SLAHQR(l) ) SLAHQR(l)
SLAHQR - i an auxiliary routine called by SHSEQR to update the eigenvalues and Schur
decomposition already computed by SHSEQR, by dealing with the Hessenberg submatrix in rows
and columns ILO to IHI
SUBROUTINE SLAHQR( 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
REAL H( LDH, * ), WI( * ), WR( * ), Z( LDZ, * )
SLAHQR is an auxiliary routine called by SHSEQR to update the eigenvalues and Schur decom-
position already computed by SHSEQR, 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). SLAHQR 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) REAL 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) REAL array, dimension (N)
WI (output) REAL array, dimension (N) The real and imaginary parts, respec-
tively, 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 transformations must be
applied if WANTZ is .TRUE.. 1 <= ILOZ <= ILO; IHI <= IHIZ <= N.
Z (input/output) REAL array, dimension (LDZ,N)
If WANTZ is .TRUE., on entry Z must contain the current matrix Z of transforma-
tions accumulated by SHSEQR, 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: SLAHQR 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 SLAHQR(l)