potrf_batch (USM 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::lapacknamespace.

Syntax

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 stride_a, std::int64_t batch_size, T *scratchpad, std::int64_t scratchpad_size, const cl::sycl::vector_class<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

Description

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

Ai = UiT * Ui for real data, Ai = UiH * Ui for complex data. if uplo = mkl::uplo::upper,

Ai = LiT * Li for real data, Ai = LiH * Li for complex data if uplo = mkl::uplo::lower

Where Li is a lower triangular matrix and Ui is an upper triangular matrix.

Input Parameters

queue

Device queue where calculations will be performed.

uplo

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

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

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

n

Specifies the order of the matrices Ai, (0 n).

a

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

lda

The leading dimension of Ai.

stride_a

The stride between the beginnings of matrices Ai 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).

events

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

Output Parameters

a

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

Exceptions

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.