MAGMA  2.3.0 Matrix Algebra for GPU and Multicore Architectures

## Functions

magma_int_t magma_cpotrf (magma_uplo_t uplo, magma_int_t n, magmaFloatComplex *A, magma_int_t lda, magma_int_t *info)
CPOTRF computes the Cholesky factorization of a complex Hermitian positive definite matrix A. More...

magma_int_t magma_cpotrf3_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, magmaFloatComplex_ptr d_lA[], magma_int_t ldda, magmaFloatComplex_ptr d_lP[], magma_int_t lddp, magmaFloatComplex *A, magma_int_t lda, magma_int_t h, magma_queue_t queues[][3], magma_event_t events[][5], magma_int_t *info)
CPOTRF computes the Cholesky factorization of a complex Hermitian positive definite matrix dA. More...

magma_int_t magma_cpotrf_gpu (magma_uplo_t uplo, magma_int_t n, magmaFloatComplex_ptr dA, magma_int_t ldda, magma_int_t *info)
CPOTRF computes the Cholesky factorization of a complex Hermitian positive definite matrix dA. More...

magma_int_t magma_cpotrf_m (magma_int_t ngpu, magma_uplo_t uplo, magma_int_t n, magmaFloatComplex *A, magma_int_t lda, magma_int_t *info)
CPOTRF computes the Cholesky factorization of a complex Hermitian positive definite matrix A. More...

magma_int_t magma_cpotrf_mgpu (magma_int_t ngpu, magma_uplo_t uplo, magma_int_t n, magmaFloatComplex_ptr d_lA[], magma_int_t ldda, magma_int_t *info)
CPOTRF computes the Cholesky factorization of a complex Hermitian positive definite matrix dA. More...

magma_int_t magma_dpotrf (magma_uplo_t uplo, magma_int_t n, double *A, magma_int_t lda, magma_int_t *info)
DPOTRF computes the Cholesky factorization of a real symmetric positive definite matrix A. More...

magma_int_t magma_dpotrf3_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, magmaDouble_ptr d_lA[], magma_int_t ldda, magmaDouble_ptr d_lP[], magma_int_t lddp, double *A, magma_int_t lda, magma_int_t h, magma_queue_t queues[][3], magma_event_t events[][5], magma_int_t *info)
DPOTRF computes the Cholesky factorization of a real symmetric positive definite matrix dA. More...

magma_int_t magma_dpotrf_gpu (magma_uplo_t uplo, magma_int_t n, magmaDouble_ptr dA, magma_int_t ldda, magma_int_t *info)
DPOTRF computes the Cholesky factorization of a real symmetric positive definite matrix dA. More...

magma_int_t magma_dpotrf_m (magma_int_t ngpu, magma_uplo_t uplo, magma_int_t n, double *A, magma_int_t lda, magma_int_t *info)
DPOTRF computes the Cholesky factorization of a real symmetric positive definite matrix A. More...

magma_int_t magma_dpotrf_mgpu (magma_int_t ngpu, magma_uplo_t uplo, magma_int_t n, magmaDouble_ptr d_lA[], magma_int_t ldda, magma_int_t *info)
DPOTRF computes the Cholesky factorization of a real symmetric positive definite matrix dA. More...

magma_int_t magma_spotrf (magma_uplo_t uplo, magma_int_t n, float *A, magma_int_t lda, magma_int_t *info)
SPOTRF computes the Cholesky factorization of a real symmetric positive definite matrix A. More...

magma_int_t magma_spotrf3_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, magmaFloat_ptr d_lA[], magma_int_t ldda, magmaFloat_ptr d_lP[], magma_int_t lddp, float *A, magma_int_t lda, magma_int_t h, magma_queue_t queues[][3], magma_event_t events[][5], magma_int_t *info)
SPOTRF computes the Cholesky factorization of a real symmetric positive definite matrix dA. More...

magma_int_t magma_spotrf_gpu (magma_uplo_t uplo, magma_int_t n, magmaFloat_ptr dA, magma_int_t ldda, magma_int_t *info)
SPOTRF computes the Cholesky factorization of a real symmetric positive definite matrix dA. More...

magma_int_t magma_spotrf_m (magma_int_t ngpu, magma_uplo_t uplo, magma_int_t n, float *A, magma_int_t lda, magma_int_t *info)
SPOTRF computes the Cholesky factorization of a real symmetric positive definite matrix A. More...

magma_int_t magma_spotrf_mgpu (magma_int_t ngpu, magma_uplo_t uplo, magma_int_t n, magmaFloat_ptr d_lA[], magma_int_t ldda, magma_int_t *info)
SPOTRF computes the Cholesky factorization of a real symmetric positive definite matrix dA. More...

