#!/usr/bin/env python
# coding: utf-8

# Trying to figure out the shape of information entropy in 3D.
# 
# 2D case is clear as seen in https://en.wikipedia.org/wiki/Entropy_(information_theory)

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'''
======================
3D surface (color map)
======================

Demonstrates plotting a 3D surface colored with the coolwarm color map.
The surface is made opaque by using antialiased=False.

Also demonstrates using the LinearLocator and custom formatting for the
z axis tick labels.
'''

from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
from matplotlib import cm
from matplotlib.ticker import LinearLocator, FormatStrFormatter
import numpy as np

get_ipython().run_line_magic('matplotlib', 'notebook')


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fig = plt.figure()
ax = fig.gca(projection='3d')


Xs = np.arange(0.01, 1, 0.01)
Ys = np.arange(0.01, 1, 0.01)

Xs, Ys = np.meshgrid(Xs, Ys)

Z = - (Xs * np.log(Xs) + Ys * np.log(Ys) + (1 - Xs - Ys) * np.log(1 - Xs - Ys))

ax.contour(Xs, Ys, Z)
# ax.plot_surface(Xs, Ys, Z, cmap=cm.coolwarm, linewidth=0, antialiased=False)


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res = []
p1s = []
p2s = []
zs = []
for p1 in np.arange(0.01, 1, 0.01):
    for p2 in np.arange(0.01, 1 - p1, 0.01):
        p3 = 1 - p1 - p2
        z = - np.sum(p1 * np.log(p1) + p2 * np.log(p2) + p3 * np.log(p3))
        p1s.append(p1)
        p2s.append(p2)
        zs.append(z)

p1s = np.array(p1s)
p2s = np.array(p2s)
zs = np.array(zs)
# Y = np.arange(0, X, 0.01)
# X, Y = np.meshgrid(X, Y)
# Z = np.sum(X * np.log(X) + Y * np.log(Y) + (1 - X - Y) * np.log(1 - X - Y))

# # Plot the surface.
# surf = ax.plot_surface(X, Y, Z, cmap=cm.coolwarm,
#                        linewidth=0, antialiased=False)

# # Customize the z axis.
# ax.set_zlim(-1.01, 1.01)
# ax.zaxis.set_major_locator(LinearLocator(10))
# ax.zaxis.set_major_formatter(FormatStrFormatter('%.02f'))

# # Add a color bar which maps values to colors.
# fig.colorbar(surf, shrink=0.5, aspect=5)

# plt.show()


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p1s.shape


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p2s.shape


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zs.shape


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X, Y = np.meshgrid(p1s, p2s)


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X.shape


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np.meshgrid([1, 2], [3, 4])


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