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From: Dan Mcleran (dan.mcleran_at_[hidden])
Date: 2002-10-24 10:39:02

1D Numerical Integration


I have replied to my own post to start a discussion on the interface for a
1D numerical integration library. It seems that most everyone agrees that
separation of the interface for 1D, 2D, etc. is the right thing to do. I
also think everyone agrees that 1D numerical integration is straightforward
and could be part of boost.

Here are what I would suggest to be the high-level requirements for
whichever direction we go for 1D numerical integration:

1. They must be able to integrate a user-defined function from point a to
point b in increments of deltax.
2. They must be able to integrate a set of results, i.e. results of f(x),
from point a to point b, given that the deltax can either be provided by the
user or it is implied that the deltax can be calculated by 1/(number of data
points - 1).

As I see it, there are many ways to do this and I've tried to outline what I
see as the viable ways to go:

STL-style algorithm(s):

    We could have an algorithm for each type of numerical integration (I
have omitted parameters to simplify the discussion)

    area = trapezoidal_integral();
    area = simpsons_integral();
    area = romberg_integral();

    We could also have a generic algorithm where the integration routine
could be a template parameter (maybe a combination of algorithms
and functors). I have added params here for clarity. The example
below would be an algoritm that takes begin and end points, deltax, the
function to integrate, and the integration method.

    area = integrate(a,b,deltax,Function,TrapezoidalIntegrator);


    We could have numerous function objects:


First-class Object(s)

    Or we could have a class that could take a template parameter for which
method to use:

    Integrator<TrapezoidalRule> i;

    area = i.integrate();

My vote would be a collection of STL-style algorithms. I think these are the
most straightforward and very self-documenting.

Other ideas for alternative interfaces would be welcome.


Dan McLeran

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