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dpotf2.f
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*>
\
brief
\
b
DPOTF2
computes
the
Cholesky
factorization
of
a
symmetric
/
Hermitian
positive
definite
matrix
(
unblocked
algorithm
)
.
*
*
===========
DOCUMENTATION
===========
*
*
Online
html
documentation
available
at
*
http
:
//
www
.
netlib
.
org
/
lapack
/
explore
-
html
/
*
*>
\
htmlonly
*>
Download
DPOTF2
+
dependencies
*>
<
a
href
=
"http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dpotf2.f"
>
*>
[
TGZ
]
</
a
>
*>
<
a
href
=
"http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dpotf2.f"
>
*>
[
ZIP
]
</
a
>
*>
<
a
href
=
"http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dpotf2.f"
>
*>
[
TXT
]
</
a
>
*>
\
endhtmlonly
*
*
Definition
:
*
===========
*
*
SUBROUTINE
DPOTF2
(
UPLO
,
N
,
A
,
LDA
,
INFO
)
*
*
..
Scalar
Arguments
..
*
CHARACTER
UPLO
*
INTEGER
INFO
,
LDA
,
N
*
..
*
..
Array
Arguments
..
*
DOUBLE PRECISION
A
(
LDA
,
*
)
*
..
*
*
*>
\
par
Purpose
:
*
=============
*>
*>
\
verbatim
*>
*>
DPOTF2
computes
the
Cholesky
factorization
of
a
real
symmetric
*>
positive
definite
matrix
A
.
*>
*>
The
factorization
has
the
form
*>
A
=
U
**
T
*
U
,
if
UPLO
=
'U'
,
or
*>
A
=
L
*
L
**
T
,
if
UPLO
=
'L'
,
*>
where
U
is
an
upper
triangular
matrix
and
L
is
lower
triangular
.
*>
*>
This
is
the
unblocked
version
of
the
algorithm
,
calling
Level
2
BLAS
.
*>
\
endverbatim
*
*
Arguments
:
*
==========
*
*>
\
param
[
in
]
UPLO
*>
\
verbatim
*>
UPLO
is
CHARACTER
*
1
*>
Specifies
whether
the
upper
or
lower
triangular
part
of
the
*>
symmetric
matrix
A
is
stored
.
*>
=
'U'
:
Upper
triangular
*>
=
'L'
:
Lower
triangular
*>
\
endverbatim
*>
*>
\
param
[
in
]
N
*>
\
verbatim
*>
N
is
INTEGER
*>
The
order
of
the
matrix
A
.
N
>=
0.
*>
\
endverbatim
*>
*>
\
param
[
in
,
out
]
A
*>
\
verbatim
*>
A
is
DOUBLE PRECISION
array
,
dimension
(
LDA
,
N
)
*>
On
entry
,
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
.
*>
*>
On
exit
,
if
INFO
=
0
,
the
factor
U
or
L
from
the
Cholesky
*>
factorization
A
=
U
**
T
*
U
or
A
=
L
*
L
**
T
.
*>
\
endverbatim
*>
*>
\
param
[
in
]
LDA
*>
\
verbatim
*>
LDA
is
INTEGER
*>
The
leading
dimension
of
the
array
A
.
LDA
>=
max
(
1
,
N
)
.
*>
\
endverbatim
*>
*>
\
param
[
out
]
INFO
*>
\
verbatim
*>
INFO
is
INTEGER
*>
=
0
:
successful
exit
*>
<
0
:
if
INFO
=
-
k
,
the
k
-
th
argument
had
an
illegal
value
*>
>
0
:
if
INFO
=
k
,
the
leading
minor
of
order
k
is
not
*>
positive
definite
,
and
the
factorization
could
not
be
*>
completed
.
*>
\
endverbatim
*
*
Authors
:
*
========
*
*>
\
author
Univ
.
of
Tennessee
*>
\
author
Univ
.
of
California
Berkeley
*>
\
author
Univ
.
of
Colorado
Denver
*>
\
author
NAG
Ltd
.
*
*>
\
date
September
2012
*
*>
\
ingroup
doublePOcomputational
*
*
=====================================================================
SUBROUTINE
DPOTF2
(
UPLO
,
N
,
A
,
LDA
,
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
..
CHARACTER
UPLO
INTEGER
INFO
,
LDA
,
N
*
..
*
..
Array
Arguments
..
DOUBLE PRECISION
A
(
LDA
,
*
)
*
..
