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DLASD5(l)					)					DLASD5(l)

NAME
       DLASD5  - subroutine computes the square root of the I-th eigenvalue of a positive symmet-
       ric 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 * trans-
       pose(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	eigenval-
	      ue.

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

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

LAPACK version 3.0			   15 June 2000 				DLASD5(l)
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