Rungekutta

RungeKutta

Bases: _Generator_

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

Source code in phaseportrait/trajectories/rungekutta.py

class RungeKutta(_Generator_):
    """
    This class is an implementation of _Generator_ for a Runge-Kutta 4th order data generator.
    """
    def __init__(self, portrait, dF, dimension, max_values, *, dt=0.1, dF_args=None, initial_values=None, thermalization=0):
        """
        Args:
            portrait (Object) : 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.
            dt (float, 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.
        """
        super().__init__(portrait, dF, dimension, max_values, dF_args=dF_args,
                         initial_values=initial_values, thermalization=thermalization)

        self.dt = dt
        self.positions = self._create_values_array()
        self.velocities = self._create_values_array()

    @classmethod
    def instance_and_compute_all(cls, 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.

        Args:
            portrait (Object):  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 (float, optional, 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.
        """
        instance = cls(portrait, dF, dimension, dt=dt, dF_args=dF_args, initial_values=initial_values, thermalization=thermalization)

        instance.compute_all()
        return instance


    def _next(self):
        """
        Generates from `self.position` its following value via the Runge-Kutta 4th order method.
        """
        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)
        if (self.velocity == 0).all():
            self.flag_stop = True
        self.position += self.velocity*self.dt


    def save(self, i):
        """
        Saves `self.position` in the attribute `self.positions`, and `self.velocity` in `self.velocities`.

        Args:
            i (int) : Index in which the data is saved.
        """
        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)


    def clear_values(self):
        """
        Clears the data arrays `self.positions` and `self.velocities`.
        """
        self.positions[:,1:] = 0
        self.velocity[:,1:] = 0

__init__(portrait, dF, dimension, max_values, *, dt=0.1, dF_args=None, initial_values=None, thermalization=0)

Parameters:

Name	Type	Description	Default
portrait	Object)	Class that uses the RungeKutta objects.	required
dF	callable)	A dF type funcion.	required
dimension	int)	Number of dimensions in which it calculates the next values. Must equal the amount of outputs the dF funcion gives.	required
max_values	int)	Max number of values saved.	required
dt	float, optional, by default 0.1)	Time interval used in the Runge-Kutta 4th order method.	0.1
dF_args	dict)	If necesary, must contain the kargs for the dF funcion. By default, None.	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.	None
thermalization	int, optional)	Thermalization steps before data is saved, by default None. If None, thermalization steps are set to 0.	0

Source code in phaseportrait/trajectories/rungekutta.py

def __init__(self, portrait, dF, dimension, max_values, *, dt=0.1, dF_args=None, initial_values=None, thermalization=0):
    """
    Args:
        portrait (Object) : 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.
        dt (float, 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.
    """
    super().__init__(portrait, dF, dimension, max_values, dF_args=dF_args,
                     initial_values=initial_values, thermalization=thermalization)

    self.dt = dt
    self.positions = self._create_values_array()
    self.velocities = self._create_values_array()

clear_values()

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

Source code in phaseportrait/trajectories/rungekutta.py

def clear_values(self):
    """
    Clears the data arrays `self.positions` and `self.velocities`.
    """
    self.positions[:,1:] = 0
    self.velocity[:,1:] = 0

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

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

Parameters:

Name	Type	Description	Default
portrait	Object	Class that uses the RungeKutta objects.	required
dF	callable)	A dF type funcion.	required
dimension	int)	Number of dimensions in which it calculates the next values. Must equal the amount of outputs the dF funcion gives.	required
dF_args	dict)	If necesary, must contain the kargs for the dF funcion. By default, None.	required
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	required
max_values	int)	Max number of values saved.	required
save_freq	int, optional, by default 1)	Number of values computed before saving them.	1
dt	float, optional, by default 0.1)	Time interval used in the Runge-Kutta 4th order method.	0.1
thermalization	int, optional)	Thermalization steps before data is saved, by default None. If None, thermalization steps are set to 0.	0

Source code in phaseportrait/trajectories/rungekutta.py

@classmethod
def instance_and_compute_all(cls, 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.

    Args:
        portrait (Object):  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 (float, optional, 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.
    """
    instance = cls(portrait, dF, dimension, dt=dt, dF_args=dF_args, initial_values=initial_values, thermalization=thermalization)

    instance.compute_all()
    return instance

save(i)

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

Parameters:

Name	Type	Description	Default
i	int)	Index in which the data is saved.	required

Source code in phaseportrait/trajectories/rungekutta.py

def save(self, i):
    """
    Saves `self.position` in the attribute `self.positions`, and `self.velocity` in `self.velocities`.

    Args:
        i (int) : Index in which the data is saved.
    """
    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)