MAGMA
2.3.0
Matrix Algebra for GPU and Multicore Architectures

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 events[], magma_int_t *info) 
CLAHEF computes a partial factorization of a complex Hermitian matrix A using the BunchKaufman diagonal pivoting method. More...  
magma_int_t  magma_dlasyf_gpu (magma_uplo_t uplo, magma_int_t n, magma_int_t nb, magma_int_t *kb, double *hA, magma_int_t lda, magmaDouble_ptr dA, magma_int_t ldda, magma_int_t *ipiv, magmaDouble_ptr dW, magma_int_t lddw, magma_queue_t queues[], magma_event_t events[], magma_int_t *info) 
DLASYF computes a partial factorization of a real symmetric matrix A using the BunchKaufman diagonal pivoting method. More...  
magma_int_t  magma_slasyf_gpu (magma_uplo_t uplo, magma_int_t n, magma_int_t nb, magma_int_t *kb, float *hA, magma_int_t lda, magmaFloat_ptr dA, magma_int_t ldda, magma_int_t *ipiv, magmaFloat_ptr dW, magma_int_t lddw, magma_queue_t queues[], magma_event_t events[], magma_int_t *info) 
SLASYF computes a partial factorization of a real symmetric matrix A using the BunchKaufman diagonal pivoting method. More...  
magma_int_t  magma_zlahef_gpu (magma_uplo_t uplo, magma_int_t n, magma_int_t nb, magma_int_t *kb, magmaDoubleComplex *hA, magma_int_t lda, magmaDoubleComplex_ptr dA, magma_int_t ldda, magma_int_t *ipiv, magmaDoubleComplex_ptr dW, magma_int_t lddw, magma_queue_t queues[], magma_event_t events[], magma_int_t *info) 
ZLAHEF computes a partial factorization of a complex Hermitian matrix A using the BunchKaufman diagonal pivoting method. More...  
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  events[],  
magma_int_t *  info  
) 
CLAHEF computes a partial factorization of a complex Hermitian matrix A using the BunchKaufman diagonal pivoting method.
The partial factorization has the form:
A = ( I U12 ) ( A11 0 ) ( I 0 ) if UPLO = MagmaUpper, or: ( 0 U22 ) ( 0 D ) ( U12' U22' )
A = ( L11 0 ) ( D 0 ) ( L11' L21' ) if UPLO = MagmaLower ( 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 NB1, 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 = MagmaUpper) or A22 (if UPLO = MagmaLower).
[in]  uplo  CHARACTER Specifies whether the upper or lower triangular part of the Hermitian matrix A is stored:

[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 2by2 pivot blocks. 
[out]  kb  INTEGER The number of columns of A that were actually factored. KB is either NB1 or NB, or N if N <= NB. 
[in,out]  hA  COMPLEX array, dimension (LDA,N) On entry, the Hermitian matrix A. If UPLO = MagmaUpper, the leading nbyn 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 nbyn 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). 
[in,out]  dA  COMPLEX array on GPU, dimension (LDDA,N) On entry, the Hermitian matrix A. If UPLO = MagmaUpper, the leading nbyn 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 nbyn 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]  ldda  INTEGER The leading dimension of the array A. LDDA >= max(1,N). 
[out]  ipiv  INTEGER array, dimension (N) Details of the interchanges and the block structure of D. If UPLO = MagmaUpper, only the last KB elements of ipiv are set; if UPLO = MagmaLower, 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 1by1 diagonal block. If UPLO = MagmaUpper and ipiv(k) = ipiv(k1) < 0, then rows and columns k1 and ipiv(k) were interchanged and D(k1:k,k1:k) is a 2by2 diagonal block. If UPLO = MagmaLower 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 2by2 diagonal block. 
[out]  dW  (workspace) COMPLEX array, dimension (LDDW,NB) 
[in]  lddw  INTEGER The leading dimension of the array W. LDDW >= max(1,N). 
[in]  queues  magma_queue_t queues contain the queues used for the partial factorization. Currently, only one queue is used. 
[in]  events  magma_event_t events contain the events used for the partial factorization. Currently, only one event is used. 
[out]  info  INTEGER

