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# NAME

ZLAHQR2 - 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 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 eigenvalues and Schur decomposition already computed by ZHSEQR, by dealing with the Hessenberg submatrix in rows and columns ILO to IHI. This version 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 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. 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, 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: 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 successfully computed.

# FURTHER DETAILS

Modified by Mark R. Fahey, June, 2000

 13 August 2001 ScaLAPACK version 1.7

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