LAPACK  3.4.2 LAPACK: Linear Algebra PACKage
zlaqr5.f File Reference

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## 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 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:
 [in] WANTT ``` WANTT is logical scalar WANTT = .true. if the triangular Schur factor is being computed. WANTT is set to .false. otherwise.``` [in] WANTZ ``` WANTZ is logical scalar WANTZ = .true. if the unitary Schur factor is being computed. WANTZ is set to .false. otherwise.``` [in] 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.``` [in] N ``` N is integer scalar N is the order of the Hessenberg matrix H upon which this subroutine operates.``` [in] KTOP ` KTOP is integer scalar` [in] 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.``` [in] NSHFTS ``` NSHFTS is integer scalar NSHFTS gives the number of simultaneous shifts. NSHFTS must be positive and even.``` [in,out] S ``` S 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.``` [in,out] H ``` H is COMPLEX*16 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.``` [in] LDH ``` LDH is integer scalar LDH is the leading dimension of H just as declared in the calling procedure. LDH.GE.MAX(1,N).``` [in] ILOZ ` ILOZ is INTEGER` [in] 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``` [in,out] Z ``` Z 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.``` [in] LDZ ``` LDZ is integer scalar LDA is the leading dimension of Z just as declared in the calling procedure. LDZ.GE.N.``` [out] V ` V is COMPLEX*16 array of size (LDV,NSHFTS/2)` [in] LDV ``` LDV is integer scalar LDV is the leading dimension of V as declared in the calling procedure. LDV.GE.3.``` [out] U ``` U is COMPLEX*16 array of size (LDU,3*NSHFTS-3)``` [in] 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.``` [in] NH ``` NH is integer scalar NH is the number of columns in array WH available for workspace. NH.GE.1.``` [out] WH ` WH is COMPLEX*16 array of size (LDWH,NH)` [in] LDWH ``` LDWH is integer scalar Leading dimension of WH just as declared in the calling procedure. LDWH.GE.3*NSHFTS-3.``` [in] NV ``` NV is integer scalar NV is the number of rows in WV agailable for workspace. NV.GE.1.``` [out] WV ``` WV is COMPLEX*16 array of size (LDWV,3*NSHFTS-3)``` [in] LDWV ``` LDWV is integer scalar LDWV is the leading dimension of WV as declared in the in the calling subroutine. LDWV.GE.NV.```
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 zlaqr5.f.

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