Langevin integrator for SDEs with constant drift and diffusion on continuous intervals with circular boundary conditions.

## CILES: Continuous Interval Langevin Equation Simulator

Langevin integrator for SDEs with constant drift and diffusion on continuous intervals with circular boundary conditions.

CILES is written in Cython and uses GSL for interpolation of drift & diffusion fields, to be able to simulate continuous variables.

### Description

Given a discretized drift field A(x) and a (position dependent) diffusion coefficient B(x) this tool performs simple time-forward integration of the SDE:

dx(t)/dt = A(x(t)) + sqrt(B(x(t))) * eta(t)

where eta(t) is a gaussian white noise term and x is a variable on an interval with circular boundaries (commonly 0 <= x < 2PI).

Both drift field A and diffusion B need to be arrays of the same
dimension. They are internally interpolated (using
`gsl_interp_cspline_periodic`) to provide continuous fields, which are
then used in the forward integration.

Forward integration is performed with the Euler-Murayama scheme: x(t+dt) = x(t) + dt * A(x(t)) + r * sqrt(dt * B(x(t))), where r is a normally distributed random number with zero mean and unit variance.

### Dependencies

- Numpy
- Cython
- Cython-gsl

### Installation

- Clone repository
`python setup.py install`- To test (using
`nosetests`):`nosetests`

### Example use

from ciles.integrator import LangevinIntegrator as LI import numpy as np drift = np.zeros(100) # no drift field diff = np.ones(100) # constant diffusion with 1 deg^2/s dt = 1e-3 # 1 ms timestep tmax = 1. # simulate until 1s # initialize the integrator li = LI(drift, diff, dt=dt, tmax=tmax) # simulate a single trajectory li.run() out = li.out

### More examples

Below are the plot results of the currently available examples from ciles.examples.

#### Final distributions after 2s diffusion

See the source

#### Trajectories for drift-field with 2 fixed points

See the source

## Release History

## Download Files

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File Name & Checksum SHA256 Checksum Help | Version | File Type | Upload Date |
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ciles-0.1.0-cp27-cp27m-macosx_10_11_x86_64.whl (32.5 kB) Copy SHA256 Checksum SHA256 | cp27 | Wheel | Dec 6, 2017 |

ciles-0.1.0.tar.gz (61.4 kB) Copy SHA256 Checksum SHA256 | – | Source | Dec 6, 2017 |