Re: [boost] Numerical Quadrature Library/Boost.Accumulators

From: Matthias Schabel (boost_at_[hidden])
Date: 2006-12-07 15:29:04

> Ok...then we ought to discuss those extra parameters as well:
>
> 1. Precision: what should be its type? Return type would be natural,
> but it is problematic for complex integrands.
> 2. How to evaluate if the desired precision is reached? In the code I
> uploaded I explicitely let the user use it's own predicate, which I
> would say is important especially as some people would like to
> compare things in ULPs.

If there is a push to begin thinking about numerical libraries to be  
incorporated into Boost,
I would vote to think seriously about having a return type that  
includes error estimates (as
GSL does with it's result type or, perhaps, something like the  
measurement class I threw
together as a demo for mcs::units, attached). If implicit conversion  
to the result type was
allowed, it would be transparent to functions that didn't care about  
errors and visible to those
that do.

As far as I can see, precision needs to be the same type as the  
return type since it represents
uncertainty in the latter. That is, the range of possible return  
values would be [result - n*error,
result + n*error]. Do you have a case in mind where this isn't true?

Also, though I haven't looked closely at it, it seems like  
integrators, in 1D at least, are general
accumulators and might fit into the Boost.Accmulators framework  
nicely...

Matthias

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Matthias Schabel, Ph.D.
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