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cgeesx-f(3)

cgeesx.f –

Synopsis

Functions/Subroutines

subroutine cgeesx (JOBVS, SORT, SELECT, SENSE, N, A, LDA, SDIM, W, VS, LDVS, RCONDE, RCONDV, WORK, LWORK, RWORK, BWORK, INFO)
CGEESX computes the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors for GE matrices

Function/Subroutine Documentation

subroutine cgeesx (characterJOBVS, characterSORT, logical, externalSELECT, characterSENSE, integerN, complex, dimension( lda, * )A, integerLDA, integerSDIM, complex, dimension( * )W, complex, dimension( ldvs, * )VS, integerLDVS, realRCONDE, realRCONDV, complex, dimension( * )WORK, integerLWORK, real, dimension( * )RWORK, logical, dimension( * )BWORK, integerINFO)

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

Purpose:

 CGEESX 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;
 computes a reciprocal condition number for the average of the
 selected eigenvalues (RCONDE); and computes a reciprocal condition
 number for the right invariant subspace corresponding to the
 selected eigenvalues (RCONDV). The leading columns of Z form an
 orthonormal basis for this invariant subspace.
 For further explanation of the reciprocal condition numbers RCONDE
 and RCONDV, see Section 4.10 of the LAPACK Users' Guide (where
 these quantities are called s and sep respectively).
 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 procedure) 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.
 An eigenvalue W(j) is selected if SELECT(W(j)) is true.

SENSE

 SENSE is CHARACTER*1
 Determines which reciprocal condition numbers are computed.
 = 'N': None are computed;
 = 'E': Computed for average of selected eigenvalues only;
 = 'V': Computed for selected right invariant subspace only;
 = 'B': Computed for both.
 If SENSE = 'E', 'V' or 'B', SORT must equal 'S'.

N

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

A

 A is COMPLEX array, dimension (LDA, N)
 On entry, the N-by-N matrix A.
 On exit, A is 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, and if
 JOBVS = 'V', LDVS >= N.

RCONDE

 RCONDE is REAL
 If SENSE = 'E' or 'B', RCONDE contains the reciprocal
 condition number for the average of the selected eigenvalues.
 Not referenced if SENSE = 'N' or 'V'.

RCONDV

 RCONDV is REAL
 If SENSE = 'V' or 'B', RCONDV contains the reciprocal
 condition number for the selected right invariant subspace.
 Not referenced if SENSE = 'N' or 'E'.

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).
 Also, if SENSE = 'E' or 'V' or 'B', LWORK >= 2*SDIM*(N-SDIM),
 where SDIM is the number of selected eigenvalues computed by
 this routine. Note that 2*SDIM*(N-SDIM) <= N*N/2. Note also
 that an error is only returned if LWORK < max(1,2*N), but if
 SENSE = 'E' or 'V' or 'B' this may not be large enough.
 For good performance, LWORK must generally be larger.
 If LWORK = -1, then a workspace query is assumed; the routine
 only calculates upper bound on the optimal size of the
 array WORK, 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 transformation 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 238 of file cgeesx.f.

Author

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