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dlahqr examples
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Man Page Details
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NAME
       DLAHQR - An auxiliary routine called by DHSEQR to update the  eigenval-
       ues 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 )

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

           LOGICAL        WANTT, WANTZ

           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; 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: 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 computed.

  Further Details
  ===============

  2-96 Based on modifications by
     David Day, Sandia National Laboratory, USA

