05-Support Vector Machine.ipynb

{
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  {
   "cell_type": "markdown",
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   "source": [
    "# Support Vector Machine (SVM)\n",
    "\n",
    "Invented in [1963](https://en.wikipedia.org/wiki/Support_vector_machine#History) by [Vladimir N. Vapnik](https://en.wikipedia.org/wiki/Vladimir_Vapnik) and Alexey Ya. Chervonenkis while working at AT&T Bell Labs. Vladimir N. Vapnik joined Facebook AI Research in Nov 2014.\n",
    "\n",
    "In 1992, Bernhard E. Boser, Isabelle M. Guyon and Vladimir N. Vapnik suggested a way to create nonlinear classifiers by applying the kernel trick to maximum-margin hyperplanes.\n",
    "\n",
    "The current standard incarnation (soft margin) was proposed by Corinna Cortes and Vapnik in 1993 and published in 1995.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "References:\n",
    "\n",
    "1. [Support Vector Machine in Javascript Demo by Karpathy](http://cs.stanford.edu/people/karpathy/svmjs/demo/)\n",
    "\n",
    "2. [SVM](http://www.svms.org/tutorials/)\n",
    "\n",
    "3. [Statsoft](http://www.statsoft.com/Textbook/Support-Vector-Machines)\n",
    "\n",
    "4. [Wikipedia](https://en.wikipedia.org/wiki/Support_vector_machine)\n",
    "\n",
    "5. [Scikit-Learn](http://scikit-learn.org/stable/modules/svm.html)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "### Learning Outcomes:\n",
    "\n",
    "* Introduction\n",
    "* Linear SVM Classification\n",
    "* Polynomial Kernal\n",
    "* Radial Basis Function /  Gaussian Kernel\n",
    "* Support Vector Regression\n",
    "\n",
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1. Introduction\n",
    "\n",
    "Supervised learning methods used for classification, regression and outliers detection.\n",
    "\n",
    "Let's assume we have two classes here - black and purple. In classification, we are interested in the best way to separate the two classes. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src='img//SVM_1.png' width=50%>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can separate them with a line such as the example below. You can consider this as an example of how logistic regression would segregate the two classes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src='img//SVM_2.png' width=50%>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "However, there are infinite lines (in 2-dimensional space) or hyperplanes (in 3-dimensional space) that can be used to separate the two classes as the example below illustrates. \n",
    "\n",
    "The term hyperplane essentially means it is a subspace of one dimension less than its ambient space. If a space is 3-dimensional then its hyperplanes are the 2-dimensional planes, while if the space is 2-dimensional, its hyperplanes are the 1-dimensional lines. ~ [Wikipedia](https://en.wikipedia.org/wiki/Hyperplane)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src='img//SVM_3.png' width=50%>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In SVM, the **separating line**, the solid brown line, is the line that allows for largest margin between the two classes. \n",
    "\n",
    "SVM would place the separating line in the middle of the margin, also called maximum margin. SVM will optimise and locate the hyperplane that maximises the margin of the two classes.\n",
    "\n",
    "The samples that are closest to the hyperplane are called **support vectors**, circled in red. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src='img//SVM_4.png' width=50%>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n",
    "# 2. Linear SVM Classification\n",
    "\n",
    "\n",
    "* Support Vectors\n",
    "\n",
    "* Separate with a straight line (linearly separable)\n",
    "\n",
    "* Margin\n",
    "\n",
    "  * Hard margin classification\n",
    "      * Strictly based on those that are at the margin between the two classes\n",
    "      * However, this is sensitive to outliers\n",
    "      \n",
    "  * Soft margin classification\n",
    "      * Widen the margin and allows for violation\n",
    "      * With Python Scikit-Learn, you control the width of the margin\n",
    "      * Control with `C` hyperparameter\n",
    "        * smaller `C` leads to a wider street but more margin violations\n",
    "        * High `C` - fewer margin violations but ends up with a smaller margin\n",
    "\n",
    "\n",
    "\n",
    "**Note:**\n",
    "\n",
    "* SVM are sensitive to feature scaling\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.16.5\n",
      "0.25.1\n",
      "3.7.4 (default, Aug 13 2019, 15:17:50) \n",
      "[Clang 4.0.1 (tags/RELEASE_401/final)]\n",
      "0.21.3\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "from sklearn import datasets\n",
    "from sklearn import svm\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "sns.set_style('whitegrid')\n",
    "\n",
    "print(np.__version__)\n",
    "print(pd.__version__)\n",
    "import sys\n",
    "print(sys.version)\n",
    "import sklearn\n",
    "print(sklearn.__version__)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sepal_length</th>\n",
       "      <th>sepal_width</th>\n",
       "      <th>petal_length</th>\n",
       "      <th>petal_width</th>\n",
       "      <th>species</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>5.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>4.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>4.7</td>\n",
       "      <td>3.2</td>\n",
       "      <td>1.3</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>4.6</td>\n",
       "      <td>3.1</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>5.0</td>\n",
       "      <td>3.6</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   sepal_length  sepal_width  petal_length  petal_width species\n",
       "0           5.1          3.5           1.4          0.2  setosa\n",
       "1           4.9          3.0           1.4          0.2  setosa\n",
       "2           4.7          3.2           1.3          0.2  setosa\n",
       "3           4.6          3.1           1.5          0.2  setosa\n",
       "4           5.0          3.6           1.4          0.2  setosa"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = sns.load_dataset('iris')\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<style scoped>\n",
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       "\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>petal_length</th>\n",
       "      <th>petal_width</th>\n",
       "      <th>species</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>1.3</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      "text/plain": [
       "   petal_length  petal_width species\n",
       "0           1.4          0.2  setosa\n",
       "1           1.4          0.2  setosa\n",
       "2           1.3          0.2  setosa\n",
       "3           1.5          0.2  setosa\n",
       "4           1.4          0.2  setosa"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "col = ['petal_length', 'petal_width', 'species']\n",
    "df.loc[:, col].head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['setosa', 'versicolor', 'virginica'], dtype=object)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.species.unique()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "col = ['petal_length', 'petal_width']\n",
    "X = df.loc[:, col]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "species_to_num = {'setosa': 0,\n",
    "                  'versicolor': 1,\n",
    "                  'virginica': 2}\n",
    "df['tmp'] = df['species'].map(species_to_num)\n",
    "y = df['tmp']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Documentations on each:\n",
    "\n",
    "* [LinearSVC](http://scikit-learn.org/stable/modules/generated/sklearn.svm.LinearSVC.html#sklearn.svm.LinearSVC)\n",
    "\n",
    "  Similar to SVC with parameter kernel=’linear’, but implemented in terms of liblinear rather than libsvm, so it has more flexibility in the choice of penalties and loss functions and should scale better to large numbers of samples.\n",
    "  \n",
    "  \n",
    "  \n",
    "* [SVC](http://scikit-learn.org/stable/modules/generated/sklearn.svm.SVC.html#sklearn.svm.SVC)\n",
    "\n",
    "  C-Support Vector Classification.\n",
    "  \n",
    "  The implementation is based on libsvm. The fit time complexity is more than quadratic with the number of samples which makes it hard to scale to dataset with more than a couple of 10000 samples."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SVC(C=0.001, cache_size=200, class_weight=None, coef0=0.0,\n",
       "    decision_function_shape='ovr', degree=3, gamma='auto_deprecated',\n",
       "    kernel='linear', max_iter=-1, probability=False, random_state=None,\n",
       "    shrinking=True, tol=0.001, verbose=False)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C = 0.001\n",
    "clf = svm.SVC(kernel='linear', C=C)\n",
    "#clf = svm.LinearSVC(C=C, loss='hinge')\n",
    "#clf = svm.SVC(kernel='poly', degree=3, C=C)\n",
    "#clf = svm.SVC(kernel='rbf', gamma=0.7, C=C)\n",
    "clf.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "clf.predict([[6, 2]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "Xv = X.values.reshape(-1,1)\n",
    "h = 0.02\n",
    "x_min, x_max = Xv.min(), Xv.max() + 1\n",
    "y_min, y_max = y.min(), y.max() + 1\n",
    "xx, yy = np.meshgrid(np.arange(x_min, x_max, h),\n",
