Re: [boost] [rfc] Quadrature library for numerical integration of definite integrals

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