www.pudn.com > starter.zip > mchol.m, change:2011-01-04,size:1287b

```function [l,d,perm] = mchol(A,mu)
% Compute a modified LDL factorization of A
% (MEX ME!)

if nargin < 2
mu = 1e-12;
end

n = size(A,1);
l = eye(n);
d = zeros(n,1);
perm = 1:n;

for i = 1:n
c(i,i) = A(i,i);
end

% Compute modification parameters
gamma = max(abs(diag(A)));
xi = max(max(abs(setdiag(A,0))));
delta = mu*max(gamma+xi,1);
if n > 1
beta = sqrt(max([gamma xi/sqrt(n^2-1) mu]));
else
beta = sqrt(max([gamma mu]));
end

for j = 1:n

% Find q that results in Best Permutation with j
[maxVal maxPos] = max(abs(diag(c(j:end,j:end))));
q = maxPos+j-1;

% Permute d,c,l,a
d([j q]) = d([q j]);
perm([j q]) = perm([q j]);
c([j q],:) = c([q j],:);
c(:,[j q]) = c(:,[q j]);
l([j q],:) = l([q j],:);
l(:,[j q]) = l(:,[q j]);
A([j q],:) = A([q j],:);
A(:,[j q]) = A(:,[q j]);

for s = 1:j-1
l(j,s) = c(j,s)/d(s);
end
for i = j+1:n
c(i,j) = A(i,j) - sum(l(j,1:j-1).*c(i,1:j-1));
end
theta = 0;
if j < n && j > 1
theta = max(abs(c(j+1:n,j)));
end
d(j) = max([abs(c(j,j)) (theta/beta)^2 delta]);
if j < n
for i = j+1:n
c(i,i) = c(i,i) - (c(i,j)^2)/d(j);
end
end
end```