MAGMA 2.9.0
Matrix Algebra for GPU and Multicore Architectures
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Functions
posv: Solves Ax = b using Cholesky factorization (driver)
Batched LA » Linear system solvers » Symmetric/Hermitian positive definite: Cholesky

Functions

magma_int_t magma_cposv_batched (magma_uplo_t uplo, magma_int_t n, magma_int_t nrhs, magmaFloatComplex **dA_array, magma_int_t ldda, magmaFloatComplex **dB_array, magma_int_t lddb, magma_int_t *dinfo_array, magma_int_t batchCount, magma_queue_t queue)
 CPOSV computes the solution to a complex system of linear equations A * X = B, where A is an N-by-N Hermitian positive definite matrix and X and B are N-by-NRHS matrices.
 
magma_int_t magma_dposv_batched (magma_uplo_t uplo, magma_int_t n, magma_int_t nrhs, double **dA_array, magma_int_t ldda, double **dB_array, magma_int_t lddb, magma_int_t *dinfo_array, magma_int_t batchCount, magma_queue_t queue)
 DPOSV computes the solution to a real system of linear equations A * X = B, where A is an N-by-N symmetric positive definite matrix and X and B are N-by-NRHS matrices.
 
magma_int_t magma_sposv_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 *dinfo_array, magma_int_t batchCount, magma_queue_t queue)
 SPOSV computes the solution to a real system of linear equations A * X = B, where A is an N-by-N symmetric positive definite matrix and X and B are N-by-NRHS matrices.
 
magma_int_t magma_zposv_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 *dinfo_array, magma_int_t batchCount, magma_queue_t queue)
 ZPOSV computes the solution to a complex system of linear equations A * X = B, where A is an N-by-N Hermitian positive definite matrix and X and B are N-by-NRHS matrices.
 

Detailed Description

Function Documentation

◆ magma_cposv_batched()

magma_int_t magma_cposv_batched ( magma_uplo_t uplo,
magma_int_t n,
magma_int_t nrhs,
magmaFloatComplex ** dA_array,
magma_int_t ldda,
magmaFloatComplex ** dB_array,
magma_int_t lddb,
magma_int_t * dinfo_array,
magma_int_t batchCount,
magma_queue_t queue )

CPOSV computes the solution to a complex system of linear equations A * X = B, where A is an N-by-N Hermitian positive definite matrix and X and B are N-by-NRHS matrices.

The Cholesky decomposition is used to factor A as 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 a lower triangular matrix. The factored form of A is then used to solve the system of equations A * X = B.

Parameters
[in]uplomagma_uplo_t
  • = MagmaUpper: Upper triangle of A is stored;
  • = MagmaLower: Lower triangle of A is stored.
[in]nINTEGER The order of the matrix A. N >= 0.
[in]nrhsINTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
[in,out]dA_arrayArray of pointers, dimension (batchCount). Each is a COMPLEX array on the GPU, dimension (LDDA,N) On entry, each pointer is a 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 dA 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 corresponding entry in dinfo_array = 0, each pointer is the factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H.
[in]lddaINTEGER The leading dimension of each array A. LDA >= max(1,N).
[in,out]dB_arrayArray of pointers, dimension (batchCount). Each is a COMPLEX array on the GPU, dimension (LDB,NRHS) On entry, each pointer is a right hand side matrix B. On exit, each pointer is the corresponding solution matrix X.
[in]lddbINTEGER The leading dimension of each array B. LDB >= max(1,N).
[out]dinfo_arrayArray of INTEGERs, dimension (batchCount), for corresponding matrices.
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value
[in]batchCountINTEGER The number of matrices to operate on.
[in]queuemagma_queue_t Queue to execute in.

◆ magma_dposv_batched()

magma_int_t magma_dposv_batched ( magma_uplo_t uplo,
magma_int_t n,
magma_int_t nrhs,
double ** dA_array,
magma_int_t ldda,
double ** dB_array,
magma_int_t lddb,
magma_int_t * dinfo_array,
magma_int_t batchCount,
magma_queue_t queue )

DPOSV computes the solution to a real system of linear equations A * X = B, where A is an N-by-N symmetric positive definite matrix and X and B are N-by-NRHS matrices.

The Cholesky decomposition is used to factor A as 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 a lower triangular matrix. The factored form of A is then used to solve the system of equations A * X = B.