*
*
=====================================================================
*
*
..
Parameters
..
DOUBLE PRECISION
ONE
,
ZERO
PARAMETER
(
ONE
=
1.0
D
+
0
,
ZERO
=
0.0
D
+
0
)
*
..
*
..
Local
Scalars
..
LOGICAL
UPPER
INTEGER
J
DOUBLE PRECISION
AJJ
*
..
*
..
External
Functions
..
LOGICAL
LSAME
,
DISNAN
DOUBLE PRECISION
DDOT
EXTERNAL
LSAME
,
DDOT
,
DISNAN
*
..
*
..
External
Subroutines
..
EXTERNAL
DGEMV
,
DSCAL
,
XERBLA
*
..
*
..
Intrinsic
Functions
..
INTRINSIC
MAX
,
SQRT
*
..
*
..
Executable
Statements
..
*
*
Test
the
input
parameters
.
*
INFO
=
0
UPPER
=
LSAME
(
UPLO
,
'U'
)
IF
(
.NOT.
UPPER
.AND.
.NOT.
LSAME
(
UPLO
,
'L'
)
)
THEN
INFO
=
-
1
ELSE IF
(
N
.LT.
0
)
THEN
INFO
=
-
2
ELSE IF
(
LDA
.LT.
MAX
(
1
,
N
)
)
THEN
INFO
=
-
4
END IF
IF
(
INFO
.NE.
0
)
THEN
CALL
XERBLA
(
'DPOTF2'
,
-
INFO
)
RETURN
END IF
*
*
Quick
return if
possible
*
IF
(
N
.EQ.
0
)
$
RETURN
*
IF
(
UPPER
)
THEN
*
*
Compute
the
Cholesky
factorization
A
=
U
**
T
*
U
.
*
DO
10
J
=
1
,
N
*
*
Compute
U
(
J
,
J
)
and
test
for
non
-
positive
-
definiteness
.
*
AJJ
=
A
(
J
,
J
)
-
DDOT
(
J
-
1
,
A
(
1
,
J
),
1
,
A
(
1
,
J
),
1
)
IF
(
AJJ
.LE.
ZERO
.OR.
DISNAN
(
AJJ
)
)
THEN
A
(
J
,
J
)
=
AJJ
GO
TO
30
END IF
AJJ
=
SQRT
(
AJJ
)
A
(
J
,
J
)
=
AJJ
*
*
Compute
elements
J
+
1
:
N
of
row
J
.
*
IF
(
J
.LT.
N
)
THEN
CALL
DGEMV
(
'Transpose'
,
J
-
1
,
N
-
J
,
-
ONE
,
A
(
1
,
J
+
1
),
$
LDA
,
A
(
1
,
J
),
1
,
ONE
,
A
(
J
,
J
+
1
),
LDA
)
CALL
DSCAL
(
N
-
J
,
ONE
/
AJJ
,
A
(
J
,
J
+
1
),
LDA
)
END IF
10
CONTINUE
ELSE
*
*
Compute
the
Cholesky
factorization
A
=
L
*
L
**
T
.
*
DO
20
J
=
1
,
N
*
*
Compute
L
(
J
,
J
)
and
test
for
non
-
positive
-
definiteness
.
*
AJJ
=
A
(
J
,
J
)
-
DDOT
(
J
-
1
,
A
(
J
,
1
),
LDA
,
A
(
J
,
1
),
$
LDA
)
IF
(
AJJ
.LE.
ZERO
.OR.
DISNAN
(
AJJ
)
)
THEN
A
(
J
,
J
)
=
AJJ
GO
TO
30
END IF
AJJ
=
SQRT
(
AJJ
)
A
(
J
,
J
)
=
AJJ
*
*
Compute
elements
J
+
1
:
N
of
column
J
.
*
IF
(
J
.LT.
N
)
THEN
CALL
DGEMV
(
'No transpose'
,
N
-
J
,
J
-
1
,
-
ONE
,
A
(
J
+
1
,
1
),
$
LDA
,
A
(
J
,
1
),
LDA
,
ONE
,
A
(
J
+
1
,
J
),
1
)
CALL
DSCAL
(
N
-
J
,
ONE
/
AJJ
,
A
(
J
+
1
,
J
),
1
)
END IF
20
CONTINUE
END IF
GO
TO
40
*
30
CONTINUE
INFO
=
J
*
40
CONTINUE
RETURN
*
*
End
of
DPOTF2
*
END
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