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. More...

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. More...

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. More...

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 computes the Cholesky factorization of a complex Hermitian positive definite matrix A. More...

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. More...

## Function Documentation

 magma_int_t magma_cpotrf ( magma_uplo_t uplo, magma_int_t n, magmaFloatComplex * A, magma_int_t lda, magma_int_t * info )

CPOTRF 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.

This uses multiple queues to overlap communication and computation.

Parameters
 [in] uplo magma_uplo_t = MagmaUpper: Upper triangle of A is stored; = MagmaLower: Lower triangle of A is stored. [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, 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 = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value or another error occured, such as memory allocation failed. > 0: if INFO = i, the leading minor of order i is not positive definite, and the factorization could not be completed.
 magma_int_t magma_cpotrf3_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, magmaFloatComplex_ptr d_lA[], magma_int_t ldda, magmaFloatComplex_ptr d_lP[], magma_int_t lddp, magmaFloatComplex * A, magma_int_t lda, magma_int_t h, magma_queue_t queues[][3], magma_event_t events[][5], magma_int_t * info )

CPOTRF computes the Cholesky factorization of a complex Hermitian positive definite matrix dA.

Auxiliary subroutine for cpotrf2_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.

Parameters
 [in] ngpu INTEGER Number of GPUs to use. ngpu > 0. [in] uplo magma_uplo_t = MagmaUpper: Upper triangle of dA is stored; = MagmaLower: Lower triangle of dA is stored. [in] m INTEGER The number of rows of the submatrix to be factorized. [in] n INTEGER The number of columns of the submatrix to be factorized. [in] off_i INTEGER The first row index of the submatrix to be factorized. [in] off_j INTEGER The first column index of the submatrix to be factorized. [in] nb INTEGER The block size used for the factorization and distribution. [in,out] d_lA COMPLEX array of pointers on the GPU, dimension (ngpu). On entry, the Hermitian matrix dA distributed over GPU. (d_lAT[d] points to the local matrix on d-th GPU). If UPLO = MagmaLower or MagmaUpper, it respectively uses a 1D block column or row cyclic format (with the block size nb), and each local matrix is stored by column. 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,out] d_lP COMPLEX array of pointers on the GPU, dimension (ngpu). d_LAT[d] points to workspace of size h*lddp*nb on d-th GPU. [in] lddp INTEGER The leading dimension of the array dP. LDDA >= max(1,N). [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. [in,out] A COMPLEX array on the CPU, dimension (LDA,H*NB) On exit, the panel is copied back to the CPU [in] lda INTEGER The leading dimension of the array A. LDA >= max(1,N). [in] h INTEGER It specifies the size of the CPU workspace, A. [in] queues magma_queue_t queues is of dimension (ngpu,3) and contains the queues used for the partial factorization. [in] events magma_event_t events is of dimension(ngpu,5) and contains the events used for the partial factorization. [out] info INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, the leading minor of order i is not positive definite, and the factorization could not be completed.
 magma_int_t magma_cpotrf_gpu ( magma_uplo_t uplo, magma_int_t n, magmaFloatComplex_ptr dA, magma_int_t ldda, magma_int_t * info )

CPOTRF 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.

Parameters
 [in] uplo magma_uplo_t = MagmaUpper: Upper triangle of dA is stored; = MagmaLower: Lower triangle of dA is stored. [in] n INTEGER The order of the matrix dA. N >= 0. [in,out] dA COMPLEX 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 = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, the leading minor of order i is not positive definite, and the factorization could not be completed.
 magma_int_t magma_cpotrf_m ( magma_int_t ngpu, magma_uplo_t uplo, magma_int_t n, magmaFloatComplex * A, magma_int_t lda, magma_int_t * info )

CPOTRF 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.

Parameters
 [in] ngpu INTEGER Number of GPUs to use. ngpu > 0. [in] uplo magma_uplo_t = MagmaUpper: Upper triangle of A is stored; = MagmaLower: Lower triangle of A is stored. [in] n INTEGER The order of the matrix A. N >= 0. [in,out] A COMPLEX 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 = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value or another error occured, such as memory allocation failed. > 0: if INFO = i, the leading minor of order i is not positive definite, and the factorization could not be completed.
 magma_int_t magma_cpotrf_mgpu ( magma_int_t ngpu, magma_uplo_t uplo, magma_int_t n, magmaFloatComplex_ptr d_lA[], magma_int_t ldda, magma_int_t * info )

CPOTRF 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.

