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## zlaqr1()

subroutine zlaqr1 | ( | integer | n,
|  | complex*16, dimension( ldh, * ) | h,
|  | integer | ldh,
|  | complex*16 | s1,
|  | complex*16 | s2,
|  | complex*16, dimension( * ) | v )

ZLAQR1 sets a scalar multiple of the first column of the product of 2-by-2 or 3-by-3 matrix H and specified shifts.

Download ZLAQR1 + dependencies [TGZ] [ZIP] [TXT]

Purpose:

      !>
      !>      Given a 2-by-2 or 3-by-3 matrix H, ZLAQR1 sets v to a
      !>      scalar multiple of the first column of the product
      !>
      !>      (*)  K = (H - s1*I)*(H - s2*I)
      !>
      !>      scaling to avoid overflows and most underflows.
      !>
      !>      This is useful for starting double implicit shift bulges
      !>      in the QR algorithm.
      !>

Parameters

  [in]

  N

      !>          N is INTEGER
      !>              Order of the matrix H. N must be either 2 or 3.
      !>

  [in]

  H

      !>          H is COMPLEX*16 array, dimension (LDH,N)
      !>              The 2-by-2 or 3-by-3 matrix H in (*).
      !>

  [in]

  LDH

      !>          LDH is INTEGER
      !>              The leading dimension of H as declared in
      !>              the calling procedure.  LDH >= N
      !>

  [in]

  S1

      !>          S1 is COMPLEX*16
      !>

  [in]

  S2

      !>          S2 is COMPLEX*16
      !>
      !>          S1 and S2 are the shifts defining K in (*) above.
      !>

  [out]

  V

      !>          V is COMPLEX*16 array, dimension (N)
      !>              A scalar multiple of the first column of the
      !>              matrix K in (*).
      !>

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