On Tuesday, 21. November 2006 18:49, Matthias Troyer wrote:
On 20 Nov 2006, at 00:44, Michael Stevens wrote:
The 'variance' accumulator has a lazy calculation of variance using the formula \sigma_n^2 = M_n^{(2)} - \mu_n^2. This formal is specifically cited for it poor performance in the presence of rounding error. Indeed it may even return negative results.
That's exactly why there is not only the lazy version but also an accurate one
Looking at variance.hpp there is a 'lazy' version and a 'iterative' version. The naming confused me. I was expecting lazy to have access to all the da and so be the most accurate. I guess my comments with regard to the lazy version are simply a matter of documenting the poor numerics. The iterative formal is via (n-1)/n * variance[n-1] + 1/(n-1) * (difference)^2. This is still numerically different from accumalating the differences squared iteratively and applying the 1/n is the result. I guess there is always a good reason to apply build ones own implementation to meet specific numericical requirements. Thanks, Michael -- ___________________________________ Michael Stevens Systems Engineering 34128 Kassel, Germany Phone/Fax: +49 561 5218038 Navigation Systems, Estimation and Bayesian Filtering http://bayesclasses.sf.net ___________________________________