Understanding and predict round-off errors sign on simple functions

5 messages · c.jallet at laposte.net, Bert Gunter, Marc Schwartz +2 more

Original

1

5

c.jallet at laposte.net

Wed, Jun 29, 2016 2:55 AM #

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)

[,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)

[,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

[,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

Bert Gunter

Wed, Jun 29, 2016 8:13 AM #

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)

            [,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]]

______________________________________________
R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
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.

Wed, Jun 29, 2016 11:06 AM #

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)

           [,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

Wed, Jun 29, 2016 3:31 PM #

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]]
>
>______________________________________________
>R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
>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.

DIGHE, NILESH [AG/2362]

Thu, Jun 30, 2016 5:02 AM #

Using "runmean" function from caTools package within your SMA function appears to solve the issue.  Please see details below.

library(caTools)

structure(c(-0.626453810742332, 0.183643324222082, -0.835628612410047, 
1.59528080213779, 0.329507771815361, -0.820468384118015, 0.487429052428485, 
0.738324705129217, 0.575781351653492, -0.305388387156356, 3.51178116845085, 
2.38984323641143, 1.3787594194582, -0.2146998871775, 3.12493091814311, 
1.95506639098477, 1.98380973690105, 2.9438362106853, 2.82122119509809, 
2.59390132121751, 5.91897737160822, 5.78213630073107, 5.07456498336519, 
3.01064830413663, 5.61982574789471, 4.943871260471, 4.84420449329467, 
3.52924761610073, 4.52184994489138, 5.4179415601997), .Dim = c(10L, 
3L))

function (x, n = 10, ...) 
{
    ma <- runmean(x, n)
    if (!is.null(dim(ma))) {
        colnames(ma) <- "SMA"
    }
    return(ma)
}


mma <- apply(m, 2, SMA, n=1)

results<-mma-m

structure(c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), .Dim = c(10L, 3L))

Nilesh
-----Original Message-----
From: R-help [mailto:r-help-bounces at r-project.org] On Behalf Of Marc Schwartz
Sent: Wednesday, June 29, 2016 1:07 PM
To: Bert Gunter
Cc: R-help
Subject: Re: [R] Understanding and predict round-off errors sign on simple functions

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)

           [,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

______________________________________________
R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see 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.
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