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dlahqr

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

 SYNOPSIS
      SUBROUTINE DLAHQR( WANTT, WANTZ, N, ILO, IHI, H, LDH, WR,
                         WI, ILOZ, IHIZ, Z, LDZ, INFO )

          LOGICAL        WANTT, WANTZ

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

          DOUBLE         PRECISION H( LDH, * ), WI( * ), WR( * ),
                         Z( LDZ, * )

 PURPOSE
      DLAHQR is an auxiliary routine called by DHSEQR to update
      the eigenvalues and Schur decomposition already computed by
      DHSEQR, 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 quasi-triangular in rows and columns
              IHI+1:N, and that H(ILO,ILO-1) = 0 (unless ILO = 1).
              DLAHQR 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) DOUBLE PRECISION array, dimension (LDH,N)
              On entry, the upper Hessenberg matrix H.  On exit,
              if WANTT is .TRUE., H is upper quasi-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).

      WR      (output) DOUBLE PRECISION array, dimension (N)
              WI      (output) DOUBLE PRECISION array, dimension
              (N) The real and imaginary parts, respectively, of
              the computed eigenvalues ILO to IHI are stored in
              the corresponding elements of WR and WI. If two
              eigenvalues are computed as a complex conjugate
              pair, they are stored in consecutive elements of WR
              and WI, say the i-th and (i+1)th, with WI(i) > 0 and
              WI(i+1) < 0. If WANTT is .TRUE., the eigenvalues are
              stored in the same order as on the diagonal of the
              Schur form returned in H, with WR(i) = H(i,i), and,
              if H(i:i+1,i:i+1) is a 2-by-2 diagonal block, WI(i)
              = sqrt(H(i+1,i)*H(i,i+1)) and WI(i+1) = -WI(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) DOUBLE PRECISION array, dimension (LDZ,N)
              If WANTZ is .TRUE., on entry Z must contain the
              current matrix Z of transformations accumulated by
              DHSEQR, and on exit Z has been updated; transforma-
              tions 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: DLAHQR failed to compute all the eigenvalues
              ILO to IHI in a total of 30*(IHI-ILO+1) iterations;
              if INFO = i, elements i+1:ihi of WR and WI contain
              those eigenvalues which have been successfully com-
              puted.