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potrf_batch (Group Version)

Computes the Cholesky factorizations of a batch of symmetric (or Hermitian, for complex data) positive-definite matrices. This routine belongs to the oneapi::mkl::lapack namespace.

Description

The routine forms the Cholesky factorizations of a symmetric positive-definite or, for complex data, Hermitian positive-definite matrices A_i, iϵ{1...batch_size}:

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

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

Where L_i is a lower triangular matrix and U_i is an upper triangular matrix, 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.

API

Syntax

namespace oneapi::mkl::lapack {
  cl::sycl::event potrf_batch(cl::sycl::queue &queue,
  mkl::uplo *uplo,
  std::int64_t *n,
  T **a,
  std::int64_t *lda,
  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.

a

Array of batch_size pointers to input matrices A_i, each being of size lda_g*n_g (g is an index of the group to which A_i belongs) and holding either upper or lower triangular part as specified by uplo_g.

lda

Array of group_count parameters lda_g.

Each lda_g specifies the leading dimension of matrices from a 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 potrf_batch_scratchpad_size (Group Version).

events

List of events to wait for before starting computation. Defaults to empty list.

Output Parameters

a

The matrices pointed to by array a are overwritten by the Cholesky factors U_i or L_i, as specified by uplo_g from the corresponding group of parameters.

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.

potrf_batch (Buffer Strided Version) potrf_batch (USM Strided Version)