Re: Switching default integrator for multiple variable to quadcc

[Daniel J Sebald]

On 01/19/2013 05:14 PM, twinclouds wrote:
> @Rik
> I don't know if this is related to the problem I am having right now.  When
> I use Octave 3.2.4, the integration is pretty fast.  The only problem is
> when the area gets too large, i.e., most area are zeros, it shows "warning:
> quadgk: non-finite integrand encountered."  When I use Octave 3.6.3, I don't
> have this problem but it gets very slow, from a few seconds to a few
> minutes.  I would like to change the default integrator but don't know how
> to.  Add the name of the integrator as the last argument of dblquad yields
> all sorts of errors.  Any suggestions?

Twinclouds,

The change that Rik made is in the scripts portion of the source tree. 
The latest source code can be found here:

http://hg.savannah.gnu.org/hgweb/octave/file/d56dd6794a20/scripts/general

There are a small number of related changesets associated with Rik's mod 
in this log (search CNTRL-F for "dbl"):

http://hg.savannah.gnu.org/hgweb/octave/shortlog/68a59630798d

The most relevant changeset is here:

http://hg.savannah.gnu.org/hgweb/octave/rev/eb4afb6a1a51

which should give a good idea of the changes Rik made and what you can 
do if you want to make changes.  (Start by getting the most recent 
version and go from there.)

...

I'm curious how the error you describe is coming about.  "Non-finite 
integrand" suggests your function might have a singularity somewhere. 
If you are integrating through a singularity, that might be where the 
slowness is coming from.  But you described an integrand with a lot of 
negligible area--that sort of thing is usually not a problem for 
adaptive integrators and runs pretty fast.  Discontinuities and 
singularities are typically where numerical integration slows down and 
often breaks with poor accuracy.  Some tricks you can try is that if you 
know where there is a singularity or discontinuity, the problem can be 
broken up into multiple sections.

Dan



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--

Dan Sebald
email: daniel(DOT)sebald(AT)ieee(DOT)org
URL: http://www(DOT)dansebald(DOT)com