boost.numeric (was Re: Re: matrix library?)

From: Eric Ford (eford_at_[hidden])
Date: 2001-03-21 02:17:51

> Here would be my wishlist:

I generally agree with Kevin (hi, kevin), but thought I'd add my
comments...  While I like the idea of matrix routines, I think MTL is
making reasonable progress and making a blitz matrix library might be
redundant/premature.  Personally, I'd find a good library for
integrating DEs much more valuable than yet another matrix library.  I
hope the original subject line doens't bias towards matricies too
much.

> Numerical Integration of nonlinear systems of differential equations
> (standard algorithms include things like Runge-Kutta,
Bulirsch-Stoer,
> shooting, and relaxation methods (Chapters 16 and 17 or Numerical
> Recipes).

Personally, I solve ODEs most often, PDEs second most often.  While
Numerical Recipies is generally good algorithmically (but poorly
implemented), there are licensing problems that make it a pain to
share source code.  Hence, I'd very much like to see a templatized set
of routines for DEs.  Important template parameters (probably in
traits) would include things like integrator, error control, stopping
conditions, interpolation algorithms, guessing (initial conditions for
shooting methods) algorithm.  There also needs to be a reasonable
way to pass parameters (at either run or compile time) into the
inner-most function evaluating derivatives.    

(I've started making such a library, but I've never had time to think
first and do a good job, so while I might be able to offer some
warnings, I don't think my code would be a valuable addition.  Also, I
still have several routines which are merely fancy interfaces to NR
routines and not written from scratch, so I couldn't legally post any
wokring, non-trivial code.) 

 
> Monte Carlo function integration routines.

Yes.  I'd also like to see routines for integrating functions with
trapazoidal or simpson type methods, since these can be much faster
for functinos known to be well behaved.  Again things like singularity
types and locations should be included in traits.
 
> A portable collection of special functions.

Yes.  
 
> Statistical data analysis routines (including, particularly, curve
> fitting algorithms with error estimation and root finding
algorithms)
 
Lower on my list, but still important.  I'd want to include traits to
allow different estimators, especially to allow robust statistics.
 
> I'd also hope to see a boost numerics library generally focus on
> optimizing for "standard types", such as double and complex<double>;
> generally speaking, I think it is less important for these libraries
to
> be accessible for generic numeric types if that genericity causes
> substantial performance impacts when they are used with the built-in
and
> complex types.

Agreed.

I hope something good comes out of this.

Eford