Developer Reference

  • 2020.2
  • 07/15/2020
  • Public Content
Contents

?gees

Computes the eigenvalues and Schur factorization of a general matrix, and orders the factorization so that selected eigenvalues are at the top left of the Schur form.

Syntax

call sgees
(
jobvs
,
sort
,
select
,
n
,
a
,
lda
,
sdim
,
wr
,
wi
,
vs
,
ldvs
,
work
,
lwork
,
bwork
,
info
)
call dgees
(
jobvs
,
sort
,
select
,
n
,
a
,
lda
,
sdim
,
wr
,
wi
,
vs
,
ldvs
,
work
,
lwork
,
bwork
,
info
)
call cgees
(
jobvs
,
sort
,
select
,
n
,
a
,
lda
,
sdim
,
w
,
vs
,
ldvs
,
work
,
lwork
,
rwork
,
bwork
,
info
)
call zgees
(
jobvs
,
sort
,
select
,
n
,
a
,
lda
,
sdim
,
w
,
vs
,
ldvs
,
work
,
lwork
,
rwork
,
bwork
,
info
)
call gees
(
a
,
wr
,
wi
[
,
vs
]
[
,
select
]
[
,
sdim
]
[
,
info
]
)
call gees
(
a
,
w
[
,
vs
]
[
,
select
]
[
,
sdim
]
[
,
info
]
)
Include Files
  • mkl.fi
    ,
    lapack.f90
Description
The routine computes for an
n
-by-
n
real/complex nonsymmetric matrix
A
, the eigenvalues, the real Schur form
T
, and, optionally, the matrix of Schur vectors
Z
. This gives the Schur factorization
A
=
Z
*
T
*
Z
H
.
Optionally, it also orders the eigenvalues on the diagonal of the real-Schur/Schur form so that selected eigenvalues are at the top left. The leading columns of
Z
then form an orthonormal basis for the invariant subspace corresponding to the selected eigenvalues.
A real matrix is in real-Schur form if it is upper quasi-triangular with 1-by-1 and 2-by-2 blocks. 2-by-2 blocks will be standardized in the form
Equation
where
b
*
c
< 0
. The eigenvalues of such a block are Equation
A complex matrix is in Schur form if it is upper triangular.
Input Parameters
jobvs
CHARACTER*1
.
Must be
'N'
or
'V'
.
If
jobvs
=
'N'
, then Schur vectors are not computed.
If
jobvs
=
'V'
, then Schur vectors are computed.