    "                     np.arange(y_min, y_max, h))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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9n7+OreTjnu9fM4EcTz/BsLmjuTO4DR+0e4la7kEcTj/GL/t+Y2b8bGYNnoqXixdQmJDfWPM2a0+u5dHIkbwZ8yRGSz5LTq5m4JxhvN/9HfpF9C5q+9DFw4z8/UG6hXXk4w6vEuTmz4G0I/y0ezpzD/zO1Psn46Zzq8iP+aZsSdjGI4uf5P6G9/Bt53fx0XuxM2UfX2z6ioWHl/Jt3y/Qqm/P9HR7jlo4tTRCiI+Lo5skZXGT1p3ewMy9s1nU92eC3P93N55lyqFraEfea/8SAe7+6DQ6QjxqEtIqiPY1W/PW9i9oEdAUV60LGrWaczkXmNnzSyIDmuDr6gPAkMZ96VOvGyNXPMPUvTN5sPXoMuOwKTbGL3yU51qNZ3h4/6LjIZ416RLWgVc3f8Tra97iy3s/AWDuwT/YenYLi/v9jLfeq+j6F6Ifple9zoxc8QxRNSOp61sHs83MuAWP8Ebbp+nXoEextruF3clz6yfyzroPeb/7W3b7XO0hqyCLRxY/ydd3v0XHkLZFx2t71uLeep0Zv/pFvtn+Pc+1e8qBUTrO7fuMQDit0IFS+/q2UIHvK0/e9SvPtnqwWEI2WvL57dgS3m73At56T/LMeQCYbWYURaFP/W4082vM4pOrAJh1ZCF963ejY3AbTBZTscIf7jo3Xm3zJD/v/hWbYiszjnWnN+Cq1jOscb8S59QqNa+2fYoVx1dxMfciiqIwefcU/t3miWIJ+R/N/BozqOG9TIufVdh24kZCPWoWS8j/0Kg1vBH7LPMPLySrIOs6P7XKMe/gAjoExxRLyP/Qa/S83vZZpu6ZgdlqdkB0jidJWQhR6aznVRVW3UtRFNaf3UTvesUXkh1IPUI9r9qEegbjqnHBdPmXfoHVhItGjwroXa8Lm5N3ALDp3E561y2cN3bR6DFZTcXaa1OzJdkF2ZzPSSkzlg1nN3Nv3bvLnHv21nsRW7MV25J2klmQydmMs9wZUvYTot71urDhzEYAdqTs5N66ncu8Nsg9gEj/CHaf21vmNY6w4czGcuNu4tcQT507x9NPVF5QTkSSshCi0lm9I1FykyqsfUVR0F01J2lVbGhUl4+pVIDyz9X8kzO1Ki1WpfCO2GqzolVrLl9fsg+VSoVWpSm3dKbVZkWrKn+WUKfWYlNsWG1W1Co1qtI6u0x7+VoofDSuUWnKbVur0jpdaU+bYi3x3VxNp9YVfQ+3G0nKQohqRaVSER3ckjUJm4sdb+bfmKMZJ0k1plNgNaFTF65M1ql1FFy+a16TuInooMK1/9FBkaxJ3IyiKJis5hIrmQ+lH0NRqQj2qlVmLDEhrYkrp9yn0ZLP1vO7aV2rJX5uftRw82XPxQNlXr8mYRPRwa0BaBEQydqkLWVem2XKZm/qQbuWE7WH6JBo1iSWHXdCdjIpeRdpWKNBJUblPCQpCyEcQsnMrbB55fHR4/gy/hfyzMaiY956L/rW78ane34i15SLu84dABeNC4piY9v5PWxI3sGgxn0AGNVkEL8dW8qRS8fRqjXFVgNbbVY+3vU9o1uOLHeV8L2NenIyK4G4MpLQ9/tm0CYkhjCfUFQqFeNaj+GT3T+UOp+anJPCDMOCooVlPet0Y2/qIbad31Nq21/t/ZUu9e8m0CPwGp9W5RrZYhjLTq/hcPrxEucUReGT3T8wpPkgp1w1XhkkKQunlEYIB+bNcHQYogJV5K5R/cJ706p2awYve4xVZ9djsVkwW820Doxk9tFFvLz5A45knEBRFDJMWcw7voyhfz1B++Bocs1GFEVBQaGBTx36L32IP0+vJdech6IobD23mzErn8OmUfNU7KPlxqHT6Pix/yRe2PAOX+yZzIW8VBRF4eilk7yy8X0Wnl7Jf3u+V3T9+NZj8HTzZeSKZ9iYtB2bYsNoyWfu0aUMXvYoT97xOE0DmwCF70J/2+dLHlv7Kt/tm0aa8RKKonAo/RjPrZvIunPbea/bRLt/trcq0COQD3q8w+iVzzL10DyyTNkoisLuC/uZ8PdLJBov8vKdzzs6TIdRKYpy7avsaNuWLUp2auVsdF4ZEhMSCA0Lc3QYFcpRYzTO/y/dnn25Uvq6Hb5HcL5x6t33o63fA3TN7dZmQkIiYWGhKIrCgiOL+Xn3FPalFD4SbhsSzcio4SRmJTNr3xySc86jVWvp3fgeBkT0Ze3p9cw/vJA8sxFfVx+GRQ4hOrglcw/8wZpT61BQaFijPmNajWJ01IjrLs5xIv0k3+38iYWHF1NgNRHg5s/wFkN5OGYcfm5+xa612CzM2j+XqXumc/Ty3WTnup14uM147qp7Z4lxHkk18P3OySw+8idmm5kg90AeiBrOwzHj8HZx3mpiu8/t4fsdP7PixCpsio0w79qMavkA41uPwVXrCvxvjFXdrl2Hd8XExLS5nmslKd8iZ/slVxEkKVcfzjZOnXkrulb3VUhSvpLFZkGFCo26+MIos9WMVq0ttjpaURQsNkuJhPvPYqxbqZJVVttlsdgsqFXqUguUXD3OG23bWZQX9+2YlKV4iBCi2itr3re0RKBSqUo9rlapUWvKn/HLt+Qza/9cZu2bw5nMs3jrvenfpC8ToscS6l27RNvx5/fx0+5fWXtyHRbFQsuaLRjbajS9G99TuLr7BqpalRV3ZbHYLMw/vIhpe2dyNO0Yblo37mnUg4dixhHu37jMv+fouJ2NzCkLpyXzytWfzeiJ9cIhKmJeubJlF2QzaM4I1hxdxRsxT7F16CJm3vMlSr6R3jPuY89V7wvPOTCPsfMfoplnXZYPmM6mwfMZ3qA3n238nBdWvFJuURJnY7aaGb/wUWbsns6TzUeyZehCFvT5kUCNB4PmDGf1yTWODrHKkDtl4bxCw0lJjJPNKaqxojrY5hTQVezmFBXtzbXv0MSnHh90+L+ix+Heei9ei32aO2q1YsKix9n28Hp0Gh3H00/w3roP+b33DzTwqVPURr8GPehepxMjlj/FrP1zGRU13FHDuSFfbvsWm9nEnF6Tiu56vfVePNf6Ie4Obc+4ZS+wYfxq/N39HRyp85M7ZeG0QmOl9vXtwHpeBXllV8WqCtKN6fx1bAWvxDxRavWu7nU60dC7Dn8eWw7AlD0zGBE+oFhC/oeb1pWXoh/ll91TqOw1PzfDbDUzI34Wr7V9utTH0K0Dm9MjrBOzD8xzQHRVjyRlIYS4RXvP7yPKvyk1Lm9aUZp76tzF5rOFhUS2Jm6jZ527yry2Q3AbErOSyCzItHus9nbi0kk8de408q1X5jU963RiW8K2yguqCpOkLIRwuIp6X7myKIpSZn3rYtdx/Xe+KlRV4k5ZUZRyS4NC4WIu5x+Jc5CkLIRwqKI62Oaq+wi7Va0o4lMPkVHOjkyrEjbQPuwOAGJrt2V1wsYyr91ybhfBXrXwdfW1e6z21tCvAZmmbE5kninzmpVn1hMbWnJXKFGSJGXh9GQFdvVnPa+q0quw/d396dmoOx/v+r7Uu9u1CZs5mnGavuH3AjCu9ShmGhZwOiuxxLX5lgI+2fMDD7Yee113346m1+gZGTWCD3ZMwmKzlDi/L/UwKxM28ECLoQ6IruqRpCycWlpoZ1KSkx0dhqhgRXfLFbjHckV7t+t/iL9k4OG/X2H7+T0YLfmczkrko53f8q+N7/LTgG/Ra/QAhPs35pVOLzH0r8f59eBvpBrTyTHl8tfptQxe9ih1/RswuuUIB4/o+j3f/inMaoWRK54hLnELeWYj53IvMCl+CuNWvcBnvT4iwL1qr66vLPJKlHBqobGxGBPjSI3fTkBLWY1dnVnPq1B5pKEpe62UU/N28WbB8N+YsW8Or237lDOZCXjrvegX0YelI+dT17f4SutRUcNpGhDBj7t+4bP5kzHbLLQIasbj7R6nf0SfUqt4OSu9Rs/U+ycz9+B8Pon/mWNpx3HVunBPox7MHTqzqF63uDZJysLppRHi6BBEJbB6R6Il3dFhlOmfTSquTpb/PK5WqVS469x5JGY8j8SMx6bYSk2sVx6PCWnNDyFfl9mnTbGhQuW0j7GvHLtOo2Nk1DBGRg1zcFRVmyRlIYSTSQWc51HnzuTdfL9jMqtPrsFis9AkIJzRLR/AVevK9PhZxKfsR61S06lOB0ZGDedY+glm7ZtDQlYSnnoP+kX0oW/4vaw4vpoFhxeRVZBNba9ghrcYxkPRY/G56jUqq83KvEPz+XXPdA5eOIRGraFrvbt5uM14OoS1c9CnUNyqE38zedevbEncjoJCm+DWjI8eR9/we532fyCqCknKQginUbQK20mqe805MI+PNnzCU1Hj+OiOf+GudWPbuT18sPMbjmWc5su7J9Kt59eYbRbmHlvC+IWP0bPOXUy6+x0i/SO4aExj5pEFDJs7moGN7mXFgBnU8gjkyKUT/HxwDn1nDuSP4bMJ8ggCCutHP770Wc5nJvJiywncGdKWfEsBi0+t4umlz/FkuycY33qMQz+TDzd+wpLDS3m+1UNM7vwBapWK1Wc38vmmL9iSsI33uk2UxHwLqs6khRCi2nOmVdinM87wTtwHzOk1iTFNB+Gt90Kr1hIdFMkv3T4mtmZLTmScQafR4a5zY/eF/TzYdAjvt3+ZpjUaoVapqekWwOiIgUzv+QWbknfg5+qLWqWmmV9jPu30BvfWuZtXVr1R1OeUvTNIy0rht17f0jm0PVq1Fk+9Bw9E3MfvfX7gi81fcSTV4LDPZMOZTSw8tJgFfX5iQMOeuGpd0Gv09K7fld97f8+Ws5tZdmyFw+KrDiQpiyohPi7O0SGISlC0CtsJTIufxdDGfUuUwswzG/Fx8eb/Yp5g+pE/sNqsXDSmsSZhM/+KfhgPnRt5ZiMA+VYTGpWaLqHtifSPYOmp1cXaeqrlOLYnbicxKwlFUZiyZxovxzxWarnKUM9gRkUMZOremRU36Gv4ZfdUHm8xqtTKZV56T56OGseve6Y6ILLqQ5KycHqhA0cBkBq/3cGRiNvJzqRddA3tUOzYP3v/6jV6mvuHY1MUzuVdYH/qEVoFNsNb74WLxgWz1QSA2WrC5fJrUN1CO7AzpfgrX25aV+6oFc3uc3u5lH+J1Lw0ooNalBlT17AO7EjaaeeRXr+dybvpFtaxzPM96tzFjuTdVaISmbOSpCyqBFmBfZtxgupeKpUKq2ItfqzonxQURSlcSY0aFSqsNlvRuf9d+b+/YVMU1KXMtVoVK2qVuqisZnmlOMta0V1Z1Co1tnISrsVmcerV4lWBJGUhhFNxlnnljnU6sPzMuuIHVSp0ai0FFhO7L+7HXedGLY9AWgdFsj/tCKnGdPKtJvSXHz/rNTryL981LzuzlvbBMcWayzJls+38HmJrx+Dr6kuod202J5d9J/zXmTg6hLW370BvQPuwdvx1uuy9kZedXktHJ1khXlVJUhZVhswr3x6cZV55dNRwFp9aRfzFQ8WOu+vduZifzrs7vubBZkNQq9T4unjTt3533t3xNbnmXNx17gC4aFxQUFhwYjkJOcn0qtu5qB1FUfho53d0a9CFII8gVCoVD8U8yIe7viXHlFsiniPpJ5h3fCnjWo+q0HGX56GYcfxwYCZJOedLnEs1pvP1vik8FPOgAyKrPjQTJ06s1A6TEhMnmvLyKrXPipSVlYW3TxUtQXSdnGGM3k2jsBzehLebDvdate3evjOMsTJUlXFqdBdQ+0cB7jf8d7OysvDx8b7lGLxcvGhYoyFPrHqJPLORIPcAzDYzaxO28K+N73IqM4Gude4k0M2f9PxLJOac45dDv7En9RBB7gF46tw5lZ3Ajwdn8cHOSXQIaUMDnzqoVSp2XdjHm1s/IyEvhe/7fYWL1gWAyKBmHEg9wsc7vsVN44q/aw1S8y8x9dA8/rPtU97pNpF2obF2HeeNCPEKRqPR8eLaN1EBgW7+5JrzmH/8L17c9B7Do4bZtca1I8ZYEc6dSz0XEhLy4/VcK+8piyojjRDOHz0q5TZvF07wvnKvxj1o6FefX/ZMY/TK5zBZzTQLbMJb3d7ETevGlD3T+TL+V9QqFXfV68SfIxdwNP0438TP4GxmAl56T/o36cfacctZfnw1z298h8yCLGp7hzCixTCGNh+Iq9a1qD+VSsWH3d/h71NrmbpnBh/v+QGtWkOX+p35behWMbcHAAAgAElEQVQMpyhX+VD0OFrXasnPe6bw47I5ALSpHcNXvT8r2gVL3DxJyqLqCA0H21FHRyEqQWEd7ENoajcv9bzFZiHPnIeHzgONWlN03GQ1kWPOKbG/cZ45DxUq3HRuRcdsio1cUy6uWtdSX0H6R2P/RnzQ/W0+6P52iXN31+tU4lh0SGuGRw4pcbx5UDP+1eGZMvv5h0qlonuDrnRv0PWa19qb1WYtevyuVZedHmJCWhMT0rrUc4qikGPKweXyO8zixkhSFkI4Hat3JJrc/WA+CLr/JebTGWeYtP0HFh1ZAhQmsPubDOCO0LYsOLyI9Wc2oUaFv7sfI1uOwFvvzaz9czhx6SSKAs0CmzAyajhJWcnM3j+XHFMOZpuFbg0680TbR8tMNNXduexzfLP9B/44tACrzYqCQr+IPjwV+xgN/RpcVxt55jx+3PULM+JnkZGficVm5a66HXms7cNOUx60Kig3KUdEROiAX4B6gAvwrsFgWHzF+X7Am4AF+MVgMPxUcaEKIW4nSmbxxU4HLxzigd/H8UB4f9YO/I0g9wBS8i4y+cBsHl3yFC9FP8akkRPRqbQcvnScj3ZOYuv53Xzb5X261bkTRVFYfHIVz698lV51OzOjxxeE+zUgx5TL/BPLeXDBw7zf/R36RtzroBE7xslLpxj82wMMqN+DFQNmEOJZkzTjJWYZFnLf7KFMHfgT0cHl/89KjimHYXNHE+zqz+Su/6W5fzhGSz6LT67iySXP8spdL5b69ECUdK3V16OANIPB0Am4F/jmnxOXE/bnQE/gbuCRiIiIWhUVqBDi9qUoCk/++Ryvt32aF6IfIejy3rwBrn483HwEn975OivOxhUV6mjkU5fPO/2HPvW6se38HtQqNRq1hk3J2xnTZBDvtnuJut6FCwY99R6MaTqIaT2/4KWV/yYjP8Nh43SE5/56kSciR/Fq26cI8awJgL9bDZ5u9SAfdniFJ5Y+i9VmLbeNjzd9QQPP2nzb5T2a+4cDhYVRhoX3Y869k3hr7XskZ5+r8LFUB9dKyvOAN6742XLFPzcFjhsMhksGg8EEbARKTrAIYSehsbGkJCc7OgxRiQrfV4bNCVtRbDYGNOhZ7LzRbMRV48LQxn3JMxvZfWE/UPgo1UvvzgutH2be8T/JtxSQUZDF8jPreK7VBDx0bhgvl8L8R3P/cDrXbsdvB/6onME5gYMXDpGUmcTIJveXer5n3bupofdm7el1pZ6Hwu9g3sE/eCH64VKLhjTwqcOABj2ZsW+O3eKuzspNygaDIcdgMGRHRER4Ab8Dr19x2hvIvOLnbMD537UQVVoaIRyYN8PRYYhKYNa1u7xr1EHiU/Zzd8gdJX7pm20WXDR61Co1d9dux96LB0EpPK5X66njFUKgqx+nshI4kn6ciBoN8HP1Ra/RY7aZS/TZObQ9e8/HV9YQHS4+ZT93hsSWu6irc+127Dm3r8zzpzPOEOQWQKhncLltxJ+7fT7XW3HNhV4RERFhwALgW4PBMOuKU1mA1xU/ewHXfO5jsVhITEi40TidlslkqlbjKY0zjTHV1Y+srNN2j8dkdp4xVqSqNk5/t3No/TPJysgm31KA1XrVY1SlsNyloigUWE2oUReVqVRQQIECawFqRYVKUWGymouuB0q0ZzTnU2A0kZCQWCnjuxUm063HeSk9E6M5v+TnegWjOR/FTJl9Xci8iNFsvGYb5gLzDcdrjzFWNdda6FUTWAk8ZTAY/r7q9GGgcUREhB+QA9wFfHLNDrVaQsPCbjJc55OYkFCtxlMapxrjuXN429LtHo9TjbECVbVx6sxJ6Lx9GNCqDw/MG8vEds8Xe33JRetSmHRVKlYlbOCRqFGoVCpcNHoKrCaOZpzCqthoVKMeZpuFhJxznMlOItDND73GBY1GU6y/v86uZWjL4YSFhVb2UG9YQkLiLcc5wKcPk6Z+S4HNhPsVr4v9w6bY+OvsOr7v/zVhwaX3FVI7GNsmhUOXjtEioPT3qP86G8c9TXvecLz2GKMzuHDh8HVfe6055VeBGsAbERERcZf/jIyIiHjEYDCYgReAFcAWCldfO742nqj2ZF759mK9cIimgU0ID2jMF3t/LrYDkZvOjQKriQ93fUtUQFMa+tQFwF3nzkVjOhO3fc6DzYaiUWtw1bowMuI+3tj6CZmm7BJJaOmp1RzPOkvf8Ntn9XWod23urHsnH+ycVOrOTt/tm0aQZyCtarUssw2NWsP46HG8vf0LjJb8EufXJW5la8oehjQvfd5aFFfunbLBYHgWeLac80uAJfYOSoiyhMbGkph4lAPzZhA5xHE1gEXlMOvaob/8vvI3fT5n2LzRHEo/xugmA6nnHcapzLP8fGgO6xO3MTxiAHsuHMBT687Oi/v5Ov5XzudeoFtYRwyXTmBTFFSoWZ+8nVErn+PJlmNpFdicdOMl5h5byrrk7Uwf9HNRycvbxSf3vM+IeWMZueIZxjUdTCPf+iTmJDPjyEKOZZ1m3tCZ19z16dE2EziSaqDfkvFMaDaM2FqtyCzIYv6J5fx1Jo6fB3yPt0vVL5dZGaR4iKhyQgeOImX+f4l0dCCiUiiZuZCXQqBPc5aOnM8fhxYx6eBMUvNSCfQIZHiLIXzc+2PmHVzAv7d+TLYxh+bBzfjvPR/g51aDX/fO4PG411Gr1LQLu4PVY//kbGYCM+Pn8NW+KXjoPOgb0ZvXe7xJgLtjy3o6greLN/OHz2GRYSm/7J/HuZzz+Ln5MajZ/Xzd/H489Z7XbEOtUvNFr4+JO72eaXtn8sPBWbhqXenV+B5W3r2EWp7ytuz1kqQshHBqNuP/koK7zp3RLUcwuuWIEte91PE5Hooey4mzp2jZqEXR3PMnPd/nyMUjqFRqmgY0Qa1W0yywKb0a9SzRBhQWwsgqyKaGq2+xspzOLqsgixxTLv5ufjd8t++idWFo80EMbT7opvtXqVR0qX83XerffdNtCEnKQohqYNWJv/lm23ccTjXgqnZBWQ2Dmt3HwQuH2Xh2M2qVCkVRUKvV9Grci+/7flniNaADFw7y+ZavWX96I556D3LNedzb+B6eb/809XzrOmhk17Y1cTtfbZ3EjqRdeOo9MFryua9Jf55v/xQ1LxcDEVWH7KcshHBqVu9IrDlphXWwSzF59xReW/0fxkcMZu+I5WwftoTfe3/P6QvH2JKwlWk9PuPk2E2cGreZ6T2+wHD+IB1/7orNZitqY9PZLQyfN4b2/i3YPmwJ24ctYf2g3wnT+zNg1hCOpBoqa7g3ZIlhGY8ufpI+oXeze8RfbB+2hFX3zcLFqtBv1mCSsmRRZFUjSVkI4fRsyUeLqntd6UzGWT7f/BVz7/2W3vW7Fj2y9nfx5f32rzCscT/+TtyEWqVCrVJxZ0hblvb7FbM5n/c3/hcAs9XM08te4Ou73mJssyF46j0K23CrwbOtJ/Bi9CO8sPyVyhvsdco25fDyyleZ2uNzhob3xfXyI+taHoG8HvsMwxr14bW//+PgKMWNkqQsqiyp7HX7uLK615Wmxc9icKPe1L5qIVG+JR9vvQfPthrPwpMrybuipKa7zo3nWz3EjPjZAKw6+Td1PIO5s3bp+3QPadSHi7kX2Zey386jujV/nV5Bp5DYolrTV3uo+Qi2J+6Qu+UqRpKyqJLSQjvL+8q3GSUzt8Td8sELB7kzpO1VF4Ki2NBr9AR7BFHLPYAz2cVLKNxduz3pxnQA9qccokOtmDL71ag1dKgVw4FS7tQd6eilY3QILjtud50bLQObczj1SCVGJW6VJGVRJYXGln5XI6ovs67knrwuGj255rziBy+/UqtQWE4z12xEf0UVMCjcsEKtKvz1p9PoMFpLFr0odr3FiP7yDlTOQqfRYbQYy70mz2LERXN7vXdd1UlSFkJUWV0adGHJqdUljmvUGoyWAvZcPIBWraG+d/HSon+c+IsGNRoA0KNBF5ae+rvM7QmzTNlsSN5Opzod7D+AW9AhuD2LSxn7PxKykzmWcYqYkPL3QhbORZKyEKJquWJeeXCz+9h98SDLT8cVu8RD78m53BRe2/oJDzUfUXRXDLA/zcCk/VN5/e7CxVstakZSt0ZdPt39Y4lSk1ablYlbP+eeRj2c7vWiDsF3kGctYOqheSXOmawmXt/yCSOjhuOuc3dAdOJmyXvKQogqw5Z8FABN7eYAeOo9mTrwJ8bMf4gVZ9cxsGEvPLTu7Lq4n6/3/sqFvFRig1qy7fwerDYbi0+tYoZhAQ/FPEjvxr2K2v2u71cMnzeGvamHGBlxH6GewRzLOMW0I3/g5ebDlD4/OWS85dGoNUwdOJkR88aw8dxOhjXuS6CbP/vTjjD18O80Dozg5Y4vODpMcYMkKYsqLTV+OwEtZX75dlFUC5tUoLAkZlTNFqwdt5w5B37nywPTyM7LJjKkOdMH/0pWQTZvx73PnGNLUKlUNPBrwMIRc2kfdkexdgM9Alk2aiFLji7jt4MLSM1LI8QrmGc7PkP3Bl3L3W/Yker51mX12GX8cXgRvxz5g8yCLOr61uGtbv+hU92OxZ4QiKrBOf9NE+I6pIV2Jj4ujm6SlKut0zkprEuLJ0DvQ6+gNkVbLRpST3Dy0m4a+TWgsX8jarjV4PG2D/N424dLbPfXqU4HzmYmoFKpqOMTVmaCddG6MLjZ/Qxudv27GeWYctiWuAOdWke70Fj02sLFYFkFWZzLPo+Pq/c16z7bFBtnMxMwW83U8Qm7ZonMjPwMUnIukGvMI4xQPPQejGn5AGNaPnDdcRvNRhKzktBr9NTxCbvmhhOi8khSFlVWaGwsxsQ4R4chKsCWtENM2PU5WbZ8gtwCyDHn8OS+76jnEkA2uaSbPiPAzY9UYzoB7gG83fVNBjW7r1gbJquJL7d+y8x9s3HTuGLDhsVm5cHoMTzW5qFbuvtNz0vngT/GsSt5D36uPlhsVvIs+XQIa0eQRyBrT68j0M2f9PxLNPRrwHPtn6Zr/c7F2lAUhSl7Z/DTrp8pMOfjqnUloyCLoZGD+VeHZ0psBHEi/ST/3fQ5606vJ9DNnwu5qUTubsbzHZ7hzutchJaZn8lHGz9jweFF+Ln6kmc24u3qzWNtH2Z45BBJzk5AkrIQwqlsTD3IiJ0fMr7ZMJ6OGkctt0Bsio2ViRt4cdN7xATF8EPn93HTuZFnNjL72CKeWPosWQXZPNh6NFBYpWvs/IfQKSpm9vyS8MsrrQ+kGXh/x9fsO3+A7/t9dVOPdzPyM2jz4520q9mK9YPm0ci3HgA7U/bxyuYPiD+3l01DF+Hn5ovFZmHlmfW8uPwV/u+ul4s2fFAUhdf+nsjuxJ181vF1ooNaoFKpOJudxBd7fmbo3FHMGzoTj8vVxY6kGhg6dxQPNxvO+0Oew1vvRb4pnxUJ63lq6XO8020i/SJ6lxt3Zn4m988ZRmv/ZiwfMJ0Qz5ooisLW87uZuO1zTmWc5tVOL9/w5yHsSyYcRJWXGr/d0SEIO3po9xc83PwB3rvjJWq5BQKFWwO2qRnFX/2nsvfiQc7lXQAKC2RMaDacn7p+yKur38RiswAwc/9vWMz5/Nj1w6KEDBDpH8GUHp9xNv0US4/+dVPxPbbkGaL8I/il+ydFCRkgOiiShX0m465zZ+rhwhXRWrWW3vW7MuOer3hzzdtk5mcChZtIrD25llm9viamZlTRHWodr9p82ukNQt2C+G7n5KK2X175Ki+2foTHokbjrfcCCt9THtCwJ790/4RXVr1G3tXva1/l081f0cqvCR92/D9CLq8kV6lUtA+OYXavb5i3/w8OXCi9vrioPJKURZWWRgjxcXGODkPYyaHMM+TaCngmalyx4wU2E2qVmjDPEIY06sO0I/OLnb+nbmdCPIL4bkfhKunpe2fyZNRYNGpNiT70Gj2PRD7A9L0zbzg+m83GutPreTn6MTRX3GUrKCiAp86d51pNKPGaUmPf+nQJbc/cg4VxT907k/HNhuJVyl7FKpWKp1s+yMz42VhtVg5fPEJSZhJDGvcpNaYWAU2ICWrBYsOfZcZdYCng90PzearluFLP+7n6MrrJQKbexGci7EuSsqjSQgeOAuRuubpYcWEXYZ7BBLj6FTtuUazo1YVVudrViuZ4xuli59UqFXfVvoNtSTtRFAVD2jHuqFV20Yx2wdEcST16w/Fl5GeQbzURExRV/IRSWEhMpVLRoVYMlwoyS/zdO2q2Ltpt6mjaUWLLia+JX0MKLPlk5GdwJPUoMUFR5c6Bt6vZmsMXy97J6lzOeTx1HoR5hZTdRq3WTrsb1u1EkrKo8tIo+xeNqFp8tR7kWvJKFPFQoSo6lm3KuVw2s/g1WQXZuGldUalUuGhdyDblltlPtikXF+2Nl81017ujKDbyLWWX5cwy55R6h55tyikqeemicSHblFNmG2armQKrCRetC65aF7LNZY8FINucU+6qbTetK7nmXGyKrcxrskw5uGldy+1HVDxJykIIpzGyThcyCrLYcXFfseMuah35VhMAf5xYTs86d13OyYWJOceUx59n1vJ424cB6NmwGwtPLC+znwUnltOzYY8bjs9V60ptrxD+OHHVfLRKhULhAq7fji6huV/xnZsURWHByRX0Dr+nML5GPVhwYkWZ/fx1Zi0xIa3x1HvSsU579l48yIW81FKvtSk2Fp5cRa9G3ctsL8gjiFCfMNYlbi3zmgUnV3BPo55lnheVQ5KyEMJp6DV6Ij3CeHbDRNIKMoqOa1Qa9GotUw7P43jGKe5r0IN/ErLZZuaFjW9T2yuE6OBWADzaZgKT9k/jSPqJEn3suXCAGYYFTIgee1MxPtPuSd7a/kWxR+gqCu/m1ydtY7phPhPbFa+kNWnfFHQ6FzqGtQdgVNQwViVsIC5xS4n2E3PO8eHO73js8v9geLt4M7zFUF7e9D4F1oJi1yqKwse7vifYK5jWtVqVGbNKpeLJ2EeZuP1zUvIulji/7NQatqfEM6T59b+jLSqGvBIlhHAqi9u/RZu1T3PHvP481GwE7Wq15lJBJjMMC9iYvIMQz5rMPrqE+t6hnMxM4IeDs8g257Ll4biiNlrVasnELm8wbPkT9K/fg+5hd2JVrCw/E8eKs+v5qvenNPRrUHYQ5Xi0zQQOXjhE5/nDGBlxHz3rdMJkNbPg5HIWn1qNl86LHSnx5FsLuJCXxtzjS0ktyGDOkGlFq6wDPQL55b4fGL/wUTrUiqZ/gx64alzYkLyDuceW8q+OzxV7r/nVTi/x1LIXuGfhaEZH3E8Tv0YkZZ/nt+NLyVfMzBo85ZrvGPeP6MPpjDPcu2gMwxv3p0NwDDnmPBaeXMHuiweZNnAy3i7eN/WZCPtRXT13U9G2bdmiZKeW/himKkpMSCA0LOzaF1Zhzj7GxPkzaBYCkUNG3XwbTj5Ge6lK4/zp1DK+PL4Ik1K4e1NTz9p83fIJFpzbzG9JG8izGvF09WBs9EM8Gfto0UKoKyt6nc85z/T4OWxP3IFGraZ9WDtGRg0jwD3gluPblriDiXHvcir9NGqVmpbBUbzX9T9kFGQyPX42ZzMS8Hb15v6m/bm3UU90V20fCYWVv3478AdrT8VhtlqIqtWC0S1HUM+3bolrFUVhR/IuZu6bQ2JmEi6KnpExI+jZsFupbZflePoJpu2dxaGLh3HVutC9YTcGN7uvRLESZ3B1dbaqateuw7tiYmLaXM+1kpRvUVX6JXezqsIYjfP/S8vOnW+6DnZVGKM9VOY4k4ypXCjIwE/vRV13+++wpMk6gLZhCJraXYAAbIoNQ+pRTiaepn2TWPzc/K7ZRlVWXRJWearLGG8kKcvja1EtyAps57En4zifHl/A0dxkwjxrkZx7gdqufrzQ8H46+DezWz9W70jUyVtRBzZl6oFlTFr7NUqmETeThnOeeXSP6MF/er1BsFew3foUoqJJUhZC2M3W9MM8s/8HXm/7DP3qFT5WtdgsrEzYyAtbP+HtiJH0rBlj1z7fjZvM8jV/86/tzWiS6YfNaiPPxcr8g4fpm9CPPx9Zes1NIYRwFrL6WlQb54/eeDEIYT82xcarh6byaac3GdiwV9E8p1atpXfdzvzY9UPePDIDk81stz4P56QyZ9MiPoyLpWmmPyoKFzt5WfSMPdqUO3d58MGqD+3WnxAVTZKyqB5Cw0lJTnZ0FLe1relHcNd70jnkjlLPRwdGEl6jAatSdtutz5nHj9DrSAje5tIXOg060Yg/D/1JVkGW3foUoiJJUhbVQmhsLGmEcGDeDEeHcts6npNMmys2VyhNdFAUJ3LP2a1PQ46Rphe94fJGFFfzMbsQlO9OYlaS3foUoiJJUhbVR2j4ta8RFcZd68Kl/JI1n690KT8Td03Z5SBvlIfOlSytGUWxASVLSNpQyNQU4K5zt1ufQlQkScpCCLvoEtiS9cnbyCjjUXG+pYBlp9fQo2a03frs3aADf0dcBKul1LvlvX4XCPIPpq5PHbv1KURFkqQshLALf703A2q144WN71JwuU71Pyw2C/+3+SPa14iw6zvLvWvGcqG2jSV1z5Y4l+pi5Js7DvNsjxeuWe1KCGchr0QJIezmtYjh/Gv/T3Rf8AAjIu6joU9dErKTmXV0IbX1PkyKetKu/blodEy769+MtU1kU1o6XY/Wxs2k4XBwFn83PM8z3Z/nvib97NqnEBVJkrKoVlKSk4l0dBC3MZ1ay1ctHyc+8yS/J21kR8JWAvRevBf+AG1qhFfIHWtd95qs6fAYq/WpLEtIIj0jl5jwTqyOHkmYT9WvBiVuL5KURbURGhuLMTGOA/Nm3FIdbHHrorzr46LWcaEgA3+9N8286pSbkLPMeRzIOg1Ac++6+Og8bqg/tW9L+pi3cl+vsSRkhRcrzZiRn8GBC4cAaFmzBV4uXjc+oApkNBvZcz4ei81Ck4BwgjyCHB2ScCBJyqJaSQvtTE2bFBFxpE1pB/lg9wzSMtIJyfUgxS0PNx9PXm49gh5XVfPKteTzwf5ZLD67ifpZXqgUFSd9Mukd1p7XWozE6wZWTduMnlhz0op+zirI4s2//sPSA0tpmO2LgsIp7ywGtx7Mmz3ewE3nZrcx3wyz1czHmz5n5r451PcOw03ryv60I9xd7y7e6fqGJOfblCRlIYTdxF2M54UNX/PMlma0S2mBGhUKCrsDLvJqzvfktX+QAbU7AFBgNTN24wfU2JfPj/vvxK/AFYBL+gKmtDjC6Iz3mX33G7hd5ytUVu9ItKQDkGvKZeAvg6i7w8jPhzrhay5sO83FyE8Jaxhx/jDzxs69od2V7Mmm2Hh86bPkGbNY3O9n6njVBiDLlM33+2Zw3+yhLHngD/zd/R0Sn3AcWX0thLALq2Ll9R2T+b/1UXRICUZ9ueSlChUxqUG8vTaGt3ZPIf/yyuzfk9bD8Sz+tbNlUUIGqGFy4bldUbgdNzI3Yf0Nx+HqmsvUPTPwPZDJ0/EtihIygH+BGy/vaE3+gbPMP7zoFkd889aeWsfJtOP81O3DooQM4K334uU2j3NnrTZM2vGjw+ITjiNJWQhhF5vSDuGVDq3SA0s93zDbh4YXPFmZsguAWUdWMfhgvaLkfSUVKgYdqsfMIytuKAYlNwl3yzGmbf6VwYfrF9XCvpIaFfcfDGPKhp9vqG17mhE/m/HNhqHX6Es9/3DkA/y2fx6WMiqViepLkrKodqQGtmOczk2h8UXvcq9pdN6D03kpAJzNv0B4Zo0yrw3P8OVMwYUbisF6XgV5lziTk1B+21l+nM48c0Nt29PpjDNEBTQt83w971BAISM/o/KCEk5BkrKoVkJjYwFIjd/u4EhuP146Ny55mMq9JtPDgpe2cIGVu9qVSy75ZV6b4VKAp9q1zPOlsXpHYs1OwFPrToZLQdlt6/PxvMEV3vbkofcgzZhe5vk8sxGjJV/Kg96GJCmLaicttDPxcXGODuO20zWwFfFBaVzSl54MjRoLm+qmcE/NNgD0rdueFfUSymxvRd0E+tZpf1Ox9G9+DyvCyr4TXlkvkQGtB95U2/bQv0lffju2pMzzi06u5K66d0pSvg1JUhbVzj93y6Jy+eg8GN6wGx+134tRU3wu1Kyy8nFsPD3DYglxK1xRPK5hL1Y3TWFHYEqJtvb4X+Sv5sk82Ojem4rlsah2LIpKJr5GycffWwKTWd80jfFtx91U2/YwPHIwOy7sZ+7RpSXOHUo/xqd7fuSpOx53QGTC0eSVKCGE3bzcfDivmXKZ4LOO7sdCCMvy4LxnHivDz9E2rDnvtp5QdG2YeyCTO73EY+rPqH8+gfanAlABW+ulcSw4m+86/It6HrVuOIbsE0YatHNh8ujPeUT7Ik2SEog9XQObSmFzw3TOBpuZPmoGIV7Bdhz5jfF28WbOkGmMmT+BeceX0q9+d1w1rqxP3sb6pG38t+f7tAmx38YdouqQpCyqrdT47QS0lLvmyqRVa/go5hGOR/Tl96brOJqdSqBHbX6tO4Fm3iV3aoqu0Zj1937J0vPb2Jp8AEVRuD+kA/2C2133+8lXy9U3RMlN4s7wUex8YQfzDy9m27HNqFQqxjXpTL/w3rho7bd95M1q7N+I9eNXs/LE3/x9ai0Wq4W29drzcZ+P8XYpf8GcqL4kKYtqKY0Q4uPi6CZJ+YaZbGa2ph8hx2KkrntNmnvXveE2Qlx82Z19nOO55wizBvK02wAA8q0mtqUfIc9aQH2PWjTxCsNVo+eugBZ4a91RgFY+DcpNyCabiVln13LWeJH67rUYEdYZrVpLnqWAbZeOkJiZhDXbjaaAu86d7g064+9WA5VKRZuQaKdIyP/QaXT0Ce9Fn/Bejg5FOAlJyqJaCh04CuP8/zo6jCpFURR+Ov4nPx5ZQnCGKzXyXTjuk4lfDT/eaTuB1r6Nrqud9n8/y5nUJALyXKiT6Umi50maJo5D5+aCHx7UueSBj0nPEd9LBNUIxN/Nm90XjhKZ7ocKeNEvnbuDW/JO9ARq6N6v47MAACAASURBVD2LtT3xwDR+PbwM/2w9YVkeLPTO4XWvn2hZuwlJBek082uMu8aN7zYfpPbhHXi5BBF/fj9tarZEQeG5v16iZ6PuvNv1P3I3KpzSdSXliIiIO4CPDAZD56uOvwBMAC5ePvSowWAw2DVCIUSl+OjgHNbu2cRHm2MIyy3ctMGKjQ3ByYzP/ZBfOv+b1r4Ny22j7eonSUtJ5cO1bYg+74/68lrS/YHp/KfLbgpsOXy8pisAOVoTj3Rag//5XH423ImvrfBVqVytmenNjjIi+21+7/IWnpdfoXpp748s3r+Wj+JiaHGhBirU2LDyxr37sNRzYV63Hwj3rYfVaiWjIJ2eSyfQo04EXw+ah6+rDwCZBVl8uOtbRswbyx/DZ+OqvbFXroSoaNdcfR0REfEyMBko7d/eaGCMwWDofPmPJGQhqqCEvIvMObqa9+LaFiVkAA1qOp8L5ZGt4by3e1q5baTm/T97dx5eRXU+cPw7M3e/yc2+JyQsyWXfCSDIqrghKqi1lmrtYrW1q120WqvWbra2tb/a1rbazWoVBRdUFBVEkH1fb9izkX3P3Wfm98eFhJAEEkhys5zP8/g8ZWbumfdcaN7MnHPeU0thZQm/+GAyk0sSmhKyjs7o8hieem8q1VY/x2yhghir0/IZUhnJNzePRPc0z9a2B418dc9IEg9rvJS/BoAafwMv5q3m16tzGVsWh3S67by4eiqyDLw4/SmizFHoug7AS0ffZWbqFB7J/XaLGKPMDn4+/Yc4DDZe2b/8Er81Qeh6HVkSdRRob0HfJOBBp9O53ul0Pth1YQmC0JOW5X/MvGMpOAJtl32cfSqN/Kpijja0Xy1t8dbHyKqJYEx5bJvnB9dGMr4kjgdzNwLwbsZJFh/MwqIZCGoqqq41XSshsfjQYF5yrQbgd0eWM7I8mmHVUS3afH9UKUtH3kykYsWgSTSqoWIkLx9+m6+M+ixWgwV/0I92dtuSxFdG3caLe/7XgW9GEHrWBZOyy+V6DQi0c/p/wD3APGCm0+lc2IWxCYLQQ/JrSxhS2f4+wwZdJrPBQaGnov023BU4K6PPe58RFVGU2zwAlFrdDKkObdeoILVInABD66Io8oe2YjzaUIyzPKpVe2WxAUbGhMa6DZpMUNfQdZ3CxlOMjBmGLEkosoymtWx7RGw2hXVF541VEMLhoid6OZ1OCfi9y+WqPf3nt4EJQOvV8GcJBoMUFrRfxaev8fv9/ao/bemrfayri+DT5/7EoAXXX/Baf6Bv9rGz2uunIQDlFjeqqrb5OR2dMmMj3qp6Cr1tf09WjJTZPee9f4ndgzWooKoq9oCRSqsXe8CAio6maah68/3LzI3YdTOFBQWY/BJlER5Ab9FehFum1Bv6RUGVdBQ99CQcaYygxFNBqj0JTdPQNR2V5raL60uxylYKCgrPG29v5vf7+3T8HTEQ+niuS5l97QD2OZ3OEUAjoafl5y94Q4OB9IyMS7ht71JYUNCv+tOWPtvHL3wNz/InOxR7n+1jJ7XXz89FXs03in7DbUdzUNp4gXYgugo9xsSVOdORpbZfsD1r/hafqXuMMpuHRLe11fk6o5+Ps0r40fbJKIrC3FPprBpWyBd35SDLEmaDEc7a1em9YYXcNHQW6RkZPBC9lHlF36bG7Cfa17yk6fIDsby4fwU3ZVxJQNGIMlpB07lh8BW8lPcW9429A0WWMRpb7pu87Ojb3DJ2CRkZ6R396nqdgoLCPh1/R/SXPpaVHezwtZ0us+l0Om93Op13n35C/hGwBvgE2O9yud7pbHuC0J0qSRWbU3TA+KihDEnN5A8T9xKUWr7qLbW6+c1le/jWmFvaTcgAsxLHYjAaeHjeduqMzRtTSEh4lCCPzN2BrMOVpaF1zzecHMJHQ07x4eBi7AYrZyfkT5NO8dGIMu4aFlq/mxOZxui4ITwydzuNxubRtKlFiVQXFvOE668okoxyOr4vjbiVfx1cxjsn1mA3mIDmPr1x9H3ey1/HneNuv+jvSxC6S4eelF0u1wlg2un//eJZx/8D/KdbIhMEocdIksQz077Ft+Q/clfax8zPSybaa+JoYgMbM8r49thbWZJx+QXbcV3/D4a9cSe33PoRC46mkVUTQXGkm3eyC/AZVAYRw7+dh3B4jRxKrscfrfDPefmsqali2tE4JCQ2D6mkLCHIczN+SLq1eW/m1+f8lOu0B7kl9kOuOpJGem0EBdENHDGWU5y3gk9KNnPT0GuINNrZVrYbb8DNjz/9Fa/kvcoVmXNRkVl18mMqfTW8ePM/SYpI6s6vVBAuiigeIvR7JXl5otxmB0QabTw/4wfsrzvJytGbaPC5yY1K4RdpM4g1tT8J7Gw2o43im5fxzJE3+Zn9v+BT0U0y33Qu4cHht7G79hjvjt5Mg9/L7Oh0fpd2GXbFwgflO9lUuh8d+GriVVyZOBGj3PLHk8Vg4sMFT7Gx8iC/y3yVIw01JETEsXzEPUyOzmFHzRFWl+3geG0Vuck5/Gz277EoJj44sYIdjQeQLVncd9nXuWLIPAyy+NEn9E7iX6bQr6UvXkrp8icZHe5AekiJt5pNVQcJ6iqjHVkMj+z8OPkoR2aHS2tqmsZrxevZVHUIu8HMnYMWMDQiha8PW8TXhy1qdf1gWzJjYobQqHoZak/FYbAhSRJRBjtuKfRaOtpoxygb0HWdXbVHOdxQhE0xc3n8GKKMdqbHjWD6ZT9u1fakmGwmxWS3GjdfGD+CJePGQNS8Tn8XF0PTNTYWbCa/toBIcyRzs2ZhN4Vv72ahbxFJWej3zowr9+en5fqAm4d3PsdHRTuZVBqPSZX5VVIlWXFp/GbqvWTauv5V7VunNvPdT/8PY6PGuNJYGkxBnk9eSU50Bq/PfQKHqXkv4KCm8uT+//G/Yx8xqjwGh9fIM/E1EGWi1F+D1+1hcnECEvC51NWYbBaSTdFodX5GlkdTbwnwo/i/cvOQOTw4+vZWT9EXojZUokRVAPFd+h2ca83xj3now59gkU2MiRtOmaeSH7z/I7408Qt8Z/o3zjsmLwggkrIg9HkBLchdG35F4i4//9k9B5sammkckDTezjrBre7HeH3+E6RY2i7qcTE+LNvJvZ/8hvs3jObKY2lN1btqzD5+fdkeZvm/xY7rnkWWQ8cf2PFXju9y8dfNM4n1hYoDBnWV92KO8kxuCb9cM4WxZaF9lg/EV/HA/K1cvy2GayuHYpBCP6aqTT5+m7uL+721PD3lPiRJaiOy1lTHaJTGvRAoBWP3JeVPTm7gW+/cz9OzHmVG6pSm+IoaSrhv7Y+p9zXw6NyHuu3+Qv8gfm0ThD7unZItBE7U8M0dY5oSMoBRl7nx+BBm743jL663uvSeD25+li/uyOGqYxlNCRkg2mfm0bUTocLL30+sAmBf3QnWHd/BT9ZPakrIAPUBD9MLE7lvyyheGn206fiLo49xz7YRXJ6fTH2ged1zjN/Mjz+dyLYT+9hde6xT8aolErhLL7a7F6TrOo+ueYJfzniAmWm5LX5hSItI5p9XPsWy/a9SUDuw1twKnSeSsiD0cS/nfciiAxnItP3kuOhYFitOriOotV0YpLMK3OUUuytZeLjt8WqjrrDkQBb/OPA2AMuOf8zVrjQsWssXc341gDVoYN7xFI5H11Nid1Np9ZIXV8P846lYggp+NdjiMyZN4ZpDabxybE2X9KWr7C8/QKO/kfkZM9s8H2V2cOPQq3l5/2s9HJnQ14ikLAwIJXl54Q6h25xyVzKoof1tCBO9NvSg1lQX+lLlNRQS5TMR4W+7TjbA4JoI6r0NABTXl5FZF9HqGh0dRZMw6DIp9TYqrT4qrF6SGq2YVQWDJqGfU8ELILMuguL68lbHL0RtqOz0ZzqquP4Uw6KzzjtmnBM9mOL69muHCwKIpCwMBOk5lBb33x