From: Hugo Duncan (hugoduncan_at_[hidden])
Date: 2007-12-06 15:27:41
On Thu, 06 Dec 2007 Neal Becker wrote:
> Haven't studied it yet - but one question. Does this address
> multi-dimensional integration? Could it? Should it?
It is capable of simultaneously integrating multiple functions of the
same, single, variable. I use this to integrate x,y coordinates depending
on an independent variable (where the cost of calculating both x and y is
approximately the same as the cost of calculating either one).
It does not address multi-dimensional integration. By using Fubini's
theorem, it could be made to, somewhat inefficiently. Other methods (eg
Monte-Carlo) have no similarities implementation wise.
There are a number of other "integration" problems that could be
addressed, such as ODE's, but again the algorithm's required are
different. I would prefer to limit the scope to 1D integration methods.
Even with 1D integrals there are areas not covered by the library -
semi-infinte and infinite ranges (QUADPACK's QAGI), specification of known
singularites (QAGP), Cauchy Principal Value integration (QAWC), etc