# Source code for pyFTS.data.lorentz

    """
    Lorenz, Edward Norton (1963). "Deterministic nonperiodic flow". Journal of the Atmospheric Sciences. 20 (2): 130–141.
    https://doi.org/10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2

    dx/dt = a(y -x)
    dy/dt = x(b - z) - y
    dz/dt = xy - cz
    """

    import numpy as np
    import pandas as pd

    def get_data(var, a = 10.0, b = 28.0, c = 8.0 / 3.0, dt = 0.01,
                      initial_values = [0.1, 0, 0], iterations=1000):
        """
            Get a simple univariate time series data.

            :param var: the dataset field name to extract
            :return: numpy array
            """
        return get_dataframe(a, b, c, dt, initial_values, iterations)[var].values

    def get_dataframe(a = 10.0, b = 28.0, c = 8.0 / 3.0, dt = 0.01,
                      initial_values = [0.1, 0, 0], iterations=1000):
        '''
        Return a dataframe with the multivariate Lorenz Map time series (x, y, z).

        :param a: Equation coefficient. Default value: 10
        :param b: Equation coefficient. Default value: 28
        :param c: Equation coefficient. Default value: 8.0/3.0
        :param dt: Time differential for continuous time integration. Default value: 0.01
        :param initial_values: numpy array with the initial values of x,y and z. Default: [0.1, 0, 0]
        :param iterations: number of iterations. Default: 1000
        :return: Panda dataframe with the x, y and z values
        '''

        x = [initial_values[0]]
        y = [initial_values[1]]
        z = [initial_values[2]]

        for t in np.arange(0, iterations):
            dxdt = a * (y[t] - x[t])
            dydt = x[t] * (b - z[t]) - y[t]
            dzdt = x[t] * y[t] - c * z[t]
            x.append(x[t] + dt * dxdt)
            y.append(y[t] + dt * dydt)
            z.append(z[t] + dt * dzdt)

        return pd.DataFrame({'x': x, 'y':y, 'z': z})