Developer Reference

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getrs_batch (Group Version)

Solves a batch of systems of linear equations with a batch of LU-factored square coefficient matrices, with multiple right-hand sides. This routine belongs to the
oneapi::mkl::lapack
namespace.

Description

The routine solves for
X
i
(
iϵ{1...batch_size}
) the following systems of linear equations:
  • A
    i
    *
    X
    i
    =
    B
    i
    If
    trans = mkl::transpose::notrans
  • A
    i
    T
    *
    X
    i
    =
    B
    i
    If
    trans = mkl::transpose::trans
  • A
    i
    H
    *
    X
    i
    =
    B
    i
    If
    trans = mkl::transpose::conjtrans
Before calling this routine you must call getrf_batch (Group Version) to compute the LU factorization of
A
1
.
The total number of problems to solve,
batch_size
, is a sum of sizes of all of the groups of parameters as provided by``group_sizes`` array.

API

Syntax
namespace oneapi::mkl::lapack { cl::sycl::event getrs_batch(cl::sycl::queue &queue, mkl::transpose *trans, std::int64_t *n, std::int64_t *nrhs, T **a, std::int64_t *lda, std::int64_t **ipiv, T **b, std::int64_t *ldb, std::int64_t group_count, std::int64_t *group_sizes, T *scratchpad, std::int64_t scratchpad_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.
trans
Array of
group_count
parameters trans
g
indicating the form of the equations for the group
g
:
If trans = mkl::transpose::nontrans, then
A
i
*
X
i
=
B
i
is solved for
X
i
.
If trans = mkl::transpose::trans, then
A
i
T
*
X
i
=
B
i
is solved for
X
i
.
If trans = mkl::transpose::conjtrans, then
A
i
H
*
X
i
=
B
i
is solved for
X
i
.
n
Array of
group_count
parameters
n
g
specifying the order of the matrices
A
i
and the number of rows in matrices
B
i
(0 ≤
n
g
) belonging to group
g
.
nrhs
Array of
group_count
parameters nrhs
g
specifying the number of right hand sides
(0≤nrhs)
for group
g
.
a
Array of
batch_size
pointers to factorization of the matrices
A
i
, as returned by getrf_batch (Group Version).
lda
Array of
group_count
parameters lda
g
specifying the leading dimension of
A
i
from group
g
.
ipiv
The ipiv array, as returned by getrf_batch (Group Version).
b
The array containing @
batch_size
pointers to the matrices
B
i
whose columns are the right-hand sides for the systems of equations.
ldb
Array of
group_count
parameters ldb
g
specifying the leading dimensions of
B
i
in the 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
Scratchpad memory to be used by routine for storing intermediate results.
scratchpad_size
Size of scratchpad memory as a number of floating point elements of type T. Size should not be less then the value returned by getrs_batch_scratchpad_size (Group Version).
events
List of events to wait for before starting computation. Defaults to empty list.
Output Parameters
b
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.