zlahqr(3F)

NAME
     ZLAHQR - i an auxiliary routine called by ZHSEQR to update the
     eigenvalues and Schur decomposition already computed by ZHSEQR, by
     dealing with the Hessenberg submatrix in rows and columns ILO to IHI

SYNOPSIS
     SUBROUTINE ZLAHQR( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ, IHIZ, Z,
                        LDZ, INFO )

         LOGICAL        WANTT, WANTZ

         INTEGER        IHI, IHIZ, ILO, ILOZ, INFO, LDH, LDZ, N

         COMPLEX*16     H( LDH, * ), W( * ), Z( LDZ, * )

PURPOSE
     ZLAHQR is an auxiliary routine called by ZHSEQR to update the eigenvalues
     and Schur decomposition already computed by ZHSEQR, by dealing with the
     Hessenberg submatrix in rows and columns ILO to IHI.


ARGUMENTS
     WANTT   (input) LOGICAL
             = .TRUE. : the full Schur form T is required;
             = .FALSE.: only eigenvalues are required.

     WANTZ   (input) LOGICAL
             = .TRUE. : the matrix of Schur vectors Z is required;
             = .FALSE.: Schur vectors are not required.

     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 IHI+1:N, and that H(ILO,ILO-1) = 0
             (unless ILO = 1).  ZLAHQR works primarily with the Hessenberg
             submatrix in rows and columns ILO to IHI, but applies
             transformations to all of H if WANTT is .TRUE..  1 <= ILO <=
             max(1,IHI); IHI <= N.

     H       (input/output) COMPLEX*16 array, dimension (LDH,N)
             On entry, the upper Hessenberg matrix H.  On exit, if WANTT is
             .TRUE., H is upper triangular in rows and columns ILO:IHI, with
             any 2-by-2 diagonal blocks in standard form. If WANTT is .FALSE.,
             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*16 array, dimension (N)
             The computed eigenvalues ILO to IHI are stored in the
             corresponding elements of W. If WANTT is .TRUE., 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).

     ILOZ    (input) INTEGER
             IHIZ    (input) INTEGER Specify the rows of Z to which
             transformations must be applied if WANTZ is .TRUE..  1 <= ILOZ <=
             ILO; IHI <= IHIZ <= N.

     Z       (input/output) COMPLEX*16 array, dimension (LDZ,N)
             If WANTZ is .TRUE., on entry Z must contain the current matrix Z
             of transformations accumulated by ZHSEQR, and on exit Z has been
             updated; transformations are applied only to the submatrix
             Z(ILOZ:IHIZ,ILO:IHI).  If WANTZ is .FALSE., Z is not referenced.

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

     INFO    (output) INTEGER
             = 0: successful exit
             > 0: if INFO = i, ZLAHQR failed to compute all the eigenvalues
             ILO to IHI in a total of 30*(IHI-ILO+1) iterations; elements
             i+1:ihi of W contain those eigenvalues which have been
             successfully computed.