ZLAHQR(l) ) ZLAHQR(l)
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
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, * )
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.
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, with any 2-by-2 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
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 eigenval-
ues which have been successfully computed.
LAPACK version 3.0 15 June 2000 ZLAHQR(l)