Re: [R] - round() strange behaviour
(Ted Harding) wrote: ... Thus always up or always down means that the difference between rounded numbers is always the same as between the unrounded numbers which for other methods the differences can differ by 2.0. This may or may not matter, but it is something to think about when choosing a rounding method. Ah, but Ted, this is why, as I remarked in a private message to the original poster, we were also taught never to round until the final result. Had I not had a rather extended debate with an engineer who apparently thought that one could get away with successive rounding, I would not be so sensitive on the issue. Jim __ 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] - round() strange behaviour
In R you may be tempted to use rounding to index something in an array. Hence my concern and suggestion that there be another argument to round() (and signif()) that explicitly sets the rounding mechanism. In Fortran IDNINT does as I would expect. You could do floor(x+0.5) but many people, myself included before this conversation, will unwittingly round and it will almost always work but the exception is something that may even be difficult to reproduce where random numbers are involved without setting the seed. In this context you cannot leave rounding until the end of course! Clearly in an arithmetic context, rounding should always be left to the end but I don't think that is to avoid rounding-to-even but just to avoid unnecessary loss of precision in the calculation. Ask most engineers - and even physicists - and I suspect they would not be aware of this debate even though it dates from the 1940s. On Monday 06 August 2007 10:31:22 Jim Lemon wrote: (Ted Harding) wrote: ... Thus always up or always down means that the difference between rounded numbers is always the same as between the unrounded numbers which for other methods the differences can differ by 2.0. This may or may not matter, but it is something to think about when choosing a rounding method. Ah, but Ted, this is why, as I remarked in a private message to the original poster, we were also taught never to round until the final result. Had I not had a rather extended debate with an engineer who apparently thought that one could get away with successive rounding, I would not be so sensitive on the issue. Jim __ 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. -- Best wishes John John Logsdon Try to make things as simple Quantex Research Ltd, Manchester UK as possible but not simpler [EMAIL PROTECTED] [EMAIL PROTECTED] +44(0)161 445 4951/G:+44(0)7717758675 www.quantex-research.com __ 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] - round() strange behaviour
On 06/08/2007 5:46 AM, John Logsdon wrote:
In R you may be tempted to use rounding to index something in an array.
Hence
my concern and suggestion that there be another argument to round() (and
signif()) that explicitly sets the rounding mechanism.
In Fortran IDNINT does as I would expect. You could do floor(x+0.5) but many
people, myself included before this conversation, will unwittingly round and
it will almost always work but the exception is something that may even be
difficult to reproduce where random numbers are involved without setting the
seed.
As you mention, where you want to round 0.5 upwards, you can use the
function
roundup - function(x, digits=0) {
factor - 10^digits
trunc(x*factor + 0.5)/factor
}
But beware of floating point representations: most decimal numbers
ending in 5 can't be represented exactly, so you'll see oddities like this:
roundup(2.45, 1)
[1] 2.5
roundup(2.4 + 0.05, 1)
[1] 2.4
which is partially explained by this:
2.45 - (2.4 + 0.05)
[1] 4.440892e-16
I suspect the same sort of thing would happen in Fortran's IDNINT though
it might be harder to see, because most Fortran compilers do fairly
substantial optimizations, and it might be that they actually store 2.4
+ 0.05 and 2.45 as the same constant. So I don't think round() leaves
any new traps for the unwary: if x = 0.5 is the result of a
calculation, it might actually be stored as 0.499 and round(x)
should return 0 even using roundup().
Duncan Murdoch
In this context you cannot leave rounding until the end of course! Clearly
in
an arithmetic context, rounding should always be left to the end but I don't
think that is to avoid rounding-to-even but just to avoid unnecessary loss of
precision in the calculation. Ask most engineers - and even physicists - and
I suspect they would not be aware of this debate even though it dates from
the 1940s.
On Monday 06 August 2007 10:31:22 Jim Lemon wrote:
(Ted Harding) wrote:
...
Thus always up or always down means that the difference between
rounded numbers is always the same as between the unrounded numbers
which for other methods the differences can differ by 2.0.
This may or may not matter, but it is something to think about
when choosing a rounding method.
