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

[MacQueen, Don]

For all practical purposes, the differences are zero.

If you want them to also look like zero, try
  round( m - mma , 3)
or
  signif( m - mma , 3)

(or some number of digits other than three;  I picked 3 rather arbitrarily)


For anticipating the sign of these minuscule differences, I doubt there is
a way (but I don't know why it would matter, either). If you want them all
positive, use
  abs(round(m-mma,3))
or similar.

Other programming languages will produce similar very small numbers,
depending on how the calculation is done, but I would not expect exactly
the same very small numbers.

Finally, it would appear that your round-off errors are being generated
inside the runMean function, and we don't know where that function comes
from. It's not in base R. You could try
  x <- rnorm(1) ;   x - runMean(x , 1)
many times and see how often runMean does not return the value it was
supplied with, and then study the definition of runMean to try to
understand why it does not always return the value it was supplied with.

This all assumes I've accurately read your example code and and reduced it
to its core behavior.

-Don

-- 
Don MacQueen

Lawrence Livermore National Laboratory
7000 East Ave., L-627
Livermore, CA 94550
925-423-1062





On 6/29/16, 2:55 AM, "R-help on behalf of Sirhc via R-help"
<r-help-bounces at r-project.org on behalf of 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
>
> 
>
>
>	[[alternative HTML version deleted]]
>
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