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DLAED4(l)					)					DLAED4(l)

NAME
       DLAED4 - subroutine computes the I-th updated eigenvalue of a symmetric rank-one modifica-
       tion to a diagonal matrix whose elements are given in the array d, and that  D(i)  <  D(j)
       for i < j  and that RHO > 0

SYNOPSIS
       SUBROUTINE DLAED4( N, I, D, Z, DELTA, RHO, DLAM, INFO )

	   INTEGER	  I, INFO, N

	   DOUBLE	  PRECISION DLAM, RHO

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

PURPOSE
       This  subroutine computes the I-th updated eigenvalue of a symmetric rank-one modification
       to a diagonal matrix whose elements are given in the array d, and that D(i) < D(j) for i <
       j and that RHO > 0. This is arranged by the calling routine, and is no loss in generality.
       The rank-one modified system is thus

		  diag( D )  +	RHO *  Z * Z_transpose.

       where we assume the Euclidean norm of Z is 1.

       The method consists of approximating the rational functions in  the  secular  equation  by
       simpler interpolating rational functions.

ARGUMENTS
       N      (input) INTEGER
	      The length of all arrays.

       I      (input) INTEGER
	      The index of the eigenvalue to be computed.  1 <= I <= N.

       D      (input) DOUBLE PRECISION array, dimension (N)
	      The original eigenvalues.  It is assumed that they are in order, D(I) < D(J)  for I
	      < J.

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

       DELTA  (output) DOUBLE PRECISION array, dimension (N)
	      If N .ne. 1, DELTA contains (D(j) - lambda_I) in its  j-th component.  If  N  =  1,
	      then  DELTA(1)  =  1.   The vector DELTA contains the information necessary to con-
	      struct 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.

       INFO   (output) INTEGER
	      = 0:  successful exit
	      > 0:  if INFO = 1, the updating process failed.

PARAMETERS
       Logical variable ORGATI (origin-at-i?) is used for distinguishing whether D(i)  or  D(i+1)
       is treated as the origin.

       ORGATI = .true.	  origin at i ORGATI = .false.	 origin at i+1

       Logical	variable  SWTCH3 (switch-for-3-poles?) is for noting if we are working with THREE
       poles!

       MAXIT is the maximum number of iterations allowed for each eigenvalue.

       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 				DLAED4(l)
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