Contents

# potrs_batch (Group Version)

Solves a batch of systems 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 systems 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
g
=
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
g
=
mkl::uplo::lower
where
L
i
is a lower triangular matrix and
U
i
is upper triangular,
g
is an index of group of parameters corresponding to
A
i
, and the total number of problems to solve,
batch_size
, is a sum of sizes for all of the groups of parameters as provided by the
group_sizes
array.
The systems are solved with multiple right-hand sides stored in the columns of the matrices
B
i
.
Before calling this routine, matrices
A
i
should be factorized by a call to potrf_batch (Group 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,
T **b,
std::int64_t *ldb,
std::int64_t group_count,
std::int64_t *group_sizes,
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
Array of
group_count
uplo
g
parameters.
Each of uplo
g
indicates whether the upper or lower triangular parts of the input matrices are provided:
If uplo
g
=
mkl::uplo::upper
, input matrices from array
a
belonging to group
g
store the upper triangular parts.
If uplo
g
=
mkl::uplo::lower
, input matrices from array
a
belonging to group
g
store the lower triangular parts.
n
Array of
group_count
parameters
n
g
.
Each
n
g
specifies the order of the input matrices from array
a
belonging to group
g
.
nrhs
Array of
group_count
parameters nrhs
g
parameters.
Each nrhs
g
specifies the number of right-hand sides supplied for group
g
in corresponding part of array
b
.
a
Array of
batch_size
pointers to Cholesky factored matrices
A
i
as returned by potrf_batch (Group Version).
lda
Array of
group_count
parameters lda
g
.
Each lda
g
specifies the leading dimension of matrices from
a
belonging to group
g
.
b
Array of
batch_size
pointers to right-hand side matrices
B
i
, each of size ldb
g
*nrhs
g
, where
g
is an index of group corresponding to
B
i
.
ldb
Array of
group_count
parameters ldb
g
.
Each ldb
g
specifies the leading dimension of matrices from
b
belonging to group
g
.
group_count
Specifies the number of groups of parameters. Must be at least 0.
group_sizes
Array of group_count integers. Array element with index
g
specifies the number of problems to solve for each of the groups of parameters
g
. So the total number of problems to solve,
batch_size
, is a sum of all parameter group sizes.
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 potrs_batch_scratchpad_size (Group Version).
events
List of events to wait for before starting computation. Defaults to empty list.
Output Parameters
b
The matrices pointed to by array b are overwritten by the solution matrices
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.