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# zlahqr

```
NAME
ZLAHQR - 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; 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: ZLAHQR 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 W contain those
eigenvalues which have been successfully computed.
```