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.
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.
- Numpy
- Cython
- Cython-gsl
To install ciles in your Python distribution:
- Clone repository
- python setup.py install
- To test (using nosetests): nosetests
You can also use ciles locally without installing:
- Clone repository
- python setup.py build_ext --inplace
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(1)
out = li.outBelow are the plot results of the currently available examples from ciles.examples.
See the source
See the source
