From plummerm at iarc.fr  Wed Jul 17 19:37:10 2013
From: plummerm at iarc.fr (Martyn Plummer)
Date: Wed, 17 Jul 2013 17:37:10 +0000
Subject: [Rd] Problem following an R bug fix to integrate()
In-Reply-To: <CAML4n3P5tekMoE+k3287tm+BDy5DqqwK=bXx4j1shwEuAPeyQw@mail.gmail.com>
References: <CAML4n3P5tekMoE+k3287tm+BDy5DqqwK=bXx4j1shwEuAPeyQw@mail.gmail.com>
Message-ID: <1374082630.2272.43.camel@braque.iarc.fr>

On Tue, 2013-07-16 at 13:55 +0200, Hans W Borchers wrote:
> I have been told by the CRAN administrators that the following code generated
> an error on 64-bit Fedora Linux (gcc, clang) and on Solaris machines (sparc,
> x86), but runs well on all other systems):
> 
>     > fn <- function(x, y) ifelse(x^2 + y^2 <= 1, 1 - x^2 - y^2, 0)
> 
>     > tol <- 1.5e-8
>     > fy <- function(x) integrate(function(y) fn(x, y), 0, 1,
>                             subdivisions = 300, rel.tol = tol)$value
>     > Fy <- Vectorize(fy)
> 
>     > xa <- -1; xb <- 1
>     > Q  <- integrate(Fy, xa, xb,
>                 subdivisions = 300, rel.tol = tol)$value
> 
>     Error in integrate(Fy, xa, xb, subdivisions = 300, rel.tol = tol) :
>     roundoff error was detected
> 
> Obviously, this realizes a double integration, split up into two 1-dimensional
> integrations, and the result shall be pi/4. I wonder what a 'roundoff error'
> means in this situation.
> 
> In my package, this test worked well, w/o error or warnings, since July 2011,
> on Windows, Max OS X, and Ubuntu Linux. I have no chance to test it on one of
> the above mentioned systems. Of course, I can simply disable these tests, but
> I would not like to do so w/o good reason.
> 
> If there is a connection to a bug fix to integrate(), with NEWS item
> 
>     "integrate() reverts to the pre-2.12.0 behaviour.  (PR#15219)",
> 
> then I do not understand what this pre-2.12.0 behavior really means.
> 
> Thanks for any help or a hint to what shall be changed.

You can see the bug report here:

https://bugs.r-project.org/bugzilla3/show_bug.cgi?id=15219

It concerns the behaviour of integrate with a small error tolerance.
>From 2.12.0 to 3.0.1 integrate was not working correctly with small
error tolerance values, in the sense that small values did not improve
accuracy and the accuracy was mis-reported.

The tolerance in your example (1.5e-8) is considerably smaller than the
default (1.2e-4). My guess is that the rounding error always existed but
was not detected due to the bug.  You might try a larger tolerance. I
have tested your example and increasing the tolerance to 1.5e-7 removes
the error.

Martyn


> Hans W Borchers
> 
> PS:
> This kind of tricky definition in function 'fn' has caused some discussion on
> this list in July 2009. I still think it should be allowed to proceed in this
> way.
> 
> ______________________________________________
> R-devel at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-devel

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[Rd] Problem following an R bug fix to integrate()
Martyn Plummer