Simulate systems from ODEs or SDEs, analyze timeseries.

## Project description

## Simulation

nsim is for systems in physics, biology and finance that are modelled in continuous time with differential equations. nsim makes it easy to define and simulate these (including proper treatment of noise) and to analyze the resulting time series.

- Automatic parallel computing / cluster computing: For multiple or repeated simulations, nsim distributes these across a cluster or Amazon EC2 cloud (or across the CPUs of one computer) without needing to do any parallel programming.(First configure an IPython cluster. e.g. on a single computer can type
`ipcluster start`) To define a scalar or vector ODE system, subclass

`ODEModel`. (see examples) To define a scalar or vector SDE system, subclass`ItoModel`or`StratonovichModel`. Multiple driving Wiener processes are now supported. Order 1.0 strong stochastic Runge-Kutta algorithms (Rößler2010) are used for SDE integration by default. To define a scalar or vector Caputo fractional ODE system, subclass`CaputoModel`.Model parameters can be specified as random distributions, to create multiple non-identical simulations.

The

`NetworkModel`class allows you to simulate many subsystems coupled together into a network, with the network structure specified as a weighted directed graph. Sub-models can all be identical but they don’t have to be. (The networkx package can optionally be used to generate various kinds of random, clustered and small world graphs useful in a NetworkModel). The sub-models in a NetworkModel can even be other NetworkModels, for simulating networks of networks.

## Analyzing time series

Besides time series from simulations, empirical time series data can also be loaded from MATLAB .mat files or .EDF files for distributed analysis.

- nsim provides a
`Timeseries`class. This is a numpy array.It allows slicing the array by time instead of by array index, e.g. can write`ts.t[10.5:30]`to slice from t=10.5 to t=30 seconds. When manipulating the array it will keep track of any channel names (or variable names) of a multivariate time series. - As well as the usual methods of numpy arrays, the
`Timeseries`objects have extra methods for easy filtering, plotting and analysis. Analyses can be chained together in a pipeline. For example with a`Timeseries`instance`ts`you can write a chain of analyses like`ts.t[10:30].bandpass(20, 35).hilbert().abs().plot()`This can be extended with your own analysis functions by calling`Timeseries.add_analyses()`Analysis of multiple time series is distributed on the cluster, without needing to do any parallel programming. For best results use numpy with the

`__numpy_ufunc__`feature enabled (not yet released). This enables us to support distributed computation when analysing the resulting time series. You can get numpy with this experimental feature enabled here: https://github.com/mattja/numpy/archive/master.zip

## TODO

- Auto-generate multiple simulations covering a lattice of points in parameter space, to run in parallel.
- Optionally allow the equations to be specified and integrated in C, for speed
- Add support for models with time delays (DDEs and delay SDEs)
- Currently a single CPU core is used to simulate each single instance of a Model, including a NetworkModel. Ideally could use shared memory and multiple CPU cores on each cluster host for simulation of a Model instance, splitting degrees of freedom evenly across CPUs on a single host.

## Thanks

Incorporates extra time series analyses from Forrest Sheng Bao’s
`pyeeg` http://fsbao.net

`ipyparallel` interactive parallel computing:
https://ipyparallel.readthedocs.org/

## See also:

`sdeint`: Library of SDE integration algorithms that is used by `nsim` to do the simulations. https://github.com/mattja/sdeint

`fodeint`: Library of fractional ODE integration algorithms used by `nsim`. https://github.com/mattja/fodeint

## Project details

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