single precision
[Cholesky solve: computational]

Functions

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.
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.
magma_int_t magma_spotrf_batched (magma_uplo_t uplo, magma_int_t n, float **dA_array, magma_int_t ldda, magma_int_t *info_array, magma_int_t batchCount, magma_queue_t queue)
 SPOTRF computes the Cholesky factorization of a real symmetric positive definite matrix dA.
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.
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_OOC computes the Cholesky factorization of a real symmetric positive definite matrix A.
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.
magma_int_t magma_spotrf_mgpu_right (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.
magma_int_t magma_spotri (magma_uplo_t uplo, magma_int_t n, float *A, magma_int_t lda, magma_int_t *info)
 SPOTRI 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 SPOTRF.
magma_int_t magma_spotri_gpu (magma_uplo_t uplo, magma_int_t n, magmaFloat_ptr dA, magma_int_t ldda, magma_int_t *info)
 SPOTRI 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 SPOTRF.
magma_int_t magma_spotrs_batched (magma_uplo_t uplo, magma_int_t n, magma_int_t nrhs, float **dA_array, magma_int_t ldda, float **dB_array, magma_int_t lddb, magma_int_t batchCount, magma_queue_t queue)
 SPOTRS solves a system of linear equations A*X = B with a symmetric positive definite matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by SPOTRF.
magma_int_t magma_spotrs_gpu (magma_uplo_t uplo, magma_int_t n, magma_int_t nrhs, magmaFloat_ptr dA, magma_int_t ldda, magmaFloat_ptr dB, magma_int_t lddb, magma_int_t *info)
 SPOTRS solves a system of linear equations A*X = B with a symmetric positive definite matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by SPOTRF.
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)
 SPOTRF computes the Cholesky factorization of a real symmetric positive definite matrix A.

Function Documentation

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.

If the current stream is NULL, this version replaces it with a new stream to overlap computation with communication.

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] 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_batched ( magma_uplo_t  uplo,
magma_int_t  n,
float **  dA_array,
magma_int_t  ldda,
magma_int_t *  info_array,
magma_int_t  batchCount,
magma_queue_t  queue 
)

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. If the current stream is NULL, this version replaces it with a new stream to overlap computation with communication.

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_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. If the current stream is NULL, this version replaces it with a new stream to overlap computation with communication.

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_OOC 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_spotrf_mgpu_right ( 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] 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 (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

  • = 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_spotri ( magma_uplo_t  uplo,
magma_int_t  n,
float *  A,
magma_int_t  lda,
magma_int_t *  info 
)

SPOTRI 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 SPOTRF.

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 triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T, as computed by SPOTRF. 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

  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value
  • > 0: if INFO = i, the (i,i) element of the factor U or L is zero, and the inverse could not be computed.
magma_int_t magma_spotri_gpu ( magma_uplo_t  uplo,
magma_int_t  n,
magmaFloat_ptr  dA,
magma_int_t  ldda,
magma_int_t *  info 
)

SPOTRI 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 SPOTRF.

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] dA REAL 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 SPOTRF. 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

  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value
  • > 0: if INFO = i, the (i,i) element of the factor U or L is zero, and the inverse could not be computed.
magma_int_t magma_spotrs_batched ( magma_uplo_t  uplo,
magma_int_t  n,
magma_int_t  nrhs,
float **  dA_array,
magma_int_t  ldda,
float **  dB_array,
magma_int_t  lddb,
magma_int_t  batchCount,
magma_queue_t  queue 
)

SPOTRS solves a system of linear equations A*X = B with a symmetric positive definite matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by SPOTRF.

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] nrhs INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
[in] dA REAL 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 SPOTRF.
[in] ldda INTEGER The leading dimension of the array A. LDDA >= max(1,N).
[in,out] dB REAL 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

  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value
magma_int_t magma_spotrs_gpu ( magma_uplo_t  uplo,
magma_int_t  n,
magma_int_t  nrhs,
magmaFloat_ptr  dA,
magma_int_t  ldda,
magmaFloat_ptr  dB,
magma_int_t  lddb,
magma_int_t *  info 
)

SPOTRS solves a system of linear equations A*X = B with a symmetric positive definite matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by SPOTRF.

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] nrhs INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
[in] dA REAL 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 SPOTRF.
[in] ldda INTEGER The leading dimension of the array A. LDDA >= max(1,N).
[in,out] dB REAL 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

  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value
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 
)

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.

If the current stream is NULL, this version replaces it with a new stream to overlap computation with communication.

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.

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