+GMaZIyqzuds/XGf2oCtgUc7vXdEaGNZE6kx+fEmz3mhK7B4sx9Ko61hpFqa11+U0JCU3SUSWdCpsXh99IlM9EpdVHUNJQJb3NZ/9Sq4dYW+s62OejOkajNxZBYH+nPtdRsdZYihpONe1S1ZaihhJirV03ri/0TyIpC/1eem5o1nV/rex1U/Zs3slpf6xyVeZJrkmd0ukZy+3JiUwjxhzJh1lt/6Kjo7Fi5Elucs4JxTf4ct4fXoxKy0phRkXBa1DZllpOtNdMep2d5EYbSQ1WNqWX4TWorWLW0Fk1opjFg2d1Om61REItO9Dpz3XExJTxeFQfO8r2tnner/pZdvhtloy4oVvuL/QfIikLA0Jl+px++wp7cdpMirNUXs4+jHbO694tCSUsH1fAPV2cDH4w6XP8ceoB9iZUtTgelFSemXKQsvgA3xl2EwBTY4aTnprO05P2EjirhKfDYCMvrpbfTN/L0r1DkU4/Fy/dO4zfT93PofgaIo3Ny6oCksYfx+8lPi2Jy+JGdjpm1dF9q9VlSeb7M77Lt9Y9xvHalht2eIM+vvnxT8jNyGVEwvBui0HoH8SSKEHo4+wGCy/OepivGX/PeznrmHk0AVNQZmdWDRXxKn+b/gOyI9K69J5LB82nzFvD/crLOCscTCmMp9EU5L1hhZgirKy64tfYDKHX15Ik8ZfLvsv9hj9xZ9oaZh1LwuE14kppYHdCBTXBAP839QD7j1UjIbFm8CmqIwL88rpDjKkoZ0RxJPXmIOuGljI2JYe/5X69V673XTLyRhoDbm5Y+SUuS5nE6LgcSt2VrDz+AXOHzOE3C34R7hCFPkAkZWHAKC0u7reVvVKscSyf+zi7ao/ycfkegprKN6KHMC9hPAZZ6ZZ7fjdnCXcPuYYn85axq/IIZqOdpzJv4fqUqa2ujTBYefay+znSUMyq0m24Ax5ujkzj+eQpmCUjfz3xDu85t6Gj84XkJdwz+DqCusa7pVs5UldEvMHMV5MmkRN5aTsGNY0rG0ddUjvtuWPc7SwesYg3Dq3kRE0+GQlDeXvGfWRGD+qW+wn9j0jKwoCQnpuLp3At+5a9wOhbloY7nFZ0XWdnzRH21B1HRuby+NEMtid3qg1JkpgQPYwJ0cNaHFdVlUcPvcAnFXvRAyrfkW/hxrTLaAi6+d3hFRx3l5BgiuKbQ28kzRbPkYYi/nTsLWoCjYyMzOS+IYuwGEx8ULaDVwvXo6JyZcJEbk67HJti4eqkKQy2JWOSjUw6fW+v6ufDsp2U+KqJMzm4InECEQYrDqONeJMDt2IizhSJSTYgSzL3DFnIPUMWtojbANyUOgNSL+mrbfldlEhI9gMoad2TlAEiTBF8buxt3da+0L+JpCwMGJXpc0jSet+4squ+kO9s+j/qq2qZWBhHwKDz+/T/MT4ph9/k3tvhzSDa8vvDy/n1jheJc5uZUpSAxxjkm+W/4x7DUyi6jLMiiuxKBwcjD5N7cBUWoxmv38e0okTi3GZeT9jP73a9jEkxIntVZuYnY9RkHs3YygP2Z4m1OIiqVRhzKhqPWeXJ1BfIiEqmsKGMnIoo0mqslDq8PJL4d7IiUzhee4rcUwk4PEZeTarjoVidX+Tezaz4MV34jbavqboX3V9yUxAuhkjKghBGhZ5ylq59gjs2ZnFl4bimAiCBHSr/HOViqfdnLJ/7OBal/TXB7fnvyQ95csd/efCTccw9kdJUeeutYfn8e/xhHl43nrHlcU0TrI5F1fKLmbuZcCqZr+0IPUm6DQHuuXY9U4sS+fyeYTgCoWVV920ZyXLncZaNOs5vP5lHsj+0Drlab+S3Y3eRFKHw+MZJyITWGj80eSNevYI/b59KIs1rqnfGlfNt39P8Zfb3yI0Vk6AEoffNlhCEAeQvrje5cm8iVxVmtqjIZdQVvrxvBLaTPt46temi2v7J9uf5wq5s5p9ork0dkFReGnuUJz6aRFZtJH4lVOXLr6hEeU08uTqXj4acosoSKjSyenAR2VVRfGWHk4CiwenZ3T5F5UZXJguOprEs8zAQegUf9AV4cMM4/KhsSwiVtTwUXU2BrZ6frpkMXg1Nb56BPaEyga9ucvLkrpcuqo8XLdB9JTcF4VKIpCwIYRLUVN7I38D1x7PaPC8hsehgBq+4Pux020WeChoDXq53tdyCcUdKJQmNFpxV0ViCCj45lJQ9ShCLqhDjMzMjP5E1macAWD20iOvzMjBqMpIu4VM0NEknIGuYVYXr8wbx0aDQGmmfFkDRJEyqwnV5Gbyflh9qIzWfaw6nY1YVTKqMTwu0iGlmSSonqos42Y21qc+m1zZ223plQbhUIikLA0pvquzlVn3oqk6cz9ruNWmNEZR5qzvd9qH6AqxBA1HnlMKstPlIqw/t7atooYpaAJqko2ihHwfpdXaqrD4Aqi0+0uoikJBQdAlV0tAlHVkP/dKQ0mCjwRjEL6lop8tmAqTV2agyh562Ky1e0upC641ljRZPyhDaOCPZa6fcV9vpfl6MgHFaaBY2FT1yP0HoDJGUhQGjt1X2silmkKWm5NWWYlsj8ZboTredE5GOxxCkzuhvcTzGY6I4MlSSU5V1ZD2URGVdQj2doIsj3UR7Q8k82muiOLIRnVA5TEUPPTFrUqh2dandgy2gYNIVZCRUOdRGSYSHaF9o/DnGZ6bYEbqnJtNqjXFQ0ig1u4k3tV+/WxAGCpGUhQGlMn0Ou9euDXcYABhkhYUZ03k760Sb53V0Vg4v4JacuZ1uO8OWgM1gYWVOy+pSk4vjKbV7OBJTi1dRMWmhNcxW1YDXoFJv9LN+UCnzTqYAcMWxNN7OKSAgh56QzaqMrEsYNRmforEyp4B5BaG1w2bZiCrrBCSVt535LCgOrc29smgQq4YV4pdV/IqGWTa2iOnTpFOkxyST1cklYJdMjCsLvZBIysKAcuZpube4d/gi3h1bwpqUwhY7IgUkjX+NcFGTZeCG1Msuqu2HJ97B8xPyWDfoFNrputNGXeGze4bw8LztFEU2YlZDSdmkKjSY/Hz/yi3MPpFMnCf0Sn3B8TQOxNfwr3GHMaoynJ6MZlEV3snO591hBXzmpBMIrZM2moz8+rK9yJLMlLIkAEbWxJLstfPY7B1IZqXFk/L+6Er+PM3F98d/9qL6eLHEuLLQW4klUYIQRpm2JP49+yG+aXqa/1UdZ1J+LAGDzqeZZeQkZPLCtO9ivcjdne4afBUl/moel14lucHK9IJE3MYga7NO4TapfOu6TYwpjSWn0kFRpJtN6eUYDQaOxeVTY/MT67ZwILGGEoeH5eMKeNtZyOwToXXKn2SWUm8PEmWO4BezdzOmMJpGS5BPM8pIcMRyyl3PEzN3klZlpSzax+EUN2m2BL6WtYnphUk43AqHUhoojfPxZO7XLqqW9aUIGKdhatzbrdW9BOFiiKQsCGE20jGI1Qt+w6aqg+ypPY5BVrg3bhTDIzMuue0Hnbdx/7DFPLD/H2waehA9oPFEzlf5XOZ8qvx1PJX3GifcpaSZHKzPXsxgezL7ak/wzLG3qA40MidyPG9mLybCYOPN4o0sL96AT9f4XsLVfH7QfHRJZ13FPlz1BVgUEz9IGEemLYmGoIf3S7dT6qthsimSp5MmE2W0c8pTyeqynbhVL/PtKcxLGNdlu1d1ll7bGJb7CsL5iKQsCL2AJElMjxvJ9Et8YtxXd4JPKvYR1FXGOLKYFT8GRVa4LjmXLFsS7tp6JsXmABBrcvCz0Xe1aiPGFMGUmGzqgx6ybEkYpNCPiUWp01mUOr3FtQEtiP/0f7IkE9BCS6wiDFYWp81s1XaKNY47Mq9ocUzXdbZV57Gl2oWOzpQYJ7kxTiSprd2UBaF/E0lZGJAqdm8hflzvGl++FKXear6x6Q/klxcx41giRlVi5aAPuD82gKRBUrWJsfnReAwBPn98Hc7ELJ6e9g3izprx7FMDPLzzOd7P38LM/CSiG4x8mtLIY4n/5JGJX+DGtJZj2xsq93P/pmdIrDAxutCB2xzkr1nLGZeSw29zv06U0X7BuE+6S/nap7+jrqKG6cdDZS9fHfwelrgInpn+bYZGdGHh67a4SyFKvL4Weg+RlIUBp5JUSvLy+k1Sdgd9LF33M6Zti+CxQ7NRTs/fPFpUw3emreO+LaOYV5OFQVJQVZW7D0j8a6SLO/y/YMW8xzGdng19/9Y/UbuzgH9vmYtVPf2jIQ+ORdbyiPcf2GaZWZA0CYCdNUf5xrrf8cC6sYyvTGiK5St7Nf469gBf9P+Kl2f/5Lw7VFX46rht7eMs2ZTG9SfGNpX7/NJBnVWD8rnd/wRvzv8ZSZaY7vjaCBinITdUotjEuLLQe4jZ18KAk754aa8qInKpXi/eQPxJnc8fcjYlZIAXh7r4/O5sphcm4g40r4U26DJf3D8cc76Xd0u2ArC/7iRbC/bzwKbxzQn5tCH1Udz/6Rh+vfNFdD00Q/zpvcu4c+vQFgkZQoVA7t09CndhNWsqdp837hdOfMCEPAeLTgxuSsgQKkpyTX4m0w7F8O/jqy/uS+kgrThPzMIWehWRlAWhj1t+eC3XHmq5z7BHCbI1oYwrj6VhVhW8mr/FkisJiWsPpfHq4TUAvJ6/ngV5KRj1tp9sx1fG461tZF/dCSr9dWyvcDGvuO2JaDIS1x5MY/mRteeNe8XRj1l4pP19hhceHcRrR8/fxqVqqu4V2N+t9xGEjhJJWRD6uEpfHcmeluO3DcYA1qBCRMAYqtql0/SUe0ay20aFN1TasryxmqQGW7v3kJBI9tip9NdR7W8gJmDBrLX/ajrJbaPCXXP+uIP1JLvbH3dOdtupUhvO20ZX0GsbQ2PLgtALiKQsDEiVpLJv2QvhDqNLJFljKLTXtzgW6TfiNajUmfyh+taS1Go2c0FEAym2OABSIuIpiGp/iZCGTpG9gWRLLPFmB9VGHx4l2O71BRENJEfEnTfuRGMUBRH17Z4viKgnydj5EqOdpXkiuv0egtBRIikLA1J/Gle+NWc+b40oaPF62qIZmFGayts5BXiVIFbF1GLcVkNn5chCbs2ZD8DNmbP4ILu43US7ObGE2OhYnBHpRBsjmJE0mlUZJ9u8NihpvDOyiFuHzT9/3NnzecPZdhsAb+Sc5DPD5p23DUHob0RSFoQ+bmHKVLSsCP40bj9euTmp3nYkm1dGHWP10CIshubdojxKkKcn7sE+KI4rEiYAMDQilQWDp/HYzO1UmVpukLErtpynLzvAgxOXNj1tf3vMLbw8KZ+PU4pa/DLQYAjwmym7SRuUzowLrLm+PXMex4cFeMHpIiA17xwVkDT+l32Yg9kePpd1xXla6BqqYzRqQ6UYVxZ6BbEkShD6OJNs5F+XP8gD1mf5/OA15J5KxBiU2ZlSSXpMKquvbODtmg2MK4nFLQfYnl7JnNTxPD/pKy2WLP10/F382vQyd8d/wNjSOKLdRo4k1NMQA09N+QYz4pqXDQ2PzOD52T/kB5Y/80L1UcaUxNBoDrItuYKrM3J5fMJdrXaDOpfDaON/sx/hfuufuMO5hsmn4pGQ2JZSTk5CFi/nPkKMqWdeLWvFeSgRcWLNshB2IikLQj8QZbTz5+nfpdBTzobKAwQ1lXuiBjM2ajC6rrOr9ij7607SUF3Hz3NmkWJtPd5rkBUeHH07X3PewJry3dQHPdxqS2RG3EgUqfWkrvHRQ3lvwa/ZXnOYQ6fLbP4ybnSn1hUnWWJ4YdZDHGkoZmu1Cx34bnQ2OZHpF/xsVxLjykJvIZKyMKAVeyp5s3gjx0ryGRbI4obU6d1WrKIrHW8sYWXxJmp9DWREJnFD6nSiDHYKPRWcbChBVVWijXZGRGZglA1MiB7GhOhhFEoFbSbks0UZ7dzYwZ2pJElickwOk2NyLqk/wyJSGdbd1bsEoQ8QSVkYkFRd5QXHSba+8U3mFmeSWGNiV2wBf8x8laU5C/j+yM/0ytrLPjXAD7c/y7qCXcw5lkRso5lP4vfyZPp/MRvNRNUpzDgSj1lV+HvWVh5P+CdPT/8m02JHhDv0Xu3MuLKo7iWEm0jKwoD034IXKfHC31fNINYcg6qqKCcU7trr45HZ6zErRr41fEm4w2zle9v+TO2OfP61eU7TOmHtqE7e1jIen7WD6486WVg4BIDPHIOdceXcG3yKl+b9pEt2nerPxLiy0BuI2dfCgFMTqOXjkjU8sjkXe8CIFvA3nYsKmHl4/USed71DfcAdxihbO9xQxMaCPfxg8/gWhTu8qp+kBgs/WTuRF7JdBM+ayTyhMoGbd2byl4NvhiPkPiVgnBaahS0IYSSSsjDgbK7bxtSiRCIDJrQ2/i+Q4LUyqiyGj8p3hSG69r1VuJF5R1IwnVNJy6v6sAQVhtY4iHOb2RvbMrFcnT+I905tJaC1X+xDCNEbi4CKcIchDGAiKQsDTkOwgYQ643mvSag3UxNov8JVOFR760hotLQ6ruk68unCIAluC/VGf4vzkUETBlXCrfp6JE5BEC6eSMrCgBNviuNEvCf0B8VAwOdvdc2JuEZSLzBLuaelRiRwMq71LwqKJKNKOjo6J6IaSPRYW5wvtbqRDQp2pXVCF1rSaxuhdk+4wxAGMJGUhQEn1zGZfUk1FNkbUEyhSld6MNB0/rCjhuI4L3Pix4YrxDYtTp/Jx5klVJtaPvFaDWa8BpUtqWUYUXDWtlzStWLYMZYMnn3evY2FkOZxZfEKWwgPkZSFAceqWPhM5m08MmcbRx01LcaVD0RX8djsHTw04Q6Mcu9anJBkieGu4dfy0JytFNqbd08yKQZ2p1Tx88t3c8fh4U01rgOSyqtDj7BxVA1fzV4YrrD7nNC4siCER+/6qSMIPWRBwhUYJSOP2P5HfKlKutdOSXyQhmidRyZ8iYWp08IdYpu+M3wJEUYr34t6g0FVNuLcFo5H16FFm5jiGMPTEQf4qLwUoyqxN6EKZ3wWr0x5tE8URBEEQSRlYQCbGz+by+NmsPbdPxA73MjEyfOZGutss6RkbyFJEncPu447By9gfeU+6oMe0q3xVkAFAAAAIABJREFUTIrORpIkKnx1bK46iKprPBKVxRB7SrhD7nOaxpWjxA5VQs8TSVkY0AySgeHeRMYaYhl+gV2N2nOovoAn9v+XgpoSrCYLd2ZfxWfSZiPLrUeHglqQZ469xcoTGwgEVUYlDuHhEbe3W/qyxFvNawWfkF97imhrJAvTpzMmajBmxcj8xAmtro83O7guZWqLY/UBN28Ub2RfxTH8Hi+LLLOYFT+GU94qXiv4hKK6MmJtUdyQMUMUGCFUB1ttqESJqgDiwx2OMMCIpCwIwOEtWxg+/9pOf+7OjU/yYf5W5h5P4eqyaKptPp4o/DtPOP7NqgVPkmFLaLp2c+UhPrv2ceJqjFxzOB1LQGFr2kEmHbmHe0ffwI9HLm26Vtd1/uBawXMHVzL7RDJDKiKoshVzd/bHjEwbxtNT7yPCYG0rpBZWlWzlgS3PMq44hrGFMbhlPz8/8Tfuc3iQgirzj6eRVRVBmb2Iz+d8SG76aJ6aci8WxXTBtvsr1TEauXgTSuJIMIqkLPSsDiVlp9M5FfiVy+Wac87x64FHgCDwvMvl+luXRygI3Sx98VIqX3iUit1biB+X2+HPfW/ns+x07eGFd+eQ6G5OkHfszub30/ZzNd9n76LnkWWZCl8dt655lC9uGcbNB7OQTk8uuzEvi7zYGr4TfItBtiTuzLoSgH8ff583t3/AX9dcTqy/eSnTZ/NyeHriHr7FH3luxvfPG9+26jx+9Omz/OyjSWTXRQOgqiqqAmsS83lo/SQy5bimGt+fczn5de4ufig/y9O53+jw9yAIQte54Oxrp9P5A+DvgOWc40bgd8ACYDZwt9PpTO6OIAWhuxXE5lKSl9fh64NakGVH1vDwuvEtEjKAjMy3N41Crg3y34KPAHji4AuMKYriloNDmhLyGTlV0Xx96wh+u+t/AAS0IM8ceJ0fbhjXIiEDGHSZb+4Yy77iw+yvO3neGJ/Zt5wvbBvWlJABvEqQ17KO8JOPJxLlNeLVmtdoG3WZ720dxycFuznRWNLh76LfcpeGOwJhAOrIkqijwOI2jo8AjrhcrmqXy+UH1gOXd2VwgtBbLS/aQHSjgVHl0W2el5G54eAg/n14FQAfHt3K9a5B7bY370QqFb5aitwVbK3OI77GSFaDo81rjbrM/LxkVhZubLe9+oCbLRWHmFvccl/infEVDKmOJLnRhllV8AZbFk4xaQqzjyWx8tSWdtseCM6MK4v1ykJPu+Dra5fL9ZrT6cxq45QDqD3rz/VA1IXaCwaDFBYUdDjA3s7v9/er/rRlIPQxGAhQV1fX4X4eLj1JrMd8ek2w3uY1sR4TtQ2VFBYU4A36iPOY273WElSwBg3szT9ERbCeqEYjqqq2e/9ot5GiipJ24y0L1GIOyBgCoNLcTr3RT6zHBOjIuoSmq63uE1NvpKi8mEJz3/w79we64t9rFHEHt2GRrVQFx3dJXF3N7/dTUFAY7jC61UDo47kuZaJXHRB51p8jgZoL3tBgID2j/8zwLCwo6Ff9actA6GPF3r04HI4O93O2dSLP5b1NQNIw6m0voXLF15ERl0J6RgYxNgeHY+oYWRHb5rXlVg8eY5DLhkyk0FvBnw68jqTITTWtz3U8yc34tAntxpuoJRPcK1Ft8xPva369nuq289rgenQgKGkosoKitIz/WIqbK9Ky++zfeVf9e1XqajFoHjIyLPTGWdgFBYVkZKRf+MI+rL/0sazsYIevvZSKXgeBbKfTGet0Ok3ALKD992mC0I/MjB+N1WJl9dC2qz9VW3ysGlbIA6M/C8CdI6/llTHH8cttP/0uG3kcZ/QgHCYbIyIziI2JZX1ycZvXVpg9bBhUyk3pM9uNzyQbuSFzBiuGHWtxfFRVLKoBtqWU4zOqWA3mFueLbY3sSK1kUcr0dtseKFTHaLTiPFELW+hRnU7KTqfzdqfTebfL5QoA3wXeI5SMn3e5XKI+ndAnxY8ZQ2lxMRW7Oz6W+tOpX+bpaft5d2g+Qak52R6NqeXbV21iYupwpsQ4Afjq4GtREmw8NH8bJfbmfZo9hiD/GXOYN0bl8/TU0IxnSZJ4bPIXeeayQ6xNKUSleX/kI44afjR3K/eOuolEc9vj2WfcN/wmNoyp4aXsPLxyaNtGCYmlR5z8dPYutqdVYTyrHvbB6CoenrOV7429DYfR1uHvoT/TPBHhDkEYYCRdb3uMq7ts3rhRr6/oP5MnBsKr3YHSR7Z+zMhUGH3L0gt/4LTXitbz0Ka/EvT6GVbtoNrip9jh5urMqTw75TstCoi4g15uXfc4OysOM7Q6EmvAwKG4GmJtDv4+6wdMislp0fb26sM8vv2flFaXM6Quikqrl9oolW+OWsLtWfM7FF+xp5If73iObaWHGFETS6PkJz/OzWUpYzhRXURdTR2Z9RGU2jz4omS+M+ZWlmT07fmaXfnvVanbh3ncmF5Z3au/vNo9n/7Sx+3bD26fNGnS5I5cK4qHCMIZ6TmgdXxZFMCStJksWTKTD8p2sLPmKLGmCD6bPhebofU2iTaDhZXzfk6Zt4ZlRevwqH5+njC2VTI+Y1JMNm9c8TMO1RdQ6KnAYbAyMTq7U7s9pVrjeG7GDyjyVHCovoCaiiquzpmB3WBB13UO1OdzyltFjDGC8dFDenWJ0XAR1b2EniSSsiB0gSsSJ3JF4sQOXZtoiebrQxd1uO3hkRmXXP4yzRpPmjWeQl8B9tO/MEiSxChHJqMcmZfUdn/WVN0rIq5XPi0L/Y/YulEQTkvPzaW0uO3JVcLAJcaVhZ4kkrIgnKWSVPYteyHcYQiCMECJpCwIZ0lfvFQ8LQutiOpeQk8RSVkQBOE8VMdo9MYisV5Z6BEiKQuCIFyAWiKdfloWhO4lkrIgCMIFqI7R4Q5BGCBEUhYEQegwMa4sdC+RlAWhDWIGtnAuMa4s9ASRlAXhHJXpc8QMbKGV5nFl8bQsdB+RlAXhHOm5ueEOQeiFmmZhC0I3EklZEARBEHoJkZQFoR1iXFloU6A03BEI/ZhIyoLQBjGuLLRFLZFQyw4gxpWF7iKSsiC0QYwrC20R48pCdxNJWRAEQRB6CZGUBUEQOkuMKwvdRCRlQRCEThDjykJ3EklZEM6jYveWcIcg9DJN48riaVnoBiIpC0I7Kkll99q14Q5D6IX02sZwhyD0UyIpC0I70hcvBcTTsiAIPUckZUE4j0pSwx