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.