# trtrs¶

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.

Syntax

void `trtrs`(cl::sycl::queue &queue, mkl::uplo uplo, mkl::transpose trans, mkl::diag diag, std::int64_t n, std::int64_t nrhs, cl::sycl::buffer<T> &a, std::int64_t lda, cl::sycl::buffer<T> &b, std::int64_t ldb, cl::sycl::buffer<T> &scratchpad, std::int64_t scratchpad_size)

`trtrs` 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 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).

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

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)`.

Buffer holding 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.

Output Parameters

 b Overwritten by the solution matrix `X`.

Exceptions

 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.

Info

info

Buffer containing error information.

If `info` = 0, the execution is successful.

If `info` = -`i`, the `i`-th parameter had an illegal value.

Known Limitations

GPU support for this function does not include error reporting through the `info` parameter.