DLAHQR(l) ) DLAHQR(l)
DLAHQR - i an auxiliary routine called by DHSEQR to update the eigenvalues and Schur
decomposition already computed by DHSEQR, by dealing with the Hessenberg submatrix in rows
and columns ILO to IHI
SUBROUTINE DLAHQR( WANTT, WANTZ, N, ILO, IHI, H, LDH, WR, WI, ILOZ, IHIZ, Z, LDZ, INFO )
LOGICAL WANTT, WANTZ
INTEGER IHI, IHIZ, ILO, ILOZ, INFO, LDH, LDZ, N
DOUBLE PRECISION H( LDH, * ), WI( * ), WR( * ), Z( LDZ, * )
DLAHQR is an auxiliary routine called by DHSEQR to update the eigenvalues and Schur decom-
position already computed by DHSEQR, 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 quasi-triangular in
rows and columns IHI+1:N, and that H(ILO,ILO-1) = 0 (unless ILO = 1). DLAHQR 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) DOUBLE PRECISION array, dimension (LDH,N)
On entry, the upper Hessenberg matrix H. On exit, if WANTT is .TRUE., H is upper
quasi-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).
WR (output) DOUBLE PRECISION array, dimension (N)
WI (output) DOUBLE PRECISION array, dimension (N) The real and imaginary
parts, respectively, of the computed eigenvalues ILO to IHI are stored in the cor-
responding elements of WR and WI. If two eigenvalues are computed as a complex
conjugate pair, they are stored in consecutive elements of WR and WI, say the i-th
and (i+1)th, with WI(i) > 0 and WI(i+1) < 0. If WANTT is .TRUE., the eigenvalues
are stored in the same order as on the diagonal of the Schur form returned in H,
with WR(i) = H(i,i), and, if H(i:i+1,i:i+1) is a 2-by-2 diagonal block, WI(i) =
sqrt(H(i+1,i)*H(i,i+1)) and WI(i+1) = -WI(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) DOUBLE PRECISION array, dimension (LDZ,N)
If WANTZ is .TRUE., on entry Z must contain the current matrix Z of transforma-
tions accumulated by DHSEQR, 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: DLAHQR failed to compute all the eigenvalues ILO to IHI in a total of
30*(IHI-ILO+1) iterations; if INFO = i, elements i+1:ihi of WR and WI contain
those eigenvalues which have been successfully computed.
2-96 Based on modifications by
David Day, Sandia National Laboratory, USA
LAPACK version 3.0 15 June 2000 DLAHQR(l)