ZLAQR5, called by ZLAQR0, performs a
    single small-bulge multi-shift QR sweep.

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: Same as KACC22 = 1. This option used to enable exploiting
             the 2-by-2 structure during matrix multiplications, but
             this is no longer supported.

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 >= 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 <= ILOZ <= IHIZ <= 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 >= 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 >= 3.

U

          U is COMPLEX*16 array, dimension (LDU,2*NSHFTS)

LDU

          LDU is INTEGER
             LDU is the leading dimension of U just as declared in the
             in the calling subroutine.  LDU >= 2*NSHFTS.

NV

          NV is INTEGER
             NV is the number of rows in WV agailable for workspace.
             NV >= 1.

WV

          WV is COMPLEX*16 array, dimension (LDWV,2*NSHFTS)

LDWV

          LDWV is INTEGER
             LDWV is the leading dimension of WV as declared in the
             in the calling subroutine.  LDWV >= NV.

NH

          NH is INTEGER
             NH is the number of columns in array WH available for
             workspace. NH >= 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 >= 2*NSHFTS.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Karen Braman and Ralph Byers, Department of Mathematics, University of Kansas, USA

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.