Parameters
 [in] ngpu INTEGER Number of GPUs to use. ngpu > 0. [in] uplo magma_uplo_t = MagmaUpper: Upper triangle of dA is stored; = MagmaLower: Lower triangle of dA is stored. [in] n INTEGER The order of the matrix dA. N >= 0. [in,out] d_lA COMPLEX 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 = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, the leading minor of order i is not positive definite, and the factorization could not be completed.
 magma_int_t magma_dpotrf ( magma_uplo_t uplo, magma_int_t n, double * A, magma_int_t lda, magma_int_t * info )

DPOTRF computes the Cholesky factorization of a real symmetric 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.

This uses multiple queues to overlap communication and computation.

Parameters
 [in] uplo magma_uplo_t = MagmaUpper: Upper triangle of A is stored; = MagmaLower: Lower triangle of A is stored. [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, 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 = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value or another error occured, such as memory allocation failed. > 0: if INFO = i, the leading minor of order i is not positive definite, and the factorization could not be completed.
 magma_int_t magma_dpotrf3_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, magmaDouble_ptr d_lA[], magma_int_t ldda, magmaDouble_ptr d_lP[], magma_int_t lddp, double * A, magma_int_t lda, magma_int_t h, magma_queue_t queues[][3], magma_event_t events[][5], magma_int_t * info )

DPOTRF computes the Cholesky factorization of a real symmetric positive definite matrix dA.

Auxiliary subroutine for dpotrf2_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.

Parameters
 [in] ngpu INTEGER Number of GPUs to use. ngpu > 0. [in] uplo magma_uplo_t = MagmaUpper: Upper triangle of dA is stored; = MagmaLower: Lower triangle of dA is stored. [in] m INTEGER The number of rows of the submatrix to be factorized. [in] n INTEGER The number of columns of the submatrix to be factorized. [in] off_i INTEGER The first row index of the submatrix to be factorized. [in] off_j INTEGER The first column index of the submatrix to be factorized. [in] nb INTEGER The block size used for the factorization and distribution. [in,out] d_lA DOUBLE PRECISION array of pointers on the GPU, dimension (ngpu). On entry, the symmetric matrix dA distributed over GPU. (d_lAT[d] points to the local matrix on d-th GPU). If UPLO = MagmaLower or MagmaUpper, it respectively uses a 1D block column or row cyclic format (with the block size nb), and each local matrix is stored by column. 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,out] d_lP DOUBLE PRECISION array of pointers on the GPU, dimension (ngpu). d_LAT[d] points to workspace of size h*lddp*nb on d-th GPU. [in] lddp INTEGER The leading dimension of the array dP. LDDA >= max(1,N). [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. [in,out] A DOUBLE PRECISION array on the CPU, dimension (LDA,H*NB) On exit, the panel is copied back to the CPU [in] lda INTEGER The leading dimension of the array A. LDA >= max(1,N). [in] h INTEGER It specifies the size of the CPU workspace, A. [in] queues magma_queue_t queues is of dimension (ngpu,3) and contains the queues used for the partial factorization. [in] events magma_event_t events is of dimension(ngpu,5) and contains the events used for the partial factorization. [out] info INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, the leading minor of order i is not positive definite, and the factorization could not be completed.
 magma_int_t magma_dpotrf_gpu ( magma_uplo_t uplo, magma_int_t n, magmaDouble_ptr dA, magma_int_t ldda, magma_int_t * info )

DPOTRF computes the Cholesky factorization of a real symmetric 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.

Parameters
 [in] uplo magma_uplo_t = MagmaUpper: Upper triangle of dA is stored; = MagmaLower: Lower triangle of dA is stored. [in] n INTEGER The order of the matrix dA. N >= 0. [in,out] dA DOUBLE PRECISION array on the GPU, dimension (LDDA,N) On entry, the symmetric 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 = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, the leading minor of order i is not positive definite, and the factorization could not be completed.
 magma_int_t magma_dpotrf_m ( magma_int_t ngpu, magma_uplo_t uplo, magma_int_t n, double * A, magma_int_t lda, magma_int_t * info )

DPOTRF computes the Cholesky factorization of a real symmetric 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.

