
DLAED4(l) ) DLAED4(l)
NAME
DLAED4  subroutine computes the Ith updated eigenvalue of a symmetric rankone 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 Ith updated eigenvalue of a symmetric rankone 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 rankone 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 jth 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 Ith updated eigenvalue.
INFO (output) INTEGER
= 0: successful exit
> 0: if INFO = 1, the updating process failed.
PARAMETERS
Logical variable ORGATI (originati?) 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 (switchfor3poles?) 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 RenCang Li, Computer Science Division, University of California
at Berkeley, USA
LAPACK version 3.0 15 June 2000 DLAED4(l) 
