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 (integerN, complex*16, dimension( ldh, * )H, integerLDH, complex*16S1, complex*16S2,
       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

       Definition at line 108 of file zlaqr1.f.

Author

       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2                                    Wed Feb 26 2014                                     zlaqr1.f(3)