HW8/Practical/ML2021S-HW8.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "heading_collapsed": true,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "# CE-40717: Machine Learning"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "heading_collapsed": true,
    "hidden": true,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "## HW8-Clustering & Reinforcement Learning\n",
    "\n",
    "Amir Pourmand - 99210259"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "heading_collapsed": true,
    "hidden": true,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "### Kmeans & GMM:\n",
    "\n",
    "At this question, we tend to implement Kmeans & GMM algorithms. For this purpose, `DO NOT EMPLOY` ready-for-use python libraries. Use this implementation for solving the following questions. Kmeans should continue till centeroids won't change. Furthermore, GMM also should continue till the difference of two consecutive likelihood logarithm would be less than 0.1. Notice that after executing the Kmeans part, the primitive centroids of GMM should be identical with ultimate Kmeans centroids."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-06-10T16:26:04.775907Z",
     "start_time": "2021-06-10T16:26:04.771870Z"
    },
    "hidden": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/amir/anaconda3/lib/python3.8/site-packages/sklearn/utils/deprecation.py:143: FutureWarning: The sklearn.datasets.samples_generator module is  deprecated in version 0.22 and will be removed in version 0.24. The corresponding classes / functions should instead be imported from sklearn.datasets. Anything that cannot be imported from sklearn.datasets is now part of the private API.\n",
      "  warnings.warn(message, FutureWarning)\n"
     ]
    }
   ],
   "source": [
    "from sklearn.datasets.samples_generator import make_classification, make_moons, make_circles\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "heading_collapsed": true,
    "hidden": true,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "#### Part 1:\n",
    "\n",
    "Utilize the subsequent cell in order to create the Dataset. Afterwards, try to execute the algorithm with k=2 centroids. At Kmeans, it is recommended to execute the algorithm with several various starting states in order to eventually choose the best respective result."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "X,Y = make_classification(n_samples=700, n_features=10, n_informative=5,\n",
    "                          n_redundant=0, n_clusters_per_class=2, n_classes=3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## KMeans Implementation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "class KMeans:\n",
    "\n",
    "    def __init__(self, n_clusters = 3, tolerance = 0.01, max_iter = 100, runs = 1):\n",
    "        self.n_clusters = n_clusters\n",
    "        self.tolerance = tolerance\n",
    "        self.cluster_means = np.zeros(n_clusters)\n",
    "        self.max_iter = max_iter\n",
    "        self.runs = runs\n",
    "        \n",
    "    def fit(self, X,Y):\n",
    "        row_count, col_count = X.shape\n",
    "        \n",
    "        X_values = self.__get_values(X)\n",
    "        \n",
    "        X_labels = np.zeros(row_count)\n",
    "        \n",
    "        costs = np.zeros(self.runs)\n",
    "        all_clusterings = []\n",
    "\n",
    "        for i in range(self.runs):\n",
    "            cluster_means =  self.__initialize_means(X_values, row_count)\n",
    "\n",
    "            for _ in range(self.max_iter):            \n",
    "                previous_means = np.copy(cluster_means)\n",
    "                \n",
    "                distances = self.__compute_distances(X_values, cluster_means, row_count)\n",
    "            \n",
    "                X_labels = self.__label_examples(distances)\n",
    "            \n",
    "                cluster_means = self.__compute_means(X_values, X_labels, col_count)\n",
    "\n",
    "                clusters_not_changed = np.abs(cluster_means - previous_means) < self.tolerance\n",
    "                if np.all(clusters_not_changed) != False:\n",
    "                    break\n",
    "            \n",
    "            X_values_with_labels = np.append(X_values, X_labels[:, np.newaxis], axis = 1)\n",
    "            \n",
    "            all_clusterings.append( (cluster_means, X_values_with_labels) )\n",
    "            costs[i] = self.__compute_cost(X_values, X_labels, cluster_means)\n",
    "        \n",
    "        best_clustering_index = costs.argmin()\n",
    "        \n",
    "        self.costs = costs\n",
    "        self.cost_ = costs[best_clustering_index]\n",
    "        \n",
    "        self.centroid,self.items = all_clusterings[best_clustering_index]\n",
    "        self.y = Y\n",
    "        return all_clusterings[best_clustering_index]\n",
    "        \n",
    "    def __initialize_means(self, X, row_count):\n",
    "        return X [ np.random.choice(row_count, size=self.n_clusters, replace=False) ]\n",
    "        \n",
    "        \n",
    "    def __compute_distances(self, X, cluster_means, row_count):\n",
    "        distances = np.zeros((row_count, self.n_clusters))\n",
    "        for cluster_mean_index, cluster_mean in enumerate(cluster_means):\n",
    "            distances[:, cluster_mean_index] = np.linalg.norm(X - cluster_mean, axis = 1)\n",
    "            \n",
    "        return distances\n",
    "    \n",
    "    def __label_examples(self, distances):\n",
    "        return distances.argmin(axis = 1)\n",
    "    \n",
    "    def __compute_means(self, X, labels, col_count):\n",
    "        cluster_means = np.zeros((self.n_clusters, col_count))\n",
    "        for cluster_mean_index, _ in enumerate(cluster_means):\n",
    "            cluster_elements = X [ labels == cluster_mean_index ]\n",
    "            if len(cluster_elements):\n",
    "                cluster_means[cluster_mean_index, :] = cluster_elements.mean(axis = 0)\n",
    "                \n",
    "        return cluster_means\n",
    "    \n",
    "    def __compute_cost(self, X, labels, cluster_means):\n",
    "        cost = 0\n",
    "        for cluster_mean_index, cluster_mean in enumerate(cluster_means):\n",
    "            cluster_elements = X [ labels == cluster_mean_index ]\n",
    "            cost += np.linalg.norm(cluster_elements - cluster_mean, axis = 1).sum()\n",
    "        \n",
    "        return cost\n",
    "            \n",
    "    def __get_values(self, X):\n",
    "        if isinstance(X, np.ndarray):\n",
    "            return X\n",
    "        return np.array(X)\n",
    "    \n",
    "    def predict(self):\n",
    "        data=pd.DataFrame(self.items)\n",
    "        added_column=list(data.columns)[-1]\n",
    "        data['Label'] = self.y\n",
    "        resultOfClustering=data.groupby([added_column])['Label'].agg(lambda x: x.value_counts().index[0])\n",
    "        mapping = dict()\n",
    "        for label in range(self.n_clusters):\n",
    "            label_predicted = resultOfClustering[label]\n",
    "            mapping[label] = label_predicted\n",
    "        data['PredictedLabels']=data[added_column].map(mapping)\n",
    "        return np.array(data['PredictedLabels'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       "  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<!-- Created with matplotlib (https://matplotlib.org/) -->\n",
       "<svg height=\"263.63625pt\" version=\"1.1\" viewBox=\"0 0 381.65 263.63625\" width=\"381.65pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       " <defs>\n",
       "  <style type=\"text/css\">\n",
       "*{stroke-linecap:butt;stroke-linejoin:round;}\n",
       "  </style>\n",
       " </defs>\n",
       " <g id=\"figure_1\">\n",
       "  <g id=\"patch_1\">\n",
       "   <path d=\"M -0 263.63625 \n",
       "L 381.65 263.63625 \n",
       "L 381.65 0 \n",
       "L -0 0 \n",
       "z\n",
       "\" style=\"fill:none;\"/>\n",
       "  </g>\n",
       "  <g id=\"axes_1\">\n",
       "   <g id=\"patch_2\">\n",
       "    <path d=\"M 39.65 239.758125 \n",
       "L 374.45 239.758125 \n",
       "L 374.45 22.318125 \n",
       "L 39.65 22.318125 \n",
       "z\n",
       "\" style=\"fill:#ffffff;\"/>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_1\">\n",
       "    <g id=\"xtick_1\">\n",
       "     <g id=\"line2d_1\">\n",
       "      <defs>\n",
       "       <path d=\"M 0 0 \n",
       "L 0 3.5 \n",
       "\" id=\"m37b6bebd2b\" style=\"stroke:#000000;stroke-width:0.8;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"54.868182\" xlink:href=\"#m37b6bebd2b\" y=\"239.758125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_1\">\n",
       "      <!-- 0 -->\n",
       "      <defs>\n",
       "       <path d=\"M 31.78125 66.40625 \n",
       "Q 24.171875 66.40625 20.328125 58.90625 \n",
       "Q 16.5 51.421875 16.5 36.375 \n",
       "Q 16.5 21.390625 20.328125 13.890625 \n",
       "Q 24.171875 6.390625 31.78125 6.390625 \n",
       "Q 39.453125 6.390625 43.28125 13.890625 \n",
       "Q 47.125 21.390625 47.125 36.375 \n",
       "Q 47.125 51.421875 43.28125 58.90625 \n",
       "Q 39.453125 66.40625 31.78125 66.40625 \n",
       "z\n",
       "M 31.78125 74.21875 \n",
       "Q 44.046875 74.21875 50.515625 64.515625 \n",
       "Q 56.984375 54.828125 56.984375 36.375 \n",
       "Q 56.984375 17.96875 50.515625 8.265625 \n",
       "Q 44.046875 -1.421875 31.78125 -1.421875 \n",
       "Q 19.53125 -1.421875 13.0625 8.265625 \n",
       "Q 6.59375 17.96875 6.59375 36.375 \n",
       "Q 6.59375 54.828125 13.0625 64.515625 \n",
       "Q 19.53125 74.21875 31.78125 74.21875 \n",
       "z\n",
       "\" id=\"DejaVuSans-48\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(51.686932 254.356563)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_2\">\n",
       "     <g id=\"line2d_2\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"70.887321\" xlink:href=\"#m37b6bebd2b\" y=\"239.758125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_2\">\n",
       "      <!-- 1 -->\n",
       "      <defs>\n",
       "       <path d=\"M 12.40625 8.296875 \n",
       "L 28.515625 8.296875 \n",
       "L 28.515625 63.921875 \n",
       "L 10.984375 60.40625 \n",
       "L 10.984375 69.390625 \n",
       "L 28.421875 72.90625 \n",
       "L 38.28125 72.90625 \n",
       "L 38.28125 8.296875 \n",
       "L 54.390625 8.296875 \n",
       "L 54.390625 0 \n",
       "L 12.40625 0 \n",
       "z\n",
       "\" id=\"DejaVuSans-49\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(67.706071 254.356563)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-49\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_3\">\n",
       "     <g id=\"line2d_3\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"86.906459\" xlink:href=\"#m37b6bebd2b\" y=\"239.758125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_3\">\n",
       "      <!-- 2 -->\n",
       "      <defs>\n",
       "       <path d=\"M 19.1875 8.296875 \n",
       "L 53.609375 8.296875 \n",
       "L 53.609375 0 \n",
       "L 7.328125 0 \n",
       "L 7.328125 8.296875 \n",
       "Q 12.9375 14.109375 22.625 23.890625 \n",
       "Q 32.328125 33.6875 34.8125 36.53125 \n",
       "Q 39.546875 41.84375 41.421875 45.53125 \n",
       "Q 43.3125 49.21875 43.3125 52.78125 \n",
       "Q 43.3125 58.59375 39.234375 62.25 \n",
       "Q 35.15625 65.921875 28.609375 65.921875 \n",
       "Q 23.96875 65.921875 18.8125 64.3125 \n",
       "Q 13.671875 62.703125 7.8125 59.421875 \n",
       "L 7.8125 69.390625 \n",
       "Q 13.765625 71.78125 18.9375 73 \n",
       "Q 24.125 74.21875 28.421875 74.21875 \n",
       "Q 39.75 74.21875 46.484375 68.546875 \n",
       "Q 53.21875 62.890625 53.21875 53.421875 \n",
       "Q 53.21875 48.921875 51.53125 44.890625 \n",
       "Q 49.859375 40.875 45.40625 35.40625 \n",
       "Q 44.1875 33.984375 37.640625 27.21875 \n",
       "Q 31.109375 20.453125 19.1875 8.296875 \n",
       "z\n",
       "\" id=\"DejaVuSans-50\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(83.725209 254.356563)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-50\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_4\">\n",
       "     <g id=\"line2d_4\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"102.925598\" xlink:href=\"#m37b6bebd2b\" y=\"239.758125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_4\">\n",
       "      <!-- 3 -->\n",
       "      <defs>\n",
       "       <path d=\"M 40.578125 39.3125 \n",
       "Q 47.65625 37.796875 51.625 33 \n",
       "Q 55.609375 28.21875 55.609375 21.1875 \n",
       "Q 55.609375 10.40625 48.1875 4.484375 \n",
       "Q 40.765625 -1.421875 27.09375 -1.421875 \n",
       "Q 22.515625 -1.421875 17.65625 -0.515625 \n",
       "Q 12.796875 0.390625 7.625 2.203125 \n",
       "L 7.625 11.71875 \n",
       "Q 11.71875 9.328125 16.59375 8.109375 \n",
       "Q 21.484375 6.890625 26.8125 6.890625 \n",
       "Q 36.078125 6.890625 40.9375 10.546875 \n",
       "Q 45.796875 14.203125 45.796875 21.1875 \n",
       "Q 45.796875 27.640625 41.28125 31.265625 \n",
       "Q 36.765625 34.90625 28.71875 34.90625 \n",
       "L 20.21875 34.90625 \n",
       "L 20.21875 43.015625 \n",
       "L 29.109375 43.015625 \n",
       "Q 36.375 43.015625 40.234375 45.921875 \n",
       "Q 44.09375 48.828125 44.09375 54.296875 \n",
       "Q 44.09375 59.90625 40.109375 62.90625 \n",
       "Q 36.140625 65.921875 28.71875 65.921875 \n",
       "Q 24.65625 65.921875 20.015625 65.03125 \n",
       "Q 15.375 64.15625 9.8125 62.3125 \n",
       "L 9.8125 71.09375 \n",
       "Q 15.4375 72.65625 20.34375 73.4375 \n",
       "Q 25.25 74.21875 29.59375 74.21875 \n",
