UDFactor 1.0

[U D] = UDFactor(P) returns matrices U and D such that U.'*D*U = P[U D] = UDFactor(P,uflag) returns matrices U and D such that U*D*U.' = Pwhen uflag is set to TRUE. Setting uflag to FALSE is equivalent torunning UDFactor with only one argument.The alogrithm of UDFactor is similar to the Cholesky decomposition exceptthat the matrix is factored into a unitary upper triangular matrix (U)and diagonal matrix (D) such that P = U*D*U.' (or U.'*D*U). Note thatwhile this is equivalent to P = (U*D^0.5)*(U*D^0.5).' = S*S.' where S isthe upper triangular square root of P, no square roots are taken in thecalculations of U and D. This makes this factorization ideal for asquare-root implementation of a Kalman filter (a U-D filter). For moredetails, see Bierman, G. J., Factorization methods for discretesequential estimation, 1977.Note: This factorization is only guaranteed to work for symmetricmatrices.Examples: %create symmetric matrix P = rand(5)*10;, P = triu(P)+triu(P).'; %factor [U1,D1] = UDFactor(P); [U2,D2] = UDFactor(P,true); %check factorization P - U1.'*D1*U1 P - U2*D2*U2.'

Requirements:	No special requirements
Platforms:	Matlab
Keyword:	Bierman,  Calculations,  Details,  Factorization,  Filter,  Implementation,  Kalman,  Methods,  Squareroot
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