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geqrf_batch (Group Version)

Computes the batch of QR factorizations of a general m-by-n matrices. This routine belongs to the
oneapi::mkl::lapack
namespace.

Description

The routine forms the
Q
i
R
i
factorizations of a general
m
-by-
n
matrix
A
i
,
iϵ{1...batch_size}
, where
batch_size
is a sum of all parameter group sizes as provided with the
group_sizes
array. No pivoting is performed during factorization.
The routine does not form the matrix
Q
i
explicitly. Instead,
Q
i
is represented as a product of min(
m
,
n
) elementary reflectors. Routines are provided to work with
Q
i
in this representation.
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 geqrf_batch(cl::sycl::queue &queue, std::int64_t *m, std::int64_t *n, T **a, std::int64_t *lda, T **tau, 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.
m
Array of
group_count
parameters m
g
parameters.
Each of m
g
specifies the number of rows in the matrices
A
i
from array
a
, belonging to group
g
.
n
Array of
group_count
parameters n
g
parameters.
Each of n
g
specifies the number of columns in the matrices
A
i
from array
a
, belonging to group
g
.
a
Array of
batch_size
pointers to input matrices
A
i
, each being of size
lda
g
*
n
g
(
g
is an index of group to which
A
i
belongs).
lda
Array of
group_count
lda
g
parameters, each representing the leading dimensions of input matrices
A
i
, from array
a
, 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
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 geqrf_batch_scratchpad_size (Group Version).
events
List of events to wait for before starting computation. Defaults to empty list.
Output Parameters
a
Matrices pointed to by array
a
are overwritten by the factorization data as follows:
The elements on and above the diagonal of
A
i
contain the
min(mg,mng)
-by-
n
g
upper trapezoidal matrices
R
i
(
R
i
is upper triangular if
mg≥ng
); the elements below the diagonal, with the array
tau
i
, present the orthogonal matrix
Q
i
as a rpoduct of
min(mg,ng)
elementary reflectors.
Here,
g
is an index of parameters group corresponding to
i
-th decomposition.
tau
Array of pointers to store
tau
i
, each of size
m
g
,
n
g
, containing scalars that define elementary reflectors for the matrices
Q
i
in its decomposition in a product of elementary reflectors.
Here,
g
is an index of parameters group corresponding to
i
-th decomposition.
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.
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.