       "Q 40.828125 74.21875 47.359375 69.109375 \n",
       "Q 53.90625 64.015625 53.90625 55.328125 \n",
       "Q 53.90625 49.265625 50.4375 45.09375 \n",
       "Q 46.96875 40.921875 40.578125 39.3125 \n",
       "z\n",
       "\" id=\"DejaVuSans-51\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(99.744348 254.356563)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-51\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_5\">\n",
       "     <g id=\"line2d_5\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"118.944737\" xlink:href=\"#m37b6bebd2b\" y=\"239.758125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_5\">\n",
       "      <!-- 4 -->\n",
       "      <defs>\n",
       "       <path d=\"M 37.796875 64.3125 \n",
       "L 12.890625 25.390625 \n",
       "L 37.796875 25.390625 \n",
       "z\n",
       "M 35.203125 72.90625 \n",
       "L 47.609375 72.90625 \n",
       "L 47.609375 25.390625 \n",
       "L 58.015625 25.390625 \n",
       "L 58.015625 17.1875 \n",
       "L 47.609375 17.1875 \n",
       "L 47.609375 0 \n",
       "L 37.796875 0 \n",
       "L 37.796875 17.1875 \n",
       "L 4.890625 17.1875 \n",
       "L 4.890625 26.703125 \n",
       "z\n",
       "\" id=\"DejaVuSans-52\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(115.763487 254.356563)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-52\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_6\">\n",
       "     <g id=\"line2d_6\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"134.963876\" xlink:href=\"#m37b6bebd2b\" y=\"239.758125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_6\">\n",
       "      <!-- 5 -->\n",
       "      <defs>\n",
       "       <path d=\"M 10.796875 72.90625 \n",
       "L 49.515625 72.90625 \n",
       "L 49.515625 64.59375 \n",
       "L 19.828125 64.59375 \n",
       "L 19.828125 46.734375 \n",
       "Q 21.96875 47.46875 24.109375 47.828125 \n",
       "Q 26.265625 48.1875 28.421875 48.1875 \n",
       "Q 40.625 48.1875 47.75 41.5 \n",
       "Q 54.890625 34.8125 54.890625 23.390625 \n",
       "Q 54.890625 11.625 47.5625 5.09375 \n",
       "Q 40.234375 -1.421875 26.90625 -1.421875 \n",
       "Q 22.3125 -1.421875 17.546875 -0.640625 \n",
       "Q 12.796875 0.140625 7.71875 1.703125 \n",
       "L 7.71875 11.625 \n",
       "Q 12.109375 9.234375 16.796875 8.0625 \n",
       "Q 21.484375 6.890625 26.703125 6.890625 \n",
       "Q 35.15625 6.890625 40.078125 11.328125 \n",
       "Q 45.015625 15.765625 45.015625 23.390625 \n",
       "Q 45.015625 31 40.078125 35.4375 \n",
       "Q 35.15625 39.890625 26.703125 39.890625 \n",
       "Q 22.75 39.890625 18.8125 39.015625 \n",
       "Q 14.890625 38.140625 10.796875 36.28125 \n",
       "z\n",
       "\" id=\"DejaVuSans-53\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(131.782626 254.356563)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_7\">\n",
       "     <g id=\"line2d_7\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"150.983014\" xlink:href=\"#m37b6bebd2b\" y=\"239.758125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_7\">\n",
       "      <!-- 6 -->\n",
       "      <defs>\n",
       "       <path d=\"M 33.015625 40.375 \n",
       "Q 26.375 40.375 22.484375 35.828125 \n",
       "Q 18.609375 31.296875 18.609375 23.390625 \n",
       "Q 18.609375 15.53125 22.484375 10.953125 \n",
       "Q 26.375 6.390625 33.015625 6.390625 \n",
       "Q 39.65625 6.390625 43.53125 10.953125 \n",
       "Q 47.40625 15.53125 47.40625 23.390625 \n",
       "Q 47.40625 31.296875 43.53125 35.828125 \n",
       "Q 39.65625 40.375 33.015625 40.375 \n",
       "z\n",
       "M 52.59375 71.296875 \n",
       "L 52.59375 62.3125 \n",
       "Q 48.875 64.0625 45.09375 64.984375 \n",
       "Q 41.3125 65.921875 37.59375 65.921875 \n",
       "Q 27.828125 65.921875 22.671875 59.328125 \n",
       "Q 17.53125 52.734375 16.796875 39.40625 \n",
       "Q 19.671875 43.65625 24.015625 45.921875 \n",
       "Q 28.375 48.1875 33.59375 48.1875 \n",
       "Q 44.578125 48.1875 50.953125 41.515625 \n",
       "Q 57.328125 34.859375 57.328125 23.390625 \n",
       "Q 57.328125 12.15625 50.6875 5.359375 \n",
       "Q 44.046875 -1.421875 33.015625 -1.421875 \n",
       "Q 20.359375 -1.421875 13.671875 8.265625 \n",
       "Q 6.984375 17.96875 6.984375 36.375 \n",
       "Q 6.984375 53.65625 15.1875 63.9375 \n",
       "Q 23.390625 74.21875 37.203125 74.21875 \n",
       "Q 40.921875 74.21875 44.703125 73.484375 \n",
       "Q 48.484375 72.75 52.59375 71.296875 \n",
       "z\n",
       "\" id=\"DejaVuSans-54\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(147.801764 254.356563)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-54\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_8\">\n",
       "     <g id=\"line2d_8\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"167.002153\" xlink:href=\"#m37b6bebd2b\" y=\"239.758125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_8\">\n",
       "      <!-- 7 -->\n",
       "      <defs>\n",
       "       <path d=\"M 8.203125 72.90625 \n",
       "L 55.078125 72.90625 \n",
       "L 55.078125 68.703125 \n",
       "L 28.609375 0 \n",
       "L 18.3125 0 \n",
       "L 43.21875 64.59375 \n",
       "L 8.203125 64.59375 \n",
       "z\n",
       "\" id=\"DejaVuSans-55\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(163.820903 254.356563)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-55\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_9\">\n",
       "     <g id=\"line2d_9\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"183.021292\" xlink:href=\"#m37b6bebd2b\" y=\"239.758125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_9\">\n",
       "      <!-- 8 -->\n",
       "      <defs>\n",
       "       <path d=\"M 31.78125 34.625 \n",
       "Q 24.75 34.625 20.71875 30.859375 \n",
       "Q 16.703125 27.09375 16.703125 20.515625 \n",
       "Q 16.703125 13.921875 20.71875 10.15625 \n",
       "Q 24.75 6.390625 31.78125 6.390625 \n",
       "Q 38.8125 6.390625 42.859375 10.171875 \n",
       "Q 46.921875 13.96875 46.921875 20.515625 \n",
       "Q 46.921875 27.09375 42.890625 30.859375 \n",
       "Q 38.875 34.625 31.78125 34.625 \n",
       "z\n",
       "M 21.921875 38.8125 \n",
       "Q 15.578125 40.375 12.03125 44.71875 \n",
       "Q 8.5 49.078125 8.5 55.328125 \n",
       "Q 8.5 64.0625 14.71875 69.140625 \n",
       "Q 20.953125 74.21875 31.78125 74.21875 \n",
       "Q 42.671875 74.21875 48.875 69.140625 \n",
       "Q 55.078125 64.0625 55.078125 55.328125 \n",
       "Q 55.078125 49.078125 51.53125 44.71875 \n",
       "Q 48 40.375 41.703125 38.8125 \n",
       "Q 48.828125 37.15625 52.796875 32.3125 \n",
       "Q 56.78125 27.484375 56.78125 20.515625 \n",
       "Q 56.78125 9.90625 50.3125 4.234375 \n",
       "Q 43.84375 -1.421875 31.78125 -1.421875 \n",
       "Q 19.734375 -1.421875 13.25 4.234375 \n",
       "Q 6.78125 9.90625 6.78125 20.515625 \n",
       "Q 6.78125 27.484375 10.78125 32.3125 \n",
       "Q 14.796875 37.15625 21.921875 38.8125 \n",
       "z\n",
       "M 18.3125 54.390625 \n",
       "Q 18.3125 48.734375 21.84375 45.5625 \n",
       "Q 25.390625 42.390625 31.78125 42.390625 \n",
       "Q 38.140625 42.390625 41.71875 45.5625 \n",
       "Q 45.3125 48.734375 45.3125 54.390625 \n",
       "Q 45.3125 60.0625 41.71875 63.234375 \n",
       "Q 38.140625 66.40625 31.78125 66.40625 \n",
       "Q 25.390625 66.40625 21.84375 63.234375 \n",
       "Q 18.3125 60.0625 18.3125 54.390625 \n",
       "z\n",
       "\" id=\"DejaVuSans-56\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(179.840042 254.356563)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-56\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_10\">\n",
       "     <g id=\"line2d_10\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"199.040431\" xlink:href=\"#m37b6bebd2b\" y=\"239.758125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_10\">\n",
       "      <!-- 9 -->\n",
       "      <defs>\n",
       "       <path d=\"M 10.984375 1.515625 \n",
       "L 10.984375 10.5 \n",
       "Q 14.703125 8.734375 18.5 7.8125 \n",
       "Q 22.3125 6.890625 25.984375 6.890625 \n",
       "Q 35.75 6.890625 40.890625 13.453125 \n",
       "Q 46.046875 20.015625 46.78125 33.40625 \n",
       "Q 43.953125 29.203125 39.59375 26.953125 \n",
       "Q 35.25 24.703125 29.984375 24.703125 \n",
       "Q 19.046875 24.703125 12.671875 31.3125 \n",
       "Q 6.296875 37.9375 6.296875 49.421875 \n",
       "Q 6.296875 60.640625 12.9375 67.421875 \n",
       "Q 19.578125 74.21875 30.609375 74.21875 \n",
       "Q 43.265625 74.21875 49.921875 64.515625 \n",
       "Q 56.59375 54.828125 56.59375 36.375 \n",
       "Q 56.59375 19.140625 48.40625 8.859375 \n",
       "Q 40.234375 -1.421875 26.421875 -1.421875 \n",
       "Q 22.703125 -1.421875 18.890625 -0.6875 \n",
       "Q 15.09375 0.046875 10.984375 1.515625 \n",
       "z\n",
       "M 30.609375 32.421875 \n",
       "Q 37.25 32.421875 41.125 36.953125 \n",
       "Q 45.015625 41.5 45.015625 49.421875 \n",
       "Q 45.015625 57.28125 41.125 61.84375 \n",
       "Q 37.25 66.40625 30.609375 66.40625 \n",
       "Q 23.96875 66.40625 20.09375 61.84375 \n",
       "Q 16.21875 57.28125 16.21875 49.421875 \n",
       "Q 16.21875 41.5 20.09375 36.953125 \n",
       "Q 23.96875 32.421875 30.609375 32.421875 \n",
       "z\n",
       "\" id=\"DejaVuSans-57\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(195.859181 254.356563)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-57\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_11\">\n",
       "     <g id=\"line2d_11\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"215.059569\" xlink:href=\"#m37b6bebd2b\" y=\"239.758125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_11\">\n",
       "      <!-- 10 -->\n",
       "      <g transform=\"translate(208.697069 254.356563)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-49\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_12\">\n",
       "     <g id=\"line2d_12\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"231.078708\" xlink:href=\"#m37b6bebd2b\" y=\"239.758125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_12\">\n",
       "      <!-- 11 -->\n",
       "      <g transform=\"translate(224.716208 254.356563)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-49\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-49\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_13\">\n",
       "     <g id=\"line2d_13\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"247.097847\" xlink:href=\"#m37b6bebd2b\" y=\"239.758125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_13\">\n",
       "      <!-- 12 -->\n",
       "      <g transform=\"translate(240.735347 254.356563)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-49\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_14\">\n",
       "     <g id=\"line2d_14\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"263.116986\" xlink:href=\"#m37b6bebd2b\" y=\"239.758125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_14\">\n",
       "      <!-- 13 -->\n",
       "      <g transform=\"translate(256.754486 254.356563)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-49\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-51\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_15\">\n",
       "     <g id=\"line2d_15\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"279.136124\" xlink:href=\"#m37b6bebd2b\" y=\"239.758125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_15\">\n",
       "      <!-- 14 -->\n",
       "      <g transform=\"translate(272.773624 254.356563)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-49\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-52\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_16\">\n",
       "     <g id=\"line2d_16\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"295.155263\" xlink:href=\"#m37b6bebd2b\" y=\"239.758125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_16\">\n",
       "      <!-- 15 -->\n",
       "      <g transform=\"translate(288.792763 254.356563)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-49\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_17\">\n",
       "     <g id=\"line2d_17\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"311.174402\" xlink:href=\"#m37b6bebd2b\" y=\"239.758125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_17\">\n",
       "      <!-- 16 -->\n",
       "      <g transform=\"translate(304.811902 254.356563)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-49\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-54\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_18\">\n",
       "     <g id=\"line2d_18\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"327.193541\" xlink:href=\"#m37b6bebd2b\" y=\"239.758125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_18\">\n",
       "      <!-- 17 -->\n",
       "      <g transform=\"translate(320.831041 254.356563)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-49\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-55\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_19\">\n",
       "     <g id=\"line2d_19\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"343.212679\" xlink:href=\"#m37b6bebd2b\" y=\"239.758125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_19\">\n",
       "      <!-- 18 -->\n",
       "      <g transform=\"translate(336.850179 254.356563)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-49\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-56\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_20\">\n",
