Developer Reference

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

?orghr

Generates the real orthogonal matrix Q determined by
?gehrd
.

Syntax

call sorghr
(
n
,
ilo
,
ihi
,
a
,
lda
,
tau
,
work
,
lwork
,
info
)
call dorghr
(
n
,
ilo
,
ihi
,
a
,
lda
,
tau
,
work
,
lwork
,
info
)
call orghr
(
a
,
tau
[
,
ilo
]
[
,
ihi
]
[
,
info
]
)
Include Files
  • mkl.fi
    ,
    lapack.f90
Description
The routine explicitly generates the orthogonal matrix
Q
that has been determined by a preceding call to
sgehrd
/
dgehrd
. (The routine
?gehrd
reduces a real general matrix
A
to upper Hessenberg form
H
by an orthogonal similarity transformation,
A
=
Q*H*Q
T
, and represents the matrix
Q
as a product of
ihi
-
ilo
elementary reflectors. Here
ilo
and
ihi
are values determined by
sgebal
/
dgebal
when balancing the matrix; if the matrix has not been balanced,
ilo
= 1
and
ihi
=
n
.)
The matrix
Q
generated by
?orghr
has the structure:
Equation
where
Q
22
occupies rows and columns
ilo
to
ihi
.
Input Parameters
n
INTEGER
.
The order of the matrix
Q
(
n
0
).
ilo
,
ihi
INTEGER
.
These must be the same parameters
ilo
and
ihi
, respectively, as supplied to
?gehrd
. (If
n
> 0
, then
1
ilo
ihi
n
; if
n
=
0
,
ilo
= 1
and
ihi
= 0
.)
a
,
tau
,
work
REAL
for
sorghr
DOUBLE PRECISION
for
dorghr
Arrays:
a
(
lda
,*)
contains details of the vectors which define the elementary reflectors, as returned by
?gehrd
.
The second dimension of
a
must be at least max(1,
n
).
tau
(*)
contains further details of the elementary reflectors, as returned by
?gehrd
.
The dimension of
tau
must be at least max (1,
n
-1).
work
is a workspace array, its dimension
max(1,
lwork
)
.
lda
INTEGER
.
The leading dimension of
a
; at least max(1,
n
).
lwork
INTEGER
.
The size of the
work
array;
lwork
max(1,
ihi
-
ilo
)
.
If
lwork
= -1
, then a workspace query is assumed; the routine only calculates the optimal size of the
work
array, returns this value as the first entry of the
work
array, and no error message related to
lwork
is issued by xerbla.
See
Application Notes
for the suggested value of
lwork
.
Output Parameters