DLAED4(1) LAPACK routine (version 3.2) DLAED4(1)NAME
DLAED4 - subroutine compute 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 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 .GT. 2, DELTA contains (D(j) - lambda_I) in its j-th com‐
ponent. If N = 1, then DELTA(1) = 1. If N = 2, see DLAED5 for
detail. The vector DELTA contains the information necessary to
construct the eigenvectors by DLAED3 and DLAED9.
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, University of California at Berkeley, USA
LAPACK routine (version 3.2) November 2008 DLAED4(1)
