Functions | |
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) |
ZPOTRF computes the Cholesky factorization of a complex Hermitian positive definite matrix A. | |
magma_int_t | magma_zpotrf (magma_uplo_t uplo, magma_int_t n, magmaDoubleComplex *A, magma_int_t lda, magma_int_t *info) |
ZPOTRF computes the Cholesky factorization of a complex Hermitian positive definite matrix A. | |
magma_int_t | magma_zpotrf3_mgpu (magma_int_t ngpu, magma_uplo_t uplo, magma_int_t m, magma_int_t n, magma_int_t off_i, magma_int_t off_j, magma_int_t nb, magmaDoubleComplex_ptr d_lA[], magma_int_t ldda, magmaDoubleComplex_ptr d_lP[], magma_int_t lddp, magmaDoubleComplex *A, magma_int_t lda, magma_int_t h, magma_queue_t queues[][3], magma_event_t events[][5], magma_int_t *info) |
ZPOTRF computes the Cholesky factorization of a complex Hermitian positive definite matrix dA. | |
magma_int_t | magma_zpotrf_batched (magma_uplo_t uplo, magma_int_t n, magmaDoubleComplex **dA_array, magma_int_t ldda, magma_int_t *info_array, magma_int_t batchCount, magma_queue_t queue) |
ZPOTRF computes the Cholesky factorization of a complex Hermitian positive definite matrix dA. | |
magma_int_t | magma_zpotrf_gpu (magma_uplo_t uplo, magma_int_t n, magmaDoubleComplex_ptr dA, magma_int_t ldda, magma_int_t *info) |
ZPOTRF computes the Cholesky factorization of a complex Hermitian positive definite matrix dA. | |
magma_int_t | magma_zpotrf_m (magma_int_t ngpu, magma_uplo_t uplo, magma_int_t n, magmaDoubleComplex *A, magma_int_t lda, magma_int_t *info) |
ZPOTRF_OOC computes the Cholesky factorization of a complex Hermitian positive definite matrix A. | |
magma_int_t | magma_zpotrf_mgpu (magma_int_t ngpu, magma_uplo_t uplo, magma_int_t n, magmaDoubleComplex_ptr d_lA[], magma_int_t ldda, magma_int_t *info) |
ZPOTRF computes the Cholesky factorization of a complex Hermitian positive definite matrix dA. | |
magma_int_t | magma_zpotrf_mgpu_right (magma_int_t ngpu, magma_uplo_t uplo, magma_int_t n, magmaDoubleComplex_ptr d_lA[], magma_int_t ldda, magma_int_t *info) |
ZPOTRF computes the Cholesky factorization of a complex Hermitian positive definite matrix dA. | |
magma_int_t | magma_zpotri (magma_uplo_t uplo, magma_int_t n, magmaDoubleComplex *A, magma_int_t lda, magma_int_t *info) |
ZPOTRI computes the inverse of a real symmetric positive definite matrix A using the Cholesky factorization A = U**T*U or A = L*L**T computed by ZPOTRF. | |
magma_int_t | magma_zpotri_gpu (magma_uplo_t uplo, magma_int_t n, magmaDoubleComplex_ptr dA, magma_int_t ldda, magma_int_t *info) |
ZPOTRI computes the inverse of a real symmetric positive definite matrix A using the Cholesky factorization A = U**T*U or A = L*L**T computed by ZPOTRF. | |
magma_int_t | magma_zpotrs_batched (magma_uplo_t uplo, magma_int_t n, magma_int_t nrhs, magmaDoubleComplex **dA_array, magma_int_t ldda, magmaDoubleComplex **dB_array, magma_int_t lddb, magma_int_t batchCount, magma_queue_t queue) |
ZPOTRS solves a system of linear equations A*X = B with a Hermitian positive definite matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by ZPOTRF. | |
magma_int_t | magma_zpotrs_gpu (magma_uplo_t uplo, magma_int_t n, magma_int_t nrhs, magmaDoubleComplex_ptr dA, magma_int_t ldda, magmaDoubleComplex_ptr dB, magma_int_t lddb, magma_int_t *info) |
ZPOTRS solves a system of linear equations A*X = B with a Hermitian positive definite matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by ZPOTRF. |
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 | |||
) |
ZPOTRF computes the Cholesky factorization of a complex Hermitian positive definite 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 * U, if uplo = MagmaUpper, or A = L * L**H, if uplo = MagmaLower, where U is an upper triangular matrix and L is lower triangular.
