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*>
\
brief
\
b
DSYGST
*
*
===========
DOCUMENTATION
===========
*
*
Online
html
documentation
available
at
*
http
:
//
www
.
netlib
.
org
/
lapack
/
explore
-
html
/
*
*>
\
htmlonly
*>
Download
DSYGST
+
dependencies
*>
<
a
href
=
"http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsygst.f"
>
*>
[
TGZ
]
</
a
>
*>
<
a
href
=
"http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsygst.f"
>
*>
[
ZIP
]
</
a
>
*>
<
a
href
=
"http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsygst.f"
>
*>
[
TXT
]
</
a
>
*>
\
endhtmlonly
*
*
Definition
:
*
===========
*
*
SUBROUTINE
DSYGST
(
ITYPE
,
UPLO
,
N
,
A
,
LDA
,
B
,
LDB
,
INFO
)
*
*
..
Scalar
Arguments
..
*
CHARACTER
UPLO
*
INTEGER
INFO
,
ITYPE
,
LDA
,
LDB
,
N
*
..
*
..
Array
Arguments
..
*
DOUBLE PRECISION
A
(
LDA
,
*
),
B
(
LDB
,
*
)
*
..
*
*
*>
\
par
Purpose
:
*
=============
*>
*>
\
verbatim
*>
*>
DSYGST
reduces
a
real
symmetric
-
definite
generalized
eigenproblem
*>
to
standard
form
.
*>
*>
If
ITYPE
=
1
,
the
problem
is
A
*
x
=
lambda
*
B
*
x
,
*>
and
A
is
overwritten
by
inv
(
U
**
T
)
*
A
*
inv
(
U
)
or
inv
(
L
)
*
A
*
inv
(
L
**
T
)
*>
*>
If
ITYPE
=
2
or
3
,
the
problem
is
A
*
B
*
x
=
lambda
*
x
or
*>
B
*
A
*
x
=
lambda
*
x
,
and
A
is
overwritten
by
U
*
A
*
U
**
T
or
L
**
T
*
A
*
L
.
*>
*>
B
must
have
been
previously
factorized
as
U
**
T
*
U
or
L
*
L
**
T
by
DPOTRF
.
*>
\
endverbatim
*
*
Arguments
:
*
==========
*
*>
\
param
[
in
]
ITYPE
*>
\
verbatim
*>
ITYPE
is
INTEGER
*>
=
1
:
compute
inv
(
U
**
T
)
*
A
*
inv
(
U
)
or
inv
(
L
)
*
A
*
inv
(
L
**
T
);
*>
=
2
or
3
:
compute
U
*
A
*
U
**
T
or
L
**
T
*
A
*
L
.
*>
\
endverbatim
*>
*>
\
param
[
in
]
UPLO
*>
\
verbatim
*>
UPLO
is
CHARACTER
*
1
*>
=
'U'
:
Upper
triangle
of
A
is
stored
and
B
is
factored
as
*>
U
**
T
*
U
;
*>
=
'L'
:
Lower
triangle
of
A
is
stored
and
B
is
factored
as
*>
L
*
L
**
T
.
*>
\
endverbatim
*>
*>
\
param
[
in
]
N
*>
\
verbatim
*>
N
is
INTEGER
*>
The
order
of
the
matrices
A
and
B
.
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
transformed
matrix
,
stored
in
the
*>
same
format
as
A
.
*>
\
endverbatim
*>
*>
\
param
[
in
]
LDA
*>
\
verbatim
*>
LDA
is
INTEGER
*>
The
leading
dimension
of
the
array
A
.
LDA
>=
max
(
1
,
N
)
.
*>
\
endverbatim
*>
*>
\
param
[
in
]
B
*>
\
verbatim
*>
B
is
DOUBLE PRECISION
array
,
dimension
(
LDB
,
N
)
*>
The
triangular
factor
from
the
Cholesky
factorization
of
B
,
*>
as
returned
by
DPOTRF
.
