subroutine slasd4 (N, I, D, Z, DELTA, RHO, SIGMA, WORK, INFO)
SLASD4 computes the square root of the i-th updated eigenvalue of a positive symmetric rank-one modification to a positive diagonal matrix. Used by sbdsdc.
SLASD4 computes the square root of the i-th updated eigenvalue of a positive symmetric rank-one modification to a positive diagonal matrix. Used by sbdsdc.
Purpose:
This subroutine computes the square root of the I-th updated
eigenvalue of a positive symmetric rank-one modification to
a positive diagonal matrix whose entries are given as the squares
of the corresponding entries in the array d, and that
0 <= 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 ) * 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.
Parameters:
N is INTEGER
The length of all arrays.
I
I is INTEGER
The index of the eigenvalue to be computed. 1 <= I <= N.
D
D is REAL array, dimension ( N )
The original eigenvalues. It is assumed that they are in
order, 0 <= D(I) < D(J) for I < J.
Z
Z is REAL array, dimension ( N )
The components of the updating vector.
DELTA
DELTA is REAL array, dimension ( N )
If N .ne. 1, DELTA contains (D(j) - sigma_I) in its j-th
component. If N = 1, then DELTA(1) = 1. The vector DELTA
contains the information necessary to construct the
(singular) eigenvectors.
RHO
RHO is REAL
The scalar in the symmetric updating formula.
SIGMA
SIGMA is REAL
The computed sigma_I, the I-th updated eigenvalue.
WORK
WORK is REAL array, dimension ( N )
If N .ne. 1, WORK contains (D(j) + sigma_I) in its j-th
component. If N = 1, then WORK( 1 ) = 1.
INFO
INFO is 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.
Author:
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
Contributors:
Definition at line 155 of file slasd4.f.
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