
DLASD4(l) ) DLASD4(l)
NAME
DLASD4  subroutine computes the square root of the Ith updated eigenvalue of a positive
symmetric rankone modification to a positive diagonal matrix whose entries are given as
the squares of the corresponding entries in the array d, and that 0 <= D(i) < D(j) for i
< j and that RHO > 0
SYNOPSIS
SUBROUTINE DLASD4( N, I, D, Z, DELTA, RHO, SIGMA, WORK, INFO )
INTEGER I, INFO, N
DOUBLE PRECISION RHO, SIGMA
DOUBLE PRECISION D( * ), DELTA( * ), WORK( * ), Z( * )
PURPOSE
This subroutine computes the square root of the Ith updated eigenvalue of a positive sym
metric rankone modification to a positive diagonal matrix whose entries are given as the
squares of the corresponding entries in the array d, and that 0 <= 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 ) * 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, 0 <= 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)  sigma_I) in its jth component. If N = 1,
then DELTA(1) = 1. The vector DELTA contains the information necessary to con
struct the (singular) eigenvectors.
RHO (input) DOUBLE PRECISION
The scalar in the symmetric updating formula.
SIGMA (output) DOUBLE PRECISION
The computed lambda_I, the Ith updated eigenvalue.
WORK (workspace) DOUBLE PRECISION array, dimension ( N )
If N .ne. 1, WORK contains (D(j) + sigma_I) in its jth component. If N = 1, then
WORK( 1 ) = 1.
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 DLASD4(l) 
