if UPLO = 'L' ( L21 I ) ( 0 A22 ) ( 0 I )

where the order of D is at most NB. The actual order is returned in the argument KB, and is either NB or NB-1, or N if N <= NB. Note that U' denotes the conjugate transpose of U.

CLAHEF is an auxiliary routine called by CHETRF. It uses blocked code (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = 'U') or A22 (if UPLO = 'L').

Parameters:
[in] uplo CHARACTER Specifies whether the upper or lower triangular part of the Hermitian matrix A is stored:

  • = 'U': Upper triangular
  • = 'L': Lower triangular
[in] n INTEGER The order of the matrix A. N >= 0.
[in] nb INTEGER The maximum number of columns of the matrix A that should be factored. NB should be at least 2 to allow for 2-by-2 pivot blocks.
[out] kb INTEGER The number of columns of A that were actually factored. KB is either NB-1 or NB, or N if N <= NB.
[in,out] hA COMPLEX array, dimension (LDA,N) On entry, the Hermitian matrix A. If UPLO = 'U', 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 = 'L', 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, A contains details of the partial factorization.
[in] lda INTEGER The leading dimension of the array A. LDA >= max(1,N).
[out] ipiv INTEGER array, dimension (N) Details of the interchanges and the block structure of D. If UPLO = 'U', only the last KB elements of ipiv are set; if UPLO = 'L', only the first KB elements are set.
If ipiv(k) > 0, then rows and columns k and ipiv(k) were interchanged and D(k,k) is a 1-by-1 diagonal block. If UPLO = 'U' and ipiv(k) = ipiv(k-1) < 0, then rows and columns k-1 and -ipiv(k) were interchanged and D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = 'L' and ipiv(k) = ipiv(k+1) < 0, then rows and columns k+1 and -ipiv(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
[out] dW (workspace) COMPLEX array, dimension (LDW,NB)
[in] lddw INTEGER The leading dimension of the array W. LDW >= max(1,N).
[out] info INTEGER

  • = 0: successful exit
  • > 0: if INFO = k, D(k,k) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular.

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