Re: [Boost-users] math

28 Apr 2008

      ...
Hicham Mouline wrote:
...
...
Are there libraries with class templates for the following concepts:
. notion of mathematical function f(x1,x2,.,xn), and perhaps 
derivation/integration
. any-order multidim partial differential equations?
. multidim stochastic differential equations? 
Not at present, sorry, 
Regards, John.
If I were to attempt to implement such things, I would need to familiarize
myself
with boost::function maybe, boost::mpl, boost::math for special functions?

I just finished reading the interesting "c++ template metaprogramming" which
highlights
such a large number of ideas that I will read once more.

Assuming the general case of a set of stochastic processes x1....xm (X is a
vector of xi):
dx1 = a1(t, X) dt + b11(t,X) dW1 + b12(t,X)dW2 + .... + b1n(t,X) dWn 
...
dxm = am(t, X) dt + bm1(t,X) dW1 + bm2(t,X)dW2 + .... + bmn(t,X) dWn

where

ai: functionals of time and the state vector X
bij: functionals of time and the state vector X
Wj: non deterministic processes, governed by various statistical
distributions (e.g. Normal)
(perhaps ones listed in boost::math), with correlation matrix M

n and m would have to be runtime variables in my case as the end-user might
have
thousands of processes.

How would one model such a thing?

class StochasticProcessesSet {
  template
  explicit StochasticProcessesSet(const std::vector, 
                                  const std::vector,
                                  const std::vector)
  {
     // 1. for correctness, runtime assertion that the sizes of the 3
vectors
     //  are consistent with the system of equations above
     // 2. how to enforce that A and B are functionals that take the
appropriate
     //  number of arguments.
     //  It seems impossible to mix a compile-time check on the template
arguments
     //  with the runtime variables n and m
     // 3. How to enforce W is one of the stat distributions
  }
};

I would want to have special cases (perhaps for efficiency) for the above
such as:
1 stochastic process dependent on n Wi with functionals dependent just on
itself and time
class StochasticProcess {
....
};

What relationship should StochasticProcess have with StochasticProcessesSet?

A final special case would be 1 process driven only by source of randomness,
not n.

Clearly, these first thoughts are not applicable, given than n and m need to
be runtime.

Regards,