This is the block version of the algorithm, calling Level 3 BLAS.
If the current stream is NULL, this version replaces it with a new stream to overlap computation with communication.
[in] | uplo | magma_uplo_t
|
[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 * U or A = L * L**H. Higher performance is achieved if A is in pinned memory, e.g. allocated using magma_malloc_pinned. |
[in] | lda | INTEGER The leading dimension of the array A. LDA >= max(1,N). |
[out] | info | INTEGER
|
magma_int_t magma_zpotrf | ( | magma_uplo_t | uplo, | |
magma_int_t | n, | |||
magmaDoubleComplex * | A, | |||
magma_int_t | lda, | |||
magma_int_t * | info | |||
) |
ZPOTRF computes the Cholesky factorization of a complex Hermitian positive definite 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 * U, if uplo = MagmaUpper, or A = L * L**H, if uplo = MagmaLower, where U is an upper triangular matrix and L is lower triangular.
This is the block version of the algorithm, calling Level 3 BLAS.
If the current stream is NULL, this version replaces it with a new stream to overlap computation with communication.
[in] | uplo | magma_uplo_t
|
[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 * U or A = L * L**H. Higher performance is achieved if A is in pinned memory, e.g. allocated using magma_malloc_pinned. |
[in] | lda | INTEGER The leading dimension of the array A. LDA >= max(1,N). |
[out] | info | INTEGER
|
magma_int_t magma_zpotrf3_mgpu | ( | magma_int_t | ngpu, | |
magma_uplo_t | uplo, | |||
magma_int_t | m, | |||
magma_int_t | n, | |||
magma_int_t | off_i, | |||
magma_int_t | off_j, | |||
magma_int_t | nb, | |||
magmaDoubleComplex_ptr | d_lA[], | |||
magma_int_t | ldda, | |||
magmaDoubleComplex_ptr | d_lP[], | |||
magma_int_t | lddp, | |||
magmaDoubleComplex * | A, | |||
magma_int_t | lda, | |||
magma_int_t | h, | |||
magma_queue_t | queues[][3], | |||
magma_event_t | events[][5], | |||
magma_int_t * | info | |||
) |
ZPOTRF computes the Cholesky factorization of a complex Hermitian positive definite matrix dA.
Auxiliary subroutine for zpotrf2_ooc. It is multiple gpu interface to compute Cholesky of a "rectangular" matrix.
The factorization has the form dA = U**H * U, if UPLO = MagmaUpper, or dA = L * L**H, if UPLO = MagmaLower, where U is an upper triangular matrix and L is lower triangular.
This is the block version of the algorithm, calling Level 3 BLAS.
[in] | uplo | magma_uplo_t
|
[in] | n | INTEGER The order of the matrix dA. N >= 0. |
[in,out] | dA | COMPLEX_16 array on the GPU, dimension (LDDA,N) On entry, the Hermitian matrix dA. If UPLO = MagmaUpper, the leading N-by-N upper triangular part of dA contains the upper triangular part of the matrix dA, and the strictly lower triangular part of dA is not referenced. If UPLO = MagmaLower, the leading N-by-N lower triangular part of dA contains the lower triangular part of the matrix dA, and the strictly upper triangular part of dA is not referenced. On exit, if INFO = 0, the factor U or L from the Cholesky factorization dA = U**H * U or dA = L * L**H. |
[in] | ldda | INTEGER The leading dimension of the array dA. LDDA >= max(1,N). To benefit from coalescent memory accesses LDDA must be divisible by 16. |
[out] | info | INTEGER
|
magma_int_t magma_zpotrf_batched | ( | magma_uplo_t | uplo, | |
magma_int_t | n, | |||
magmaDoubleComplex ** | dA_array, | |||
magma_int_t | ldda, | |||
magma_int_t * | info_array, | |||
magma_int_t | batchCount, | |||
magma_queue_t | queue | |||
) |
ZPOTRF computes the Cholesky factorization of a complex Hermitian positive definite matrix dA.
