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dgeqr2.f
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*>
\
brief
\
b
DGEQR2
computes
the
QR
factorization
of
a
general
rectangular
matrix
using
an
unblocked
algorithm
.
*
*
===========
DOCUMENTATION
===========
*
*
Online
html
documentation
available
at
*
http
:
//
www
.
netlib
.
org
/
lapack
/
explore
-
html
/
*
*>
\
htmlonly
*>
Download
DGEQR2
+
dependencies
*>
<
a
href
=
"http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgeqr2.f"
>
*>
[
TGZ
]
</
a
>
*>
<
a
href
=
"http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgeqr2.f"
>
*>
[
ZIP
]
</
a
>
*>
<
a
href
=
"http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgeqr2.f"
>
*>
[
TXT
]
</
a
>
*>
\
endhtmlonly
*
*
Definition
:
*
===========
*
*
SUBROUTINE
DGEQR2
(
M
,
N
,
A
,
LDA
,
TAU
,
WORK
,
INFO
)
*
*
..
Scalar
Arguments
..
*
INTEGER
INFO
,
LDA
,
M
,
N
*
..
*
..
Array
Arguments
..
*
DOUBLE PRECISION
A
(
LDA
,
*
),
TAU
(
*
),
WORK
(
*
)
*
..
*
*
*>
\
par
Purpose
:
*
=============
*>
*>
\
verbatim
*>
*>
DGEQR2
computes
a
QR
factorization
of
a
real
m
by
n
matrix
A
:
*>
A
=
Q
*
R
.
*>
\
endverbatim
*
*
Arguments
:
*
==========
*
*>
\
param
[
in
]
M
*>
\
verbatim
*>
M
is
INTEGER
*>
The
number
of
rows
of
the
matrix
A
.
M
>=
0.
*>
\
endverbatim
*>
*>
\
param
[
in
]
N
*>
\
verbatim
*>
N
is
INTEGER
*>
The
number
of
columns
of
the
matrix
A
.
N
>=
0.
*>
\
endverbatim
*>
*>
\
param
[
in
,
out
]
A
*>
\
verbatim
*>
A
is
DOUBLE PRECISION
array
,
dimension
(
LDA
,
N
)
*>
On
entry
,
the
m
by
n
matrix
A
.
*>
On
exit
,
the
elements
on
and
above
the
diagonal
of
the
array
*>
contain
the
min
(
m
,
n
)
by
n
upper
trapezoidal
matrix
R
(
R
is
*>
upper
triangular
if
m
>=
n
);
the
elements
below
the
diagonal
,
*>
with
the
array
TAU
,
represent
the
orthogonal
matrix
Q
as
a
*>
product
of
elementary
reflectors
(
see
Further
Details
)
.
*>
\
endverbatim
*>
*>
\
param
[
in
]
LDA
*>
\
verbatim
*>
LDA
is
INTEGER
*>
The
leading
dimension
of
the
array
A
.
LDA
>=
max
(
1
,
M
)
.
*>
\
endverbatim
*>
*>
\
param
[
out
]
TAU
*>
\
verbatim
*>
TAU
is
DOUBLE PRECISION
array
,
dimension
(
min
(
M
,
N
))
*>
The
scalar
factors
of
the
elementary
reflectors
(
see
Further
*>
Details
)
.
*>
\
endverbatim
*>
*>
\
param
[
out
]
WORK
*>
\
verbatim
*>
WORK
is
DOUBLE PRECISION
array
,
dimension
(
N
)
*>
\
endverbatim
*>
*>
\
param
[
out
]
INFO
*>
\
verbatim
*>
INFO
is
INTEGER
*>
=
0
:
successful
exit
*>
<
0
:
if
INFO
=
-
i
,
the
i
-
th
argument
had
an
illegal
value
*>
\
endverbatim
*
*
Authors
:
*
========
*
*>
\
author
Univ
.
of
Tennessee
*>
\
author
Univ
.
of
California
Berkeley
*>
\
author
Univ
.
of
Colorado
Denver
*>
\
author
NAG
Ltd
.
