Code covered by the BSD License

UD Factorization & Kalman Filtering

Gerard Van Willigenburg (view profile)

15 Aug 2011 (Updated )

UD and LD factorization of nonnegative matrices and associated Kalman filter implementations.

[uti,r]=utinv(ut,tolp,toln)
```% UTINV : inverse of upper triangular ut
%
%         function [uti,r]=utinv(ut,tolp,toln)
%
%         ut  : U'DU factorization
%         tolp: tolerance for positiveness
%         toln: error generation if diagonal part < toln,  default: tolp
%               if toln < 0 all the diagonal parts < max(0,tolp) are set to zero
%
%         uti : inv(ut)
%         r   : rank(di)
%
%         Used to compute : inv(p)=inv(u)'*inv(u)
%         [uti]=utinv(ut) computes inv(u)
%         Then: inv(p)=utt2sym(utinv(sym2ud(p)))
%
%
%         References: Factorization methods for discrete sequential estimation
%                     1977, Gerald J. Bierman
%
% L.G. van Willigenburg, W.L. de Koning, Update August 2011

function [uti,r]=utinv(ut,tolp,toln)

if nargin > 3; error('  one, two or three input arguments required'); end;
if nargin==1; tolp=1e-12; toln=tolp;
elseif nargin==2; toln=tolp; end; tolp=max(0,tolp);
if (toln>tolp); error('  toln > tolp'); end;

[n,m]=size(ut);
if n~=m; error(' ut must be square'); end;
if n==0; error('  Compatible but empty inputs'); end;

r=n;
for i=1:n
if ut(i,i)<toln; error('  toln violated');
elseif ut(i,i)<=tolp; uti(i,i)=0; r=r-1;
else uti(i,i)=1/ut(i,i); end
end;

for j=2:n
jm1=j-1;
for k=1:jm1
sum=0;
for i=k:jm1
sum=sum-uti(k,i)*ut(i,j);
end
uti(k,j)=sum*uti(j,j);
end
end
```