
cgees.f(3) LAPACK cgees.f(3)
NAME
cgees.f 
SYNOPSIS
Functions/Subroutines
subroutine cgees (JOBVS, SORT, SELECT, N, A, LDA, SDIM, W, VS, LDVS, WORK, LWORK, RWORK,
BWORK, INFO)
CGEES computes the eigenvalues, the Schur form, and, optionally, the matrix of Schur
vectors for GE matrices
Function/Subroutine Documentation
subroutine cgees (characterJOBVS, characterSORT, logical, externalSELECT, integerN, complex,
dimension( lda, * )A, integerLDA, integerSDIM, complex, dimension( * )W, complex,
dimension( ldvs, * )VS, integerLDVS, complex, dimension( * )WORK, integerLWORK, real,
dimension( * )RWORK, logical, dimension( * )BWORK, integerINFO)
CGEES computes the eigenvalues, the Schur form, and, optionally, the matrix of Schur
vectors for GE matrices
Purpose:
CGEES computes for an NbyN complex nonsymmetric matrix A, the
eigenvalues, the 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
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 complex matrix is in Schur form if it is upper triangular.
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 one COMPLEX argument
SELECT must be declared EXTERNAL in the calling subroutine.
If SORT = 'S', SELECT is used to select eigenvalues to order
to the top left of the Schur form.
IF SORT = 'N', SELECT is not referenced.
The eigenvalue W(j) is selected if SELECT(W(j)) is true.
N
N is INTEGER
The order of the matrix A. N >= 0.
A
A is COMPLEX array, dimension (LDA,N)
On entry, the NbyN matrix A.
On exit, A has been overwritten by its 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 for which
SELECT is true.
W
W is COMPLEX array, dimension (N)
W contains the computed eigenvalues, in the same order that
they appear on the diagonal of the output Schur form T.
VS
VS is COMPLEX array, dimension (LDVS,N)
If JOBVS = 'V', VS contains the unitary 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 COMPLEX array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK
LWORK is INTEGER
The dimension of the array WORK. LWORK >= max(1,2*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.
RWORK
RWORK is REAL array, dimension (N)
BWORK
BWORK is LOGICAL array, dimension (N)
Not referenced if SORT = 'N'.
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = i, the ith argument had an illegal value.
> 0: if INFO = i, and i is
<= N: the QR algorithm failed to compute all the
eigenvalues; elements 1:ILO1 and i+1:N of W
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 illconditioned);
= 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 197 of file cgees.f.
Author
Generated automatically by Doxygen for LAPACK from the source code.
Version 3.4.2 Tue Sep 25 2012 cgees.f(3) 
