SVM.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np \n",
    "import matplotlib.pyplot as plt\n",
    "import math\n",
    "import sys\n",
    "import subprocess\n",
    "#to install cvxopt \n",
    "subprocess.check_call([sys.executable, '-m', 'pip', 'install', 'cvxopt'])\n",
    "import cvxopt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "path1 = \"Data1.xlsx\"\n",
    "path2 = \"Data2.xlsx\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Q1 - Data 1 Visualization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "df1 = pd.read_excel(path1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": true
   },
   "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>Variable 1</th>\n",
       "      <th>Variable 2</th>\n",
       "      <th>Class</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.97430</td>\n",
       "      <td>4.6057</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2.28530</td>\n",
       "      <td>3.8689</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2.98810</td>\n",
       "      <td>4.5751</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2.94200</td>\n",
       "      <td>3.5619</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3.58720</td>\n",
       "      <td>2.8660</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>4.02500</td>\n",
       "      <td>3.2037</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>3.39140</td>\n",
       "      <td>3.4391</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>3.92130</td>\n",
       "      <td>4.1861</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>2.79220</td>\n",
       "      <td>4.0531</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>2.56180</td>\n",
       "      <td>4.6262</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>3.37980</td>\n",
       "      <td>3.9201</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>3.11480</td>\n",
       "      <td>3.0809</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>1.92820</td>\n",
       "      <td>4.0634</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>2.27380</td>\n",
       "      <td>4.3806</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>2.66550</td>\n",
       "      <td>3.5108</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>3.19550</td>\n",
       "      <td>4.2988</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>3.66790</td>\n",
       "      <td>3.8792</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>3.92130</td>\n",
       "      <td>3.4391</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>3.61020</td>\n",
       "      <td>3.1321</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>3.04570</td>\n",
       "      <td>3.3265</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>1.59410</td>\n",
       "      <td>3.3675</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>2.02030</td>\n",
       "      <td>3.2139</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>1.96270</td>\n",
       "      <td>2.7943</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>2.28530</td>\n",
       "      <td>2.7227</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>2.31990</td>\n",
       "      <td>2.9684</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>2.83830</td>\n",
       "      <td>2.6409</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>3.05730</td>\n",
       "      <td>2.3031</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>2.49270</td>\n",
       "      <td>2.0473</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>2.51570</td>\n",
       "      <td>2.3953</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>1.88210</td>\n",
       "      <td>2.0677</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>2.02030</td>\n",
       "      <td>2.3646</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>1.23690</td>\n",
       "      <td>2.3339</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>1.90510</td>\n",
       "      <td>2.9274</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>1.57100</td>\n",
       "      <td>3.0809</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>1.55950</td>\n",
       "      <td>2.7023</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>1.69780</td>\n",
       "      <td>2.4157</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>1.50190</td>\n",
       "      <td>2.0371</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>0.97200</td>\n",
       "      <td>2.6920</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>1.17930</td>\n",
       "      <td>2.9376</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>0.82220</td>\n",
       "      <td>3.0092</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>0.98350</td>\n",
       "      <td>3.3981</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>41</th>\n",
       "      <td>1.26000</td>\n",
       "      <td>3.2037</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>1.32910</td>\n",
       "      <td>3.5209</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>43</th>\n",
       "      <td>2.23920</td>\n",
       "      <td>2.2110</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>44</th>\n",
       "      <td>2.45820</td>\n",
       "      <td>2.6511</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45</th>\n",
       "      <td>2.80380</td>\n",
       "      <td>1.9756</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>46</th>\n",
       "      <td>2.10100</td>\n",
       "      <td>1.6277</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47</th>\n",
       "      <td>2.55030</td>\n",
       "      <td>2.8967</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>48</th>\n",
       "      <td>0.91440</td>\n",
       "      <td>3.0298</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>49</th>\n",
       "      <td>0.77615</td>\n",
       "      <td>2.5999</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Variable 1  Variable 2  Class\n",
       "0      1.97430      4.6057      1\n",
       "1      2.28530      3.8689      1\n",
       "2      2.98810      4.5751      1\n",
       "3      2.94200      3.5619      1\n",
       "4      3.58720      2.8660      1\n",
       "5      4.02500      3.2037      1\n",
       "6      3.39140      3.4391      1\n",
       "7      3.92130      4.1861      1\n",
       "8      2.79220      4.0531      1\n",
       "9      2.56180      4.6262      1\n",
       "10     3.37980      3.9201      1\n",
       "11     3.11480      3.0809      1\n",
       "12     1.92820      4.0634      1\n",
       "13     2.27380      4.3806      1\n",
       "14     2.66550      3.5108      1\n",
       "15     3.19550      4.2988      1\n",
       "16     3.66790      3.8792      1\n",
       "17     3.92130      3.4391      1\n",
       "18     3.61020      3.1321      1\n",
       "19     3.04570      3.3265      1\n",
       "20     1.59410      3.3675     -1\n",
       "21     2.02030      3.2139     -1\n",
       "22     1.96270      2.7943     -1\n",
       "23     2.28530      2.7227     -1\n",
       "24     2.31990      2.9684     -1\n",
       "25     2.83830      2.6409     -1\n",
       "26     3.05730      2.3031     -1\n",
       "27     2.49270      2.0473     -1\n",
       "28     2.51570      2.3953     -1\n",
       "29     1.88210      2.0677     -1\n",
       "30     2.02030      2.3646     -1\n",
       "31     1.23690      2.3339     -1\n",
       "32     1.90510      2.9274     -1\n",
       "33     1.57100      3.0809     -1\n",
       "34     1.55950      2.7023     -1\n",
       "35     1.69780      2.4157     -1\n",
       "36     1.50190      2.0371     -1\n",
       "37     0.97200      2.6920     -1\n",
       "38     1.17930      2.9376     -1\n",
       "39     0.82220      3.0092     -1\n",
       "40     0.98350      3.3981     -1\n",
       "41     1.26000      3.2037     -1\n",
       "42     1.32910      3.5209     -1\n",
       "43     2.23920      2.2110     -1\n",
       "44     2.45820      2.6511     -1\n",
       "45     2.80380      1.9756     -1\n",
       "46     2.10100      1.6277     -1\n",
       "47     2.55030      2.8967     -1\n",
       "48     0.91440      3.0298     -1\n",
       "49     0.77615      2.5999     -1"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Data1\n",
    "df1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4.0249999999999995   0.77615\n"
     ]
    }
   ],
   "source": [
    "#Maximum and Minimum values of Variable 1 in Data1 \n",
    "print(df1['Variable 1'].max(), \" \", df1['Variable 1'].min())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4.6262   1.6277\n"
     ]
    }
   ],
   "source": [
    "#Maximum and Minimum values of Variable 2 in Data1 \n",
    "print(df1['Variable 2'].max(), \" \", df1['Variable 2'].min())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(50, 2)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Feature matrix for Data1\n",
    "X1 = df1.drop(['Class'], axis = 1).to_numpy()\n",
    "X1.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(50,)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Class matrix for Data1\n",
    "Y11 = df1.drop(['Variable 1', 'Variable 2'], axis = 1).to_numpy()\n",
    "Y1 = np.reshape(Y11, (X1.shape[0],))\n",
    "Y1.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Scatter Plot for Data1\n",
    "fig = plt.figure(figsize = (6, 6))\n",
    "plt.scatter(*X1[Y1 == (-1)].T, s = 8, color = \"blue\", alpha = 0.5)\n",
    "plt.scatter(*X1[Y1 == 1].T, s = 8, color = \"red\", alpha = 0.5)\n",
    "plt.xlim(0.0, 5.0)\n",
    "plt.ylim(1.0, 5.0)\n",
    "plt.ylabel(r'$Variable 2$')\n",
    "plt.xlabel(r'$Variable 1$')\n",
    "plt.title(\"Data1\") \n",
    "#plt.savefig(\"C:\\Me\\sem6\\cll788\\A3\\Data1_scatter.jpeg\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Q2 - SVM Implementation on Data 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(50, 1)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#tn\n",
    "tn = Y1\n",
    "tn = np.reshape(tn, (tn.shape[0], 1))\n",
    "tn.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "#H = tn*tm*xn.T*xm\n",
    "#P parameter for cvxopt solver\n",
    "a1 = tn*X1\n",
    "a2 = a1.T\n",
    "H = np.dot(a1, a2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "size1 = X1.shape[0]\n",
