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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.
```