       "     <g id=\"line2d_20\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"359.231818\" xlink:href=\"#m37b6bebd2b\" y=\"239.758125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_20\">\n",
       "      <!-- 19 -->\n",
       "      <g transform=\"translate(352.869318 254.356563)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-49\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-57\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_2\">\n",
       "    <g id=\"ytick_1\">\n",
       "     <g id=\"line2d_21\">\n",
       "      <defs>\n",
       "       <path d=\"M 0 0 \n",
       "L -3.5 0 \n",
       "\" id=\"m26d1a608f9\" style=\"stroke:#000000;stroke-width:0.8;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"39.65\" xlink:href=\"#m26d1a608f9\" y=\"216.628691\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_21\">\n",
       "      <!-- 2589 -->\n",
       "      <g transform=\"translate(7.2 220.42791)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-50\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-53\"/>\n",
       "       <use x=\"127.246094\" xlink:href=\"#DejaVuSans-56\"/>\n",
       "       <use x=\"190.869141\" xlink:href=\"#DejaVuSans-57\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_2\">\n",
       "     <g id=\"line2d_22\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"39.65\" xlink:href=\"#m26d1a608f9\" y=\"177.572718\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_22\">\n",
       "      <!-- 2590 -->\n",
       "      <g transform=\"translate(7.2 181.371937)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-50\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-53\"/>\n",
       "       <use x=\"127.246094\" xlink:href=\"#DejaVuSans-57\"/>\n",
       "       <use x=\"190.869141\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_3\">\n",
       "     <g id=\"line2d_23\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"39.65\" xlink:href=\"#m26d1a608f9\" y=\"138.516746\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_23\">\n",
       "      <!-- 2591 -->\n",
       "      <g transform=\"translate(7.2 142.315964)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-50\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-53\"/>\n",
       "       <use x=\"127.246094\" xlink:href=\"#DejaVuSans-57\"/>\n",
       "       <use x=\"190.869141\" xlink:href=\"#DejaVuSans-49\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_4\">\n",
       "     <g id=\"line2d_24\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"39.65\" xlink:href=\"#m26d1a608f9\" y=\"99.460773\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_24\">\n",
       "      <!-- 2592 -->\n",
       "      <g transform=\"translate(7.2 103.259991)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-50\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-53\"/>\n",
       "       <use x=\"127.246094\" xlink:href=\"#DejaVuSans-57\"/>\n",
       "       <use x=\"190.869141\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_5\">\n",
       "     <g id=\"line2d_25\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"39.65\" xlink:href=\"#m26d1a608f9\" y=\"60.4048\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_25\">\n",
       "      <!-- 2593 -->\n",
       "      <g transform=\"translate(7.2 64.204018)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-50\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-53\"/>\n",
       "       <use x=\"127.246094\" xlink:href=\"#DejaVuSans-57\"/>\n",
       "       <use x=\"190.869141\" xlink:href=\"#DejaVuSans-51\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"line2d_26\">\n",
       "    <path clip-path=\"url(#p18d7e99fac)\" d=\"M 54.868182 68.843742 \n",
       "L 70.887321 68.984703 \n",
       "L 86.906459 80.540839 \n",
       "L 102.925598 229.874489 \n",
       "L 118.944737 161.699138 \n",
       "L 134.963876 198.156919 \n",
       "L 150.983014 209.852337 \n",
       "L 167.002153 32.201761 \n",
       "L 183.021292 229.874489 \n",
       "L 199.040431 229.874489 \n",
       "L 215.059569 229.874489 \n",
       "L 231.078708 62.400082 \n",
       "L 247.097847 62.400082 \n",
       "L 263.116986 229.874489 \n",
       "L 279.136124 62.400082 \n",
       "L 295.155263 74.191262 \n",
       "L 311.174402 229.874489 \n",
       "L 327.193541 65.189431 \n",
       "L 343.212679 195.558203 \n",
       "L 359.231818 68.984703 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-linecap:square;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_3\">\n",
       "    <path d=\"M 39.65 239.758125 \n",
       "L 39.65 22.318125 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_4\">\n",
       "    <path d=\"M 374.45 239.758125 \n",
       "L 374.45 22.318125 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_5\">\n",
       "    <path d=\"M 39.65 239.758125 \n",
       "L 374.45 239.758125 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_6\">\n",
       "    <path d=\"M 39.65 22.318125 \n",
       "L 374.45 22.318125 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"text_26\">\n",
       "    <!-- error of different runs -->\n",
       "    <defs>\n",
       "     <path d=\"M 56.203125 29.59375 \n",
       "L 56.203125 25.203125 \n",
       "L 14.890625 25.203125 \n",
       "Q 15.484375 15.921875 20.484375 11.0625 \n",
       "Q 25.484375 6.203125 34.421875 6.203125 \n",
       "Q 39.59375 6.203125 44.453125 7.46875 \n",
       "Q 49.3125 8.734375 54.109375 11.28125 \n",
       "L 54.109375 2.78125 \n",
       "Q 49.265625 0.734375 44.1875 -0.34375 \n",
       "Q 39.109375 -1.421875 33.890625 -1.421875 \n",
       "Q 20.796875 -1.421875 13.15625 6.1875 \n",
       "Q 5.515625 13.8125 5.515625 26.8125 \n",
       "Q 5.515625 40.234375 12.765625 48.109375 \n",
       "Q 20.015625 56 32.328125 56 \n",
       "Q 43.359375 56 49.78125 48.890625 \n",
       "Q 56.203125 41.796875 56.203125 29.59375 \n",
       "z\n",
       "M 47.21875 32.234375 \n",
       "Q 47.125 39.59375 43.09375 43.984375 \n",
       "Q 39.0625 48.390625 32.421875 48.390625 \n",
       "Q 24.90625 48.390625 20.390625 44.140625 \n",
       "Q 15.875 39.890625 15.1875 32.171875 \n",
       "z\n",
       "\" id=\"DejaVuSans-101\"/>\n",
       "     <path d=\"M 41.109375 46.296875 \n",
       "Q 39.59375 47.171875 37.8125 47.578125 \n",
       "Q 36.03125 48 33.890625 48 \n",
       "Q 26.265625 48 22.1875 43.046875 \n",
       "Q 18.109375 38.09375 18.109375 28.8125 \n",
       "L 18.109375 0 \n",
       "L 9.078125 0 \n",
       "L 9.078125 54.6875 \n",
       "L 18.109375 54.6875 \n",
       "L 18.109375 46.1875 \n",
       "Q 20.953125 51.171875 25.484375 53.578125 \n",
       "Q 30.03125 56 36.53125 56 \n",
       "Q 37.453125 56 38.578125 55.875 \n",
       "Q 39.703125 55.765625 41.0625 55.515625 \n",
       "z\n",
       "\" id=\"DejaVuSans-114\"/>\n",
       "     <path d=\"M 30.609375 48.390625 \n",
       "Q 23.390625 48.390625 19.1875 42.75 \n",
       "Q 14.984375 37.109375 14.984375 27.296875 \n",
       "Q 14.984375 17.484375 19.15625 11.84375 \n",
       "Q 23.34375 6.203125 30.609375 6.203125 \n",
       "Q 37.796875 6.203125 41.984375 11.859375 \n",
       "Q 46.1875 17.53125 46.1875 27.296875 \n",
       "Q 46.1875 37.015625 41.984375 42.703125 \n",
       "Q 37.796875 48.390625 30.609375 48.390625 \n",
       "z\n",
       "M 30.609375 56 \n",
       "Q 42.328125 56 49.015625 48.375 \n",
       "Q 55.71875 40.765625 55.71875 27.296875 \n",
       "Q 55.71875 13.875 49.015625 6.21875 \n",
       "Q 42.328125 -1.421875 30.609375 -1.421875 \n",
       "Q 18.84375 -1.421875 12.171875 6.21875 \n",
       "Q 5.515625 13.875 5.515625 27.296875 \n",
       "Q 5.515625 40.765625 12.171875 48.375 \n",
       "Q 18.84375 56 30.609375 56 \n",
       "z\n",
       "\" id=\"DejaVuSans-111\"/>\n",
       "     <path id=\"DejaVuSans-32\"/>\n",
       "     <path d=\"M 37.109375 75.984375 \n",
       "L 37.109375 68.5 \n",
       "L 28.515625 68.5 \n",
       "Q 23.6875 68.5 21.796875 66.546875 \n",
       "Q 19.921875 64.59375 19.921875 59.515625 \n",
       "L 19.921875 54.6875 \n",
       "L 34.71875 54.6875 \n",
       "L 34.71875 47.703125 \n",
       "L 19.921875 47.703125 \n",
       "L 19.921875 0 \n",
       "L 10.890625 0 \n",
       "L 10.890625 47.703125 \n",
       "L 2.296875 47.703125 \n",
       "L 2.296875 54.6875 \n",
       "L 10.890625 54.6875 \n",
       "L 10.890625 58.5 \n",
       "Q 10.890625 67.625 15.140625 71.796875 \n",
       "Q 19.390625 75.984375 28.609375 75.984375 \n",
       "z\n",
       "\" id=\"DejaVuSans-102\"/>\n",
       "     <path d=\"M 45.40625 46.390625 \n",
       "L 45.40625 75.984375 \n",
       "L 54.390625 75.984375 \n",
       "L 54.390625 0 \n",
       "L 45.40625 0 \n",
       "L 45.40625 8.203125 \n",
       "Q 42.578125 3.328125 38.25 0.953125 \n",
       "Q 33.9375 -1.421875 27.875 -1.421875 \n",
       "Q 17.96875 -1.421875 11.734375 6.484375 \n",
       "Q 5.515625 14.40625 5.515625 27.296875 \n",
       "Q 5.515625 40.1875 11.734375 48.09375 \n",
       "Q 17.96875 56 27.875 56 \n",
       "Q 33.9375 56 38.25 53.625 \n",
       "Q 42.578125 51.265625 45.40625 46.390625 \n",
       "z\n",
       "M 14.796875 27.296875 \n",
       "Q 14.796875 17.390625 18.875 11.75 \n",
       "Q 22.953125 6.109375 30.078125 6.109375 \n",
       "Q 37.203125 6.109375 41.296875 11.75 \n",
       "Q 45.40625 17.390625 45.40625 27.296875 \n",
       "Q 45.40625 37.203125 41.296875 42.84375 \n",
       "Q 37.203125 48.484375 30.078125 48.484375 \n",
       "Q 22.953125 48.484375 18.875 42.84375 \n",
       "Q 14.796875 37.203125 14.796875 27.296875 \n",
       "z\n",
       "\" id=\"DejaVuSans-100\"/>\n",
       "     <path d=\"M 9.421875 54.6875 \n",
       "L 18.40625 54.6875 \n",
       "L 18.40625 0 \n",
       "L 9.421875 0 \n",
       "z\n",
       "M 9.421875 75.984375 \n",
       "L 18.40625 75.984375 \n",
       "L 18.40625 64.59375 \n",
       "L 9.421875 64.59375 \n",
       "z\n",
       "\" id=\"DejaVuSans-105\"/>\n",
       "     <path d=\"M 54.890625 33.015625 \n",
       "L 54.890625 0 \n",
       "L 45.90625 0 \n",
       "L 45.90625 32.71875 \n",
       "Q 45.90625 40.484375 42.875 44.328125 \n",
       "Q 39.84375 48.1875 33.796875 48.1875 \n",
       "Q 26.515625 48.1875 22.3125 43.546875 \n",
       "Q 18.109375 38.921875 18.109375 30.90625 \n",
       "L 18.109375 0 \n",
       "L 9.078125 0 \n",
       "L 9.078125 54.6875 \n",
       "L 18.109375 54.6875 \n",
       "L 18.109375 46.1875 \n",
       "Q 21.34375 51.125 25.703125 53.5625 \n",
       "Q 30.078125 56 35.796875 56 \n",
       "Q 45.21875 56 50.046875 50.171875 \n",
       "Q 54.890625 44.34375 54.890625 33.015625 \n",
       "z\n",
       "\" id=\"DejaVuSans-110\"/>\n",
       "     <path d=\"M 18.3125 70.21875 \n",
       "L 18.3125 54.6875 \n",
       "L 36.8125 54.6875 \n",
       "L 36.8125 47.703125 \n",
       "L 18.3125 47.703125 \n",
       "L 18.3125 18.015625 \n",
       "Q 18.3125 11.328125 20.140625 9.421875 \n",
       "Q 21.96875 7.515625 27.59375 7.515625 \n",
       "L 36.8125 7.515625 \n",
       "L 36.8125 0 \n",
       "L 27.59375 0 \n",
       "Q 17.1875 0 13.234375 3.875 \n",
       "Q 9.28125 7.765625 9.28125 18.015625 \n",
       "L 9.28125 47.703125 \n",
       "L 2.6875 47.703125 \n",
       "L 2.6875 54.6875 \n",
       "L 9.28125 54.6875 \n",
       "L 9.28125 70.21875 \n",
       "z\n",
       "\" id=\"DejaVuSans-116\"/>\n",
       "     <path d=\"M 8.5 21.578125 \n",
       "L 8.5 54.6875 \n",
       "L 17.484375 54.6875 \n",
       "L 17.484375 21.921875 \n",
       "Q 17.484375 14.15625 20.5 10.265625 \n",
       "Q 23.53125 6.390625 29.59375 6.390625 \n",
       "Q 36.859375 6.390625 41.078125 11.03125 \n",
       "Q 45.3125 15.671875 45.3125 23.6875 \n",
       "L 45.3125 54.6875 \n",
       "L 54.296875 54.6875 \n",
       "L 54.296875 0 \n",
       "L 45.3125 0 \n",
       "L 45.3125 8.40625 \n",
       "Q 42.046875 3.421875 37.71875 1 \n",
       "Q 33.40625 -1.421875 27.6875 -1.421875 \n",
       "Q 18.265625 -1.421875 13.375 4.4375 \n",
       "Q 8.5 10.296875 8.5 21.578125 \n",
       "z\n",
       "M 31.109375 56 \n",
       "z\n",
       "\" id=\"DejaVuSans-117\"/>\n",
       "     <path d=\"M 44.28125 53.078125 \n",
       "L 44.28125 44.578125 \n",
       "Q 40.484375 46.53125 36.375 47.5 \n",
       "Q 32.28125 48.484375 27.875 48.484375 \n",
       "Q 21.1875 48.484375 17.84375 46.4375 \n",
       "Q 14.5 44.390625 14.5 40.28125 \n",
       "Q 14.5 37.15625 16.890625 35.375 \n",
       "Q 19.28125 33.59375 26.515625 31.984375 \n",
       "L 29.59375 31.296875 \n",
       "Q 39.15625 29.25 43.1875 25.515625 \n",
       "Q 47.21875 21.78125 47.21875 15.09375 \n",
       "Q 47.21875 7.46875 41.1875 3.015625 \n",
       "Q 35.15625 -1.421875 24.609375 -1.421875 \n",
       "Q 20.21875 -1.421875 15.453125 -0.5625 \n",
       "Q 10.6875 0.296875 5.421875 2 \n",
       "L 5.421875 11.28125 \n",
       "Q 10.40625 8.6875 15.234375 7.390625 \n",
       "Q 20.0625 6.109375 24.8125 6.109375 \n",
       "Q 31.15625 6.109375 34.5625 8.28125 \n",
       "Q 37.984375 10.453125 37.984375 14.40625 \n",
       "Q 37.984375 18.0625 35.515625 20.015625 \n",
       "Q 33.0625 21.96875 24.703125 23.78125 \n",
       "L 21.578125 24.515625 \n",
       "Q 13.234375 26.265625 9.515625 29.90625 \n",
       "Q 5.8125 33.546875 5.8125 39.890625 \n",
       "Q 5.8125 47.609375 11.28125 51.796875 \n",
       "Q 16.75 56 26.8125 56 \n",
       "Q 31.78125 56 36.171875 55.265625 \n",
       "Q 40.578125 54.546875 44.28125 53.078125 \n",
       "z\n",
       "\" id=\"DejaVuSans-115\"/>\n",
       "    </defs>\n",
       "    <g transform=\"translate(142.255625 16.318125)scale(0.12 -0.12)\">\n",
       "     <use xlink:href=\"#DejaVuSans-101\"/>\n",
