ZLAHQR (3lapack)

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.