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trtrs (USM Version)

Solves a system of linear equations with a triangular coefficient matrix, with multiple right-hand sides. This routine belongs to the oneapi::mkl::lapack namespace.

Description

The routine solves for X the following systems of linear equations with a triangular matrix A, with multiple right-hand sides stored in B:

A*X = B

if transa =transpose::nontrans,

AT*X = B

if transa =transpose::trans,

AH*X = B

if transa =transpose::conjtrans (for complex matrices only).

API

Syntax

namespace oneapi::mkl::lapack {
  cl::sycl::event trtrs(cl::sycl::queue &queue,
  mkl::uplo uplo,
  mkl::transpose trans,
  mkl::diag diag,
  std::int64_t n,
  std::int64_t nrhs,
  T *a,
  std::int64_t lda,
  T *b,
  std::int64_t ldb,
  T *scratchpad,
  std::int64_t scratchpad_size,
  const std::vector<cl::sycl::event> &events = {})
}

trtrs (USM version) 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 A is upper or lower triangular:

If uplo = uplo::upper, then A is upper triangular.

If uplo = uplo::lower, then A is lower triangular.

trans

If transa = transpose::nontrans, then A*X = B is solved for X.

If transa = transpose::trans, then AT*X = B is solved for X.

If transa = transpose::conjtrans, then AH*X = B is solved for X.

diag

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

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

n

The order of A; the number of rows in B; n≥ 0.

nrhs

The number of right-hand sides; nrhs≥ 0.

a

Array containing the matrix A.

The second dimension of a must be at least max(1,n).

lda

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

b

Array containing the matrix B whose columns are the right-hand sides for the systems of equations.

The second dimension of b at least max(1,nrhs).

ldb

The leading dimension of b; ldb≥ 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 trtrs_scratchpad_size function.

events

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

Output Parameters

b

Overwritten by the solution matrix X.

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 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.

trtrs trtrs_scratchpad_size