       "     <use x=\"61.523438\" xlink:href=\"#DejaVuSans-114\"/>\n",
       "     <use x=\"100.886719\" xlink:href=\"#DejaVuSans-114\"/>\n",
       "     <use x=\"139.75\" xlink:href=\"#DejaVuSans-111\"/>\n",
       "     <use x=\"200.931641\" xlink:href=\"#DejaVuSans-114\"/>\n",
       "     <use x=\"242.044922\" xlink:href=\"#DejaVuSans-32\"/>\n",
       "     <use x=\"273.832031\" xlink:href=\"#DejaVuSans-111\"/>\n",
       "     <use x=\"335.013672\" xlink:href=\"#DejaVuSans-102\"/>\n",
       "     <use x=\"370.21875\" xlink:href=\"#DejaVuSans-32\"/>\n",
       "     <use x=\"402.005859\" xlink:href=\"#DejaVuSans-100\"/>\n",
       "     <use x=\"465.482422\" xlink:href=\"#DejaVuSans-105\"/>\n",
       "     <use x=\"493.265625\" xlink:href=\"#DejaVuSans-102\"/>\n",
       "     <use x=\"528.470703\" xlink:href=\"#DejaVuSans-102\"/>\n",
       "     <use x=\"563.675781\" xlink:href=\"#DejaVuSans-101\"/>\n",
       "     <use x=\"625.199219\" xlink:href=\"#DejaVuSans-114\"/>\n",
       "     <use x=\"664.0625\" xlink:href=\"#DejaVuSans-101\"/>\n",
       "     <use x=\"725.585938\" xlink:href=\"#DejaVuSans-110\"/>\n",
       "     <use x=\"788.964844\" xlink:href=\"#DejaVuSans-116\"/>\n",
       "     <use x=\"828.173828\" xlink:href=\"#DejaVuSans-32\"/>\n",
       "     <use x=\"859.960938\" xlink:href=\"#DejaVuSans-114\"/>\n",
       "     <use x=\"901.074219\" xlink:href=\"#DejaVuSans-117\"/>\n",
       "     <use x=\"964.453125\" xlink:href=\"#DejaVuSans-110\"/>\n",
       "     <use x=\"1027.832031\" xlink:href=\"#DejaVuSans-115\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "  </g>\n",
       " </g>\n",
       " <defs>\n",
       "  <clipPath id=\"p18d7e99fac\">\n",
       "   <rect height=\"217.44\" width=\"334.8\" x=\"39.65\" y=\"22.318125\"/>\n",
       "  </clipPath>\n",
       " </defs>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "kmeans=KMeans(2,max_iter=10000,runs=20)\n",
    "centroids,kmeans_items=kmeans.fit(X,Y)\n",
    "plt.plot(np.arange(len(kmeans.costs)),kmeans.costs)\n",
    "plt.title('error of different runs')\n",
    "plt.xticks(np.arange(len(kmeans.costs)))\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Gaussian Mixture Model Implementation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "import scipy.stats as sp\n",
    "class GaussianMixModel():\n",
    "    def __init__(self, X, k=2):\n",
    "        X = np.asarray(X)\n",
    "        self.m, self.n = X.shape\n",
    "        self.data = X.copy()\n",
    "        self.k = k\n",
    "        \n",
    "        self.sigma_arr = np.array([np.asmatrix(np.identity(self.n)) for i in range(self.k)])\n",
    "        self.phi = np.ones(self.k)/self.k\n",
    "        self.Z = np.asmatrix(np.empty((self.m, self.k), dtype=float))\n",
    "\n",
    "     \n",
    "    def initialize_means(self,means):\n",
    "        self.mean_arr = means\n",
    "    \n",
    "    def fit(self, tol=0.1):\n",
    "\n",
    "        num_iters = 0\n",
    "        logl = 1\n",
    "        previous_logl = 0\n",
    "        while(logl-previous_logl > tol):\n",
    "            previous_logl = self.loglikelihood()\n",
    "            self.e_step()\n",
    "            self.m_step()\n",
    "            num_iters += 1\n",
    "            logl = self.loglikelihood()\n",
    "            print('Iteration %d: log-likelihood is %.6f'%(num_iters, logl))\n",
    "        print('Terminate at %d-th iteration:log-likelihood is %.6f'%(num_iters, logl))\n",
    "\n",
    "    def loglikelihood(self):\n",
    "        logl = 0\n",
    "        for i in range(self.m):\n",
    "            tmp = 0\n",
    "            for j in range(self.k):\n",
    "                tmp += sp.multivariate_normal.pdf(self.data[i, :],self.mean_arr[j, :].A1,self.sigma_arr[j, :]) * self.phi[j]\n",
    "            logl += np.log(tmp)\n",
    "        return logl\n",
    "\n",
    "\n",
    "    def e_step(self):\n",
    "        for i in range(self.m):\n",
    "            den = 0\n",
    "            for j in range(self.k):\n",
    "                num = sp.multivariate_normal.pdf(self.data[i, :],\n",
    "                                                       self.mean_arr[j].A1,\n",
    "                                                       self.sigma_arr[j]) *\\\n",
    "                      self.phi[j]\n",
    "                den += num\n",
    "\n",
    "                self.Z[i, j] = num\n",
    "            self.Z[i, :] /= den\n",
    "            assert self.Z[i, :].sum() - 1 < 1e-4  # Program stop if this condition is false\n",
    "\n",
    "    def m_step(self):\n",
    "         for j in range(self.k):\n",
    "            const = self.Z[:, j].sum()\n",
    "            self.phi[j] = 1/self.m * const\n",
    "            _mu_j = np.zeros(self.n)\n",
    "            _sigma_j = np.zeros((self.n, self.n))\n",
    "            for i in range(self.m):\n",
    "                _mu_j += (self.data[i, :] * self.Z[i, j])\n",
    "                _sigma_j += self.Z[i, j] * ((self.data[i, :] - self.mean_arr[j, :]).T * (self.data[i, :] - self.mean_arr[j, :]))\n",
    "\n",
    "            self.mean_arr[j] = _mu_j / const\n",
    "            self.sigma_arr[j] = _sigma_j / const\n",
    "    \n",
    "    def predict(self):\n",
    "        return np.array(np.argmax(gmm.Z,axis=1)).flatten()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration 1: log-likelihood is -11240.664685\n",
      "Iteration 2: log-likelihood is -11217.578370\n",
      "Iteration 3: log-likelihood is -11207.984489\n",
      "Iteration 4: log-likelihood is -11203.316664\n",
      "Iteration 5: log-likelihood is -11200.584656\n",
      "Iteration 6: log-likelihood is -11198.589541\n",
      "Iteration 7: log-likelihood is -11196.950208\n",
      "Iteration 8: log-likelihood is -11195.598834\n",
      "Iteration 9: log-likelihood is -11194.560923\n",
      "Iteration 10: log-likelihood is -11193.809382\n",
      "Iteration 11: log-likelihood is -11193.259931\n",
      "Iteration 12: log-likelihood is -11192.838590\n",
      "Iteration 13: log-likelihood is -11192.504004\n",
      "Iteration 14: log-likelihood is -11192.235454\n",
      "Iteration 15: log-likelihood is -11192.019740\n",
      "Iteration 16: log-likelihood is -11191.845614\n",
      "Iteration 17: log-likelihood is -11191.703256\n",
      "Iteration 18: log-likelihood is -11191.584824\n",
      "Iteration 19: log-likelihood is -11191.484495\n",
      "Iteration 20: log-likelihood is -11191.398087\n",
      "Terminate at 20-th iteration:log-likelihood is -11191.398087\n"
     ]
    }
   ],
   "source": [
    "gmm=GaussianMixModel(X,k=2)\n",
    "gmm.initialize_means(np.asmatrix(centroids))\n",
    "gmm.fit()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "heading_collapsed": true,
    "hidden": true,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "#### Part 2:\n",
    "\n",
    "In a separated cell, implement `Purity` and `Rand-Index` criteria in order to compare the performance of mentioned algorithms."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## KMeans "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "print('Purity Of kmeans: ',np.sum(kmeans.predict()==Y)/len(Y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 447,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.special import comb\n",
    "def rand_index_score(clusters, classes):\n",
    "    A = np.c_[(clusters, classes)]\n",
    "    tp = sum(comb(np.bincount(A[A[:, 0] == i, 1]), 2).sum()\n",
    "             for i in set(clusters))\n",
    "    fp = comb(np.bincount(clusters), 2).sum() - tp\n",
    "    fn = comb(np.bincount(classes), 2).sum() - tp\n",
    "    tn = comb(len(A), 2) - tp - fp - fn\n",
    "    return (tp + tn) / (tp + fp + fn + tn)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 448,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "rand index of kmeans 0.626176170038831\n"
     ]
    }
   ],
   "source": [
    "print('rand index of kmeans', rand_index_score(kmeans.predict(),Y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Gaussian Mixture Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 449,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "purity index:  0.3442857142857143\n"
     ]
    }
   ],
   "source": [
    "print('purity index: ', np.sum(gmm.predict() == Y)/len(Y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 450,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "rand index 0.6612957285918659\n"
     ]
    }
   ],
   "source": [
    "print('rand index', rand_index_score(gmm.predict(),Y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "heading_collapsed": true,
    "hidden": true,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "#### Part 3:\n",
    "\n",
    "Use the following cell in order to create new Datasets. Afterwards, try to execute mentioned algorithms on new Dataset and eventually compare the recent results with the help of visualization(there is no problem for using relevant python libraries like `matplotlib`). Consider two clusters for this part."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 496,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "X, Y = make_classification(n_samples=700, n_features=2, n_informative=2, n_redundant=0, n_classes=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 497,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "k=2\n",
    "kmeans=KMeans(k,max_iter=10000,runs=20)\n",
    "centroids,kmeans_items=kmeans.fit(X,Y)\n",
    "\n",
    "color_s =[\"green\",\"blue\",\"navy\",\"maroon\",'orange'] \n",
    "for i in range(k):\n",
    "    plt.scatter(kmeans_items[kmeans_items[:,2]==i,0] , kmeans_items[kmeans_items[:,2]==i,1] \n",
    "                ,s=100, label = \"cluster \"+str(i), color =color_s[i])\n",
    "\n",
    "plt.scatter(centroids[:,0] , centroids[:,1] , s = 300, color = 'red')\n",
    "plt.title('Our clusters')\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 498,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration 1: log-likelihood is -2315.565750\n",
      "Iteration 2: log-likelihood is -2306.061991\n",
      "Iteration 3: log-likelihood is -2300.517351\n",
      "Iteration 4: log-likelihood is -2297.679316\n",
      "Iteration 5: log-likelihood is -2296.523375\n",
      "Iteration 6: log-likelihood is -2296.079572\n",
      "Iteration 7: log-likelihood is -2295.873169\n",
      "Iteration 8: log-likelihood is -2295.745392\n",
      "Iteration 9: log-likelihood is -2295.650630\n",
      "Terminate at 9-th iteration:log-likelihood is -2295.650630\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "gmm=GaussianMixModel(X,k)\n",
    "gmm.initialize_means(np.asmatrix(centroids))\n",
    "gmm.fit();\n",
    "gmm_result = gmm.predict()\n",
    "data=pd.DataFrame(X)\n",
    "data['Predicted'] = gmm_result\n",
    "\n",
    "for i in range(k):\n",
    "    plt.scatter(data[data['Predicted']==i][0], data[data['Predicted']==i][1]\n",
    "                ,s=100, label = \"cluster \"+str(i), color =color_s[i])\n",
    "\n",
    "plt.scatter(np.array(gmm.mean_arr[:,0]).flatten() , np.array(gmm.mean_arr[:,1]).flatten() , s = 300, color = 'red')\n",
    "plt.show();\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 499,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "X, Y = make_moons(n_samples=700, noise=0.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 500,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "k=2\n",
    "kmeans=KMeans(k,max_iter=10000,runs=20)\n",
    "centroids,kmeans_items=kmeans.fit(X,Y)\n",
    "\n",
    "color_s =[\"green\",\"blue\",\"navy\",\"maroon\",'orange'] \n",
    "for i in range(k):\n",
    "    plt.scatter(kmeans_items[kmeans_items[:,2]==i,0] , kmeans_items[kmeans_items[:,2]==i,1] \n",
    "                ,s=100, label = \"cluster \"+str(i), color =color_s[i])\n",
    "\n",
    "plt.scatter(centroids[:,0] , centroids[:,1] , s = 300, color = 'red')\n",
    "plt.title('Our clusters')\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 501,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration 1: log-likelihood is -1398.603461\n",
      "Iteration 2: log-likelihood is -1393.737290\n",
      "Iteration 3: log-likelihood is -1388.745843\n",
      "Iteration 4: log-likelihood is -1380.915371\n",
      "Iteration 5: log-likelihood is -1369.135334\n",
      "Iteration 6: log-likelihood is -1353.728904\n",
      "Iteration 7: log-likelihood is -1338.594814\n",
      "Iteration 8: log-likelihood is -1328.926162\n",
      "Iteration 9: log-likelihood is -1325.052040\n",
      "Iteration 10: log-likelihood is -1323.946423\n",
      "Iteration 11: log-likelihood is -1323.666447\n",
      "Iteration 12: log-likelihood is -1323.588633\n",
      "Terminate at 12-th iteration:log-likelihood is -1323.588633\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "gmm=GaussianMixModel(X,k)\n",
    "gmm.initialize_means(np.asmatrix(centroids))\n",
    "gmm.fit();\n",
    "gmm_result = gmm.predict()\n",
    "data=pd.DataFrame(X)\n",
    "data['Predicted'] = gmm_result\n",
    "\n",
    "for i in range(k):\n",
    "    plt.scatter(data[data['Predicted']==i][0], data[data['Predicted']==i][1]\n",
    "                ,s=100, label = \"cluster \"+str(i), color =color_s[i])\n",
    "\n",
    "plt.scatter(np.array(gmm.mean_arr[:,0]).flatten() , np.array(gmm.mean_arr[:,1]).flatten() , s = 300, color = 'red')\n",
    "plt.show();\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 505,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "X, Y = make_circles(n_samples=700, noise=0.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 506,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "k=2\n",
    "kmeans=KMeans(k,max_iter=10000,runs=20)\n",
    "centroids,kmeans_items=kmeans.fit(X,Y)\n",