Parameters
 [in] ngpu INTEGER Number of GPUs to use. ngpu > 0. [in] uplo magma_uplo_t = MagmaUpper: Upper triangle of A is stored; = MagmaLower: Lower triangle of A is stored. [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, 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 = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value or another error occured, such as memory allocation failed. > 0: if INFO = i, the leading minor of order i is not positive definite, and the factorization could not be completed.
 magma_int_t magma_dpotrf_mgpu ( magma_int_t ngpu, magma_uplo_t uplo, magma_int_t n, magmaDouble_ptr d_lA[], magma_int_t ldda, magma_int_t * info )

DPOTRF computes the Cholesky factorization of a real symmetric 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.

Parameters
 [in] ngpu INTEGER Number of GPUs to use. ngpu > 0. [in] uplo magma_uplo_t = MagmaUpper: Upper triangle of dA is stored; = MagmaLower: Lower triangle of dA is stored. [in] n INTEGER The order of the matrix dA. N >= 0. [in,out] d_lA DOUBLE PRECISION array of pointers on the GPU, dimension (ngpu) On entry, the symmetric 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 = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, the leading minor of order i is not positive definite, and the factorization could not be completed.
 magma_int_t magma_spotrf ( magma_uplo_t uplo, magma_int_t n, float * A, magma_int_t lda, magma_int_t * info )

SPOTRF computes the Cholesky factorization of a real symmetric 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.

This uses multiple queues to overlap communication and computation.

Parameters
 [in] uplo magma_uplo_t = MagmaUpper: Upper triangle of A is stored; = MagmaLower: Lower triangle of A is stored. [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, 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 = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value or another error occured, such as memory allocation failed. > 0: if INFO = i, the leading minor of order i is not positive definite, and the factorization could not be completed.
 magma_int_t magma_spotrf3_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, magmaFloat_ptr d_lA[], magma_int_t ldda, magmaFloat_ptr d_lP[], magma_int_t lddp, float * A, magma_int_t lda, magma_int_t h, magma_queue_t queues[][3], magma_event_t events[][5], magma_int_t * info )

SPOTRF computes the Cholesky factorization of a real symmetric positive definite matrix dA.

Auxiliary subroutine for spotrf2_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.

Parameters
 [in] ngpu INTEGER Number of GPUs to use. ngpu > 0. [in] uplo magma_uplo_t = MagmaUpper: Upper triangle of dA is stored; = MagmaLower: Lower triangle of dA is stored. [in] m INTEGER The number of rows of the submatrix to be factorized. [in] n INTEGER The number of columns of the submatrix to be factorized. [in] off_i INTEGER The first row index of the submatrix to be factorized. [in] off_j INTEGER The first column index of the submatrix to be factorized. [in] nb INTEGER The block size used for the factorization and distribution. [in,out] d_lA REAL array of pointers on the GPU, dimension (ngpu). On entry, the symmetric matrix dA distributed over GPU. (d_lAT[d] points to the local matrix on d-th GPU). If UPLO = MagmaLower or MagmaUpper, it respectively uses a 1D block column or row cyclic format (with the block size nb), and each local matrix is stored by column. 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,out] d_lP REAL array of pointers on the GPU, dimension (ngpu). d_LAT[d] points to workspace of size h*lddp*nb on d-th GPU. [in] lddp INTEGER The leading dimension of the array dP. LDDA >= max(1,N). [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. [in,out] A REAL array on the CPU, dimension (LDA,H*NB) On exit, the panel is copied back to the CPU [in] lda INTEGER The leading dimension of the array A. LDA >= max(1,N). [in] h INTEGER It specifies the size of the CPU workspace, A. [in] queues magma_queue_t queues is of dimension (ngpu,3) and contains the queues used for the partial factorization. [in] events magma_event_t events is of dimension(ngpu,5) and contains the events used for the partial factorization. [out] info INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, the leading minor of order i is not positive definite, and the factorization could not be completed.
 magma_int_t magma_spotrf_gpu ( magma_uplo_t uplo, magma_int_t n, magmaFloat_ptr dA, magma_int_t ldda, magma_int_t * info )

SPOTRF computes the Cholesky factorization of a real symmetric 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.

Parameters
 [in] uplo magma_uplo_t = MagmaUpper: Upper triangle of dA is stored; = MagmaLower: Lower triangle of dA is stored. [in] n INTEGER The order of the matrix dA. N >= 0. [in,out] dA REAL array on the GPU, dimension (LDDA,N) On entry, the symmetric 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 = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, the leading minor of order i is not positive definite, and the factorization could not be completed.
 magma_int_t magma_spotrf_m ( magma_int_t ngpu, magma_uplo_t uplo, magma_int_t n, float * A, magma_int_t lda, magma_int_t * info )

SPOTRF computes the Cholesky factorization of a real symmetric 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.

