zlaqr5 (3)  Linux Manuals
NAME
zlaqr5.f 
SYNOPSIS
Functions/Subroutines
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 smallbulge multishift QR sweep.
Function/Subroutine Documentation
subroutine zlaqr5 (logicalWANTT, logicalWANTZ, integerKACC22, integerN, integerKTOP, integerKBOT, integerNSHFTS, complex*16, dimension( * )S, complex*16, dimension( ldh, * )H, integerLDH, integerILOZ, integerIHIZ, complex*16, dimension( ldz, * )Z, integerLDZ, complex*16, dimension( ldv, * )V, integerLDV, complex*16, dimension( ldu, * )U, integerLDU, integerNV, complex*16, dimension( ldwv, * )WV, integerLDWV, integerNH, complex*16, dimension( ldwh, * )WH, integerLDWH)
ZLAQR5 performs a single smallbulge multishift QR sweep.
Purpose:

ZLAQR5, called by ZLAQR0, performs a single smallbulge multishift QR sweep.
Parameters:

WANTT
WANTT is logical scalar WANTT = .true. if the triangular Schur factor is being computed. WANTT is set to .false. otherwise.
WANTZWANTZ is logical scalar WANTZ = .true. if the unitary Schur factor is being computed. WANTZ is set to .false. otherwise.
KACC22KACC22 is integer with value 0, 1, or 2. Specifies the computation mode of farfromdiagonal orthogonal updates. = 0: ZLAQR5 does not accumulate reflections and does not use matrixmatrix multiply to update farfromdiagonal matrix entries. = 1: ZLAQR5 accumulates reflections and uses matrixmatrix multiply to update the farfromdiagonal matrix entries. = 2: ZLAQR5 accumulates reflections, uses matrixmatrix multiply to update the farfromdiagonal matrix entries, and takes advantage of 2by2 block structure during matrix multiplies.
NN is integer scalar N is the order of the Hessenberg matrix H upon which this subroutine operates.
KTOPKTOP is integer scalar
KBOTKBOT 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,KTOP1) = 0 and either KBOT = N or H(KBOT+1,KBOT) = 0.
NSHFTSNSHFTS is integer scalar NSHFTS gives the number of simultaneous shifts. NSHFTS must be positive and even.
SS 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.
HH is COMPLEX*16 array of size (LDH,N) On input H contains a Hessenberg matrix. On output a multishift QR sweep with shifts SR(J)+i*SI(J) is applied to the isolated diagonal block in rows and columns KTOP through KBOT.
LDHLDH is integer scalar LDH is the leading dimension of H just as declared in the calling procedure. LDH.GE.MAX(1,N).
ILOZILOZ is INTEGER
IHIZIHIZ is INTEGER Specify the rows of Z to which transformations must be applied if WANTZ is .TRUE.. 1 .LE. ILOZ .LE. IHIZ .LE. N
ZZ 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.
LDZLDZ is integer scalar LDA is the leading dimension of Z just as declared in the calling procedure. LDZ.GE.N.
VV is COMPLEX*16 array of size (LDV,NSHFTS/2)
LDVLDV is integer scalar LDV is the leading dimension of V as declared in the calling procedure. LDV.GE.3.
UU is COMPLEX*16 array of size (LDU,3*NSHFTS3)
LDULDU is integer scalar LDU is the leading dimension of U just as declared in the in the calling subroutine. LDU.GE.3*NSHFTS3.
NHNH is integer scalar NH is the number of columns in array WH available for workspace. NH.GE.1.
WHWH is COMPLEX*16 array of size (LDWH,NH)
LDWHLDWH is integer scalar Leading dimension of WH just as declared in the calling procedure. LDWH.GE.3*NSHFTS3.
NVNV is integer scalar NV is the number of rows in WV agailable for workspace. NV.GE.1.
WVWV is COMPLEX*16 array of size (LDWV,3*NSHFTS3)
LDWVLDWV 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 MultiShift QR Algorithm Part I: Maintaining Well Focused Shifts, and Level 3 Performance, SIAM Journal of Matrix Analysis, volume 23, pages 929947, 2002.
Definition at line 250 of file zlaqr5.f.
Author
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