    "\n",
    "color_s =[\"green\",\"blue\",\"navy\",\"maroon\",'orange'] \n",
    "for i in range(k):\n",
    "    plt.scatter(kmeans_items[kmeans_items[:,2]==i,0] , kmeans_items[kmeans_items[:,2]==i,1] \n",
    "                ,s=100, label = \"cluster \"+str(i), color =color_s[i])\n",
    "\n",
    "plt.scatter(centroids[:,0] , centroids[:,1] , s = 300, color = 'red')\n",
    "plt.title('Our clusters')\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 507,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration 1: log-likelihood is -1430.499494\n",
      "Iteration 2: log-likelihood is -1420.656967\n",
      "Iteration 3: log-likelihood is -1420.536376\n",
      "Iteration 4: log-likelihood is -1420.405494\n",
      "Iteration 5: log-likelihood is -1420.246694\n",
      "Iteration 6: log-likelihood is -1420.047562\n",
      "Iteration 7: log-likelihood is -1419.792324\n",
      "Iteration 8: log-likelihood is -1419.458444\n",
      "Iteration 9: log-likelihood is -1419.012108\n",
      "Iteration 10: log-likelihood is -1418.400887\n",
      "Iteration 11: log-likelihood is -1417.541077\n",
      "Iteration 12: log-likelihood is -1416.295229\n",
      "Iteration 13: log-likelihood is -1414.432159\n",
      "Iteration 14: log-likelihood is -1411.558106\n",
      "Iteration 15: log-likelihood is -1407.013733\n",
      "Iteration 16: log-likelihood is -1399.794125\n",
      "Iteration 17: log-likelihood is -1388.812963\n",
      "Iteration 18: log-likelihood is -1374.346416\n",
      "Iteration 19: log-likelihood is -1360.407653\n",
      "Iteration 20: log-likelihood is -1352.311886\n",
      "Iteration 21: log-likelihood is -1349.627012\n",
      "Iteration 22: log-likelihood is -1348.909115\n",
      "Iteration 23: log-likelihood is -1348.583644\n",
      "Iteration 24: log-likelihood is -1348.324640\n",
      "Iteration 25: log-likelihood is -1348.085898\n",
      "Iteration 26: log-likelihood is -1347.862059\n",
      "Iteration 27: log-likelihood is -1347.652813\n",
      "Iteration 28: log-likelihood is -1347.458349\n",
      "Iteration 29: log-likelihood is -1347.278751\n",
      "Iteration 30: log-likelihood is -1347.113916\n",
      "Iteration 31: log-likelihood is -1346.963547\n",
      "Iteration 32: log-likelihood is -1346.827163\n",
      "Iteration 33: log-likelihood is -1346.704131\n",
      "Iteration 34: log-likelihood is -1346.593698\n",
      "Iteration 35: log-likelihood is -1346.495023\n",
      "Terminate at 35-th iteration:log-likelihood is -1346.495023\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "gmm=GaussianMixModel(X,k)\n",
    "gmm.initialize_means(np.asmatrix(centroids))\n",
    "gmm.fit();\n",
    "gmm_result = gmm.predict()\n",
    "data=pd.DataFrame(X)\n",
    "data['Predicted'] = gmm_result\n",
    "\n",
    "for i in range(k):\n",
    "    plt.scatter(data[data['Predicted']==i][0], data[data['Predicted']==i][1]\n",
    "                ,s=100, label = \"cluster \"+str(i), color =color_s[i])\n",
    "\n",
    "plt.scatter(np.array(gmm.mean_arr[:,0]).flatten() , np.array(gmm.mean_arr[:,1]).flatten() , s = 300, color = 'red')\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "heading_collapsed": true,
    "hidden": true,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "### Reinforcement Learning:\n",
    "\n",
    "At the bellow cell, besides the required libraries have been imported, feel free for changing the num_states variable with your desired number."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-06-10T16:26:26.673884Z",
     "start_time": "2021-06-10T16:26:26.589336Z"
    },
    "hidden": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import random\n",
    "import gym"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "env = gym.make(\"MountainCar-v0\")\n",
    "num_actions = 3\n",
    "num_states = 50\n",
    "\n",
    "# first I should note that first one is position and second one is velocity! \n",
    "# so each state should be recognized using two discretized states\n",
    "q_table = np.zeros(shape=(num_states,num_states, num_actions))\n",
    "\n",
    "# You may change the inputs of any function as you desire.\n",
    "SPACE_LOW = env.observation_space.low\n",
    "SPACE_HIGH = env.observation_space.high\n",
    "DISCOUNT_FACTOR = 0.95\n",
    "EXPLORATION = 0.15\n",
    "\n",
    "EPISODES = 100000\n",
    "STEP_COUNT_MAX = 20000\n",
    "DISPLAY=False"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "heading_collapsed": true,
    "hidden": true,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "#### Part 1:\n",
    "\n",
    "Next cell wants you supplement two functions. First for transforming the continuous space into discrete one (in order to make using q_table feasible), second for updating q_values based on the last action done by agent."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "def discretize_state():\n",
    "    return np.abs(SPACE_HIGH-SPACE_LOW)/num_states\n",
    "\n",
    "def env_state_to_Q_state(state):\n",
    "    return np.round((state - SPACE_LOW)/discretize_state()).astype(int)\n",
    "\n",
    "#p is position , v is velocity, p_ is position_new, v_ is velocity_new\n",
    "def update_q(p, v, p_, v_, action, eta, reward):\n",
    "    if np.random.uniform(0,1) < EXPLORATION:\n",
    "        action_after = np.random.choice(env.action_space.n)\n",
    "    else:\n",
    "        action_after = np.argmax(q_table[p_][v_])\n",
    "    q_table[p][v][action] = q_table[p][v][action] + eta * (reward + DISCOUNT_FACTOR *  q_table[p_][v_][action_after] - q_table[p][v][action])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "heading_collapsed": true,
    "hidden": true,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "#### Part 2:\n",
    "\n",
    "At the following cell, the ends of two functions are getting current action based on the policy and defining the training process respectively."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "# You may change the inputs of any function as you desire.\n",
    "def get_action():\n",
    "    global EXPLORATION\n",
    "    sum_reward_every_thousand = 0\n",
    "    eta = 0.1\n",
    "    for episode in range(EPISODES):\n",
    "        state = env.reset()\n",
    "        sum_reward = 0\n",
    "        \n",
    "        if episode < 30000:\n",
    "            EXPLORATION = 0.15\n",
    "            eta = 0.1\n",
    "        else:\n",
    "            EXPLORATION = (0.15)* (0.99)**((episode-30000)//100)\n",
    "            eta = (0.1) * (0.99)**((episode-30000)//10000)\n",
    "\n",
    "\n",
    "        for step in range(STEP_COUNT_MAX):\n",
    "\n",
    "            if episode % 1000 == 1 and DISPLAY:\n",
    "                env.render()\n",
    "\n",
    "            p, v = env_state_to_Q_state(state)\n",
    "            if np.random.uniform(0, 1) < EXPLORATION:\n",
    "                action = np.random.choice(env.action_space.n) \n",
    "            else:\n",
    "                action = np.argmax(q_table[p][v])\n",
    "            state, reward, done, _ = env.step(action)\n",
    "            sum_reward += reward\n",
    "\n",
    "            p_, v_ = env_state_to_Q_state(state)\n",
    "            update_q(p,v,p_, v_, action, eta, reward)\n",
    "\n",
    "            if done:\n",
    "                break\n",
    "        \n",
    "        sum_reward_every_thousand+= sum_reward\n",
    "\n",
    "        if episode % 1000 == 1:\n",
    "            print(f'Episode: {episode}, Total Reward: {sum_reward}, Mean Reward for previous thousand: {sum_reward_every_thousand/1000}')\n",
    "            sum_reward_every_thousand=0\n",
    "        \n",
    "        \n",
    "\n",
    "def q_learning():\n",
    "    return np.argmax(q_table, axis=2) \n",
    "\n",
    "\n",
    "def save_policy():\n",
    "    np.save('policy.npy', q_learning())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Episode: 1, Total Reward: -179.0, Mean Reward for previous thousand: -0.301\n",
      "Episode: 1001, Total Reward: -193.0, Mean Reward for previous thousand: -157.109\n",
      "Episode: 2001, Total Reward: -115.0, Mean Reward for previous thousand: -152.583\n",
      "Episode: 3001, Total Reward: -117.0, Mean Reward for previous thousand: -143.079\n",
      "Episode: 4001, Total Reward: -149.0, Mean Reward for previous thousand: -166.126\n",
      "Episode: 5001, Total Reward: -115.0, Mean Reward for previous thousand: -160.521\n",
      "Episode: 6001, Total Reward: -159.0, Mean Reward for previous thousand: -146.022\n",
      "Episode: 7001, Total Reward: -150.0, Mean Reward for previous thousand: -145.918\n",
      "Episode: 8001, Total Reward: -126.0, Mean Reward for previous thousand: -146.489\n",
      "Episode: 9001, Total Reward: -146.0, Mean Reward for previous thousand: -144.533\n",
      "Episode: 10001, Total Reward: -158.0, Mean Reward for previous thousand: -149.24\n",
      "Episode: 11001, Total Reward: -147.0, Mean Reward for previous thousand: -145.605\n",
      "Episode: 12001, Total Reward: -144.0, Mean Reward for previous thousand: -151.54\n",
      "Episode: 13001, Total Reward: -150.0, Mean Reward for previous thousand: -143.567\n",
      "Episode: 14001, Total Reward: -113.0, Mean Reward for previous thousand: -147.717\n",
      "Episode: 15001, Total Reward: -145.0, Mean Reward for previous thousand: -144.082\n",
      "Episode: 16001, Total Reward: -164.0, Mean Reward for previous thousand: -149.133\n",
      "Episode: 17001, Total Reward: -140.0, Mean Reward for previous thousand: -141.656\n",
      "Episode: 18001, Total Reward: -141.0, Mean Reward for previous thousand: -144.041\n",
      "Episode: 19001, Total Reward: -145.0, Mean Reward for previous thousand: -143.146\n",
      "Episode: 20001, Total Reward: -143.0, Mean Reward for previous thousand: -144.561\n",
      "Episode: 21001, Total Reward: -146.0, Mean Reward for previous thousand: -154.918\n",
      "Episode: 22001, Total Reward: -118.0, Mean Reward for previous thousand: -146.952\n",
      "Episode: 23001, Total Reward: -164.0, Mean Reward for previous thousand: -143.887\n",
      "Episode: 24001, Total Reward: -167.0, Mean Reward for previous thousand: -144.984\n",
      "Episode: 25001, Total Reward: -191.0, Mean Reward for previous thousand: -139.732\n",
      "Episode: 26001, Total Reward: -200.0, Mean Reward for previous thousand: -150.19\n",
      "Episode: 27001, Total Reward: -135.0, Mean Reward for previous thousand: -148.45\n",
      "Episode: 28001, Total Reward: -133.0, Mean Reward for previous thousand: -147.619\n",
      "Episode: 29001, Total Reward: -118.0, Mean Reward for previous thousand: -145.583\n",
      "Episode: 30001, Total Reward: -156.0, Mean Reward for previous thousand: -144.799\n",
      "Episode: 31001, Total Reward: -122.0, Mean Reward for previous thousand: -156.688\n",
      "Episode: 32001, Total Reward: -92.0, Mean Reward for previous thousand: -141.966\n",
      "Episode: 33001, Total Reward: -115.0, Mean Reward for previous thousand: -138.183\n",
      "Episode: 34001, Total Reward: -143.0, Mean Reward for previous thousand: -136.637\n",
      "Episode: 35001, Total Reward: -155.0, Mean Reward for previous thousand: -134.013\n",
      "Episode: 36001, Total Reward: -150.0, Mean Reward for previous thousand: -135.702\n",
      "Episode: 37001, Total Reward: -155.0, Mean Reward for previous thousand: -136.64\n",
      "Episode: 38001, Total Reward: -110.0, Mean Reward for previous thousand: -134.927\n",
      "Episode: 39001, Total Reward: -170.0, Mean Reward for previous thousand: -124.576\n",
      "Episode: 40001, Total Reward: -94.0, Mean Reward for previous thousand: -123.188\n",
      "Episode: 41001, Total Reward: -151.0, Mean Reward for previous thousand: -127.61\n",
      "Episode: 42001, Total Reward: -157.0, Mean Reward for previous thousand: -129.317\n",
      "Episode: 43001, Total Reward: -166.0, Mean Reward for previous thousand: -129.223\n",
      "Episode: 44001, Total Reward: -150.0, Mean Reward for previous thousand: -130.183\n",
      "Episode: 45001, Total Reward: -157.0, Mean Reward for previous thousand: -128.477\n",
      "Episode: 46001, Total Reward: -169.0, Mean Reward for previous thousand: -130.575\n",
      "Episode: 47001, Total Reward: -141.0, Mean Reward for previous thousand: -136.959\n",
      "Episode: 48001, Total Reward: -110.0, Mean Reward for previous thousand: -133.705\n",
      "Episode: 49001, Total Reward: -111.0, Mean Reward for previous thousand: -132.777\n",
      "Episode: 50001, Total Reward: -115.0, Mean Reward for previous thousand: -126.226\n",
      "Episode: 51001, Total Reward: -108.0, Mean Reward for previous thousand: -126.466\n",
      "Episode: 52001, Total Reward: -105.0, Mean Reward for previous thousand: -122.987\n",
      "Episode: 53001, Total Reward: -143.0, Mean Reward for previous thousand: -125.58\n",
      "Episode: 54001, Total Reward: -92.0, Mean Reward for previous thousand: -121.866\n",
      "Episode: 55001, Total Reward: -114.0, Mean Reward for previous thousand: -120.685\n",
      "Episode: 56001, Total Reward: -161.0, Mean Reward for previous thousand: -122.66\n",
      "Episode: 57001, Total Reward: -113.0, Mean Reward for previous thousand: -120.863\n",
      "Episode: 58001, Total Reward: -106.0, Mean Reward for previous thousand: -121.389\n",
      "Episode: 59001, Total Reward: -155.0, Mean Reward for previous thousand: -120.685\n",
      "Episode: 60001, Total Reward: -111.0, Mean Reward for previous thousand: -125.054\n",
      "Episode: 61001, Total Reward: -91.0, Mean Reward for previous thousand: -123.145\n",
      "Episode: 62001, Total Reward: -89.0, Mean Reward for previous thousand: -123.642\n",
