SLAED4 - 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 SLAED4( N, I, D, Z, DELTA, RHO, DLAM, INFO )
INTEGER I, INFO, N
REAL DLAM, RHO
REAL 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 call
ing 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 func
tions 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) REAL array, dimension (N)
The original eigenvalues. It is assumed that they
are in order, D(I) < D(J) for I < J.
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 construct the eigenvectors.
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.
PARAMETERS
Logical variable ORGATI (origin-at-i?) is used for distin
guishing 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 not
ing 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
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