zgeesx.f (3) - Linux Manuals

NAME

zgeesx.f -

SYNOPSIS

Functions/Subroutines

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

Function/Subroutine Documentation

subroutine zgeesx (characterJOBVS, characterSORT, logical, externalSELECT, characterSENSE, integerN, complex*16, dimension( lda, * )A, integerLDA, integerSDIM, complex*16, dimension( * )W, complex*16, dimension( ldvs, * )VS, integerLDVS, double precisionRCONDE, double precisionRCONDV, complex*16, dimension( * )WORK, integerLWORK, double precision, dimension( * )RWORK, logical, dimension( * )BWORK, integerINFO)

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

Purpose:

 ZGEESX 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*16 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*16 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*16 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*16 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 DOUBLE PRECISION
          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 DOUBLE PRECISION
          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*16 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 DOUBLE PRECISION 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 zgeesx.f.

Author

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