getrs¶

Solves a system of linear equations with an LU-factored square coefficient matrix, with multiple right-hand sides.

getrs supports the following precisions.

T

float

double

std::complex<float>

std::complex<double>

Description

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

`A*X = B`	if `trans`=`onemkl::transpose::nontrans`
`AT*X = B`	if `trans`=`onemkl::transpose::trans`
`AH*X = B`	if `trans`=`onemkl::transpose::conjtrans`

Before calling this routine, you must call getrf to compute the LU factorization of A.

getrs (BUFFER Version)¶

Syntax

void onemkl::lapack::getrs(cl::sycl::queue &queue, onemkl::transpose trans, std::int64_t n, std::int64_t nrhs, cl::sycl::buffer<T, 1> &a, std::int64_t lda, cl::sycl::buffer<std::int64_t, 1> &ipiv, cl::sycl::buffer<T, 1> &b, std::int64_t ldb, cl::sycl::buffer<T, 1> &scratchpad, std::int64_t scratchpad_size)¶

Input Parameters

queue

The queue where the routine should be executed.

trans

Indicates the form of the equations:

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

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

If trans=onemkl::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

Buffer containing the factorization of the matrix A, as returned by getrf. The second dimension of a must be at least max(1, n).

lda

The leading dimension of a.

ipiv

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

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

The leading dimension of b.

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 getrs_scratchpad_size function.

Output Parameters

b: The buffer b is overwritten by the solution matrix X.
scratchpad: Buffer holding scratchpad memory to be used by routine for storing intermediate results.

Throws

onemkl::lapack::exception

Exception is thrown in case of problems happened during calculations. The info code of the problem can be obtained by get_info() method of 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 equals to value passed as scratchpad size, and get_detail() returns non zero, then passed scratchpad is of insufficient size, and required size should not be less than value return by get_detail() method of exception object.

getrs (USM Version)¶