*>
\
endverbatim
*>
*>
\
param
[
in
]
LDB
*>
\
verbatim
*>
LDB
is
INTEGER
*>
The
leading
dimension
of
the
array
B
.
LDB
>=
max
(
1
,
N
)
.
*>
\
endverbatim
*>
*>
\
param
[
out
]
INFO
*>
\
verbatim
*>
INFO
is
INTEGER
*>
=
0
:
successful
exit
*>
<
0
:
if
INFO
=
-
i
,
the
i
-
th
argument
had
an
illegal
value
*>
\
endverbatim
*
*
Authors
:
*
========
*
*>
\
author
Univ
.
of
Tennessee
*>
\
author
Univ
.
of
California
Berkeley
*>
\
author
Univ
.
of
Colorado
Denver
*>
\
author
NAG
Ltd
.
*
*>
\
date
November
2011
*
*>
\
ingroup
doubleSYcomputational
*
*
=====================================================================
SUBROUTINE
DSYGST
(
ITYPE
,
UPLO
,
N
,
A
,
LDA
,
B
,
LDB
,
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
,
ITYPE
,
LDA
,
LDB
,
N
*
..
*
..
Array
Arguments
..
DOUBLE PRECISION
A
(
LDA
,
*
),
B
(
LDB
,
*
)
*
..
*
*
=====================================================================
*
*
..
Parameters
..
DOUBLE PRECISION
ONE
,
HALF
PARAMETER
(
ONE
=
1.0
D0
,
HALF
=
0.5
D0
)
*
..
*
..
Local
Scalars
..
LOGICAL
UPPER
INTEGER
K
,
KB
,
NB
*
..
*
..
External
Subroutines
..
EXTERNAL
DSYGS2
,
DSYMM
,
DSYR2K
,
DTRMM
,
DTRSM
,
XERBLA
*
..
*
..
Intrinsic
Functions
..
INTRINSIC
MAX
,
MIN
*
..
*
..
External
Functions
..
LOGICAL
LSAME
INTEGER
ILAENV
EXTERNAL
LSAME
,
ILAENV
*
..
*
..
Executable
Statements
..
*
*
Test
the
input
parameters
.
*
INFO
=
0
UPPER
=
LSAME
(
UPLO
,
'U'
)
IF
(
ITYPE
.LT.
1
.OR.
ITYPE
.GT.
3
)
THEN
INFO
=
-
1
ELSE IF
(
.NOT.
UPPER
.AND.
.NOT.
LSAME
(
UPLO
,
'L'
)
)
THEN
INFO
=
-
2
ELSE IF
(
N
.LT.
0
)
THEN
INFO
=
-
3
ELSE IF
(
LDA
.LT.
MAX
(
1
,
N
)
)
THEN
INFO
=
-
5
ELSE IF
(
LDB
.LT.
MAX
(
1
,
N
)
)
THEN
INFO
=
-
7
END IF
IF
(
INFO
.NE.
0
)
THEN
CALL
XERBLA
(
'DSYGST'
,
-
INFO
)
RETURN
END IF
*
*
Quick
return if
possible
*
IF
(
N
.EQ.
0
)
$
RETURN
*
*
Determine
the
block
size
for
this
environment
.
*
NB
=
ILAENV
(
1
,
'DSYGST'
,
UPLO
,
N
,
-
1
,
-
1
,
-
1
)
*
IF
(
NB
.LE.
1
.OR.
NB
.GE.
N
)
THEN
*
*
Use
unblocked
code
*
CALL
DSYGS2
(
ITYPE
,
UPLO
,
N
,
A
,
LDA
,
B
,
LDB
,
INFO
)
ELSE
*
*
Use
blocked
code
*
IF
(
ITYPE
.EQ.
1
)
THEN
IF
(
UPPER
)
THEN
*
*
Compute
inv
(
U
**
T
)
*
A
*
inv
(
U
)
*
DO
10
K
=
1
,
N
,
NB
KB
=
MIN
(
N
-
K
+
1
,
NB
)
*
*
Update
the
upper
triangle
of
A
(
k
:
n
,
k
:
n
)
*
CALL
DSYGS2
(
ITYPE
,
UPLO
,
KB
,
A
(
K
,
K
),
LDA
,
$
B
(
K
,
K
),
LDB
,
INFO
)
IF
(
K
+
KB
.LE.
