cgees-f(3)

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

 A is COMPLEX array, dimension (LDA,N)
 On entry, the N-by-N 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 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 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 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 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 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 197 of file cgees.f.

Author

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