The factorization has the form dA = U**H * U, if UPLO = MagmaUpper, or dA = L * L**H, if UPLO = MagmaLower, where U is an upper triangular matrix and L is lower triangular.
This is the block version of the algorithm, calling Level 3 BLAS. If the current stream is NULL, this version replaces it with a new stream to overlap computation with communication.
[in] | uplo | magma_uplo_t
|
[in] | n | INTEGER The order of the matrix dA. N >= 0. |
[in,out] | dA | COMPLEX_16 array on the GPU, dimension (LDDA,N) On entry, the Hermitian matrix dA. If UPLO = MagmaUpper, the leading N-by-N upper triangular part of dA contains the upper triangular part of the matrix dA, and the strictly lower triangular part of dA is not referenced. If UPLO = MagmaLower, the leading N-by-N lower triangular part of dA contains the lower triangular part of the matrix dA, and the strictly upper triangular part of dA is not referenced. On exit, if INFO = 0, the factor U or L from the Cholesky factorization dA = U**H * U or dA = L * L**H. |
[in] | ldda | INTEGER The leading dimension of the array dA. LDDA >= max(1,N). To benefit from coalescent memory accesses LDDA must be divisible by 16. |
[out] | info | INTEGER
|
magma_int_t magma_zpotrf_gpu | ( | magma_uplo_t | uplo, | |
magma_int_t | n, | |||
magmaDoubleComplex_ptr | dA, | |||
magma_int_t | ldda, | |||
magma_int_t * | info | |||
) |
ZPOTRF computes the Cholesky factorization of a complex Hermitian positive definite matrix dA.
The factorization has the form dA = U**H * U, if UPLO = MagmaUpper, or dA = L * L**H, if UPLO = MagmaLower, where U is an upper triangular matrix and L is lower triangular.
This is the block version of the algorithm, calling Level 3 BLAS. If the current stream is NULL, this version replaces it with a new stream to overlap computation with communication.
[in] | uplo | magma_uplo_t
|
[in] | n | INTEGER The order of the matrix dA. N >= 0. |
[in,out] | dA | COMPLEX_16 array on the GPU, dimension (LDDA,N) On entry, the Hermitian matrix dA. If UPLO = MagmaUpper, the leading N-by-N upper triangular part of dA contains the upper triangular part of the matrix dA, and the strictly lower triangular part of dA is not referenced. If UPLO = MagmaLower, the leading N-by-N lower triangular part of dA contains the lower triangular part of the matrix dA, and the strictly upper triangular part of dA is not referenced. On exit, if INFO = 0, the factor U or L from the Cholesky factorization dA = U**H * U or dA = L * L**H. |
[in] | ldda | INTEGER The leading dimension of the array dA. LDDA >= max(1,N). To benefit from coalescent memory accesses LDDA must be divisible by 16. |
[out] | info | INTEGER
|
magma_int_t magma_zpotrf_m | ( | magma_int_t | ngpu, | |
magma_uplo_t | uplo, | |||
magma_int_t | n, | |||
magmaDoubleComplex * | A, | |||
magma_int_t | lda, | |||
magma_int_t * | info | |||
) |
ZPOTRF_OOC computes the Cholesky factorization of a complex Hermitian positive definite matrix A.
This version does not require work space on the GPU passed as input. GPU memory is allocated in the routine. The matrix A may exceed the GPU memory.
The factorization has the form A = U**H * U, if UPLO = MagmaUpper, or A = L * L**H, if UPLO = MagmaLower, where U is an upper triangular matrix and L is lower triangular.
This is the block version of the algorithm, calling Level 3 BLAS.
