Example 2: (Fine-Grained) Permutation Entropy

Import the x, y, and z components of the Lorenz system of equations.

Data = EH.ExampleData('lorenz');

from matplotlib.pyplot import fig, scatter, axis

fig = figure(facecolor='k')
ax = fig.add_subplot(111, projection='3d')
ax.set_facecolor('k')
ax.scatter(Data[:,0], Data[:,1], Data[:,2], c='g')
ax.axis('off')

Calculate fine-grained permutation entropy of the z component in dits (logarithm base 10) with an embedding dimension of 3, time delay of 2, an alpha parameter of 1.234. Return Pnorm normalised w.r.t the number of all possible permutations (m!) and the condition permutation entropy (cPE) estimate.

Z = Data[:,2];

Perm, Pnorm, cPE = EH.PermEn(Z, m = 3, tau = 2, Typex = 'finegrain',
                                tpx = 1.234, Logx = 10, Norm = False)

>>> Perm
    array([-0. , 0.8687, 0.9468])
>>> Pnorm
    array([ nan, 0.8687, 0.4734])
>>> cPE
    array([0.8687, 0.0781])