chseqr(3F)

NAME
     CHSEQR - compute the eigenvalues of a complex upper Hessenberg matrix H,
     and, optionally, the matrices T and Z from the Schur decomposition H = Z
     T Z**H, where T is an upper triangular matrix (the Schur form), and Z is
     the unitary matrix of Schur vectors

SYNOPSIS
     SUBROUTINE CHSEQR( JOB, COMPZ, N, ILO, IHI, H, LDH, W, Z, LDZ, WORK,
                        LWORK, INFO )

         CHARACTER      COMPZ, JOB

         INTEGER        IHI, ILO, INFO, LDH, LDZ, LWORK, N

         COMPLEX        H( LDH, * ), W( * ), WORK( * ), Z( LDZ, * )

PURPOSE
     CHSEQR computes the eigenvalues of a complex upper Hessenberg matrix H,
     and, optionally, the matrices T and Z from the Schur decomposition H = Z
     T Z**H, where T is an upper triangular matrix (the Schur form), and Z is
     the unitary matrix of Schur vectors.

     Optionally Z may be postmultiplied into an input unitary matrix Q, so
     that this routine can give the Schur factorization of a matrix A which
     has been reduced to the Hessenberg form H by the unitary matrix Q:  A =
     Q*H*Q**H = (QZ)*T*(QZ)**H.


ARGUMENTS
     JOB     (input) CHARACTER*1
             = 'E': compute eigenvalues only;
             = 'S': compute eigenvalues and the Schur form T.

     COMPZ   (input) CHARACTER*1
             = 'N': no Schur vectors are computed;
             = 'I': Z is initialized to the unit matrix and the matrix Z of
             Schur vectors of H is returned; = 'V': Z must contain an unitary
             matrix Q on entry, and the product Q*Z is returned.

     N       (input) INTEGER
             The order of the matrix H.  N >= 0.

     ILO     (input) INTEGER
             IHI     (input) INTEGER It is assumed that H is already upper
             triangular in rows and columns 1:ILO-1 and IHI+1:N. ILO and IHI
             are normally set by a previous call to CGEBAL, and then passed to
             CGEHRD when the matrix output by CGEBAL is reduced to Hessenberg
             form. Otherwise ILO and IHI should be set to 1 and N
             respectively.  1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0,
             if N=0.
     H       (input/output) COMPLEX array, dimension (LDH,N)
             On entry, the upper Hessenberg matrix H.  On exit, if JOB = 'S',
             H contains the upper triangular matrix T from the Schur
             decomposition (the Schur form). If JOB = 'E', the contents of H
             are unspecified on exit.

     LDH     (input) INTEGER
             The leading dimension of the array H. LDH >= max(1,N).

     W       (output) COMPLEX array, dimension (N)
             The computed eigenvalues. If JOB = 'S', the eigenvalues are
             stored in the same order as on the diagonal of the Schur form
             returned in H, with W(i) = H(i,i).

     Z       (input/output) COMPLEX array, dimension (LDZ,N)
             If COMPZ = 'N': Z is not referenced.
             If COMPZ = 'I': on entry, Z need not be set, and on exit, Z
             contains the unitary matrix Z of the Schur vectors of H.  If
             COMPZ = 'V': on entry Z must contain an N-by-N matrix Q, which is
             assumed to be equal to the unit matrix except for the submatrix
             Z(ILO:IHI,ILO:IHI); on exit Z contains Q*Z.  Normally Q is the
             unitary matrix generated by CUNGHR after the call to CGEHRD which
             formed the Hessenberg matrix H.

     LDZ     (input) INTEGER
             The leading dimension of the array Z.  LDZ >= max(1,N) if COMPZ =
             'I' or 'V'; LDZ >= 1 otherwise.

     WORK    (workspace) COMPLEX array, dimension (N)

     LWORK   (input) INTEGER
             This argument is currently redundant.

     INFO    (output) INTEGER
             = 0:  successful exit
             < 0:  if INFO = -i, the i-th argument had an illegal value
             > 0:  if INFO = i, CHSEQR failed to compute all the eigenvalues
             in a total of 30*(IHI-ILO+1) iterations; elements 1:ilo-1 and
             i+1:n of W contain those eigenvalues which have been successfully
             computed.