Contents

potri (USM Version)

Computes the inverse of a symmetric (Hermitian) positive-definite matrix using the Cholesky factorization. This routine belongs to the oneapi::mkl::lapack namespace.

Description

The routine computes the inverse inv(A) of a symmetric positive definite or, for complex flavors, Hermitian positive-definite matrix A. Before calling this routine, call potrf (USM Version) to factorize A.

API

Syntax

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

potri (USM version) supports the following precisions and devices:

T

Devices Supported

float

Host, CPU, GPU

double

Host, CPU, GPU

std::complex<float>

Host, CPU, GPU

std::complex<double>

Host, CPU, GPU

Input Parameters

queue

Device queue where calculations will be performed.

uplo

Indicates how the input matrix A has been factored:

If uplo = mkl::uplo::upper, the upper triangle of A is stored.

If uplo = mkl::uplo::lower, the lower triangle of A is stored.

n

Specifies the order of the matrix A (0≤n).

a

Contains the factorization of the matrix A, as returned by potrf (USM Version). The second dimension of a must be at least max(1, n).

lda

The leading dimension of a.

scratchpad

Pointer to scratchpad memory to be used by the 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 than the value returned by the potri_scratchpad_size function.

events

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

Output Parameters

a

Overwritten by the upper or lower triangle of the inverse of A. Specified by uplo.

Exceptions

Exception

Description

mkl::lapack::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 = -i, the i-th parameter had an illegal value.

If info = i, the i-th diagonal element of the Cholesky factor (and therefore the factor itself) is zero, and the inversion could not be completed.

If info is equal to the value passed as scratchpad size, and detail() returns non zero, then the passed scratchpad has an insufficient size, and the required size should not be less than the value returned by the detail() method of the exception object.

Return Values

Output event to wait on to ensure computation is complete.

potri potri_scratchpad_size