Parameters
 [in] ngpu INTEGER Number of GPUs to use. ngpu > 0. [in] uplo magma_uplo_t = MagmaUpper: Upper triangle of A is stored; = MagmaLower: Lower triangle of A is stored. [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, 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 = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value or another error occured, such as memory allocation failed. > 0: if INFO = i, the leading minor of order i is not positive definite, and the factorization could not be completed.
 magma_int_t magma_spotrf_mgpu ( magma_int_t ngpu, magma_uplo_t uplo, magma_int_t n, magmaFloat_ptr d_lA[], magma_int_t ldda, magma_int_t * info )

SPOTRF computes the Cholesky factorization of a real symmetric 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.

Parameters
 [in] ngpu INTEGER Number of GPUs to use. ngpu > 0. [in] uplo magma_uplo_t = MagmaUpper: Upper triangle of dA is stored; = MagmaLower: Lower triangle of dA is stored. [in] n INTEGER The order of the matrix dA. N >= 0. [in,out] d_lA REAL array of pointers on the GPU, dimension (ngpu) On entry, the symmetric 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 = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, the leading minor of order i is not positive definite, and the factorization could not be completed.
 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.

This uses multiple queues to overlap communication and computation.

Parameters
 [in] uplo magma_uplo_t = MagmaUpper: Upper triangle of A is stored; = MagmaLower: Lower triangle of A is stored. [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 = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value or another error occured, such as memory allocation failed. > 0: if INFO = i, the leading minor of order i is not positive definite, and the factorization could not be completed.
 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.

Parameters
 [in] ngpu INTEGER Number of GPUs to use. ngpu > 0. [in] uplo magma_uplo_t = MagmaUpper: Upper triangle of dA is stored; = MagmaLower: Lower triangle of dA is stored. [in] m INTEGER The number of rows of the submatrix to be factorized. [in] n INTEGER The number of columns of the submatrix to be factorized. [in] off_i INTEGER The first row index of the submatrix to be factorized. [in] off_j INTEGER The first column index of the submatrix to be factorized. [in] nb INTEGER The block size used for the factorization and distribution. [in,out] d_lA COMPLEX_16 array of pointers on the GPU, dimension (ngpu). On entry, the Hermitian matrix dA distributed over GPU. (d_lAT[d] points to the local matrix on d-th GPU). If UPLO = MagmaLower or MagmaUpper, it respectively uses a 1D block column or row cyclic format (with the block size nb), and each local matrix is stored by column. 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,out] d_lP COMPLEX_16 array of pointers on the GPU, dimension (ngpu). d_LAT[d] points to workspace of size h*lddp*nb on d-th GPU. [in] lddp INTEGER The leading dimension of the array dP. LDDA >= max(1,N). [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. [in,out] A COMPLEX_16 array on the CPU, dimension (LDA,H*NB) On exit, the panel is copied back to the CPU [in] lda INTEGER The leading dimension of the array A. LDA >= max(1,N). [in] h INTEGER It specifies the size of the CPU workspace, A. [in] queues magma_queue_t queues is of dimension (ngpu,3) and contains the queues used for the partial factorization. [in] events magma_event_t events is of dimension(ngpu,5) and contains the events used for the partial factorization. [out] info INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, the leading minor of order i is not positive definite, and the factorization could not be completed.
 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.

Parameters
 [in] uplo magma_uplo_t = MagmaUpper: Upper triangle of dA is stored; = MagmaLower: Lower triangle of dA is stored. [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 = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, the leading minor of order i is not positive definite, and the factorization could not be completed.
 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 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.

Parameters
 [in] ngpu INTEGER Number of GPUs to use. ngpu > 0. [in] uplo magma_uplo_t = MagmaUpper: Upper triangle of A is stored; = MagmaLower: Lower triangle of A is stored. [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 = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value or another error occured, such as memory allocation failed. > 0: if INFO = i, the leading minor of order i is not positive definite, and the factorization could not be completed.
 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.

Parameters
 [in] ngpu INTEGER Number of GPUs to use. ngpu > 0. [in] uplo magma_uplo_t = MagmaUpper: Upper triangle of dA is stored; = MagmaLower: Lower triangle of dA is stored. [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 = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, the leading minor of order i is not positive definite, and the factorization could not be completed.