Finding sufficiently accurate rational approximations to a real number, can be done using fractions() in MASS, which uses continued fractions. "Sufficient" accuracy can be specified using the number of cycles and maximum denominator size options (note that max.denom is the final term in the continued fraction).
Some examples: > library(MASS) > fractions(0.333333,max.denom=100000) [1] 1/3 > fractions(0.333333,max.denom=1000000) [1] 1519169814041/4557513999637 > fractions(0.333333,max.denom=1000000,cycles=11) [1] 8587703744937/25763136997948 > fractions(pi,max=1) [1] 3 > fractions(pi,max=10) [1] 22/7 > fractions(pi,max=100) [1] 355/113 > fractions(pi,max=1000) [1] 4272943/1360120 > fractions(pi,max=1000,cycles=12) [1] 80143857/25510582 This last rational approximation to pi is quite accurate, up to machine precision (i.e. 16 digits) Ravi. ---------------------------------------------------------------------------- ------- Ravi Varadhan, Ph.D. Assistant Professor, The Center on Aging and Health Division of Geriatric Medicine and Gerontology Johns Hopkins University Ph: (410) 502-2619 Fax: (410) 614-9625 Email: [EMAIL PROTECTED] Webpage: http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html ---------------------------------------------------------------------------- -------- -----Original Message----- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Thomas Lumley Sent: Thursday, September 13, 2007 11:34 AM To: Mauro Arnoldi Cc: r-help@r-project.org Subject: Re: [R] Number -> Fraction On Thu, 13 Sep 2007, Mauro Arnoldi wrote: > Hi everybody! > I'm new to this list and also to the R program. > > I'd like to know if there is a function able to convert results into > Fractional form like my scientific calculator have. For example: > >> 1/3 > [1] 0.3333333 > >> function_that_return_a_fraction_from_numbers(0.3333333) > [1] 1/3 > This must have some restrictions (so it doesn't return 3333333/1000000, which would be a more accurate fraction). One approach is > unfrac <- function(x, max=100, tol=0.01){ num <- x * (1:max) err <- (num - round(num)) * (1:max) if (!any(abs(err) < tol)) return(NA) i <- which.min(abs(err)) c(round(num[i]), i) } This returns the best fraction approximation with denominator up to `max`, where `best` is in terms of the non-integer part of the numerator, and no answer is given if the non-integer part of the numerator is more than `tol` > unfrac(0.3333333) [1] 1 3 > unfrac(pi) [1] NA > unfrac(pi,max=1000) [1] 355 113 > unfrac(pi,tol=0.1) [1] 22 7 -thomas ______________________________________________ R-help@r-project.org 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@r-project.org 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.
