getrs (USM Version)¶

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

Syntax

cl::sycl::event `getrs`(cl::sycl::queue &queue, mkl::transpose trans, std::int64_t n, std::int64_t nrhs, T *a, std::int64_t lda, std::int64_t *ipiv, T *b, std::int64_t ldb, T *scratchpad, std::int64_t scratchpad_size, const cl::sycl::vector_class<cl::sycl::event> &events = {})

`getrs` (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

Description

The routine solves for `X` the following systems of linear equations:

`A*X = B`

if `trans`=`mkl::transpose::nontrans`

`AT*X = B`

if `trans`=`mkl::transpose::trans`

`AH*X = B`

if `trans`=`mkl::transpose::conjtrans`

Before calling this routine, you must call the getrf (USM Version) function to compute the `LU` factorization of `A`.

Input Parameters

queue

Device queue where calculations will be performed.

trans

Indicates the form of the equations:

If `trans=mkl::transpose::nontrans`, then `A*X = B` is solved for `X`.

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

If `trans=mkl::transpose::conjtrans`, then `AH*X = B` is solved for `X`.

n

The order of the matrix `A` and the number of rows in matrix `B(0≤n)`.

nrhs

The number of right-hand sides (`0≤nrhs`).

a

Pointer to the array containing the factorization of the matrix `A`, as returned by getrf (USM Version). The second dimension of a must be at least `max(1, n)`.

lda

ipiv

Array, size at least `max(1, n)`. The ipiv array, as returned by getrf (USM Version).

b

The array b contains the matrix `B` whose columns are the right-hand sides for the systems of equations. The second dimension of b must be at least `max(1,nrhs)`.

ldb

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 getrs_scratchpad_size function.

events

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

Output Parameters

b

The buffer b is 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 = i`, the `i`-th diagonal element of `U` is zero, and the solve 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.