CLAHQR(3) MathKeisan LAPACK routine CLAHQR(3)
NAME
CLAHQR - An auxiliary routine called by CHSEQR to update the eigenval-
ues and Schur decomposition already computed by CHSEQR, by dealing
with the Hessenberg submatrix in rows and columns ILO to IHI
SYNOPSIS
SUBROUTINE CLAHQR( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ, IHIZ, Z,
LDZ, INFO )
INTEGER IHI, IHIZ, ILO, ILOZ, INFO, LDH, LDZ, N
LOGICAL WANTT, WANTZ
COMPLEX H( LDH, * ), W( * ), Z( LDZ, * )
PURPOSE
CLAHQR is an auxiliary routine called by CHSEQR to update the
eigenvalues and Schur decomposition already computed by CHSEQR, 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). 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 INFO is
zero and if WANTT is .TRUE., then H is upper triangular in rows
and columns ILO:IHI. If INFO is zero and if WANTT is .FALSE.,
then the contents of H are unspecified on exit. The output
state of H in case INF is positive is below under the descrip-
tion of INFO.
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 accumulated by CHSEQR, 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
eigenvalues ILO to IHI in a total of 30 iterations per eigen-
value; elements i+1:ihi of W contain those eigenvalues which
have been successfully computed.
If INFO .GT. 0 and WANTT is .FALSE., then on exit, the remain-
ing unconverged eigenvalues are the eigenvalues of the upper
Hessenberg matrix rows and columns ILO thorugh INFO of the
final, output value of H.
If INFO .GT. 0 and WANTT is .TRUE., then on exit (*)
(initial value of H)*U = U*(final value of H) where U is an
orthognal matrix. The final value of H is upper Hessenberg
and triangular in rows and columns INFO+1 through IHI.
If INFO .GT. 0 and WANTZ is .TRUE., then on exit (final value
of Z) = (initial value of Z)*U where U is the orthogonal
matrix in (*) (regardless of the value of WANTT.)
FURTHER DETAILS
02-96 Based on modifications by
David Day, Sandia National Laboratory, USA
12-04 Further modifications by
Ralph Byers, University of Kansas, USA
This is a modified version of CLAHQR from LAPACK version 3.0.
It is (1) more robust against overflow and underflow and
(2) adopts the more conservative Ahues & Tisseur stopping
criterion (LAWN 122, 1997).
LAPACK auxiliary routine (versionNo3v.e1m)ber 2006 CLAHQR(3)