      "Episode: 63001, Total Reward: -109.0, Mean Reward for previous thousand: -121.458\n",
      "Episode: 64001, Total Reward: -149.0, Mean Reward for previous thousand: -121.11\n",
      "Episode: 65001, Total Reward: -109.0, Mean Reward for previous thousand: -118.842\n",
      "Episode: 66001, Total Reward: -105.0, Mean Reward for previous thousand: -117.851\n",
      "Episode: 67001, Total Reward: -93.0, Mean Reward for previous thousand: -118.363\n",
      "Episode: 68001, Total Reward: -108.0, Mean Reward for previous thousand: -118.588\n",
      "Episode: 69001, Total Reward: -155.0, Mean Reward for previous thousand: -117.849\n",
      "Episode: 70001, Total Reward: -103.0, Mean Reward for previous thousand: -117.886\n",
      "Episode: 71001, Total Reward: -154.0, Mean Reward for previous thousand: -119.152\n",
      "Episode: 72001, Total Reward: -88.0, Mean Reward for previous thousand: -119.221\n",
      "Episode: 73001, Total Reward: -105.0, Mean Reward for previous thousand: -118.423\n",
      "Episode: 74001, Total Reward: -141.0, Mean Reward for previous thousand: -118.104\n",
      "Episode: 75001, Total Reward: -84.0, Mean Reward for previous thousand: -116.182\n",
      "Episode: 76001, Total Reward: -86.0, Mean Reward for previous thousand: -114.815\n",
      "Episode: 77001, Total Reward: -171.0, Mean Reward for previous thousand: -116.111\n",
      "Episode: 78001, Total Reward: -154.0, Mean Reward for previous thousand: -116.999\n",
      "Episode: 79001, Total Reward: -89.0, Mean Reward for previous thousand: -115.477\n",
      "Episode: 80001, Total Reward: -104.0, Mean Reward for previous thousand: -116.467\n",
      "Episode: 81001, Total Reward: -109.0, Mean Reward for previous thousand: -115.918\n",
      "Episode: 82001, Total Reward: -90.0, Mean Reward for previous thousand: -115.687\n",
      "Episode: 83001, Total Reward: -106.0, Mean Reward for previous thousand: -116.255\n",
      "Episode: 84001, Total Reward: -89.0, Mean Reward for previous thousand: -116.218\n",
      "Episode: 85001, Total Reward: -90.0, Mean Reward for previous thousand: -115.675\n",
      "Episode: 86001, Total Reward: -159.0, Mean Reward for previous thousand: -114.176\n",
      "Episode: 87001, Total Reward: -105.0, Mean Reward for previous thousand: -115.347\n",
      "Episode: 88001, Total Reward: -84.0, Mean Reward for previous thousand: -115.736\n",
      "Episode: 89001, Total Reward: -145.0, Mean Reward for previous thousand: -114.92\n",
      "Episode: 90001, Total Reward: -108.0, Mean Reward for previous thousand: -114.142\n",
      "Episode: 91001, Total Reward: -108.0, Mean Reward for previous thousand: -115.576\n",
      "Episode: 92001, Total Reward: -105.0, Mean Reward for previous thousand: -115.641\n",
      "Episode: 93001, Total Reward: -108.0, Mean Reward for previous thousand: -115.379\n",
      "Episode: 94001, Total Reward: -105.0, Mean Reward for previous thousand: -115.35\n",
      "Episode: 95001, Total Reward: -153.0, Mean Reward for previous thousand: -114.946\n",
      "Episode: 96001, Total Reward: -106.0, Mean Reward for previous thousand: -114.093\n",
      "Episode: 97001, Total Reward: -106.0, Mean Reward for previous thousand: -114.282\n",
      "Episode: 98001, Total Reward: -89.0, Mean Reward for previous thousand: -114.929\n",
      "Episode: 99001, Total Reward: -104.0, Mean Reward for previous thousand: -115.684\n"
     ]
    }
   ],
   "source": [
    "get_action()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "save_policy()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "heading_collapsed": true,
    "hidden": true,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "#### Part 3:\n",
    "\n",
    "Ultimately, the score function examines the average performance of Agent (after nearly 1000 times) based on previous implementations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "hidden": true,
    "tags": [
     "outputPrepend"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "*****Episode 306\n",
      "Score:-150\n",
      "******Episode 307\n",
      "Score:-156\n",
      "******Episode 308\n",
      "Score:-111\n",
      "******Episode 309\n",
      "Score:-91\n",
      "******Episode 310\n",
      "Score:-84\n",
      "******Episode 311\n",
      "Score:-109\n",
      "******Episode 312\n",
      "Score:-158\n",
      "******Episode 313\n",
      "Score:-104\n",
      "******Episode 314\n",
      "Score:-85\n",
      "******Episode 315\n",
      "Score:-108\n",
      "******Episode 316\n",
      "Score:-147\n",
      "******Episode 317\n",
      "Score:-104\n",
      "******Episode 318\n",
      "Score:-105\n",
      "******Episode 319\n",
      "Score:-90\n",
      "******Episode 320\n",
      "Score:-104\n",
      "******Episode 321\n",
      "Score:-106\n",
      "******Episode 322\n",
      "Score:-147\n",
      "******Episode 323\n",
      "Score:-104\n",
      "******Episode 324\n",
      "Score:-85\n",
      "******Episode 325\n",
      "Score:-104\n",
      "******Episode 326\n",
      "Score:-149\n",
      "******Episode 327\n",
      "Score:-90\n",
      "******Episode 328\n",
      "Score:-109\n",
      "******Episode 329\n",
      "Score:-85\n",
      "******Episode 330\n",
      "Score:-90\n",
      "******Episode 331\n",
      "Score:-93\n",
      "******Episode 332\n",
      "Score:-106\n",
      "******Episode 333\n",
      "Score:-156\n",
      "******Episode 334\n",
      "Score:-88\n",
      "******Episode 335\n",
      "Score:-84\n",
      "******Episode 336\n",
      "Score:-106\n",
      "******Episode 337\n",
      "Score:-95\n",
      "******Episode 338\n",
      "Score:-85\n",
      "******Episode 339\n",
      "Score:-125\n",
      "******Episode 340\n",
      "Score:-106\n",
      "******Episode 341\n",
      "Score:-154\n",
      "******Episode 342\n",
      "Score:-104\n",
      "******Episode 343\n",
      "Score:-106\n",
      "******Episode 344\n",
      "Score:-150\n",
      "******Episode 345\n",
      "Score:-89\n",
      "******Episode 346\n",
      "Score:-110\n",
      "******Episode 347\n",
      "Score:-109\n",
      "******Episode 348\n",
      "Score:-88\n",
      "******Episode 349\n",
      "Score:-157\n",
      "******Episode 350\n",
      "Score:-105\n",
      "******Episode 351\n",
      "Score:-110\n",
      "******Episode 352\n",
      "Score:-109\n",
      "******Episode 353\n",
      "Score:-108\n",
      "******Episode 354\n",
      "Score:-173\n",
      "******Episode 355\n",
      "Score:-174\n",
      "******Episode 356\n",
      "Score:-150\n",
      "******Episode 357\n",
      "Score:-96\n",
      "******Episode 358\n",
      "Score:-84\n",
      "******Episode 359\n",
      "Score:-157\n",
      "******Episode 360\n",
      "Score:-89\n",
      "******Episode 361\n",
      "Score:-147\n",
      "******Episode 362\n",
      "Score:-106\n",
      "******Episode 363\n",
      "Score:-105\n",
      "******Episode 364\n",
      "Score:-110\n",
      "******Episode 365\n",
      "Score:-105\n",
      "******Episode 366\n",
      "Score:-105\n",
      "******Episode 367\n",
      "Score:-104\n",
      "******Episode 368\n",
      "Score:-105\n",
      "******Episode 369\n",
      "Score:-106\n",
      "******Episode 370\n",
      "Score:-105\n",
      "******Episode 371\n",
      "Score:-160\n",
      "******Episode 372\n",
      "Score:-106\n",
      "******Episode 373\n",
      "Score:-105\n",
      "******Episode 374\n",
      "Score:-106\n",
      "******Episode 375\n",
      "Score:-106\n",
      "******Episode 376\n",
      "Score:-104\n",
      "******Episode 377\n",
      "Score:-107\n",
      "******Episode 378\n",
      "Score:-106\n",
      "******Episode 379\n",
      "Score:-86\n",
      "******Episode 380\n",
      "Score:-157\n",
      "******Episode 381\n",
      "Score:-110\n",
      "******Episode 382\n",
      "Score:-86\n",
      "******Episode 383\n",
      "Score:-104\n",
      "******Episode 384\n",
      "Score:-101\n",
      "******Episode 385\n",
      "Score:-106\n",
      "******Episode 386\n",
      "Score:-158\n",
      "******Episode 387\n",
      "Score:-101\n",
      "******Episode 388\n",
      "Score:-84\n",
      "******Episode 389\n",
      "Score:-109\n",
      "******Episode 390\n",
      "Score:-111\n",
      "******Episode 391\n",
      "Score:-104\n",
      "******Episode 392\n",
      "Score:-88\n",
      "******Episode 393\n",
      "Score:-105\n",
      "******Episode 394\n",
      "Score:-106\n",
      "******Episode 395\n",
      "Score:-107\n",
      "******Episode 396\n",
      "Score:-157\n",
      "******Episode 397\n",
      "Score:-165\n",
      "******Episode 398\n",
      "Score:-84\n",
      "******Episode 399\n",
      "Score:-106\n",
      "******Episode 400\n",
      "Score:-110\n",
      "******Episode 401\n",
      "Score:-105\n",
      "******Episode 402\n",
      "Score:-156\n",
      "******Episode 403\n",
      "Score:-98\n",
      "******Episode 404\n",
      "Score:-85\n",
      "******Episode 405\n",
      "Score:-150\n",
      "******Episode 406\n",
      "Score:-106\n",
      "******Episode 407\n",
      "Score:-105\n",
      "******Episode 408\n",
      "Score:-109\n",
      "******Episode 409\n",
      "Score:-104\n",
      "******Episode 410\n",
      "Score:-95\n",
      "******Episode 411\n",
      "Score:-103\n",
      "******Episode 412\n",
      "Score:-102\n",
      "******Episode 413\n",
      "Score:-110\n",
      "******Episode 414\n",
      "Score:-106\n",
      "******Episode 415\n",
      "Score:-106\n",
      "******Episode 416\n",
      "Score:-109\n",
      "******Episode 417\n",
      "Score:-150\n",
      "******Episode 418\n",
      "Score:-106\n",
      "******Episode 419\n",
      "Score:-109\n",
      "******Episode 420\n",
      "Score:-150\n",
      "******Episode 421\n",
      "Score:-161\n",
      "******Episode 422\n",
      "Score:-106\n",
      "******Episode 423\n",
      "Score:-106\n",
      "******Episode 424\n",
      "Score:-156\n",
      "******Episode 425\n",
      "Score:-106\n",
      "******Episode 426\n",
      "Score:-150\n",
      "******Episode 427\n",
      "Score:-150\n",
      "******Episode 428\n",
      "Score:-159\n",
      "******Episode 429\n",
      "Score:-109\n",
      "******Episode 430\n",
      "Score:-84\n",
      "******Episode 431\n",
      "Score:-90\n",
      "******Episode 432\n",
      "Score:-159\n",
      "******Episode 433\n",
      "Score:-105\n",
      "******Episode 434\n",
      "Score:-150\n",
      "******Episode 435\n",
      "Score:-86\n",
      "******Episode 436\n",
      "Score:-151\n",
      "******Episode 437\n",
      "Score:-154\n",
      "******Episode 438\n",
      "Score:-105\n",
      "******Episode 439\n",
      "Score:-106\n",
      "******Episode 440\n",
      "Score:-108\n",
      "******Episode 441\n",
      "Score:-147\n",
      "******Episode 442\n",
      "Score:-106\n",
      "******Episode 443\n",
      "Score:-154\n",
      "******Episode 444\n",
      "Score:-105\n",
      "******Episode 445\n",
      "Score:-105\n",
      "******Episode 446\n",
      "Score:-154\n",
      "******Episode 447\n",
      "Score:-96\n",
      "******Episode 448\n",
      "Score:-147\n",
      "******Episode 449\n",
      "Score:-150\n",
      "******Episode 450\n",
      "Score:-144\n",
      "******Episode 451\n",
      "Score:-99\n",
      "******Episode 452\n",
      "Score:-159\n",
      "******Episode 453\n",
      "Score:-106\n",
      "******Episode 454\n",
      "Score:-175\n",
      "******Episode 455\n",
      "Score:-109\n",
      "******Episode 456\n",
      "Score:-90\n",
      "******Episode 457\n",
      "Score:-86\n",
      "******Episode 458\n",
      "Score:-110\n",
      "******Episode 459\n",
      "Score:-98\n",
      "******Episode 460\n",
      "Score:-150\n",
      "******Episode 461\n",
      "Score:-110\n",
      "******Episode 462\n",
      "Score:-131\n",
      "******Episode 463\n",
      "Score:-105\n",
      "******Episode 464\n",
      "Score:-151\n",
      "******Episode 465\n",
      "Score:-159\n",
      "******Episode 466\n",
      "Score:-99\n",
      "******Episode 467\n",
      "Score:-105\n",
      "******Episode 468\n",
      "Score:-150\n",
      "******Episode 469\n",
      "Score:-158\n",
      "******Episode 470\n",
      "Score:-104\n",
      "******Episode 471\n",
      "Score:-113\n",
      "******Episode 472\n",
      "Score:-93\n",
      "******Episode 473\n",
      "Score:-90\n",
      "******Episode 474\n",
      "Score:-104\n",
      "******Episode 475\n",
      "Score:-109\n",
      "******Episode 476\n",
      "Score:-84\n",
      "******Episode 477\n",
      "Score:-147\n",
      "******Episode 478\n",
      "Score:-89\n",
      "******Episode 479\n",
      "Score:-154\n",
      "******Episode 480\n",
      "Score:-104\n",
      "******Episode 481\n",
      "Score:-103\n",
      "******Episode 482\n",
      "Score:-158\n",
      "******Episode 483\n",
      "Score:-156\n",
      "******Episode 484\n",
      "Score:-104\n",
      "******Episode 485\n",
      "Score:-154\n",
      "******Episode 486\n",
      "Score:-110\n",
      "******Episode 487\n",
      "Score:-105\n",
      "******Episode 488\n",
      "Score:-106\n",
      "******Episode 489\n",
      "Score:-106\n",
      "******Episode 490\n",
      "Score:-151\n",
      "******Episode 491\n",
      "Score:-145\n",
      "******Episode 492\n",
      "Score:-90\n",
      "******Episode 493\n",
      "Score:-84\n",
      "******Episode 494\n",
      "Score:-91\n",
      "******Episode 495\n",
      "Score:-156\n",
      "******Episode 496\n",
      "Score:-109\n",
      "******Episode 497\n",
      "Score:-109\n",