    "#q parameter for cvxopt solver\n",
    "q = -1*np.ones((size1, 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "#G parameter for cvxopt solver\n",
    "G = -1*np.eye(size1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "#h parameter for cvxopt solver\n",
    "#for this case we have h as a 0 matrix\n",
    "h = np.zeros((size1, 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "#A parameter for cvxopt solver\n",
    "A = tn.reshape(1, -1)\n",
    "A = A.astype('float')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "#b parameter for cvxopt solver\n",
    "b_cvx = np.zeros(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     pcost       dcost       gap    pres   dres\n",
      " 0: -9.8635e+00 -1.8817e+01  1e+02  1e+01  2e+00\n",
      " 1: -1.5021e+01 -1.0777e+01  2e+01  2e+00  3e-01\n",
      " 2: -1.2100e+01 -9.6312e+00  1e+01  9e-01  1e-01\n",
      " 3: -8.2568e+00 -8.0984e+00  2e+00  1e-01  2e-02\n",
      " 4: -7.9274e+00 -7.9429e+00  4e-02  1e-03  2e-04\n",
      " 5: -7.9397e+00 -7.9399e+00  4e-04  1e-05  2e-06\n",
      " 6: -7.9398e+00 -7.9398e+00  4e-06  1e-07  2e-08\n",
      " 7: -7.9398e+00 -7.9398e+00  4e-08  1e-09  2e-10\n",
      "Optimal solution found.\n"
     ]
    }
   ],
   "source": [
    "#cvxopt solver for quadratic optimization\n",
    "sol = cvxopt.solvers.qp(cvxopt.matrix(H), cvxopt.matrix(q), cvxopt.matrix(G), cvxopt.matrix(h), cvxopt.matrix(A), \n",
    "                        cvxopt.matrix(b_cvx))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "#lambda values\n",
    "lambdas = np.array(sol['x'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2.54140955],\n",
       "       [3.0693502 ]])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#weights\n",
    "w = np.dot(X1.T, (tn*lambdas))\n",
    "w"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "#tolerance used to filter values with lambda>0\n",
    "tolerance = 0.000001"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3\n",
      "(3, 2)\n",
      "(3, 1)\n"
     ]
    }
   ],
   "source": [
    "#filteration of points with lambda>tolerance \n",
    "Ns = 0\n",
    "xs = []\n",
    "ys = []\n",
    "for i in range(lambdas.shape[0]):\n",
    "    if lambdas[i]>=tolerance:\n",
    "        Ns = Ns + 1\n",
    "        xs.append(X1[i])\n",
    "        ys.append(tn[i])\n",
    "xs = np.array(xs)\n",
    "ys = np.array(ys)\n",
    "print(Ns)\n",
    "print(xs.shape)\n",
    "print(ys.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3, 1)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bn = ys - np.dot(xs, w) \n",
    "bn.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-16.372343517060063]\n"
     ]
    }
   ],
   "source": [
    "#bias term\n",
    "b = 0\n",
    "for i in range(bn.shape[0]):\n",
    "    b = b + bn[i][0]\n",
    "b = [b/Ns]\n",
    "print(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "#prediction function y = w.T*x + b\n",
    "def predict1(w, b, x):\n",
    "    \n",
    "    m, n = x.shape\n",
    "    y = []\n",
    "    \n",
    "    for i in range(m):\n",
    "        y.append(((w[0]*x[i][0] + w[1]*x[i][1] + b)))\n",
    "                 \n",
    "    yn = np.array(y)\n",
    "                 \n",
    "    return yn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(50, 1)"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#predicted values\n",
    "y_p = predict1(w, b, X1)\n",
    "y_p.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "accuracy =  98.0 %\n"
     ]
    }
   ],
   "source": [
    "#accuracy computation \n",
    "count = 0\n",
    "for i in range(y_p.shape[0]):\n",
    "    if y_p[i][0]>=1:\n",
    "        y_p[i] = 1\n",
    "    else:\n",
    "        y_p[i] = -1\n",
    "    if tn[i] == y_p[i]:\n",
    "        count = count + 1\n",
    "print(\"accuracy = \", (count/y_p.shape[0])*100, \"%\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_p = y_p.reshape(y_p.shape[0], )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.3341399416933974"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#intercept of decision function\n",
    "c = -b[0]/w[1][0]\n",
    "c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.827995954766148"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#slope of decisin function\n",
    "slope = -w[0][0]/w[1][0]\n",
    "slope"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(5.659941799938993, 5.008338083447802)"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#intercepts for line passing through support vectors\n",
    "c11 = c + math.sqrt((1 + slope*slope))/math.sqrt((w[0][0]*w[0][0] + w[1][0]*w[1][0]))\n",
    "c12 = c - math.sqrt((1 + slope*slope))/math.sqrt((w[0][0]*w[0][0] + w[1][0]*w[1][0]))\n",
    "(c11, c12)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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NsLAw/v77b605WrnrO/OkJOjZE1JSIDnZ/rlnT/c7T8PIhikON+D2229n7ty5REVF8fXXX2vLKVasGHFxccTGxjJ06FCtBWLs2LE0atTIcwuEO78z378f/P2vvM3Pz367Ybg5UxxuUP369Zk3bx7jx4/X+qKdWSDWrl3L8OHDtXYxvfHGG/Tt25fAwEAtGdq4+zvzChUgNfXK2y5ftt+uk7u2pAyPYorDTQgPD2flypWcPHkSnddaFC9enLi4OFauXMmrr76qtUD06tWLy5cv0759e06dOqUlx+nc/Z15SAhER0NQEAQH2z9HR9tv18WdW1KGRzHF4SaJCD///DONGzfm+++/15ZTokQJ4uPjiYmJYdSoUdpywD5j6s4776RBgwbaFyF0irx6Z34jOnSAAwcgLs7+uUMHfVnu3pIyPIopDregXr16zJw5k2bNmrFp0yZtOSEhIcTHx7N06VJGjx6tLUdEePfdd3n88ceJjIzUuuaTU+TFO/ObERICderoPy93b0kZHsUsn+EEK1eu5MyZM3Ts2FFrTmJiIqGhobRr144RI0Zoy1FK8fPPP/PAAw+QmpqK/9UvOO4mKcn+AlihgvsVBldKSrJ3JaWk/HNbUJC9xZKf/12MK5jlM1woMjKSjh078umnn2odgyhZsiQ2m40FCxbw+uuva8sRER544AHi4uKoW7cuZ86c0ZblFK56Z+7uPKUlZXgElxUHEfERke0isjKb+7qLSJKI/Oj4eMZV5+VMxYsXp0mTJmzbtk1bxu23347NZmPu3LmMGzdOWw5AWFgYDz30EBEREZw9e1ZrluEkrhzjMLyaK1sOA4Bfr3P/QqVUDcfHdFedlDM1a9aMTz75hMaNG/PLL79oy7njjjuw2WzMmjWL8ePHa8sRESZNmsSDDz6ofTDccCLTkjKcwNcVISJSBmgCjAUGuSIzr7Ro0YJChQpRpkwZrTmlSpUiISGBevXq4ePjw+DBg7XkWCwWJk+eTGpqKkePHiU4OJhChQppyTIMw324quXwATAEuN70lygR+UlElohI2ewOEJFeIvKDiPygcxG8W1W/fn0KFy5MREQEO3bs0JZz5513kpCQwNSpU3n33Xe15VgsFgIDA/n4449p3Lgx586d05ZlGIZ70F4cRCQSSFRKbb3OYSuACkqpB4A4YFZ2Bymlpiqlaiulaoe4eZPZx8eHnj170rBhQ3766SdtOaVLlyYhIYEpU6bw/vvva8sBGDVqFFWqVCEyMpLz589rzTIMI2+5ouXwONBMRPYDCwCriMzJeoBS6m+l1CXHt9OAWi44L+3atGnDhAkTtL/bLlOmDAkJCUyaNIkJEyZoy7FYLEyfPp27776brVuvV+sNw/B0Lr3OQUTqAS8ppSKvur2UUuqY4+uWwMtKqUeu91zudJ1DTg4dOkTZsmVJTk6mSJEi2nIOHjxIvXr1GDhwIP3799eWk2n+/Pk0b96cAgUKaM8yDMM53P46BxEZIyLNHN++ICI7RWQH8ALQPa/OS4eyZcvyxx9/cO+997Jr1y5tOeXKlSMhIYH33nuPyZMna8sB+4Vya9asoXnz5qRkvejKMAyvYK6QdqE5c+bw8ssvEx8fT7Vq1bTl7N+/n3r16jFkyBD69u2rLSc9PZ2uXbuSlJRETEwMQUFB2rIMw3CO3LYcXDKV1bDr3LkzGRkZDB8+nKVLl2rLqVChwv+muVosFvr06aMlx8fHh1mzZvHee+9p35TIMAzXMstnuFjXrl1ZtGgRSUlJ7NmzR1tOxYoVSUhIYNy4cUydOlVbjq+vL0OGDOHs2bP06dOHixcvastyGbMfgmGY4pAXfHx82LBhA1arVWuBqFSpEjabjddff53p0/VedF68eHFOnjxJVFQUly5dyvkB7srsh2AYgCkOeaZ169aMHDkSq9XK3r17teVUqVKF+Ph4Ro8ezYwZM7Tl+Pr6MnfuXIKCgrSvTquN2Q/BMP7HjDnkoWeeeQalFDt27KBKlSracqpWrUp8fDxWqxWLxUL37t215Pj5+TF//ny2b98O2AesfXx8tGRpkbkfQtbZV5n7Ibj5RZeG4Wym5ZDHnn32WaKiopg5cyb79u3TlnPXXXcRHx/Pf//7Xz777DNtOX5+fjz88MMsWbKEqKgoUq/eqc2decLOcobhIqY4uIkLFy5gtVrZr3HXrrvvvpu4uDiGDh3KnDlzcn7ALWjWzH4JS/v27bl8+bLWLKcx+yEYxv+Y4uAm+vbty+DBgwkNDeXgwYPacqpVq0ZcXBxDhgxh7ty52nL8/f1ZtGgRaWlpvP3229pynM7sh2AYgBlzcCvPP/88ISEhFC1aVGvOPffcQ1xcHPXr18disdBB0wugv78/ixcvJiMjg7/++ovixYvj5+enJcupQkLyZ2vBbLdqZGFaDm6mbdu2+Pv706xZM60tiOrVq7N+/XoGDRrEwoULteUEBAQQFBTEqFGj6NSpE2lpadqyjFtgpvAaVzHFwQ0FBgYSGhpKaGgohw4d0pZz3333sX79el588UUWLVqkLQfggw8+4MyZM3Tp0sUUCHdjpvAa2TDFwU0NHDiQvn37Eh4ernXGz/3338+6det44YUXWLJkibacwMBAPv/8cy5cuKB1AyTjJmRO4c0qcwqvkW+ZMQc39n//939ERkbi7+9PSkqKtoXtHnjgAdauXUtERAQWi4VWrVppycksECJCTEwMkZGRnnUdhLcyU3iNbJiWg5u7++672bZtGw899BBHjx7VllOjRg3WrFlD3759+fzzz7XliAhpaWlMnDiRp59+mvT0dG1ZRi6ZKbxGNkxx8AA1a9akW7duWK1Wjh07pi3noYceYvXq1fTu3ZuYmBhtOb6+vnzxxRccPnyYHj16mALhDswUXuMqpjh4iKFDh9KlSxeGDRumNadmzZqsXr2aXr16sWLFCm05BQoUYMWKFZQtW9ZzLpLzdiEhUKeOaTEYgNnsx+OkpqZy6tQpAG6//XZtOVu2bCEyMpLo6GgiIyNzfsAtOHz4MFOmTOG1117DYjHvVwxDJ7ffJtS4Of7+/ixdupSwsDASExO15dSpU4cVK1bQo0cPVq9erS0HoGjRonz99df07t2bjIwMrVmGlzN7cTiNKQ4eqG/fvkRFRREWFkaSxv8EDz/8MCtWrKB79+6sXbtWW06hQoVYvXo1u3fvZsCAAdpyDC9nLuRzKtOt5KGUUowePZqHH36Yxo0ba83auHEjzZs3Z/bs2TRs2FBbztmzZ9mxYwdPPPEESilERFuW4WWSkuwFIety60FB9sF1M4ZyBdOt5OVEhFGjRtG4cWPmzJnDiRMntGU9+uijfP7553Tp0oX169dryylcuDBPPPEEM2bMoF+/fmZfaiP3zIV8TmeKgxfYuXMn4eHh/P3339oyHnvsMZYtW0anTp2Ii4vTlgMQFRXF1q1beeGFF0yBMHLHXMjndKY4eIFx48YRHh5OeHg4J0+e1JbzxBNPsGzZMjp06IDNZtOWU6RIEdatW8fmzZuZNm2athzDi5gL+ZzOjDl4CaUUH3/8MZ07d6Zw4cJaszZs2ECbNm1YtGgR9erV05aTnJxMQEAA58+fp1ixYmYMwsiZWXY8R2bMIZ8REZ577jkyMjLo1KkTp0+f1pZVt25dFi1aRNu2bdmwYYO2nCJFihAYGEivXr146aWXTBeTkTNzIZ/TmOLgZYKDgwkJCaFBgwYkJydry6lXrx4LFiygTZs2fPXVV9pyAKZPn86XX37JkCFDTIEwDBcxxcHLiAjvv/8+jzzyCE2aNNF6UZnVamX+/Pm0bt2ab775RlvObbfdRmxsLN999x179uzRlmMYxj/MmIOXUkrx448/8tBDD3H58mWt23PGxcXRsWNHli9fzuOPP64tJ/NvNT4+nrAHHkAOHDB9y4Zxg8yYQz4nIjz00EPEx8dTr149zp49qy2rfv36zJkzh5YtW/Ldd99pyxERUlJS+L+ePflv6dKo+vW9/0pYsxyEkUdMcfByoaGh3H///TRq1EhrgWjQoAGzZ8+mRYsWfP/999pyCpw/T1xiIl+kpTHizBmUN29paZaDMPKQKQ5ezmKx8NFHH1G9enVGjhypNathw4bMmjWLZs2asWnTJj0h+/cTEhBAPHAGSAfvvBLW7Ots5DFTHPIBi8XCxx9/zOuvv85ff/3FuXPntGU1atSITz/9lKZNm7J582bnBziuhC0JTAAOARNSUrzvSlizHISRx1xWHETER0S2i8jKbO4LEJGFIrJXRDaJSAVXnVd+YbFYKFCgAB999BGRkZGcP39eW1aTJk2Ijo6madOmOH3SwFVXwhYIDOSTkiV57eOPnZuT18xyEEYec2XLYQDw6zXu6wmcUkpVAd4H3nTZWeUzo0aNomLFijRt2pQLFy5oy2natCnTpk2jSZMmbNu2zblPnmVLy9sPHsT2ww/MmzePN9/0oj8bsxyEkcdcUhxEpAzQBJh+jUOaA7McXy8BwsSslaCFxWJh+vTpVKpUSU+3TxbNmjXjk08+oVGjRmzfvt25T57lStg77rgDm83GI4884tyMvGb2dTbykK+Lcj4AhgDXWvSnNPbuY5RSaSKSDBQHrliHWkR6Ab0AypUrp+1kvZ2Pjw/Tp9vr9OLFi4mMjCQoKEhLVosWLVBK0ahRI9auXUuNGjW05JQqVYpSpUoxYcIELl68yMsvv6wlx+VCQkxrwcgT2lsOIhIJJCqltl7vsGxu+9fVeUqpqUqp2kqp2iHmP8wtU0oRExND8+bNScm6SYqTtWzZksmTJxMREcGOHTu05QC0bt2a6dOn8/bbb2vNMQxv54pupceBZiKyH1gAWEVkzlXHHAbKAoiIL1AE0Lf2tAHYLyqbOXMmJUqUoEWLFly8eFFbVlRUFBMnTiQiIoKffvpJW07p0qVJSEjgk08+YdmyZdpyDMPbaS8OSqmhSqkySqkKQHvAppTqfNVhXwDdHF+3dhzjmet6eBhfX18+++wz6tatS3p6utasNm3aMGHCBBo2bMgvv/yiLadMmTJ8/fXXNGnSROuFf4bhzfLsOgcRGSMizRzfRgPFRWQvMAh4Ja/OKz/y9fVl2LBhnD9/nueff55Lly5py2rbti3vv/8+4eHh7Ny5U1tOqVKlCAgIoGnTpnz44YfacvI9s7yH13LVgDQASqkvgS8dX4/IcvtFoI0rz8X4t9tuu43jx48TFRXF0qVLCQgI0JLTvn17MjIyCA8PJy4ujurVq2vJAZg1axb16tXDYrHQr18/bTn50vz59qu2/f3t12RER5sZVV7EXCFt/I+fnx/z58/H39+fTp06ac3q2LEjb731FvXr1+fXX691+cutK1++PAkJCUyZMoWjR49qy8l3zPIeXs+lLQfD/fn5+bFgwQK2brVPLsvIyMBi0fMeonPnzmRkZFC/fn1sNht33323lpwKFSqwY8cOfHx82LRpE//5z3+05OQrmct7ZJ3llrm8x