Re: [R] Matrix Multiplication, Floating-Point, etc.
On Mon, 30 Jul 2007, Moshe Olshansky wrote: > After multiplication by 10 you get 6*8 = 48 - the > result is an exact machine number so there is no > roundoff, while 0.6*0.8 = 0.48, where neither of the 3 > numbers (0.6, 0.8, 0.48) is an exact machine mumber. > However, (-0.6)*0.8 should be equal EXACTLY to > -(0.6*0.8), and in fact you get that sum(ev1*ev2) is > exactly 0. > What is strange is that you are not getting this > result from ev1 %*% ev2. This means that either %^% > uses some non-straightforward algorithm or it somehow > sets the rounding control to something different from > "round to nearest". In the later case (-0.6) does not > necessarily equal to -(0.6) and the rounding after > multiplication is not necessarily symetric. Mr Olshansky seems unaware of the effects of extended-precision intermediate arithmetic on ix86 CPUs. sum() does use a higher-precision accumulator (where available, including on Windows), but ev1*ev2 is done in R and so stored to basic precision. OTOH, %*% (sic) calls the BLAS routine dgemm and hence may accumulate in 80-bit floating-point registers. What result you get will depend on what compiler, compiler flags and BLAS is in use, but with the default reference BLAS it is very likely that some of the intermediate results are stored in FP registers to extended precision. It is a simple experiment to confirm this: recompile the BLAS with -fforce-store and you do get 0 (at least on my Windows build system). Let's see less speculation and more homework in future. > > Regards, > > Moshe. > > --- 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 -- 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, UKFax: +44 1865 272595 __ 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.
Re: [R] Matrix Multiplication, Floating-Point, etc.
> -Original Message- > From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] > On Behalf Of Talbot Katz > Sent: Monday, July 30, 2007 10:55 AM > To: [EMAIL PROTECTED] > Cc: [EMAIL PROTECTED]; r-help@stat.math.ethz.ch > Subject: Re: [R] Matrix Multiplication, Floating-Point, etc. > > 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 > There may other issues involved here besides R version, floating point precision, and OS version. On my WinXP system running R-2.5.1 binary from CRAN, I get what you expected: > ev2<-c(0.8,-0.6) > ev1<-c(0.6,0.8) > ev1%*%ev2 [,1] [1,]0 > There could be differences in OS release, service packs installed, cpu, etc. But the moral you draw is probably a reasonable one. Dan Daniel Nordlund Bothell, WA __ 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.
Re: [R] Matrix Multiplication, Floating-Point, etc.
After multiplication by 10 you get 6*8 = 48 - the result is an exact machine number so there is no roundoff, while 0.6*0.8 = 0.48, where neither of the 3 numbers (0.6, 0.8, 0.48) is an exact machine mumber. However, (-0.6)*0.8 should be equal EXACTLY to -(0.6*0.8), and in fact you get that sum(ev1*ev2) is exactly 0. What is strange is that you are not getting this result from ev1 %*% ev2. This means that either %^% uses some non-straightforward algorithm or it somehow sets the rounding control to something different from "round to nearest". In the later case (-0.6) does not necessarily equal to -(0.6) and the rounding after multiplication is not necessarily symetric. Regards, Moshe. --- 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 -- > >>212-460-5430home > >>917-656-5351cell > >> > >>__ > >>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. > __ 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.
Re: [R] Matrix Multiplication, Floating-Point, etc.
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.
Re: [R] Matrix Multiplication, Floating-Point, etc.
Talbot The general advice on this list is to read the following http://docs.sun.com/source/806-3568/ncg_goldberg.html > -Original Message- > From: Talbot Katz [mailto:[EMAIL PROTECTED] > Sent: Monday, July 30, 2007 1:55 PM > To: [EMAIL PROTECTED] > Cc: r-help@stat.math.ethz.ch; Doran, Harold > Subject: Re: [R] Matrix Multiplication, Floating-Point, etc. > > 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 -- > >>212-460-5430home > >>917-656-5351cell > >> > >>__ > >>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.
Re: [R] Matrix Multiplication, Floating-Point, etc.
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 -- 212-460-5430home 917-656-5351cell >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.
Re: [R] Matrix Multiplication, Floating-Point, etc.
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.
Re: [R] Matrix Multiplication, Floating-Point, etc.
This is giving you exactly what you are asking for. The operator * does element by element multiplication. So, .48 + -.48 =0, right? Is there another mathematical possibility you were expecting? > -Original Message- > From: [EMAIL PROTECTED] > [mailto:[EMAIL PROTECTED] On Behalf Of Talbot Katz > Sent: Friday, July 27, 2007 6:31 PM > To: r-help@stat.math.ethz.ch > Subject: [R] Matrix Multiplication, Floating-Point, etc. > > 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. > __ 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.
[R] Matrix Multiplication, Floating-Point, etc.
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 -- 212-460-5430home 917-656-5351cell __ 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.
