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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 X_i the systems of linear equations A_i*X_i = B_i with a symmetric positive-definite or, for complex data, Hermitian positive-definite matrices A_i, given the Cholesky factorization of A_i, i ϵ{1...batch_size} :

• A_i = U_i^T*U_i for real data, A_i = U_i^H*U_i for complex data if uplo_g=mkl::uplo::upper

• A_i = L_i*L_i^T for real data, A_i = L_i*L_i^H for complex data if uplo_g=mkl::uplo::lower

where L_i is a lower triangular matrix and U_i is upper triangular, g is an index of group of parameters corresponding to A_i, 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 B_i.

Before calling this routine, matrices A_i should be factorized by a call to potrf_batch (Group Version).

API

Syntax

namespace oneapi::mkl::lapack {
  cl::sycl::event potrs_batch(cl::sycl::queue &queue,
  mkl::uplo *uplo, std::int64_t *n,
  std::int64_t *nrhs,
  T **a,
  std::int64_t *lda,
  T **b,
  std::int64_t *ldb,
  std::int64_t group_count,
  std::int64_t *group_sizes,
  T *scratchpad,
  std::int64_t scratchpad_size,
  const std::vector<cl::sycl::event> &events = {})
}

Function supports the following precisions and devices.

T	Devices supported
float	Host, CPU, and GPU
double	Host, CPU, and GPU
std::complex<float>	Host, CPU, and GPU
std::complex<double>	Host, CPU, and GPU

Input Parameters

queue

Device queue where calculations will be performed.

uplo

Array of group_countuplo_g parameters.

Each of uplo_g indicates whether the upper or lower triangular parts of the input matrices are provided:

If uplo_g=mkl::uplo::upper, input matrices from array a belonging to group g store the upper triangular parts.

If uplo_g=mkl::uplo::lower, input matrices from array a belonging to group g store the lower triangular parts.

n

Array of group_count parameters n_g.

Each n_g specifies the order of the input matrices from array a belonging to group g.

nrhs

Array of group_count parameters nrhs_g parameters.

Each nrhs_g specifies the number of right-hand sides supplied for group g in corresponding part of array b.

a

Array of batch_size pointers to Cholesky factored matrices A_i as returned by potrf_batch (Group Version).

lda

Array of group_count parameters lda_g.

Each lda_g specifies the leading dimension of matrices from a belonging to group g.

b

Array of batch_size pointers to right-hand side matrices B_i, each of size ldb_g*nrhs_g, where g is an index of group corresponding to B_i.

ldb

Array of group_count parameters ldb_g.

Each ldb_g specifies the leading dimension of matrices from b belonging to group g.

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 g specifies the number of problems to solve for each of the groups of parameters g. 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 X_i.

Exceptions

Exception

Description

mkl::lapack::batch_exception

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 info = -n, the n-th parameter had an illegal value. If info equals the value passed as scratchpad size, and detail() returns non-zero, then the passed scratchpad is of insufficient size, and the required size should be not less then value returned by the detail() method of the exception object. If info is zero, then the diagonal element of some of Ui is zero, and the solve could not be completed. The indexes of such matrices in the batch can be obtained with the ids() method of the exception object. You can obtain the indexes of the first zero diagonal elements in these Ui matrices using the infos() method of the exception object.

Return Values

Output event to wait on to ensure computation is complete.

potrs_batch (Buffer Strided Version) potrs_batch (USM Strided Version)