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function L = choldn (Lold,w)
%CHOLDN Cholesky downdate
% given Lold and w, compute L so that L*L' = Lold*Lold' - w*w'
%
% Example:
% L = cholnd (Lold,w)
% See also: testall
% CXSparse, Copyright (c) 2006-2022, Timothy A. Davis. All Rights Reserved.
% SPDX-License-Identifier: LGPL-2.1+
n = size (Lold,1) ;
L = Lold ;
alpha = 1 ;
beta = 1 ;
wold = w ;
wnew = zeros (n,1) ;
for i = 1:n
a = w (i) / L(i,i) ;
alpha = alpha - a^2 ;
if (alpha <= 0)
error ('not pos def') ;
end
beta_new = sqrt (alpha) ;
b = beta_new / beta ;
c = (a / (beta*beta_new)) ;
beta = beta_new ;
% L (i,i) = b * L (i,i) ;
wnew (i) = a ;
for k = i:n
w (k) = w (k) - a * L (k,i) ;
L (k,i) = b * L (k,i) - c * w(k) ;
end
end
% w
% wnew
disp (wnew - Lold\wold)
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