From ravi.varadhan at jhu.edu  Thu May 30 16:20:19 2013
From: ravi.varadhan at jhu.edu (Ravi Varadhan)
Date: Thu, 30 May 2013 14:20:19 +0000
Subject: [Rd] RFC: a "safe" uniroot() function for future R
In-Reply-To: <CA+COuteo2iQHZyneAy+x7qsfB7G_Erc2GVXpcSTyxez-FVTuOQ@mail.gmail.com>
References: <20903.2899.135264.914688@stat.math.ethz.ch>
	<CA+COuteo2iQHZyneAy+x7qsfB7G_Erc2GVXpcSTyxez-FVTuOQ@mail.gmail.com>
Message-ID: <2F9EA67EF9AE1C48A147CB41BE2E15C344EA4A@DOM-EB-MAIL2.win.ad.jhu.edu>

Dear Martin,

I am not sure I like this idea of expanding the interval. It can have bad consequences.  The best feature of uniroot is that it makes the user think about the behavior of the function.  Your suggestion is in the spirit of making him unthink (if there is such a word!).

Here is a cautionary example:

> f <- function(x) exp(-x)

> unirootS(f, c(0,2))
$root
[1] 1312.7

$f.root
[1] 0

$iter
[1] 0

$estim.prec
[1] 0

The existing `uniroot' does the right thing.

> uniroot(f, c(0,2))
Error in uniroot(f, c(0, 2)) : 
  f() values at end points not of opposite sign
>

Best,
Ravi

> -----Original Message-----
> From: r-devel-bounces at r-project.org [mailto:r-devel-bounces at r-project.org]
> On Behalf Of Duncan Murdoch
> Sent: Thursday, May 30, 2013 5:28 AM
> To: Martin Maechler
> Cc: R. Devel List
> Subject: Re: [Rd] RFC: a "safe" uniroot() function for future R
> 
> On Thu, May 30, 2013 at 4:18 AM, Martin Maechler
> <maechler at 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
> >
> > ______________________________________________
> > R-devel at r-project.org mailing list
> > https://stat.ethz.ch/mailman/listinfo/r-devel
> >
> 
> 	[[alternative HTML version deleted]]



[Rd] RFC: a "safe" uniroot() function for future R
Ravi Varadhan