subroutine dlaqr5 (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)
DLAQR5 performs a single small-bulge multi-shift QR sweep.
DLAQR5 performs a single small-bulge multi-shift QR sweep.
Purpose:
DLAQR5, called by DLAQR0, 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: DLAQR5 does not accumulate reflections and does not use matrix-matrix multiply to update far-from-diagonal matrix entries. = 1: DLAQR5 accumulates reflections and uses matrix-matrix multiply to update the far-from-diagonal matrix entries. = 2: DLAQR5 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 DOUBLE PRECISION array, dimension (NSHFTS)
SI
SI is DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 dlaqr5.f.
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