Contents

# ormrq

Multiplies a real matrix by the orthogonal matrix Q of the RQ factorization formed by
gerqf
.

## Description

The routine multiplies a real
m
-by-
n
matrix
C
by
Q
or
Q
T
, where
Q
is the real orthogonal matrix defined as a product of
k
elementary reflectors
H
i
:
Q = H1H2 ... Hk
as returned by the
RQ
factorization routine gerqf.
Depending on the parameters
side
and
trans
, the routine can form one of the matrix products
Q*C
,
QT*C
,
C*Q
, or
C*QT
(overwriting the result over
C
).

## API

Syntax
``````namespace oneapi::mkl::lapack {
void ormrq(cl::sycl::queue &queue,
mkl::side side,
mkl::transpose trans,
std::int64_t m,
std::int64_t n,
std::int64_t k,
cl::sycl::buffer<T> &a,
std::int64_t lda,
cl::sycl::buffer<T> &tau,
cl::sycl::buffer<T> &c,
std::int64_t ldc,
}``````
ormrq
supports the following precisions and devices:
T
Devices supported
float
Host and CPU
double
Host and CPU
Input Parameters
queue
Device queue where calculations will be performed.
side
If
side
=
mkl::side::left
,
Q
or
Q
T
is applied to
C
from the left. If
side
=
mkl::side::right
,
Q
or
Q
T
is applied to
C
from the right.
trans
If
trans=mkl::transpose::trans
, the routine multiplies
C
by
Q
.
If
trans=mkl::transpose::nontrans
, the routine multiplies
C
by
Q
T
.
m
The number of rows in the matrix
A
(
0≤m
).
n
The number of columns in the matrix
A
(
0≤n≤m
).
k
The number of elementary reflectors whose product defines the matrix
Q
(
0≤k≤n
).
a
Buffer holding the result of the gerqf function. The second dimension of
a
must be at least
max(1,k)
.
lda
The leading dimension of a.
tau
Buffer holding tau returned by the gerqf function.
c
Buffer holding the matrix
C
. The second dimension of c must be at least
max(1,n)
.
ldc
The leading dimension of c.
Buffer holding scratchpad memory to be used by the routine for storing intermediate results.
Size of scratchpad memory as a number of floating point elements of type
T
. Size should not be less than the value returned by the ormrq_scratchpad_size function.
Output Parameters
c
Overwritten by the product
Q
*
C
,
Q
T
*
C
,
C
*
Q
, or
C
*
Q
T
(as specified by side and trans).
Exceptions
Exception
Description
mkl::lapack::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 = -i
, the
i
-th parameter had an illegal value. If
info
is equal to the value passed as scratchpad size, and detail() returns non zero, then the passed scratchpad has an insufficient size, and the required size should not be less than the value returned by the detail() method of the exception object.
Application Notes
The complex counterpart of this routine is unmrq.

#### Product and Performance Information

1

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.