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dlarfg.f
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*>
\
brief
\
b
DLARFG
generates
an
elementary
reflector
(
Householder
matrix
)
.
*
*
===========
DOCUMENTATION
===========
*
*
Online
html
documentation
available
at
*
http
:
//
www
.
netlib
.
org
/
lapack
/
explore
-
html
/
*
*>
\
htmlonly
*>
Download
DLARFG
+
dependencies
*>
<
a
href
=
"http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlarfg.f"
>
*>
[
TGZ
]
</
a
>
*>
<
a
href
=
"http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlarfg.f"
>
*>
[
ZIP
]
</
a
>
*>
<
a
href
=
"http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlarfg.f"
>
*>
[
TXT
]
</
a
>
*>
\
endhtmlonly
*
*
Definition
:
*
===========
*
*
SUBROUTINE
DLARFG
(
N
,
ALPHA
,
X
,
INCX
,
TAU
)
*
*
..
Scalar
Arguments
..
*
INTEGER
INCX
,
N
*
DOUBLE PRECISION
ALPHA
,
TAU
*
..
*
..
Array
Arguments
..
*
DOUBLE PRECISION
X
(
*
)
*
..
*
*
*>
\
par
Purpose
:
*
=============
*>
*>
\
verbatim
*>
*>
DLARFG
generates
a
real
elementary
reflector
H
of
order
n
,
such
*>
that
*>
*>
H
*
(
alpha
)
=
(
beta
),
H
**
T
*
H
=
I
.
*>
(
x
)
(
0
)
*>
*>
where
alpha
and
beta
are
scalars
,
and
x
is
an
(
n
-
1
)
-
element
real
*>
vector
.
H
is
represented
in
the
form
*>
*>
H
=
I
-
tau
*
(
1
)
*
(
1
v
**
T
)
,
*>
(
v
)
*>
*>
where
tau
is
a
real
scalar
and
v
is
a
real
(
n
-
1
)
-
element
*>
vector
.
*>
*>
If
the
elements
of
x
are
all
zero
,
then
tau
=
0
and
H
is
taken
to
be
*>
the
unit
matrix
.
*>
*>
Otherwise
1
<=
tau
<=
2.
*>
\
endverbatim
*
*
Arguments
:
*
==========
*
*>
\
param
[
in
]
N
*>
\
verbatim
*>
N
is
INTEGER
*>
The
order
of
the
elementary
reflector
.
*>
\
endverbatim
*>
*>
\
param
[
in
,
out
]
ALPHA
*>
\
verbatim
*>
ALPHA
is
DOUBLE PRECISION
*>
On
entry
,
the
value
alpha
.
*>
On
exit
,
it
is
overwritten
with
the
value
beta
.
*>
\
endverbatim
*>
*>
\
param
[
in
,
out
]
X
*>
\
verbatim
*>
X
is
DOUBLE PRECISION
array
,
dimension
*>
(
1
+
(
N
-
2
)
*
abs
(
INCX
))
*>
On
entry
,
the
vector
x
.
*>
On
exit
,
it
is
overwritten
with
the
vector
v
.
*>
\
endverbatim
*>
*>
\
param
[
in
]
INCX
*>
\
verbatim
*>
INCX
is
INTEGER
*>
The
increment
between
elements
of
X
.
INCX
>
0.
*>
\
endverbatim
*>
*>
\
param
[
out
]
TAU
*>
\
verbatim
*>
TAU
is
DOUBLE PRECISION
*>
The
value
tau
.
*>
\
endverbatim
*
*
Authors
:
*
========
*
*>
\
author
Univ
.
of
Tennessee
*>
\
author
Univ
.
of
California
Berkeley
*>
\
author
Univ
.
of
Colorado
Denver
*>
\
author
NAG
Ltd
.
*
*>
\
date
September
2012
*
*>
\
ingroup
doubleOTHERauxiliary
*
*
=====================================================================
SUBROUTINE
DLARFG
(
N
,
ALPHA
,
X
,
INCX
,
TAU
)
*
*
--
LAPACK
auxiliary
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
INCX
,
N
DOUBLE PRECISION
ALPHA
,
TAU
*
..
*
..
Array
Arguments
..
DOUBLE PRECISION
X
(
*
)
*
..
*
*
=====================================================================
*
*
..
Parameters
..
DOUBLE PRECISION
ONE
,
ZERO
PARAMETER
(
ONE
=
1.0
D
+
0
,
ZERO
=
0.0
D
+
0
)
*
..
*
..
Local
Scalars
..
INTEGER
J
,
KNT
DOUBLE PRECISION
BETA
,
RSAFMN
,
SAFMIN
,
XNORM
*
..
*
..
External
Functions
..
DOUBLE PRECISION
DLAMCH
,
DLAPY2
,
DNRM2
EXTERNAL
DLAMCH
,
DLAPY2
,
DNRM2
*
..
*
..
Intrinsic
Functions
..
INTRINSIC
ABS
,
SIGN
*
..
*
..
External
Subroutines
..
EXTERNAL
DSCAL
*
..
*
..
Executable
Statements
..
*
IF
(
N
.LE.
1
)
THEN
TAU
=
ZERO
RETURN
END IF
*
XNORM
=
DNRM2
(
N
-
1
,
X
,
INCX
)
*
IF
(
XNORM
.EQ.
ZERO
)
THEN
*
*
H
=
I
*
TAU
=
ZERO
ELSE
*
*
general
case
*
BETA
=
-
SIGN
(
DLAPY2
(
ALPHA
,
XNORM
),
ALPHA
)
SAFMIN
=
DLAMCH
(
'S'
)
/
DLAMCH
(
'E'
)
KNT
=
0
IF
(
ABS
(
BETA
)
.LT.
SAFMIN
)
THEN
*
*
XNORM
,
BETA
may
be
inaccurate
;
scale
X
and
recompute
them
*
RSAFMN
=
ONE
/
SAFMIN
10
CONTINUE
KNT
=
KNT
+
1
CALL
DSCAL
(
N
-
1
,
RSAFMN
,
X
,
INCX
)
BETA
=
BETA
*
RSAFMN
ALPHA
=
ALPHA
*
RSAFMN
IF
(
ABS
(
BETA
)
.LT.
SAFMIN
)
$
GO
TO
10
*
*
New
BETA
is
at
most
1
,
at
least
SAFMIN
*
XNORM
=
DNRM2
(
N
-
1
,
X
,
INCX
)
BETA
=
-
SIGN
(
DLAPY2
(
ALPHA
,
XNORM
),
ALPHA
)
END IF
TAU
=
(
BETA
-
ALPHA
)
/
BETA
CALL
DSCAL
(
N
-
1
,
ONE
/
(
ALPHA
-
BETA
),
X
,
INCX
)
*
*
If
ALPHA
is
subnormal
,
it
may
lose
relative
accuracy
*
DO
20
J
=
1
,
KNT
BETA
=
BETA
*
SAFMIN
20
CONTINUE
ALPHA
=
BETA
END IF
*
RETURN
*
*
End
of
DLARFG
*
END
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