On Thu, May 30, 2013 at 4:18 AM, Martin Maechler <maechler@stat.math.ethz.ch
> wrote:

> With main R releases only happening yearly in spring, now is
> good time to consider *and* discuss new features for what we
> often call "R-devel" and more officially is
>   R Under development (unstable) (.....) -- "Unsuffered Consequences"
>
> Here is one such example I hereby expose to public scrutiny:
>
> A few minutes ago, I've committed the following to R-devel
> (the 'trunk' in the svn repository for R):
>
> ------------------------------------------------------------------------
> r62834 | maechler | 2013-05-30 10:01:33 +0200 (Thu, 30 May 2013) | 1 line
> Changed paths:
>    M doc/NEWS.Rd
>    M src/library/stats/NAMESPACE
>    M src/library/stats/R/nlm.R
>    M src/library/stats/man/uniroot.Rd
>    M tests/Examples/stats-Ex.Rout.save
>
> new "safe" uniroot() =: unirootS()  [may change; see R-devel e-mail]
> ------------------------------------------------------------------------
>
> The help file says
>
>      ‘unirootS()’ is a “safe” version of ‘uniroot()’, built on
>      ‘uniroot()’, also useful as drop-in replacement of ‘uniroot()’ in
>      some cases.  “Safe” means searching for the correct ‘interval =
>      c(lower,upper)’ if ‘sign(f(x))’ does not satisfy the requirements
>      at the interval end points; see the ‘Details’ section.
>
> We've had this function, called  safeUroot() in our package
> copula for a while now, where an earlier not-exported version
> has been in my package nor1mix even longer.
> When I was tempted to introduce it into yet another CRAN package
> I maintain,  I decided that this may be a sign that such a
> simple [ utility for / generalization of ] uniroot() should
> probably rather be added to R itself.
>
> The function definition, also visible in R's devel.sources, at the bottom
> of
>  https://svn.r-project.org/R/trunk/src/library/stats/R/nlm.R ,
> shows that unirootS() is a wrapper for uniroot() and
> is in principle 100% back compatible to uniroot() itself for all
> the cases where f(lower) and f(upper) are of differing sign and
> hence uniroot() does not give a quick error.
> unirootS() just has three new optional arguments, all with their
> defaults set such as to remain uniroot() compatible.
>
> So, one option instead of the currently commited one would be to
> adopt  unirootS() as "the new uniroot()" and rename current
> uniroot to .uniroot() {and still export both}.
>

I would probably prefer this.


>
> The capital "S" in the function name and the 'Sig' name is of
> course quite a matter of taste, and this case corresponds to my
> taste, but even that is part of the RFC.
>
>
> unirootS <- function(f, interval, ...,
>                      lower = min(interval), upper = max(interval),
>                      f.lower = f(lower, ...), f.upper = f(upper, ...),
>                      Sig = NULL, check.conv = FALSE,
>                      tol = .Machine$double.eps^0.25, maxiter = 1000, trace
> = 0)
>

A few comments:

1.  I don't think the name "Sig" conveys the meaning of that parameter
well.  If specified, it determines whether the function is increasing
or decreasing at the root, so maybe "Increasing" or "Upcrossing" (with a
logical value, default NA) would be better?

2.  In case 2 where the interval is expanded, wouldn't we save a bit of
time by saving the initial values?  E.g. if Sig == 1 so we want an
upcrossing,  but f.lower is positive, shouldn't we set upper to lower as we
expand lower downwards?

3.  Sometimes a user will want to force the solution to be between lower
and upper, and will want to signal an error if they are not acceptable.
If you do decide to merge this into uniroot that should be an option.

4.  It should count the search for the interval among the iterations, and
quit if it can't find an interval in that time.  For example,

unirootS( function(x) 1, c(0,1) )

never terminates.

Duncan Murdoch



{
>     if (   is.null(Sig) && f.lower * f.upper > 0 ||
>         is.numeric(Sig) && (Sig*f.lower > 0 || Sig*f.upper < 0)) {
>         if(trace)
>             cat(sprintf("search in [%g,%g]%s", lower, upper,
>                         if(trace >= 2)"\n" else " ... "))
>         Delta <- function(u) 0.01* pmax(1e-7, abs(u))
>         ## Two cases:
>         if(is.null(Sig)) {
>             ## case 1)  'Sig' unspecified --> extend (lower, upper) at the
> same time
>             delta <- Delta(c(lower,upper))
>             while(isTRUE(f.lower*f.upper > 0) && any(iF <-
> is.finite(c(lower,upper)))) {
>                 if(iF[1]) f.lower <- f(lower <- lower - delta[1])
>                 if(iF[2]) f.upper <- f(upper <- upper + delta[2])
>                 if(trace >= 2)
>                     cat(sprintf(" .. modified lower,upper: (%15g,%15g)\n",
>                                 lower,upper))
>                 delta <- 2 * delta
>             }
>         } else {
>             ## case 2) 'Sig' specified --> typically change only *one* of
> lower, upper
>             ## make sure we have Sig*f(lower) < 0 and Sig*f(upper) > 0:
>             delta <- Delta(lower)
>             while(isTRUE(Sig*f.lower > 0)) {
>                 f.lower <- f(lower <- lower - delta)
>                 if(trace) cat(sprintf(" .. modified lower: %g\n", lower))
>                 delta <- 2 * delta
>             }
>             delta <- Delta(upper)
>             while(isTRUE(Sig*f.upper < 0)) {
>                 f.upper <- f(upper <- upper + delta)
>                 if(trace) cat(sprintf(" .. modified upper: %g\n", upper))
>                 delta <- 2 * delta
>             }
>         }
>         if(trace && trace < 2)
>             cat(sprintf("extended to [%g, %g]\n", lower, upper))
>     }
>     if(!isTRUE(f.lower * f.upper <= 0))
>         stop("did not succeed extending the interval endpoints for
> f(lower) * f(upper) <= 0")
>     if(check.conv) {
>         r <- tryCatch(uniroot(f, ..., lower=lower, upper=upper,
>                               f.lower=f.lower, f.upper=f.upper,
>                               tol=tol, maxiter=maxiter),
>                       warning = function(w)w)
>         if(inherits(r, "warning"))
>             stop("convergence problem in zero finding: ", r$message)
>         else r
>     }
>     else
>         uniroot(f, ..., lower=lower, upper=upper,
>                 f.lower=f.lower, f.upper=f.upper,
>                 tol=tol, maxiter=maxiter)
> }
>
> -----------
>
> As said, your comments are very welcome!
> Note that I'm less interested in variations which gain 10-20% in
> speed benchmarks, rather I'd appreciate proposals for changes
> that give a "better" (in your sense) user interface.
>
> Martin Maechler, ETH Zurich
>
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> https://stat.ethz.ch/mailman/listinfo/r-devel
>

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