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dlansy.f
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dlansy.f
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*>
\
brief
\
b
DLANSY
returns
the
value
of
the
1
-
norm
,
or
the
Frobenius
norm
,
or
the
infinity
norm
,
or
the
element
of
largest
absolute
value
of
a
real
symmetric
matrix
.
*
*
===========
DOCUMENTATION
===========
*
*
Online
html
documentation
available
at
*
http
:
//
www
.
netlib
.
org
/
lapack
/
explore
-
html
/
*
*>
\
htmlonly
*>
Download
DLANSY
+
dependencies
*>
<
a
href
=
"http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlansy.f"
>
*>
[
TGZ
]
</
a
>
*>
<
a
href
=
"http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlansy.f"
>
*>
[
ZIP
]
</
a
>
*>
<
a
href
=
"http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlansy.f"
>
*>
[
TXT
]
</
a
>
*>
\
endhtmlonly
*
*
Definition
:
*
===========
*
*
DOUBLE PRECISION
FUNCTION
DLANSY
(
NORM
,
UPLO
,
N
,
A
,
LDA
,
WORK
)
*
*
..
Scalar
Arguments
..
*
CHARACTER
NORM
,
UPLO
*
INTEGER
LDA
,
N
*
..
*
..
Array
Arguments
..
*
DOUBLE PRECISION
A
(
LDA
,
*
),
WORK
(
*
)
*
..
*
*
*>
\
par
Purpose
:
*
=============
*>
*>
\
verbatim
*>
*>
DLANSY
returns
the
value
of
the
one
norm
,
or
the
Frobenius
norm
,
or
*>
the
infinity
norm
,
or
the
element
of
largest
absolute
value
of
a
*>
real
symmetric
matrix
A
.
*>
\
endverbatim
*>
*>
\
return
DLANSY
*>
\
verbatim
*>
*>
DLANSY
=
(
max
(
abs
(
A
(
i
,
j
))),
NORM
=
'M'
or
'm'
*>
(
*>
(
norm1
(
A
),
NORM
=
'1'
,
'O'
or
'o'
*>
(
*>
(
normI
(
A
),
NORM
=
'I'
or
'i'
*>
(
*>
(
normF
(
A
),
NORM
=
'F'
,
'f'
,
'E'
or
'e'
*>
*>
where
norm1
denotes
the
one
norm
of
a
matrix
(
maximum
column
sum
),
*>
normI
denotes
the
infinity
norm
of
a
matrix
(
maximum
row
sum
)
and
*>
normF
denotes
the
Frobenius
norm
of
a
matrix
(
square
root
of
sum
of
*>
squares
)
.
Note
that
max
(
abs
(
A
(
i
,
j
)))
is
not
a
consistent
matrix
norm
.
*>
\
endverbatim
*
*
Arguments
:
*
==========
*
*>
\
param
[
in
]
NORM
*>
\
verbatim
*>
NORM
is
CHARACTER
*
1
*>
Specifies
the
value
to
be
returned
in
DLANSY
as
described
*>
above
.
*>
\
endverbatim
*>
*>
\
param
[
in
]
UPLO
*>
\
verbatim
*>
UPLO
is
CHARACTER
*
1
*>
Specifies
whether
the
upper
or
lower
triangular
part
of
the
*>
symmetric
matrix
A
is
to
be
referenced
.
*>
=
'U'
:
Upper
triangular
part
of
A
is
referenced
*>
=
'L'
:
Lower
triangular
part
of
A
is
referenced
*>
\
endverbatim
*>
*>
\
param
[
in
]
N
*>
\
verbatim
*>
N
is
INTEGER
*>
The
order
of
the
matrix
A
.
N
>=
0.
When
N
=
0
,
DLANSY
is
*>
set
to
zero
.
*>
\
endverbatim
*>
*>
\
param
[
in
]
A
*>
\
verbatim
*>
A
is
DOUBLE PRECISION
array
,
dimension
(
LDA
,
N
)
*>
The
symmetric
matrix
A
.
If
UPLO
=
'U'
,
the
leading
n
by
n
*>
upper
triangular
part
of
A
contains
the
upper
triangular
part
*>
of
the
matrix
A
,
and
the
strictly
lower
triangular
part
of
A
*>
is
not
referenced
.
If
UPLO
=
'L'
,
the
leading
n
by
n
lower
*>
triangular
part
of
A
contains
the
lower
triangular
part
of
*>
the
matrix
A
,
and
the
strictly
upper
triangular
part
of
A
is
*>
not
referenced
.
*>
\
endverbatim
*>
*>
\
param
[
in
]
LDA
*>
\
verbatim
*>
LDA
is
INTEGER
*>
The
leading
dimension
of
the
array
A
.
LDA
>=
max
(
N
,
1
)
.
*>
\
endverbatim
*>
*>
\
param
[
out
]
WORK
*>
\
verbatim
*>
WORK
is
DOUBLE PRECISION
array
,
dimension
(
MAX
(
1
,
LWORK
)),
*>
where
LWORK
>=
N
when
NORM
=
'I'
or
'1'
or
'O'
;
otherwise
,
*>
WORK
is
not
referenced
.
*>
\
endverbatim
*
*
Authors
:
*
========
*
*>
\
author
Univ
.
of
Tennessee
*>
\
author
Univ
.
of
California
Berkeley
*>
\
author
Univ
.
of
Colorado
Denver
*>
\
author
NAG
Ltd
.
