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zpptrf.f
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*>
\
brief
\
b
ZPPTRF
*
*
===========
DOCUMENTATION
===========
*
*
Online
html
documentation
available
at
*
http
:
//
www
.
netlib
.
org
/
lapack
/
explore
-
html
/
*
*>
\
htmlonly
*>
Download
ZPPTRF
+
dependencies
*>
<
a
href
=
"http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zpptrf.f"
>
*>
[
TGZ
]
</
a
>
*>
<
a
href
=
"http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zpptrf.f"
>
*>
[
ZIP
]
</
a
>
*>
<
a
href
=
"http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zpptrf.f"
>
*>
[
TXT
]
</
a
>
*>
\
endhtmlonly
*
*
Definition
:
*
===========
*
*
SUBROUTINE
ZPPTRF
(
UPLO
,
N
,
AP
,
INFO
)
*
*
..
Scalar
Arguments
..
*
CHARACTER
UPLO
*
INTEGER
INFO
,
N
*
..
*
..
Array
Arguments
..
*
COMPLEX
*
16
AP
(
*
)
*
..
*
*
*>
\
par
Purpose
:
*
=============
*>
*>
\
verbatim
*>
*>
ZPPTRF
computes
the
Cholesky
factorization
of
a
complex
Hermitian
*>
positive
definite
matrix
A
stored
in
packed
format
.
*>
*>
The
factorization
has
the
form
*>
A
=
U
**
H
*
U
,
if
UPLO
=
'U'
,
or
*>
A
=
L
*
L
**
H
,
if
UPLO
=
'L'
,
*>
where
U
is
an
upper
triangular
matrix
and
L
is
lower
triangular
.
*>
\
endverbatim
*
*
Arguments
:
*
==========
*
*>
\
param
[
in
]
UPLO
*>
\
verbatim
*>
UPLO
is
CHARACTER
*
1
*>
=
'U'
:
Upper
triangle
of
A
is
stored
;
*>
=
'L'
:
Lower
triangle
of
A
is
stored
.
*>
\
endverbatim
*>
*>
\
param
[
in
]
N
*>
\
verbatim
*>
N
is
INTEGER
*>
The
order
of
the
matrix
A
.
N
>=
0.
*>
\
endverbatim
*>
*>
\
param
[
in
,
out
]
AP
*>
\
verbatim
*>
AP
is
COMPLEX
*
16
array
,
dimension
(
N
*
(
N
+
1
)
/
2
)
*>
On
entry
,
the
upper
or
lower
triangle
of
the
Hermitian
matrix
*>
A
,
packed
columnwise
in
a
linear
array
.
The
j
-
th
column
of
A
*>
is
stored
in
the
array
AP
as
follows
:
*>
if
UPLO
=
'U'
,
AP
(
i
+
(
j
-
1
)
*
j
/
2
)
=
A
(
i
,
j
)
for
1
<=
i
<=
j
;
*>
if
UPLO
=
'L'
,
AP
(
i
+
(
j
-
1
)
*
(
2
n
-
j
)
/
2
)
=
A
(
i
,
j
)
for
j
<=
i
<=
n
.
*>
See
below
for
further
details
.
*>
*>
On
exit
,
if
INFO
=
0
,
the
triangular
factor
U
or
L
from
the
*>
Cholesky
factorization
A
=
U
**
H
*
U
or
A
=
L
*
L
**
H
,
in
the
same
*>
storage
format
as
A
.
*>
\
endverbatim
*>
*>
\
param
[
out
]
INFO
*>
\
verbatim
*>
INFO
is
INTEGER
*>
=
0
:
successful
exit
*>
<
0
:
if
INFO
=
-
i
,
the
i
-
th
argument
had
an
illegal
value
*>
>
0
:
if
INFO
=
i
,
the
leading
minor
of
order
i
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
November
2011
*
*>
\
ingroup
complex16OTHERcomputational
*
*>
\
par
Further
Details
:
*
=====================
*>
*>
\
verbatim
*>
*>
The
packed
storage
scheme
is
illustrated
by
the
following
example
*>
when
N
=
4
,
UPLO
=
'U'
:
*>
*>
Two
-
dimensional
storage
of
the
Hermitian
matrix
A
:
*>
*>
a11
a12
a13
a14
*>
a22
a23
a24
*>
a33
a34
(
aij
=
conjg
(
aji
))
*>
a44
*>
*>
Packed
storage
of
the
upper
triangle
of
A
:
*>
*>
AP
=
[
a11
,
a12
,
a22
,
a13
,
a23
,
a33
,
a14
,
a24
,
a34
,
a44
]
*>
\
endverbatim
*>
*
=====================================================================
SUBROUTINE
ZPPTRF
(
UPLO
,
N
,
AP
,
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
..
