Zlaqr5.f -
subroutine zlaqr5 (WANTT, WANTZ, KACC22, N, KTOP, KBOT, NSHFTS, S, H, LDH, ILOZ, IHIZ, Z, LDZ, V, LDV, U, LDU, NV, WV, LDWV, NH, WH, LDWH)
ZLAQR5 performs a single small-bulge multi-shift QR sweep.
ZLAQR5 performs a single small-bulge multi-shift QR sweep.
Purpose:
ZLAQR5, called by ZLAQR0, performs a
single small-bulge multi-shift QR sweep.
Parameters:
WANTT
WANTT is logical scalar
WANTT = .true. if the triangular Schur factor
is being computed. WANTT is set to .false. otherwise.
WANTZ
WANTZ is logical scalar
WANTZ = .true. if the unitary Schur factor is being
computed. WANTZ is set to .false. otherwise.
KACC22
KACC22 is integer with value 0, 1, or 2.
Specifies the computation mode of far-from-diagonal
orthogonal updates.
= 0: ZLAQR5 does not accumulate reflections and does not
use matrix-matrix multiply to update far-from-diagonal
matrix entries.
= 1: ZLAQR5 accumulates reflections and uses matrix-matrix
multiply to update the far-from-diagonal matrix entries.
= 2: ZLAQR5 accumulates reflections, uses matrix-matrix
multiply to update the far-from-diagonal matrix entries,
and takes advantage of 2-by-2 block structure during
matrix multiplies.
N
N is integer scalar
N is the order of the Hessenberg matrix H upon which this
subroutine operates.
KTOP
KTOP is integer scalar
KBOT
KBOT is integer scalar
These are the first and last rows and columns of an
isolated diagonal block upon which the QR sweep is to be
applied. It is assumed without a check that
either KTOP = 1 or H(KTOP,KTOP-1) = 0
and
either KBOT = N or H(KBOT+1,KBOT) = 0.
NSHFTS
NSHFTS is integer scalar
NSHFTS gives the number of simultaneous shifts. NSHFTS
must be positive and even.
S
S is COMPLEX*16 array of size (NSHFTS)
S contains the shifts of origin that define the multi-
shift QR sweep. On output S may be reordered.
H
H is COMPLEX*16 array of size (LDH,N)
On input H contains a Hessenberg matrix. On output a
multi-shift QR sweep with shifts SR(J)+i*SI(J) is applied
to the isolated diagonal block in rows and columns KTOP
through KBOT.
LDH
LDH is integer scalar
LDH is the leading dimension of H just as declared in the
calling procedure. LDH.GE.MAX(1,N).
ILOZ
ILOZ is INTEGER
IHIZ
IHIZ is INTEGER
Specify the rows of Z to which transformations must be
applied if WANTZ is .TRUE.. 1 .LE. ILOZ .LE. IHIZ .LE. N
Z
Z is COMPLEX*16 array of size (LDZ,IHI)
If WANTZ = .TRUE., then the QR Sweep unitary
similarity transformation is accumulated into
Z(ILOZ:IHIZ,ILO:IHI) from the right.
If WANTZ = .FALSE., then Z is unreferenced.
LDZ
LDZ is integer scalar
LDA is the leading dimension of Z just as declared in
the calling procedure. LDZ.GE.N.
V
V is COMPLEX*16 array of size (LDV,NSHFTS/2)
LDV
LDV is integer scalar
LDV is the leading dimension of V as declared in the
calling procedure. LDV.GE.3.
U
U is COMPLEX*16 array of size
(LDU,3*NSHFTS-3)
LDU
LDU is integer scalar
LDU is the leading dimension of U just as declared in the
in the calling subroutine. LDU.GE.3*NSHFTS-3.
NH
NH is integer scalar
NH is the number of columns in array WH available for
workspace. NH.GE.1.
WH
WH is COMPLEX*16 array of size (LDWH,NH)
LDWH
LDWH is integer scalar
Leading dimension of WH just as declared in the
calling procedure. LDWH.GE.3*NSHFTS-3.
NV
NV is integer scalar
NV is the number of rows in WV agailable for workspace.
NV.GE.1.
WV
WV is COMPLEX*16 array of size
(LDWV,3*NSHFTS-3)
LDWV
LDWV is integer scalar
LDWV is the leading dimension of WV as declared in the
in the calling subroutine. LDWV.GE.NV.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
September 2012
Contributors:
Karen Braman and Ralph Byers, Department of Mathematics, University of Kansas, USA
References:
K. Braman, R. Byers and R. Mathias, The Multi-Shift QR Algorithm Part I: Maintaining Well Focused Shifts, and Level 3 Performance, SIAM Journal of Matrix Analysis, volume 23, pages 929--947, 2002.
Definition at line 250 of file zlaqr5.f.
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