magma_int_t magma_dlasyf_gpu  (  magma_uplo_t  uplo, 
magma_int_t  n,  
magma_int_t  nb,  
magma_int_t *  kb,  
double *  hA,  
magma_int_t  lda,  
magmaDouble_ptr  dA,  
magma_int_t  ldda,  
magma_int_t *  ipiv,  
magmaDouble_ptr  dW,  
magma_int_t  lddw,  
magma_queue_t  queues[],  
magma_event_t  events[],  
magma_int_t *  info  
) 
DLASYF computes a partial factorization of a real symmetric matrix A using the BunchKaufman diagonal pivoting method.
The partial factorization has the form:
A = ( I U12 ) ( A11 0 ) ( I 0 ) if UPLO = MagmaUpper, or: ( 0 U22 ) ( 0 D ) ( U12' U22' )
A = ( L11 0 ) ( D 0 ) ( L11' L21' ) if UPLO = MagmaLower ( 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 NB1, or N if N <= NB. Note that U' denotes the conjugate transpose of U.
DLASYF is an auxiliary routine called by DSYTRF. It uses blocked code (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = MagmaUpper) or A22 (if UPLO = MagmaLower).
[in]  uplo  CHARACTER Specifies whether the upper or lower triangular part of the symmetric matrix A is stored:

[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 2by2 pivot blocks. 
[out]  kb  INTEGER The number of columns of A that were actually factored. KB is either NB1 or NB, or N if N <= NB. 
[in,out]  hA  DOUBLE PRECISION array, dimension (LDA,N) On entry, the symmetric matrix A. If UPLO = MagmaUpper, the leading nbyn 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 nbyn 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). 
[in,out]  dA  DOUBLE PRECISION array on GPU, dimension (LDDA,N) On entry, the symmetric matrix A. If UPLO = MagmaUpper, the leading nbyn 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 nbyn 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]  ldda  INTEGER The leading dimension of the array A. LDDA >= max(1,N). 
[out]  ipiv  INTEGER array, dimension (N) Details of the interchanges and the block structure of D. If UPLO = MagmaUpper, only the last KB elements of ipiv are set; if UPLO = MagmaLower, 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 1by1 diagonal block. If UPLO = MagmaUpper and ipiv(k) = ipiv(k1) < 0, then rows and columns k1 and ipiv(k) were interchanged and D(k1:k,k1:k) is a 2by2 diagonal block. If UPLO = MagmaLower 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 2by2 diagonal block. 
[out]  dW  (workspace) DOUBLE PRECISION array, dimension (LDDW,NB) 
[in]  lddw  INTEGER The leading dimension of the array W. LDDW >= max(1,N). 
[in]  queues  magma_queue_t queues contain the queues used for the partial factorization. Currently, only one queue is used. 
[in]  events  magma_event_t events contain the events used for the partial factorization. Currently, only one event is used. 
[out]  info  INTEGER

magma_int_t magma_slasyf_gpu  (  magma_uplo_t  uplo, 
magma_int_t  n,  
magma_int_t  nb,  
magma_int_t *  kb,  
float *  hA,  
magma_int_t  lda,  
magmaFloat_ptr  dA,  
magma_int_t  ldda,  
magma_int_t *  ipiv,  
magmaFloat_ptr  dW,  
magma_int_t  lddw,  
magma_queue_t  queues[],  
magma_event_t  events[],  
magma_int_t *  info  
) 
SLASYF computes a partial factorization of a real symmetric matrix A using the BunchKaufman diagonal pivoting method.
The partial factorization has the form:
A = ( I U12 ) ( A11 0 ) ( I 0 ) if UPLO = MagmaUpper, or: ( 0 U22 ) ( 0 D ) ( U12' U22' )
A = ( L11 0 ) ( D 0 ) ( L11' L21' ) if UPLO = MagmaLower ( 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 NB1, or N if N <= NB. Note that U' denotes the conjugate transpose of U.
SLASYF is an auxiliary routine called by SSYTRF. It uses blocked code (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = MagmaUpper) or A22 (if UPLO = MagmaLower).
[in]  uplo  CHARACTER Specifies whether the upper or lower triangular part of the symmetric matrix A is stored:

