potrs_batch (Group Version)#
Solves a batch of systems of linear equations with a Cholesky-factored
symmetric (Hermitian) positive-definite coefficient matrices. This
routine belongs to the oneapi::mkl::lapack namespace.
Description#
The routine solves for Xi the systems of linear
equations Ai*Xi = Bi with
a symmetric positive-definite or, for complex data, Hermitian
positive-definite matrices Ai, given the Cholesky
factorization of Ai, i ϵ{1...batch_size} :
Ai =UiT*Ui for real data,Ai =UiH*Ui for complex data if uplog=mkl::uplo::upperAi =Li*LiT for real data,Ai =Li*LiH for complex data if uplog=mkl::uplo::lower
where Li is a lower triangular matrix and
Ui is upper triangular, g is an index of group of
parameters corresponding to Ai, and the total number of
problems to solve, batch_size, is a sum of sizes for all of the
groups of parameters as provided by the group_sizes array.
The systems are solved with multiple right-hand sides stored in the
columns of the matrices Bi.
Before calling this routine, matrices Ai should be
factorized by a call to potrf_batch (Group Version).
API#
Syntax#
namespace oneapi::mkl::lapack {
sycl::event potrs_batch(sycl::queue &queue,
mkl::uplo *uplo, int64_t *n,
int64_t *nrhs,
const T * const *a,
int64_t *lda,
T **b,
int64_t *ldb,
int64_t group_count,
int64_t *group_sizes,
T *scratchpad,
int64_t scratchpad_size,
const std::vector<sycl::event> &events = {})
}
This function supports the following precisions and devices:
T |
Devices supported |
|---|---|
|
CPU and GPU |
|
CPU and GPU |
|
CPU and GPU |
|
CPU and GPU |
Input Parameters#
- queue
Device queue where calculations will be performed.
- uplo
Array of
group_countuplog parameters.Each of uplog indicates whether the upper or lower triangular parts of the input matrices are provided:
If uplog=
mkl::uplo::upper, input matrices from arrayabelonging to groupgstore the upper triangular parts.If uplog=
mkl::uplo::lower, input matrices from arrayabelonging to groupgstore the lower triangular parts.- n
Array of
group_countparametersng.Each
ng specifies the order of the input matrices from arrayabelonging to groupg(ng ≥ 0).- nrhs
Array of
group_countparameters nrhsg parameters.Each nrhsg specifies the number of right-hand sides supplied for group
gin corresponding part of arrayb(nrhsg ≥ 0).- a
Array of
batch_sizepointers to Cholesky factored matricesAi as returned by potrf_batch (Group Version).- lda
Array of
group_countparameters ldag.Each ldag specifies the leading dimension of matrices from
abelonging to groupg(ldag ≥max(1, ng)).- b
Array of
batch_sizepointers to right-hand side matricesBi, each of size ldbg*nrhsg, wheregis an index of group corresponding toBi.- ldb
Array of
group_countparameters ldbg.Each ldbg specifies the leading dimension of matrices from
bbelonging to groupg(ldbg ≥max(1, ng)).- group_count
Specifies the number of groups of parameters. Must be at least 0.
- group_sizes
Array of group_count integers. Array element with index
gspecifies the number of problems to solve for each of the groups of parametersg. So the total number of problems to solve,batch_size, is a sum of all parameter group sizes.- scratchpad
Scratchpad memory to be used by routine for storing intermediate results.
- scratchpad_size
Size of scratchpad memory as a number of floating point elements of type T. Size should not be less then the value returned by potrs_batch_scratchpad_size (Group Version).
- events
List of events to wait for before starting computation. Defaults to empty list.
Output Parameters#
- b
The matrices pointed to by array b are overwritten by the solution matrices
Xi.
Exceptions#
Exception |
Description |
|---|---|
|
This exception is thrown when problems occur during calculations. You can obtain the info code of the problem using the info() method of the exception object: If If If |
Return Values#
Output event to wait on to ensure computation is complete.