dlaqr5 (3)

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.

subroutine dlaqr5 (logicalWANTT, logicalWANTZ, integerKACC22, integerN, integerKTOP, integerKBOT, integerNSHFTS, double precision, dimension( * )SR, double precision, dimension( * )SI, double precision, dimension( ldh, * )H, integerLDH, integerILOZ, integerIHIZ, double precision, dimension( ldz, * )Z, integerLDZ, double precision, dimension( ldv, * )V, integerLDV, double precision, dimension( ldu, * )U, integerLDU, integerNV, double precision, dimension( ldwv, * )WV, integerLDWV, integerNH, double precision, dimension( ldwh, * )WH, integerLDWH)

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

Purpose:

    DLAQR5, called by DLAQR0, performs a
    single small-bulge multi-shift QR sweep.

Parameters:

WANTT

          WANTT is logical scalar
             WANTT = .true. if the quasi-triangular Schur factor
             is being computed.  WANTT is set to .false. otherwise.

WANTZ

          WANTZ is logical scalar
             WANTZ = .true. if the orthogonal 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: 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.

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.

SR

          SR is DOUBLE PRECISION array of size (NSHFTS)

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.

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.

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 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.

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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 258 of file dlaqr5.f.

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