Loading...
Searching...
No Matches

## claqr5()

subroutine claqr5 | ( | logical | wantt,
|  | logical | wantz,
|  | integer | kacc22,
|  | integer | n,
|  | integer | ktop,
|  | integer | kbot,
|  | integer | nshfts,
|  | complex, dimension( * ) | s,
|  | complex, dimension( ldh, * ) | h,
|  | integer | ldh,
|  | integer | iloz,
|  | integer | ihiz,
|  | complex, dimension( ldz, * ) | z,
|  | integer | ldz,
|  | complex, dimension( ldv, * ) | v,
|  | integer | ldv,
|  | complex, dimension( ldu, * ) | u,
|  | integer | ldu,
|  | integer | nv,
|  | complex, dimension( ldwv, * ) | wv,
|  | integer | ldwv,
|  | integer | nh,
|  | complex, dimension( ldwh, * ) | wh,
|  | integer | ldwh )

CLAQR5 performs a single small-bulge multi-shift QR sweep.

Download CLAQR5 + dependencies [TGZ] [ZIP] [TXT]

Purpose:

      !>
      !>    CLAQR5 called by CLAQR0 performs a
      !>    single small-bulge multi-shift QR sweep.
      !>

Parameters

  [in]

  WANTT

      !>          WANTT is LOGICAL
      !>             WANTT = .true. if the triangular Schur factor
      !>             is being computed.  WANTT is set to .false. otherwise.
      !>

  [in]

  WANTZ

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

  [in]

  N

      !>          N is INTEGER
      !>             N is the order of the Hessenberg matrix H upon which this
      !>             subroutine operates.
      !>

  [in]

  KTOP

      !>          KTOP is INTEGER
      !>

  [in]

  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.
      !>

  [in]

  NSHFTS

      !>          NSHFTS is INTEGER
      !>             NSHFTS gives the number of simultaneous shifts.  NSHFTS
      !>             must be positive and even.
      !>

  [in,out]

  S

      !>          S is COMPLEX array, dimension (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 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.
      !>

  [in]

  LDH

      !>          LDH is INTEGER
      !>             LDH is the leading dimension of H just as declared in the
      !>             calling procedure.  LDH >= 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 <= ILOZ <= IHIZ <= N
      !>

  [in,out]

  Z

      !>          Z is COMPLEX 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.
      !>

  [in]

  LDZ

      !>          LDZ is INTEGER
      !>             LDA is the leading dimension of Z just as declared in
      !>             the calling procedure. LDZ >= N.
      !>

  [out]

  V

      !>          V is COMPLEX array, dimension (LDV,NSHFTS/2)
      !>

  [in]

  LDV

      !>          LDV is INTEGER
      !>             LDV is the leading dimension of V as declared in the
      !>             calling procedure.  LDV >= 3.
      !>

  [out]

  U

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

  [in]

  LDU

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

  [in]

  NV

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

  [out]

  WV

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

  [in]

  LDWV

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

  [in]

  NH

      !>          NH is INTEGER
      !>             NH is the number of columns in array WH available for
      !>             workspace. NH >= 1.
      !>

  [out]

  WH

      !>          WH is COMPLEX array, dimension (LDWH,NH)
      !>

  [in]

  LDWH

      !>          LDWH is INTEGER
      !>             Leading dimension of WH just as declared in the
      !>             calling procedure.  LDWH >= 2*NSHFTS.
      !>

Author
  Univ. of Tennessee
  Univ. of California Berkeley
  Univ. of Colorado Denver
  NAG Ltd.

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

Lars Karlsson, Daniel Kressner, and Bruno Lang

Thijs Steel, Department of Computer science, KU Leuven, Belgium

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.

Lars Karlsson, Daniel Kressner, and Bruno Lang, Optimally packed chains of bulges in multishift QR algorithms. ACM Trans. Math. Softw. 40, 2, Article 12 (February 2014).