zlaqr5.f - Online Linux Manual PageSection : 3
Updated : Tue Nov 14 2017
Source : Version 3.8.0
Note : LAPACK
NAMEzlaqr5.f
SYNOPSIS
Functions/Subroutinessubroutine 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​.
Function/Subroutine Documentation
subroutine zlaqr5 (logical WANTT, logical WANTZ, integer KACC22, integer N, integer KTOP, integer KBOT, integer NSHFTS, complex*16, dimension( * ) S, complex*16, dimension( ldh, * ) H, integer LDH, integer ILOZ, integer IHIZ, complex*16, dimension( ldz, * ) Z, integer LDZ, complex*16, dimension( ldv, * ) V, integer LDV, complex*16, dimension( ldu, * ) U, integer LDU, integer NV, complex*16, dimension( ldwv, * ) WV, integer LDWV, integer NH, complex*16, dimension( ldwh, * ) WH, integer LDWH)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 WANTT = .true. if the triangular Schur factor is being computed. WANTT is set to .false. otherwise.
WANTZ WANTZ is LOGICAL 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 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.
S S is COMPLEX*16 array, dimension (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, 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 COMPLEX*16 array, dimension (LDZ,IHIZ) If WANTZ = .TRUE., then the QR Sweep unitary 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 COMPLEX*16 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 COMPLEX*16 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 COMPLEX*16 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 COMPLEX*16 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 Tennessee Univ​. of California Berkeley Univ​. of Colorado Denver NAG Ltd​. Date: June 2016 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 251 of file zlaqr5​.f​.
AuthorGenerated automatically by Doxygen for LAPACK from the source code​. 0
Johanes Gumabo
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