Ah, but Ted, this is why, as I remarked in a private message to the
original poster, we were also taught never to round until the final
result. Had I not had a rather extended debate with an engineer who
apparently thought that one could get away with successive rounding, I
would not be so sensitive on the issue.
Jim
__
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.
__
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PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
Re: [R] - round() strange behaviour
I use round() to prepare numbers for display in Sweave documents. While I had appreciated the round to even issue before, I had not given it much thought when automatically writing my output functions/scripts/Sexprs... On 04/08/07, Ted Harding [EMAIL PROTECTED] wrote: On 04-Aug-07 21:57:28, John Logsdon wrote: I must admit I had never realised this so thanks to Monica for raising it. Round-to-even is used for statistical reasons and there is some point as it obviously reduces bias. But why should the decision be to round to the nearest even number? rounding to the nearest odd number would be equally valid. (signif(x,0) is the same as round(). ) A fair point! But see below. There is a debate and sometimes you need symmetric rounding. Perhaps there should be an option in round that defaults to round-to-even for compatibility but includes the various other rounding approaches as seen for example in http://en.wikipedia.org/wiki/Rounding As wikipedia says: Round-to-even is used rather than round-to-odd as the latter rule would prevent rounding to a result of zero. And there's also stochastic rounding -- toss a penny. But you wouldn't get the same answer next time. And I can recall -- man years ago -- being in an environment where the practice was to round alternately up and down. (These were engineers). John's comparisons between FORTRAN, octave and (implicitly) R are interesting. As a general reflection: any method of rounding involves throwing away some of the information in the data, and this will have consequences. So the question is: what consequences are you happiest with? One consequence of rounding to nearest even (or nearest odd) is that this can give the worst possible outcome in terms of (rounded X - rounded Y) compared with (unrounded X - unrounded Y). For example, rounding to even integer X =1.5 -- 2.0 and Y = 0.5 -- 0.0 gives X - Y = 1.0 , rounded X - rounded Y = 2.0 whereas the difference is 1.0 if you always round up, or always down, and this is also exactly the difference between the unrounded values.. Rounding to nearest odd would give X = 1.5 -- 1.0, Y = 0.5 -- 1.0 thus difference 0.0 in this case, but again difference 2.0 for X = 2.5 -- 3.0, Y = 1.5 -- 1.0 And alternate rounding would give either 2.0 or 0.0 depending on the phase of X and Y. Thus always up or always down means that the difference between rounded numbers is always the same as between the unrounded numbers which for other methods the differences can differ by 2.0. This may or may not matter, but it is something to think about when choosing a rounding method. [...] Best wishes to all, Ted. E-Mail: (Ted Harding) [EMAIL PROTECTED] Fax-to-email: +44 (0)870 094 0861 Date: 04-Aug-07 Time: 23:53:50 -- XFMail -- __ 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. __ This email has been scanned by the MessageLabs Email Security System. For more information please visit http://www.messagelabs.com/email __ -- Dr. Mark Wardle Clinical research fellow and specialist registrar, Neurology Cardiff, UK __ 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] - round() strange behaviour
I must admit I had never realised this so thanks to Monica for raising it. Round-to-even is used for statistical reasons and there is some point as it obviously reduces bias. But why should the decision be to round to the nearest even number? rounding to the nearest odd number would be equally valid. (signif(x,0) is the same as round(). ) There is a debate and sometimes you need symmetric rounding. Perhaps there should be an option in round that defaults to round-to-even for compatibility but includes the various other rounding approaches as seen for example in http://en.wikipedia.org/wiki/Rounding BTW with Fortran the 'nearest integer' approach is used: REAL*8 TEST 10CONTINUE READ(*,*)TEST WRITE(*,*)TEST,IDNINT(TEST) GOTO 10 END Compiling this under g77 and gfortran gives the result: ~ $ g77 idnint.f -o idnint ~ $ ./idnint 1.5 1.5 2 2.5 2.5 3 ~ $ gfortran idnint.f -o idnint ~ $ ./idnint 2.5 2.503 