      "******Episode 498\n",
      "Score:-89\n",
      "******Episode 499\n",
      "Score:-165\n",
      "******Episode 500\n",
      "Score:-109\n",
      "******Episode 501\n",
      "Score:-109\n",
      "******Episode 502\n",
      "Score:-104\n",
      "******Episode 503\n",
      "Score:-150\n",
      "******Episode 504\n",
      "Score:-106\n",
      "******Episode 505\n",
      "Score:-110\n",
      "******Episode 506\n",
      "Score:-106\n",
      "******Episode 507\n",
      "Score:-107\n",
      "******Episode 508\n",
      "Score:-106\n",
      "******Episode 509\n",
      "Score:-159\n",
      "******Episode 510\n",
      "Score:-152\n",
      "******Episode 511\n",
      "Score:-178\n",
      "******Episode 512\n",
      "Score:-89\n",
      "******Episode 513\n",
      "Score:-105\n",
      "******Episode 514\n",
      "Score:-110\n",
      "******Episode 515\n",
      "Score:-161\n",
      "******Episode 516\n",
      "Score:-106\n",
      "******Episode 517\n",
      "Score:-161\n",
      "******Episode 518\n",
      "Score:-109\n",
      "******Episode 519\n",
      "Score:-159\n",
      "******Episode 520\n",
      "Score:-105\n",
      "******Episode 521\n",
      "Score:-90\n",
      "******Episode 522\n",
      "Score:-90\n",
      "******Episode 523\n",
      "Score:-84\n",
      "******Episode 524\n",
      "Score:-147\n",
      "******Episode 525\n",
      "Score:-172\n",
      "******Episode 526\n",
      "Score:-93\n",
      "******Episode 527\n",
      "Score:-158\n",
      "******Episode 528\n",
      "Score:-106\n",
      "******Episode 529\n",
      "Score:-106\n",
      "******Episode 530\n",
      "Score:-105\n",
      "******Episode 531\n",
      "Score:-86\n",
      "******Episode 532\n",
      "Score:-88\n",
      "******Episode 533\n",
      "Score:-158\n",
      "******Episode 534\n",
      "Score:-149\n",
      "******Episode 535\n",
      "Score:-106\n",
      "******Episode 536\n",
      "Score:-89\n",
      "******Episode 537\n",
      "Score:-109\n",
      "******Episode 538\n",
      "Score:-105\n",
      "******Episode 539\n",
      "Score:-104\n",
      "******Episode 540\n",
      "Score:-105\n",
      "******Episode 541\n",
      "Score:-86\n",
      "******Episode 542\n",
      "Score:-105\n",
      "******Episode 543\n",
      "Score:-151\n",
      "******Episode 544\n",
      "Score:-88\n",
      "******Episode 545\n",
      "Score:-118\n",
      "******Episode 546\n",
      "Score:-106\n",
      "******Episode 547\n",
      "Score:-106\n",
      "******Episode 548\n",
      "Score:-156\n",
      "******Episode 549\n",
      "Score:-151\n",
      "******Episode 550\n",
      "Score:-107\n",
      "******Episode 551\n",
      "Score:-160\n",
      "******Episode 552\n",
      "Score:-106\n",
      "******Episode 553\n",
      "Score:-105\n",
      "******Episode 554\n",
      "Score:-150\n",
      "******Episode 555\n",
      "Score:-89\n",
      "******Episode 556\n",
      "Score:-105\n",
      "******Episode 557\n",
      "Score:-106\n",
      "******Episode 558\n",
      "Score:-86\n",
      "******Episode 559\n",
      "Score:-110\n",
      "******Episode 560\n",
      "Score:-101\n",
      "******Episode 561\n",
      "Score:-109\n",
      "******Episode 562\n",
      "Score:-108\n",
      "******Episode 563\n",
      "Score:-109\n",
      "******Episode 564\n",
      "Score:-106\n",
      "******Episode 565\n",
      "Score:-154\n",
      "******Episode 566\n",
      "Score:-88\n",
      "******Episode 567\n",
      "Score:-110\n",
      "******Episode 568\n",
      "Score:-106\n",
      "******Episode 569\n",
      "Score:-151\n",
      "******Episode 570\n",
      "Score:-155\n",
      "******Episode 571\n",
      "Score:-165\n",
      "******Episode 572\n",
      "Score:-150\n",
      "******Episode 573\n",
      "Score:-115\n",
      "******Episode 574\n",
      "Score:-102\n",
      "******Episode 575\n",
      "Score:-104\n",
      "******Episode 576\n",
      "Score:-104\n",
      "******Episode 577\n",
      "Score:-105\n",
      "******Episode 578\n",
      "Score:-150\n",
      "******Episode 579\n",
      "Score:-109\n",
      "******Episode 580\n",
      "Score:-86\n",
      "******Episode 581\n",
      "Score:-104\n",
      "******Episode 582\n",
      "Score:-107\n",
      "******Episode 583\n",
      "Score:-150\n",
      "******Episode 584\n",
      "Score:-156\n",
      "******Episode 585\n",
      "Score:-110\n",
      "******Episode 586\n",
      "Score:-158\n",
      "******Episode 587\n",
      "Score:-108\n",
      "******Episode 588\n",
      "Score:-109\n",
      "******Episode 589\n",
      "Score:-127\n",
      "******Episode 590\n",
      "Score:-109\n",
      "******Episode 591\n",
      "Score:-108\n",
      "******Episode 592\n",
      "Score:-110\n",
      "******Episode 593\n",
      "Score:-104\n",
      "******Episode 594\n",
      "Score:-104\n",
      "******Episode 595\n",
      "Score:-102\n",
      "******Episode 596\n",
      "Score:-106\n",
      "******Episode 597\n",
      "Score:-147\n",
      "******Episode 598\n",
      "Score:-90\n",
      "******Episode 599\n",
      "Score:-106\n",
      "******Episode 600\n",
      "Score:-95\n",
      "******Episode 601\n",
      "Score:-107\n",
      "******Episode 602\n",
      "Score:-150\n",
      "******Episode 603\n",
      "Score:-175\n",
      "******Episode 604\n",
      "Score:-152\n",
      "******Episode 605\n",
      "Score:-88\n",
      "******Episode 606\n",
      "Score:-159\n",
      "******Episode 607\n",
      "Score:-151\n",
      "******Episode 608\n",
      "Score:-107\n",
      "******Episode 609\n",
      "Score:-96\n",
      "******Episode 610\n",
      "Score:-89\n",
      "******Episode 611\n",
      "Score:-110\n",
      "******Episode 612\n",
      "Score:-178\n",
      "******Episode 613\n",
      "Score:-86\n",
      "******Episode 614\n",
      "Score:-106\n",
      "******Episode 615\n",
      "Score:-105\n",
      "******Episode 616\n",
      "Score:-91\n",
      "******Episode 617\n",
      "Score:-150\n",
      "******Episode 618\n",
      "Score:-160\n",
      "******Episode 619\n",
      "Score:-107\n",
      "******Episode 620\n",
      "Score:-149\n",
      "******Episode 621\n",
      "Score:-174\n",
      "******Episode 622\n",
      "Score:-105\n",
      "******Episode 623\n",
      "Score:-109\n",
      "******Episode 624\n",
      "Score:-109\n",
      "******Episode 625\n",
      "Score:-106\n",
      "******Episode 626\n",
      "Score:-106\n",
      "******Episode 627\n",
      "Score:-108\n",
      "******Episode 628\n",
      "Score:-111\n",
      "******Episode 629\n",
      "Score:-144\n",
      "******Episode 630\n",
      "Score:-109\n",
      "******Episode 631\n",
      "Score:-90\n",
      "******Episode 632\n",
      "Score:-109\n",
      "******Episode 633\n",
      "Score:-110\n",
      "******Episode 634\n",
      "Score:-88\n",
      "******Episode 635\n",
      "Score:-113\n",
      "******Episode 636\n",
      "Score:-91\n",
      "******Episode 637\n",
      "Score:-174\n",
      "******Episode 638\n",
      "Score:-150\n",
      "******Episode 639\n",
      "Score:-150\n",
      "******Episode 640\n",
      "Score:-109\n",
      "******Episode 641\n",
      "Score:-106\n",
      "******Episode 642\n",
      "Score:-88\n",
      "******Episode 643\n",
      "Score:-150\n",
      "******Episode 644\n",
      "Score:-109\n",
      "******Episode 645\n",
      "Score:-109\n",
      "******Episode 646\n",
      "Score:-104\n",
      "******Episode 647\n",
      "Score:-104\n",
      "******Episode 648\n",
      "Score:-95\n",
      "******Episode 649\n",
      "Score:-102\n",
      "******Episode 650\n",
      "Score:-106\n",
      "******Episode 651\n",
      "Score:-89\n",
      "******Episode 652\n",
      "Score:-104\n",
      "******Episode 653\n",
      "Score:-158\n",
      "******Episode 654\n",
      "Score:-145\n",
      "******Episode 655\n",
      "Score:-106\n",
      "******Episode 656\n",
      "Score:-88\n",
      "******Episode 657\n",
      "Score:-106\n",
      "******Episode 658\n",
      "Score:-86\n",
      "******Episode 659\n",
      "Score:-109\n",
      "******Episode 660\n",
      "Score:-150\n",
      "******Episode 661\n",
      "Score:-113\n",
      "******Episode 662\n",
      "Score:-105\n",
      "******Episode 663\n",
      "Score:-104\n",
      "******Episode 664\n",
      "Score:-109\n",
      "******Episode 665\n",
      "Score:-84\n",
      "******Episode 666\n",
      "Score:-106\n",
      "******Episode 667\n",
      "Score:-105\n",
      "******Episode 668\n",
      "Score:-90\n",
      "******Episode 669\n",
      "Score:-112\n",
      "******Episode 670\n",
      "Score:-109\n",
      "******Episode 671\n",
      "Score:-158\n",
      "******Episode 672\n",
      "Score:-158\n",
      "******Episode 673\n",
      "Score:-90\n",
      "******Episode 674\n",
      "Score:-106\n",
      "******Episode 675\n",
      "Score:-104\n",
      "******Episode 676\n",
      "Score:-106\n",
      "******Episode 677\n",
      "Score:-104\n",
      "******Episode 678\n",
      "Score:-125\n",
      "******Episode 679\n",
      "Score:-108\n",
      "******Episode 680\n",
      "Score:-103\n",
      "******Episode 681\n",
      "Score:-147\n",
      "******Episode 682\n",
      "Score:-93\n",
      "******Episode 683\n",
      "Score:-108\n",
      "******Episode 684\n",
      "Score:-105\n",
      "******Episode 685\n",
      "Score:-106\n",
      "******Episode 686\n",
      "Score:-106\n",
      "******Episode 687\n",
      "Score:-106\n",
      "******Episode 688\n",
      "Score:-91\n",
      "******Episode 689\n",
      "Score:-108\n",
      "******Episode 690\n",
      "Score:-173\n",
      "******Episode 691\n",
      "Score:-86\n",
      "******Episode 692\n",
      "Score:-159\n",
      "******Episode 693\n",
      "Score:-158\n",
      "******Episode 694\n",
      "Score:-106\n",
      "******Episode 695\n",
      "Score:-106\n",
      "******Episode 696\n",
      "Score:-110\n",
      "******Episode 697\n",
      "Score:-106\n",
      "******Episode 698\n",
      "Score:-109\n",
      "******Episode 699\n",
      "Score:-105\n",
      "******Episode 700\n",
      "Score:-106\n",
      "******Episode 701\n",
      "Score:-158\n",
      "******Episode 702\n",
      "Score:-106\n",
      "******Episode 703\n",
      "Score:-109\n",
      "******Episode 704\n",
      "Score:-90\n",
      "******Episode 705\n",
      "Score:-109\n",
      "******Episode 706\n",
      "Score:-106\n",
      "******Episode 707\n",
      "Score:-148\n",
      "******Episode 708\n",
      "Score:-104\n",
      "******Episode 709\n",
      "Score:-173\n",
      "******Episode 710\n",
      "Score:-150\n",
      "******Episode 711\n",
      "Score:-84\n",
      "******Episode 712\n",
      "Score:-115\n",
      "******Episode 713\n",
      "Score:-150\n",
      "******Episode 714\n",
      "Score:-166\n",
      "******Episode 715\n",
      "Score:-106\n",
      "******Episode 716\n",
      "Score:-109\n",
      "******Episode 717\n",
      "Score:-106\n",
      "******Episode 718\n",
      "Score:-147\n",
      "******Episode 719\n",
      "Score:-93\n",
      "******Episode 720\n",
      "Score:-160\n",
      "******Episode 721\n",
      "Score:-109\n",
      "******Episode 722\n",
      "Score:-110\n",
      "******Episode 723\n",
      "Score:-105\n",
      "******Episode 724\n",
      "Score:-90\n",
      "******Episode 725\n",
      "Score:-84\n",
      "******Episode 726\n",
      "Score:-106\n",
      "******Episode 727\n",
      "Score:-107\n",
      "******Episode 728\n",
      "Score:-160\n",
      "******Episode 729\n",
      "Score:-109\n",
      "******Episode 730\n",
      "Score:-109\n",
      "******Episode 731\n",
      "Score:-147\n",
      "******Episode 732\n",
      "Score:-159\n",
      "******Episode 733\n",
      "Score:-106\n",
      "******Episode 734\n",
      "Score:-158\n",
      "******Episode 735\n",
      "Score:-102\n",
      "******Episode 736\n",
      "Score:-106\n",
      "******Episode 737\n",
      "Score:-98\n",
      "******Episode 738\n",
      "Score:-109\n",
      "******Episode 739\n",
      "Score:-85\n",
      "******Episode 740\n",
      "Score:-105\n",
      "******Episode 741\n",
      "Score:-86\n",
      "******Episode 742\n",
      "Score:-86\n",
      "******Episode 743\n",
      "Score:-107\n",
      "******Episode 744\n",
      "Score:-109\n",
      "******Episode 745\n",
      "Score:-93\n",
      "******Episode 746\n",
      "Score:-153\n",
      "******Episode 747\n",
      "Score:-174\n",
      "******Episode 748\n",
      "Score:-89\n",
      "******Episode 749\n",
      "Score:-109\n",
      "******Episode 750\n",
      "Score:-90\n",
      "******Episode 751\n",
      "Score:-88\n",
      "******Episode 752\n",
      "Score:-113\n",
      "******Episode 753\n",
      "Score:-98\n",
      "******Episode 754\n",
      "Score:-105\n",
      "******Episode 755\n",
      "Score:-86\n",
      "******Episode 756\n",
      "Score:-108\n",
      "******Episode 757\n",
      "Score:-160\n",
      "******Episode 758\n",
      "Score:-108\n",
      "******Episode 759\n",
      "Score:-150\n",
      "******Episode 760\n",
      "Score:-105\n",
      "******Episode 761\n",
      "Score:-155\n",
      "******Episode 762\n",
      "Score:-104\n",
      "******Episode 763\n",
      "Score:-104\n",
      "******Episode 764\n",
      "Score:-105\n",
      "******Episode 765\n",
      "Score:-109\n",
      "******Episode 766\n",
      "Score:-106\n",
      "******Episode 767\n",
      "Score:-108\n",
      "******Episode 768\n",
      "Score:-106\n",
      "******Episode 769\n",
