SLASD5  -  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 SLASD5( I, D, Z, DELTA, RHO, DSIGMA, WORK )

           INTEGER        I

           REAL           DSIGMA, RHO

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

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

       DELTA  (output) REAL 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) REAL
              The scalar in the symmetric updating formula.

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

       WORK   (workspace) REAL array, dimension ( 2 )
              WORK contains (D(j) + sigma_I) in its  j-th  compo­
              nent.

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


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