[Rd] [External] Re: zapsmall(x) for scalar x

[Steve Martin]

Thanks for sharing, Martin. You're right that the interface for mFUN
should be more general than I initially thought.*

Perhaps you have other cases/examples where the ina argument is
useful, in which case ignore me, but your example with the robust mFUN
doesn't use the ina argument. What about having mFUN be only an
argument of x (NAs and all), with a default of \(x) max(abs(x), na.rm
= TRUE)? It's a minor difference, but it might make the mFUN argument
a bit simpler to use (no need to carry a dummy argument when NAs in x
can be handled directly).

Steve

* Tangent: Does boxplot.stats() use the number of NA values? The
documentation says NAs are omitted, and a quick scan of the code and
some tests suggests boxplot.stats(x) should give the same result as
boxplot.stats(x[!is.na(x)]), although I may be missing something. But
your point is well taken, and the interface should be more general
than I initially thought.

On Tue, 19 Dec 2023 at 11:25, Martin Maechler
<maechler using stat.math.ethz.ch> wrote:
>
> >>>>> Steve Martin
> >>>>>     on Mon, 18 Dec 2023 07:56:46 -0500 writes:
>
>     > Does mFUN() really need to be a function of x and the NA values of x? I
>     > can't think of a case where it would be used on anything but the non-NA
>     > values of x.
>
>     > I think it would be easier to specify a different mFUN() (and document this
>     > new argument) if the function has one argument and is applied to the non-NA
>     > values of x.
>
>     > zapsmall <- function(x,
>     >     digits = getOption("digits"),
>     >     mFUN = function(x) max(abs(x)),
>     >     min.d = 0L) {
>     >     if (length(digits) == 0L)
>     >         stop("invalid 'digits'")
>     >     if (all(ina <- is.na(x)))
>     >         return(x)
>     >     mx <- mFUN(x[!ina])
>     >     round(x, digits = if(mx > 0) max(min.d, digits - as.numeric(log10(mx)))
>     > else digits)
>     > }
>
>     > Steve
>
> Thank you, Steve,
> you are right that it would look simpler to do it that way.
>
> On the other hand, in your case, mFUN() no longer sees the
> original  n observations, and would not know if there where NAs
> in that case how many NAs there were in the original data.
>
> The examples I have on my version of zapsmall's help page (see below)
> uses a robust mFUN, "the upper hinge of a box plot":
>
>    mF_rob <- function(x, ina) boxplot.stats(x, do.conf=FALSE)$stats[5]
>
> and if you inspect boxplot.stats() you may know that indeed it
> also wants to use the full data 'x' to compute its statistics and
> then deal with NAs directly.  Your simplified mFUN interface
> would not be fully consistent with boxplot(), and I think could
> not be made so,  hence my more flexible 2-argument "design" for  mFUN().
>
> .... and BTW, these examples also exemplify the use of  `min.d`
> about which  Serguei Sokol asked for an example or two.
>
> Here I repeat my definition of zapsmall, and then my current set
> of examples:
>
> zapsmall <- function(x, digits = getOption("digits"),
>                      mFUN = function(x, ina) max(abs(x[!ina])), min.d = 0L)
> {
>     if (length(digits) == 0L)
>         stop("invalid 'digits'")
>     if (all(ina <- is.na(x)))
>         return(x)
>     mx <- mFUN(x, ina)
>     round(x, digits = if(mx > 0) max(min.d, digits - as.numeric(log10(mx))) else digits)
> }
>
>
> ##--- \examples{
> x2 <- pi * 100^(-2:2)/10
>    print(  x2, digits = 4)
> zapsmall(  x2) # automatical digits
> zapsmall(  x2, digits = 4)
> zapsmall(c(x2, Inf)) # round()s to integer ..
> zapsmall(c(x2, Inf), min.d=-Inf) # everything  is small wrt  Inf
>
> (z <- exp(1i*0:4*pi/2))
> zapsmall(z)
>
> zapShow <- function(x, ...) rbind(orig = x, zapped = zapsmall(x, ...))
> zapShow(x2)
>
> ## using a *robust* mFUN
> mF_rob <- function(x, ina) boxplot.stats(x, do.conf=FALSE)$stats[5]
> ## with robust mFUN(), 'Inf' is no longer distorting the picture:
> zapShow(c(x2, Inf), mFUN = mF_rob)
> zapShow(c(x2, Inf), mFUN = mF_rob, min.d = -5) # the same
> zapShow(c(x2, 999), mFUN = mF_rob) # same *rounding* as w/ Inf
> zapShow(c(x2, 999), mFUN = mF_rob, min.d =  3) # the same
> zapShow(c(x2, 999), mFUN = mF_rob, min.d =  8) # small diff
> ##--- }
>
>
>
>     > On Mon, Dec 18, 2023, 05:47 Serguei Sokol via R-devel <r-devel using r-project.org>
>     > wrote:
>
> > Le 18/12/2023 à 11:24, Martin Maechler a écrit :
> > >>>>>> Serguei Sokol via R-devel
> > >>>>>>      on Mon, 18 Dec 2023 10:29:02 +0100 writes:
> > >      > Le 17/12/2023 à 18:26, Barry Rowlingson a écrit :
> > >      >> I think what's been missed is that zapsmall works relative to the absolute
> > >      >> largest value in the vector. Hence if there's only one
> > >      >> item in the vector, it is the largest, so its not zapped. The function's
> > >      >> raison d'etre isn't to replace absolutely small values,
> > >      >> but small values relative to the largest. Hence a vector of similar tiny
> > >      >> values doesn't get zapped.
> > >      >>
> > >      >> Maybe the line in the docs:
> > >      >>
> > >      >> " (compared with the maximal absolute value)"
> > >      >>
> > >      >> needs to read:
> > >      >>
> > >      >> " (compared with the maximal absolute value in the vector)"
> > >
> > >      > I agree that this change in the doc would clarify the situation but
> > >      > would not resolve proposed corner cases.
> > >
> > >      > I think that an additional argument 'mx' (absolute max value of
> > >      > reference) would do. Consider:
> > >
> > >      > zapsmall2 <-
> > >      > function (x, digits = getOption("digits"), mx=max(abs(x),  na.rm=TRUE))
> > >      > {
> > >      >     if (length(digits) == 0L)
> > >      >         stop("invalid 'digits'")
> > >      >     if (all(ina <- is.na(x)))
> > >      >         return(x)
> > >      >     round(x, digits = if (mx > 0) max(0L, digits - as.numeric(log10(mx))) else digits)
> > >      > }
> > >
> > >      > then zapsmall2() without explicit 'mx' behaves
> > >      > identically to actual
> > >      > zapsmall() and for a scalar or a vector of identical value, user
> > can
> > >      > manually fix the scale of what should be considered as small:
> > >
> > >      >> zapsmall2(y)
> > >      > [1] 2.220446e-16
> > >      >> zapsmall2(y, mx=1)
> > >      > [1] 0
> > >      >> zapsmall2(c(y, y), mx=1)
> > >      > [1] 0 0
> > >      >> zapsmall2(c(y, NA))
> > >      > [1] 2.220446e-16           NA
> > >      >> zapsmall2(c(y, NA), mx=1)
> > >      > [1]  0 NA
> > >
> > >      > Obviously, the name 'zapsmall2' was chosen just for this
> > explanation.
> > >      > The original name 'zapsmall' could be reused as a full backward
> > >      > compatibility is preserved.
> > >
> > >      > Best,
> > >      > Serguei.
> [.......................]
>