1.5 1.502 Octave: octave:1 round(1.5) ans = 2 octave:2 round(2.5) ans = 3 On Thursday 02 August 2007 21:46:36 Monica Pisica wrote: Hi again, Mea culpa for not reading help pages before hand - but one would not go there when the function syntax is obvious and known besides other programming languages (for example IDL) with same function do not round to the next even number so i do get 3 for round(2.5), and i didn't realize that it is normal for R to give a 2 instead of 3. Date: Thu, 2 Aug 2007 22:38:49 +0200 From: [EMAIL PROTECTED] To: [EMAIL PROTECTED] CC: r-help@stat.math.ethz.ch Subject: Re: [R] - round() strange behaviour On Thu, 2 Aug 2007, Monica Pisica wrote: Hi, I am getting some strange results using round - it seems that it depends if the number before the decimal point is odd or even For example:round(1.5)[1] 2 round(2.5)[1] 2 While i would expect that round(2.5) be 3 and not 2. Do you have any explanation for that? Yes: you obviously did not read the man page! Please do. Z I really appreciate your input, Monica _ [[trailing spam removed]] [[alternative HTML version deleted]] __ 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. _ Messenger Caf� � open for fun 24/7. Hot games, cool activities served daily. Visit now. [[alternative HTML version deleted]] -- Best wishes John John Logsdon Try to make things as simple Quantex Research Ltd, Manchester UK as possible but not simpler [EMAIL PROTECTED] [EMAIL PROTECTED] +44(0)161 445 4951/G:+44(0)7717758675 www.quantex-research.com __ 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] - round() strange behaviour
On 04-Aug-07 21:57:28, John Logsdon wrote: I must admit I had never realised this so thanks to Monica for raising it. Round-to-even is used for statistical reasons and there is some point as it obviously reduces bias. But why should the decision be to round to the nearest even number? rounding to the nearest odd number would be equally valid. (signif(x,0) is the same as round(). ) A fair point! But see below. There is a debate and sometimes you need symmetric rounding. Perhaps there should be an option in round that defaults to round-to-even for compatibility but includes the various other rounding approaches as seen for example in http://en.wikipedia.org/wiki/Rounding As wikipedia says: Round-to-even is used rather than round-to-odd as the latter rule would prevent rounding to a result of zero. And there's also stochastic rounding -- toss a penny. But you wouldn't get the same answer next time. And I can recall -- man years ago -- being in an environment where the practice was to round alternately up and down. (These were engineers). John's comparisons between FORTRAN, octave and (implicitly) R are interesting. As a general reflection: any method of rounding involves throwing away some of the information in the data, and this will have consequences. So the question is: what consequences are you happiest with? One consequence of rounding to nearest even (or nearest odd) is that this can give the worst possible outcome in terms of (rounded X - rounded Y) compared with (unrounded X - unrounded Y). For example, rounding to even integer X =1.5 -- 2.0 and Y = 0.5 -- 0.0 gives X - Y = 1.0 , rounded X - rounded Y = 2.0 whereas the difference is 1.0 if you always round up, or always down, and this is also exactly the difference between the unrounded values.. Rounding to nearest odd would give X = 1.5 -- 1.0, Y = 0.5 -- 1.0 thus difference 0.0 in this case, but again difference 2.0 for X = 2.5 -- 3.0, Y = 1.5 -- 1.0 And alternate rounding would give either 2.0 or 0.0 depending on the phase of X and Y. Thus always up or always down means that the difference between rounded numbers is always the same as between the unrounded numbers which for other methods the differences can differ by 2.0. This may or may not matter, but it is something to think about when choosing a rounding method. [...] Best wishes to all, Ted. E-Mail: (Ted Harding) [EMAIL PROTECTED] Fax-to-email: +44 (0)870 094 0861 Date: 04-Aug-07 Time: 23:53:50 -- XFMail -- __ 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] - round() strange behaviour
Hi, I am getting some strange results using round - it seems that it depends if the number before the decimal point is odd or even For example: round(1.5)[1] 2 round(2.5)[1] 2 While i would expect that round(2.5) be 3 and not 2. Do you have any explanation for that? I really appreciate your input, Monica _ [[trailing spam removed]] [[alternative HTML version deleted]] __ 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] - round() strange behaviour