N
)
THEN
CALL
DTRSM
(
'Left'
,
UPLO
,
'Transpose'
,
'Non-unit'
,
$
KB
,
N
-
K
-
KB
+
1
,
ONE
,
B
(
K
,
K
),
LDB
,
$
A
(
K
,
K
+
KB
),
LDA
)
CALL
DSYMM
(
'Left'
,
UPLO
,
KB
,
N
-
K
-
KB
+
1
,
-
HALF
,
$
A
(
K
,
K
),
LDA
,
B
(
K
,
K
+
KB
),
LDB
,
ONE
,
$
A
(
K
,
K
+
KB
),
LDA
)
CALL
DSYR2K
(
UPLO
,
'Transpose'
,
N
-
K
-
KB
+
1
,
KB
,
-
ONE
,
$
A
(
K
,
K
+
KB
),
LDA
,
B
(
K
,
K
+
KB
),
LDB
,
$
ONE
,
A
(
K
+
KB
,
K
+
KB
),
LDA
)
CALL
DSYMM
(
'Left'
,
UPLO
,
KB
,
N
-
K
-
KB
+
1
,
-
HALF
,
$
A
(
K
,
K
),
LDA
,
B
(
K
,
K
+
KB
),
LDB
,
ONE
,
$
A
(
K
,
K
+
KB
),
LDA
)
CALL
DTRSM
(
'Right'
,
UPLO
,
'No transpose'
,
$
'Non-unit'
,
KB
,
N
-
K
-
KB
+
1
,
ONE
,
$
B
(
K
+
KB
,
K
+
KB
),
LDB
,
A
(
K
,
K
+
KB
),
$
LDA
)
END IF
10
CONTINUE
ELSE
*
*
Compute
inv
(
L
)
*
A
*
inv
(
L
**
T
)
*
DO
20
K
=
1
,
N
,
NB
KB
=
MIN
(
N
-
K
+
1
,
NB
)
*
*
Update
the
lower
triangle
of
A
(
k
:
n
,
k
:
n
)
*
CALL
DSYGS2
(
ITYPE
,
UPLO
,
KB
,
A
(
K
,
K
),
LDA
,
$
B
(
K
,
K
),
LDB
,
INFO
)
IF
(
K
+
KB
.LE.
N
)
THEN
CALL
DTRSM
(
'Right'
,
UPLO
,
'Transpose'
,
'Non-unit'
,
$
N
-
K
-
KB
+
1
,
KB
,
ONE
,
B
(
K
,
K
),
LDB
,
$
A
(
K
+
KB
,
K
),
LDA
)
CALL
DSYMM
(
'Right'
,
UPLO
,
N
-
K
-
KB
+
1
,
KB
,
-
HALF
,
$
A
(
K
,
K
),
LDA
,
B
(
K
+
KB
,
K
),
LDB
,
ONE
,
$
A
(
K
+
KB
,
K
),
LDA
)
CALL
DSYR2K
(
UPLO
,
'No transpose'
,
N
-
K
-
KB
+
1
,
KB
,
$
-
ONE
,
A
(
K
+
KB
,
K
),
LDA
,
B
(
K
+
KB
,
K
),
$
LDB
,
ONE
,
A
(
K
+
KB
,
K
+
KB
),
LDA
)
CALL
DSYMM
(
'Right'
,
UPLO
,
N
-
K
-
KB
+
1
,
KB
,
-
HALF
,
$
A
(
K
,
K
),
LDA
,
B
(
K
+
KB
,
K
),
LDB
,
ONE
,
$
A
(
K
+
KB
,
K
),
LDA
)
CALL
DTRSM
(
'Left'
,
UPLO
,
'No transpose'
,
$
'Non-unit'
,
N
-
K
-
KB
+
1
,
KB
,
ONE
,
$
B
(
K
+
KB
,
K
+
KB
),
LDB
,
A
(
K
+
KB
,
K
),
$
LDA
)
END IF
20
CONTINUE
END IF
ELSE
IF
(
UPPER
)
THEN
