RungeKutta

class phaseportrait.trajectories.RungeKutta(portrait, dF, dimension, max_values, *, dt=0.1, dF_args=None, initial_values=None, thermalization=0)

This class is used internally in Trajectories. It is not intended to be used by the user.

This class is an implementation of _Generator_ for a Runge-Kutta 4th order data generator.

Parameters

• portrait :

  Class that uses the RungeKutta objects.

• dF : callable

  A dF type funcion.

• dimension : int

  Number of dimensions in which it calculates the next values. Must equal the amount of outputs the dF funcion gives.

• max_values : int

  Max number of values saved.

Key Arguments

• dt : double, optional, by default 0.1

  Time interval used in the Runge-Kutta 4th order method.

• dF_args : dict

  If necesary, must contain the kargs for the dF funcion. By default, None.

• initial_values : float, list, optional

  Initial set of conditions, by default None. If None, random initial conditions are aplied in the interval [0,1) for each coordinate.

• thermalization : int, optional

  Thermalization steps before data is saved, by default None. If None, thermalization steps are set to 0.

Overwritten methods

_Generator_._next

_Generator_._next()

Generates from self.position its following value via the Runge-Kutta 4th order method. Explicitly:

def _next(self):
    k1 = np.array(self.dF(*(self.position), **self.dF_args))
    k2 = np.array(self.dF(*(self.position+0.5*k1*self.dt), **self.dF_args))
    k3 = np.array(self.dF(*(self.position+0.5*k2*self.dt), **self.dF_args))
    k4 = np.array(self.dF(*(self.position+k3*self.dt), **self.dF_args))
    self.velocity = 1/6*(k1+2*k2+2*k3+k4)
    self.position += self.velocity*self.dt

Returns

• None

_Generator_.save

_Generator_.save(i)

Saves self.position in the attribute self.positions, and self.velocity in self.velocities.

Parameters

• i : int

  Index in which the data is saved.

Explicitly:

def save(self, i):
    try:
        self.positions[:, i] = self.position
        self.velocities[:, i] = self.velocity
    except IndexError:
        np.concatenate(self.positions, self._create_values_array(), axis=1)
        np.concatenate(self.velocities, self._create_values_array(), axis=1)
        self.max_values += 2000
        self.save(i)

Returns

• None

_Generator_.clear_values

_Generator_.clear_values()

Clears the data arrays self.positions and self.velocities.

Returns

• None

Methods

_Generator_.instance_and_compute_all

_Generator_.instance_and_compute_all(portrait, dF, dimension, dF_args, initial_values, max_values, save_freq=1, dt=0.1, thermalization=0)

Creates an instance of phase-portrait.trajectories.RungeKutta. Computes all the data requested and returns the instance.

Parameters

• portrait :

  Class that uses the RungeKutta objects.

• dF : callable

  A dF type funcion.

• dimension : int

  Number of dimensions in which it calculates the next values. Must equal the amount of outputs the dF funcion gives.

• dF_args : dict

  If necesary, must contain the kargs for the dF funcion. By default, None.

• initial_values : float, list, optional

  Initial set of conditions, by default None. If None, random initial conditions are aplied in the interval [0,1) for each coordinat

• max_values : int

  Max number of values saved.

• save_freq : int, optional, by default 1

  Number of values computed before saving them.

• dt : double, by default 0.1

  Time interval used in the Runge-Kutta 4th order method.

• thermalization : int, optional

  Thermalization steps before data is saved, by default None. If None, thermalization steps are set to 0.

Returns

• phase-portrait.trajectories.RungeKutta

Examples

This class is implemented in other classes, check out:

• Trajectory