jens
7b34529b24
git-svn-id: http://moon:8086/svn/matlab/trunk@91 801c6759-fa7c-4059-a304-17956f83a07c
60 lines
1.3 KiB
Matlab
60 lines
1.3 KiB
Matlab
function [l,d,perm] = mchol(A,mu)
|
|
% [l,d,perm] = mchol(A,mu)
|
|
% Compute the Gill-Murray modified LDL factorization of A,
|
|
|
|
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
|
|
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 |