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

[Martin Maechler]

>>>>> 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.
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