Monica Pisica wrote: Hi, I am getting some strange results using round - it seems that it depends if the number before the decimal point is odd or even For example: round(1.5)[1] 2 round(2.5)[1] 2 While i would expect that round(2.5) be 3 and not 2. Do you have any explanation for that? http://www.google.com/search?q=round+to+even; __ 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] - round() strange behaviour
On Thu, 2 Aug 2007, Monica Pisica wrote: Hi, I am getting some strange results using round - it seems that it depends if the number before the decimal point is odd or even Yes. This is explained in the help page for round(). -thomas Thomas Lumley Assoc. Professor, Biostatistics [EMAIL PROTECTED] University of Washington, Seattle __ 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] - round() strange behaviour
On 2 Aug 2007 at 20:16, Monica Pisica wrote: Hi, I am getting some strange results using round - it seems that it depends if the number before the decimal point is odd or even For example: round(1.5)[1] 2 round(2.5)[1] 2 While i would expect that round(2.5) be 3 and not 2. Do you have any explanation for that? I wouldn't call that strange behaviour; I'd call that correct. ---JRG I really appreciate your input, Monica _ [[trailing spam removed]] [[alternative HTML version deleted]] __ 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. John R. Gleason Associate Professor Syracuse University 430 Huntington Hall Voice: 315-443-3107 Syracuse, NY 13244-2340 USA FAX: 315-443-4085 PGP public key at keyservers __ 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] - round() strange behaviour
Hi again, Mea culpa for not reading help pages before hand - but one would not go there when the function syntax is obvious and known besides other programming languages (for example IDL) with same function do not round to the next even number so i do get 3 for round(2.5), and i didn't realize that it is normal for R to give a 2 instead of 3. Date: Thu, 2 Aug 2007 22:38:49 +0200 From: [EMAIL PROTECTED] To: [EMAIL PROTECTED] CC: r-help@stat.math.ethz.ch Subject: Re: [R] - round() strange behaviour On Thu, 2 Aug 2007, Monica Pisica wrote:Hi, I am getting some strange results using round - it seems that it depends if the number before the decimal point is odd or even For example:round(1.5)[1] 2 round(2.5)[1] 2 While i would expect that round(2.5) be 3 and not 2. Do you have any explanation for that? Yes: you obviously did not read the man page! Please do. Z I really appreciate your input, Monica _ [[trailing spam removed]] [[alternative HTML version deleted]] __ 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. _ Messenger Café open for fun 24/7. Hot games, cool activities served daily. Visit now. [[alternative HTML version deleted]] __ 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] - round() strange behaviour
On Thu, 2 Aug 2007, Monica Pisica wrote: Hi, I am getting some strange results using round - it seems that it depends if the number before the decimal point is odd or even For example: round(1.5)[1] 2 round(2.5)[1] 2 While i would expect that round(2.5) be 3 and not 2. Do you have any explanation for that? Yes: you obviously did not read the man page! Please do. Z I really appreciate your input, Monica _ [[trailing spam removed]] [[alternative HTML version deleted]] __ 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] - round() strange behaviour
That is what it is supposed to do. From ?round we get Note that for rounding off a 5, the IEC 60559 standard is expected to be used, “go to the even digit”. Therefore round(0.5) is 0 and round(-1.5) is -2. However, this is dependent on OS services and on representation error (since e.g. 0.15 is not represented exactly, the rounding rule applies to the represented number and not to the printed number, and so round(0.15, 1) could be either 0.1 or 0.2). Monica Pisica wrote: Hi, I am getting some strange results using round - it seems that it depends if the number before the decimal point is odd or even For example: round(1.5)[1] 2 round(2.5)[1] 2 While i would expect that round(2.5) be 3 and not 2. Do you have any explanation for that? I really appreciate your input, Monica _ [[trailing spam removed]] [[alternative HTML version deleted]] __ 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. -- David C. Howell PO Box 770059 627 Meadowbrook Circle Steamboat Springs, CO 80477 __ 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.
