A library for stochastic delay differential equations implementing published numerical schemes, utilities for constructing network models and handling simulation results, as well as bindings for MATLAB, Python. Our intent is to make it possible to use and benchmark available schemes on your favorite model, not invent new numerical schemes, so we have attempted to follow published results, documenting caveats, assumptions etc. Care will be taken to handle calculation of partial erivatives, to enable higher order schemes, optimization and inversion techniques.
The current focus is nailing down 'software carpentry' aspects of building a scientific library, and only preliminary sets of mathematical components are implemented, not for use pending v0.1 release, though I have stopped ruthless rebasing of master so it's safe to fork.
Currently the overview, documentation, tests and benchmark are the best places to look to understand what you can do with SDDEKit.
Python, MATLAB bindings and C++ header are in the works, on separate
(ctype/cython/py-c-api, matlab, cpp respectively) branches of
this repo.
You can build the tests and benchmark if you have GCC (or a C99 compiler) and Make:
$ make tests
...
$ make bench_net_exc
...Running the tests will generate some data files from one of the tests, which
tests different integration schemes on the same system. These can be compared with
the gnuplot script fig/exc_em_emcolor_heun.gpi
$ gnuplot fig/exc_em_emcolor_heun.gpiwhich produces
Running the benchmark will produce a trace bench_net_exc.dat which can be visualized
with fig/bench_net_exc.py, producing
As stated, these are in place to help build up the library at this point. In the future extensive examples for different kinds of systems & networks will be provided.
Current implemented
- a generic solver driver
- Euler-Maruyama, Heun & colored noise variants
- network system
- simple excitable, generic 2d oscillator & reduced Wong-Wang systems
- temporal averaging, convolution, spatial filter, memory buffer and write to file
- linear interpolation history buffer
- If you're a programmer, we'd be happy to have help! See
DEVELOP.md. - If you wish to use sddekit in a webpage, see
JS.md. - Numerical analysis references
- Kloeden & Platen 1999 Numerical Solution of Stochastic Differential Equations.
- Fox et al 1998
- Mannella 200?
- Jimenez et al 2015
- Kuechler & Platen 2000