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UD Factorization & Kalman Filtering

UD Factorization & Kalman Filtering

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15 Aug 2011 (Updated )

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

[p]=ldt2sym(ld)
% LDT2SYM: Recover P=L'DL, LD an LDL factorization of P
%          L upper triangular, D diagonal, P nonnegative symmetric
%
%          [p]=udt2sym(ld)
%
%          p=l'*d*l
%
%          Used to compute : inv(p)=inv(l)'*inv(d)*inv(l)
%          [ldi]=ldinv(ld) computes inv(l),inv(l)
%          Then: inv(p)=ldt2sym(ldinv(sym2ud(p)))
%
%          See also ldinv, ld2sym, sym2ld
%
%          References: Factorization methods for discrete sequential estimation
%                      1977, Gerald J. Bierman
%
% L.G. van Willigenburg, W.L. de Koning, Update August 2011

  function [p]=ldt2sym(ld)
  
  [n,m]=size(ld);
  if n~=m; error('  ld must be square'); end;
  if n==0; error('  Compatible but empty inputs'); end;

  d=diag(diag(ld));
  l=ld-d+diag(ones(1,n));
  p=l'*d*l;

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