On Thu, Oct 6, 2011 at 4:30 PM, Edwin Woollett <woollett at charter.net> wrote:
> On Oct. 6, 2011, Raymond Toy wrote:
> ------------------------------**-
>
> So? I think it just means that quadpack was rather conservative in its
>> estimate of what the relative error actually was >and the limit was too low
>> for quadpack to refine the estimate any further.
>>
>> But what if you didn't know the analytical solution and therefore the
>> "true" error? All you would have is the >estimated value. Then what?
>>
>
> The first step should be to roughly estimate the size of the
> integral. I think quad_qag with key = 6, limit = 800, epsrel = 1.0E-2
> just to get a rough value, even if an oscillatory integrand.
>
What will you do with the rough value? Why not just try both qag and qags
and choose the one that gives the "better" answer?
You might find the following interesting:
http://trac.common-lisp.net/f2cl/browser/packages/quadpack/quadpack-tests.lisp
It's in lisp, but you don't need to know lisp. Just read the comments.
These are a bunch of tests given in the quadpack book. There are a bunch of
tests illustrating the performance of several algorithms on different
integrals. Some are comparisons of the same integral with different
algorithms.
The book also said something about having to do some thinking before
applying the algorithms. I believe there was an example there that was very
difficult for quadpack, but a little bit of thought allowed you to change
the integral into something that was much easier. There was also some tips
on how to do multiple integrals that might be useful. (There was a
restriction there on using different algorithms for the multiple integrals,
but maxima shouldn't have that problem because all the storage is local, so
recursive calls should not be a problem.)
I will look into suppressing the slatec messages.
Ray