*
*>
\
date
September
2012
*
*>
\
ingroup
doubleSYauxiliary
*
*
=====================================================================
DOUBLE PRECISION
FUNCTION
DLANSY
(
NORM
,
UPLO
,
N
,
A
,
LDA
,
WORK
)
*
*
--
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
..
CHARACTER
NORM
,
UPLO
INTEGER
LDA
,
N
*
..
*
..
Array
Arguments
..
DOUBLE PRECISION
A
(
LDA
,
*
),
WORK
(
*
)
*
..
*
*
=====================================================================
*
*
..
Parameters
..
DOUBLE PRECISION
ONE
,
ZERO
PARAMETER
(
ONE
=
1.0
D
+
0
,
ZERO
=
0.0
D
+
0
)
*
..
*
..
Local
Scalars
..
INTEGER
I
,
J
DOUBLE PRECISION
ABSA
,
SCALE
,
SUM
,
VALUE
*
..
*
..
External
Subroutines
..
EXTERNAL
DLASSQ
*
..
*
..
External
Functions
..
LOGICAL
LSAME
,
DISNAN
EXTERNAL
LSAME
,
DISNAN
*
..
*
..
Intrinsic
Functions
..
INTRINSIC
ABS
,
SQRT
*
..
*
..
Executable
Statements
..
*
IF
(
N
.EQ.
0
)
THEN
VALUE
=
ZERO
ELSE IF
(
LSAME
(
NORM
,
'M'
)
)
THEN
*
*
Find
max
(
abs
(
A
(
i
,
j
)))
.
*
VALUE
=
ZERO
IF
(
LSAME
(
UPLO
,
'U'
)
)
THEN
DO
20
J
=
1
,
N
DO
10
I
=
1
,
J
SUM
=
ABS
(
A
(
I
,
J
)
)
IF
(
VALUE
.LT.
SUM
.OR.
DISNAN
(
SUM
)
)
VALUE
=
SUM
10
CONTINUE
20
CONTINUE
ELSE
DO
40
J
=
1
,
N
DO
30
I
=
J
,
N
SUM
=
ABS
(
A
(
I
,
J
)
)
IF
(
VALUE
.LT.
SUM
.OR.
DISNAN
(
SUM
)
)
VALUE
=
SUM
30
CONTINUE
40
CONTINUE
END IF
ELSE IF
(
(
LSAME
(
NORM
,
'I'
)
)
.OR.
(
LSAME
(
NORM
,
'O'
)
)
.OR.
$
(
NORM
.EQ.
'1'
)
)
THEN
*
*
Find
normI
(
A
)
(
=
norm1
(
A
),
since
A
is
symmetric
)
.
*
VALUE
=
ZERO
IF
(
LSAME
(
UPLO
,
'U'
)
)
THEN
DO
60
J
=
1
,
N
SUM
=
ZERO
DO
50
I
=
1
,
J
-
1
ABSA
=
ABS
(
A
(
I
,
J
)
)
SUM
=
SUM
+
ABSA
WORK
(
I
)
=
WORK
(
I
)
+
ABSA
50
CONTINUE
WORK
(
J
)
=
SUM
+
ABS
(
A
(
J
,
J
)
)
60
CONTINUE
DO
70
I
=
1
,
N
SUM
=
WORK
(
I
)
IF
(
VALUE
.LT.
SUM
.OR.
DISNAN
(
SUM
)
)
VALUE
=
SUM
70
CONTINUE
ELSE
DO
80
I
=
1
,
N
WORK
(
I
)
=
ZERO
80
CONTINUE
DO
100
J
=
1
,
N
SUM
=
WORK
(
J
)
+
ABS
(
A
(
J
,
J
)
)
DO
90
I
=
J
+
1
,
N
ABSA
=
ABS
(
A
(
I
,
J
)
)
SUM
=
SUM
+
ABSA
WORK
(
I
)
=
WORK
(
I
)
+
ABSA
90
CONTINUE
IF
(
VALUE
.LT.
SUM
.OR.
DISNAN
(
SUM
)
)
VALUE
=
SUM
100
CONTINUE
END IF
ELSE IF
(
(
LSAME
(
NORM
,
'F'
)
)
.OR.
(
LSAME
(
NORM
,
'E'
)
)
)
THEN
*
*
Find
normF
(
A
)
.
*
SCALE
=
ZERO
SUM
=
ONE
IF
(
LSAME
(
UPLO
,
'U'
)
)
THEN
DO
110
J
=
2
,
N
CALL
DLASSQ
(
J
-
1
,
A
(
1
,
J
),
1
,
SCALE
,
SUM
)
110
CONTINUE
ELSE
DO
120
J
=
1
,
N
-
1
CALL
DLASSQ
(
N
-
J
,
A
(
J
+
1
,
J
),
1
,
SCALE
,
SUM
)
120
CONTINUE
END IF
SUM
=
2
*
SUM
CALL
DLASSQ
(
N
,
A
,
LDA
+
1
,
SCALE
,
SUM
)
VALUE
=
SCALE
*
SQRT
(
SUM
)
END IF
*
DLANSY
=
VALUE
RETURN
*
*
End
of
DLANSY
*
END
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