.rst .pdf

Contents

potrf_batch (Buffer Strided 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 uplo = mkl::uplo::upper,

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

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

API

Syntax

namespace oneapi::mkl::lapack {
  void potrf_batch(cl::sycl::queue &queue,
  mkl::uplo uplo,
  std::int64_t n,
  cl::sycl::buffer<T> &a,
  std::int64_t lda,
  std::int64_t stride_a,
  std::int64_t batch_size,
  cl::sycl::buffer<T> &scratchpad,
  std::int64_t scratchpad_size)
}

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

Indicates whether the upper or lower triangular part of A_i is stored and how A_i is factored:

If uplo = mkl::uplo::upper, the array a stores the upper triangular parts of the matrices A_i.

If uplo = mkl::uplo::lower, the array a stores the lower triangular parts of the matrices A_i.

n

Specifies the order of the matrices A_i, (0 ≤ n).

a

Array containing a batch of input matrices A_i, each of A_i being of size lda*n and holding either uppoer or lower triangular parts of the matrices A_i (see uplo).

lda

The leading dimension of A_i.

stride_a

The stride between the beginnings of matrices A_i inside the batch.

batch_size

Specifies the number of problems in a batch.

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 (Strided Version).

Output Parameters

a

The batch array a is overwritten by the Cholesky factor U_i or L_i, as specified by uplo .

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.

potrf (USM Version) potrf_batch (Group Version)