CHARACTER
UPLO
INTEGER
INFO
,
N
*
..
*
..
Array
Arguments
..
COMPLEX
*
16
AP
(
*
)
*
..
*
*
=====================================================================
*
*
..
Parameters
..
DOUBLE PRECISION
ZERO
,
ONE
PARAMETER
(
ZERO
=
0.0
D
+
0
,
ONE
=
1.0
D
+
0
)
*
..
*
..
Local
Scalars
..
LOGICAL
UPPER
INTEGER
J
,
JC
,
JJ
DOUBLE PRECISION
AJJ
*
..
*
..
External
Functions
..
LOGICAL
LSAME
COMPLEX
*
16
ZDOTC
EXTERNAL
LSAME
,
ZDOTC
*
..
*
..
External
Subroutines
..
EXTERNAL
XERBLA
,
ZDSCAL
,
ZHPR
,
ZTPSV
*
..
*
..
Intrinsic
Functions
..
INTRINSIC
DBLE
,
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
END IF
IF
(
INFO
.NE.
0
)
THEN
CALL
XERBLA
(
'ZPPTRF'
,
-
INFO
)
RETURN
END IF
*
*
Quick
return if
possible
*
IF
(
N
.EQ.
0
)
$
RETURN
*
IF
(
UPPER
)
THEN
*
*
Compute
the
Cholesky
factorization
A
=
U
**
H
*
U
.
*
JJ
=
0
DO
10
J
=
1
,
N
JC
=
JJ
+
1
JJ
=
JJ
+
J
*
*
Compute
elements
1
:
J
-
1
of
column
J
.
*
IF
(
J
.GT.
1
)
$
CALL
ZTPSV
(
'Upper'
,
'Conjugate transpose'
,
'Non-unit'
,
$
J
-
1
,
AP
,
AP
(
JC
),
1
)
*
*
Compute
U
(
J
,
J
)
and
test
for
non
-
positive
-
definiteness
.
*
AJJ
=
DBLE
(
AP
(
JJ
)
)
-
ZDOTC
(
J
-
1
,
AP
(
JC
),
1
,
AP
(
JC
),
$
1
)
IF
(
AJJ
.LE.
ZERO
)
THEN
AP
(
JJ
)
=
AJJ
GO
TO
30
END IF
AP
(
JJ
)
=
SQRT
(
AJJ
)
10
CONTINUE
ELSE
*
*
Compute
the
Cholesky
factorization
A
=
L
*
L
**
H
.
*
JJ
=
1
DO
20
J
=
1
,
N
*
*
Compute
L
(
J
,
J
)
and
test
for
non
-
positive
-
definiteness
.
*
AJJ
=
DBLE
(
AP
(
JJ
)
)
IF
(
AJJ
.LE.
ZERO
)
THEN
AP
(
JJ
)
=
AJJ
GO
TO
30
END IF
AJJ
=
SQRT
(
AJJ
)
AP
(
JJ
)
=
AJJ
*
*
Compute
elements
J
+
1
:
N
of
column
J
and
update
the
trailing
*
submatrix
.
*
IF
(
J
.LT.
N
)
THEN
CALL
ZDSCAL
(
N
-
J
,
ONE
/
AJJ
,
AP
(
JJ
+
1
),
1
)
CALL
ZHPR
(
'Lower'
,
N
-
J
,
-
ONE
,
AP
(
JJ
+
1
),
1
,
$
AP
(
JJ
+
N
-
J
+
1
)
)
JJ
=
JJ
+
N
-
J
+
1
END IF
20
CONTINUE
END IF
GO
TO
40
*
30
CONTINUE
INFO
=
J
*
40
CONTINUE
RETURN
*
*
End
of
ZPPTRF
*
END
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