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<class A, class B, class W> explicit StochasticProcessesSet(const std::vector<const A*>, const std::vector<const B*>, const std::vector<const W*>) { // 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,