[boost] Request for commentary about Boost interest in a new numerics package

From: Marcus Mendenhall (marcus.h.mendenhall_at_[hidden])
Date: 2006-03-21 14:13:15

I have been working on a compact (1 header, 1 cpp file, total about  
1500 lines) and highly portable package for numerical operations on  
smooth functions.  The package is in internal use by my research  
collaborators at Vanderbilt, and is very stable.

The package consists of routines for manipulating smooth functions,  
which are defined as functions which are capable of not only  
returning their value, but the first two derivatives.  Obvious cases  
are analytic functions, and cubic splines.  The name of the package  
(and the objects it represents) is C2Functions.

The most important and interesting parts of the package are

1) Very general spline support, including transparent change of  
variables in both X and Y to permit storage of linearized spline  
tables, while still presenting the function externally as it was  
established.  Examples are LogLogInterpolatingFunction,  
LogLinInterpolatingFunction, etc., but the class is extensible to  
other schemes.  These transformations allow high accuracy  
representation of functions by reducing the second derivatives in the  
spline tables, while exactly reconstructing the derivatives when  
evaluated.

2) Functional algebra, allowing one to generate new functions,  
constructed of old ones, which automatically keep track of the  
derivatives correctly.  Thus, one can trivially write a new function  
g=C2Sin(f) where f is another C2Function, and  g will correctly carry  
the derivatives through the composition.  Available operators include  
basic binary functions, and composition.  This allows a very compact  
representation of 'stiff' functions, such as the sine of a slowly  
varying phase error superimposed on a time, since the phase error can  
be embedded in an InterpolatingFunction, and the composition  
operation will reconstruct the exact derivatives of the rapidly  
varying sinusoid.

3) Very fast root finding and adaptive integration.  Since the  
functions are smooth, and have exactly known derivatives, numerical  
methods are be introduced which are extraordinarily efficient.

4) Very light weight implementation.  The C2Functions package is very  
shallowly nested, and the objects it creates are very low consumers  
of memory.  They do almost no memory management themselves, leaving  
the user to be in charge of remembering to create and destroy them.  
In many cases, a lot of the work can be done with statically  
constructed functional compositions, etc., into which one plugs a  
pointer at run time to a particular function to which the operations  
will apply.

As it currently stands, the only conflicts with Boost style are
1) naming... if the package is considered 'likely to be interesting',  
I will rename all functions to conform to Boost style
2) exception specification... I put these in while writing the code,  
thinking them to be a good idea, but I agree with the Boost  
rationale, and would gladly eliminate them.

If this package is deemed interesting by the Boost community, it can  
be quickly cleaned up for actual submission. At present, I am working  
on a package of documentation for it, which describes both the thoery  
behind the package and its application. This still needs a bit of work.

Comments?

Thanks in advance.

Marcus Mendenhall
Research Associate Professor of Physics
Vanderbilt University