Developer Reference

  • 2020.2
  • 07/15/2020
  • Public Content
Contents

?orgr2/?ungr2

Generates all or part of the orthogonal/unitary matrix Q from an RQ factorization determined by
?gerqf
(unblocked algorithm).

Syntax

call sorgr2
(
m
,
n
,
k
,
a
,
lda
,
tau
,
work
,
info
)
call dorgr2
(
m
,
n
,
k
,
a
,
lda
,
tau
,
work
,
info
)
call cungr2
(
m
,
n
,
k
,
a
,
lda
,
tau
,
work
,
info
)
call zungr2
(
m
,
n
,
k
,
a
,
lda
,
tau
,
work
,
info
)
Include Files
  • mkl.fi
Description
The routine
?orgr2
/
?ungr2
generates an
m
-by-
n
real matrix
Q
with orthonormal rows, which is defined as the last
m
rows of a product of
k
elementary reflectors of order
n
Q
=
H
(1)*
H
(2)*...*
H
(
k
)
for real flavors, or
Q
= (
H
(1))
H
*(
H
(2))
H
*...*(
H
(
k
))
H
for complex flavors as returned by ?gerqf.
Input Parameters
m
INTEGER
. The number of rows of the matrix
Q
.
m
0
.
n
INTEGER
. The number of columns of the matrix
Q
.
n
m
k
INTEGER
.
The number of elementary reflectors whose product defines the matrix
Q
.
m
k
0
.
a
REAL
for
sorgr2
DOUBLE PRECISION
for
dorgr2
COMPLEX
for
cungr2
DOUBLE COMPLEX
for
zungr2
.
Array,
DIMENSION
(
lda
,
n
).
On entry, the (
m
-
k
+i)-th row must contain the vector which defines the elementary reflector
H
(
i
), for
i
= 1,2,...,
k
, as returned by
?gerqf
in the last
k
rows of its array argument
a
.
lda
INTEGER
. The leading dimension of the array
a
.
lda
max(1,
m
)
.
tau
REAL
for
sorgr2
DOUBLE PRECISION
for
dorgr2
COMPLEX
for
cungr2
DOUBLE COMPLEX
for
zungr2
.
Array,
DIMENSION
(
k
).
tau
(
i
) must contain the scalar factor of the elementary reflector
H
(
i
), as returned by