83OJDRbfLoV03Iw/sXf359HH32UZcuWERUVxeXLl7Vlde3alXHjxhEWFsbvv/+uLcfX15eTJ0/Stm1bPvnkk5wfYPrSr8/Zy3uYFWjdjikOxjVFRkaSnp5O+/bttRaIbt268dprrxEWFqZ1p7fixYtjs9kYO3Ys06ZNu/aB5oUqZ85c3sN0UbklUxyMa/L392fx4sVcunRJ+7pFTz/9NKNGjcJqtbJ3715tOZUrV8Zms7Ft27bs96M2L1S556zlPcwKtG7JjDkY1xUQEMDSpUtJT08nMTGRYsWK4eur58+mZ8+eZGRkYLVaSUhIoHLlylpyqlSpwpQpU9i7dy9btmyhQ9YXNR196d7MGct7mBVo3ZIpDkaOMqe0Dho0iNOnTzNnzhxtBeLZZ59FKfW/AlGpUiUtOWAfbB88eDCpqal06+a4BtO8ULleZhdVz572Qnz5slmB1g2YbiUj1z744ANOnTpF165dSUtL05bTq1cvhg4ditVq5c8//9SWc9dddxEXF8ewYcOYM8exootZKjtvmBVo3Y5pORi5FhgYyOeff06bNm348ccfqV27trasPn36kJ6e/r8WRAVN79yrVatGXFwciYmJ/9zYoQPUr2+mVbqaWYHWrYinLmFUu3Zt5fRdxoxcUdyDVfUAACAASURBVEohIqxcuZJGjRrh4+OjLWvixIm8//77JCQkUL58eW05AOPHj6dcuXJ07NhRa45h5CUR2aqUyvGdnWk5GDdMREhLS+P9999nyZIlREdHaysQ/fv3JyMjg9DQUL788kut+3g0bdqU8PBwLBYL7du315ZjGJ7AjDkYN8XX15cVK1Zw4MABnnnmGTIyMrRlDRgwgP79+xMaGsqhQ4e05dx7772sX7+egQMHsmHDBm05huEJTHEwblqBAgVYuXIlt99+O6lXz/BxsoEDB/L8889jtVo5cuSItpz77ruPr7/+mkcffVTr/haG4e5McTBuScGCBRk/fjx///03I0aM0NqCGDRoEL179yY0NFRrgahSpQq+vr488cQTLF26VFuOYbgzM+ZgOEWRIkVISEjg+PHjTJkyRdtifS+99NIVF8rdeeedWnIsFgvTp08nIiICEaFVq1ZacgzDXZmWg+EUhQoVYvXq1fzyyy8MHDhQa9aQIUN4+umnsVqtHDt2TFtOjRo1WL16NYMHD+b06dPacgzDHZmWg+E0hQsXZs2aNWzfvh34Z8qrDq+88soVLYg77rhDS07NmjXZtWsX/v7+7Ny5k3vvvVdLjmG4G9NyMJwqODiYunXrMmvWLF544YXsF7dzkmHDhtGxY0esVivHjx/XlhMQEMDhw4exWq2sXLlSW45huBNTHAwtWrRowebNm3nxxRe1FohXX32Vdu3aYbVar7zK2cnKli3LypUr6dmzJ6tWrdKWYxjuwhQHQ4siRYqwbt06Nm7cyNSpU7VmjRw5ktatW2O1WknSuLR2nTp1+OKLL1ixYoW2DMNwF2b5DEOr06dPExAQQEpKCrfddpu2MQilFCNGjCAmJob4+HhCNK/R89tvv3Hw4EHCw8O15hiGs+V2+QzTcjC0Klq0KEFBQfTq1YvBgwdr62ISEcaMGUPTpk2pX78+J06c0JKT6dSpU3Tq1In169drzTGMvGKKg+ESU6dOJT4+npdffllrgXj99ddp3Lgx4eHh/P3331pyAB555BGWL19O586diY2N1ZZjGHnFFAfDJYoVK0ZcXBxfffUVv/32m7YcEWHcuHE0aNCA8PBwTp48qS3r8ccfZ+nSpQQGBmrLMIy8YoqD4TLFixfnu+++o1q1aiQkJGhtQYwfP56wsDDCw8M5deqUlhyAJ598kieffJIxY8aQkJCgLccwXM0UB8OlLBYLFy5cYMCAAYwYMUJrgXjrrbeoV68e4eHh2q9wfuqpp2jbti1ffvml1hzDcBVTHAyXK1CgAPHx8SxfvpzRo0dryxER3nnnHZ588kkaNGigtUDUq1ePhQsX0qZNG3766SdtOYbhKqY4GHkiJCQEm83GiRMntO5HLSK89957PProozRs2JDk5GRtWVarldjYWO655x6tP1O2kpJgyxb7Z8NwAlMcjDxTsmRJJk2axJEjR5g0aZK2HBHhgw8+oE6dOjRs2JAzZ85oy6pRowZKKWrVqsU333yjLecK8+dD+fIQHm7/PH++a3INr2aKg5HnAgICmDx5MmPHjtWWISJMnDiRmjVrEhERobVA+Pv78/bbb9OqVSu+++47bTmAvaXQsyekpEBysv1zz56mBWHcMlMcjGy5spfijjvuwGazMXv2bN566y1tOSLCpEmTePDBB2nUqBFnz57VltWgQQNmz55Nly5d9O4ot38/+PtfeZufn/12w7gFpjgY/5IXvRSlSpUiISGB2rVzvKr/llgsFiZPnsx9991H48aNOXfunLashg0bsmPHDgICAth/rRfrW63CFSrA1Vu0Xr5sv90wboH24iAigSKyWUR2iMhOEfnX9BQR6S4iSSLyo+PjGd3nZWQvL3spSpUqhdVqZdKkSbz99tvaciwWC1OmTKFatWraC0ShQoXYtWsXDz/8MJs3b77yTmdU4ZAQiI6GoCAIDrZ/jo62324Yt0IppfUDEKCQ42s/YBPwyFXHdAcm3cjz1qpVSxnOt3mzUkWKKAX/fAQH2293lUOHDqnKlSurd955R2tOenq66tGjh6pbt646d+6c1qwvvvhChYSEqC1btthvSExUKijoyn/ooCD77TcjMdH+S7rZxxv5BvCDysVrrPaWg+N8Mt+a+Tk+PHMp2HzAHXopypQpQ0JCAh999BHLli3TlmOxWJg2bRoVK1YkMjKSCxcuaMtq2rQp06dP59NPP7Xf4OyxgpAQqFPHtBgMp3HJmIOI+IjIj0AiEKuU2pTNYVEi8pOILBGRstd4nl4i8oOI/KBz3f78zF16KcqWLcvXX3+tvdvHYrEwffp0ypcvT9OmTbUWiGbNmjF58mR+/fVXtp05k/dV2DCuwyXFQSmVrpSqAZQBHhaR+646ZAVQQSn1ABAHzLrG80xVStVWStXWvV5/ftahAxw4AHFx9s8dOuTNedx5550EBgbSrFkzrddB+Pj4EB0dTenSpWnWrBkpKSnasgD27t1L406d2P7qq3lfhQ3jGly+2Y+IjATOK6Xeucb9PsBJpVSR6z2P2ewn/9i/fz+hoaEMHjyYvn37astJT0+na9euJCUlERMTQ1BQkLasZcuW0bdvX9bOm0eNwoXtLQZPLAxJSfauMHc5f3c7HzfkNpv9iEiIiBR1fB0E1Ad2X3VMqSzfNgN+1X1ehueoUKECNpuNiRMncuTIEW05Pj4+zJo1ixIlStCiRQut1ye0atWKyZMncyEw0HPHCtztymx3Ox8Pp73lICIPYO8m8sFejBYppcaIyBjso+ZfiMgb2ItCGnASeE4ptfuaT4ppOeRHaWlp+Pj4sG3bNmrVqqU1p3PnziQnJ7N8+XLt+zWMGjWKqKgo7r//fq05TpWUZH8BztoFFxRk74fMi0Lnbufjxtym5aCU+kkp9ZBS6gGl1H1KqTGO20copb5wfD1UKXWvUupBpVRoToXBsMtva635+vpy6tQpWrZsybRp07TmzJkzh8KFCxMVFcWlS5e0ZQFUq1aNBg0a8Msvv2jNcSp3uzLb3c7HC5grpD1Ufm1BFytWDJvNxpgxY4iOjtaW4+vry9y5cylQoID2AtG+fXveffddGjRocO0rqd2NO8x5zsrdzscLmOLggfL7WmtVqlTBZrOxadMmbZsFAfj5+TFv3jwCAgJo06YNqVe/+DhRx44dWbBgAWXKlCEjI0NbjtO4y5xndz0fL+Dy2UrOkp/HHLZssbcYsm5NEBxsn3pap07enVd2dE8e2bdvH1u2bKFdu3bOf3KHy5cv065dOzIyMli0aBH+V3dfONG5c+eoW7cuc+fOpVq1atpynMbdZge52/m4IbcZczCcz1Na0K7o+rp8+TL/93//x+zZs53/5A5+fn4sWLAAgHbt2nH58mVtWYUKFeKFF16gfv36/Pbbb9pynMbdrsx2t/PxYKY4eCBPaEG7quvr7rvvJjY2lldeeYW5c+c698mz8Pf3Z9GiRaSnp9O+fXutBaJbt268/vrrtGrVivT0dG05hnE9pjh4KHe5ivlaXDl55J577iE2NpZSpUrlfPAt8Pf3Z/HixVy6dIkOHTpoLRDdu3fnq6++wmKxcPz48Vt7svw2rc1wClMcPJg7t6Bd3fVVvXp1rFYrb7/9NvM1Tt0KCAhg6dKlpKSk0KlTJ617RRcvXpzvvvuOOnXqsHfv3pt7kvw6rc24ZaY4GFrkVddXREQEgwYNYuHChdoyMgvE2bNn6dy5s9YC8fjjj/Pf//4Xq9XKH3/8cWMPzu/T2oxbYoqDoU1edH3df//9rFu3jgEDBrBhwwZtOYGBgSxfvpxTp07RpUsXrQWiV69eDBs2jI8++ujGHmguDDNugZnKanilPXv2UK5cOcD+Tl+XlJQUmjdvTkhICJ999hk+Pj7aspRS7Nq1i4IFC1IhN/1zZkkJIxtmKquRr1WtWhU/Pz+efPJJli9fri0nKCiImJgYEhMTefrpp7XOLhIRNm7ciNVq5cCBAzk/wBOmtRluyxQHw2tZLBY+/vhj+vTpQ0xMjLaczAJx5MgRevToobVAPPPMMwwcOJDQ0FAOHjyY8wPcfVqb4bZMt5Lh9bZu3UqbNm3Ytm0bRYsW1ZZz4cIFIiMjKV++PNHR0Vgs+t57TZ48mYcffpg67nZJvOH2nNqtJCLVRCRMRApddXvEzZ6gYbhKrVq12LVrF0WKFGH3bn0L/hYoUIAVK1bw559/8uyzz2pdI+n555+ndu3ajBkzhkOHDmnLMfKvHIuDiLwAxAD9gV9EpHmWu8fpOjHDuBnXut4rMDCQw4cP89RTT7Fq1Spt+QULFmTVqlXs2bOH3r17ay0QIkKBAgWwWq1aN0Ey8qfctByeBWoppVoA9YBXRWSA4z7RdWKGa3nDRbQ5Xe9VtmxZVqxYwdNPP82aNWu0nUfBggVZvXo1u3fvpk+fPloLxEsvvcSzzz5LaGgoSZ78y3MFb/gjdyWl1HU/gF1XfV8IWAu8B/yY0+N1fdSqVUsZzjFvnlJBQUoVKWL/PG9eXp/RjUtMtJ87/PMRFGS//WobN25UPXv21H5OZ86cUY899pjq3bu3Sk9P15q1YsUKlZaWpjIyMrTmeCxv+CN3Euw7cOb4GpublsNfIlIjSzE5B0QCJQAP2tfQyI63XER7I9d7PfLII0yfPp29e/cSHx+v7ZwKFy7MmjVr+Omnn+jXr5/WvSciIyM5efIkdevW5a+//tKW45G85Y/cxXJTHLoCV/y1KaXSlFJdgae0nJXhMt5yEe3NrOWUmJhIhw4diI2N1XZewcHBrF27lu3bt9O/f3+tBSIkJIQGDRoQGhp664v1eRNv+SN3sRyLg1LqsFLqLxGpKiIzRGRylvu+1Xt6hm6esjdETm7meq/HHnuMpUuX0rFjR60tiMwCsWXLFgYMGKC1QPz3v/+lffv2tGrVSmuOR/GWP3IXu5GJ2LOBxcCTACJyn4h8puWsDJfxpotob+Z6ryeffJKlS5dqXfYCoEiRIqxbt47vv/+egQMHan3hHjlyJIsWLUIpRXLW7QLzK2/6I3ehXF8EJyKblVIPi8h2pdRDjtu2KaVqaj3DazAXwTmX2V0Rxo4dy+OPP069evW0ZZw+fZrw8HCefPJJ3n33XUT0TfhbsWIFw4YNw2azEeKOv1RX/9GZP3JAz9pKR0WkIqAcAQIE3eT5GW7GnfeGcJXHHnuMNm3aaF3NtWjRoqxfv54NGzYwePBg7YPUzZs3JywsjBMnTmjLuSl5sc+E+SO/ITfScqgATAeqA8OBCMCilGqj6+Sux7QcDB1sNhvt2rUjLi6OBx98UFvOyZMnqV+/PvXr1+fNN9/U1oJQSjF8+HD8/f0ZNWqUlowbZlaLzVO5bTn45vYJlVL7HctltAQeADYAM27+FA3D/VitVtatW8c999xDenq6trGIYsWKERsbS1hYGBaLhTfeeENLgRARxo4di1KKnTt3UqpUKYoVK+b0nBuSOXsoa3HInD1kioPbyM3yGZ+JyCARsQJFlFKLlVKvKqU+UkpddME5Gh7Iky9GrVmzJiJC7dq1+e6777TlFC9enLi4ONasWcPw4cO1dTGJCBaLhSVLllC/fn1OnjyZt78fM3vII+RmzGGW43M3IF5E/hCRlSLyuojkSZeS4d68YdtiPz8/xo8fT4sWLdi4caO2nBIlShAfH8/KlSt59dVXtY5BjBgxgtDQUGrXbkC5cqfy7vdjZg95hBtesltEfLGPOzwIPKCUGqzjxHJixhzck7d1J69Zs4bnn3+enTt3EhSkb/5FUlISVquVVq1aMXr0aG05iYmK0qVHkJbWGvt/4Tz8/ZjZQ3nC6WMOmZRSacBPjg/DuIK3dSc3atSIH3/8kcDAQA4ePPi/rUedLSQkhPj4eEJDQ7FYLIwcOVJLzoEDQsGCr5GcnAG8BfTGz69I3vx+QkI8848in8j1VFYReUpEvhKRnSIyT0TMLiMu5Cl9+N7YnRwcHMyvv/5KnTp10NlaLVmyJDabjYULF/Laa69pyfjn9yPAIaAhqalnPPr3Y+hxI9c5zABew75s92fABBFpq+OkjCt5Uh++t3YnV69enenTp9OkSRO2bt2qLef222/HZrMxb948xo4d6/Tn/+f3IxQu/CE+PrUoU6YhQUHnnJ5leLYbuc7he6XUI1m+LwR8r5S6L4fHBQJfAQHYu7GWKKVGXnVMAPaCUwv4G2inlNp/vef11jGHq7thPbUP31u7k2NiYli7di1TpkzRmnPs2DFCQ0Pp1q0bQ4cOdfrzZ/5+ypdXrF8/lw4dOmhfQsRwD7kdc8jNfg6fAS8C7wAjAF/H7X7kYl1w7O3XQlkeswl45Kpj+gIfO75uDyzM6Xm9cT+H7Jac37zZ/n3WfQqCg+23G3ln9+7davv27Vozjh49qu666y41fvx4rTlKKfXnn3+qZs2aqTNnzmjPMvJWbl63VS73c4jGvmRGMaAFsFdE4oDdwOpcFB+l7HtAZBYHP8fzZdWcf6bMLgHCROeiM27oWkvOFyrkfX343uC3334jIiKCHTt2aMsoVaoUNpuN6dOn8/bbb2vLAShXrhy33347TZo04dw508Vk5G7J7g1KqQlKqR7KvsheZWAgMIpcrq0kIj4i8iOQCMQqpTZddUhp7KNjmbOhkoHiuf4pvMC1lpw/d847+/A9SXaTAZo1a8akSZNo2LCh1gJRunRpEhIS+OSTT3j33Xe15VgsFj7++GPuuusuunTpoi3H8By5nsoqIsWBtsBFYCf2sYPZuXmsUiodqCEiRYHlInKfUuqXrE+f3cOyOYdeQC9A25TCvHK9WT516kD9+t7Zh+/u5s+3t+D8/e2/n+jof5YCb926NUopzpw5o/UcypQpQ0JCwv+muQ4cOFBLjsViYerUqezfv5+MjAwuXbqk9doOw83lpu/J3k3FV9jHHI5hX1cpFfg1t4/P8jwjgZeuum0d8Kjja1/gBI7B8mt9ePOYQ3Bwvt/m1i3cyL7Ur732mvr555+1ns+BAwdUpUqV1AcffKA1RymlPv30UxUaGqrOnz+vPctwLZw45pCpsFJqDHBcKVUX6ADMzOlBIhLiaDEgIkFAfezjFVl9gX15DoDWgM3xQ+QrN7NZzY3ylOsl3MGN7C5ZuXJlGjRowK5du7SdT7ly5bDZbEyYMIGJEydqywHo0qULZcuWpVmzZqRknSpn5Bs3UhwyF9m7JCJBSqmlQONcPK4UkCAiPwFbsI85rBSRMSLSzHFMNFBcRPYCg4BXbuC8vIrOJec96XqJ63FVgbuRC/o6dOjAO++8Q3h4OPs17k1cvnx5bDYb7733HpMnT875ATfJx8eHGTNmUKpUKT755BNtOYYby03zwvEmPgr7jKX/A+YD/YG9uX28sz+8sVtJpxvpInFn2U33dUVebrv6EhISVGpqqsrIyNB6Xvv27VPly5dXH330kdactLQ0lZ6ernbt2qUuXLigNctwDZzVrSQimResHQMuK6XexT6FtQz2KaiGB7iRLhJ3da3pvjpbEDfa1VevXj1SU1N5+OGH+e2337S1cipWrIjNZmP8+PFa39n7+PhgsViYMGECLVu25OJFs0p/fpGbbqX1js8vAptE5HfsrYhLwD26TsxwLm9Y8yivCtyNdvUVLFiQ559/nsceC6Ns2d+1deNVqlQJm83G2LFjmTZtmnOf/CqTJk2iSJEipkDkI7m5zmGj43NbpVR14H5gDPAH8B+9p2c4izeseeRJBa5Jk+6cPTuGS5dakJycpq2VU7lyZWw2G6+99hrR0dHOffIsfH19mTt3LmXLltU6pmK4kdz0PWEvIsNyc6yrPsyYw81JTLQvveFpYw2ZPGW67z/LniQpyFCQqHXZk99//12VKVNGRUdH6wnIIi0tTU2cOFFdvHjx5p7A0/8IPRzOnMqqlMrAPgXV8HA6Z0O5gium+zrDP62cEsBGoBaXLv2hrZVTtWpV4uLiGDFiBDNnztQT4pCRkYHNZqNt27akXt2Uy4m3TJnLB25kKut2ERkpIjfyGMNwOk8ocFd24z2Gn98wChe2cvbsPm2Zd999N3FxcQwfPpzPPvtMW46fnx8LFixARGjbti2XL1/O3QPzYkaBcdNu5IW+LPYVU4+KSIyIvGb2kDaMa8vayjlypA+jR7+s/eK1atWqERcXx9ChQ5kzZ462HH9/fxYtWkTDhg1zv9S3N0yZy0duZg/pAOBe7APT9yulXtJxYjnx1v0cDO+mlGL37t0EBQVRQeNI+q5du6hfvz5vv/02nTp10pYDsHv3bt555x2mTJmCn5/ftQ/01M1JvExu93O4kW1Ci4vIc0BH7OsfLcqrwmAYWXnSkiAiwjfffIPVauXgwYPacqpXr05sbCyDBw9mvuZ+/YoVK3Ls2DE6dux4/S4mb5gyl4/cSLfSciAEGAe8DSSLyK9azsowcskTxzefffZZBgwYQGhoKIcOHdKWc++997J+/XoGDRrEwoULteUEBASwdOlSzp8/T//+/a9/sKfMKDByv2Q3joX3RKSVUqquiEQBVXSdmGHkJOv4ZmZPRc+e9uXN3f3N6IABA7BYLBw5coSyZctqy7nvvvtYv349DRo0wGKx0KaNnmHCwMBAli1bxoEDB0hPT0cpha/vNV5eQkLc/xdkuGThPcPQwtPHN/v3789//vMfxo0bx5EjR7Tl3H///axdu5b+/fuzdOlSbTmBgYHcfffdTJgwgW7dupGenq4ty9AvN2srVXN8+Y6IFAMWAjNEpD/2HdwMI0940hXT1yIi+Pr6EhoaytGjR7XlPPjgg6xdu5bnn3+eZcuWacsBeO6550hMTKR79+6mQHiw3LQcVovIDGCLUuqkUuo97AvvlcUsvGfkIW8Z3xwyZAg9evQgNDSUJI2j6jVq1GD16tU899xzfP7559pygoKCiImJ4ejRo1qn0xp65TiVVUT8gd7Y91mIAV5XSp1wwbldl5nKamRKSnL+Fqo6njMnMTExNGnS5Np99U6ydetWGjduzNSpU2neXN/7u4sXL+Lv78++ffuoWLFi7q+HMLRy2lRWpVSqUmoi9hVYDwObHRv1FHbCeRrGLXP2FdN5NQOqefPmnD59mtDQUI4fP64tp1atWqxatYpevXqxYsUKbTmBgYFYLBYGDx7MM888Q0ZGhrYsw/lyPSCtlLqolHoH+8VvF4FtImKuczCy5UnXHmSV1ys8lChRAqvVitVq1VogateuzcqVK+nZsycrV67UlgMwZ84c9u3bR69evUyB8CA3chFcBRGJAJ4BygFnsV/zYOQBd37x9cRrDzK5wwyoV199lTZt2tCyZUtudAWDG1GnTh1WrFhBjx49WL16tbacggULsmrVKk6ePKn1ug7DyXJathX4CTgJ/AgsAEYCbbG3IPxzs/Srjo/8vGS3q7fKvBGevh2pu5x/RkaGOnjwoMrIyFDJyclaszZu3KhCQkLUmjVrtOYoZV/ue+bMmSo9PV17lpE9nLhkd0uguFKqhlKqvVJqtFJqkVLqZ6XUDa7Xa9yqvO72yIk7vPO+Fe4yA0pEKFu2LCtXruSJJ57gxAl9c0AeeeQRYmJi6Nq1K+vXr8/5Abfg4sWLTJ06lX79+mltFRm3LjcD0n8o81t0G+7+4usN1x7czAoPurr5IiMjadKkCWFhYfz999/OffIsHn30UZYvX07nzp2JjY3VllOwYEHWrFnD9u3bTYFwc2ZvBg/j7i++7vLO+1bdyAwonWMsIsK4ceNo1KgR48ZN0DrO9Pjjj7Ns2TI6depEfHy8nhAgODiYtWvXUqlSJVMc3Flu+p7c8cOMObj3Vpn5ZSdIV41RzJ2boQID01ShQrtUYODfWn/nGzZsUCVKlFDx8fH6Qhy2b9+uhg4dqjIyMrRnGXY4c5tQw714wsKWnrBbmzO4opsvKQmeeUa4eNGHc+cWcfFiA3r0OKWtBfHUU0+xZMkS2rVrx5dffqknxKFChQrExsYyaNAg04pwM6Y4uIGb6a/OLy++7s4V3XxXFqARwFOkpjbg559POy/kKnXr1mXRokW0adOGDRs2aMspWrQo69ev5+uvv2bMmDHacowbZ4pDHvPkawIM14yxXFmABHgXi6UB8KfzQrIRGhrKwoULad26NV999ZW2nNtuu43Y2Fjatm37v+W+DTeQm74nd/zwhjEHd5lTb9w63WMs2Y0zpaenq3feeUedPn1aT6hDbGysKlGihPr666+15iil1IgRI9SQIUPMGIRGmDEH9+fu01KN3NPdzZfdOJOIsG/fPiIiIjhz5oyeYKB+/frMmzePVq1a8e2332rLAXjhhRdYt24dw4YNMy2IPGaKQx5y92mphnu5ugCJCJMmTeKhhx4iIiKCc+fOacsODw9n9uzZtGzZko0bN2rLKV68OHFxcaxatUr7mk/G9ZnikIe85ZoAI+9kFojevXsTFBSkNathw4Z89tlnNG/enO+//15bTokSJfjmm2+IjIzk8OHD2nKM6zPFIY95wrRUw71ZLBa6devG4cOHadWqldYWREREBDNnzqRZs2Zs3rxZW05wcDAA7dq1Y/To0dpyjGszxcENmGmphjOULVuW2267jSZNmnD+/HltOY0bN2bGjBlERkayZcsWbTkiwvLly1m0aJGZ5poHtBcHESkrIgki8quI7BSRAdkcU09EkkXkR8fHCN3nZRjexmKxMG3aNCpVqkTnzp21ZkVGRhIdHU1kZCQ6d2QsWbIkNpuNhIQErVuoGv+W4zahtxwgUgoopZTa5tg9bivQQim1K8sx9YCXlFKRuX1es02oYWQvPT2dP//8k0qVKpGamkpgYKC2rJiYGHr16sWaNWuoWbOmthyAtLQ0Vq1apXVr0/zAaduE3iql1DGl1DbH12eBX4HSunMNI7/y8fGhSpUqzJkzhyZNmnDhwgVtWc2bN+fjjz+mUaNGbN++XVsOwOnTp3n55ZcZP3681hzDzqVjDiJSAXgI2JTN3Y+KnyrDpQAAIABJREFUyA4RWSMi917j8b1E5AcR+cE0MQ3j+jp16sSdd95J8+bNSUlJ0ZbTsmVLpkyZQqNGjfjxxx+15ZQoUQKbzcaMGTN46623tOUYdi4rDiJSCFgKvKiUuvqKnW1AeaXUg8BE4PPsnkMpNVUpVVspVTvEjN4axnX5+Pgwc+ZMSpYsyZQpU7RmtWrVikmTJhEREcGOHTu05dx5550kJCRw+fJlc5GcZtrHHABExA9YCaxTSr2Xi+P3A7WVUtfc/sqMORhG7qSlpSEi7N27l/Lly2sdg1i8eDH9+/dn/fr1PPDAA9pyADZt2sTmzZvp37+/1hxvk9sxB18XnIgA0cCv1yoMInIHcFwppUTkYewtGn3bXhlGPuLra/9v/v7773Pw4EGWL19OQECAlqw2bdqQkZFBw4YNiY2N5b777tOSA1CqVCk++OAD0tPTefHFF7Xl5Feu6FZ6HOgCWLNMVW0sIn1EpI/jmNbALyKyA/gQaK9Mm9Hr6dpa08jepEmTKFSoEFFRUVy6dElbTrt27Xjvvfdo0KABO3fu1JZTrlw5bDYbH374IVOnTtWWk19pbzkopb7Bvs7w9Y6ZBEzSfS6G+5g/H3r2tC88mJpqXzbEXB2ul6+vL3PnzqVPnz7s27ePe+65R1tWhw4dUEoRHh5OXFwc1atX15JTvnx5EhISuHDhAkop7B0VhjO4ZMxBBzPm4LmSkux7V2SdQBMUZF8+xFvmGSQl2VfXrVDBPX+mjIwMPvnkE3r27In/1UsDO9GcOXN4+eWXiY+Pp1q1atpyAAYNGkSVKlXo27ev1hxP5zbXORjG1bx9qXJP2MApPT2d9evX07ZtW1KvXhrYiTp37sy4ceMICwvjt99+05YD0L9/f958803tM7PyC1McDJfz5qXKk5Ls3WUpKZCcbP/cs6f7jav4+fmxcOFClFK0a9eOy5cva8vq1q0bY8eOJSwsjN9//11bTsWKFbHZbLzxxhva953ID0xxMFxO51LleT3I7UmtIn9/fxYvXkxYWBgWi96Xgu7duzNmzBjCwsLYs2ePtpzKlSvzww8/8Nhjj3HixDVnwhu5YIqDkSd0LFXuDt05ntYq8vf3p1+/fuzdu5devXppbUH06NGDkSNHYrVa2bt3r7ackiVLkpGRwVNPPcWMGTO05Xg7Uxzyubx8p+3MpcrdpTvHUzdwKl++PIcPH6Zz586kpaVpy3nmmWd49dVXsVqt/PHHH9pyfHx8+PzzzxkxYgQzZ87UluPNTHHIx9zhnbazuFN3jidu4BQYGMiyZctITk6mX79+WrN69erF8OHDsVqt7Nu3T1vOXXfdRXx8PJMnT9a6AZK3MlNZ8ylvm07qbT9PXklJSWH//v3cfffdKKXw8fHRljVlyhTefPNNvvzySypo7HdTSpGWlsa3335LvXr1tOV4CjOV1bgud3qn7Qye2p3jKrntPgwKCuKee+5h4sSJdO/enfT0dG3n9NxzzzF48GBCQ0M5cOCAthwR4ciRI3Tq1Im5c+dqy/E6SimP/KhVq5Yybl5iolJBQUrBPx9BQfbbPVliolKbN3v+z+FM8+bZf7dFitg/z5uX82MuXLigwsLCVJcuXVRaWprW8/vwww9VxYoV1YEDB7Tm7Ny5U5UqVUrNy80/gBcDflC5eI01LYd8ylvfaZv9uK90swP1QUFBfPHFFxw+fJjZs2drPcf+/fvzwgsvEBoayqFDh7TlVK9endjYWK0zpbyJ9rWVDPfV4f/bu/s4m+v8/+OP1xnjejI7LnIxMjbtMC5GSFJi5sy4VjuUi1lSmyFGUcLXl1La3bbYiFIpVBJ+FmEMw1wgyUWkUlSyQhl8G02umjDv3x/niMUwmPe5mPO6325zm3Hmcz7Pt7PbefpcnPe7F8TF+fY0D+r6nD19eP61mLOnD6/0v3fZsmVZtmwZpUqVYvfu3URERFj7PMTQoUMxxhATE8Pq1asJDw+3klO/fn3q16/PunXrOHDgAPfff7+VnOJAyyHAVa6spVCcXe/nLsqUKQPAsGHDCAsL480337RWEI8//jj5+fm/F0SNGvZWEw4JCeG+++5DRLjvvvus5fgzPa2kVDFWVKcPZ82axTfffMOAAQPIz8+3M1hcJdS/f39iYmL44YcfrOVER0ezYsUKBg8ezOLFi63l+DM9clCqmCuK04fly5cnNTWV3r17s3fvXqu3ng4fPpz8/HxiY2PJysqievXqVnIaN27M8uXLKVu2rJX9+zs9clDKzdvzMtlUFBfqQ0JCWLx4MTVr1uS9996zuobzyJEjefDBB4mNjeXAgQPWcm699VYiIyMZOHCgHkFcQMtBKYrXp8VtO3nyJK+++iqPPvqo1YIYNWoUffr0ITY2luzsbGs54JrWo3///ixdutRqjj/RclABz1fmZfIX5cuXZ8WKFWzevJnHHnvMakGMHj2axMREnE4nBw8etJbTtGlTli1bRr9+/fjqq6+s5fgTLQcV8Irbp8U9oUKFCqSlpREeHm61HACeeuopunfvjtPp5NChQ9ZymjVrxqZNm6hXrx6//PKLtRx/oeWgAp6/TbPtK0JDQxk5ciRffPEFY8aMsVoSY8eOpWvXrjidTg5bPKSrVasWeXl5v1+sDmRaDirgFddPi3vKTTfdxIoVK3jyySetFsSzzz7Lvffei9PptLqQT+nSpZk9ezZ9+/YlLS3NWo6v01lZlXI7fFg/LX6tjhw5QlxcHPfccw9jx461lmOMYfTo0SxbtozMzEwqVqxoLWv9+vUkJyezadMmgoODreV4WmFnZdVyUEoViZycHH788UeioqIQEUTESo4xhlGjRpGWlkZ6errVgjhz5gxnzpxh+/btNGnSxFqOJ+mU3UopjwoLC6NBgwY899xzjB492topJhHh+eefJz4+nvj4eHJycqzkgGtFuZ07d9KuXTsyMjKs5fgiLQelVJFKTk4mJSWFp556ympBvPDCC8TGxhIfH8+RI0es5AA0atSIf//73/Ts2ZOsrCxrOb5Gy0EpVaQqVapERkYGixcvtvqhMhFh/PjxtG7dmvj4eH7++WdrWa1bt2b+/Pl89NFH1jJ8jV5zUEpZkZubS0hICNnZ2dbmRwLXNYjHH3+c9evXs3LlSkJDQ61lAaxevRqHw8Hdd99tNccWveagip3iPPdRcVShQgVEhO7du/Pss89ayxERJk6cSIsWLWjfvj25ubnWssB1kbpbt258+OGHVnO8TctB+QV/mftIC+y/iQgLFixg3rx5PPfcc1ZzXn75ZZo1a0b79u2tfsLZ6XQyZ84cunbtyvr1663leJuWgyoSNt8U/WXuI38pME+78cYbyczMZNWqVVanvxARpkyZwq233kr79u05evSotay4uDjmzp1LlSpVrGV4m5aDum623xT9Ye4jfykwb6latSpr1qyhYsWK1i9Sv/LKKzRq1IgOHTpYLQin00mdOnVISkpiw4YN1nK8RctBXRdPvCn6w9xH/lBg3iYiHDlyhCeffJIXX3zRWo7D4WDq1KlERUXRsWNHjh07Zi0LICEhgXvuuYeNGzdazfE06+UgIjVFJEtEdojIlyIy5BLbiIhMFpFdIvK5iBSPjyIGAE+8KfrD3Ef+UGC+oFKlSmRmZvLmm28yYcIEazkOh4PXX3+dyMhI6wXRsWNHZs6cSZcuXdi3b5+1HE/zxJHDaWCYMaYe0AJIFpGoC7bpANzi/uoPvOaBcaki4Kk3xV694PvvIT3d9b1Xr6Ld//XyhwLzFTVq1CArK4sTJ05YnajP4XAwbdo06tSpQ+fOnTl+/Li1rE6dOrF27VrCw8P59ddfreV4kvVyMMYcMMZsdf98FNgB1Lhgs3uBd43LBiBURKrZHpu6fp58UyyKpS5tslVgxfEOqPDwcJ5++mm2bNnC1KlTreU4HA7eeustateuTefOnTlx4oS1rLp165Kbm0u9evXYsmWLtRxP8eg1BxGJAG4FLjw5VwM4/3hsPxcXCCLSX0Q+EZFPbM7prq6Or/+r3pOKusCK+x1QVapUYcKECUyZMsVaxtmCuOmmm+jSpYvVgggNDWXixIl07NiRrVu3WsvxCGOMR76A8sAWoOslfrcMuOu8P2cATS+3v6ZNmxqlirNDh4wpU8YYOPdVpozr8eJkz549pnbt2mbatGlWc06fPm169+5t4uLizIkTJ6xmLVy40DRr1sycOXPGas61AD4xhXjP9siRg4gEAwuA2caYhZfYZD9Q87w/hwM/emJsSvmqQLkDqlatWmRmZtKyZUur1yCCgoJ4++23qVKlCvfeey8nT560lpWQkMC6des4deoU33zzjbUcmzxxt5IA04EdxpiXCthsCfCA+66lFkCuMeaA7bEp5csC6Q6oiIgI6tevz/Dhw3n99det5QQFBfHOO+9QsWJFEhISrF48LlWqFBs2bODuu+/m888/t5ZjiyeOHO4E+gCxIrLN/dVRRB4RkUfc26QCu4FdwJvAIA+MSymfFoh3QA0aNIh//OMfvPHGG9YySpQowaxZs6hQoYL1gmjdujUvv/wy7dq1Y/v27dZybNBZWZXycYG2fOmuXbuIiYlhzpw53HXXXdZyTp8+TWJiIsePH2fhwoWUKlXKWtbcuXPZu3cvI0aMsJZRWLpMqFLKbx08eJAqVapw5MgRwsLCrOWcOnWKXr168euvv7JgwQKrBQGQmZlJ1apViYq68KNenqNTdiul/NaNN95Ifn4+rVq1YubMmdZygoODmTNnDiVLluT+++/ntwsv8hSx7Oxs4uPj2blzp9WcoqDloJTySUFBQSxcuJCnnnqKd955x1pOcHAwc+fOJSgoiO7du1stiMTERP75z38SFxfH119/bS2nKGg5KKV8VmRkJOnp6UyePNnq/EglS5Zk3rx5GGPo0aMHp06dspbVp08f/vWvfxEcHGwtoyhoOSilfFrdunXZvHkzpUuXtrr6WsmSJZk/fz5nzpyhZ8+eVguiR48e1K5dm6SkJJ/9HISWg1LK5zkcDvbv30+PHj14//33reWcLYi8vDwSExOtFoSI0KJFC5xOJ99++621nGul5aCU8gsRERGsXLmSYcOGMXfuXGs5pUqVYsGCBRw/fpzevXtz+vRpa1kPP/wwTz/9NE6nk59++slazrXQclBK+Y0GDRqwatUq63f7lCpVioULF5Kbm0ufPn2sFkRSUhILFy4kLCzMas7V0nJQSvmVBg0a8Mwzz7B+/XoWLFhgLad06dJ88MEH5OTk8MADD1h9427WrBkHDhygYcOG/Oc//7GWczW0HJRSfqls2bIkJyd7pCAOHz7Mgw8+yJkzZ6xlVa9enUcffZTY2Fj2+MDsiloOSim/1LhxY5YvX86gQYNYsmSJtZwyZcqwePFisrOzeeihh6wWxKBBgxg2bBgPPfSQtYzC0ukzlFJ+bevWrZQpU4Z69epZzTlx4gSdO3emZs2azJgxg6CgIGtZx44do0SJEuTk5FC9evUi3bdOn6GUCghNmjShXr16DB482OoRRNmyZVm6dCl79+6lX79+5OfnW8sqX748y5cvp1WrVuzbt+/KT7BAy0EpVSz07duXfv36kZKSYi2jXLlypKSksHv3bpKSkqwWREJCAsnJycTExLB//35rOQXRclBKFQu33XYbKSkp/PWvf7W6dkK5cuVYtmwZ3377LQMGDLBaEE888QSPPPIIixYtspZREL3moJQqVvbs2UOtWrU4fvw45cuXt5Zz7NgxOnToQFRUFK+99hoOh91/a2dmZlK3bt3rvgah1xyUUgEpIiKCvLw8oqOjSUtLs5ZTvnx5UlNT2b59O8nJyVbXvwbYsmULsbGxHDjgmRWUtRyUUsVO6dKlmTVrFn369GHlypXWckJCQli+fDnbtm1j8ODBVgti+PDh9OnTh9jYWLKzs63lnKXloJQqllq2bMmiRYsYPny41TUabrjhBlasWMGWLVt47LHHrBbE6NGjGTRoEHl5edYyztJyUEoVW3feeSdbtmxBRNi2bZu1nAoVKpCWlsamTZsYOnSo1YJ49NFHqVGjBoMHD+bgwYPWcrQclFLFWokSJdi5cydt27Zl9erV1nLOFsT69et5/PHHrRZEiRIlqFixIk6nk0OHDlnJ0HJQShV7DRs2ZP78+XTv3p01a9ZYywkNDWXlypWsW7eOYcOGWS2IZ555hoSEBJxOJydOnCjy/Ws5qIBw+DBs3uz6rgJT69atmTdvntWjB4A//OEPrFq1ijVr1jB8+HBrBSEijBs3jsmTJ1O2bNki/7yFloMq9ubMgVq1ID7e9X3OHG+PSHlLTEwMY8eO5cMPP7S65OjZgsjIyGDkyJFWCyImJoadO3fSsmXLIl0wSMtBFWuHD8PDD8PJk5Cb6/r+8MN6BBHo8vLy6Nq1K+vWrbOWERYWRnp6OitXrmTUqFFWTzFFRkZy9913Ex8fT05OTpHsU8tBFWt79kDJkv/9WHCw63EVuOLi4pg9ezZdu3bl448/tpZTsWJF0tPTSU1NZcyYMVaPIF544QViY2NJSkoqkn2WKJK9KOWjIiLgwlvcT51yPa4CW9u2bZk9ezZhYWFWcypVqkRGRgaxsbE4HA7GjRuHiBR5jogwfvx4jhw5wsmTJ8nLyyM0NPSa96dHDqpYq1wZpk+HMmXghhtc36dPdz2uVHx8PJGRkQwcOJCNGzday6lcuTIZGRksWrSIZ5991lqOiBAWFsasWbNo27YtP//88zXvS8tBFXu9esH330N6uut7r17eHpHyNV26dKFLly5s2rTJWkaVKlXIzMxk/vz5VgsCICkpiTvuuIN27dqRm5t7TfvQclABoXJluO02PWJQl9axY0dmzJhB586d2bt3r7WcswUxb948nnvuOWs5IsKkSZNo3rz5NU/3rVN2K6WU25dffklUVBS//fYbpUqVspaTnZ1NTEwMvXv3ZvTo0dZyjDGICGvXrqVx48bccMMNOmW3Ukpdrfr165Obm0tUVBRbt261llO1alUyMzOZNWsWzz//vLWcsxe+FyxYQIcOHTh69Gihn2u9HERkhogcEpFLLs0kIm1EJFdEtrm/nrY9JqWUKkhoaCgTJkygQ4cOfPrpp9ZyqlWrRmZmJjNnzuSFF16wlgMwceJEGjRoQIcOHQr9HE8cObwNtL/CNh8aYxq7v8Z5YExKKVWghIQEpk6dSr9+/awuA1q9enWysrJ46623GD9+vLUch8PBa6+9Rvv2V3orPu851kbjZoxZCxTNR/aUUspDunXrxkcffcTp06fZtWuXtZwaNWqQlZXFG2+8wUsvvWQtx+FwMGbMmMJvb20kV+cOEflMRJaLSP2CNhKR/iLyiYh8cljnP1BKWVa6dGk+/vhjWrVqxfbtlzwzXiTCw8PJysri1VdfZdKkSdZyroYvlMNWoJYxJhqYAnxQ0IbGmGnGmGbGmGaV9Z5EpZQHtG7dmpdeeon4+Hi+/PJLazk1a9YkKyuLyZMnM3nyZGs5heX16TOMMb+c93OqiEwVkUrGmP/z5riUUuqsXr16YYxhyZIl1K9f4MmN63bTTTeRlZVFmzZtcDgcDB482FrWlXi9HESkKnDQGGNEpDmuo5mim3dWKaWKQGJiIgBr1qyhSpUq1KtXz0pOrVq1fi8IESE5OdlKzpVYLwcRmQO0ASqJyH5gLBAMYIx5HbgPGCgip4GTQE/jr5/MU0oVe/v27SMxMZGMjAzq1q1rJSMiIuK/jiAGDhxoJedyrJeDMeayM9kYY14BXrE9DqWUKgq9e/fmzJkzxMXFkZGRQWRkpJWc2rVrk5WVRUxMDA6HgwEDBljJKYjXTysppZS/6du3L8HBwQQFBVnN+eMf/0hmZubvBVFUazUUhi/craSUUn4nMTGRm2++mYEDB/Ltt99ay7n55pvJzMxk3LhxTJ8+3VrOhbQclFLqGokITZo0wel08t1331nLqVOnDpmZmYwdO5YZM2ZYyzmfnlZSSqnrkJSUhDGG2NhYtm7dSsWKFa3k3HLLLWRkZOB0OgkKCqJv375Wcs7SclBKqevUv39/oqOjCQsL4/Tp05QoYeetNTIykvT0dJxOJw6Hgz59+ljJAT2tpJRSReL2228nOzub6Oho9uzZYy2nbt26pKenM3LkSN577z1rOVoOSilVRKpVq8bAgQOJiYnh+++/t5ZTr1490tPTGTFiBO+//76VDD2tpJRSRWjw4MHk5+fzwAMPsHr16t8X3ClqUVFRrFy5kvj4eBwOBz179izS/esyoUopZcHRo0cpWbIkOTk5VKtWzVrOF198Qdu2bZk0aRI9evS44va6TKhSSnlRSEgIqamptGrViv3791vLadiwIWlpaQwZMoT58+cX2X71tJJSSlmSkJDAd999R0xMDKtXr6ZGjRpWcho1akRaWhrt2rXD4XDQrVu3696nloNSSln05JNPkp+fz/z58xk6dKi1nOjoaFasWEH79u0REbp27Xpd+9NyUEopy0aMGAG4pvv+05/+ZO0aROPGjUlNTaVDhw44HA7+/Oc/X/O+9JqDUkp5yMaNG4mNjSU7O9taRpMmTUhNTWXAgAEsWbLkmvej5aCUUh4yYsQI/vKXvxAbG8vBgwet5TRt2pSUlBT69etHSkrKNe1DTysppZQHjRkzhpCQEE6cOGE157bbbiMlJYXOnTszc+ZMOnXqdFXP1yMHpZTysCFDhlCzZk2GDh3K4cOHreU0b96cpUuX8tBDD7F8+fKreq6Wg1JKeUFQUBAhISE4nU6rBXH77bezePFi+vbty4oVKwr9PD2tpJRSXiAijBs3jvz8fJxOJx9//DHlypWzknXHHXfwwQcfXNXdS3rkoJRSXiIi/O1vf2PixImUK1cOm9MZtWzZkkWLFhV6ey0HpZTyIhHB6XTyzTffcNddd5GTk2Mt68477yz0tloOSinlA2655RZatmxJfHy81YIoLC0HpZTyASLCiy++SJs2bejXr5+3h6MXpJVSyleICBMmTOCnn37i119/JS8vjwoVKnhlLHrkoJRSPkREqFSpEu+++y7x8fHk5uZ6ZRxaDkop5YOSkpJo3rw57dq145dffvF4vpaDUkr5IBFhypQpNG3atEgX8SksveaglFI+SkR45ZVXEBE++ugjGjVqREhIiEey9chBKaV8mIgAMG/ePDp27MjRo0c9kqvloJRSfmDSpEnUrVuXTp06cezYMet5Wg5KKeUHHA4Hb7zxBq1ateLIkSP282wHiMgMETkkItsL+L2IyGQR2SUin4tIE9tjUkopf+RwOPj73/9O5cqVGT16NMePH7eXZW3P57wNtL/M7zsAt7i/+gOveWBMSinlt4KDg/nhhx/o0qWLtUWDrJeDMWYtcLmJQu4F3jUuG4BQEbGz+rZSShUDQUFBTJ8+nfDwcLp06cKpU6eKPMMXbmWtAew778/73Y8d8M5wlFLK9wUFBTFz5kyWLl1KcHAwxpjf72wqCr5QDpf621xyUnMR6Y/r1BNAXkHXMQJQJeD/vD0IH6GvxTn6Wpyjr8U5kYXZyBfKYT9Q87w/hwM/XmpDY8w0YBqAiHxijGlmf3i+T1+Lc/S1OEdfi3P0tThHRD4pzHa+cCvrEuAB911LLYBcY4yeUlJKKS+yfuQgInOANkAlEdkPjAWCAYwxrwOpQEdgF3ACeMj2mJRSSl2e9XIwxvS6wu8NkHwNu552bSMqlvS1OEdfi3P0tThHX4tzCvVaiM0FrZVSSvknX7jmoJRSysf4ZTmISHsR+do95cb/eHs83nKlqUkCiYjUFJEsEdkhIl+KyBBvj8lbRKS0iGwSkc/cr8Wz3h6TN4lIkIh8KiIp3h6Lt4nIHhH5QkS2XemuJb87rSQiQcA3QDyu22A3A72MMV95dWBeICJ3A8dwfcK8gbfH403uT9VXM8ZsFZEQYAvw5wD9/4UA5Ywxx0QkGFgHDHHPQBBwROQJoBlwgzGms7fH400isgdoZoy54mc+/PHIoTmwyxiz2xjzGzAX1xQcAacQU5MEDGPMAWPMVvfPR4EduD5pH3DcU9GcndM52P3lX/8KLCIiEg50At7y9lj8jT+WQ0HTbSgFgIhEALcCG707Eu9xn0rZBhwCVhljAvW1mASMAPK9PRAfYYCVIrLFPeNEgfyxHAo93YYKPCJSHlgADDXGeH5Vdh9hjDljjGmMa8aB5iIScKcdRaQzcMgYs8XbY/EhdxpjmuCaDTvZfWr6kvyxHAo93YYKLO7z6wuA2caYhd4ejy8wxvwMrOby0+YXV3cC97jPs88FYkXkPe8OybuMMT+6vx8CFuE6TX9J/lgOm4FbRKS2iJQEeuKagkMFMPdF2OnADmPMS94ejzeJSGURCXX/XAaIA3Z6d1SeZ4wZZYwJN8ZE4HqfyDTG9PbysLxGRMq5b9ZARMoBbYEC73T0u3IwxpwGBgNpuC46/j9jzJfeHZV3uKcm+RiIFJH9IvKwt8fkRXcCfXD963Cb+6ujtwflJdWALBH5HNc/plYZYwL+Nk7FjcA6EfkM2AQsM8asKGhjv7uVVSmllH1+d+SglFLKPi0HpZRSF9FyUEopdREtB6WUUhfRclBKKXURLQellFIX0XJQSil1ES0HFZBEpI6IfHHBY6VE5D8iEnUV+2l5ufUSRKSNiMwq4HdxBf3uvG10zQ7lFVoOKlDtBmqKyPn/DfQH1hRmDQj3uiIYY9YbY8ZeZtPGwKcF/C4a+OwKUW8TmPMiKS/TclAByRiTD+wFIuD3OYiGAc+IyH0issG9kto6Eans3ma+iLwkIlnAqPMeu6ug5+AqgBoislFEdotIm/OGEQ1sc++ntogsFpFP3Ku4RbrHqWt2KK/QclCBbAdQ1/1zMrDEGLMHyDLGtDDGRAOrgO7ubRoCx4wxMcaYv7kfawB8cZnnNAaOGmNuBx4BnjsvPxr4zD2b7FvAE8aYZsAzQMAuf6t8QwlvD0ApL9qBa9LO0O6JAAABXklEQVTCtbjKoYX78QdFpAdQCqgK/K+IlAbCgHFnn+x+LNgYkysiwy7xnBJAReAf7qdsAyq5nxuMa9nKwyJyP1AfWOCaXJYSwIcW/95KXZGWgwpkO4BYYAiuNSAOisgDuOa4j3WvwbwW+BLXm/dG96zAZ9UHvrrMc6JwLWn7m3v7Jpy7xhDlzgfXEcRoY8x0a39Tpa6SnlZSgWwHrjf1vwLj3Y81BNa73+S7AS1xnTZqCHx+wfPPPlbQc6KB2u67oMoDY3EtWwnnXW8ADgDtzl4cF5GG7vUplPIaLQcVyL7G9cY+zRiT637sHeAxEfkQ+BOw2xhznMuXQ0HPiQZmA+txzZ8/2Rizwf3c8+9UmoHrv8Ud7nWfRxr3XPq6ZofyFl3PQSml1EX0yEEppdRFtByUUkpdRMtBKaXURbQclFJKXUTLQSml1EW0HJRSSl1Ey0EppdRFtByUUkpd5P8DgQQvmPm9e6EAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#scatter plot with decision boundary on predicted values\n",
    "fig = plt.figure(figsize = (6, 6))\n",
    "xl = np.array([0.0, 5.0])\n",
    "yl = slope*xl + c\n",
    "yl1 = slope*xl + c11\n",
    "yl2 = slope*xl + c12\n",
    "plt.plot(xl, yl, \"k\", lw = 1, ls = \"-\")\n",
    "plt.plot(xl, yl1, \"k\", lw = 1, ls = \"--\")\n",
    "plt.plot(xl, yl2, \"k\", lw = 1, ls = \"--\")\n",
    "\n",
    "plt.scatter(*X1[y_p == (-1)].T, s = 20, color = \"blue\", alpha = 1.0)\n",
    "plt.scatter(*X1[y_p == 1].T, s = 20, color = \"red\", alpha = 1.0)\n",
    "plt.xlim(0.0, 5.0)\n",
    "plt.ylim(1.0, 5.0)\n",
    "plt.ylabel(r'$Variable 2$')\n",
    "plt.xlabel(r'$Variable 1$')\n",
    "plt.title(\"SVM predicted Data 1\") \n",
    "#plt.savefig(\"C:\\Me\\sem6\\cll788\\A3\\Data1_svm.jpeg\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Q3 - Modified SVM on Data 2 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "df2 = pd.read_excel(path2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "scrolled": true
   },
   "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>Variable 1</th>\n",
       "      <th>Variable 2</th>\n",
       "      <th>Class</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.9743</td>\n",
       "      <td>4.6057</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2.2853</td>\n",
       "      <td>3.8689</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2.9881</td>\n",
       "      <td>4.5751</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2.9421</td>\n",
       "      <td>3.5619</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3.5872</td>\n",
       "      <td>2.8669</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>4.0251</td>\n",
       "      <td>3.2037</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>2.2134</td>\n",
       "      <td>2.8541</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>3.3914</td>\n",
       "      <td>3.4391</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>3.9213</td>\n",
       "      <td>4.1861</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>2.7922</td>\n",
       "      <td>4.0531</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>0.1103</td>\n",
       "      <td>3.8129</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>0.0864</td>\n",
       "      <td>4.1045</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>2.5618</td>\n",
       "      <td>4.6262</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>3.3798</td>\n",
       "      <td>3.9201</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>3.1148</td>\n",
       "      <td>3.0809</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>1.9282</td>\n",
       "      <td>4.0634</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>2.2738</td>\n",
       "      <td>4.3806</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>2.6655</td>\n",
       "      <td>3.5108</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>3.1955</td>\n",
       "      <td>4.2988</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>3.6679</td>\n",
       "      <td>3.8792</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>3.9213</td>\n",
       "      <td>3.4391</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>3.6102</td>\n",
       "      <td>3.1321</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>3.0457</td>\n",
       "      <td>3.3265</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>1.5941</td>\n",
       "      <td>3.3675</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>2.0203</td>\n",
       "      <td>3.2139</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>1.9627</td>\n",
       "      <td>2.7943</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>2.2853</td>\n",
       "      <td>2.7227</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>2.3199</td>\n",
       "      <td>2.9684</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>2.8383</td>\n",
       "      <td>2.6409</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>3.0573</td>\n",
       "      <td>2.3031</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>2.4927</td>\n",
       "      <td>2.0473</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>2.5157</td>\n",
       "      <td>2.3953</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>1.8821</td>\n",
       "      <td>2.0677</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>2.0203</td>\n",
       "      <td>2.3646</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>1.2369</td>\n",
       "      <td>2.3339</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>1.9051</td>\n",
       "      <td>2.9274</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>1.5710</td>\n",
       "      <td>3.0809</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>1.5595</td>\n",
       "      <td>2.7023</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>1.6978</td>\n",
       "      <td>2.4157</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>1.5019</td>\n",
       "      <td>2.0371</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>0.9720</td>\n",
       "      <td>2.6920</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>41</th>\n",
       "      <td>1.1793</td>\n",
       "      <td>2.9376</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>0.8222</td>\n",
       "      <td>3.0092</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>43</th>\n",
       "      <td>0.9835</td>\n",
       "      <td>3.3981</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>44</th>\n",
       "      <td>1.2618</td>\n",
       "      <td>3.2037</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45</th>\n",
       "      <td>3.7239</td>\n",
       "      <td>2.8310</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>46</th>\n",
       "      <td>1.3291</td>\n",
       "      <td>3.5209</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47</th>\n",
       "      <td>2.2392</td>\n",
       "      <td>2.2110</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>48</th>\n",
       "      <td>2.4582</td>\n",
       "      <td>2.6511</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>49</th>\n",
       "      <td>2.8038</td>\n",
       "      <td>1.9756</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50</th>\n",
       "      <td>2.1010</td>\n",
       "      <td>1.6277</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>51</th>\n",
       "      <td>2.5503</td>\n",
       "      <td>2.8967</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>52</th>\n",
       "      <td>0.9144</td>\n",
       "      <td>3.0298</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>53</th>\n",
       "      <td>0.7761</td>\n",
       "      <td>2.5999</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>54</th>\n",
       "      <td>4.3111</td>\n",
       "      <td>3.5628</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Variable 1  Variable 2  Class\n",
       "0       1.9743      4.6057      1\n",
       "1       2.2853      3.8689      1\n",
       "2       2.9881      4.5751      1\n",
       "3       2.9421      3.5619      1\n",
       "4       3.5872      2.8669      1\n",
       "5       4.0251      3.2037      1\n",
       "6       2.2134      2.8541      1\n",
       "7       3.3914      3.4391      1\n",
       "8       3.9213      4.1861      1\n",
       "9       2.7922      4.0531      1\n",
       "10      0.1103      3.8129      1\n",
       "11      0.0864      4.1045      1\n",
       "12      2.5618      4.6262      1\n",
       "13      3.3798      3.9201      1\n",
       "14      3.1148      3.0809      1\n",
       "15      1.9282      4.0634      1\n",
       "16      2.2738      4.3806      1\n",
       "17      2.6655      3.5108      1\n",
       "18      3.1955      4.2988      1\n",
       "19      3.6679      3.8792      1\n",