*
*>
\
date
September
2012
*
*>
\
ingroup
doubleGEcomputational
*
*>
\
par
Further
Details
:
*
=====================
*>
*>
\
verbatim
*>
*>
The
matrix
Q
is
represented
as
a
product
of
elementary
reflectors
*>
*>
Q
=
H
(
1
)
H
(
2
)
.
.
.
H
(
k
),
where
k
=
min
(
m
,
n
)
.
*>
*>
Each
H
(
i
)
has
the
form
*>
*>
H
(
i
)
=
I
-
tau
*
v
*
v
**
T
*>
*>
where
tau
is
a
real
scalar
,
and
v
is
a
real
vector
with
*>
v
(
1
:
i
-
1
)
=
0
and
v
(
i
)
=
1
;
v
(
i
+
1
:
m
)
is
stored
on
exit
in
A
(
i
+
1
:
m
,
i
),
*>
and
tau
in
TAU
(
i
)
.
*>
\
endverbatim
*>
*
=====================================================================
SUBROUTINE
DGEQR2
(
M
,
N
,
A
,
LDA
,
TAU
,
WORK
,
INFO
)
*
*
--
LAPACK
computational
routine
(
version
3.4.2
)
--
*
--
LAPACK
is
a
software
package
provided
by
Univ
.
of
Tennessee
,
--
*
--
Univ
.
of
California
Berkeley
,
Univ
.
of
Colorado
Denver
and
NAG
Ltd
..
--
*
September
2012
*
*
..
Scalar
Arguments
..
INTEGER
INFO
,
LDA
,
M
,
N
*
..
*
..
Array
Arguments
..
DOUBLE PRECISION
A
(
LDA
,
*
),
TAU
(
*
),
WORK
(
*
)
*
..
*
*
=====================================================================
*
*
..
Parameters
..
DOUBLE PRECISION
ONE
PARAMETER
(
ONE
=
1.0
D
+
0
)
*
..
*
..
Local
Scalars
..
INTEGER
I
,
K
DOUBLE PRECISION
AII
*
..
*
..
External
Subroutines
..
EXTERNAL
DLARF
,
DLARFG
,
XERBLA
*
..
*
..
Intrinsic
Functions
..
INTRINSIC
MAX
,
MIN
*
..
*
..
Executable
Statements
..
*
*
Test
the
input
arguments
*
INFO
=
0
IF
(
M
.LT.
0
)
THEN
INFO
=
-
1
ELSE IF
(
N
.LT.
0
)
THEN
INFO
=
-
2
ELSE IF
(
LDA
.LT.
MAX
(
1
,
M
)
)
THEN
INFO
=
-
4
END IF
IF
(
INFO
.NE.
0
)
THEN
CALL
XERBLA
(
'DGEQR2'
,
-
INFO
)
RETURN
END IF
*
K
=
MIN
(
M
,
N
)
*
DO
10
I
=
1
,
K
*
*
Generate
elementary
reflector
H
(
i
)
to
annihilate
A
(
i
+
1
:
m
,
i
)
*
CALL
DLARFG
(
M
-
I
+
1
,
A
(
I
,
I
),
A
(
MIN
(
I
+
1
,
M
),
I
),
1
,
$
TAU
(
I
)
)
IF
(
I
.LT.
N
)
THEN
*
*
Apply
H
(
i
)
to
A
(
i
:
m
,
i
+
1
:
n
)
from
the
left
*
AII
=
A
(
I
,
I
)
A
(
I
,
I
)
=
ONE
CALL
DLARF
(
'Left'
,
M
-
I
+
1
,
N
-
I
,
A
(
I
,
I
),
1
,
TAU
(
I
),
$
A
(
I
,
I
+
1
),
LDA
,
WORK
)
A
(
I
,
I
)
=
AII
END IF
10
CONTINUE
RETURN
*
*
End
of
DGEQR2
*
END
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