      "Score:-104\n",
      "******Episode 770\n",
      "Score:-109\n",
      "******Episode 771\n",
      "Score:-90\n",
      "******Episode 772\n",
      "Score:-147\n",
      "******Episode 773\n",
      "Score:-89\n",
      "******Episode 774\n",
      "Score:-150\n",
      "******Episode 775\n",
      "Score:-89\n",
      "******Episode 776\n",
      "Score:-123\n",
      "******Episode 777\n",
      "Score:-84\n",
      "******Episode 778\n",
      "Score:-104\n",
      "******Episode 779\n",
      "Score:-84\n",
      "******Episode 780\n",
      "Score:-91\n",
      "******Episode 781\n",
      "Score:-89\n",
      "******Episode 782\n",
      "Score:-106\n",
      "******Episode 783\n",
      "Score:-118\n",
      "******Episode 784\n",
      "Score:-109\n",
      "******Episode 785\n",
      "Score:-149\n",
      "******Episode 786\n",
      "Score:-90\n",
      "******Episode 787\n",
      "Score:-108\n",
      "******Episode 788\n",
      "Score:-109\n",
      "******Episode 789\n",
      "Score:-105\n",
      "******Episode 790\n",
      "Score:-156\n",
      "******Episode 791\n",
      "Score:-150\n",
      "******Episode 792\n",
      "Score:-109\n",
      "******Episode 793\n",
      "Score:-116\n",
      "******Episode 794\n",
      "Score:-102\n",
      "******Episode 795\n",
      "Score:-158\n",
      "******Episode 796\n",
      "Score:-91\n",
      "******Episode 797\n",
      "Score:-105\n",
      "******Episode 798\n",
      "Score:-85\n",
      "******Episode 799\n",
      "Score:-109\n",
      "******Episode 800\n",
      "Score:-106\n",
      "******Episode 801\n",
      "Score:-160\n",
      "******Episode 802\n",
      "Score:-110\n",
      "******Episode 803\n",
      "Score:-104\n",
      "******Episode 804\n",
      "Score:-106\n",
      "******Episode 805\n",
      "Score:-89\n",
      "******Episode 806\n",
      "Score:-159\n",
      "******Episode 807\n",
      "Score:-84\n",
      "******Episode 808\n",
      "Score:-85\n",
      "******Episode 809\n",
      "Score:-150\n",
      "******Episode 810\n",
      "Score:-109\n",
      "******Episode 811\n",
      "Score:-104\n",
      "******Episode 812\n",
      "Score:-103\n",
      "******Episode 813\n",
      "Score:-150\n",
      "******Episode 814\n",
      "Score:-86\n",
      "******Episode 815\n",
      "Score:-156\n",
      "******Episode 816\n",
      "Score:-156\n",
      "******Episode 817\n",
      "Score:-104\n",
      "******Episode 818\n",
      "Score:-109\n",
      "******Episode 819\n",
      "Score:-106\n",
      "******Episode 820\n",
      "Score:-110\n",
      "******Episode 821\n",
      "Score:-105\n",
      "******Episode 822\n",
      "Score:-109\n",
      "******Episode 823\n",
      "Score:-104\n",
      "******Episode 824\n",
      "Score:-86\n",
      "******Episode 825\n",
      "Score:-84\n",
      "******Episode 826\n",
      "Score:-159\n",
      "******Episode 827\n",
      "Score:-110\n",
      "******Episode 828\n",
      "Score:-104\n",
      "******Episode 829\n",
      "Score:-110\n",
      "******Episode 830\n",
      "Score:-89\n",
      "******Episode 831\n",
      "Score:-109\n",
      "******Episode 832\n",
      "Score:-86\n",
      "******Episode 833\n",
      "Score:-110\n",
      "******Episode 834\n",
      "Score:-91\n",
      "******Episode 835\n",
      "Score:-104\n",
      "******Episode 836\n",
      "Score:-105\n",
      "******Episode 837\n",
      "Score:-104\n",
      "******Episode 838\n",
      "Score:-104\n",
      "******Episode 839\n",
      "Score:-98\n",
      "******Episode 840\n",
      "Score:-107\n",
      "******Episode 841\n",
      "Score:-88\n",
      "******Episode 842\n",
      "Score:-107\n",
      "******Episode 843\n",
      "Score:-96\n",
      "******Episode 844\n",
      "Score:-96\n",
      "******Episode 845\n",
      "Score:-147\n",
      "******Episode 846\n",
      "Score:-158\n",
      "******Episode 847\n",
      "Score:-89\n",
      "******Episode 848\n",
      "Score:-90\n",
      "******Episode 849\n",
      "Score:-160\n",
      "******Episode 850\n",
      "Score:-89\n",
      "******Episode 851\n",
      "Score:-158\n",
      "******Episode 852\n",
      "Score:-106\n",
      "******Episode 853\n",
      "Score:-105\n",
      "******Episode 854\n",
      "Score:-85\n",
      "******Episode 855\n",
      "Score:-104\n",
      "******Episode 856\n",
      "Score:-105\n",
      "******Episode 857\n",
      "Score:-88\n",
      "******Episode 858\n",
      "Score:-107\n",
      "******Episode 859\n",
      "Score:-149\n",
      "******Episode 860\n",
      "Score:-158\n",
      "******Episode 861\n",
      "Score:-90\n",
      "******Episode 862\n",
      "Score:-152\n",
      "******Episode 863\n",
      "Score:-86\n",
      "******Episode 864\n",
      "Score:-150\n",
      "******Episode 865\n",
      "Score:-105\n",
      "******Episode 866\n",
      "Score:-109\n",
      "******Episode 867\n",
      "Score:-84\n",
      "******Episode 868\n",
      "Score:-106\n",
      "******Episode 869\n",
      "Score:-84\n",
      "******Episode 870\n",
      "Score:-106\n",
      "******Episode 871\n",
      "Score:-156\n",
      "******Episode 872\n",
      "Score:-129\n",
      "******Episode 873\n",
      "Score:-90\n",
      "******Episode 874\n",
      "Score:-109\n",
      "******Episode 875\n",
      "Score:-109\n",
      "******Episode 876\n",
      "Score:-109\n",
      "******Episode 877\n",
      "Score:-109\n",
      "******Episode 878\n",
      "Score:-108\n",
      "******Episode 879\n",
      "Score:-90\n",
      "******Episode 880\n",
      "Score:-89\n",
      "******Episode 881\n",
      "Score:-88\n",
      "******Episode 882\n",
      "Score:-84\n",
      "******Episode 883\n",
      "Score:-90\n",
      "******Episode 884\n",
      "Score:-152\n",
      "******Episode 885\n",
      "Score:-104\n",
      "******Episode 886\n",
      "Score:-95\n",
      "******Episode 887\n",
      "Score:-110\n",
      "******Episode 888\n",
      "Score:-159\n",
      "******Episode 889\n",
      "Score:-159\n",
      "******Episode 890\n",
      "Score:-105\n",
      "******Episode 891\n",
      "Score:-84\n",
      "******Episode 892\n",
      "Score:-109\n",
      "******Episode 893\n",
      "Score:-106\n",
      "******Episode 894\n",
      "Score:-106\n",
      "******Episode 895\n",
      "Score:-84\n",
      "******Episode 896\n",
      "Score:-105\n",
      "******Episode 897\n",
      "Score:-110\n",
      "******Episode 898\n",
      "Score:-110\n",
      "******Episode 899\n",
      "Score:-157\n",
      "******Episode 900\n",
      "Score:-149\n",
      "******Episode 901\n",
      "Score:-106\n",
      "******Episode 902\n",
      "Score:-90\n",
      "******Episode 903\n",
      "Score:-89\n",
      "******Episode 904\n",
      "Score:-158\n",
      "******Episode 905\n",
      "Score:-86\n",
      "******Episode 906\n",
      "Score:-105\n",
      "******Episode 907\n",
      "Score:-104\n",
      "******Episode 908\n",
      "Score:-104\n",
      "******Episode 909\n",
      "Score:-109\n",
      "******Episode 910\n",
      "Score:-88\n",
      "******Episode 911\n",
      "Score:-106\n",
      "******Episode 912\n",
      "Score:-109\n",
      "******Episode 913\n",
      "Score:-106\n",
      "******Episode 914\n",
      "Score:-85\n",
      "******Episode 915\n",
      "Score:-110\n",
      "******Episode 916\n",
      "Score:-104\n",
      "******Episode 917\n",
      "Score:-104\n",
      "******Episode 918\n",
      "Score:-108\n",
      "******Episode 919\n",
      "Score:-105\n",
      "******Episode 920\n",
      "Score:-104\n",
      "******Episode 921\n",
      "Score:-150\n",
      "******Episode 922\n",
      "Score:-111\n",
      "******Episode 923\n",
      "Score:-108\n",
      "******Episode 924\n",
      "Score:-158\n",
      "******Episode 925\n",
      "Score:-109\n",
      "******Episode 926\n",
      "Score:-89\n",
      "******Episode 927\n",
      "Score:-89\n",
      "******Episode 928\n",
      "Score:-84\n",
      "******Episode 929\n",
      "Score:-86\n",
      "******Episode 930\n",
      "Score:-152\n",
      "******Episode 931\n",
      "Score:-104\n",
      "******Episode 932\n",
      "Score:-85\n",
      "******Episode 933\n",
      "Score:-109\n",
      "******Episode 934\n",
      "Score:-109\n",
      "******Episode 935\n",
      "Score:-159\n",
      "******Episode 936\n",
      "Score:-111\n",
      "******Episode 937\n",
      "Score:-109\n",
      "******Episode 938\n",
      "Score:-158\n",
      "******Episode 939\n",
      "Score:-106\n",
      "******Episode 940\n",
      "Score:-90\n",
      "******Episode 941\n",
      "Score:-105\n",
      "******Episode 942\n",
      "Score:-84\n",
      "******Episode 943\n",
      "Score:-86\n",
      "******Episode 944\n",
      "Score:-104\n",
      "******Episode 945\n",
      "Score:-155\n",
      "******Episode 946\n",
      "Score:-159\n",
      "******Episode 947\n",
      "Score:-108\n",
      "******Episode 948\n",
      "Score:-85\n",
      "******Episode 949\n",
      "Score:-88\n",
      "******Episode 950\n",
      "Score:-88\n",
      "******Episode 951\n",
      "Score:-106\n",
      "******Episode 952\n",
      "Score:-84\n",
      "******Episode 953\n",
      "Score:-109\n",
      "******Episode 954\n",
      "Score:-107\n",
      "******Episode 955\n",
      "Score:-106\n",
      "******Episode 956\n",
      "Score:-109\n",
      "******Episode 957\n",
      "Score:-152\n",
      "******Episode 958\n",
      "Score:-147\n",
      "******Episode 959\n",
      "Score:-105\n",
      "******Episode 960\n",
      "Score:-105\n",
      "******Episode 961\n",
      "Score:-108\n",
      "******Episode 962\n",
      "Score:-101\n",
      "******Episode 963\n",
      "Score:-89\n",
      "******Episode 964\n",
      "Score:-107\n",
      "******Episode 965\n",
      "Score:-150\n",
      "******Episode 966\n",
      "Score:-93\n",
      "******Episode 967\n",
      "Score:-96\n",
      "******Episode 968\n",
      "Score:-89\n",
      "******Episode 969\n",
      "Score:-110\n",
      "******Episode 970\n",
      "Score:-104\n",
      "******Episode 971\n",
      "Score:-86\n",
      "******Episode 972\n",
      "Score:-104\n",
      "******Episode 973\n",
      "Score:-105\n",
      "******Episode 974\n",
      "Score:-159\n",
      "******Episode 975\n",
      "Score:-158\n",
      "******Episode 976\n",
      "Score:-104\n",
      "******Episode 977\n",
      "Score:-159\n",
      "******Episode 978\n",
      "Score:-84\n",
      "******Episode 979\n",
      "Score:-150\n",
      "******Episode 980\n",
      "Score:-105\n",
      "******Episode 981\n",
      "Score:-109\n",
      "******Episode 982\n",
      "Score:-109\n",
      "******Episode 983\n",
      "Score:-96\n",
      "******Episode 984\n",
      "Score:-144\n",
      "******Episode 985\n",
      "Score:-86\n",
      "******Episode 986\n",
      "Score:-159\n",
      "******Episode 987\n",
      "Score:-106\n",
      "******Episode 988\n",
      "Score:-88\n",
      "******Episode 989\n",
      "Score:-158\n",
      "******Episode 990\n",
      "Score:-106\n",
      "******Episode 991\n",
      "Score:-104\n",
      "******Episode 992\n",
      "Score:-159\n",
      "******Episode 993\n",
      "Score:-85\n",
      "******Episode 994\n",
      "Score:-104\n",
      "******Episode 995\n",
      "Score:-110\n",
      "******Episode 996\n",
      "Score:-90\n",
      "******Episode 997\n",
      "Score:-106\n",
      "******Episode 998\n",
      "Score:-85\n",
      "******Episode 999\n",
      "Score:-105\n",
      "Average score over 1000 run : -114.59\n"
     ]
    }
   ],
   "source": [
    "# Attention: don't change this function. we will use this to grade your policy which you will hand in with policy.npy\n",
    "# btw you can use it to see how you are performing. Uncomment two lines which are commented to be able to see what is happening visually.\n",
    "def score():\n",
    "    policy, scores = np.load(\"policy.npy\"), []\n",
    "    for episode in range(1000):\n",
    "        print(f\"******Episode {episode}\")\n",
    "        state, score, done, step = env_state_to_Q_state(env.reset()), 0, False, 0\n",
    "        while not done:\n",
    "            # time.sleep(0.04)\n",
    "            p,v = state\n",
    "            action = policy[p,v]\n",
    "            state, reward, done, _ = env.step(action)\n",
    "            state = env_state_to_Q_state(state)\n",
    "            step += 1\n",
    "            score += int(reward)\n",
    "            \n",
    "        print(f\"Score:{score}\")\n",
    "        scores.append(score)\n",
    "    print(f\"Average score over 1000 run : {np.array(scores).mean()}\")\n",
    "\n",
    "score()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "interpreter": {
   "hash": "84499dc17ab2a5fccb274f1e4d02e09fe70145d6d2a02ca59b85715038bf2fe5"
  },
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.3"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": false
  },
  "varInspector": {
   "cols": {
    "lenName": 16,
    "lenType": 16,
    "lenVar": 40
   },
   "kernels_config": {
    "python": {
     "delete_cmd_postfix": "",
     "delete_cmd_prefix": "del ",
     "library": "var_list.py",
     "varRefreshCmd": "print(var_dic_list())"
    },
    "r": {
     "delete_cmd_postfix": ") ",
     "delete_cmd_prefix": "rm(",
     "library": "var_list.r",
     "varRefreshCmd": "cat(var_dic_list()) "
    }
   },
   "types_to_exclude": [
    "module",
    "function",
    "builtin_function_or_method",
    "instance",
    "_Feature"
   ],
   "window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}