Contents

# ?ormrq

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

## Syntax

Include Files
• mkl.h
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
=
H
1
H
2
...
H
k
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
,
Q
T
*
C
,
C
*
Q
, or
C
*
Q
T
(overwriting the result over
C
).
Input Parameters
matrix_layout
Specifies whether matrix storage layout is row major (
LAPACK_ROW_MAJOR
) or column major (
LAPACK_COL_MAJOR
).
side
Must be either
'L'
or
'R'
.
If
side
=
'L'
,
Q
or
Q
T
is applied to
C
from the left.
If
side
=
'R'
,
Q
or
Q
T
is applied to
C
from the right.
trans
Must be either
'N'
or
'T'
.
If
trans
=
'N'
, the routine multiplies
C
by
Q
.
If
trans
=
'T'
, the routine multiplies
C
by
Q
T
.
m
The number of rows in the matrix
C
(
m
0
).
n
The number of columns in
C
(
n
0
).
k
The number of elementary reflectors whose product defines the matrix
Q
. Constraints:
0
k
m
, if
side
=
'L'
;
0
k
n
, if
side
=
'R'
.
a
,
tau
,
c
Arrays:
a
(size for
side
= 'L': max(1,
lda
*
m
) for column major layout and max(1,
lda
*
k
) for row major layout; for
side
= 'R': max(1,
lda
*
n
) for column major layout and max(1,
lda
*
k
) for row major layout),
tau
,
c
(size max(1,
ldc
*
n
) for column major layout and max(1,
ldc
*
m
) for row major layout).
On entry, the
i
th row of
a
must contain the vector which defines the elementary reflector
H
i
, for i = 1,2,...,
k
, as returned by
sgerqf
/
dgerqf
in the last
k
rows of its array argument
a
.
tau
[
i
- 1]
must contain the scalar factor of the elementary reflector
H
i
, as returned by
sgerqf
/
dgerqf
.
The size of
tau
must be at least max(1,
k
).
c
contains the
m
-by-
n
matrix
C
.
lda
a
;
lda
max(1,
k
)
for column major layout. For row major layout,
lda
max(1,
m
)
if
side
= 'L', and
lda
max(1,
n
)
if
side
= 'R'
.
ldc
c
;
ldc
max(1,
m
)
for column major layout and max(1,
n
) for row major layout
.
Output Parameters
c
Overwritten by the product
Q
*
C
,
Q
T
*
C
,
C
*
Q
, or
C
*
Q
T
(as specified by
side
and
trans
).
Return Values
This function returns a value
info
.
If
info
=0
, the execution is successful.
If
info
=
-i
, the
i
-th parameter had an illegal value.
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.