Developer Reference

  • 0.9
  • 09/09/2020
  • Public Content
Contents

?orgrq

Generates the real matrix Q of the RQ factorization formed by
?gerqf
.

Syntax

lapack_int
LAPACKE_sorgrq
(
int
matrix_layout
,
lapack_int
m
,
lapack_int
n
,
lapack_int
k
,
float
*
a
,
lapack_int
lda
,
const
float
*
tau
);
lapack_int
LAPACKE_dorgrq
(
int
matrix_layout
,
lapack_int
m
,
lapack_int
n
,
lapack_int
k
,
double
*
a
,
lapack_int
lda
,
const
double
*
tau
);
Include Files
  • mkl.h
Description
The routine generates an
m
-by-
n
real matrix with orthonormal rows, which is defined as the last
m
rows of a product of
k
elementary reflectors
H
(
i
)
of order
n
:
Q
=
H
(1)*
H
(2)
*...*
H
(
k
)
as returned by the routines gerqf. Use this routine after a call to
sgerqf
/
dgerqf
.
Input Parameters
matrix_layout
Specifies whether matrix storage layout is row major (
LAPACK_ROW_MAJOR
) or column major (
LAPACK_COL_MAJOR
).
m
The number of rows of the matrix
Q
(
m
0
).
n
The number of columns of the matrix
Q
(
n
 
m
).
k
The number of elementary reflectors whose product defines the matrix
Q
(
m
 
k
0
).
a
,
tau
Arrays:
a
(size max(1,
lda
*
n
) for column major layout and max(1,
lda
*
m
) for row major layout)
,
tau
.
On entry, the (
m
-
k
+
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
).
lda
The leading dimension of
a
; at least max(1,
m
)
for column major layout and max(1,
n
) for row major layout
.
Output Parameters
a
Overwritten by the last
m
rows of the
n
-by-
n
orthogonal matrix
Q
.
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 ungrq.

Product and Performance Information

1

Intel's compilers may or may not optimize to the same degree for non-Intel microprocessors for optimizations that are not unique to Intel microprocessors. These optimizations include SSE2, SSE3, and SSSE3 instruction sets and other optimizations. Intel does not guarantee the availability, functionality, or effectiveness of any optimization on microprocessors not manufactured by Intel. Microprocessor-dependent optimizations in this product are intended for use with Intel microprocessors. Certain optimizations not specific to Intel microarchitecture are reserved for Intel microprocessors. Please refer to the applicable product User and Reference Guides for more information regarding the specific instruction sets covered by this notice.

Notice revision #20110804