       "20      3.9213      3.4391      1\n",
       "21      3.6102      3.1321      1\n",
       "22      3.0457      3.3265      1\n",
       "23      1.5941      3.3675     -1\n",
       "24      2.0203      3.2139     -1\n",
       "25      1.9627      2.7943     -1\n",
       "26      2.2853      2.7227     -1\n",
       "27      2.3199      2.9684     -1\n",
       "28      2.8383      2.6409     -1\n",
       "29      3.0573      2.3031     -1\n",
       "30      2.4927      2.0473     -1\n",
       "31      2.5157      2.3953     -1\n",
       "32      1.8821      2.0677     -1\n",
       "33      2.0203      2.3646     -1\n",
       "34      1.2369      2.3339     -1\n",
       "35      1.9051      2.9274     -1\n",
       "36      1.5710      3.0809     -1\n",
       "37      1.5595      2.7023     -1\n",
       "38      1.6978      2.4157     -1\n",
       "39      1.5019      2.0371     -1\n",
       "40      0.9720      2.6920     -1\n",
       "41      1.1793      2.9376     -1\n",
       "42      0.8222      3.0092     -1\n",
       "43      0.9835      3.3981     -1\n",
       "44      1.2618      3.2037     -1\n",
       "45      3.7239      2.8310     -1\n",
       "46      1.3291      3.5209     -1\n",
       "47      2.2392      2.2110     -1\n",
       "48      2.4582      2.6511     -1\n",
       "49      2.8038      1.9756     -1\n",
       "50      2.1010      1.6277     -1\n",
       "51      2.5503      2.8967     -1\n",
       "52      0.9144      3.0298     -1\n",
       "53      0.7761      2.5999     -1\n",
       "54      4.3111      3.5628     -1"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Data2\n",
    "df2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4.3111   0.0864\n"
     ]
    }
   ],
   "source": [
    "#Maximum and Minimum values of Variable 1 in Data2\n",
    "print(df2['Variable 1'].max(), \" \", df2['Variable 1'].min())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4.6262   1.6277\n"
     ]
    }
   ],
   "source": [
    "#Maximum and Minimum values of Variable 1 in Data2\n",
    "print(df2['Variable 2'].max(), \" \", df2['Variable 2'].min())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(55, 2)"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Feature matrix for Data2\n",
    "X2 = df2.drop(['Class'], axis = 1).to_numpy()\n",
    "X2.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(55,)"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Class matrix for Data2\n",
    "Y21 = df2.drop(['Variable 1', 'Variable 2'], axis = 1).to_numpy()\n",
    "Y2 = np.reshape(Y21, (X2.shape[0],))\n",
    "Y2.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Scatter plot for Data2\n",
    "fig = plt.figure(figsize = (6, 6))\n",
    "plt.scatter(*X2[Y2 == (-1)].T, s = 8, color = \"blue\", alpha = 0.5)\n",
    "plt.scatter(*X2[Y2 == 1].T, s = 8, color = \"red\", alpha = 0.5)\n",
    "plt.xlim(0.0, 5.0)\n",
    "plt.ylim(1.0, 5.0)\n",
    "plt.ylabel(r'$Variable 2$')\n",
    "plt.xlabel(r'$Variable 1$')\n",
    "plt.title(\"Data2\") \n",
    "#plt.savefig(\"C:\\Me\\sem6\\cll788\\A3\\Data2_scatter.jpeg\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Prediction function y = w.T*x + b\n",
    "def predict2(w, b, x):\n",
    "    \n",
    "    m, n = x.shape\n",
    "    y = []\n",
    "    \n",
    "    for i in range(m):\n",
    "        y.append(((w[0]*x[i][0] + w[1]*x[i][1] + b)))\n",
    "                 \n",
    "    yn = np.array(y)\n",
    "                 \n",
    "    return yn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Different values of C \n",
    "C = [0.01, 0.1, 1, 10, 100, 1000, 10000, 100000, 1000000, 10000000]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(55, 1)"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#tn for Data2\n",
    "tn2 = Y2\n",
    "tn2 = np.reshape(tn2, (tn2.shape[0], 1))\n",
    "tn2.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Weight, Bias, Accuracy and Prediction matrices for different values of C\n",
    "W = []\n",
    "B = []\n",
    "Accuracy = []\n",
    "Y_P = []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     pcost       dcost       gap    pres   dres\n",
      " 0: -1.1037e+01 -1.5711e+00  4e+02  2e+01  1e-14\n",
      " 1: -8.6740e-01 -1.5053e+00  1e+01  5e-01  1e-14\n",
      " 2: -3.8906e-01 -1.1627e+00  8e-01  4e-03  1e-15\n",
      " 3: -4.0580e-01 -5.0648e-01  1e-01  5e-04  7e-16\n",
      " 4: -4.1626e-01 -4.4803e-01  3e-02  1e-04  4e-16\n",
      " 5: -4.2540e-01 -4.3068e-01  5e-03  8e-06  5e-16\n",
      " 6: -4.2696e-01 -4.2856e-01  2e-03  1e-06  5e-16\n",
      " 7: -4.2751e-01 -4.2774e-01  2e-04  1e-07  5e-16\n",
      " 8: -4.2760e-01 -4.2764e-01  4e-05  1e-08  5e-16\n",
      " 9: -4.2762e-01 -4.2762e-01  5e-07  1e-10  4e-16\n",
      "10: -4.2762e-01 -4.2762e-01  5e-09  1e-12  5e-16\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0: -1.1980e+01 -1.2049e+01  4e+02  2e+01  1e-14\n",
      " 1: -2.1122e+00 -1.1472e+01  1e+01  2e-01  1e-14\n",
      " 2: -2.1269e+00 -3.1536e+00  1e+00  1e-03  3e-15\n",
      " 3: -2.5606e+00 -2.7559e+00  2e-01  2e-04  3e-15\n",
      " 4: -2.6672e+00 -2.6839e+00  2e-02  1e-05  4e-15\n",
      " 5: -2.6756e+00 -2.6759e+00  3e-04  2e-07  4e-15\n",
      " 6: -2.6758e+00 -2.6758e+00  3e-06  2e-09  3e-15\n",
      " 7: -2.6758e+00 -2.6758e+00  3e-08  2e-11  3e-15\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0: -2.1039e+01 -1.2166e+02  5e+02  3e+00  2e-14\n",
      " 1: -1.3384e+01 -7.5093e+01  9e+01  2e-01  2e-14\n",
      " 2: -1.3340e+01 -2.2498e+01  1e+01  2e-02  2e-14\n",
      " 3: -1.5825e+01 -1.8128e+01  2e+00  4e-03  2e-14\n",
      " 4: -1.6528e+01 -1.7092e+01  6e-01  6e-04  2e-14\n",
      " 5: -1.6681e+01 -1.6869e+01  2e-01  1e-04  2e-14\n",
      " 6: -1.6741e+01 -1.6797e+01  6e-02  3e-05  2e-14\n",
      " 7: -1.6767e+01 -1.6769e+01  2e-03  5e-07  2e-14\n",
      " 8: -1.6768e+01 -1.6768e+01  3e-05  6e-09  2e-14\n",
      " 9: -1.6768e+01 -1.6768e+01  3e-07  6e-11  2e-14\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0: -7.4905e+01 -3.4610e+03  7e+03  6e-01  1e-13\n",
      " 1: -2.4163e+01 -7.1857e+02  7e+02  3e-03  1e-13\n",
      " 2: -9.1896e+01 -2.1496e+02  1e+02  4e-04  1e-13\n",
      " 3: -1.1694e+02 -1.7234e+02  6e+01  1e-04  1e-13\n",
      " 4: -1.2643e+02 -1.6103e+02  3e+01  8e-05  1e-13\n",
      " 5: -1.3349e+02 -1.4740e+02  1e+01  1e-05  1e-13\n",
      " 6: -1.3626e+02 -1.4248e+02  6e+00  3e-06  1e-13\n",
      " 7: -1.3868e+02 -1.3953e+02  8e-01  9e-15  2e-13\n",
      " 8: -1.3904e+02 -1.3907e+02  3e-02  4e-15  1e-13\n",
      " 9: -1.3905e+02 -1.3905e+02  3e-04  1e-14  1e-13\n",
      "10: -1.3905e+02 -1.3905e+02  3e-06  1e-14  1e-13\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  3.0594e+03 -2.7240e+05  5e+05  4e-01  1e-12\n",
      " 1:  5.0911e+03 -4.0699e+04  5e+04  7e-03  1e-12\n",
      " 2: -3.2552e+02 -7.0010e+03  7e+03  5e-04  1e-12\n",
      " 3: -8.7310e+02 -2.6113e+03  2e+03  1e-04  1e-12\n",
      " 4: -1.0528e+03 -1.8205e+03  8e+02  4e-05  9e-13\n",
      " 5: -1.1047e+03 -1.6645e+03  6e+02  2e-05  1e-12\n",
      " 6: -1.2159e+03 -1.4970e+03  3e+02  1e-05  1e-12\n",
      " 7: -1.2812e+03 -1.4191e+03  1e+02  3e-06  1e-12\n",
      " 8: -1.3296e+03 -1.3668e+03  4e+01  2e-07  2e-12\n",
      " 9: -1.3401e+03 -1.3431e+03  3e+00  2e-08  2e-12\n",
      "10: -1.3414e+03 -1.3415e+03  1e-01  5e-10  1e-12\n",
      "11: -1.3414e+03 -1.3414e+03  1e-03  5e-12  2e-12\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  4.0170e+05 -2.6504e+07  5e+07  4e-01  1e-11\n",
      " 1:  5.7141e+05 -3.8697e+06  5e+06  8e-03  3e-11\n",
      " 2:  3.4917e+04 -5.7319e+05  6e+05  5e-04  1e-11\n",
      " 3: -7.3437e+03 -4.5188e+04  4e+04  1e-05  9e-12\n",
      " 4: -9.5230e+03 -3.3903e+04  2e+04  7e-06  9e-12\n",
      " 5: -1.0293e+04 -1.9030e+04  9e+03  1e-06  9e-12\n",
      " 6: -1.0636e+04 -1.7700e+04  7e+03  9e-07  1e-11\n",
      " 7: -1.1804e+04 -1.5808e+04  4e+03  3e-07  1e-11\n",
      " 8: -1.2438e+04 -1.5214e+04  3e+03  2e-07  1e-11\n",
      " 9: -1.2659e+04 -1.4331e+04  2e+03  5e-08  1e-11\n",
      "10: -1.3062e+04 -1.3778e+04  7e+02  7e-09  2e-11\n",
      "11: -1.3344e+04 -1.3364e+04  2e+01  1e-10  2e-11\n",
      "12: -1.3350e+04 -1.3351e+04  3e-01  2e-12  1e-11\n",
      "13: -1.3351e+04 -1.3351e+04  3e-03  1e-12  2e-11\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  4.1118e+07 -2.6430e+09  5e+09  4e-01  1e-10\n",
      " 1:  5.7751e+07 -3.8495e+08  5e+08  8e-03  6e-10\n",
      " 2:  4.2652e+06 -5.7772e+07  6e+07  5e-04  9e-11\n",
      " 3: -5.3476e+04 -3.1307e+06  3e+06  8e-06  8e-11\n",
      " 4: -7.7700e+04 -4.1111e+05  3e+05  9e-07  8e-11\n",
      " 5: -9.3300e+04 -3.8618e+05  3e+05  7e-07  1e-10\n",
      " 6: -1.0023e+05 -2.0280e+05  1e+05  1e-07  1e-10\n",
      " 7: -1.0970e+05 -1.9843e+05  9e+04  8e-08  1e-10\n",
      " 8: -1.1664e+05 -1.6687e+05  5e+04  3e-08  9e-11\n",
      " 9: -1.2581e+05 -1.5240e+05  3e+04  1e-08  1e-10\n",
      "10: -1.2514e+05 -1.4587e+05  2e+04  5e-09  1e-10\n",
      "11: -1.2959e+05 -1.3929e+05  1e+04  1e-09  1e-10\n",
      "12: -1.3335e+05 -1.3364e+05  3e+02  2e-11  1e-10\n",
      "13: -1.3344e+05 -1.3344e+05  4e+00  2e-11  2e-10\n",
      "14: -1.3344e+05 -1.3344e+05  4e-02  7e-12  1e-10\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  4.1213e+09 -2.6423e+11  5e+11  4e-01  1e-09\n",
      " 1:  5.7812e+09 -3.8475e+10  5e+10  8e-03  1e-07\n",
      " 2:  4.3422e+08 -5.7816e+09  6e+09  5e-04  6e-09\n",
      " 3:  1.4602e+06 -3.2244e+08  3e+08  9e-06  1e-09\n",
      " 4: -7.3821e+05 -7.3253e+06  7e+06  2e-07  9e-10\n",
      " 5: -9.0589e+05 -3.5710e+06  3e+06  7e-08  9e-10\n",
      " 6: -8.3158e+05 -2.3411e+06  2e+06  1e-08  1e-09\n",
      " 7: -1.0333e+06 -2.1788e+06  1e+06  7e-09  9e-10\n",
      " 8: -1.1440e+06 -1.7143e+06  6e+05  2e-09  1e-09\n",
      " 9: -1.2500e+06 -1.5237e+06  3e+05  6e-10  1e-09\n",
      "10: -1.2588e+06 -1.4410e+06  2e+05  2e-10  1e-09\n",
      "11: -1.3087e+06 -1.3714e+06  6e+04  3e-11  1e-09\n",
      "12: -1.3336e+06 -1.3357e+06  2e+03  1e-10  1e-09\n",
      "13: -1.3343e+06 -1.3344e+06  3e+01  8e-15  1e-09\n",
      "14: -1.3344e+06 -1.3344e+06  3e-01  2e-10  1e-09\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  4.1222e+11 -2.6422e+13  5e+13  4e-01  1e-08\n",
