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dgetri.f
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*>
\
brief
\
b
DGETRI
*
*
===========
DOCUMENTATION
===========
*
*
Online
html
documentation
available
at
*
http
:
//
www
.
netlib
.
org
/
lapack
/
explore
-
html
/
*
*>
\
htmlonly
*>
Download
DGETRI
+
dependencies
*>
<
a
href
=
"http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgetri.f"
>
*>
[
TGZ
]
</
a
>
*>
<
a
href
=
"http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgetri.f"
>
*>
[
ZIP
]
</
a
>
*>
<
a
href
=
"http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgetri.f"
>
*>
[
TXT
]
</
a
>
*>
\
endhtmlonly
*
*
Definition
:
*
===========
*
*
SUBROUTINE
DGETRI
(
N
,
A
,
LDA
,
IPIV
,
WORK
,
LWORK
,
INFO
)
*
*
..
Scalar
Arguments
..
*
INTEGER
INFO
,
LDA
,
LWORK
,
N
*
..
*
..
Array
Arguments
..
*
INTEGER
IPIV
(
*
)
*
DOUBLE PRECISION
A
(
LDA
,
*
),
WORK
(
*
)
*
..
*
*
*>
\
par
Purpose
:
*
=============
*>
*>
\
verbatim
*>
*>
DGETRI
computes
the
inverse
of
a
matrix
using
the
LU
factorization
*>
computed
by
DGETRF
.
*>
*>
This
method
inverts
U
and
then
computes
inv
(
A
)
by
solving
the
system
*>
inv
(
A
)
*
L
=
inv
(
U
)
for
inv
(
A
)
.
*>
\
endverbatim
*
*
Arguments
:
*
==========
*
*>
\
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
factors
L
and
U
from
the
factorization
*>
A
=
P
*
L
*
U
as
computed
by
DGETRF
.
*>
On
exit
,
if
INFO
=
0
,
the
inverse
of
the
original
matrix
A
.
*>
\
endverbatim
*>
*>
\
param
[
in
]
LDA
*>
\
verbatim
*>
LDA
is
INTEGER
*>
The
leading
dimension
of
the
array
A
.
LDA
>=
max
(
1
,
N
)
.
*>
\
endverbatim
*>
*>
\
param
[
in
]
IPIV
*>
\
verbatim
*>
IPIV
is
INTEGER
array
,
dimension
(
N
)
*>
The
pivot
indices
from
DGETRF
;
for
1
<=
i
<=
N
,
row
i
of
the
*>
matrix
was
interchanged
with
row
IPIV
(
i
)
.
*>
\
endverbatim
*>
*>
\
param
[
out
]
WORK
*>
\
verbatim
*>
WORK
is
DOUBLE PRECISION
array
,
dimension
(
MAX
(
1
,
LWORK
))
*>
On
exit
,
if
INFO
=
0
,
then
WORK
(
1
)
returns
the
optimal
LWORK
.
*>
\
endverbatim
*>
*>
\
param
[
in
]
LWORK
*>
\
verbatim
*>
LWORK
is
INTEGER
*>
The
dimension
of
the
array
WORK
.
LWORK
>=
max
(
1
,
N
)
.
*>
For
optimal
performance
LWORK
>=
N
*
NB
,
where
NB
is
*>
the
optimal
blocksize
returned
by
ILAENV
.
*>
*>
If
LWORK
=
-
1
,
then
a
workspace
query
is
assumed
;
the
routine
*>
only
calculates
the
optimal
size
of
the
WORK
array
,
returns
*>
this
value
as
the
first
entry
of
the
WORK
array
,
and
no
error
*>
message
related
to
LWORK
is
issued
by
XERBLA
.
*>
\
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
,
U
(
i
,
i
)
is
exactly
zero
;
the
matrix
is
*>
singular
and
its
inverse
could
not
be
computed
.
*>
\
endverbatim
*
*
Authors
:
*
========
*
*>
\
author
Univ
.
of
Tennessee
*>
\
author
Univ
.
of
California
Berkeley
*>
\
author
Univ
.
of
Colorado
Denver
*>
\
author
NAG
Ltd
.
*
*>
\
date
November
2011
*
*>
\
ingroup
doubleGEcomputational
*
*
=====================================================================
SUBROUTINE
DGETRI
(
N
,
A
,
LDA
,
IPIV
,
WORK
,
LWORK
,
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
..
INTEGER
INFO
,
LDA
,
LWORK
,
N
*
..
*
..
Array
Arguments
..
INTEGER
IPIV
(
*
)
DOUBLE PRECISION
A
(
LDA
,
*
),
WORK
(
*
)
*
..
*
*
=====================================================================
*
*
..
Parameters
..
DOUBLE PRECISION
ZERO
,
ONE
PARAMETER
(
ZERO
=
0.0
D
+
0
,
ONE
=
1.0
D
+
0
)
*
..
*
..
Local
Scalars
..
LOGICAL
LQUERY
INTEGER
I
,
IWS
,
J
,
JB
,
JJ
,
JP
,
LDWORK
,
LWKOPT
,
NB
,
$
NBMIN
,
NN
*
..
*
..
External
Functions
..
INTEGER
ILAENV
EXTERNAL
ILAENV
*
..