[in] | ngpu | INTEGER Number of GPUs to use. ngpu > 0. |
[in] | uplo | magma_uplo_t
|
[in] | n | INTEGER The order of the matrix A. N >= 0. |
[in,out] | A | COMPLEX_16 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 * U or A = L * L**H. Higher performance is achieved if A is in pinned memory, e.g. allocated using magma_malloc_pinned. |
[in] | lda | INTEGER The leading dimension of the array A. LDA >= max(1,N). |
[out] | info | INTEGER
|
magma_int_t magma_zpotrf_mgpu | ( | magma_int_t | ngpu, | |
magma_uplo_t | uplo, | |||
magma_int_t | n, | |||
magmaDoubleComplex_ptr | d_lA[], | |||
magma_int_t | ldda, | |||
magma_int_t * | info | |||
) |
ZPOTRF computes the Cholesky factorization of a complex Hermitian positive definite matrix dA.
The factorization has the form dA = U**H * U, if UPLO = MagmaUpper, or dA = L * L**H, if UPLO = MagmaLower, where U is an upper triangular matrix and L is lower triangular.
This is the block version of the algorithm, calling Level 3 BLAS.
[in] | ngpu | INTEGER Number of GPUs to use. ngpu > 0. |
[in] | uplo | magma_uplo_t
|
[in] | n | INTEGER The order of the matrix dA. N >= 0. |
[in,out] | d_lA | COMPLEX_16 array of pointers on the GPU, dimension (ngpu) On entry, the Hermitian matrix dA distributed over GPUs (d_lA[d] points to the local matrix on the d-th GPU). It is distributed in 1D block column or row cyclic (with the block size of nb) if UPLO = MagmaUpper or MagmaLower, respectively. If UPLO = MagmaUpper, the leading N-by-N upper triangular part of dA contains the upper triangular part of the matrix dA, and the strictly lower triangular part of dA is not referenced. If UPLO = MagmaLower, the leading N-by-N lower triangular part of dA contains the lower triangular part of the matrix dA, and the strictly upper triangular part of dA is not referenced. On exit, if INFO = 0, the factor U or L from the Cholesky factorization dA = U**H * U or dA = L * L**H. |
[in] | ldda | INTEGER The leading dimension of the array d_lA. LDDA >= max(1,N). To benefit from coalescent memory accesses LDDA must be divisible by 16. |
[out] | info | INTEGER
|
magma_int_t magma_zpotrf_mgpu_right | ( | magma_int_t | ngpu, | |
magma_uplo_t | uplo, | |||
magma_int_t | n, | |||
magmaDoubleComplex_ptr | d_lA[], | |||
magma_int_t | ldda, | |||
magma_int_t * | info | |||
) |
ZPOTRF computes the Cholesky factorization of a complex Hermitian positive definite matrix dA.
The factorization has the form dA = U**H * U, if UPLO = MagmaUpper, or dA = L * L**H, if UPLO = MagmaLower, where U is an upper triangular matrix and L is lower triangular.
This is the block version of the algorithm, calling Level 3 BLAS.
[in] | uplo | magma_uplo_t
|
[in] | n | INTEGER The order of the matrix dA. N >= 0. |
[in,out] | d_lA | COMPLEX_16 array of pointers on the GPU, dimension (ngpu) On entry, the Hermitian matrix dA distributed over GPUs (dl_A[d] points to the local matrix on the d-th GPU). It is distributed in 1D block column or row cyclic (with the block size of nb) if UPLO = MagmaUpper or MagmaLower, respectively. If UPLO = MagmaUpper, the leading N-by-N upper triangular part of dA contains the upper triangular part of the matrix dA, and the strictly lower triangular part of dA is not referenced. If UPLO = MagmaLower, the leading N-by-N lower triangular part of dA contains the lower triangular part of the matrix dA, and the strictly upper triangular part of dA is not referenced. On exit, if INFO = 0, the factor U or L from the Cholesky factorization dA = U**H * U or dA = L * L**H. |
[in] | ldda | INTEGER The leading dimension of the array dA. LDDA >= max(1,N). To benefit from coalescent memory accesses LDDA must be divisible by 16. |
[out] | info | INTEGER
|
magma_int_t magma_zpotri | ( | magma_uplo_t | uplo, | |
magma_int_t | n, | |||
magmaDoubleComplex * | A, | |||
magma_int_t | lda, | |||
magma_int_t * | info | |||
) |
ZPOTRI computes the inverse of a real symmetric positive definite matrix A using the Cholesky factorization A = U**T*U or A = L*L**T computed by ZPOTRF.
