#Complexity-entropy plane for logistic map and Gaussian noise.

import numpy as np
import ordpy
from matplotlib import pylab as plt

def logistic(a=4, n=100000, x0=0.4):
    x = np.zeros(n)
    x[0] = x0
    for i in range(n-1):
        x[i+1] = a*x[i]*(1-x[i])
    return(x)

time_series = [logistic(a) for a in [3.05, 3.55, 4]]
time_series += [np.random.normal(size=100000)]

HC = [ordpy.complexity_entropy(series, dx=4) for series in time_series]


f, ax = plt.subplots(figsize=(8.19, 6.3))

for HC_, label_ in zip(HC, ['Period-2 (a=3.05)',
                            'Period-8 (a=3.55)',
                            'Chaotic (a=4)',
                            'Gaussian noise']):
    ax.scatter(*HC_, label=label_, s=100)

ax.set_xlabel('Permutation entropy, $H$')
ax.set_ylabel('Statistical complexity, $C$')

ax.legend()

#Ordinal networks for logistic map and Gaussian noise.

import numpy as np
import igraph
import ordpy
from matplotlib import pylab as plt
from IPython.core.display import display, SVG

def logistic(a=4, n=100000, x0=0.4):
    x = np.zeros(n)
    x[0] = x0
    for i in range(n-1):
        x[i+1] = a*x[i]*(1-x[i])
    return(x)

time_series = [logistic(a=4), np.random.normal(size=100000)]

vertex_list, edge_list, edge_weight_list = list(), list(), list()
for series in time_series:
    v_, e_, w_   = ordpy.ordinal_network(series, dx=4)
    vertex_list += [v_]
    edge_list   += [e_]
    edge_weight_list += [w_]

def create_ig_graph(vertex_list, edge_list, edge_weight):

    G = igraph.Graph(directed=True)

    for v_ in vertex_list:
        G.add_vertex(v_)

    for [in_, out_], weight_ in zip(edge_list, edge_weight):
        G.add_edge(in_, out_, weight=weight_)

    return G

graphs = []

for v_, e_, w_ in zip(vertex_list, edge_list, edge_weight_list):
    graphs += [create_ig_graph(v_, e_, w_)]

def igplot(g):
    f = igraph.plot(g,
                    layout=g.layout_circle(),
                    bbox=(500,500),
                    margin=(40, 40, 40, 40),
                    vertex_label = [s.replace('|','') for s in g.vs['name']],
                    vertex_label_color='#202020',
                    vertex_color='#969696',
                    vertex_size=20,
                    vertex_font_size=6,
                    edge_width=(1 + 8*np.asarray(g.es['weight'])).tolist(),
                   )
    return f

for graph_, label_ in zip(graphs, ['Chaotic (a=4)',
                                   'Gaussian noise']):
    print(label_)
    display(SVG(igplot(graph_)._repr_svg_()))