DLAED5 - subroutine computes the I-th eigenvalue of a sym­
       metric rank-one modification of a 2-by-2  diagonal  matrix
       diag( D ) + RHO * Z * transpose(Z)


SYNOPSIS

       SUBROUTINE DLAED5( I, D, Z, DELTA, RHO, DLAM )

           INTEGER        I

           DOUBLE         PRECISION DLAM, RHO

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


PURPOSE

       This  subroutine computes the I-th eigenvalue of a symmet­
       ric rank-one modification  of  a  2-by-2  diagonal  matrix
       diag(  D  )  + RHO * Z * transpose(Z) .  The diagonal ele­
       ments in the array D are assumed to satisfy

                  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 D(1) < D(2).

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

       DELTA  (output) DOUBLE PRECISION array, dimension (2)
              The vector DELTA contains the information necessary
              to construct the eigenvectors.

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

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


FURTHER DETAILS

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


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