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Benchmark Shows Scalability of Aleri’s CEP Technology Across Multi-Core Architecture
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claqr5.f(3) LAPACK claqr5.f(3) NAME
claqr5.f - SYNOPSIS
Functions/Subroutines subroutine claqr5 (WANTT, WANTZ, KACC22, N, KTOP, KBOT, NSHFTS, S, H, LDH, ILOZ, IHIZ, Z, LDZ, V, LDV, U, LDU, NV, WV, LDWV, NH, WH, LDWH) CLAQR5 performs a single small-bulge multi-shift QR sweep. Function/Subroutine Documentation subroutine claqr5 (logicalWANTT, logicalWANTZ, integerKACC22, integerN, integerKTOP, integerKBOT, integerNSHFTS, complex, dimension( * )S, complex, dimension( ldh, * )H, integerLDH, integerILOZ, integerIHIZ, complex, dimension( ldz, * )Z, integerLDZ, complex, dimension( ldv, * )V, integerLDV, complex, dimension( ldu, * )U, integerLDU, integerNV, complex, dimension( ldwv, * )WV, integerLDWV, integerNH, complex, dimension( ldwh, * )WH, integerLDWH) CLAQR5 performs a single small-bulge multi-shift QR sweep. Purpose: CLAQR5 called by CLAQR0 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: CLAQR5 does not accumulate reflections and does not use matrix-matrix multiply to update far-from-diagonal matrix entries. = 1: CLAQR5 accumulates reflections and uses matrix-matrix multiply to update the far-from-diagonal matrix entries. = 2: CLAQR5 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 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 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 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 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 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 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 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 claqr5.f. Author Generated automatically by Doxygen for LAPACK from the source code. Version 3.4.2 Tue Sep 25 2012 claqr5.f(3)
