dgees.f man page

dgees.f —

Synopsis

Functions/Subroutines

subroutine dgees (JOBVS, SORT, SELECT, N, A, LDA, SDIM, WR, WI, VS, LDVS, WORK, LWORK, BWORK, INFO)
DGEES computes the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors for GE matrices

Function/Subroutine Documentation

subroutine dgees (characterJOBVS, characterSORT, logical, externalSELECT, integerN, double precision, dimension( lda, * )A, integerLDA, integerSDIM, double precision, dimension( * )WR, double precision, dimension( * )WI, double precision, dimension( ldvs, * )VS, integerLDVS, double precision, dimension( * )WORK, integerLWORK, logical, dimension( * )BWORK, integerINFO)

DGEES computes the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors for GE matrices

Purpose:

DGEES computes for an N-by-N real 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**T).

Optionally, it also orders the eigenvalues on the diagonal of the
real 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 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
        [  a  b  ]
        [  c  a  ]

where b*c < 0. The eigenvalues of such a block are a +- sqrt(bc).

Parameters:

JOBVS

JOBVS is CHARACTER*1
= 'N': Schur vectors are not computed;
= 'V': Schur vectors are computed.

SORT

SORT is CHARACTER*1
Specifies whether or not to order the eigenvalues on the
diagonal of the Schur form.
= 'N': Eigenvalues are not ordered;
= 'S': Eigenvalues are ordered (see SELECT).

SELECT

SELECT is a LOGICAL FUNCTION of two DOUBLE PRECISION arguments
SELECT must be declared EXTERNAL in the calling subroutine.
If SORT = 'S', SELECT is used to select eigenvalues to sort
to the top left of the Schur form.
If SORT = 'N', SELECT is not referenced.
An eigenvalue WR(j)+sqrt(-1)*WI(j) is selected if
SELECT(WR(j),WI(j)) is true; i.e., if either one of a complex
conjugate pair of eigenvalues is selected, then both complex
eigenvalues are selected.
Note that a selected complex eigenvalue may no longer
satisfy SELECT(WR(j),WI(j)) = .TRUE. after ordering, since
ordering may change the value of complex eigenvalues
(especially if the eigenvalue is ill-conditioned); in this
case INFO is set to N+2 (see INFO below).

N

N is INTEGER
The order of the matrix A. N >= 0.

A

A is DOUBLE PRECISION array, dimension (LDA,N)
On entry, the N-by-N matrix A.
On exit, A has been overwritten by its real Schur form T.

LDA

LDA is INTEGER
The leading dimension of the array A.  LDA >= max(1,N).

SDIM

SDIM is INTEGER
If SORT = 'N', SDIM = 0.
If SORT = 'S', SDIM = number of eigenvalues (after sorting)
               for which SELECT is true. (Complex conjugate
               pairs for which SELECT is true for either
               eigenvalue count as 2.)

WR

WR is DOUBLE PRECISION array, dimension (N)

WI

WI is DOUBLE PRECISION array, dimension (N)
WR and WI contain the real and imaginary parts,
respectively, of the computed eigenvalues in the same order
that they appear on the diagonal of the output Schur form T.
Complex conjugate pairs of eigenvalues will appear
consecutively with the eigenvalue having the positive
imaginary part first.

VS

VS is DOUBLE PRECISION array, dimension (LDVS,N)
If JOBVS = 'V', VS contains the orthogonal matrix Z of Schur
vectors.
If JOBVS = 'N', VS is not referenced.

LDVS

LDVS is INTEGER
The leading dimension of the array VS.  LDVS >= 1; if
JOBVS = 'V', LDVS >= N.

WORK

WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) contains the optimal LWORK.

LWORK

LWORK is INTEGER
The dimension of the array WORK.  LWORK >= max(1,3*N).
For good performance, LWORK must generally be larger.

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.

BWORK

BWORK is LOGICAL array, dimension (N)
Not referenced if SORT = 'N'.

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.
> 0: if INFO = i, and i is
   <= N: the QR algorithm failed to compute all the
         eigenvalues; elements 1:ILO-1 and i+1:N of WR and WI
         contain those eigenvalues which have converged; if
         JOBVS = 'V', VS contains the matrix which reduces A
         to its partially converged Schur form.
   = N+1: the eigenvalues could not be reordered because some
         eigenvalues were too close to separate (the problem
         is very ill-conditioned);
   = N+2: after reordering, roundoff changed values of some
         complex eigenvalues so that leading eigenvalues in
         the Schur form no longer satisfy SELECT=.TRUE.  This
         could also be caused by underflow due to scaling.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2011

Definition at line 216 of file dgees.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

dgees(3) is an alias of dgees.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK