NAME

       zlaqr1.f -

SYNOPSIS

   Functions/Subroutines
       subroutine zlaqr1 (N, H, LDH, S1, S2, 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.

Function/Subroutine Documentation

   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.

       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:
           N

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

           H

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

           LDH

                     LDH is integer
                         The leading dimension of H as declared in
                         the calling procedure.  LDH.GE.N

           S1

                     S1 is COMPLEX*16

           S2

                     S2 is COMPLEX*16

                     S1 and S2 are the shifts defining K in (*) above.

           V

                     V is COMPLEX*16 array of 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.

       Date:
           September 2012

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

Author

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