[R] Understanding and predict round-off errors sign on simple functions

[Marc Schwartz]

Hi,

Just to augment Bert's comments, I presume that you are aware of the relevant R FAQ:

  https://cran.r-project.org/doc/FAQ/R-FAQ.html#Why-doesn_0027t-R-think-these-numbers-are-equal_003f

That you had an expectation of the difference being 0 suggested to me that you might not be, but my apologies if that is not the case.

That being said, there are some higher precision CRAN packages that may offer some additional functionality, with the potential limitations that Bert references below. More information is available in the Numerical Mathematics CRAN Task View:

  https://cran.r-project.org/web/views/NumericalMathematics.html

In addition, with the caveat that I have not used it, there is the 'propagate' package on CRAN that may be relevant to what you want to be able to anticipate, at some level:

  https://cran.r-project.org/web/packages/propagate/index.html

It has not been updated in a while and there are some notes for the CRAN package checks, that suggest that the maintainer may not be active at this point.

Regards,

Marc


> On Jun 29, 2016, at 10:13 AM, Bert Gunter <bgunter.4567 at gmail.com> wrote:
> 
> I am certainly no expert, but I would assume that:
> 
> 1. Roundoff errors depend on the exact numerical libraries and
> versions that are used, and so general language comparisons are
> impossible without that information;
> 
> 2. Roundoff errors depend on the exact calculations being done and
> machine precision and are very complicated to determine
> 
> So I would say the answer to your questions is no.
> 
> But you should probably address such a question to a numerical analyst
> for an authoritative answer. Maybe try stats.stackexchange.com  .
> 
> -- Bert
> 
> Bert Gunter
> 
> "The trouble with having an open mind is that people keep coming along
> and sticking things into it."
> -- Opus (aka Berkeley Breathed in his "Bloom County" comic strip )
> 
> 
> On Wed, Jun 29, 2016 at 2:55 AM, Sirhc via R-help <r-help at r-project.org> wrote:
>> Hi,
>> 
>> 
>> 
>> May be it is a basic thing but I would like to know if we can anticipate
>> round-off errors sign.
>> 
>> 
>> 
>> Here is an example :
>> 
>> 
>> 
>> # numerical matrix
>> 
>> m <- matrix(data=cbind(rnorm(10, 0), rnorm(10, 2), rnorm(10, 5)), nrow=10,
>> ncol=3)
>> 
>> 
>> 
>>> m
>> 
>>            [,1]      [,2]     [,3]
>> 
>> [1,]  0.4816247 1.1973502 3.855641
>> 
>> [2,] -1.2174937 0.7356427 4.393279
>> 
>> [3,]  0.8504074 2.5286509 2.689196
>> 
>> [4,]  1.8048642 1.8580804 6.665237
>> 
>> [5,] -0.6749397 1.0944277 4.838608
>> 
>> [6,]  0.8252034 1.5595268 3.681695
>> 
>> [7,]  1.3002208 0.9582693 4.561577
>> 
>> [8,]  1.6950923 3.5677921 6.005078
>> 
>> [9,]  0.6509285 0.9025964 5.082288
>> 
>> [10,] -0.5676040 1.3281102 4.446451
>> 
>> 
>> 
>> #weird moving average of period 1 !
>> 
>> mma <- apply(m, 2, SMA, n=1)
>> 
>> 
>> 
>>> mma
>> 
>>            [,1]      [,2]     [,3]
>> 
>> [1,]         NA        NA       NA
>> 
>> [2,] -1.2174937 0.7356427 4.393279
>> 
>> [3,]  0.8504074 2.5286509 2.689196
>> 
>> [4,]  1.8048642 1.8580804 6.665237
>> 
>> [5,] -0.6749397 1.0944277 4.838608
>> 
>> [6,]  0.8252034 1.5595268 3.681695
>> 
>> [7,]  1.3002208 0.9582693 4.561577
>> 
>> [8,]  1.6950923 3.5677921 6.005078
>> 
>> [9,]  0.6509285 0.9025964 5.082288
>> 
>> [10,] -0.5676040 1.3281102 4.446451
>> 
>> 
>> 
>> 
>> 
>> #difference should be 0 but here is the result
>> 
>>> m - mma
>> 
>>               [,1]         [,2]          [,3]
>> 
>> [1,]            NA           NA            NA
>> 
>> [2,]  0.000000e+00 0.000000e+00 -8.881784e-16
>> 
>> [3,]  0.000000e+00 0.000000e+00 -8.881784e-16
>> 
>> [4,]  0.000000e+00 4.440892e-16 -8.881784e-16
>> 
>> [5,] -1.110223e-16 4.440892e-16 -8.881784e-16
>> 
>> [6,] -1.110223e-16 2.220446e-16 -4.440892e-16
>> 
>> [7,] -2.220446e-16 2.220446e-16  0.000000e+00
>> 
>> [8,] -2.220446e-16 0.000000e+00  0.000000e+00
>> 
>> [9,] -3.330669e-16 2.220446e-16 -8.881784e-16
>> 
>> [10,] -3.330669e-16 4.440892e-16 -8.881784e-16
>> 
>> 
>> 
>> SMA function use runMean
>> 
>> # TTR / R / MovingAverages.R
>> 
>> "SMA" <- function(x, n=10, ...) { # Simple Moving Average
>> 
>>   ma <- runMean( x, n )
>> 
>>   if(!is.null(dim(ma))) {
>> 
>>     colnames(ma) <- "SMA"
>> 
>>   }
>> 
>>  return(ma)
>> 
>> }
>> 
>> 
>> 
>> 
>> 
>> Can anyone explain me that round error type?
>> 
>> Is it possible to reproduce this same error generation in another language
>> like C++ or C# ?
>> 
>> 
>> 
>> Thanks in advance for your answers
>> 
>> 
>> 
>> Regards
>> 
>> 
>> 
>> Chris