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*>
\
brief
\
b
DORGL2
*
*
===========
DOCUMENTATION
===========
*
*
Online
html
documentation
available
at
*
http
:
//
www
.
netlib
.
org
/
lapack
/
explore
-
html
/
*
*>
\
htmlonly
*>
Download
DORGL2
+
dependencies
*>
<
a
href
=
"http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dorgl2.f"
>
*>
[
TGZ
]
</
a
>
*>
<
a
href
=
"http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dorgl2.f"
>
*>
[
ZIP
]
</
a
>
*>
<
a
href
=
"http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dorgl2.f"
>
*>
[
TXT
]
</
a
>
*>
\
endhtmlonly
*
*
Definition
:
*
===========
*
*
SUBROUTINE
DORGL2
(
M
,
N
,
K
,
A
,
LDA
,
TAU
,
WORK
,
INFO
)
*
*
..
Scalar
Arguments
..
*
INTEGER
INFO
,
K
,
LDA
,
M
,
N
*
..
*
..
Array
Arguments
..
*
DOUBLE PRECISION
A
(
LDA
,
*
),
TAU
(
*
),
WORK
(
*
)
*
..
*
*
*>
\
par
Purpose
:
*
=============
*>
*>
\
verbatim
*>
*>
DORGL2
generates
an
m
by
n
real
matrix
Q
with
orthonormal
rows
,
*>
which
is
defined
as
the
first
m
rows
of
a
product
of
k
elementary
*>
reflectors
of
order
n
*>
*>
Q
=
H
(
k
)
.
.
.
H
(
2
)
H
(
1
)
*>
*>
as
returned
by
DGELQF
.
*>
\
endverbatim
*
*
Arguments
:
*
==========
*
*>
\
param
[
in
]
M
*>
\
verbatim
*>
M
is
INTEGER
*>
The
number
of
rows
of
the
matrix
Q
.
M
>=
0.
*>
\
endverbatim
*>
*>
\
param
[
in
]
N
*>
\
verbatim
*>
N
is
INTEGER
*>
The
number
of
columns
of
the
matrix
Q
.
N
>=
M
.
*>
\
endverbatim
*>
*>
\
param
[
in
]
K
*>
\
verbatim
*>
K
is
INTEGER
*>
The
number
of
elementary
reflectors
whose
product
defines
the
*>
matrix
Q
.
M
>=
K
>=
0.
*>
\
endverbatim
*>
*>
\
param
[
in
,
out
]
A
*>
\
verbatim
*>
A
is
DOUBLE PRECISION
array
,
dimension
(
LDA
,
N
)
*>
On
entry
,
the
i
-
th
row
must
contain
the
vector
which
defines
*>
the
elementary
reflector
H
(
i
),
for
i
=
1
,
2
,
...
,
k
,
as
returned
*>
by
DGELQF
in
the
first
k
rows
of
its
array
argument
A
.
*>
On
exit
,
the
m
-
by
-
n
matrix
Q
.
*>
\
endverbatim
*>
*>
\
param
[
in
]
LDA
*>
\
verbatim
*>
LDA
is
INTEGER
*>
The
first
dimension
of
the
array
A
.
LDA
>=
max
(
1
,
M
)
.
*>
\
endverbatim
*>
*>
\
param
[
in
]
TAU
*>
\
verbatim
*>
TAU
is
DOUBLE PRECISION
array
,
dimension
(
K
)
*>
TAU
(
i
)
must
contain
the
scalar
factor
of
the
elementary
*>
reflector
H
(
i
),
as
returned
by
DGELQF
.
*>
\
endverbatim
*>
*>
\
param
[
out
]
WORK
*>
\
verbatim
*>
WORK
is
DOUBLE PRECISION
array
,
dimension
(
M
)
*>
\
endverbatim
*>
*>
\
param
[
out
]
INFO
*>
\
verbatim
*>
INFO
is
INTEGER
*>
=
0
:
successful
exit
*>
<
0
:
if
INFO
=
-
i
,
the
i
-
th
argument
has
an
illegal
value
*>
\
endverbatim
*
*
Authors
:
*
========
*
*>
\
author
Univ
.
of
Tennessee
*>
\
author
Univ
.
of
California
Berkeley
*>
\
author
Univ
.
of
Colorado
Denver
*>
\
author
NAG
Ltd
.
