1function [L, w] = chol_updown (L, sigma, w)
2%CHOL_UPDOWN update or downdate a Cholesky factorization.
3% Example:
4%   [L, w] = chol_updown (L, sigma, w)
5% See also: cs_demo
6
7% Copyright 2006-2012, Timothy A. Davis, http://www.suitesparse.com
8
9beta = 1 ;
10n = size (L,1) ;
11if (n == 1)
12    L = sqrt (L*L'+sigma*w*w') ;
13    return ;
14end
15for k = 1:n
16    alpha = w(k) / L(k,k) ;
17    beta2 = sqrt (beta^2 + sigma*alpha^2) ;
18    gamma = sigma * alpha / (beta2 * beta) ;
19    if (sigma > 0)
20        % update
21        delta = beta / beta2 ;
22        L (k,k) = delta * L (k,k) + gamma * w (k) ;
23        w1 = w (k+1:n) ;
24        w (k+1:n) = w (k+1:n) - alpha * L (k+1:n,k) ;
25        L (k+1:n,k) = delta * L (k+1:n,k) + gamma * w1 ;
26    else
27        % downdate
28        delta = beta2 / beta ;
29        L (k,k) = delta * L (k,k) ;
30        w (k+1:n) = w (k+1:n) - alpha * L (k+1:n,k) ;
31        L (k+1:n,k) = delta * L (k+1:n,k) + gamma * w (k+1:n) ;
32    end
33    w (k) = alpha ;
34    beta = beta2 ;
35end
36