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function L = cholupdown (Lold, sigma, w)
%CHOLUPDOWN Cholesky update/downdate (Bischof, Pan, and Tang method)
% This version only works for the real case. See chol_updown2 for
% a code that handles both the real and complex cases.
% Example:
% L = cholupdown (Lold, sigma, w)
% See also: cs_demo
% CXSparse, Copyright (c) 2006-2022, Timothy A. Davis. All Rights Reserved.
% SPDX-License-Identifier: LGPL-2.1+
beta = 1 ;
n = size (Lold,1) ;
L = Lold ;
% x = weros (n,1) ;
% worig = w ;
for k = 1:n
alpha = w(k) / L(k,k) ;
beta_new = sqrt (beta^2 + sigma*alpha^2) ;
gamma = alpha / (beta_new * beta) ;
if (sigma < 0)
% downdate
bratio = beta_new / beta ;
w (k+1:n) = w (k+1:n) - alpha * L (k+1:n,k) ;
L (k,k) = bratio * L (k,k) ;
L (k+1:n,k) = bratio * L (k+1:n,k) - gamma*w(k+1:n) ;
else
% update
bratio = beta / beta_new ;
% wold = w (k+1:n) ;
% w (k+1:n) = w (k+1:n) - alpha * L (k+1:n,k) ;
% L (k ,k) = bratio * L (k ,k) + gamma*w(k) ;
% L (k+1:n,k) = bratio * L (k+1:n,k) + gamma*wold ;
L (k,k) = bratio * L (k,k) + gamma*w(k) ;
for i = k+1:n
wold = w (i) ;
w (i) = w (i) - alpha * L (i,k) ;
L (i,k) = bratio * L (i,k) + gamma*wold ;
end
end
w (k) = alpha ;
beta = beta_new ;
end
% norm (w-(Lold\worig))
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