SLAED5 - 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 SLAED5( I, D, Z, DELTA, RHO, DLAM )

           INTEGER        I

           REAL           DLAM, RHO

           REAL           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) REAL array, dimension (2)
              The original eigenvalues.  We assume D(1) < D(2).

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

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

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

       DLAM   (output) REAL
              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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