Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

  • 2021.1
  • 12/04/2020
  • Public Content
Contents

?ormrq

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

Syntax

lapack_int
LAPACKE_sormrq
(
int
matrix_layout
,
char
side
,
char
trans
,
lapack_int
m
,
lapack_int
n
,
lapack_int
k
,
const
float
*
a
,
lapack_int
lda
,
const
float
*
tau
,
float
*
c
,
lapack_int
ldc
);
lapack_int
LAPACKE_dormrq
(
int
matrix_layout
,
char
side
,
char
trans
,
lapack_int
m
,
lapack_int
n
,
lapack_int
k
,
const
double
*
a
,
lapack_int
lda
,
const
double
*
tau
,
double
*
c
,
lapack_int
ldc
);
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
The leading dimension of
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
The leading dimension of
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.