Contents

# potrf_batch (USM Strided Version)

Computes the Cholesky factorizations of a batch of symmetric (or Hermitian, for complex data) positive-definite matrices. This routine belongs to the
oneapi::mkl::lapack
namespace.

## Description

The routine forms the Cholesky factorizations of a symmetric positive-definite or, for complex data, Hermitian positive-definite matrices
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
T
*
L
i
for real data,
A
i
=
L
i
H
*
L
i
for complex data if
uplo = mkl::uplo::lower
Where
L
i
is a lower triangular matrix and
U
i
is an upper triangular matrix.

## API

Syntax
``````namespace oneapi::mkl::lapack {
cl::sycl::event potrf_batch(cl::sycl::queue &queue,
mkl::uplo uplo,
std::int64_t n,
T *a,
std::int64_t lda,
std::int64_t stride_a,
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 whether the upper or lower triangular part of
A
i
is stored and how
A
i
is factored:
If uplo = mkl::uplo::upper, the array
a
stores the upper triangular parts of the matrices
A
i
.
If uplo = mkl::uplo::lower, the array
a
stores the lower triangular parts of the matrices
A
i
.
n
Specifies the order of the matrices
A
i
, (
0 ≤ n
).
a
Array containing a batch of input matrices
A
i
, each of
A
i
being of size
lda
*
n
and holding either uppoer or lower triangular parts of the matrices
A
i
(see uplo).
lda
A
i
.
stride_a
The stride between the beginnings of matrices
A
i
inside the batch.
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 potrf_batch_scratchpad_size (Strided Version).
events
List of events to wait for before starting computation. Defaults to empty list.
Output Parameters
a
The batch array
a
is overwritten by the Cholesky factor
U
i
or
L
i
, as specified by uplo .
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.