      " 1:  5.7818e+11 -3.8473e+12  5e+12  8e-03  9e-06\n",
      " 2:  4.3499e+10 -5.7820e+11  6e+11  5e-04  6e-07\n",
      " 3:  2.1388e+08 -3.2335e+10  3e+10  9e-06  1e-08\n",
      " 4: -7.3211e+06 -3.7374e+08  4e+08  1e-07  8e-09\n",
      " 5: -7.7060e+06 -4.2133e+07  3e+07  1e-08  9e-09\n",
      " 6: -9.2764e+06 -3.9187e+07  3e+07  8e-09  7e-09\n",
      " 7: -9.8614e+06 -2.0765e+07  1e+07  8e-10  9e-09\n",
      " 8: -1.0917e+07 -2.0103e+07  9e+06  7e-10  9e-09\n",
      " 9: -1.1695e+07 -1.6128e+07  4e+06  3e-10  9e-09\n",
      "10: -1.2467e+07 -1.5531e+07  3e+06  6e-10  1e-08\n",
      "11: -1.2474e+07 -1.4706e+07  2e+06  2e-09  1e-08\n",
      "12: -1.2918e+07 -1.4046e+07  1e+06  1e-09  1e-08\n",
      "13: -1.3324e+07 -1.3377e+07  5e+04  1e-09  2e-08\n",
      "14: -1.3343e+07 -1.3344e+07  9e+02  2e-09  2e-08\n",
      "15: -1.3343e+07 -1.3343e+07  9e+00  1e-10  2e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  4.1223e+13 -2.6422e+15  5e+15  4e-01  1e-07\n",
      " 1:  5.7819e+13 -3.8473e+14  5e+14  8e-03  1e-03\n",
      " 2:  4.3506e+12 -5.7821e+13  6e+13  5e-04  9e-05\n",
      " 3:  2.2066e+10 -3.2345e+12  3e+12  9e-06  2e-06\n",
      " 4: -7.0962e+07 -3.3959e+10  3e+10  9e-08  8e-08\n",
      " 5: -7.3871e+07 -7.5046e+08  7e+08  6e-09  9e-08\n",
      " 6: -9.0122e+07 -3.5867e+08  3e+08  6e-09  9e-08\n",
      " 7: -8.0715e+07 -2.3846e+08  2e+08  1e-08  1e-07\n",
      " 8: -1.0293e+08 -2.1913e+08  1e+08  1e-08  1e-07\n",
      " 9: -1.1173e+08 -1.8043e+08  7e+07  1e-08  1e-07\n",
      "10: -1.2050e+08 -1.5905e+08  4e+07  9e-09  1e-07\n",
      "11: -1.2717e+08 -1.4610e+08  2e+07  6e-09  1e-07\n",
      "12: -1.3248e+08 -1.3477e+08  2e+06  7e-09  1e-07\n",
      "13: -1.3336e+08 -1.3355e+08  2e+05  4e-09  1e-07\n",
      "14: -1.3343e+08 -1.3344e+08  2e+03  2e-08  1e-07\n",
      "15: -1.3343e+08 -1.3343e+08  2e+01  1e-08  2e-07\n",
      "16: -1.3343e+08 -1.3343e+08  2e-01  2e-16  1e-07\n",
      "17: -1.3343e+08 -1.3343e+08  2e-03  1e-08  1e-07\n",
      "Terminated (singular KKT matrix).\n"
     ]
    }
   ],
   "source": [
    "#same code as for Data1 but for loop used to solve for different values of C\n",
    "a21 = tn2*X2\n",
    "a22 = a21.T\n",
    "H2 = np.dot(a21, a22)\n",
    "size2 = X2.shape[0]\n",
    "q2 = -1*np.ones((size2, 1))\n",
    "G2 = np.vstack((-1*np.eye(size2), np.eye(size2)))\n",
    "for c in C:\n",
    "    h2 = np.hstack((np.zeros((size2)), np.ones((size2))*c))\n",
    "    A2 = tn2.reshape(1, -1)\n",
    "    A2 = A2.astype('float')\n",
    "    b2_cvx = np.zeros(1)\n",
    "    sol2 = cvxopt.solvers.qp(cvxopt.matrix(H2), cvxopt.matrix(q2), cvxopt.matrix(G2), cvxopt.matrix(h2), cvxopt.matrix(A2), \n",
    "                        cvxopt.matrix(b2_cvx))\n",
    "    lambdas2 = np.array(sol2['x'])\n",
    "    w2 = np.dot(X2.T, (tn2*lambdas2))\n",
    "    tolerance2 = 0.0001\n",
    "    Ns2 = 0\n",
    "    xs2 = []\n",
    "    ys2 = []\n",
    "    for i in range(lambdas2.shape[0]):\n",
    "        if lambdas2[i]>=tolerance2:\n",
    "            Ns2 = Ns2 + 1\n",
    "            xs2.append(X2[i])\n",
    "            ys2.append(tn2[i])\n",
    "    xs2 = np.array(xs2)\n",
    "    ys2 = np.array(ys2)\n",
    "    bn2 = ys2 - np.dot(xs2, w2) \n",
    "    b2 = 0\n",
    "    for i in range(bn2.shape[0]):\n",
    "        b2 = b2 + bn2[i][0]\n",
    "    b2 = [b2/Ns2]\n",
    "    W.append(w2)\n",
    "    B.append(b2)\n",
    "    y_p2 = predict2(w2, b2, X2)\n",
    "    Y_P.append(y_p2)\n",
    "    count2 = 0\n",
    "    for i in range(y_p2.shape[0]):\n",
    "        if y_p2[i]>=1:\n",
    "            y_p2[i] = 1\n",
    "        else:\n",
    "            y_p2[i] = -1\n",
    "            \n",
    "        if tn2[i] == y_p2[i]:\n",
    "            count2 = count2 + 1\n",
    "    accuracy = (count2/y_p2.shape[0])*100\n",
    "    Accuracy.append(accuracy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "accuracy for 0.01 = 58.18181818181818\n",
      "accuracy for 0.1 = 70.9090909090909\n",
      "accuracy for 1 = 81.81818181818183\n",
      "accuracy for 10 = 83.63636363636363\n",
      "accuracy for 100 = 85.45454545454545\n",
      "accuracy for 1000 = 85.45454545454545\n",
      "accuracy for 10000 = 89.0909090909091\n",
      "accuracy for 100000 = 90.9090909090909\n",
      "accuracy for 1000000 = 90.9090909090909\n",
      "accuracy for 10000000 = 85.45454545454545\n"
     ]
    }
   ],
   "source": [
    "for i in range(len(Accuracy)):\n",
    "    print(\"accuracy for\", C[i], \"=\", Accuracy[i])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in range(len(Y_P)):\n",
    "    Y_P[i] = Y_P[i].reshape(Y_P[i].shape[0], )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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tOIc6derw008/sWTJEpKTkwF4/PHHqVq1Kg6HgxtuuAFjjM1RKqX8RgfyeVXQJgeAcuXK0aFDh/znPXsOZOLEb4iP78PVV1/J3LlzOXToENWrV6dMmaAtJCmlPKUD+bwmZK6YkyaBw9GSmTPf5PDhHfTp8xUAzz77LLVq1eLRRx9l3rx5NkeplFLBISSSQ+FebGfOGP7xj1hSUmDixIksWbKEBg0a8PXXXwMwefJkEhMTOX36tM2RK6VUYAqJ5HC+XmxXX301//znPxk7diwALpeLd999lxo1ajBgwABEBBHxa8zqIulIWKV8KiSSQ2l7sd17770sWLCAnTt3MmDAAIwxPProo9xxxx3873//I0UvOIEtnEbCahJUNgmJ5HChvdguu+wyunTpAsCbb77J/fffz9y5c2nVqhUul4ukpCT27dvnh0+gPBZOI2HDKQmqgGOCtTolLi5OVq9efda2lBTv9GJzuVyUKVOG9957j3/96180bNgQh8PB008/TfnC9VfKv1atsi6WaWl/bIuOhnnzoEUL++LytpQUKyEUbBeLjIQ9e7Q3jrooxpg1IhJ3vv1CouSQJzbWuj5c7P+dvG6vf//730lOTuaNN97g5MmTRERE8OWXX/Lyyy/zyy+/aDuFHcJlJKxOB6Fs5rfkYIwpa4xZZ4z5tpjXLjHGTDHG7DDG/GyMqe+vuM4nIiKCjh07MnLkSIwxXH/99Zw+fZrevXtz1VVXkZ6eTkZGBi6Xy+5Qw0O4jIQNlySoApY/Sw5PAltKeG0QcExErgLeBkb5LapSatasGW+99RY7duxg1qxZVK5cmY8//jh/LMXcuXPJycmxO8zQ1r+/Vb0yb571s39/uyPyvnBJgipg+aXNwRhTG/gcGAk8LSI9Cr3+A/CqiKwwxpQDkoFYOUdwxbU52Gn79u0kJCSQmJjId999x+7du9mzZw9dunQhMjLS7vBUsPJWQ5pSboHW5vAO8E+gpLqXWsA+ABHJAdKAaoV3MsYMNsasNsasDrTupnljKZYtW0ZMTAypqan5Yynuvvvu/PmflCoVbzWkKVVKPk8OxpgewBERWXOu3YrZVqTUICKfiEiciMTFBvh/lg4dOrBgwQJ27NhBt27dqFq1KlOmTKF79+6MHz+eo0eP2h2iUkqVyB8lh1uAXsaY3cBkoIMxZkKhffYDdQDc1UpVgFQ/xOZzsbGxPPTQQ5QvX55u3boxYMAAZs+ezVVXXcXWrVs5duwY+/fvtztMpZQ6i8+Tg4g8LyK1RaQ+0A9YICJ/KbTbDOB+9+993PuEXD/R6Oho+vXrx9SpUzl06BDXXHMNK1eupFmzZrRs2ZJRo0bp6GylVECwbZyDMWa4MaaX++k4oJoxZgfwNPCcXXH5S2RkJMYYbr/9dpKTkxk5ciR79uwhPT2dzZs388orr7B+/XodS6ECm07vEbJCaoR0qNi1axdjxozB6XRijGHKlCk0b94cQNelUIFj0iRr6pLy5a0xGePGhWa34hDjaW8lTQ4BTERYv349DRo0YOPGjdxzzz3Ex8fjcDi49dZbiYiIsDtEFa50eo+gFWhdWdUFMMZwww03UKVKFdq0acPChQupU6cOzz//PD/88AMnT55k5syZnDlzxu5QVbjxxfQeWkUVUII2OYTjKORrrrmG5557jpUrV9KjRw8OHz7M6NGjqVGjBvfccw/r1q2zO8TQoReqc/P29B46A23ACdrksHHjRjp37sxHH33EoUOH7A7HFldddRULFy5k+/bt3H777URERHDgwAF69OihYykuhl6ozs+b03uE0zTsQSRok0OzZs149NFHWbZsGY0bN+bmm2/mP//5D7/99pvdofldbGwsgwYNomnTpsTExHDffffx/fff07BhQyZMmICIhG0CLTW9UHnOW3Nc6Qy0ASkkGqSzsrJYsGABCQkJTJ8+nZo1a+JwOHA4HDRp0gRjihuAHfpOnz5NdnY26enpNG3alD/96U84HA769u1LvXr17A4vMIXLehGBRBu3/SqsGqTLly9P165dGTt2LAcPHuS1195ny5ZjdOvW/ax6+mBNhBcqMjKS6OhorrjiCg4fPsxrr73Grl27WLFiBTk5OYwcOZINGzaE3fdyTjpVtv/pDLQBKSRKDgUV7HqdmSm8+OJaTp1y8s0335CRkZHfFbRNmzaUK1fOhsgDw4kTJxg+fDjffPMNZcuWZcSIEfTr1w8RCduSVr68P6KICCsxaP99/9AZaP0iLMc5nK90umXLFpxOJ06nk3379tGrVy8cDgcdO3bkkksu8fMnCAx5YykiIiJo0KABzZo1o0uXLjqWQi9UKkSFVbVSnvO1azVq1Ihhw4axZs0aVq5cSZMmTXjjjTeoUaMG9957L9OmTSM9Pd3fYdsqbyxFkyZNqFixIjNnzqR27do8//zzDBs2DIClS5eG31gKnSpbhbmwKjmUJDk5mcTERJxOJytWrKBDhw44HA569OhB1apVffQJAl9ubi4iQpcuXVi7di233347Dz/8MJ07d7Y7NKXUBQrLksOFtmvVqFGDv/3tb/zwww/s2bOH3r17k5CQQP369enSpUvYjqUoW7Ys5cqVY8GCBWzbto3OnTvz+++/A/DYY4/x6aef5j9XSoWWkCo55PFWdXFGRgY//PAD33zzDbNmzaJx48Y4HA7i4+O58sorL/zAQc7lcjF58mScTidz587lkUceYdSoUaSnp1O5cmW7w1NKnUNYNkj7UmZm5lljKWrVqpU/lqJx48Zh28Pn1KlTHDlyhPr169O0aVOioqLyv5eGDRvaHZ5SqhBNDj6Um5vLsmXL8ns+RUZG5l8Q4+LiwjZRZGVlsWjRIpxOJxEREbz//vtMnTqVRo0a0bRp07D9XpQKJJoc/EREWLNmDU6nNZbi9OnTZ42lKFu2rN0h2uqll17iyy+/JCIigr/+9a/885//tDskpcKaJgcbiMhZYyn279/PnXfeicPhoEOHDmE9lmLdunXs37+fXr16MWDAAGJiYnA4HLRt2zasByMq5W+aHALArl27SEhIwOl0snnzZu644w4cDgddu3alUqVKdodnm61bt+J0OklISCAyMpIlS5awY8cOateuTYUKFewOT6mQpskhwBw6dCh/LMVPP/2UP5aiZ8+eXHrppXaHZ5uMjAwqVarE4MGDmTp1Kl27dqVPnz706dPH7tCUCkmaHAJYamoq3377LU6nkwULFtCqVSscDgd33XUXNWrUsDs82xw+fJgZM2awfft23nzzTf73v/9Rrlw5evbsSbVq1ewOT6mQoMkhSGRkZDB79mycTiezZs2iSZMm+WMpGjRoYHd4tpoxYwaff/458+bN47bbbiMxMRGXyxX2jfxKXQxNDkEobyyF0+kkMTGR2rVr53eRbdSoUdh2BT116hQbNmygVatWPPzwwyQlJeV/L+E8GFGpC6HJIcjl5OScNZaiUqVK+RfEG2+8MWwTRVZWFgsXLsxvu1m3bh3r1q3jkksuCeuFnZTylCaHECIirF69On8sxZkzZ/ITxS233BL21Sz//e9/GTlyJOXLlyc+Pp7XXnuN8oWn51VKAZocQpaIkJSUlF+iOHjwIHfeeSfx8fE6lmLdOubPn8+zzz7L2LFj2bx5s46lUKqQkE8OtWrVkrfeeovu3btTpUoVu8OxzW+//ZY/liIpKUnHUrjt2LGDqVOn5i/stHPnTrKzs6lYsWLYJlClIAySQ4MGDaRp06YsXryYv/zlL3z44YdkZ2eH78plWGMppk+fTkJCAj/99BMdO3bMX5cinMdSHDp0iJo1a/L+++/z0ksv0a1bNxwOB7169dJEocJOyCeHvGqlkydPsnv3bq677jrat2+Py+XK7wpat25du8O0TeGxFK1bt8bhcHDnnXeG/ViKxMREEhMTmTx5MklJSWzdupWePXsG98JOuqypfwXx9+1pckBEgvJx4403SmGnT5+WmTNnyoMPPig9e/YUEZF58+bJ1q1bi+wbTk6ePClff/219O/fX6pUqSJt2rSR0aNHy65du+wOzXbLli0Th8Mh0dHR0rFjRzlw4IDdIZXeV1+JREaKVKli/fzqK7sjCm1B/n0Dq8WDa6ztF/kLfRSXHIozYsQIueKKK6Rx48YyYsQIT7+/kHXmzBn57rvvZNCgQXLZZZdJ8+bNZcSIEZKUlGR3aLbKyMgQp9MpWVlZ8tlnn0nr1q3lrbfekp07d9od2rkdOWJdoOCPR2SktV15Xwh8354mh6CvVvKEy+Vi5cqVJCUl8dBDD/HCCy+QmZmJw+GgdevWlCkTUquleiwnJ4elS5fm93wquFBPnTrN2bPHBGOp+aJlZWWdNRhx0aJFVKtWjZSUlMBb2GnVKujcGdLS/tgWHQ3z5kGLFvbFFapC4PsOmzaHC7Fp0yamTZtGQkICubm5bNy4kcOHD1OtWrWwbdB2uVz5Yyk+++wbjhzJIiLCATgYP/5m7rsvPMdS5ObmUqZMGRYuXMgDDzyQv7DTE088wRVXXHHxJ7jYuuuUFKhXD06f/mNbZCTs2RN+Wd0fQuD7Dpg2B6ACsBJYD2wG/lXMPg8AKcAv7sfD5zuup9VK53P06FEREXnmmWekatWqMmDAAElISJDc3FyvHD/YHDkiUqGCS2CjwL8EmglcLgMGDJbvv/9eMjMz7Q7RNi6XS1atWiXPP/+87N27V9atWydPPPGELFy4ULKzs0t/QG/VXecdJzo6KOvAg06Qf98ESrWSscrglUQk3RgTASwFnhSRnwrs8wAQJyJDPD2uLwbBHThwgOnTp7N8+XImTJjAzJkzSU9PD6uxFMWVmitX/o1BgxJYufIbtmzZQvfu3XE4HNx+++1hPZbiwIEDfPrppyQkJLBv3z5mzJhBXFwcubm55+8i6+070CDuPROUgvj7DpiSQ8EHUBFYC7QstP0B4IPSHMtbJYdz+fbbb6VHjx4SFRUld9xxh2RmZorL5fL5ee10vva2AwcOyIcffiidOnWS6OhoiY+Ply+//FKOHTtmb+A227Vrl5w8eVKWLVsmMTEx0r9/f/n6668lPT29+DesXGmVGAp+0dHR1nalfIhA6q0ElMWqLkoHRhXz+gPAIWADMA2oU8JxBgOrgdV169b10VdXVFpamsyaNUtERF588UVp166dvPfee7J3716/xeBPnpaajx49Kp999pn06tVLoqKi5Pbbb5exY8dKcnKyfwMOMIcOHZKPP/5YunTpInPmzJFjx47J559/LqmpqX/sFAK9XlRwCqjkkH8yiAEWAk0Lba8GXOL+/RFgwfmO5Y+SQ3FOnTolM2bMkAceeEBq1qwpJ0+elO3bt8uvv/5qSzy+cuSIdRPr6bXq5MmTMnXqVOnXr59UqVJF2rZtK2+//bbs3r3bt4EGgd9++03uuusuiYqKks6dO8tPP/1kvRDkddcqOHmaHPzeW8kY8wqQISL/KeH1skCqiJyzkj8QJt5zuVyUKVOGr776iqFDh3LppZcSHx/P0KFDiY6OtjU2O505c4b58