2C0AtpnojT48qC0LVEUhYEQeik5nHl/eEORehnRFIWBEG4CGIWttAdRFIWBEG4CGIWttAdRFIWhAsoycsLdwhCL6WWSOAWSVnoOiIpC8J5pC9eSmlxsZiBLQhCjxBJWRAuQMzAFs5HbagMdwhCPyKSsiAIwkUSs7CFriaSsiB0gBhXFtojxpWFriSSsiBcgBhXFgShp4ikLAgdUEmqeFoW2iXGlYWuIpKyIHREek64IxB6KTGuLHQlQ7gDEC5ehb+S98s/YkPZZoJ6kOGObBamXk22bWi4QxOEAUUtkZDsB1DSRoU7FKGPE0m5j9pdv4+fH3wKdb8RKc+CFJRZn76HTydt4cas6/hc+q3hDlEQBgzVMRoDVeEOQ+gHRFLugyoDVfzi4FNor0diKrM2HTdUm9HyVFYsfofBEZlcFj01jFEKgiAInSXGlPug98s/JHjAgPGshHyG7FPgEzsvn1wRhsj6t9Li4nCHIPRiYlxZ6AoiKfdBn5ZuRcprnZDPMBbZKfAU0hBs6MGo+rf03FwA9i17IcyRCL2VXtso9lgWLplIyn1QUA8iqVK75yVdQtZkgrrag1H1f5Xpc8IdgtCLBYzTQk/LYitH4RKIpNwHDY/KRk3ztns+GOvFZrIRaYjowagEQRCESyWSch90fcrVyJO8aJZgq3M6OurUBm5IvwZFUsIQXf8mxpWFCxL7KwuXQCTlPmiIbTBLshYRXFKJP6MBXdKB0BNy4JpKcoYP4vrEa8McZf8jxpWFCxHjysKlEkui+qjb0pYwOGIQL8et4IQnH0mTiTTZWZR2IwsTr8YkG8MdYr9UmT4HCtcyOtyBCL1SwDgNU+NeQuPK8eEOR+iDRFLuw6ZGTWHq2Ck0qm5UXSVCsSNL4uVHd0rPzcVTuDbcYQiC0E+JpNwP2BVbiz/vazjAG0XvkFd/BEVSyI2bxPXJV5NmSQ1ThIIwwARKwSielIXOE0m5H9F1nX8UvMC7xz9E3WrGWGRDV3RWD93ERxPW8e3h94oqX4LQzfTaxtD+ylGiDrbQeRdMyk6nUwb+BIwDfMCXXS7XkbPO/wGYAdSfPnSDy+Wq7YZYhQtYX7ORd/I+wvBaPMZA88xrw3YzwWM+fr/kzwyZkEWyOSmMUQpC/xYwTkNuqESx7QejSMxC53RkAPJGwOJyuaYDDwBPnXN+InCVy+Wac/o/kZDDZNnJ12G9HTnQeimUodqMutfEu6WrwxBZ/1Oxe0u4QxB6Ma04T8zCFi5KR5LyTGAVgMvl2gRMPnPi9FN0NvBXp9O5wel0frFbohQuyK26KfQVYyyytXuNcsTK5ortPRhV/1SZPofda9eGOwyhF2uq7iVqYQud1JExZQdw9tOv6nQ6DS6XKwjYgf8DfgsowBqn07nN5XLtaa+xYDBIYUHBpcTcq/j9/l7RH7fmQVM11KCKRNslOLWAhs8f6HS8vaWP3alTfUxJwZ3n7pPfiT8wAP4ue0kf46ynMMTVUucu7Jb2/X4/BQXd03ZvMRD6eK6OJOU6IPKsP8unEzKAG3ja5XK5AZxO50eExp7bTcoGg4H0jIyLDLf3KSwo6BX90XWd+Mo4alMCGNrYPQogmOVnQsKETsfbW/rYnTrbR4/N1ie/E/F32XOMgSKMjiii4tK7pf2CgkIyMrqn7d6iv/SxrOxgh6/tyOvrDcC1AE6ncxqw96xzOcB6p9OpOJ1OI6FX3Ts6HqrQVSRJ4qb0hejTGtBlvdV5zRpEnuTl+tRrwhCdIAxQblFyU+icjjwprwCudDqdnwIScJfT6fwucMTlcr3pdDr/C2wCAsC/XS6XGEQJk6sTrmCncw+75INIm+wYSqwg6/izGpBnePjskJsZbM0Md5iCMCCIWdjCxbhgUna5XBpwzzmHD511/kngyS6OS7gIiqTwYM53+TBuLSvS3uZUIDQWM8o+glsG3cD4yLFhjrB/qdi9hfhxueEOQ+jFtOI8lIg4sWZZ6DBRPKSfUSSFBfHzWRA/P7TvMpLYLaobVJJKSV6eSMrCeWkesX2q0DkiKYeBruvsrN/DisKVHG48goTMuKjRLE6/nhzbsFbX767bw1PH/siphjKQdCRNJid2KHek3c6Gik1srd6BSpDB1ixuTL8OGYnXC9/hqOcYCgYmxYzjptSFDLENbtV2hb+St0vf46PST/DoHhIM8SzKuJq5sbMwyaae+Dr6pPTFSyld/qTYmEIQhC4lknIP03Wd5/L/w3vH1qButmAqjEWXYMvgQ2yfuou7sj/HtYkLmq5fWb6Kp/P+AnstyLtioU6BxCCu3Hweqn4M++54zHlRSEGZwyllPDHlKXSrhnl9LKaiOFRF59Oh+9g0ZTv35nyRefGzmto+6j7Oj/f/DN8eGeWgDdltpyzWx98mvcR7wz7iiZEPY1PaX/csCML5qY7RqGJcWegEsaVQD9tUu5VVR9agvBKH5YgD2WtA9hiwHIhGfiWOfxz+L8fcxwHwqB6ezvsL0nsOlNXRSOUmJJ+CVGhCetcBO+y47Y0ojUZknwLHzARfchAsAV3RkX0GFLcR895o5Fdj+PPh5yjyFgMQ1IM8fvBX+N41Y94Yg6HGjOxXMJbYML4dR/7OMp49/s8wflOC0D9oxXliFrbQYSIp97BX899A32BrsxSm0mhE227hzVPvAvCXwuegWkHa33LdsW7UkQIy8qd29DQffqsXAK/qRfLISJ9G4BlRg07z0iilzoS228zbpe8BsKV2O56SIOb81mNeEhKGzdF8WrmJumB9q/NCSCWp7Fv2QrjDEHo5Ma4sdIZIyj1I1VWOeo9jKrC3e43hhI1d1aGl4NuqdyEdtLSu0CUDqoQUUCDfhDehAR0dTVdBlaDQhGYLopvVFh9TjlnZURmq67K7ei+BQ+1PAJN9Ckq5mSPuoxfX2QEgffFSSouLRR1sQRC6jEjKPejsJ9fzXNTyqg58pM2qmnrbx8/EoLW6UVttSB2LeQCrROxRLZzfmXFlqAh3KEIfIJJyDzJIBgabMwmkNbZ7TTDTzZjokQCMjx6D7vS2vkgDFB3doEFGAEu5HQkJWZJB0SElgOxVkLwtn4TVLA/jY0LzhcfFjMboVFu3feYWJpVgopeh1iGd76ggCC1oxXlQ2271YUFoIpJyD1uSuQhmuEMJ9RyaNYg82csNqdcCcF/G3RCvojk9La6TAhIYdfSpjUglRkzu0JizRbGgWzT0GQ1YD0W3eO2tRgSQx/u4LuVqAKY6JmNOlfG38QuCjk5wci3T4qYQbYzqsr4LwkAVME47/bQsCOcnknIPmxE1jbnDLiN4cwW+rHp0g4ZmUvHl1KLeUsntw24m2zYUAKti5d5hX0S/thZtdh16dABd1tGTAmhX1KHnNmCtjkQzq+iKhpQZQLm1HiVFQ/IY0BUNzaziG16LdnMlX8r+PIMsoeLuRtnIw8O/j+E6N77J1agRobYDCR4CC6pImRzNvYPFTpyCIAg9SaxT7mGSJPG1rC8zKXY8y5Pe4oj3GDISYyNGsSRjEaMjRra4fnHSIlLMyfzB+mcqJlWCrIMqkRU1iKXpn2Fj4ma2X7YLFY1MUwY3DvosMjIrYt7mhO8kCjKTHONYnH49w+05Ldp22rP5/bhf8GbiO6ydtB4vXuKUOK5Pu4kr4+djVSw9+dX0WaKyl9BxFUB8uIMQejGRlMNAkiSmRU1h2pgpaFroNbYst3xpoaoqihIaE54encv0SaEf+rquI0nNr6Vnx8xo8x6Xx1yGrutN92tPsjmJu7Pu4u6suy6+QwNZeg6lhWtFZS/hgprrYM8LdyhCLyaSchhomsY/T73Am/mraMQNQIwczTVpV7CxeivHa0+GJmxpEGmM5PZBS6jy1bCm7BM8eIiWork2bQHXJS7ArrRcXqXpGp/UfMqK/JWc9OcjIzMucgw3p9/AyIjh4ehuv5aem0thYZ7YnEK4IM0TEaruFSWeloX2iaTcwzRN46t7vs3JomKk9REoxxyg6FSPdPPi7GWQb0beGAslRrCrNIz18GzuPzGdiCBiexLWxnjc0X5eGf82H4xcw69GP06MMRoIrYN+6sj/sfXoHvRNVizF6eiKxu7Bx9k7/Zfc5by9RQlPQRB6juoYjdK498IXCgOamOjVw/5a/A9OFhYjvxCHfNiKpEpIfhkpPgi7bEirHFBuQNIlpAYD0k4b0opY/IkeJI+EpEsYqs2Y1sRRtdnLH478pant1RUfsSVvD4blcZgKI5A0CTmgYM6LQn41ln8c+S8nPQVh7H3/VZKXF+4QBEHoB0RS7mHv5H+A9EkEUqD5q9ctGvoQL/LG08eNobFgXdFBl5BPmqHESH1mdYu2jDuj2FtzgDJ/Obqus7xgJdJGO5LW+q9VaTSi7jSzsmRV93ZwIErPobS4ONxRCH2FWK8snIdIyj3Iq3nxSB6kYy1nNeuJfigzIvkUCErNfyuyDqfre0jHTAQSzlmvrMooxRYOu4/i1jxU+CsxlLSsk302wwkbe6r3d2WXBELjyoCogy1ckFoiiepewnmJpNyD5DNf9zmToaU2jrXx4bbLYkoX/mhzG3rrOtpCl6hMnxPuEIQ+QHWMRm8sCncYQi8mknIPMskm7NjRh55TOrPEBAkBdFsQDKFZ1wBoEhhCFbb0YT5MZS33NtYNGmqql+F2JzbZSooliUCqu937q4M9TIwb18W9EgRBELqKSMo9bHHmdeiz69EtzWU2Jb+MlGdFm9mAbtTAH/prkVQJ0NGzvRAbJCI/tukzOjqB3Bomx04g1hiDJEncPOgGpJmNbZbwDEb5kcf7WZh8Vbf3URCECxDjykI7RFLuYUuTb2NkejbanRVoYxrR7Sq6QwW3BCM96DfWoGf60G0qeoIf7bIG9IU1WGrtaNF+NHOQQLKbwLWVpEyO4RtD725qe07M5czLnkHw1gq8Q+vQrEHUiAC+sTXoS6q5L/vLpJpTwth7QRDEuLJwPmKdcg+TZZnfj/4lyxPe5JWoFVQHygGJVGsSt2bcwcfJG9iVuBdN1kCXSLIn8JXM+zg1pITV2Wto1OpJNMRyffoi5sTNwiKbm9qWJIl7sr5EbtwkXk96hyPuYxgkmekxE7kx9TqyrIPC1/EBoLS4WFT2Ei6oab1y7R5R3UtoRSTli6TrOl7NR1Bvf/vDs3k1L17Nj0OOQJZlFictYlHctZQGyzBhIsESqvBzbcJVeDO8bG7chtM+jGRLclMbV8TN44j7MCNtw3GYHU3HSzxl1OsNZBkzMBqNTHJMYOLI8fh0PwoyRtl4wfhUXcWv+bHIlvOW5RTalp6bi6dwrajsJXSIWiIh2UV1L6E1kZQ7ya26eav0XVYWv0eD2oiua0zxTOLWjJuadnc625vl7/Cfoy9To9eCBgYMTIkbz8lAIcU1JaFymgCqRGp0IsWNJaCeTooSoIHVbsHj9ob+fGYGtgzx9jgqaqtCbeihcxE2O7el3MyHpz6mPFAOkkSOLZtbB93AJMeEVvGd9OTzSuEKNtVsRddC2z9ek3wFNyYvJNIQ0R1fYb9VmT5HbE4hdIjqGI1cvAklcSQYRVIWmomk3AmNaiM/3PcTTh2oQdkRgbU6hqAcYHvOYXZd9lPuH/l1pkVPabr+18f+wOoTa5E+jkRxJUMQgukeNt68FcqNSJ/EwEkjyKCPb6R4dikcsiFttiNXGdFMKoz14JnRAHkWpI8dyG4FLTqAPsVNxahKWBeJtMsWmrGdFqDh8gb+7vkXEe+nYilKBxmODCrjlzOf5jM5N3Fz6g1N8e2u38fP9v+G4EYzpsPJyH4F1eHn9fEfsG7Mpzx5VglPQRAEofuJiV6d8NyJ/3BqRy2mD2MxVIfGcqWAjOVQNNKKaH6b9wz1wQYA9tbvZ3XhGuT/xiHvtyEFpdAa4RmNoYT8YizySRMyMrImw3gP0g478qoopKrQ70qSX0Y6YEVaFguDAhAIxSHVGZA3RCCtj4QsP7Imh9opMiG9HAOFJhpmn0JCQtIkzCciUV6L4+XjyznmPg6AT/PxK9fv0N90YNkfjewP7Uil1JkwrwuV8PzTsb/37BfcD4jKXkKnuEvDHYHQy4ik3EGNqptPKjZi3O5oswCHodqMftTImsqPAfj7yX8j7bYi1Z7zMiIpgLQ+VJf6zJtoLc4PkRpstIdeQ59p3qCDJiEXm6DICCO8zccDEuy0QVwQLSbQ1LysS0jrIsGkEyTYfNxjQNtu4c1T7wLwac1mggUSxrK2K4CZdkWxs3oPVYHqNs8LrZ2p7FWxe0uYIxH6gjO7RolZ2MLZRFLuoAJvIUqtCdnb/ht/7aiRvdUHAThZW4B0vGU5TdWkghE4YWqR2PWhPig1ND2tNpFpLrN53IyefDr5KjqoErIqQ6EJUkPHT++ejFxiAlUikNHYojmlwMqBGhcA+2tcBI+cc7+zSEEZQ5mF454T7V4jtFZJKrvXrg13GEIf0FTdS6xZFs4iknIHyZIc2iDiPHRFR5FCiU6SJHT5nOvPTNSWQ8U/zpBULjy6r4SemkM3ks453vJSDQ1kWmx6Ebpvc3wG+cL9QdGRJfFPpDPSFy8NdwhCH6KWiJUOQkviJ24HZVkykR06aqS/3WsMIwNMS5gMwNiEUc2vm09TVAX8Ejh9LT940ArxAbSIYMvjqgQGPVRmM8eLlG86fRww6KGJYOl+OH38dP0vGOwH9FabU2jDPExNmATApNgJGEe2v5xLswZRE/zk2LLbvUYQBEHoWiIpd5BJNnJ9ylWos+paPwED/owGzOkyl0VPBeDLGXfCcC962jkJ+IgZfVYdul1teoEtuw1QZkC/4nTbZ5o/nTP1kR6IVOHI6UIhQQndoKHProcTZuTGM4/ZErpJQ59bh9xgxHDW43cw1os81s81iVcCMDFyHI4kG/5hda36oks6wZm1zE+YjV2xtTovCELXEePKwtlEUu6EW9MWM2HkCII3V+AbUoca6SeY4MU/qxrztT4eHfEgJjn01JphSeNr2V9Cv6UadV4tepIfPSaAXGQGm4r+hUq0yY1osQG0BH9obHiID31pJfpwb2jZU5ofbW4d+tW10KBAeiB0fJgX/cYaGO0BP2iJfrSYANqEBvQvVkC0ivlAFKrDTzDGhy+3GhbXcr/zPpLMiQAoksKjIx7EdqVOYF41gUQPaqQfX2Y9wcUVOMcM4ouZ4lWsIHQnMa4snEusU+4Eg2TgwZzvsi15J2+mvUuRpxhZlblq0DVcGT+31ZreGxIX4rTn8LfYf3Jw3GF0XSfG5OCWzC9z0lvAe5aPUGeGllCZTEYWJl/Pu7bVeGJrAT00dmzWmRs3i3WmDaipVU0FRGwOKwtirmSl8j7BsVWhG0owMWkMd6Z+jjcT3sFVdxRFkpkWP4Prkq8ixZzcIr50SyrPjPsNH6at5f0Ra3CrbpItSSxKv4bcqEkYJPHP42KJyl5CR6klEoakcEch9Bbip24nyZJMbtQkcqNCY7OFBQWkp2Q0nfdqPtyqmwjFjkk2Mdyew1Mjf95mW9/J/HqrY/dmfhl30E2JvxSHwUG8KQ6AH3E/1f4aqoPVJJmSsBtCr5W/nvnVNtsemTO8Q/2JNERwY/JCbkxe2KHrhQurJFVU9hIE4aKIpNxFTnoKeKlgGVurdyIHZTDCjLip3Ja+hGRzx34NPuHJ59eHn+ZwwzHwA0adaEM0M5Knsql0G5WBytD6ZCNk2QfxvexvkGMf1r0dEzotffFSSpc/KTanEDpMbRB1sIUQkZS7wMFGF4/u+yWB/28Q2kS2AAAHxUlEQVTv7mOrPMs4jn+f057Tjq6FwqBQXseUC8ZgI5BtDkLQiDijohuL/0g2iE6iY+4PRV2cU7OBM46YLG7qsomKxohOHUxl2QZZICHshU552YUFxLmNlXa2dJTSl/P4x1NoG+jL6Dl9Tk9/n796uE/u/p6E9Hre7uvenSL1rwoSrQWki9p4cVYVL93wKuuvuZ+pl03udY7qpqOsrfo67VVFJF4aS9BYQFgYUj+ziW0f3g5eTMHOCoKWBGFJO8fn1XJ30zp+OOf7zC3Vn3+RoUq7RklXetFrgNrDdh56/ce0P1NC8cFRJFqjdcCJs4UUV5XT/HyShw8/Qhj2vib4OwceJL2nmIIXRhI0dqx1bgsIjhQR/G40XHn2fKev4HQBiV1lhDsu57sHfpDV4xOR7OvcY1mGOxXlATrUepim2hZSb5VcdDxVXcrbDTUcOXOsxzmONh2jtvldgpe778oUFqSjNps1KTheRHpWU7fx4LURvNfcxMsN+wZ+ICISm/Yy3e2SiIryAL3R+iat1T135QkICN5IcezM8R6/80pjFUFNkqDlwg5c59ts/icF47o3FwnS0dyvNlZdcn4RySVarzzcqSgPUGFQQJDso1VeEpK9LC8qShRFm0z0Okdnge4mFZIMkn0HlUG3f8vmuCPIEBKefhNatWvUcKeiPEBXp4zErBbC4OJFNSxMk57SzJzS2T3OsaR8EVzRRljWveoG7YnONpvWTPDvou5zX5YmnNjCx8d8dOAHIhlVN2mJtnGU96X9REB7zUF0tTy8qSgP0MTCSj44ejotC+q7bTIBUR/q1oX1XD96PmOSo3uco6ywjNkjZ5JeVt+9hWc6AALC65qgOE1wtHPXqTAICZc2MK1kMhOKx184qcTq3DaOIv11vruXDGsqyhnwjRn3MOHGMtqWvxu1qRzdzNkrT9G2opbp8yaw9qo7+5xj/dX3M+4DI0mvOkl67mnCihbS05sJb24g/MgpaA0Ir2qO/n12E+nbaymbWcTGORdvTCIiIkOP1ilnwKjkSDbO2cCeKXv527Tn+F9rPWOLJvHJSR9jftm8frWrLE4Us2neY/zl5DM8NWYr9S2nSCaSLBp/EyvGf5attX9lx4RdnE03cXmyhOVTP8eKccvP99qW3FNHJfu3bOaa29RDXN6H1ncgqSYiw5WKcoakEkkWly9kcfnCS56jMFHIrRXLubVi+QVja6esYe2UNQOJKINt0gze+e9OdfaSfms/ERCUHKRgYs/voEh+0+1rkSw591y59rW9MSeRoeL8c+XWA3FHkZj0eaVsZgngUeBa4CzwBXev7jL+ReBLQBvwgLtvy1JWkSGnjsq4I8gQ03m1XIF6YQ8//blS/gxQ7O4fAr4JPHxuwMzGA3cDC4FlwAYzK7roLCIi0qfOq2WtWR6O+lOUFwF/B3D3PcCCLmPXA7vd/ay7NwDVwNyMpxQRGUbChtNxR5CY9KcolwENXT63m1lhD2ONwMgMZRMRERlW+vP29SmgtMvnhLu39TBWCtT3+gtTqdryysqeG0EPMeWV+f/MUMc4gHnvWsdJ4OTFWqTGobKSQ7mSJVvy4RgTt8A/AA71+rWamt7H80GeHOPU/n6xP0V5N/Ap4PdmdiPwzy5je4EHzawYKAJmAft7m2z+/Plj+xtORERkOAn62ue3y9vXc4l29F0FfAKodvenO96+vpPoVvh6d/9jdiOLiIjkpz6LsoiIiAwONQ8RERHJESrKIiIiOUJFWUREJEdoQ4oBMLMbgIfcfUncWbLBzJLAk8A0orfrH3D3p2MNlWFmVgA8DhjQDqxy9yPxpsoOMxsHvAIsdffX486TDWa2j87eCcfcfVWcebLBzL4FfBpIAY+6+xMxR8o4M7sDuKPjYzFwHTDe3XtdcpsPVJQvkZmtA1YC+dx65/NAnbuvNLMxwD4gr4oy0XI/3H2hmS0BNgIXbtM1xHWcYP0MOBN3lmzpWJpJvp4kA3T8H72JqLXxCOBrsQbKEnffBGwCMLOfAE8Oh4IMun09EEeAW+IOkWVbgPu6fG7r6YtDlbv/mWhJH0QL/PO14fCPgJ8Cb8UdJIuuBUaY2bNm9kJHX4V8s4yoV8SfgK1AXm8AZGYLgNnu/vO4swwWFeVL1LEeuzXuHNnk7u+5e6OZlQJ/AL4dd6ZscPc2M/sl8AjRceaVjluBJ919e9xZsqyJ6ORjGbAG+E2XlsD54gqi/Qduo/MYg3gjZdW9wPfiDjGYVJSlV2Y2GdgB/Nrdfxt3nmxx99uBGcDjZlYSd54MWw0sNbOdRM/mftWxw1u+OQxsdvfQ3Q8DdcCEmDNlWh2w3d1b3N2BZiAvuySa2ShgprvviDvLYMq3s0jJIDOrAJ4F7nL35+POkw1mthKY5O4biK600kQvfOUNd1987ueOwrzG3U/ElyhrVgNzgC+bWSXRhjlvxxsp43YBXzWzjUQnHCVEhTofLQaeizvEYFNRlt7cC5QD95nZuWfLN7t7Pr0s9BTwCzN7EUgC97h7c8yZ5NI8AWwys11ACKzusnlOXnD3bWa2mGjfgQTwFXfPq5PILgw4GneIwaY2myIiIjlCz5RFRERyhIqyiIhIjlBRFhERyREqyiIiIjlCRVlERCRHqCiLiIjkCBVlERGRHKGiLCIikiP+DyclaogwV4ViAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "z = clf.predict(np.c_[xx.ravel(), yy.ravel()])\n",