Parameters
[in]uplomagma_uplo_t
  • = MagmaUpper: Upper triangle of A is stored;
  • = MagmaLower: Lower triangle of A is stored.
[in]nINTEGER The order of the matrix A. N >= 0.
[in]nrhsINTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
[in,out]dA_arrayArray of pointers, dimension (batchCount). Each is a DOUBLE PRECISION array on the GPU, dimension (LDDA,N) On entry, each pointer is a 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 dA 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 corresponding entry in dinfo_array = 0, each pointer is the factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H.
[in]lddaINTEGER The leading dimension of each array A. LDA >= max(1,N).
[in,out]dB_arrayArray of pointers, dimension (batchCount). Each is a DOUBLE PRECISION array on the GPU, dimension (LDB,NRHS) On entry, each pointer is a right hand side matrix B. On exit, each pointer is the corresponding solution matrix X.
[in]lddbINTEGER The leading dimension of each array B. LDB >= max(1,N).
[out]dinfo_arrayArray of INTEGERs, dimension (batchCount), for corresponding matrices.
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value
[in]batchCountINTEGER The number of matrices to operate on.
[in]queuemagma_queue_t Queue to execute in.

◆ magma_sposv_batched()

magma_int_t magma_sposv_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 * dinfo_array,
magma_int_t batchCount,
magma_queue_t queue )

SPOSV computes the solution to a real system of linear equations A * X = B, where A is an N-by-N symmetric positive definite matrix and X and B are N-by-NRHS matrices.

The Cholesky decomposition is used to factor A as 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 a lower triangular matrix. The factored form of A is then used to solve the system of equations A * X = B.

Parameters
[in]uplomagma_uplo_t
  • = MagmaUpper: Upper triangle of A is stored;
  • = MagmaLower: Lower triangle of A is stored.
[in]nINTEGER The order of the matrix A. N >= 0.
[in]nrhsINTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
[in,out]dA_arrayArray of pointers, dimension (batchCount). Each is a REAL array on the GPU, dimension (LDDA,N) On entry, each pointer is a 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 dA 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 corresponding entry in dinfo_array = 0, each pointer is the factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H.
[in]lddaINTEGER The leading dimension of each array A. LDA >= max(1,N).
[in,out]dB_arrayArray of pointers, dimension (batchCount). Each is a REAL array on the GPU, dimension (LDB,NRHS) On entry, each pointer is a right hand side matrix B. On exit, each pointer is the corresponding solution matrix X.
[in]lddbINTEGER The leading dimension of each array B. LDB >= max(1,N).
[out]dinfo_arrayArray of INTEGERs, dimension (batchCount), for corresponding matrices.
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value
[in]batchCountINTEGER The number of matrices to operate on.
[in]queuemagma_queue_t Queue to execute in.

◆ magma_zposv_batched()

magma_int_t magma_zposv_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 * dinfo_array,
magma_int_t batchCount,
magma_queue_t queue )

ZPOSV computes the solution to a complex system of linear equations A * X = B, where A is an N-by-N Hermitian positive definite matrix and X and B are N-by-NRHS matrices.

The Cholesky decomposition is used to factor A as 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 a lower triangular matrix. The factored form of A is then used to solve the system of equations A * X = B.

Parameters
[in]uplomagma_uplo_t
  • = MagmaUpper: Upper triangle of A is stored;
  • = MagmaLower: Lower triangle of A is stored.
[in]nINTEGER The order of the matrix A. N >= 0.
[in]nrhsINTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
[in,out]dA_arrayArray of pointers, dimension (batchCount). Each is a COMPLEX_16 array on the GPU, dimension (LDDA,N) On entry, each pointer is a 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 dA 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 corresponding entry in dinfo_array = 0, each pointer is the factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H.
[in]lddaINTEGER The leading dimension of each array A. LDA >= max(1,N).
[in,out]dB_arrayArray of pointers, dimension (batchCount). Each is a COMPLEX_16 array on the GPU, dimension (LDB,NRHS) On entry, each pointer is a right hand side matrix B. On exit, each pointer is the corresponding solution matrix X.
[in]lddbINTEGER The leading dimension of each array B. LDB >= max(1,N).
[out]dinfo_arrayArray of INTEGERs, dimension (batchCount), for corresponding matrices.
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value
[in]batchCountINTEGER The number of matrices to operate on.
[in]queuemagma_queue_t Queue to execute in.