DLASD5  -  subroutine computes the square root of the I-th
       eigenvalue of a positive symmetric  rank-one  modification
       of a 2-by-2 diagonal matrix  diag( D ) * diag( D ) + RHO *
       Z * transpose(Z)


SYNOPSIS

       SUBROUTINE DLASD5( I, D, Z, DELTA, RHO, DSIGMA, WORK )

           INTEGER        I

           DOUBLE         PRECISION DSIGMA, RHO

           DOUBLE         PRECISION D( 2 ), DELTA( 2 ),  WORK(  2
                          ), Z( 2 )


PURPOSE

       This  subroutine  computes  the  square  root  of the I-th
       eigenvalue of a positive symmetric  rank-one  modification
       of  a 2-by-2 diagonal matrix diag( D ) * diag( D ) + RHO *
       Z * transpose(Z) .  The diagonal entries in  the  array  D
       are assumed to satisfy

                  0 <= D(i) < D(j)  for  i < j .

       We  also assume RHO > 0 and that the Euclidean norm of the
       vector Z is one.


ARGUMENTS

       I      (input) INTEGER
              The index of the eigenvalue to be computed.  I =  1
              or I = 2.

       D      (input) DOUBLE PRECISION array, dimension ( 2 )
              The  original  eigenvalues.   We assume 0 <= D(1) <
              D(2).

       Z      (input) DOUBLE PRECISION array, dimension ( 2 )
              The components of the updating vector.

       DELTA  (output) DOUBLE PRECISION array, dimension ( 2 )
              Contains (D(j) - lambda_I) in its  j-th  component.
              The vector DELTA contains the information necessary
              to construct the eigenvectors.

       RHO    (input) DOUBLE PRECISION
              The scalar in the symmetric updating formula.

              DSIGMA  (output)  DOUBLE  PRECISION  The   computed
              lambda_I, the I-th updated eigenvalue.

       WORK   (workspace) DOUBLE PRECISION array, dimension ( 2 )
              WORK  contains  (D(j)  +  sigma_I)  in  its    j-th



FURTHER DETAILS

       Based on contributions by
          Ren-Cang  Li,  Computer Science Division, University of
       California
          at Berkeley, USA


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