That crossed my mind too, but presumably someone designed choose() to handle the near-integer cases specially. Otherwise, we already have beta() -- you just need to remember what the connection is ;-).
I would expect that it has to do with the binomial and negative binomial distributions, but I can't offhand picture a calculation that leads to integer k, n plus/minus a tiny numerical error of the sort that one may encounter with, say, seq(). -pd ;-) choose(a,b) = 1/(beta(a-b+1,b+1)*(a+1)) or thereabouts > On 14 Jan 2020, at 19:36 , John Mount <jmo...@win-vector.com> wrote: > > > At the risk of throwing oil on a fire. If we are talking about fractional > values of choose() doesn't it make sense to look to the gamma function for > the correct analytic continuation? In particular k<0 may not imply the > function should evaluate to zero until we get k<=-1. > > Example: > > ``` r > choose(5, 4) > #> [1] 5 > > gchoose <- function(n, k) { > gamma(n+1)/(gamma(n+1-k) * gamma(k+1)) > } > > gchoose(5, 4) > #> [1] 5 > gchoose(5, 0) > #> [1] 1 > gchoose(5, -0.5) > #> [1] 0.2351727 > ``` > >> On Jan 14, 2020, at 10:20 AM, peter dalgaard <pda...@gmail.com> wrote: >> >> OK, I see what you mean. But in those cases, we don't get the catastrophic >> failures from the >> >> if (k < 0) return 0.; >> if (k == 0) return 1.; >> /* else: k >= 1 */ >> >> part, because at that point k is sure to be integer, possibly after >> rounding. >> >> It is when n-k is approximately but not exactly zero and we should return 1, >> that we either return 0 (negative case) or n (positive case; because the >> n(n-1)(n-2)... product has at least one factor). In the other cases, we get >> 1 or n(n-1)(n-2)...(n-k+1) which if n is near-integer gets rounded to >> produce an integer, due to the >> >> return R_IS_INT(n) ? R_forceint(r) : r; >> >> part. >> >> -pd >> >> >> >>> On 14 Jan 2020, at 17:02 , Duncan Murdoch <murdoch.dun...@gmail.com> wrote: >>> >>> On 14/01/2020 10:50 a.m., peter dalgaard wrote: >>>>> On 14 Jan 2020, at 16:21 , Duncan Murdoch <murdoch.dun...@gmail.com> >>>>> wrote: >>>>> >>>>> On 14/01/2020 10:07 a.m., peter dalgaard wrote: >>>>>> Yep, that looks wrong (probably want to continue discussion over on >>>>>> R-devel) >>>>>> I think the culprit is here (in src/nmath/choose.c) >>>>>> if (k < k_small_max) { >>>>>> int j; >>>>>> if(n-k < k && n >= 0 && R_IS_INT(n)) k = n-k; /* <- Symmetry */ >>>>>> if (k < 0) return 0.; >>>>>> if (k == 0) return 1.; >>>>>> /* else: k >= 1 */ >>>>>> if n is a near-integer, then k can become non-integer and negative. In >>>>>> your case, >>>>>> n == 4 - 1e-7 >>>>>> k == 4 >>>>>> n - k == -1e-7 < 4 >>>>>> n >= 0 >>>>>> R_IS_INT(n) = TRUE (relative diff < 1e-7 is allowed) >>>>>> so k gets set to >>>>>> n - k == -1e-7 >>>>>> which is less than 0, so we return 0. However, as you point out, 1 would >>>>>> be more reasonable and in accordance with the limit as n -> 4, e.g. >>>>>>> factorial(4 - 1e-10)/factorial(1e-10)/factorial(4) -1 >>>>>> [1] -9.289025e-11 >>>>>> I guess that the fix could be as simple as replacing n by R_forceint(n) >>>>>> in the k = n - k step. >>>>> >>>>> I think that would break symmetry: you want choose(n, k) to equal >>>>> choose(n, n-k) when n is very close to an integer. So I'd suggest the >>>>> replacement whenever R_IS_INT(n) is true. >>>>> >>>> But choose() very deliberately ensures that k is integer, so choose(n, >>>> n-k) is ill-defined for non-integer n. >>> >>> That's only true if there's a big difference. I'd be worried about cases >>> where n and k are close to integers (within 1e-7). In those cases, k is >>> silently rounded to integer. As I read your suggestion, n would only be >>> rounded to integer if k > n-k. I think both n and k should be rounded to >>> integer in this near-integer situation, regardless of the value of k. >>> >>> I believe that lchoose(n, k) already does this. >>> >>> Duncan Murdoch >>> >>>> double r, k0 = k; >>>> k = R_forceint(k); >>>> ... >>>> if (fabs(k - k0) > 1e-7) >>>> MATHLIB_WARNING2(_("'k' (%.2f) must be integer, rounded to %.0f"), >>>> k0, k); >>>> >>>>> Duncan Murdoch >>>>> >>>>>> -pd >>>>>>> On 14 Jan 2020, at 00:33 , Wright, Erik Scott <eswri...@pitt.edu> wrote: >>>>>>> >>>>>>> This struck me as incorrect: >>>>>>> >>>>>>>> choose(3.999999, 4) >>>>>>> [1] 0.9999979 >>>>>>>> choose(3.9999999, 4) >>>>>>> [1] 0 >>>>>>>> choose(4, 4) >>>>>>> [1] 1 >>>>>>>> choose(4.0000001, 4) >>>>>>> [1] 4 >>>>>>>> choose(4.000001, 4) >>>>>>> [1] 1.000002 >>>>>>> >>>>>>> Should base::choose(n, k) check whether n is within machine precision >>>>>>> of k and return 1? >>>>>>> >>>>>>> Thanks, >>>>>>> Erik >>>>>>> >>>>>>> *** >>>>>>> sessionInfo() >>>>>>> R version 3.6.0 beta (2019-04-15 r76395) >>>>>>> Platform: x86_64-apple-darwin15.6.0 (64-bit) >>>>>>> Running under: macOS High Sierra 10.13.6 >>>>>>> >>>>>>> [[alternative HTML version deleted]] >>>>>>> >>>>>>> ______________________________________________ >>>>>>> r-h...@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. >> >> -- >> Peter Dalgaard, Professor, >> Center for Statistics, Copenhagen Business School >> Solbjerg Plads 3, 2000 Frederiksberg, Denmark >> Phone: (+45)38153501 >> Office: A 4.23 >> Email: pd....@cbs.dk Priv: pda...@gmail.com >> >> ______________________________________________ >> R-devel@r-project.org mailing list >> https://stat.ethz.ch/mailman/listinfo/r-devel > > --------------- > John Mount > http://www.win-vector.com/ > Our book: Practical Data Science with R > http://practicaldatascience.com > > > > > -- Peter Dalgaard, Professor, Center for Statistics, Copenhagen Business School Solbjerg Plads 3, 2000 Frederiksberg, Denmark Phone: (+45)38153501 Office: A 4.23 Email: pd....@cbs.dk Priv: pda...@gmail.com ______________________________________________ R-devel@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-devel