[in] | uplo | magma_uplo_t
|
[in] | n | INTEGER The order of the matrix A. N >= 0. |
[in,out] | A | COMPLEX_16 array, dimension (LDA,N) On entry, the triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T, as computed by ZPOTRF. On exit, the upper or lower triangle of the (symmetric) inverse of A, overwriting the input factor U or L. |
[in] | lda | INTEGER The leading dimension of the array A. LDA >= max(1,N). |
[out] | info | INTEGER
|
magma_int_t magma_zpotri_gpu | ( | magma_uplo_t | uplo, | |
magma_int_t | n, | |||
magmaDoubleComplex_ptr | dA, | |||
magma_int_t | ldda, | |||
magma_int_t * | info | |||
) |
ZPOTRI computes the inverse of a real symmetric positive definite matrix A using the Cholesky factorization A = U**T*U or A = L*L**T computed by ZPOTRF.
[in] | uplo | magma_uplo_t
|
[in] | n | INTEGER The order of the matrix A. N >= 0. |
[in,out] | dA | COMPLEX_16 array on the GPU, dimension (LDA,N) On entry, the triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T, as computed by ZPOTRF. On exit, the upper or lower triangle of the (symmetric) inverse of A, overwriting the input factor U or L. |
[in] | ldda | INTEGER The leading dimension of the array dA. LDDA >= max(1,N). |
[out] | info | INTEGER
|
magma_int_t magma_zpotrs_batched | ( | magma_uplo_t | uplo, | |
magma_int_t | n, | |||
magma_int_t | nrhs, | |||
magmaDoubleComplex ** | dA_array, | |||
magma_int_t | ldda, | |||
magmaDoubleComplex ** | dB_array, | |||
magma_int_t | lddb, | |||
magma_int_t | batchCount, | |||
magma_queue_t | queue | |||
) |
ZPOTRS solves a system of linear equations A*X = B with a Hermitian positive definite matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by ZPOTRF.
[in] | uplo | magma_uplo_t
|
[in] | n | INTEGER The order of the matrix A. N >= 0. |
[in] | nrhs | INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0. |
[in] | dA | COMPLEX_16 array on the GPU, dimension (LDDA,N) The triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H, as computed by ZPOTRF. |
[in] | ldda | INTEGER The leading dimension of the array A. LDDA >= max(1,N). |
[in,out] | dB | COMPLEX_16 array on the GPU, dimension (LDDB,NRHS) On entry, the right hand side matrix B. On exit, the solution matrix X. |
[in] | lddb | INTEGER The leading dimension of the array B. LDDB >= max(1,N). |
[out] | info | INTEGER
|
magma_int_t magma_zpotrs_gpu | ( | magma_uplo_t | uplo, | |
magma_int_t | n, | |||
magma_int_t | nrhs, | |||
magmaDoubleComplex_ptr | dA, | |||
magma_int_t | ldda, | |||
magmaDoubleComplex_ptr | dB, | |||
magma_int_t | lddb, | |||
magma_int_t * | info | |||
) |
ZPOTRS solves a system of linear equations A*X = B with a Hermitian positive definite matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by ZPOTRF.
[in] | uplo | magma_uplo_t
|
[in] | n | INTEGER The order of the matrix A. N >= 0. |
[in] | nrhs | INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0. |
[in] | dA | COMPLEX_16 array on the GPU, dimension (LDDA,N) The triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H, as computed by ZPOTRF. |
[in] | ldda | INTEGER The leading dimension of the array A. LDDA >= max(1,N). |
[in,out] | dB | COMPLEX_16 array on the GPU, dimension (LDDB,NRHS) On entry, the right hand side matrix B. On exit, the solution matrix X. |
[in] | lddb | INTEGER The leading dimension of the array B. LDDB >= max(1,N). |
[out] | info | INTEGER
|