{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "toc": true
   },
   "source": [
    "<h1>Table of Contents<span class=\"tocSkip\"></span></h1>\n",
    "<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>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Computing entropy random signal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-19T15:54:44.958653Z",
     "start_time": "2019-09-19T15:54:43.480505Z"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import spkit as sp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-19T15:54:45.451702Z",
     "start_time": "2019-09-19T15:54:44.960653Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shannan entropy\n",
      "Entropy of x: H(x) =  4.4581180171280685\n",
      "Entropy of y: H(y) =  5.04102391756942\n",
      "-\n",
      "Rényi entropy\n",
      "Entropy of x: H(x) =  4.456806796146617\n",
      "Entropy of y: H(y) =  4.828391418226062\n",
      "-\n",
      "Mutual Information I(x,y) =  0.05934937774825322\n",
      "Joint Entropy H(x,y) =  9.439792556949234\n",
      "Conditional Entropy of : H(x|y) =  4.398768639379814\n",
      "Conditional Entropy of : H(y|x) =  4.9816745398211655\n",
      "-\n",
      "Cross Entropy of : H(x,y) = : 11.591688735915701\n",
      "Kullback–Leibler divergence : Dkl(x,y) = : 4.203058010473213\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.random.rand(10000)\n",
    "y = np.random.randn(10000)\n",
    "\n",
    "#Shannan entropy\n",
    "H_x= sp.entropy(x,alpha=1)\n",
    "H_y= sp.entropy(y,alpha=1)\n",
    "\n",
    "#Rényi entropy\n",
    "Hr_x= sp.entropy(x,alpha=2)\n",
    "Hr_y= sp.entropy(y,alpha=2)\n",
    "\n",
    "H_xy= sp.entropy_joint(x,y)\n",
    "\n",
    "H_x1y= sp.entropy_cond(x,y)\n",
    "H_y1x= sp.entropy_cond(y,x)\n",
    "\n",
    "I_xy = sp.mutual_Info(x,y)\n",
    "\n",
    "H_xy_cross= sp.entropy_cross(x,y)\n",
    "\n",
    "D_xy= sp.entropy_kld(x,y)\n",
    "\n",
    "\n",
    "print('Shannan entropy')\n",
    "print('Entropy of x: H(x) = ',H_x)\n",
    "print('Entropy of y: H(y) = ',H_y)\n",
    "print('-')\n",
    "print('Rényi entropy')\n",
    "print('Entropy of x: H(x) = ',Hr_x)\n",
    "print('Entropy of y: H(y) = ',Hr_y)\n",
    "print('-')\n",
    "print('Mutual Information I(x,y) = ',I_xy)\n",
    "print('Joint Entropy H(x,y) = ',H_xy)\n",
    "print('Conditional Entropy of : H(x|y) = ',H_x1y)\n",
    "print('Conditional Entropy of : H(y|x) = ',H_y1x)\n",
    "print('-')\n",
    "print('Cross Entropy of : H(x,y) = :',H_xy_cross)\n",
    "print('Kullback–Leibler divergence : Dkl(x,y) = :',D_xy)\n",
    "\n",
    "\n",
    "\n",
    "plt.figure(figsize=(12,5))\n",
    "plt.subplot(121)\n",
    "sp.HistPlot(x,show=False)\n",
    "\n",
    "plt.subplot(122)\n",
    "sp.HistPlot(y,show=False)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Entropy of EEG signal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-19T15:55:06.235781Z",
     "start_time": "2019-09-19T15:55:06.162773Z"
    }
   },
   "outputs": [],
   "source": [
    "from spkit.data import load_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-19T16:04:11.750327Z",
     "start_time": "2019-09-19T16:04:11.739325Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(2048, 14)\n",
      "['AF3', 'F7', 'F3', 'FC5', 'T7', 'P7', 'O1', 'O2', 'P8', 'T8', 'FC6', 'F4', 'F8', 'AF4']\n"
     ]
    }
   ],
   "source": [
    "X,ch_names = load_data.eegSample()\n",
    "print(X.shape)\n",
    "print(ch_names)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-19T16:03:38.591011Z",
     "start_time": "2019-09-19T16:03:38.559008Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shannan entropy\n",
      "Entropy of x1: H(x1) =\t  4.811416424350645\n",
      "Entropy of x2: H(x2) =\t  4.697278111823318\n",
      "-\n",
      "Rényi entropy\n",
      "Entropy of x1: H(x1) =\t  4.239955818998481\n",
      "Entropy of x2: H(x2) =\t  4.145472461333239\n",
      "-\n",
      "Joint Entropy H(x1,x2) =\t 3.655513859907648\n",
      "Mutual Information I(x1,x2) =\t 1.1559025644429965\n",
      "Conditional Entropy of : H(x1|x2) =\t 3.655513859907648\n",
      "Conditional Entropy of : H(x2|x1) =\t 3.541375547380321\n",
      "-\n",
      "Cross Entropy of : H(x1,x2) =\t 5.686498222841184\n",
      "Kullback–Leibler divergence : Dkl(x1,x2) =\t 0.7202757885313226\n"
     ]
    }
   ],
   "source": [
    "x1 =X[:,0] #'AF3' - Frontal Lobe\n",
    "x2 =X[:,6] #'O1'  - Occipital Lobe\n",
    "#Shannan entropy\n",
    "H_x1= sp.entropy(x1,alpha=1)\n",
    "H_x2= sp.entropy(x2,alpha=1)\n",
    "\n",
    "#Rényi entropy\n",
    "Hr_x1= sp.entropy(x1,alpha=2)\n",
    "Hr_x2= sp.entropy(x2,alpha=2)\n",
    "\n",
    "#Joint entropy\n",
    "H_x12= sp.entropy_joint(x1,x2)\n",
    "\n",
    "#Conditional Entropy\n",
    "H_x12= sp.entropy_cond(x1,x2)\n",
    "H_x21= sp.entropy_cond(x2,x1)\n",
    "\n",
    "#Mutual Entropy\n",
    "I_x12 = sp.mutual_Info(x1,x2)\n",
    "\n",
    "#Cross Entropy\n",
    "H_x12_cross= sp.entropy_cross(x1,x2)\n",
    "\n",
    "#Diff Entropy\n",
    "D_x12= sp.entropy_kld(x1,x2)\n",
    "\n",
    "\n",
    "print('Shannan entropy')\n",
    "print('Entropy of x1: H(x1) =\\t ',H_x1)\n",
    "print('Entropy of x2: H(x2) =\\t ',H_x2)\n",
    "print('-')\n",
    "print('Rényi entropy')\n",
    "print('Entropy of x1: H(x1) =\\t ',Hr_x1)\n",
    "print('Entropy of x2: H(x2) =\\t ',Hr_x2)\n",
    "print('-')\n",
    "print('Joint Entropy H(x1,x2) =\\t',H_x12)\n",
    "print('Mutual Information I(x1,x2) =\\t',I_x12)\n",
    "print('Conditional Entropy of : H(x1|x2) =\\t',H_x12)\n",
    "print('Conditional Entropy of : H(x2|x1) =\\t',H_x21)\n",
    "print('-')\n",
    "print('Cross Entropy of : H(x1,x2) =\\t',H_x12_cross)\n",
    "print('Kullback–Leibler divergence : Dkl(x1,x2) =\\t',D_x12)"
   ]
  }
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