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
SYNOPSIS
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,
* )
PURPOSE
SLAHQR is 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.
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). 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 >=
WR (output) REAL array, dimension (N)
WI (output) REAL 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 eigen
values 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 transformations accumulated by
SHSEQR, and on exit Z has been updated; transfor
mations are applied only to the submatrix
Z(ILOZ:IHIZ,ILO:IHI). If WANTZ is .FALSE., Z is
not referenced.
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) itera
tions; if INFO = i, elements i+1:ihi of WR and WI
contain those eigenvalues which have been success
fully computed.
FURTHER DETAILS
2-96 Based on modifications by
David Day, Sandia National Laboratory, USA
Man(1) output converted with
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