trtri (USM Version)

oneMKL - Data Parallel C++ Developer Reference

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ID 772045

Date 3/22/2024

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trtri (USM Version)

Computes the inverse of a triangular matrix. This routine belongs to the oneapi::mkl::lapack namespace.

Description
API

Description

This routine computes the inverse inv(A) of an upper or lower triangular matrix A.

API

Syntax

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

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

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

Input Parameters

queue

Device queue where calculations will be performed.

uplo

Indicates whether A is upper or lower triangular:

If uplo = uplo::upper, then the array a stores the upper triangular part of the matrix A, and the strictly lower triangular part of the matrix is not referenced.

If uplo = uplo::lower, then the array a stores the lower triangular part of the matrix A, and the strictly upper triangular part of the matrix is not referenced.

diag

If diag = diag::nonunit, then the matrix A is not a unit triangular matrix.

If diag = diag::unit, then the matrix A is unit triangular: the diagonal elements are assumed to be 1 and are not referenced.

n

The order of the matrix A(n ≥ 0).

a

Pointer to the input array, which contains either the upper or lower triangular matrix, A (see uplo). The array must be of size at least lda * max(1, n).

lda

The leading dimension of a; lda ≥ max(1, n).

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 trtri_scratchpad_size function.

events

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

Output Parameters

a

If uplo = uplo::upper, the upper triangular part of A is overwritten by its inverse.

If uplo = uplo::lower, the lower triangular part of A is overwritten by its inverse.

Exceptions

Exception	Description
`mkl::lapack::exception`	This exception is thrown when problems occur during the 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`, and detail() returns 0, `A(i,i)` is exactly zero. The triangular matrix is singular and its inverse can not be computed. If `info` is equal to the value passed as scratchpad size, and detail() returns non-zero, then the passed scratchpad has an insufficient size. The required size should not be less than the value returned by the detail() method of the exception object.

Exception

Description

mkl::lapack::exception

This exception is thrown when problems occur during the 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, and detail() returns 0, A(i,i) is exactly zero. The triangular matrix is singular and its inverse can not be computed.

If info is equal to the value passed as scratchpad size, and detail() returns non-zero, then the passed scratchpad has an insufficient size. 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.

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oneMKL - Data Parallel C++ Developer Reference

trtri (USM Version)

Description

API