Contents

# getrs

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.

## Description

The routine solves for
X
the following systems of linear equations:
Equation
Condition
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 getrf to compute the
LU
factorization of
A
.

## API

Syntax
``````namespace oneapi::mkl::lapack {
void getrs(cl::sycl::queue &queue,
mkl::transpose trans,
std::int64_t n,
std::int64_t nrhs,
cl::sycl::buffer<T> &a,
std::int64_t lda,
std::int64_t *ipiv,
cl::sycl::buffer<T> &b,
std::int64_t ldb,
}``````
getrs
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.
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
Buffer holding the array containing the factorization of the matrix
A
, as returned by getrf. 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.
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
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 getrs_scratchpad_size function.
Output Parameters
b
The buffer b is 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 = 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.
Known Limitations
For GPU support, errors are reported through the info parameter, but computation does not halt for an algorithmic error.

#### Product and Performance Information

1

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