ZLAHQR(l) ) ZLAHQR(l)NAME
ZLAHQR - i an auxiliary routine called by ZHSEQR to update the eigen‐
values 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 eigenval‐
ues 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 transfor‐
mations 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 corre‐
sponding 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 trans‐
formations 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; transformations are applied only to the submatrix
Z(ILOZ:IHIZ,ILO:IHI). If WANTZ is .FALSE., Z is not refer‐
enced.
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 success‐
fully computed.
LAPACK version 3.0 15 June 2000 ZLAHQR(l)
