One thing to realize is that although it appears that the operations are the same, the code that is being executed is different in the two cases. Due to the different sequence of instructions, there may be round-off errors that are then introduced
On 7/30/07, Talbot Katz <[EMAIL PROTECTED]> wrote: > Thank you for responding! > > I realize that floating point operations are often inexact, and indeed, the > difference between the two answers is within the all.equal tolerance, as > mentioned in FAQ 7.31 (cited by Charles): > > >(as.numeric(ev1%*%ev2))==(sum(ev1*ev2)) > [1] FALSE > >all.equal((as.numeric(ev1%*%ev2)),(sum(ev1*ev2))) > [1] TRUE > > > > I suppose that's good enough for numerical computation. But I was still > surprised to see that matrix multiplication (ev1%*%ev2) doesn't give the > exact right answer, whereas sum(ev1*ev2) does give the exact answer. I > would've expected them to perform the same two multiplications and one > addition. But I guess that's not the case. > > However, I did find that if I multiplied the two vectors by 10, making the > entries integers (although the class was still "numeric" rather than > "integer"), both computations gave equal answers of 0: > > >xf1<-10*ev1 > >xf2<-10*ev2 > >(as.numeric(xf1%*%xf2))==(sum(xf1*xf2)) > [1] TRUE > > > > Perhaps the moral of the story is that one should exercise caution and keep > track of significant digits. > > -- TMK -- > 212-460-5430 home > 917-656-5351 cell > > > > >From: "Charles C. Berry" <[EMAIL PROTECTED]> > >To: Talbot Katz <[EMAIL PROTECTED]> > >CC: r-help@stat.math.ethz.ch > >Subject: Re: [R] Matrix Multiplication, Floating-Point, etc. > >Date: Mon, 30 Jul 2007 09:27:42 -0700 > > > > > > > >7.31 Why doesn't R think these numbers are equal? > > > >On Fri, 27 Jul 2007, Talbot Katz wrote: > > > >>Hi. > >> > >>I recently tried the following in R 2.5.1 on Windows XP: > >> > >>>ev2<-c(0.8,-0.6) > >>>ev1<-c(0.6,0.8) > >>>ev1%*%ev2 > >> [,1] > >>[1,] -2.664427e-17 > >>>sum(ev1*ev2) > >>[1] 0 > >>> > >> > >>(I got the same result with R 2.4.1 on a different Windows XP machine.) > >> > >>I expect this issue is very familiar and probably has been discussed in > >>this > >>forum before. Can someone please point me to some documentation or > >>discussion about this? Is there some standard way to get the "correct" > >>answer from %*%? > >> > >>Thanks! > >> > >>-- TMK -- > >>212-460-5430 home > >>917-656-5351 cell > >> > >>______________________________________________ > >>R-help@stat.math.ethz.ch mailing list > >>https://stat.ethz.ch/mailman/listinfo/r-help > >>PLEASE do read the posting guide > >>http://www.R-project.org/posting-guide.html > >>and provide commented, minimal, self-contained, reproducible code. > >> > > > >Charles C. Berry (858) 534-2098 > > Dept of Family/Preventive > >Medicine > >E mailto:[EMAIL PROTECTED] UC San Diego > >http://famprevmed.ucsd.edu/faculty/cberry/ La Jolla, San Diego 92093-0901 > > > > > > ______________________________________________ > R-help@stat.math.ethz.ch mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. > -- Jim Holtman Cincinnati, OH +1 513 646 9390 What is the problem you are trying to solve? ______________________________________________ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
