 LAPACK  3.4.2 LAPACK: Linear Algebra PACKage
dlaqr5.f File Reference

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## Functions/Subroutines

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.

## Function/Subroutine Documentation

 subroutine dlaqr5 ( logical WANTT, logical WANTZ, integer KACC22, integer N, integer KTOP, integer KBOT, integer NSHFTS, double precision, dimension( * ) SR, double precision, dimension( * ) SI, double precision, dimension( ldh, * ) H, integer LDH, integer ILOZ, integer IHIZ, double precision, dimension( ldz, * ) Z, integer LDZ, double precision, dimension( ldv, * ) V, integer LDV, double precision, dimension( ldu, * ) U, integer LDU, integer NV, double precision, dimension( ldwv, * ) WV, integer LDWV, integer NH, double precision, dimension( ldwh, * ) WH, integer LDWH )

DLAQR5 performs a single small-bulge multi-shift QR sweep.

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Purpose:
```    DLAQR5, called by DLAQR0, performs a
single small-bulge multi-shift QR sweep.```
Parameters:
 [in] WANTT ``` WANTT is logical scalar WANTT = .true. if the quasi-triangular Schur factor is being computed. WANTT is set to .false. otherwise.``` [in] WANTZ ``` WANTZ is logical scalar WANTZ = .true. if the orthogonal 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: 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.``` [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] SR ` SR is DOUBLE PRECISION array of size (NSHFTS)` [in,out] SI ``` SI is DOUBLE PRECISION array of size (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.``` [in,out] H ``` H is DOUBLE PRECISION 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 DOUBLE PRECISION array of size (LDZ,IHI) If WANTZ = .TRUE., then the QR Sweep orthogonal 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 258 of file dlaqr5.f.

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