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*>
\
brief
\
b
DGETRF
*
*
===========
DOCUMENTATION
===========
*
*
Online
html
documentation
available
at
*
http
:
//
www
.
netlib
.
org
/
lapack
/
explore
-
html
/
*
*>
\
htmlonly
*>
Download
DGETRF
+
dependencies
*>
<
a
href
=
"http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgetrf.f"
>
*>
[
TGZ
]
</
a
>
*>
<
a
href
=
"http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgetrf.f"
>
*>
[
ZIP
]
</
a
>
*>
<
a
href
=
"http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgetrf.f"
>
*>
[
TXT
]
</
a
>
*>
\
endhtmlonly
*
*
Definition
:
*
===========
*
*
SUBROUTINE
DGETRF
(
M
,
N
,
A
,
LDA
,
IPIV
,
INFO
)
*
*
..
Scalar
Arguments
..
*
INTEGER
INFO
,
LDA
,
M
,
N
*
..
*
..
Array
Arguments
..
*
INTEGER
IPIV
(
*
)
*
DOUBLE PRECISION
A
(
LDA
,
*
)
*
..
*
*
*>
\
par
Purpose
:
*
=============
*>
*>
\
verbatim
*>
*>
DGETRF
computes
an
LU
factorization
of
a
general
M
-
by
-
N
matrix
A
*>
using
partial
pivoting
with
row
interchanges
.
*>
*>
The
factorization
has
the
form
*>
A
=
P
*
L
*
U
*>
where
P
is
a
permutation
matrix
,
L
is
lower
triangular
with
unit
*>
diagonal
elements
(
lower
trapezoidal
if
m
>
n
),
and
U
is
upper
*>
triangular
(
upper
trapezoidal
if
m
<
n
)
.
*>
*>
This
is
the
right
-
looking
Level
3
BLAS
version
of
the
algorithm
.
*>
\
endverbatim
*
*
Arguments
:
*
==========
*
*>
\
param
[
in
]
M
*>
\
verbatim
*>
M
is
INTEGER
*>
The
number
of
rows
of
the
matrix
A
.
M
>=
0.
*>
\
endverbatim
*>
*>
\
param
[
in
]
N
*>
\
verbatim
*>
N
is
INTEGER
*>
The
number
of
columns
of
the
matrix
A
.
N
>=
0.
*>
\
endverbatim
*>
*>
\
param
[
in
,
out
]
A
*>
\
verbatim
*>
A
is
DOUBLE PRECISION
array
,
dimension
(
LDA
,
N
)
*>
On
entry
,
the
M
-
by
-
N
matrix
to
be
factored
.
*>
On
exit
,
the
factors
L
and
U
from
the
factorization
*>
A
=
P
*
L
*
U
;
the
unit
diagonal
elements
of
L
are
not
stored
.
*>
\
endverbatim
*>
*>
\
param
[
in
]
LDA
*>
\
verbatim
*>
LDA
is
INTEGER
*>
The
leading
dimension
of
the
array
A
.
LDA
>=
max
(
1
,
M
)
.
*>
\
endverbatim
*>
*>
\
param
[
out
]
IPIV
*>
\
verbatim
*>
IPIV
is
INTEGER
array
,
dimension
(
min
(
M
,
N
))
*>
The
pivot
indices
;
for
1
<=
i
<=
min
(
M
,
N
),
row
i
of
the
*>
matrix
was
interchanged
with
row
IPIV
(
i
)
.
*>
\
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
factorization
*>
has
been
completed
,
but
the
factor
U
is
exactly
*>
singular
,
and
division
by
zero
will
occur
if
it
is
used
*>
to
solve
a
system
of
equations
.
*>
\
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
DGETRF
(
M
,
N
,
A
,
LDA
,
IPIV
,
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
,
M
,
N
*
..
*
..
Array
Arguments
..
INTEGER
IPIV
(
*
)
DOUBLE PRECISION
A
(
LDA
,
*
)
*
..
*
*
=====================================================================
*
*
..
Parameters
..
DOUBLE PRECISION
ONE
PARAMETER
(
ONE
=
1.0
D
+
0
)
*
..
