Contents

# 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,
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
A
T
*
X
=
B
is solved for
X
.
If transa =
transpose::conjtrans
, then
A
H
*
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
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)
.
Pointer to scratchpad memory to be used by the routine for storing intermediate results.
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.

#### Product and Performance Information

1

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.