    "z = z.reshape(xx.shape)\n",
    "fig = plt.figure(figsize=(8,6))\n",
    "ax = plt.contourf(xx, yy, z, cmap = 'afmhot', alpha=0.3);\n",
    "plt.scatter(X.values[:, 0], X.values[:, 1], c=y, s=80, \n",
    "            alpha=0.9, edgecolors='g');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src='img//svm_iris_petal_length_and_width.png' width=40%, height=20%>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linear SVM Implementation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = sns.load_dataset('iris')\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "col = ['petal_length', 'petal_width']\n",
    "X = df.loc[:, col]\n",
    "species_to_num = {'setosa': 0,\n",
    "                  'versicolor': 1,\n",
    "                  'virginica': 2}\n",
    "df['tmp'] = df['species'].map(species_to_num)\n",
    "y = df['tmp']\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y,\n",
    "                                                    train_size=0.8, \n",
    "                                                    random_state=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Scale Features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "sc_x = StandardScaler()\n",
    "X_std_train = sc_x.fit_transform(X_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SVC(C=1.0, cache_size=200, class_weight=None, coef0=0.0,\n",
       "    decision_function_shape='ovr', degree=3, gamma='auto_deprecated',\n",
       "    kernel='linear', max_iter=-1, probability=False, random_state=None,\n",
       "    shrinking=True, tol=0.001, verbose=False)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C = 1.0 #0.01\n",
    "clf = svm.SVC(kernel='linear', C=C)\n",
    "clf.fit(X_std_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import cross_val_score\n",
    "from sklearn.model_selection import cross_val_predict\n",
    "from sklearn.metrics import confusion_matrix\n",
    "from sklearn.metrics import precision_score, recall_score, f1_score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Cross Validation within Train Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average Accuracy: \t 0.9501\n",
      "Accuracy SD: \t\t 0.0538\n"
     ]
    }
   ],
   "source": [
    "res = cross_val_score(clf, X_std_train, y_train, cv=10, scoring='accuracy')\n",
    "print(\"Average Accuracy: \\t {0:.4f}\".format(np.mean(res)))\n",
    "print(\"Accuracy SD: \\t\\t {0:.4f}\".format(np.std(res)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_train_pred = cross_val_predict(clf, X_std_train, y_train, cv=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[39,  0,  0],\n",
       "       [ 0, 34,  3],\n",
       "       [ 0,  3, 41]])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "confusion_matrix(y_train, y_train_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Precision Score: \t 0.9500\n",
      "Recall Score: \t\t 0.9500\n",
      "F1 Score: \t\t 0.9500\n"
     ]
    }
   ],
   "source": [
    "print(\"Precision Score: \\t {0:.4f}\".format(precision_score(y_train, \n",
    "                                                           y_train_pred, \n",
    "                                                           average='weighted')))\n",
    "print(\"Recall Score: \\t\\t {0:.4f}\".format(recall_score(y_train,\n",
    "                                                     y_train_pred, \n",
    "                                                     average='weighted')))\n",
    "print(\"F1 Score: \\t\\t {0:.4f}\".format(f1_score(y_train,\n",
    "                                             y_train_pred, \n",
    "                                             average='weighted')))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Cross Validation within Test Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_test_pred = cross_val_predict(clf, sc_x.transform(X_test), y_test, cv=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[11,  0,  0],\n",
       "       [ 0, 13,  0],\n",
       "       [ 0,  2,  4]])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "confusion_matrix(y_test, y_test_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Precision Score: \t 0.9422\n",
      "Recall Score: \t\t 0.9333\n",
      "F1 Score: \t\t 0.9290\n"
     ]
    }
   ],
   "source": [
    "print(\"Precision Score: \\t {0:.4f}\".format(precision_score(y_test, \n",
    "                                                           y_test_pred, \n",
    "                                                           average='weighted')))\n",
    "print(\"Recall Score: \\t\\t {0:.4f}\".format(recall_score(y_test,\n",
    "                                                     y_test_pred, \n",
    "                                                     average='weighted')))\n",
    "print(\"F1 Score: \\t\\t {0:.4f}\".format(f1_score(y_test,\n",
    "                                             y_test_pred, \n",
    "                                             average='weighted')))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n",
    "# 3. Polynomial Kernel"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src='img//svm_polynomial.png' width=40%, height=40%>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SVC(C=1.0, cache_size=200, class_weight=None, coef0=0.0,\n",
       "    decision_function_shape='ovr', degree=3, gamma='auto', kernel='poly',\n",
       "    max_iter=-1, probability=False, random_state=None, shrinking=True,\n",
       "    tol=0.001, verbose=False)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C = 1.0\n",
    "clf = svm.SVC(kernel='poly', degree=3, C=C, gamma='auto')\n",
    "clf.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "Xv = X.values.reshape(-1,1)\n",
    "h = 0.02\n",
    "x_min, x_max = Xv.min(), Xv.max() + 1\n",
    "y_min, y_max = y.min(), y.max() + 1\n",
    "xx, yy = np.meshgrid(np.arange(x_min, x_max, h),\n",
    "                     np.arange(y_min, y_max, h))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "z = clf.predict(np.c_[xx.ravel(), yy.ravel()])\n",
    "z = z.reshape(xx.shape)\n",
    "fig = plt.figure(figsize=(8,6))\n",
    "ax = plt.contourf(xx, yy, z, cmap = 'afmhot', alpha=0.3);\n",
    "plt.scatter(X.values[:, 0], X.values[:, 1], c=y, s=80, \n",
    "            alpha=0.9, edgecolors='g');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Polynomial SVM Implementation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = sns.load_dataset('iris')\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "col = ['petal_length', 'petal_width']\n",
    "X = df.loc[:, col]\n",
    "species_to_num = {'setosa': 0,\n",
    "                  'versicolor': 1,\n",
    "                  'virginica': 2}\n",
    "df['tmp'] = df['species'].map(species_to_num)\n",
    "y = df['tmp']\n",
    "X_train, X_std_test, y_train, y_test = train_test_split(X, y,\n",
    "                                                        train_size=0.8, \n",
    "                                                        random_state=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Scale Features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "sc_x = StandardScaler()\n",
    "X_std_train = sc_x.fit_transform(X_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SVC(C=1.0, cache_size=200, class_weight=None, coef0=0.0,\n",
       "    decision_function_shape='ovr', degree=10, gamma='auto', kernel='poly',\n",
       "    max_iter=-1, probability=False, random_state=None, shrinking=True,\n",
       "    tol=0.001, verbose=False)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C = 1.0 #0.01\n",
    "clf = svm.SVC(kernel='poly', degree=10, C=C, gamma='auto') #5\n",
    "clf.fit(X_std_train, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Cross Validation within Train Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average Accuracy: \t 0.7864\n",
      "Accuracy SD: \t\t 0.1283\n"
     ]
    }
   ],
   "source": [
    "res = cross_val_score(clf, X_std_train, y_train, cv=10, scoring='accuracy')\n",
    "print(\"Average Accuracy: \\t {0:.4f}\".format(np.mean(res)))\n",
    "print(\"Accuracy SD: \\t\\t {0:.4f}\".format(np.std(res)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_train_pred = cross_val_predict(clf, X_std_train, y_train, cv=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[35,  0,  4],\n",
       "       [ 0, 37,  0],\n",
       "       [ 7, 18, 19]])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "confusion_matrix(y_train, y_train_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Precision Score: \t 0.7812\n",
      "Recall Score: \t\t 0.7583\n",
      "F1 Score: \t\t 0.7368\n"
     ]
    }
   ],
   "source": [
    "print(\"Precision Score: \\t {0:.4f}\".format(precision_score(y_train, \n",
    "                                                           y_train_pred, \n",
    "                                                           average='weighted')))\n",
    "print(\"Recall Score: \\t\\t {0:.4f}\".format(recall_score(y_train,\n",
    "                                                     y_train_pred, \n",
    "                                                     average='weighted')))\n",
    "print(\"F1 Score: \\t\\t {0:.4f}\".format(f1_score(y_train,\n",
    "                                             y_train_pred, \n",
    "                                             average='weighted')))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Cross Validation within Test Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_test_pred = cross_val_predict(clf, sc_x.transform(X_test), y_test, cv=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[10,  0,  1],\n",
       "       [ 0, 13,  0],\n",
       "       [ 3,  3,  0]])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "confusion_matrix(y_test, y_test_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Precision Score: \t 0.6341\n",
      "Recall Score: \t\t 0.7667\n",
