System module (tmrc.system)

Provides classes for defining dynamical systems of various types, and methods for generating simulation data of these systems.

class tmrc.system.DriftDiffusionSystem(driftdiffusion, domain)

The drift diffusion system class

Implements a dynamical system whose movement is defined by generic drift and diffuion terms. Both drift and diffusion may be location and time-dependent.

domain

an array containing the limits of the system’s domain

Type:np.array
dimension

dimension of the system’s state space

Type:int
drift(np.array)

evaluates the drift term

diffusion(np.array)

evaluates the diffusion term

generateTrajectory(t, dt, r0)

computes a single trajectory (including the steps) using the Euler-Maruyama scheme

generateBurst(t, dt, r0, showprogress=True)

computes multiple trajectories (outputting only the end points) using the Euler-Maruyama scheme

generateTestPoints(n, dist='uniform')

samples the domain of the system

generateBurst(t, dt, r0, t0, showprogress=True)

Computes in parallel multiple trajectories (outputting only the end points) using the Euler-Maruyama integration scheme.

Parameters:
  • t (float) – end time. Method integrates the system from 0 to t
  • dt (float) – time step length of the integration
  • r0 (np.array) – array containing the starting points
  • t0 (float) – start time
  • showprogress=True (bool) – flag for progress bar
Returns:

rout – array containing the end points of the trajectories
Return type:

np.array
generatePointclouds(t, dt, r0, t0, M, showprogress=True)

Computes the endpoints of multiple parallel trajectories for each starting point in the array r0 using the Euler-Maruyama integration scheme. Implemented as wrapper for generateBurst.

Parameters:
  • t (float) – end time. Method integrates the system from 0 to t
  • dt (float) – time step length of the integration
  • r0 (np.array) – array containing the starting points
  • t0 (float) – starting time
  • M (int) – number of simulations per starting point
  • showprogress=True (bool) – flag for progress bar
Returns:

pointclouds – 3D array containing pointcloud data (npoints x M x dim-array)
Return type:

np.array
generateTrajectory(t, dt, r0, t0, showprogress=True)

Computes a single trajectory (including the steps) using the Euler-Maruyama integration scheme.

Parameters:
  • t (float) – end time. Method integrates the system from 0 to t
  • dt (float) – time step length of the integration
  • r0 (np.array) – starting point
  • t0 (float) – starting time
  • showprogress=True (bool) – flag for progress bar
Returns:

rout – array containing the steps of the integration
Return type:

np.array
class tmrc.system.GradientSystem(potential, domain, beta)

The gradient system class

Implements a dynamical system whose movement is defined by a gradient drift (i.e. pointing in the negative direction of the gradient of a potential energy function) and temperature-scaled isotropic noise.

domain

an array containing the limits of the system’s domain

Type:np.array
dimension

dimension of the system’s state space

Type:int
beta

inverse temperature

Type:float
potential(np.array)

evaluates the potential energy function

gradPot(np.array)

evaluates the gradient of the potential energy function

generateTrajectory(t, dt, r0)

computes a single trajectory (including the steps) using the Euler-Maruyama scheme

generateBurst(t, dt, r0, showprogress=True)

computes multiple trajectories (outputting only the end points) using the Euler-Maruyama scheme

generateTestPoints(n, dist='uniform')

samples the domain of the system

generateBurst(t, dt, r0, showprogress=True)

Computes in parallel multiple trajectories (outputting only the end points) using the Euler-Maruyama integration scheme.

Parameters:
  • t (float) – end time. Method integrates the system from 0 to t
  • dt (float) – time step length of the integration
  • r0 (np.array) – array containing the starting points
  • showprogress=True (bool) – flag for progress bar
Returns:

rout – array containing the end points of the trajectories
Return type:

np.array
generatePointclouds(t, dt, r0, M, showprogress=True)

Computes the endpoints of multiple parallel trajectories for each starting point in the array r0 using the Euler-Maruyama integration scheme. Implemented as wrapper for generateBurst.

Parameters:
  • t (float) – end time. Method integrates the system from 0 to t
  • dt (float) – time step length of the integration
  • r0 (np.array) – array containing the starting points
  • M (int) – number of simulations per starting point
  • showprogress=True (bool) – flag for progress bar
Returns:

pointclouds – 3D array containing pointcloud data (npoints x M x dim-array)
Return type:

np.array
generateTrajectory(t, dt, r0, showprogress=True)

Computes a single trajectory (including the steps) using the Euler-Maruyama integration scheme.

Parameters:
  • t (float) – end time. Method integrates the system from 0 to t
  • dt (float) – time step length of the integration
  • r0 (np.array) – starting point
  • showprogress=True (bool) – flag for progress bar
Returns:

rout – array containing the steps of the integration
Return type:

np.array
class tmrc.system.System(domain)

Parent class for defining stochastic dynamical systems.

Only initializes some basic properties of a dynamical system. Other important properties depend on the specific kind of system.

domain

an array containing the limits of the system’s domain

Type:np.array
dimension

dimension of the system’s state space

Type:int
generateTestPoints(n, dist='uniform')

samples the domain of the system

generateTestpoints(n, dist='uniform')

Generates samples of the system’s state space

Parameters:
  • n (int) – number of points to generate
  • dist='uniform' (string) – method of distribution the points. Can be either ‘uniform’ or ‘grid’
Returns:

rsamp – array containing the generated sampling points
Return type:

np.array