# [R] Matrix Multiplication, Floating-Point, etc.

jim holtman jholtman at gmail.com
Tue Jul 31 03:50:32 CEST 2007

```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 <topkatz at msn.com> 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" <cberry at tajo.ucsd.edu>
> >To: Talbot Katz <topkatz at msn.com>
> >CC: r-help at 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
> >>
> >>Thanks!
> >>
> >>--  TMK  --
> >>212-460-5430  home
> >>917-656-5351  cell
> >>
> >>______________________________________________
> >>R-help at stat.math.ethz.ch mailing list
> >>https://stat.ethz.ch/mailman/listinfo/r-help
> >>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:cberry at tajo.ucsd.edu              UC San Diego
> >http://famprevmed.ucsd.edu/faculty/cberry/  La Jolla, San Diego 92093-0901
> >
> >
>
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> and provide commented, minimal, self-contained, reproducible code.
>

--
Jim Holtman
Cincinnati, OH
+1 513 646 9390

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