slasd4 (3)  Linux Man Pages
NAME
slasd4.f 
SYNOPSIS
Functions/Subroutines
subroutine slasd4 (N, I, D, Z, DELTA, RHO, SIGMA, WORK, INFO)
SLASD4 computes the square root of the ith updated eigenvalue of a positive symmetric rankone modification to a positive diagonal matrix. Used by sbdsdc.
Function/Subroutine Documentation
subroutine slasd4 (integerN, integerI, real, dimension( * )D, real, dimension( * )Z, real, dimension( * )DELTA, realRHO, realSIGMA, real, dimension( * )WORK, integerINFO)
SLASD4 computes the square root of the ith updated eigenvalue of a positive symmetric rankone modification to a positive diagonal matrix. Used by sbdsdc.
Purpose:

This subroutine computes the square root of the Ith updated eigenvalue of a positive symmetric rankone 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 rankone 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
N is INTEGER The length of all arrays.
II is INTEGER The index of the eigenvalue to be computed. 1 <= I <= N.
DD is REAL array, dimension ( N ) The original eigenvalues. It is assumed that they are in order, 0 <= D(I) < D(J) for I < J.
ZZ is REAL array, dimension ( N ) The components of the updating vector.
DELTADELTA is REAL array, dimension ( N ) If N .ne. 1, DELTA contains (D(j)  sigma_I) in its jth component. If N = 1, then DELTA(1) = 1. The vector DELTA contains the information necessary to construct the (singular) eigenvectors.
RHORHO is REAL The scalar in the symmetric updating formula.
SIGMASIGMA is REAL The computed sigma_I, the Ith updated eigenvalue.
WORKWORK is REAL array, dimension ( N ) If N .ne. 1, WORK contains (D(j) + sigma_I) in its jth component. If N = 1, then WORK( 1 ) = 1.
INFOINFO is INTEGER = 0: successful exit > 0: if INFO = 1, the updating process failed.
Internal Parameters:

Logical variable ORGATI (originati?) 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 (switchfor3poles?) is for noting if we are working with THREE poles! MAXIT is the maximum number of iterations allowed for each eigenvalue.
Author:

Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
 November 2013
Contributors:
 RenCang Li, Computer Science Division, University of California at Berkeley, USA
Definition at line 154 of file slasd4.f.
Author
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