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function [L, w] = chol_downdate (L, w)
%CHOL_DOWNDATE downdate a Cholesky factorization.
% Example
% [L, w] = chol_downdate (L, w)
% See also: cs_demo
% Copyright 2006-2007, Timothy A. Davis.
% http://www.cise.ufl.edu/research/sparse
beta = 1 ;
n = size (L,1) ;
for j = 1:n
alpha = w (j) / L (j,j) ;
beta2 = sqrt (beta^2 - alpha^2) ;
if (~isreal (beta2))
error ('not positive definite') ;
end
gamma = alpha / (beta2 * beta) ;
delta = beta2 / beta ;
L (j,j) = delta * L (j,j) ;
w (j) = alpha ;
beta = beta2 ;
if (j == n)
return
end
w (j+1:n) = w (j+1:n) - alpha * L (j+1:n,j) ;
L (j+1:n,j) = delta * L (j+1:n,j) - gamma * w (j+1:n) ;
end
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