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

# <h1>Table of Contents<span class="tocSkip"></span></h1>
# <div class="toc"><ul class="toc-item"><li><span><a href="#Computing-entropy-random-signal" data-toc-modified-id="Computing-entropy-random-signal-1"><span class="toc-item-num">1&nbsp;&nbsp;</span>Computing entropy random signal</a></span></li><li><span><a href="#Entropy-of-EEG-signal" data-toc-modified-id="Entropy-of-EEG-signal-2"><span class="toc-item-num">2&nbsp;&nbsp;</span>Entropy of EEG signal</a></span></li></ul></div>

# ## Computing entropy random signal

# In[1]:


import numpy as np
import matplotlib.pyplot as plt
import spkit as sp


# In[2]:


x = np.random.rand(10000)
y = np.random.randn(10000)

#Shannan entropy
H_x= sp.entropy(x,alpha=1)
H_y= sp.entropy(y,alpha=1)

#Rényi entropy
Hr_x= sp.entropy(x,alpha=2)
Hr_y= sp.entropy(y,alpha=2)

H_xy= sp.entropy_joint(x,y)

H_x1y= sp.entropy_cond(x,y)
H_y1x= sp.entropy_cond(y,x)

I_xy = sp.mutual_Info(x,y)

H_xy_cross= sp.entropy_cross(x,y)

D_xy= sp.entropy_kld(x,y)


print('Shannan entropy')
print('Entropy of x: H(x) = ',H_x)
print('Entropy of y: H(y) = ',H_y)
print('-')
print('Rényi entropy')
print('Entropy of x: H(x) = ',Hr_x)
print('Entropy of y: H(y) = ',Hr_y)
print('-')
print('Mutual Information I(x,y) = ',I_xy)
print('Joint Entropy H(x,y) = ',H_xy)
print('Conditional Entropy of : H(x|y) = ',H_x1y)
print('Conditional Entropy of : H(y|x) = ',H_y1x)
print('-')
print('Cross Entropy of : H(x,y) = :',H_xy_cross)
print('Kullback–Leibler divergence : Dkl(x,y) = :',D_xy)



plt.figure(figsize=(12,5))
plt.subplot(121)
sp.HistPlot(x,show=False)

plt.subplot(122)
sp.HistPlot(y,show=False)
plt.show()


# ## Entropy of EEG signal

# In[3]:


from spkit.data import load_data


# In[14]:


X,ch_names = load_data.eegSample()
print(X.shape)
print(ch_names)


# In[12]:


x1 =X[:,0] #'AF3' - Frontal Lobe
x2 =X[:,6] #'O1'  - Occipital Lobe
#Shannan entropy
H_x1= sp.entropy(x1,alpha=1)
H_x2= sp.entropy(x2,alpha=1)

#Rényi entropy
Hr_x1= sp.entropy(x1,alpha=2)
Hr_x2= sp.entropy(x2,alpha=2)

#Joint entropy
H_x12= sp.entropy_joint(x1,x2)

#Conditional Entropy
H_x12= sp.entropy_cond(x1,x2)
H_x21= sp.entropy_cond(x2,x1)

#Mutual Entropy
I_x12 = sp.mutual_Info(x1,x2)

#Cross Entropy
H_x12_cross= sp.entropy_cross(x1,x2)

#Diff Entropy
D_x12= sp.entropy_kld(x1,x2)


print('Shannan entropy')
print('Entropy of x1: H(x1) =\t ',H_x1)
print('Entropy of x2: H(x2) =\t ',H_x2)
print('-')
print('Rényi entropy')
print('Entropy of x1: H(x1) =\t ',Hr_x1)
print('Entropy of x2: H(x2) =\t ',Hr_x2)
print('-')
print('Joint Entropy H(x1,x2) =\t',H_x12)
print('Mutual Information I(x1,x2) =\t',I_x12)
print('Conditional Entropy of : H(x1|x2) =\t',H_x12)
print('Conditional Entropy of : H(x2|x1) =\t',H_x21)
print('-')
print('Cross Entropy of : H(x1,x2) =\t',H_x12_cross)
print('Kullback–Leibler divergence : Dkl(x1,x2) =\t',D_x12)