... Some R tutorial recommendations can be found here:
https://www.rstudio.com/online-learning/#R Hadley W.'s book might also be useful to you: http://adv-r.had.co.nz/ Cheers, 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 Sun, Apr 30, 2017 at 9:35 AM, Duncan Murdoch <murdoch.dun...@gmail.com> wrote: > On 30/04/2017 12:26 PM, Ashim Kapoor wrote: >> >> Dear All, >> >> This answer is very clear. Many thanks. >> >> I am now confused about how str*ucture works. Where can I read more about >> when does it return language / logical / chr ? I would want to read that >> so I can interpret the result of structure. I don't think ?str contains >> this.To me, logical and chr make sense, what does language mean? I think I >> need to read some more. > > > I would read the R Language Definition manual, and then bits and pieces of R > Internals, as necessary. These are both included with R. There are also > books separate from R that talk about these things, but I don't know which > to recommend. > > Duncan Murdoch > > >> >> Many thanks, >> Ashim >> >> On Tue, Apr 25, 2017 at 3:14 PM, Martin Maechler >> <maech...@stat.math.ethz.ch >>> >>> wrote: >> >> >>>>>>>> Ashim Kapoor <ashimkap...@gmail.com> >>>>>>>> on Tue, 25 Apr 2017 14:02:18 +0530 writes: >>> >>> >>> > Dear all, >>> > I am not able to understand the interplay of absolute vs relative >>> and >>> > tolerance in the use of all.equal >>> >>> > If I want to find out if absolute differences between 2 >>> numbers/vectors are >>> > bigger than a given tolerance I would do: >>> >>> > all.equal(1,1.1,scale=1,tol= .1) >>> >>> > If I want to find out if relative differences between 2 >>> numbers/vectors are >>> > bigger than a given tolerance I would do : >>> >>> > all.equal(1,1.1,tol=.1) >>> >>> > ############################################################ >>> ###################################################################### >>> >>> > I can also do : >>> >>> > all.equal(1,3,tol=1) >>> >>> > to find out if the absolute difference is bigger than 1.But here I >>> won't be >>> > able to detect absolute differences smaller than 1 in this case,so >>> I >>> don't >>> > think that this is a good way. >>> >>> > My query is: what is the reasoning behind all.equal returning the >>> absolute >>> > difference if the tolerance >= target and relative difference if >>> tolerance >>> > < target? >>> (above, it is tol >/<= |target| ie. absolute value) >>> >>> >>> The following are desiderata / restrictions : >>> >>> 1) Relative tolerance is needed to keep things scale-invariant >>> i.e., all.equal(x, y) and all.equal(1000 * x, 1000 * y) >>> should typically be identical for (almost) all (x,y). >>> >>> ==> "the typical behavior should use relative error tolerance" >>> >>> 2) when x or y (and typically both!) are very close to zero it >>> is typically undesirable to keep relative tolerances (in the >>> boundary case, they _are_ zero exactly, and "relative error" is >>> undefined). >>> E.g., for most purposes, 3.45e-15 and 1.23e-17 should be counted as >>> equal to zero and hence to themselves. >>> >>> 1) and 2) are typically reconciled by switching from relative to absolute >>> when the arguments are close to zero (*). >>> >>> The exact cutoff at which to switch from relative to absolute >>> (or a combination of the two) is somewhat arbitrary(*2) and for >>> all.equal() has been made in the 1980's (or even slightly >>> earlier?) when all.equal() was introduced into the S language at >>> Bell labs AFAIK. Maybe John Chambers (or Rick Becker or ..., >>> but they may not read R-help) knows more. >>> *2) Then, the choice for all.equal() is in some way "least arbitrary", >>> using c = 1 in the more general tolerance >= c*|target| framework. >>> >>> *) There have been alternatives in "the (applied numerical >>> analysis / algorithm) literature" seen in published algorithms, >>> but I don't have any example ready. >>> Notably some of these alternatives are _symmetric_ in (x,y) >>> where all.equal() was designed to be asymmetric using names >>> 'target' and 'current'. >>> >>> The alternative idea is along the following thoughts: >>> >>> Assume that for "equality" we want _both_ relative and >>> absolute (e := tolerance) "equality" >>> >>> |x - y| < e (|x|+|y|)/2 (where you could use |y| or |x| >>> instead of their mean; all.equal() >>> uses |target|) >>> |x - y| < e * e1 (where e1 = 1, or e1 = 10^-7..) >>> >>> If you add the two inequalities you get >>> >>> |x - y| < e (e1 + |x+y|/2) >>> >>> as check which is a "mixture" of relative and absolute tolerance. >>> >>> With a somewhat long history, my gut feeling would nowadays >>> actually prefer this (I think with a default of e1 = e) - which >>> does treat x and y symmetrically. >>> >>> Note that convergence checks in good algorithms typically check >>> for _both_ relative and absolute difference (each with its >>> tolerance providable by the user), and the really good ones for >>> minimization do check for (approximate) gradients also being >>> close to zero - as old timers among us should have learned from >>> Doug Bates ... but now I'm really diverging. >>> >>> Last but not least some R code at the end, showing that the >>> *asymmetric* >>> nature of all.equal() may lead to somewhat astonishing (but very >>> logical and as documented!) behavior. >>> >>> Martin >>> >>> > Best Regards, >>> > Ashim >>> >>> >>>> ## The "data" to use: >>>> epsQ <- lapply(seq(12,18,by=1/2), function(P) bquote(10^-.(P))); >>> >>> names(epsQ) <- sapply(epsQ, deparse); str(epsQ) >>> List of 13 >>> $ 10^-12 : language 10^-12 >>> $ 10^-12.5: language 10^-12.5 >>> $ 10^-13 : language 10^-13 >>> $ 10^-13.5: language 10^-13.5 >>> $ 10^-14 : language 10^-14 >>> $ 10^-14.5: language 10^-14.5 >>> $ 10^-15 : language 10^-15 >>> $ 10^-15.5: language 10^-15.5 >>> $ 10^-16 : language 10^-16 >>> $ 10^-16.5: language 10^-16.5 >>> $ 10^-17 : language 10^-17 >>> $ 10^-17.5: language 10^-17.5 >>> $ 10^-18 : language 10^-18 >>> >>>> str(lapply(epsQ, function(tl) all.equal(3.45e-15, 1.23e-17, tol = >>> >>> eval(tl)))) >>> List of 13 >>> $ 10^-12 : logi TRUE >>> $ 10^-12.5: logi TRUE >>> $ 10^-13 : logi TRUE >>> $ 10^-13.5: logi TRUE >>> $ 10^-14 : logi TRUE >>> $ 10^-14.5: chr "Mean relative difference: 0.9964348" >>> $ 10^-15 : chr "Mean relative difference: 0.9964348" >>> $ 10^-15.5: chr "Mean relative difference: 0.9964348" >>> $ 10^-16 : chr "Mean relative difference: 0.9964348" >>> $ 10^-16.5: chr "Mean relative difference: 0.9964348" >>> $ 10^-17 : chr "Mean relative difference: 0.9964348" >>> $ 10^-17.5: chr "Mean relative difference: 0.9964348" >>> $ 10^-18 : chr "Mean relative difference: 0.9964348" >>> >>>> ## Now swap `target` and `current` : >>>> str(lapply(epsQ, function(tl) all.equal(1.23e-17, 3.45e-15, tol = >>> >>> eval(tl)))) >>> List of 13 >>> $ 10^-12 : logi TRUE >>> $ 10^-12.5: logi TRUE >>> $ 10^-13 : logi TRUE >>> $ 10^-13.5: logi TRUE >>> $ 10^-14 : logi TRUE >>> $ 10^-14.5: chr "Mean absolute difference: 3.4377e-15" >>> $ 10^-15 : chr "Mean absolute difference: 3.4377e-15" >>> $ 10^-15.5: chr "Mean absolute difference: 3.4377e-15" >>> $ 10^-16 : chr "Mean absolute difference: 3.4377e-15" >>> $ 10^-16.5: chr "Mean absolute difference: 3.4377e-15" >>> $ 10^-17 : chr "Mean relative difference: 279.4878" >>> $ 10^-17.5: chr "Mean relative difference: 279.4878" >>> $ 10^-18 : chr "Mean relative difference: 279.4878" >>> >>>> >>> >> >> [[alternative HTML version deleted]] >> >> ______________________________________________ >> R-help@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. >> > > ______________________________________________ > R-help@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. ______________________________________________ R-help@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.
