On Wed, 13 Feb 2008, Heikki Kaskelma wrote: > hadley wickham: >> It's more than that as though, as floating point addition is no longer >> guaranteed to be commutative or associative, and multiplication does >> not distribute over addition. Many concepts that are clear cut in >> pure math become fuzzy in floating point math - equality, singularity >> of matrices etc etc. > > Even simple averages may be complicated: > > eps=1 > while(1-eps != 1) eps=eps/2 > eps=eps*2
Such calculations are dangerous: we provide .Machine to avoid the need for them. (They have plagued various LAPACK implementations, for example.) Most R implementations these days use higher-precision registers for intermediate internal calculations such as those in mean() and sum(). > (1-1*eps+1-2*eps+1-3*eps)/3 == 1-1:3*eps # TRUE FALSE FALSE Which is not an average, and the difference from the last line below just illustrates Hadley's point. > mean(1-1:3*eps) == 1-1:3*eps # FALSE TRUE FALSE > sum(1-1:3*eps)/3 == 1-1:3*eps # FALSE FALSE TRUE > ((1-1*eps)+(1-2*eps)+(1-3*eps))/3 == 1-1:3*eps # FALSE FALSE TRUE > > so sometimes all the values may lie on the same side of the "average". Only if you DIY average! Note that mean() does a better job than you managed, because it uses a higher-precision accumulator. I think the moral is to rely on the work of those to whom this is not at all 'complicated' (you should check out some of the rest of the R internals to see 'complicated'). > [Win R 2.6.1] > > > Heikki Kaskelma > Munkkiniemi, Finland > > ______________________________________________ > R-devel@r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-devel > -- Brian D. Ripley, [EMAIL PROTECTED] Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/ University of Oxford, Tel: +44 1865 272861 (self) 1 South Parks Road, +44 1865 272866 (PA) Oxford OX1 3TG, UK Fax: +44 1865 272595 ______________________________________________ R-devel@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-devel
