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zlaqr1 examples
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Man Page Details
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 Online html documentation available at 
            http://www.netlib.org/lapack/explore-html/ 

 Definition:
 ===========

       SUBROUTINE ZLAQR1( N, H, LDH, S1, S2, V )
 
       .. Scalar Arguments ..
       COMPLEX*16         S1, S2
       INTEGER            LDH, N
       ..
       .. Array Arguments ..
       COMPLEX*16         H( LDH, * ), V( * )
       ..
  

 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.

 Arguments:
 ==========

  [in] N

          N is integer
              Order of the matrix H. N must be either 2 or 3.

  [in] H

          H is COMPLEX*16 array of 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.GE.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 of dimension N
              A scalar multiple of the first column of the
              matrix K in (*).

 Authors:
 ========

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

 November 2011

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