*
*>
\
date
November
2011
*
*>
\
ingroup
doubleOTHERcomputational
*
*
=====================================================================
SUBROUTINE
DORGL2
(
M
,
N
,
K
,
A
,
LDA
,
TAU
,
WORK
,
INFO
)
*
*
--
LAPACK
computational
routine
(
version
3.4.0
)
--
*
--
LAPACK
is
a
software
package
provided
by
Univ
.
of
Tennessee
,
--
*
--
Univ
.
of
California
Berkeley
,
Univ
.
of
Colorado
Denver
and
NAG
Ltd
..
--
*
November
2011
*
*
..
Scalar
Arguments
..
INTEGER
INFO
,
K
,
LDA
,
M
,
N
*
..
*
..
Array
Arguments
..
DOUBLE PRECISION
A
(
LDA
,
*
),
TAU
(
*
),
WORK
(
*
)
*
..
*
*
=====================================================================
*
*
..
Parameters
..
DOUBLE PRECISION
ONE
,
ZERO
PARAMETER
(
ONE
=
1.0
D
+
0
,
ZERO
=
0.0
D
+
0
)
*
..
*
..
Local
Scalars
..
INTEGER
I
,
J
,
L
*
..
*
..
External
Subroutines
..
EXTERNAL
DLARF
,
DSCAL
,
XERBLA
*
..
*
..
Intrinsic
Functions
..
INTRINSIC
MAX
*
..
*
..
Executable
Statements
..
*
*
Test
the
input
arguments
*
INFO
=
0
IF
(
M
.LT.
0
)
THEN
INFO
=
-
1
ELSE IF
(
N
.LT.
M
)
THEN
INFO
=
-
2
ELSE IF
(
K
.LT.
0
.OR.
K
.GT.
M
)
THEN
INFO
=
-
3
ELSE IF
(
LDA
.LT.
MAX
(
1
,
M
)
)
THEN
INFO
=
-
5
END IF
IF
(
INFO
.NE.
0
)
THEN
CALL
XERBLA
(
'DORGL2'
,
-
INFO
)
RETURN
END IF
*
*
Quick
return if
possible
*
IF
(
M
.LE.
0
)
$
RETURN
*
IF
(
K
.LT.
M
)
THEN
*
*
Initialise
rows
k
+
1
:
m
to
rows
of
the
unit
matrix
*
DO
20
J
=
1
,
N
DO
10
L
=
K
+
1
,
M
A
(
L
,
J
)
=
ZERO
10
CONTINUE
IF
(
J
.GT.
K
.AND.
J
.LE.
M
)
$
A
(
J
,
J
)
=
ONE
20
CONTINUE
END IF
*
DO
40
I
=
K
,
1
,
-
1
*
*
Apply
H
(
i
)
to
A
(
i
:
m
,
i
:
n
)
from
the
right
*
IF
(
I
.LT.
N
)
THEN
IF
(
I
.LT.
M
)
THEN
A
(
I
,
I
)
=
ONE
CALL
DLARF
(
'Right'
,
M
-
I
,
N
-
I
+
1
,
A
(
I
,
I
),
LDA
,
$
TAU
(
I
),
A
(
I
+
1
,
I
),
LDA
,
WORK
)
END IF
CALL
DSCAL
(
N
-
I
,
-
TAU
(
I
),
A
(
I
,
I
+
1
),
LDA
)
END IF
A
(
I
,
I
)
=
ONE
-
TAU
(
I
)
*
*
Set
A
(
i
,
1
:
i
-
1
)
to
zero
*
DO
30
L
=
1
,
I
-
1
A
(
I
,
L
)
=
ZERO
30
CONTINUE
40
CONTINUE
RETURN
*
*
End
of
DORGL2
*
END
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