subroutine slaqr5 (WANTT, WANTZ, KACC22, N, KTOP, KBOT, NSHFTS, SR, SI, H, LDH, ILOZ, IHIZ, Z, LDZ, V, LDV, U, LDU, NV, WV, LDWV, NH, WH, LDWH)
SLAQR5 performs a single small-bulge multi-shift QR sweep.
SLAQR5 performs a single small-bulge multi-shift QR sweep.
Purpose:
SLAQR5, called by SLAQR0, performs a
single small-bulge multi-shift QR sweep.
Parameters:
WANTT is LOGICAL
WANTT = .true. if the quasi-triangular Schur factor
is being computed. WANTT is set to .false. otherwise.
WANTZ
WANTZ is LOGICAL
WANTZ = .true. if the orthogonal 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: SLAQR5 does not accumulate reflections and does not
use matrix-matrix multiply to update far-from-diagonal
matrix entries.
= 1: SLAQR5 accumulates reflections and uses matrix-matrix
multiply to update the far-from-diagonal matrix entries.
= 2: SLAQR5 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
N is the order of the Hessenberg matrix H upon which this
subroutine operates.
KTOP
KTOP is INTEGER
KBOT
KBOT is INTEGER
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
NSHFTS gives the number of simultaneous shifts. NSHFTS
must be positive and even.
SR
SR is REAL array, dimension (NSHFTS)
SI
SI is REAL array, dimension (NSHFTS)
SR contains the real parts and SI contains the imaginary
parts of the NSHFTS shifts of origin that define the
multi-shift QR sweep. On output SR and SI may be
reordered.
H
H is REAL array, dimension (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
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 REAL array, dimension (LDZ,IHIZ)
If WANTZ = .TRUE., then the QR Sweep orthogonal
similarity transformation is accumulated into
Z(ILOZ:IHIZ,ILOZ:IHIZ) from the right.
If WANTZ = .FALSE., then Z is unreferenced.
LDZ
LDZ is INTEGER
LDA is the leading dimension of Z just as declared in
the calling procedure. LDZ.GE.N.
V
V is REAL array, dimension (LDV,NSHFTS/2)
LDV
LDV is INTEGER
LDV is the leading dimension of V as declared in the
calling procedure. LDV.GE.3.
U
U is REAL array, dimension (LDU,3*NSHFTS-3)
LDU
LDU is INTEGER
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
NH is the number of columns in array WH available for
workspace. NH.GE.1.
WH
WH is REAL array, dimension (LDWH,NH)
LDWH
LDWH is INTEGER
Leading dimension of WH just as declared in the
calling procedure. LDWH.GE.3*NSHFTS-3.
NV
NV is INTEGER
NV is the number of rows in WV agailable for workspace.
NV.GE.1.
WV
WV is REAL array, dimension (LDWV,3*NSHFTS-3)
LDWV
LDWV is INTEGER
LDWV is the leading dimension of WV as declared in the
in the calling subroutine. LDWV.GE.NV.
Author:
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
Contributors:
References:
Definition at line 259 of file slaqr5.f.
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