[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 2by2 pivot blocks. 
[out]  kb  INTEGER The number of columns of A that were actually factored. KB is either NB1 or NB, or N if N <= NB. 
[in,out]  hA  REAL array, dimension (LDA,N) On entry, the symmetric matrix A. If UPLO = MagmaUpper, the leading nbyn 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 nbyn 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). 
[in,out]  dA  REAL array on GPU, dimension (LDDA,N) On entry, the symmetric matrix A. If UPLO = MagmaUpper, the leading nbyn 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 nbyn 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]  ldda  INTEGER The leading dimension of the array A. LDDA >= max(1,N). 
[out]  ipiv  INTEGER array, dimension (N) Details of the interchanges and the block structure of D. If UPLO = MagmaUpper, only the last KB elements of ipiv are set; if UPLO = MagmaLower, 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 1by1 diagonal block. If UPLO = MagmaUpper and ipiv(k) = ipiv(k1) < 0, then rows and columns k1 and ipiv(k) were interchanged and D(k1:k,k1:k) is a 2by2 diagonal block. If UPLO = MagmaLower 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 2by2 diagonal block. 
[out]  dW  (workspace) REAL array, dimension (LDDW,NB) 
[in]  lddw  INTEGER The leading dimension of the array W. LDDW >= max(1,N). 
[in]  queues  magma_queue_t queues contain the queues used for the partial factorization. Currently, only one queue is used. 
[in]  events  magma_event_t events contain the events used for the partial factorization. Currently, only one event is used. 
[out]  info  INTEGER

magma_int_t magma_zlahef_gpu  (  magma_uplo_t  uplo, 
magma_int_t  n,  
magma_int_t  nb,  
magma_int_t *  kb,  
magmaDoubleComplex *  hA,  
magma_int_t  lda,  
magmaDoubleComplex_ptr  dA,  
magma_int_t  ldda,  
magma_int_t *  ipiv,  
magmaDoubleComplex_ptr  dW,  
magma_int_t  lddw,  
magma_queue_t  queues[],  
magma_event_t  events[],  
magma_int_t *  info  
) 
ZLAHEF computes a partial factorization of a complex Hermitian matrix A using the BunchKaufman diagonal pivoting method.
The partial factorization has the form:
A = ( I U12 ) ( A11 0 ) ( I 0 ) if UPLO = MagmaUpper, or: ( 0 U22 ) ( 0 D ) ( U12' U22' )
A = ( L11 0 ) ( D 0 ) ( L11' L21' ) if UPLO = MagmaLower ( 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 NB1, or N if N <= NB. Note that U' denotes the conjugate transpose of U.
ZLAHEF is an auxiliary routine called by ZHETRF. It uses blocked code (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = MagmaUpper) or A22 (if UPLO = MagmaLower).
[in]  uplo  CHARACTER Specifies whether the upper or lower triangular part of the Hermitian matrix A is stored:

[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 2by2 pivot blocks. 
[out]  kb  INTEGER The number of columns of A that were actually factored. KB is either NB1 or NB, or N if N <= NB. 
[in,out]  hA  COMPLEX*16 array, dimension (LDA,N) On entry, the Hermitian matrix A. If UPLO = MagmaUpper, the leading nbyn 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 nbyn 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). 
[in,out]  dA  COMPLEX*16 array on GPU, dimension (LDDA,N) On entry, the Hermitian matrix A. If UPLO = MagmaUpper, the leading nbyn 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 nbyn 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]  ldda  INTEGER The leading dimension of the array A. LDDA >= max(1,N). 
[out]  ipiv  INTEGER array, dimension (N) Details of the interchanges and the block structure of D. If UPLO = MagmaUpper, only the last KB elements of ipiv are set; if UPLO = MagmaLower, 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 1by1 diagonal block. If UPLO = MagmaUpper and ipiv(k) = ipiv(k1) < 0, then rows and columns k1 and ipiv(k) were interchanged and D(k1:k,k1:k) is a 2by2 diagonal block. If UPLO = MagmaLower 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 2by2 diagonal block. 
[out]  dW  (workspace) COMPLEX*16 array, dimension (LDDW,NB) 
[in]  lddw  INTEGER The leading dimension of the array W. LDDW >= max(1,N). 
[in]  queues  magma_queue_t queues contain the queues used for the partial factorization. Currently, only one queue is used. 
[in]  events  magma_event_t events contain the events used for the partial factorization. Currently, only one event is used. 
[out]  info  INTEGER