*
..
Local
Scalars
..
INTEGER
I
,
IINFO
,
J
,
JB
,
NB
*
..
*
..
External
Subroutines
..
EXTERNAL
DGEMM
,
DGETF2
,
DLASWP
,
DTRSM
,
XERBLA
*
..
*
..
External
Functions
..
INTEGER
ILAENV
EXTERNAL
ILAENV
*
..
*
..
Intrinsic
Functions
..
INTRINSIC
MAX
,
MIN
*
..
*
..
Executable
Statements
..
*
*
Test
the
input
parameters
.
*
INFO
=
0
IF
(
M
.LT.
0
)
THEN
INFO
=
-
1
ELSE IF
(
N
.LT.
0
)
THEN
INFO
=
-
2
ELSE IF
(
LDA
.LT.
MAX
(
1
,
M
)
)
THEN
INFO
=
-
4
END IF
IF
(
INFO
.NE.
0
)
THEN
CALL
XERBLA
(
'DGETRF'
,
-
INFO
)
RETURN
END IF
*
*
Quick
return if
possible
*
IF
(
M
.EQ.
0
.OR.
N
.EQ.
0
)
$
RETURN
*
*
Determine
the
block
size
for
this
environment
.
*
NB
=
ILAENV
(
1
,
'DGETRF'
,
' '
,
M
,
N
,
-
1
,
-
1
)
IF
(
NB
.LE.
1
.OR.
NB
.GE.
MIN
(
M
,
N
)
)
THEN
*
*
Use
unblocked
code
.
*
CALL
DGETF2
(
M
,
N
,
A
,
LDA
,
IPIV
,
INFO
)
ELSE
*
*
Use
blocked
code
.
*
DO
20
J
=
1
,
MIN
(
M
,
N
),
NB
JB
=
MIN
(
MIN
(
M
,
N
)
-
J
+
1
,
NB
)
*
*
Factor
diagonal
and
subdiagonal
blocks
and
test
for
exact
*
singularity
.
*
CALL
DGETF2
(
M
-
J
+
1
,
JB
,
A
(
J
,
J
),
LDA
,
IPIV
(
J
),
IINFO
)
*
*
Adjust
INFO
and
the
pivot
indices
.
*
IF
(
INFO
.EQ.
0
.AND.
IINFO
.GT.
0
)
$
INFO
=
IINFO
+
J
-
1
DO
10
I
=
J
,
MIN
(
M
,
J
+
JB
-
1
)
IPIV
(
I
)
=
J
-
1
+
IPIV
(
I
)
10
CONTINUE
*
*
Apply
interchanges
to
columns
1
:
J
-
1.
*
CALL
DLASWP
(
J
-
1
,
A
,
LDA
,
J
,
J
+
JB
-
1
,
IPIV
,
1
)
*
IF
(
J
+
JB
.LE.
N
)
THEN
*
*
Apply
interchanges
to
columns
J
+
JB
:
N
.
*
CALL
DLASWP
(
N
-
J
-
JB
+
1
,
A
(
1
,
J
+
JB
),
LDA
,
J
,
J
+
JB
-
1
,
$
IPIV
,
1
)
*
*
Compute
block
row
of
U
.
*
CALL
DTRSM
(
'Left'
,
'Lower'
,
'No transpose'
,
'Unit'
,
JB
,
$
N
-
J
-
JB
+
1
,
ONE
,
A
(
J
,
J
),
LDA
,
A
(
J
,
J
+
JB
),
$
LDA
)
IF
(
J
+
JB
.LE.
M
)
THEN
*
*
Update
trailing
submatrix
.
*
CALL
DGEMM
(
'No transpose'
,
'No transpose'
,
M
-
J
-
JB
+
1
,
$
N
-
J
-
JB
+
1
,
JB
,
-
ONE
,
A
(
J
+
JB
,
J
),
LDA
,
$
A
(
J
,
J
+
JB
),
LDA
,
ONE
,
A
(
J
+
JB
,
J
+
JB
),
$
LDA
)
END IF
END IF
20
CONTINUE
END IF
RETURN
*
*
End
of
DGETRF
*
END
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