DLAED4
November 2006
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
secular equation by simpler interpolating rational functions.
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.
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
component. 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. |
Internal 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.
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
Ren-Cang Li, Computer Science Division, University of California
at Berkeley, USA