!>
!>    SLAHQR is an auxiliary routine called by SHSEQR to update the
!>    eigenvalues and Schur decomposition already computed by SHSEQR, by
!>    dealing with the Hessenberg submatrix in rows and columns ILO to
!>    IHI.
!> 

WANTT

!>          WANTT is LOGICAL
!>          = .TRUE. : the full Schur form T is required;
!>          = .FALSE.: only eigenvalues are required.
!> 

WANTZ

!>          WANTZ is LOGICAL
!>          = .TRUE. : the matrix of Schur vectors Z is required;
!>          = .FALSE.: Schur vectors are not required.
!> 

N

!>          N is INTEGER
!>          The order of the matrix H.  N >= 0.
!> 

ILO

!>          ILO is INTEGER
!> 

IHI

!>          IHI is 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). SLAHQR 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

!>          H is REAL array, dimension (LDH,N)
!>          On entry, the upper Hessenberg matrix H.
!>          On exit, if INFO is zero and 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 INFO is zero
!>          and WANTT is .FALSE., the contents of H are unspecified on
!>          exit.  The output state of H if INFO is nonzero is given
!>          below under the description of INFO.
!> 

LDH

!>          LDH is INTEGER
!>          The leading dimension of the array H. LDH >= max(1,N).
!> 

WR

!>          WR is REAL array, dimension (N)
!> 

WI

!>          WI is REAL 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

!>          ILOZ is INTEGER
!> 

IHIZ

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

Z

!>          Z is REAL array, dimension (LDZ,N)
!>          If WANTZ is .TRUE., on entry Z must contain the current
!>          matrix Z of transformations accumulated by SHSEQR, 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

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

INFO

!>          INFO is INTEGER
!>           = 0:   successful exit
!>           > 0:   If INFO = i, SLAHQR failed to compute all the
!>                  eigenvalues ILO to IHI in a total of 30 iterations
!>                  per eigenvalue; elements i+1:ihi of WR and WI
!>                  contain those eigenvalues which have been
!>                  successfully computed.
!>
!>                  If INFO > 0 and WANTT is .FALSE., then on exit,
!>                  the remaining unconverged eigenvalues are the
!>                  eigenvalues of the upper Hessenberg matrix rows
!>                  and columns ILO through INFO of the final, output
!>                  value of H.
!>
!>                  If INFO > 0 and WANTT is .TRUE., then on exit
!>          (*)       (initial value of H)*U  = U*(final value of H)
!>                  where U is an orthogonal matrix.    The final
!>                  value of H is upper Hessenberg and triangular in
!>                  rows and columns INFO+1 through IHI.
!>
!>                  If INFO > 0 and WANTZ is .TRUE., then on exit
!>                      (final value of Z)  = (initial value of Z)*U
!>                  where U is the orthogonal matrix in (*)
!>                  (regardless of the value of WANTT.)
!> 

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

!>
!>     02-96 Based on modifications by
!>     David Day, Sandia National Laboratory, USA
!>
!>     12-04 Further modifications by
!>     Ralph Byers, University of Kansas, USA
!>     This is a modified version of SLAHQR from LAPACK version 3.0.
!>     It is (1) more robust against overflow and underflow and
!>     (2) adopts the more conservative Ahues & Tisseur stopping
!>     criterion (LAWN 122, 1997).
!>