DLAHQR(l) ) DLAHQR(l)NAME
DLAHQR - i an auxiliary routine called by DHSEQR to update the eigen‐
values and Schur decomposition already computed by DHSEQR, by dealing
with the Hessenberg submatrix in rows and columns ILO to IHI
SYNOPSIS
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, * )
PURPOSE
DLAHQR is an auxiliary routine called by DHSEQR to update the eigenval‐
ues and Schur decomposition already computed by DHSEQR, 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
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 corresponding 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 trans‐
formations 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 transformations 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 refer‐
enced.
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.
FURTHER DETAILS
2-96 Based on modifications by
David Day, Sandia National Laboratory, USA
LAPACK version 3.0 15 June 2000 DLAHQR(l)
