SLAED4(l)								 )								 SLAED4(l)

NAME

       SLAED4 - 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

SYNOPSIS

       SUBROUTINE SLAED4( N, I, D, Z, DELTA, RHO, DLAM, INFO )

	   INTEGER	  I, INFO, N

	   REAL 	  DLAM, RHO

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

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

       DELTA  (output) REAL 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 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.

       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 							 SLAED4(l)