      "F1 Score: \t\t 0.6941\n"
     ]
    }
   ],
   "source": [
    "print(\"Precision Score: \\t {0:.4f}\".format(precision_score(y_test, \n",
    "                                                           y_test_pred, \n",
    "                                                           average='weighted')))\n",
    "print(\"Recall Score: \\t\\t {0:.4f}\".format(recall_score(y_test,\n",
    "                                                     y_test_pred, \n",
    "                                                     average='weighted')))\n",
    "print(\"F1 Score: \\t\\t {0:.4f}\".format(f1_score(y_test,\n",
    "                                             y_test_pred, \n",
    "                                             average='weighted')))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n",
    "# 4. Gaussian Radial Basis Function (rbf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The kernel function can be any of the following:\n",
    "\n",
    "* **linear**: $\\langle x, x'\\rangle$.\n",
    "\n",
    "\n",
    "* **polynomial**: $(\\gamma \\langle x, x'\\rangle + r)^d$. \n",
    "\n",
    "  $d$ is specified by keyword `degree`\n",
    "  \n",
    "  $r$ by `coef0`.\n",
    "\n",
    "\n",
    "* **rbf**: $\\exp(-\\gamma \\|x-x'\\|^2)$. \n",
    "\n",
    "  $\\gamma$ is specified by keyword `gamma` must be greater than 0.\n",
    "\n",
    "\n",
    "* **sigmoid** $(\\tanh(\\gamma \\langle x,x'\\rangle + r))$\n",
    "\n",
    "  where $r$ is specified by `coef0`.\n",
    "  \n",
    "[scikit-learn documentation](http://scikit-learn.org/stable/modules/svm.html#svm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = sns.load_dataset('iris')\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "col = ['petal_length', 'petal_width']\n",
    "X = df.loc[:, col]\n",
    "species_to_num = {'setosa': 0,\n",
    "                  'versicolor': 1,\n",
    "                  'virginica': 2}\n",
    "df['tmp'] = df['species'].map(species_to_num)\n",
    "y = df['tmp']\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y,\n",
    "                                                    train_size=0.8, \n",
    "                                                    random_state=0) #0.6"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Scale Features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "sc_x = StandardScaler()\n",
    "X_std_train = sc_x.fit_transform(X_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SVC(C=1.0, cache_size=200, class_weight=None, coef0=0.0,\n",
       "    decision_function_shape='ovr', degree=3, gamma=0.7, kernel='rbf',\n",
       "    max_iter=-1, probability=False, random_state=None, shrinking=True,\n",
       "    tol=0.001, verbose=False)"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C = 1.0\n",
    "clf = svm.SVC(kernel='rbf', gamma=0.7, C=C)\n",
    "clf.fit(X_std_train, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Cross Validation within Train Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average Accuracy: \t 0.9501\n",
      "Accuracy SD: \t\t 0.0538\n"
     ]
    }
   ],
   "source": [
    "res = cross_val_score(clf, X_std_train, y_train, cv=10, scoring='accuracy')\n",
    "print(\"Average Accuracy: \\t {0:.4f}\".format(np.mean(res)))\n",
    "print(\"Accuracy SD: \\t\\t {0:.4f}\".format(np.std(res)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_train_pred = cross_val_predict(clf, X_std_train, y_train, cv=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[39,  0,  0],\n",
       "       [ 0, 35,  2],\n",
       "       [ 0,  3, 41]])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "confusion_matrix(y_train, y_train_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Precision Score: \t 0.9586\n",
      "Recall Score: \t\t 0.9583\n",
      "F1 Score: \t\t 0.9584\n"
     ]
    }
   ],
   "source": [
    "print(\"Precision Score: \\t {0:.4f}\".format(precision_score(y_train, \n",
    "                                                           y_train_pred, \n",
    "                                                           average='weighted')))\n",
    "print(\"Recall Score: \\t\\t {0:.4f}\".format(recall_score(y_train,\n",
    "                                                     y_train_pred, \n",
    "                                                     average='weighted')))\n",
    "print(\"F1 Score: \\t\\t {0:.4f}\".format(f1_score(y_train,\n",
    "                                             y_train_pred, \n",
    "                                             average='weighted')))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Grid Search"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.pipeline import Pipeline "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split, GridSearchCV "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "we can improve this by scaling the features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "pipeline = Pipeline([('clf', svm.SVC(kernel='rbf', C=1, gamma=0.1))]) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "params = {'clf__C':(0.1, 0.5, 1, 2, 5, 10, 20), \n",
    "          'clf__gamma':(0.001, 0.01, 0.1, 0.25, 0.5, 0.75, 1)} "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "svm_grid_rbf = GridSearchCV(pipeline, params, n_jobs=-1,\n",
    "                            cv=3, verbose=1, scoring='accuracy') "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitting 3 folds for each of 49 candidates, totalling 147 fits\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=-1)]: Using backend LokyBackend with 4 concurrent workers.\n",
      "[Parallel(n_jobs=-1)]: Done 147 out of 147 | elapsed:    4.0s finished\n",
      "/Users/anthonyn/anaconda3/envs/ml_python_2019/lib/python3.7/site-packages/sklearn/model_selection/_search.py:814: DeprecationWarning: The default of the `iid` parameter will change from True to False in version 0.22 and will be removed in 0.24. This will change numeric results when test-set sizes are unequal.\n",
      "  DeprecationWarning)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "GridSearchCV(cv=3, error_score='raise-deprecating',\n",
       "             estimator=Pipeline(memory=None,\n",
       "                                steps=[('clf',\n",
       "                                        SVC(C=1, cache_size=200,\n",
       "                                            class_weight=None, coef0=0.0,\n",
       "                                            decision_function_shape='ovr',\n",
       "                                            degree=3, gamma=0.1, kernel='rbf',\n",
       "                                            max_iter=-1, probability=False,\n",
       "                                            random_state=None, shrinking=True,\n",
       "                                            tol=0.001, verbose=False))],\n",
       "                                verbose=False),\n",
       "             iid='warn', n_jobs=-1,\n",
       "             param_grid={'clf__C': (0.1, 0.5, 1, 2, 5, 10, 20),\n",
       "                         'clf__gamma': (0.001, 0.01, 0.1, 0.25, 0.5, 0.75, 1)},\n",
       "             pre_dispatch='2*n_jobs', refit=True, return_train_score=False,\n",
       "             scoring='accuracy', verbose=1)"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "svm_grid_rbf.fit(X_train, y_train) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9583333333333334"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "svm_grid_rbf.best_score_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "best = svm_grid_rbf.best_estimator_.get_params() "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\tclf__C: \t 0.10\n",
      "\tclf__gamma: \t 0.25\n"
     ]
    }
   ],
   "source": [
    "for k in sorted(params.keys()): \n",
    "    print('\\t{0}: \\t {1:.2f}'.format(k, best[k]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Conducting validation in the test dataset. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_test_pred = svm_grid_rbf.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[11,  0,  0],\n",
       "       [ 0, 13,  0],\n",
       "       [ 0,  0,  6]])"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "confusion_matrix(y_test, y_test_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Precision Score: \t 1.0000\n",
      "Recall Score: \t\t 1.0000\n",
      "F1 Score: \t\t 1.0000\n"
     ]
    }
   ],
   "source": [
    "print(\"Precision Score: \\t {0:.4f}\".format(precision_score(y_test, \n",
    "                                                           y_test_pred, \n",
    "                                                           average='weighted')))\n",
    "print(\"Recall Score: \\t\\t {0:.4f}\".format(recall_score(y_test,\n",
    "                                                       y_test_pred, \n",
    "                                                       average='weighted')))\n",
    "print(\"F1 Score: \\t\\t {0:.4f}\".format(f1_score(y_test,\n",
    "                                               y_test_pred, \n",
    "                                               average='weighted')))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "Xv = X.values.reshape(-1,1)\n",
    "h = 0.02\n",
    "x_min, x_max = Xv.min(), Xv.max() + 1\n",
    "y_min, y_max = y.min(), y.max() + 1\n",
    "xx, yy = np.meshgrid(np.arange(x_min, x_max, h),\n",
    "                     np.arange(y_min, y_max, h))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "z = svm_grid_rbf.predict(np.c_[xx.ravel(), yy.ravel()])\n",
    "z = z.reshape(xx.shape)\n",
    "fig = plt.figure(figsize=(8,6))\n",
    "ax = plt.contourf(xx, yy, z, cmap = 'afmhot', alpha=0.3);\n",
    "plt.scatter(X.values[:, 0], X.values[:, 1], c=y, s=80, \n",
    "            alpha=0.9, edgecolors='g');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n",
    "# 5. Support Vector Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "sns.set_style('whitegrid')\n",
    "%matplotlib inline\n",
    "import pandas as pd\n",
    "from sklearn.svm import SVR\n",
    "from sklearn.metrics import mean_squared_error, r2_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>CRIM</th>\n",
       "      <th>ZN</th>\n",
