ZLAHQR2(3)    ScaLAPACK routine of NEC Numeric Library Collection   ZLAHQR2(3)



NAME
       ZLAHQR2  - i an auxiliary routine called by ZHSEQR to update the eigen-
       values and Schur decomposition already computed by ZHSEQR,  by  dealing
       with the Hessenberg submatrix in rows and columns ILO to IHI

SYNOPSIS
       SUBROUTINE ZLAHQR2( 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
       ZLAHQR2 is an auxiliary routine called by ZHSEQR to update  the  eigen-
       values  and  Schur decomposition already computed by ZHSEQR, by dealing
       with the Hessenberg submatrix in rows and columns ILO to IHI. This ver-
       sion of ZLAHQR (not the standard LAPACK version) uses a
         double-shift algorithm (like LAPACK's DLAHQR).
       Unlike the standard LAPACK convention, this does not assume the
         subdiagonal is real, nor does it work to preserve this quality if
         given.


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 transfor-
               mations  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.  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  corre-
               sponding 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 trans-
               formations 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, and on exit Z has been updated; transfor-
               mations 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 success-
               fully computed.

FURTHER DETAILS
       Modified by Mark R. Fahey, June, 2000




ScaLAPACK routine               31 October 2017                     ZLAHQR2(3)