DLAED4(l) ) DLAED4(l)NAME
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
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 sec‐
ular 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 com‐
ponent. 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, Uni‐
versity of California at Berkeley, USA
LAPACK version 3.0 15 June 2000 DLAED4(l)
