SLAED4(l) ) SLAED4(l)
SLAED4 - subroutine computes the I-th updated eigenvalue of a symmetric rank-one 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
SUBROUTINE SLAED4( N, I, D, Z, DELTA, RHO, DLAM, INFO )
INTEGER I, INFO, N
REAL DLAM, RHO
REAL D( * ), DELTA( * ), Z( * )
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.
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
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 con-
struct 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.
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
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)