
ZLAHQR(l) ) ZLAHQR(l)
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 decom
position 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,ILO1) = 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 2by2 diagonal blocks in stan
dard 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 diago
nal 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 transforma
tions accumulated by ZHSEQR, 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*(IHIILO+1) iterations; elements i+1:ihi of W contain those eigenval
ues which have been successfully computed.
LAPACK version 3.0 15 June 2000 ZLAHQR(l) 