*
..
External
Subroutines
..
EXTERNAL
DGEMM
,
DGEMV
,
DSWAP
,
DTRSM
,
DTRTRI
,
XERBLA
*
..
*
..
Intrinsic
Functions
..
INTRINSIC
MAX
,
MIN
*
..
*
..
Executable
Statements
..
*
*
Test
the
input
parameters
.
*
INFO
=
0
NB
=
ILAENV
(
1
,
'DGETRI'
,
' '
,
N
,
-
1
,
-
1
,
-
1
)
LWKOPT
=
N
*
NB
WORK
(
1
)
=
LWKOPT
LQUERY
=
(
LWORK
.EQ.
-
1
)
IF
(
N
.LT.
0
)
THEN
INFO
=
-
1
ELSE IF
(
LDA
.LT.
MAX
(
1
,
N
)
)
THEN
INFO
=
-
3
ELSE IF
(
LWORK
.LT.
MAX
(
1
,
N
)
.AND.
.NOT.
LQUERY
)
THEN
INFO
=
-
6
END IF
IF
(
INFO
.NE.
0
)
THEN
CALL
XERBLA
(
'DGETRI'
,
-
INFO
)
RETURN
ELSE IF
(
LQUERY
)
THEN
RETURN
END IF
*
*
Quick
return if
possible
*
IF
(
N
.EQ.
0
)
$
RETURN
*
*
Form
inv
(
U
)
.
If
INFO
>
0
from
DTRTRI
,
then
U
is
singular
,
*
and
the
inverse
is
not
computed
.
*
CALL
DTRTRI
(
'Upper'
,
'Non-unit'
,
N
,
A
,
LDA
,
INFO
)
IF
(
INFO
.GT.
0
)
$
RETURN
*
NBMIN
=
2
LDWORK
=
N
IF
(
NB
.GT.
1
.AND.
NB
.LT.
N
)
THEN
IWS
=
MAX
(
LDWORK
*
NB
,
1
)
IF
(
LWORK
.LT.
IWS
)
THEN
NB
=
LWORK
/
LDWORK
NBMIN
=
MAX
(
2
,
ILAENV
(
2
,
'DGETRI'
,
' '
,
N
,
-
1
,
-
1
,
-
1
)
)
END IF
ELSE
IWS
=
N
END IF
*
*
Solve
the
equation
inv
(
A
)
*
L
=
inv
(
U
)
for
inv
(
A
)
.
*
IF
(
NB
.LT.
NBMIN
.OR.
NB
.GE.
N
)
THEN
*
*
Use
unblocked
code
.
*
DO
20
J
=
N
,
1
,
-
1
*
*
Copy
current
column
of
L
to
WORK
and
replace
with
zeros
.
*
DO
10
I
=
J
+
1
,
N
WORK
(
I
)
=
A
(
I
,
J
)
A
(
I
,
J
)
=
ZERO
10
CONTINUE
*
*
Compute
current
column
of
inv
(
A
)
.
*
IF
(
J
.LT.
N
)
$
CALL
DGEMV
(
'No transpose'
,
N
,
N
-
J
,
-
ONE
,
A
(
1
,
J
+
1
),
$
LDA
,
WORK
(
J
+
1
),
1
,
ONE
,
A
(
1
,
J
),
1
)
20
CONTINUE
ELSE
*
*
Use
blocked
code
.
*
NN
=
(
(
N
-
1
)
/
NB
)
*
NB
+
1
DO
50
J
=
NN
,
1
,
-
NB
JB
=
MIN
(
NB
,
N
-
J
+
1
)
*
*
Copy
current
block
column
of
L
to
WORK
and
replace
with
*
zeros
.
*
DO
40
JJ
=
J
,
J
+
JB
-
1
DO
30
I
=
JJ
+
1
,
N
WORK
(
I
+
(
JJ
-
J
)
*
LDWORK
)
=
A
(
I
,
JJ
)
A
(
I
,
JJ
)
=
ZERO
30
CONTINUE
40
CONTINUE
*
*
Compute
current
block
column
of
inv
(
A
)
.
*
IF
(
J
+
JB
.LE.
N
)
$
CALL
DGEMM
(
'No transpose'
,
'No transpose'
,
N
,
JB
,
$
N
-
J
-
JB
+
1
,
-
ONE
,
A
(
1
,
J
+
JB
),
LDA
,
$
WORK
(
J
+
JB
),
LDWORK
,
ONE
,
A
(
1
,
J
),
LDA
)
CALL
DTRSM
(
'Right'
,
'Lower'
,
'No transpose'
,
'Unit'
,
N
,
JB
,
$
ONE
,
WORK
(
J
),
LDWORK
,
A
(
1
,
J
),
LDA
)
50
CONTINUE
END IF
*
*
Apply
column
interchanges
.
*
DO
60
J
=
N
-
1
,
1
,
-
1
JP
=
IPIV
(
J
)
IF
(
JP
.NE.
J
)
$
CALL
DSWAP
(
N
,
A
(
1
,
J
),
1
,
A
(
1
,
JP
),
1
)
60
CONTINUE
*
WORK
(
1
)
=
IWS
RETURN
*
*
End
of
DGETRI
*
END
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