## Developer Reference

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

# ?orgbr

Generates the real orthogonal matrix
Q
or
P
T
determined by
?gebrd
.

## Syntax

Include Files
• mkl.fi
,
lapack.f90
Description
The routine generates the whole or part of the orthogonal matrices
Q
and
P
T
formed by the routines gebrd/. Use this routine after a call to
sgebrd
/
dgebrd
. All valid combinations of arguments are described in
Input parameters
. In most cases you need the following:
To compute the whole
m
-by-
m
matrix
Q
:
`call ?orgbr('Q', m, m, n, a ... )`
(note that the array
a
must have at least
m
columns).
To form the
n
Q
if
m
>
n
:
`call ?orgbr('Q', m, n, n, a ... )`
To compute the whole
n
-by-
n
matrix
P
T
:
`call ?orgbr('P', n, n, m, a ... )`
(note that the array
a
must have at least
n
rows).
To form the
m
P
T
if
m
<
n
:
`call ?orgbr('P', m, n, m, a ... )`
Input Parameters
vect
CHARACTER*1
.
Must be
'Q'
or
'P'
.
If
vect
=
'Q'
, the routine generates the matrix
Q
.
If
vect
=
'P'
, the routine generates the matrix
P
T
.
m, n
INTEGER
.
The number of rows (
m
) and columns (
n
) in the matrix
Q
or
P
T
to be returned (
m
0
,
n
0
).
If
vect
=
'Q'
,
m
n
≥ min(
m
,
k
)
.
If
vect
=
'P'
,
n
m
≥ min(
n
,
k
)
.
k
If
vect
=
'Q'
, the number of columns in the original
m
-by-
k
matrix reduced by gebrd.
If
vect
=
'P'
, the number of rows in the original
k
-by-
n
matrix reduced by gebrd.
a
REAL
for
sorgbr
DOUBLE PRECISION
for
dorgbr
The vectors which define the elementary reflectors, as returned by