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

# ## Entropy
# 
# How entropy varies from a uniform to a peaky distribution. The entropy is highest for uniform distribution as it represents the highest uncertainty from information theoretical point of view. Whereas delta function where a single value has a probability of 1, has zero uncertainty and consequently zero entropy.

# In[1]:


from IPython.display import HTML

HTML('''<script>
code_show=true; 
function code_toggle() {
 if (code_show){
 $('div.input').hide();
 } else {
 $('div.input').show();
 }
 code_show = !code_show
} 
$( document ).ready(code_toggle);
</script>
<form action="javascript:code_toggle()"><input type="submit" value="Click here to toggle on/off the raw code."></form>''')


# In[2]:


import numpy as np
import plotly
import plotly.subplots
import plotly.graph_objects as go
import plotly.express as px
import pandas as pd
import warnings

warnings.filterwarnings('ignore')


# In[3]:


def entropy(probas):
    logs = np.log(probas)
    logs[logs==(-np.inf)] = 0
    return -(probas * logs).sum(axis=1)


# In[4]:


probas = np.array(
    [
        [0.20, 0.20, 0.20, 0.20, 0.20],
        [0.10, 0.25, 0.30, 0.25, 0.10],
        [0.00, 0.30, 0.40, 0.30, 0.00],
        [0.00, 0.10, 0.80, 0.10, 0.00],
        [0.00, 0.00, 1.00, 0.00, 0.00],
    ],
)


# ### Discrete PDF plots
# 
# Goes from a uniform to a delta function (probability 0 everywhere except at x=0)

# In[5]:


m, n = probas.shape
x = np.arange(-2,3)
ncols = 2
nrows = 3

distributions = ['Uniform', 'Spread', 'Less spread', 'Peaky', '𝞭-Distribution']
fig = plotly.subplots.make_subplots(rows=nrows, cols=ncols, start_cell="bottom-left")
for i in range(n):
    fig.add_trace(go.Bar(name=distributions[i],x=x, y=probas[i]), row=nrows-(i//ncols), col=(i%ncols + 1))
fig.show()


# ### Plot of entropy as a function of peakiness of the distribution

# In[6]:


entropy_df = pd.DataFrame(
    data=dict(
        Distribution=distributions,
        Entropy=entropy(probas),
    )
)


# In[7]:


px.line(
    data_frame=entropy_df,
    x="Distribution",
    y="Entropy",
    title=r"$\text{Entropy of a Uniform distribution to a peaky } \delta-\text{distribution }(P(x=0)=1, P(x\neq 0)= 0)$",
    markers=True,
)


# In[ ]: