CLAHQR2(l) ) CLAHQR2(l)NAME
CLAHQR2 - i an auxiliary routine called by CHSEQR to update the eigen‐
values and Schur decomposition already computed by CHSEQR, by dealing
with the Hessenberg submatrix in rows and columns ILO to IHI
SYNOPSIS
SUBROUTINE CLAHQR2( 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 H( LDH, * ), W( * ), Z( LDZ, * )
PURPOSE
CLAHQR2 is an auxiliary routine called by CHSEQR to update the eigen‐
values and Schur decomposition already computed by CHSEQR, by dealing
with the Hessenberg submatrix in rows and columns ILO to IHI. This ver‐
sion of CLAHQR (not the standard LAPACK version) uses a
double-shift algorithm (like LAPACK's SLAHQR).
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). CLAHQR 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 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 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 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; transfor‐
mations 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, CLAHQR 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.
FURTHER DETAILS
Modified by Mark R. Fahey, June, 2000
ScaLAPACK version 1.7 13 August 2001 CLAHQR2(l)
