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.

          I is INTEGER
         The index of the eigenvalue to be computed.  I = 1 or I = 2.

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

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

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

          RHO is DOUBLE PRECISION
         The scalar in the symmetric updating formula.

          DSIGMA is DOUBLE PRECISION
         The computed sigma_I, the I-th updated eigenvalue.

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