       "      <th>INDUS</th>\n",
       "      <th>CHAS</th>\n",
       "      <th>NOX</th>\n",
       "      <th>RM</th>\n",
       "      <th>AGE</th>\n",
       "      <th>DIS</th>\n",
       "      <th>RAD</th>\n",
       "      <th>TAX</th>\n",
       "      <th>PTRATIO</th>\n",
       "      <th>B</th>\n",
       "      <th>LSTAT</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>0.00632</td>\n",
       "      <td>18.0</td>\n",
       "      <td>2.31</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.538</td>\n",
       "      <td>6.575</td>\n",
       "      <td>65.2</td>\n",
       "      <td>4.0900</td>\n",
       "      <td>1.0</td>\n",
       "      <td>296.0</td>\n",
       "      <td>15.3</td>\n",
       "      <td>396.90</td>\n",
       "      <td>4.98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>0.02731</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.07</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.469</td>\n",
       "      <td>6.421</td>\n",
       "      <td>78.9</td>\n",
       "      <td>4.9671</td>\n",
       "      <td>2.0</td>\n",
       "      <td>242.0</td>\n",
       "      <td>17.8</td>\n",
       "      <td>396.90</td>\n",
       "      <td>9.14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>0.02729</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.07</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.469</td>\n",
       "      <td>7.185</td>\n",
       "      <td>61.1</td>\n",
       "      <td>4.9671</td>\n",
       "      <td>2.0</td>\n",
       "      <td>242.0</td>\n",
       "      <td>17.8</td>\n",
       "      <td>392.83</td>\n",
       "      <td>4.03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>0.03237</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>6.998</td>\n",
       "      <td>45.8</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3.0</td>\n",
       "      <td>222.0</td>\n",
       "      <td>18.7</td>\n",
       "      <td>394.63</td>\n",
       "      <td>2.94</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>0.06905</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>7.147</td>\n",
       "      <td>54.2</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3.0</td>\n",
       "      <td>222.0</td>\n",
       "      <td>18.7</td>\n",
       "      <td>396.90</td>\n",
       "      <td>5.33</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      CRIM    ZN  INDUS  CHAS    NOX     RM   AGE     DIS  RAD    TAX  \\\n",
       "0  0.00632  18.0   2.31   0.0  0.538  6.575  65.2  4.0900  1.0  296.0   \n",
       "1  0.02731   0.0   7.07   0.0  0.469  6.421  78.9  4.9671  2.0  242.0   \n",
       "2  0.02729   0.0   7.07   0.0  0.469  7.185  61.1  4.9671  2.0  242.0   \n",
       "3  0.03237   0.0   2.18   0.0  0.458  6.998  45.8  6.0622  3.0  222.0   \n",
       "4  0.06905   0.0   2.18   0.0  0.458  7.147  54.2  6.0622  3.0  222.0   \n",
       "\n",
       "   PTRATIO       B  LSTAT  \n",
       "0     15.3  396.90   4.98  \n",
       "1     17.8  396.90   9.14  \n",
       "2     17.8  392.83   4.03  \n",
       "3     18.7  394.63   2.94  \n",
       "4     18.7  396.90   5.33  "
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.datasets import load_boston\n",
    "boston_data = load_boston()\n",
    "df = pd.DataFrame(boston_data.data, columns=boston_data.feature_names)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = boston_data.target\n",
    "X = df[['LSTAT']].values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SVR(C=1.0, cache_size=200, coef0=0.0, degree=3, epsilon=0.1, gamma='auto',\n",
       "    kernel='rbf', max_iter=-1, shrinking=True, tol=0.001, verbose=False)"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "svr = SVR(gamma='auto')\n",
    "svr.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "sort_idx = X.flatten().argsort()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,8))\n",
    "plt.scatter(X[sort_idx], y[sort_idx])\n",
    "plt.plot(X[sort_idx], svr.predict(X[sort_idx]), color='k')\n",
    "\n",
    "plt.xlabel('LSTAT')\n",
    "plt.ylabel('MEDV');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(X, y, \n",
    "                                                    test_size=0.3, \n",
    "                                                    random_state=42)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Linear Kernel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SVR(C=1.0, cache_size=200, coef0=0.0, degree=3, epsilon=0.1,\n",
       "    gamma='auto_deprecated', kernel='linear', max_iter=-1, shrinking=True,\n",
       "    tol=0.001, verbose=False)"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "svr = SVR(kernel='linear')\n",
    "svr.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_train_pred = svr.predict(X_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_test_pred = svr.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MSE train: 41.8187, test: 36.8372\n"
     ]
    }
   ],
   "source": [
    "print(\"MSE train: {0:.4f}, test: {1:.4f}\".\\\n",
    "      format(mean_squared_error(y_train, y_train_pred), \n",
    "             mean_squared_error(y_test, y_test_pred)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R^2 train: 0.5242, test: 0.5056\n"
     ]
    }
   ],
   "source": [
    "print(\"R^2 train: {0:.4f}, test: {1:.4f}\".\\\n",
    "      format(r2_score(y_train, y_train_pred),\n",
    "             r2_score(y_test, y_test_pred)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Polynomial"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SVR(C=1000.0, cache_size=200, coef0=0.0, degree=2, epsilon=0.1, gamma='auto',\n",
       "    kernel='poly', max_iter=-1, shrinking=True, tol=0.001, verbose=False)"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "svr = SVR(kernel='poly', C=1e3, degree=2, gamma='auto')\n",
    "svr.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_train_pred = svr.predict(X_train)\n",
    "y_test_pred = svr.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MSE train: 110.3334, test: 114.3676\n",
      "R^2 train: -0.2553, test: -0.5349\n"
     ]
    }
   ],
   "source": [
    "print(\"MSE train: {0:.4f}, test: {1:.4f}\".\\\n",
    "      format(mean_squared_error(y_train, y_train_pred), \n",
    "             mean_squared_error(y_test, y_test_pred)))\n",
    "print(\"R^2 train: {0:.4f}, test: {1:.4f}\".\\\n",
    "      format(r2_score(y_train, y_train_pred),\n",
    "             r2_score(y_test, y_test_pred)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "rbf Kernel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SVR(C=1000.0, cache_size=200, coef0=0.0, degree=3, epsilon=0.1, gamma=0.1,\n",
       "    kernel='rbf', max_iter=-1, shrinking=True, tol=0.001, verbose=False)"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "svr = SVR(kernel='rbf', C=1e3, gamma=0.1)\n",
    "svr.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_train_pred = svr.predict(X_train)\n",
    "y_test_pred = svr.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MSE train: 27.5635, test: 26.7051\n",
      "R^2 train: 0.6864, test: 0.6416\n"
     ]
    }
   ],
   "source": [
    "print(\"MSE train: {0:.4f}, test: {1:.4f}\".\\\n",
    "      format(mean_squared_error(y_train, y_train_pred), \n",
    "             mean_squared_error(y_test, y_test_pred)))\n",
    "print(\"R^2 train: {0:.4f}, test: {1:.4f}\".\\\n",
    "      format(r2_score(y_train, y_train_pred),\n",
    "             r2_score(y_test, y_test_pred)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n",
    "# 6. Advantages and Disadvantages\n",
    "\n",
    "\n",
    "\n",
    "The **advantages** of support vector machines are:\n",
    "* Effective in high dimensional spaces.\n",
    "* Uses only a subset of training points (support vectors) in the decision function.\n",
    "* Many different Kernel functions can be specified for the decision function.\n",
    "    * Linear\n",
    "    * Polynomial\n",
    "    * RBF\n",
    "    * Sigmoid\n",
    "    * Custom\n",
    "\n",
    "\n",
    "The **disadvantages** of support vector machines include:\n",
    "* Beware of overfitting when num_features > num_samples.\n",
    "* Choice of Kernel and Regularization can have a large impact on performance\n",
    "* No probability estimates\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n",
    "\n",
    "# Summary\n",
    "\n",
    "\n",
    "| Class |  Out-of-core support | Kernel Trick |\n",
    "| :- |  :- | :- | :- |\n",
    "| `SGDClassifier` |  Yes | No |\n",
    "| `LinearSVC` |  No | No |\n",
    "| `SVC` |  No | Yes |\n",
    "\n",
    "**Note:** All require features scaling\n",
    "\n",
    "Support Vector Machine algorithms are not scale invariant, so it is highly recommended to scale your data. For example, scale each attribute on the input vector X to [0,1] or [-1,+1], or standardize it to have mean 0 and variance 1. Note that the same scaling must be applied to the test vector to obtain meaningful results. See section Preprocessing data for more details on scaling and normalization. ~ [scikit-learn documentation](http://scikit-learn.org/stable/modules/svm.html#svm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Where to From Here\n",
    "\n",
    "* [LIBSVM](http://www.csie.ntu.edu.tw/~cjlin/libsvm/)\n",
    "* [LIBLINEAR](http://www.csie.ntu.edu.tw/~cjlin/liblinear/)\n",
    "* [Hands-On Machine Learning with Scikit-Learn and TensorFlow](https://www.safaribooksonline.com/library/view/hands-on-machine-learning/9781491962282/ch05.html#svm_chapter)\n",
    "* [Python Data Science Handbook](https://www.safaribooksonline.com/library/view/python-data-science/9781491912126/ch05.html#in-depth-support-vector-machines)\n",
    "* [Python Machine Learning, 2E](https://www.safaribooksonline.com/library/view/python-machine-learning/9781787125933/ch03s04.html)\n",
    "* [Statistics for Machine Learning](https://www.safaribooksonline.com/library/view/statistics-for-machine/9781788295758/f2c95085-6676-41c6-876e-ab6802666ea2.xhtml)\n",
    "* [ConvNetJS](http://cs.stanford.edu/people/karpathy/convnetjs/)\n"
   ]
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    "***"
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