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LAPACK version 3.0
dlaed4(3)

PURPOSE
  DLAED4 - 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

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

      INTEGER	     I, INFO, N

      DOUBLE	     PRECISION DLAM, RHO

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

DESCRIPTION
  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 construct 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