*
*
Compute
U
*
A
*
U
**
T
*
DO
30
K
=
1
,
N
,
NB
KB
=
MIN
(
N
-
K
+
1
,
NB
)
*
*
Update
the
upper
triangle
of
A
(
1
:
k
+
kb
-
1
,
1
:
k
+
kb
-
1
)
*
CALL
DTRMM
(
'Left'
,
UPLO
,
'No transpose'
,
'Non-unit'
,
$
K
-
1
,
KB
,
ONE
,
B
,
LDB
,
A
(
1
,
K
),
LDA
)
CALL
DSYMM
(
'Right'
,
UPLO
,
K
-
1
,
KB
,
HALF
,
A
(
K
,
K
),
$
LDA
,
B
(
1
,
K
),
LDB
,
ONE
,
A
(
1
,
K
),
LDA
)
CALL
DSYR2K
(
UPLO
,
'No transpose'
,
K
-
1
,
KB
,
ONE
,
$
A
(
1
,
K
),
LDA
,
B
(
1
,
K
),
LDB
,
ONE
,
A
,
$
LDA
)
CALL
DSYMM
(
'Right'
,
UPLO
,
K
-
1
,
KB
,
HALF
,
A
(
K
,
K
),
$
LDA
,
B
(
1
,
K
),
LDB
,
ONE
,
A
(
1
,
K
),
LDA
)
CALL
DTRMM
(
'Right'
,
UPLO
,
'Transpose'
,
'Non-unit'
,
$
K
-
1
,
KB
,
ONE
,
B
(
K
,
K
),
LDB
,
A
(
1
,
K
),
$
LDA
)
CALL
DSYGS2
(
ITYPE
,
UPLO
,
KB
,
A
(
K
,
K
),
LDA
,
$
B
(
K
,
K
),
LDB
,
INFO
)
30
CONTINUE
ELSE
*
*
Compute
L
**
T
*
A
*
L
*
DO
40
K
=
1
,
N
,
NB
KB
=
MIN
(
N
-
K
+
1
,
NB
)
*
*
Update
the
lower
triangle
of
A
(
1
:
k
+
kb
-
1
,
1
:
k
+
kb
-
1
)
*
CALL
DTRMM
(
'Right'
,
UPLO
,
'No transpose'
,
'Non-unit'
,
$
KB
,
K
-
1
,
ONE
,
B
,
LDB
,
A
(
K
,
1
),
LDA
)
CALL
DSYMM
(
'Left'
,
UPLO
,
KB
,
K
-
1
,
HALF
,
A
(
K
,
K
),
$
LDA
,
B
(
K
,
1
),
LDB
,
ONE
,
A
(
K
,
1
),
LDA
)
CALL
DSYR2K
(
UPLO
,
'Transpose'
,
K
-
1
,
KB
,
ONE
,
$
A
(
K
,
1
),
LDA
,
B
(
K
,
1
),
LDB
,
ONE
,
A
,
$
LDA
)
CALL
DSYMM
(
'Left'
,
UPLO
,
KB
,
K
-
1
,
HALF
,
A
(
K
,
K
),
$
LDA
,
B
(
K
,
1
),
LDB
,
ONE
,
A
(
K
,
1
),
LDA
)
CALL
DTRMM
(
'Left'
,
UPLO
,
'Transpose'
,
'Non-unit'
,
KB
,
$
K
-
1
,
ONE
,
B
(
K
,
K
),
LDB
,
A
(
K
,
1
),
LDA
)
CALL
DSYGS2
(
ITYPE
,
UPLO
,
KB
,
A
(
K
,
K
),
LDA
,
$
B
(
K
,
K
),
LDB
,
INFO
)
40
CONTINUE
END IF
END IF
END IF
RETURN
*
*
End
of
DSYGST
*
END
Event Timeline
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