Contents

# potrs_batch (USM Strided Version)

Solves a system of linear equations with a Cholesky-factored symmetric (Hermitian) positive-definite coefficient matrices. This routine belongs to the
oneapi::mkl::lapack
namespace.

## Description

The routine solves for
X
i
the system of linear equations
A
i
*
X
i
=
B
i
with a symmetric positive-definite or, for complex data, Hermitian positive-definite matrices
A
i
, given the Cholesky factorization of
A
i
,
i ϵ{1...batch_size}
:
• A
i
=
U
i
T
*
U
i
for real data,
A
i
=
U
i
H
*
U
i
for complex data if uplo=
mkl::uplo::upper
• A
i
=
L
i
*
L
i
T
for real data,
A
i
=
L
i
*
L
i
H
for complex data if uplo=
mkl::uplo::lower
where
L
i
is a lower triangular matrix and
U
i
is upper triangular. The system is solved with multiple right-hand sides stored in the columns of the matrix
B
i
.
Before calling this routine, matrices
A
i
should be factorized by a call to potrf_batch (USM Strided Version).

## API

Syntax
``````namespace oneapi::mkl::lapack {
cl::sycl::event potrs_batch(cl::sycl::queue &queue,
mkl::uplo uplo,
std::int64_t n,
std::int64_t nrhs,
T *a,
std::int64_t lda,
std::int64_t stride_a,
T *b,
std::int64_t ldb,
std::int64_t stride_b,
std::int64_t batch_size,
const std::vector<cl::sycl::event> &events = {})
}``````
Function 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 how the input matrix has been factored:
If uplo=
mkl::uplo::upper
, the upper triangle
U
i
of
A
i
is stored, where
A
i
=
U
i
T
*
U
i
for real data,
A
i
=
U
i
H
*
U
i
for complex data.
If uplo=
mkl::uplo::lower
, the upper triangle
L
i
of
A
i
is stored, where
A
i
=
L
i
*
L
i
T
for real data,
A
i
=
L
i
*
L
i
H
for complex data.
n
The order of the matrices
A
i
(
0 ≤ n
).
nrhs
The number of right hand sides
(0≤nrhs)
.
a
Array containing the batch of factorizations of the matrices
A
i
, as returned by potrf_batch (USM Strided Version).
lda
A
i
.
stride_a
The stride between the beginnings of matrices inside the batch array
a
.
b
The array containing the batch of matrices
B
i
whose columns are the right-hand sides for the systems of equations.
ldb
B
i
.
stride_b
The stride between the beginnings of matrices
B
i
inside the batch array
b
.
batch_size
Specifies the number of problems in a batch.
Scratchpad memory to be used by routine for storing intermediate results.
Size of scratchpad memory as a number of floating point elements of type T. Size should not be less then the value returned by stride version of potrs_batch_scratchpad_size (Strided Version) function.
events
List of events to wait for before starting computation. Defaults to empty list.
Output Parameters
b
The memory pointed to by pointer batch array b is overwritten by the solution matrix
X
i
.
Exceptions
Exception
Description
mkl::lapack::batch_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 = -n
, the
n
-th parameter had an illegal value.
If
info
equals the value passed as scratchpad size, and detail() returns non-zero, then the passed scratchpad is of insufficient size, and the required size should be not less then value returned by the detail() method of the exception object.
If
info
is zero, then the diagonal element of some of
U
i
is zero, and the solve could not be completed. The indexes of such matrices in the batch can be obtained with the ids() method of the exception object. You can obtain the indexes of the first zero diagonal elements in these
U
i
matrices using the infos() 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.