+fjdDqZMWMG9erVy+8ie+2119odnm3yFna67rrruOSSS7jvvvtwdOlC/PXX0+CWW4Ku7hoIvLr3QIsnAAVMmwMQC8S4f48EfgR6FNqnZoHf44Gfzndcu0oOJcnNzZUVK1bIc889J5mZmTJjxgx5+umnZenSpWHb80lEJDs7WxYsWCBDhgyRWrVqSaNGjWTYsGGyZs2akG+/OZfMzEyZNWuWPPzwwxIbGyvjx48Xl8slSUlJwfO9BNpI4UCLJ0ARKCUHY8z1wOdY7Q5lgKkiMtwYM9wd5AxjzBtALyAHSAUeFZGt5zpuIJQczmXHjh1MmDABp9NJSkoKK1euzB9HEc5jKVatWpU/6C47Ozu/RNG6deuwXZciNzeXrKwsjh8/TsuWLfPHUtx///2BW9IKtP7+gRZPAAuYkoOvHoFWcjiX7du3i8vlkgkTJkjVqlXl/vvvl8TERDl9+vRFHbe07QKBxOVyyYYNG+TVV1+V66+/XqpXry6DBw+W2bNn61gK91iKxMREycrKkmeeeUYWLVokOTk5dof3h0DrbRVo8QQwArFB2puPYEoOBe3du1fee+89adeunezcuVO2bdsmX331laSlpZ4YaPYAACAASURBVJXqOKFWgt6xY4e89dZb0rp1a7n00kvlL3/5izidTsnIyLA7NFudPHlSXnvtNfnzn/8ssbGx8umnn4qI2J8oAq23VaDFE8A0OQSJ1atXS/fu3fPHUmzbtu287wn1/wf79++XMWPGSMeOHSU6OlocDodMmDAh7MdS/Pbbb7J9+3Y5deqU1KhRQ+69916ZNm1ayWMpfC3QelsFWjwBSpNDkElLS5NJkybJ77//LvPmzTvnWIpgKkFfbNXX0aNH5dNPP5WePXtKVFSUdO3aVT755BM5fPiwdwMNMgcPHpSPPvpIOnfuLC+88IKIWIM2zxpL4Q+BVrcZaPEEIE0OQezUqVOSmJgo999/v1StWlUWLVok6enp+WMpgqXk4O2qrxMnTsiUKVOkb9++UqVKFbn11lvlnXfekT179ngn4CDlcrkkOztb4uPjJTo6Wrp06SIJCQl2h6UClKfJISxnZQ0m2dnZGGNYv349PXr04LLLLsPhcHDZZYP4v/+rS0QEZGfDuHHQv7/d0f7B151Hzpw5w7x58/LHUjRo0CC/59M111xz8ScIUnljKcqXL0+PHj249957adGiBfHx8TRo0MDu8FQA8LS3UnguZBBEIiIiKFeuHDfeeCMHDhxg7NixZGRkcPPNKfz880F69RrKtGkr6NvXZXeoZ9m9G8qXP3tbRIS13RsqVKhAjx49GD9+PMnJyYwaNYoDBw7QoUMHmjRpwksvvcS6desI1pufC1WpUiV69+5Nz549ARg4cCBr1ybRvPlNPPzwEwAcOXLEzhBVkNCSQxA7fPgwY8aMISEhgd9//51PP/2ULl26kJOTY/tYCru6nect7JQ3liInJyesx1JMmgSDBkFERA5ZWb8zfnx13nqrOadPn8bhcHD33Xdzww032B2m8iNd7CfMbNu2jZiYGE6cOEHLli3p2bMnDoeDzp07ExkZaUtMf1yY7Kn6EhE2btyI0+kkISGBw4cPc9ddd+FwOGjfvr3tCdTXSkrQu3a52LPHWtipTJkyvP7664wbN46rr76aW265JewSaLjRQXBhrOBYivHjx0t2drZMmTKl1GMpvCGQOo9s375d3nzzTWnVqpVceuml+Qs7hepYitL0anvzzTflhhtukMsvv1xefPFF/wer/AZtkFZ5Dh8+zEMPPcSPP/7IrbfeytChQ7ntttvsDstWeQs7OZ1OVq9eTefOnXE4HCG1sNOFVO399ttv7Nmzh/bt23PnnXfmryse7gs7hRKtVlJFpKWlMWvWLBo0aMB1111H79696dGjB/Hx8dSqVcvu8Gxz9OhRZs6cidPpZPHixbRp0waHw0GvXr24/PLL7Q7volxM1d6hQ4fyE+iZM2f48ccfWb9+PfXq1SMmJsa3gSuf0WoldU6ZmZkyffp0GThwoFStWlX+85//iIg1OjmcpaWlyeTJk+Wee+6RKlWqyG233SbvvvtuUC/s5I2qvbw1sp966qn8hZ3GjRvnpQiVP6HVSspT2dnZZGRkUL58ef70pz9RtWpV4uPj6devH40aNbI7PNucOXOGuXPn4nQ6mTlzJldeeSXx8fFhP5YiPT2d77//nm3btjFs2DDeeecdAOLj46lXr57N0anz8eo4B2PMtcaYjsaYyoW2d73QAFXgiIiIICYmhooVK7J3714+/vhjMjIyWLx4MQD//ve/WbFiBS5XYI2l8LUKFSrQs2dPPv30Uw4dOsQbb7zB/v37ad++fViPpahcuTJ33303w4YNA6BZs2Zs2rSJuLg42rVrh4hw6tQpm6NUF+u8JQdjzN+Bx4EtwA3AkyKS6H5trYg093mUxdCSg3/k5OQwfPhwnE4nqampDBs2jMcff9wqdhpjd3hF+GMhMJfLxc8//0xCQgLffPMNLpfrrLEUZcqE59jSnJwctm3bRuPGjRk8eDA//vhj/vfSvHnzgPx7CUdea5A2xmwEWotIujGmPjAN+FJE3jXGrBORP3sj4NLS5OBdnlxUf/31VzIyMvjzn/9Ms2bNiIuLw+Fw0KlTJypUqODPcIuV1/havjxkZflnXIUUGEuRt7BT3liKdu3ahfxYipK4XC5Wr7bGUixfvpxFixaxbNkyAG6++WZ7xlLoEqKAFxukgaRCzysDs4HRwC+eNGz44qEN0t5zIRPk7dmzR95991257bbb5P777xcRkaVLl8qJEyd8G2wJAmUywm3btsmoUaOkZcuWUrVqVRk4cKBMnz5dTp065d9AAtCXX34pzZo1k8svv1wGDx7s30WdQm0BlIuAt2ZlBRYANxTaVg74Asj15CS+eGhy8A5vXFTz1si+++67JSoqSnr06CHTpk3zUcTFC8RpzPft2yfvv/++tG/fXqKjo6VPnz4XtLBTqNmxY4d88sknIiIyevRo3y/sFCh3DgHC0+TgSeXoQCC5UGkjR0QGArd6VpBRgcobE+Tl1bFPnTqVffv20b9/f44fPw7A0KFDGTNmDAcOHPBOwCWoX9+qSiooO9vabpfatWszZMgQFixYwM6dO+nWrRsTJ06kdu3adO/enXHjxpGSkmJfgDZp2LAhf/3rXwHo27cvrVu3ZsyYMdSuXZv09HSSk5Pz/368wtezQIYqTzKIlWy4GhgPjPH0Pb58aMnBO3x9U5WYmCgDBgyQSy+9VAYOHCgi4rOqp2BZCCxvYae7775boqOjz7mwUzjJ+7sYO3Zs/liKsWPHXnyJQksOZ8Hbi/0APwHdgA3u502BLzx9v7cfmhy8xx8X1czMTNm5c6eIiHTs2FGuv/56efXVV2XDhg1ePU8gzeXkiYILO1WrVk1uuukmeeONN/IXdgpXJ06ckKlTp8p9990nGRkZsmjRInn77bdl9+7dF3bAYLlz8ANPk4PHg+CMMStF5KaCPZS0K2vo8GdHjtzcXFasWIHT6eTIkSNMmDCBGTNmcPnll3PTTTeFbVfQ7OxslixZkj+LbNWqVfO7gjZr1izkuoKW5m9uzZo1fPjhhyQmJlK/fn0SExOpWbNm6f5WtLcS4IPpM4DpQANgrfu5AbZ4+n5vP7TkEFreeecdady4sVxxxRUydOhQu8OxXW5urixfvlyeffZZadCggTRo0ECeeeYZWbZsWX4HgGB2oZ2HsrOzZcGCBZKTkyPjxo2Txo0by4svvihr164Vl8vl26BDBD4oOdQH/gc0BoYBXYEyInJ3qVOXF2jJITRt3bqVTZs20adPH5544gkyMjICaiyFHUSEDRs25I+l+P333/PHUtx2221BN5bCWwtB5S3slJCQkL9cbHR0NLt27QrLhZ085ZNZWY0x5YB44HrgEDBeRM5ccJQXQZND6Nu7d2/+f/zk5GS2bt3Krl27iI2NJSoqyu7wbLNt27b872XHjh0BsbBTaaxaBZ07Q1raH9uio2HePGjR4sKOmXcdW7p0KUOGDMlf2OmFF16gbt26Xog6dHhzhPQXwC/ux3oR+d07IV4cTQ6BzdvVu6dOnaJixYq89NJLvPvuu7Rr1w6Hw8HAgQPDto0CYN++ffnTaq9du5bbb78dh8PBHXfcQXR0dInvs7P63R9LyO7YsYOEhAQGDBjA3r17ef/99+nduzddunShYsWK3jlJkPLmCOmOwNPA51gJYifwLTACuNuTuitfPLTNIXD5ejDqsWPHZMKECfLYY4+Jy+WSSZMmyZgxY+TAgQPePVGQOXLkiPzvf/+TO+64Q6KioqR79+4ybtw4SUlJOWu/QBgs7M/OQykpKTJmzBjp0KGDREdHy9KlSyUzM1OOHz/uu5MGMHw1Zbe7aqkx0Ay4XkSGluoAXqIlh8Dkj7vCwhYtWsS4ceP47rvvaNy4MQsWLKBMmTKUK1fONycMAnkLOzmdTubMmUPz5s3p3bs3bdveRevWtf3671MSO0ovR48epVKlSqxfv54uXbrkL+zkcDioWrWqf4KwmS72o2xh5zQWmZmZsnz5chERef75588aSxHOPVlOnTqVv7BTdHRVKVv2JoF/C2wLiGlG7HLixAmZMmWK9O3bVxYvXiwpKSny7rvvyp49e+wOzafwQW+lW7GqkqoB64G3RWTVRSSwixJuJYdg6aJtR8mhOAXHUsyaNYvVq1eze/duMjIyaNGiRdi2Uxw8mE2DBovJynICCcBllCvnYM4cB+3aXR9yYylKY+/evbz66qvMmDGDBg0aMHr0aNq2bWt3WF7ni3EOO4DOQCxWN9blwD2evt/bj3AqOQRCHXFpBOpg1G+++UYaNWoktWrVkiFDhsixY8fsDskWef8+UVG5Ur78Mune/RmpX7++XHnllfLss8/K8uXLQ2IsxYXKzs6W+fPny65du2THjh0hN5YCX0yfUeh5ZWCTB++rAKzEKm1sBv5VzD6XAFPcCehnoP75jhuqyaHw9A/BOi1MIE9jkZSUJP/+978lOztbpkyZIg899JB8++23cubMGbtD85vC/z4ul0vWrVsnL730kjRp0kRq1qwpjz32mMybN0+ysrLsDdZGubm5smLFChk6dKhceeWV8sknn+QPUAzWBOq15IA1NfdTwH+Al4Fy7u0RnpwEayR15QLv+RloVWifx4CP3b/3A6ac77ihmByKKyEE4lTUoWTfvn3y9ttvS9u2bSUmJkb27t0rx48ft21dikCxdetWeeONN6RFixZSrVo1eeCBB2TGjBly+vRpu0OzjcvlkuzsbDl48KBcd911UqNGDXnkkUdk7dq1dodWKt5MDrcBT2LNyLoW2A3Mw+rSOtyTkxQ4VkX3MVoW2v4D1mpzYK0VcRT3GIySHqGWHEoqISQlBWfJIRgdPnxYXC6XTJkyRaKioqRXr17y2WefhX2iKLiwU5UqVeSee+6RyZMnh/33krew0w8//CBnzpyRhx9+WBISEny3LoWXeL1aKf8NUBa4DhgAvFWK9/wCpAOjinl9E1C7wPOdwGXnOmaoJYdzlRACtQ4/lB07dky+/PJLiY+Pl3Xr9sqkSZtk1KgP5eDBg3aHZqvDhw/Lf//7X+nWrVv+wk7jx48vMpYi3GRkZMgHH3yQP5bio48+EhEJyBUAfdHmUA14FHgQuAmI9PS9BY4RAywEmhbavrmY5FCtmPcPBlYDq+vWreu7b88G52tbCOQ6/FCWl5grV14vZcveJxUrxsjNN98sW7ZsCYnGyYtx/PhxmThxovTu3Vuio6Olffv28v7778u+ffvsDs1WKSkpsm/fPjl16pRUq1ZNunXrJv/973/lSID85/VFcljibnM4BCwGsriAWVmBV4BnC20L+2olES0hBJriEnaFCpkyefL3kpaWJrNmzZIbbrhBhg8fLps2bQrrZJGRkSEJCQkycOBAufTSS6Vly5YyatQo2b59u92h2SotLU0mT54s99xzj4wYMUJERCZMmGDrwk6+SA7r3D9/cf/sDfyfB++LBWLcv0cCPwI9Cu3zeKEG6annO24oJgcR35cQtATiufN1BsjJyZHFixfLU089JXXr1pX58+dLWlqa/Pzzz2GdKLKysmTOnDnyyCOPSPXq1eW6666TV155RdavXx/W34uI1U32gQcekKpVq0qLFi1k4sSJfo/BF8lhhfvnz3lVSsBiD953PbAO2OBuW3jZvX040Mv9ewXga6yurCuBK8933FBNDr4UbOMlSuKvBFeabsQul0tyc3Nl3bp1cs0110jt2rXliSeeCPs755ycHFm6dKk8/fTTUr9+fWnYsKEMHTpUVqxYEbRdQb0hKytL5s2bJ3PnzhWXyyVdu3aVl156SdatW+fzBOqL5NAbqAo8A0wCngB2ePp+bz80OZROsI6XKMzfCe5Cq/qSkpJkxIgRsnHjRtm9e7cMGjRIvvvuu7AaS1GYy+WStWvXyosvvpi/sNPjjz8u8+fPl+zsbLvDs43L5ZIVK1bIs88+K1deeaUMGjRIRES2b9/ukwTqteQAvOL+eTMQ5f59ADAKaOLJSXzx0ORQOqEwXsKuBHcxJZUjR0TmzDkqw4ePljZt2khMTIzMnDlTXC6XpKenez/YILJlyxZ5/fXXJS4uTqpVqyYPPvigzJw5M+zHUqSlpYmISNu2baVGjRry6KOPypIlS7x2Dk+TgycTzMxx/3wK+NkYs81disgEGnnwfhUA6teHrKyzt2VnW9uDxe7dUL782dsiIqztvhQbay1CU9q5oSZNsuaZuvvuarzxxj947LEf2bJlCzfffDM7d+6kZs2a3HXXXXzxxRccO3bMN8EHsGuvvZbnn3+eVatWsXbtWpo1a8Zbb71FjRo16Nu3L1OmTOHkyZN2h+lXxpj8dTiWLFnC4sWLqVevHkuXLgXg7bffJjExkdMFJy/zFU8ySMEH1lQXzYH78XCcgy8eWnIovWDvDRVMVWOexJqamipffPGF3HXXXfLVV19JVlaWjB07NuzHUiQnJ8snn3wiXbt2PWssxdGjR+0OzXYff/yxtGvXTqKjo+Uf//iHiEipq57wZpsDUAZ4wZN9/fXQ5HBhgr23UrAkuAupxjty5Ijcd999EhNjjaWYPXu2/wL2o9L8DRYeS9GhQwf54IMPZP/+/b4PNIAdOXJEfv75ZxER6dSpU4kLOxXH0+RQmim7F4hIB58UXy5AuE3Zrf7g7enLfTEd+sVMXZ6VlcWCBQuoUaMGV155JZ06dcpfJ7px48ZBPa32pEkwaJBVPZiVBePGQf/+nr331KlTzJkzB6fTybfffss111yDw+EgPj6eq666yreBB7ATJ07kL+x07Ngx5s6dy7Jly6hbty516tQpsr8vpuz+f1gD2Mp4+h5fPrTkoLzBl72fvFHKyRtL8eSTT0qdOnVk5MiRIiJBOejOm9WCmZmZ8sMPP8jf/vY3qV69ui7s5Jb32YcNGyZVq1aVm266SUaPHn3WPvig5DAVa06lS7HGOmwANojI1x4mOK/SkoO6WP5YmMibpRIR4fTp0xhjaN68ORkZGcTHxzNw4EBuvPFGb4TrU6tWQefOkJb2x7boaJg3z2rwL8zT767gwk5Op5OIiIj8pT/DeWGn7OxsFi9ezNatWxkyZAivvfYaOTk5DB8+3KOSg8ffmojcIyKNgHrAv7AGrLW88NCVspc/ej9daE+n4hhjqFixIpGRkSQlJTF79mxiY2PZvHkzIsJzzz3H999/T2Zm5sWfzAdK02Mur6dX587Wz0mTSj5u2bJladOmDaNHj2bXrl1MmTKFiIgIHnzwQerWrcsTTzzBwoULycnJ8ebHCXgRERF06tSJIUOGANC1a1dcLpfnB/CkeOEuXVz0xHvefGi1kspzoY3swdT76Xyys7Nl9Og/xlK89dZbImJVSwUST6ravPnvkpSUJCNHjpQbb7wxfyzFt99+G9ZjKQjUife89dDkoEQuvs0gWHo/lcahQ4ckKSlJXC6XNGzYUO666y754osvJDU11e7QROT8ydxXAzZ3794tb7/9ttx6661SpUoV6du3r0yZMiXs1qXwNDmUps1hnYj82Rjzi4jcYIzpDVwlIqM8L6d4j7Y5KG+1Gfiit1KgSE1N5dtvv8XpdFK9enXGjh3L7NmzueGGG6hRo4bd4RXLH21Bhw8fZsaMGTidTpYtW0a7du1wOBz07NmTatWqeeckAcoXvZUuaOI9Xz205KBCYUoQOzz00EMSExMjbdq0kc8++8zucIrlzxLdsWPHZMKECeJwOCQ6Olo6duwoY8aMkQMHDvjupDbCWyUHY8y1IrLVXVJYCDwAtACWA0+KiC0djLXkoPxxhxmqMjMzmT9/PidPnqRv374MHjyYevXq4XA4aNQoMGbFsaNEd+rUKX744QecTiffffcd1157bf5YioYNG/onCB/ztOTgSXL4DVgEvCoie93bBmB1a/1cRDZffLilp8lBwR+DqiIirJ4vpRlUpf6wePHi/K6gLVu2ZNq0aSQnJ1O9evWgHnR3MbKysli4cCFOp5Pp06dTs2bN/C6yTZo0CdrvxZvJoTzwN+BpIBEYISJHvRLlRdDkoPL4aoRzqLZDnIuIcOTIEapXr07Pnj1Zv349DoeDPn360KZNG7vDs01ubi7Lly/PT6CXXHJJfqKIi4sLqrEUXksOBQ5YARgCPAZMwJp0z7YpEzU5KF+5mCkeQomIkJSUhNPpJDk5mTFjxjBx4kSqVatGhw4dKF94kEiYEBHWrl2bnyjS09OJj48nPj6etm3bUq5cObtDPCevJ4cCB64EPIk13mGsiPznwkK8OJocAluw3nlrO8a5jRs3jvHjx5OUlES/fv346KOP7A7Jdlu2bMlPFHv37qVXr144HA46derEJZdcYnd4Rfii5FAfuBa4Bmsdh5uApiJiy+1DuCeHQL74BvOdd2mneAhXBw8eZNOmTXTp0oUHH3yQtLQ0HA4HPXr0ICYmxu7wbLN7924SEhJISEhgw4YNdOvWDYfDQbdu3ahcubLd4QHebXPYANQG9gJbgS0FHr+KSNY53u4z4ZwcAvniG+x33sEevx1SU1OZOXMmCQkJbNu2jc2bN5OUlES1atUCdiyFPxw+fJjExEScTifLly+nffv2+WMpqlataltcXhvnADTEnUQC6RGu4xwCfcqHUBh7EIqjpv0lb7qOkSNHSpUqVaRNmzYyevRon6yFHExSU1Plyy+/lPj4eImKipJOnTrJhx9+aMvCTnh7hHSgCdeSQ6BXe4TKnXdpq+0CuZrPLnljKZYvX86IESMYN24cycnJATWWwg4ZGRlnjaVo3Lhx/liKK6+80ufn91mDdKAI1+QQDBffcBt74K9qvmBPQKtWreLLL7/E6XQSExPD2rVrycnJITIyMmjHDFysvIWdnE4niYmJXHHFFfldZH21sJPXp88ItEe4ViuJBEe1R7AvR+opf1Xz+XJRIn/Lzc2VzZs3i4jIyy+/LHXr1pWnnnpKlixZEnCzyPpT4YWd/vSnP8lzzz0nK1eu9OoCRmi1UmgL9rvIUOGPar5gKC1eKBFh8+bNOJ1Ovv/+e+bPn8+WLVs4evQo7du3D+uxFGvWrMnvIpuRkZFf9dSmTZuLGkvhackheIb1hbCUFOsik5Li+Xu8uYiMunClWcDmQvljUSK7GGNo2rQpL7/8MitWrKBixYocPnyY4cOHU6NGDf7yl7+Qmppqd5h+Z4whLi6O119/na1btzJnzhxiY2N5+umnueKKK3j44YeZNWuWTxd20uRgs9KseKUCT2ys1cYQGWmVGCIjrefeTNr+SECB5I477mDZsmVs2rSJW2+9lSpVqvD555/jcDiYMGECx48ftztEv2vUqBEvvvgia9eu5eeff6ZJkya88cYb1KhRg3vvvZdp06aRnp7u1XNqtZKNQrm6INz4upov3Br5C8sbS+F0Olm4cCGbNm2iYsWK5ObmUr16dbvDs01ycnL+WIoVK1bQoUOH/LEUl156abHv0d5KQSDQu6WqwKLtTJb09HQqVarE9OnTefDBB2nWrBkOh4OBAweWeEEMB8eOHctf2Gn+/Pm0atUKh8PBnXfeSc2aNfP30+QQBLTkoNTFOXPmDPPmzcPpdDJy5EiSk5P5/vvvcTgcXHvttXaHZ5uMjAxmz56N0+lk1qxZNGnSpOBYCm2QDnT+qK9WKpRVqFCBHj16MH78eGrWrEnFihU5dOgQnTp1onHjxmzevJnc3FyC9Sb4QlWqVInevXszceJEkpOTGTZsGFu2bKFly5YeH0NLDgFAqwuU8i6Xy8WqVato2rQpP/74I4888kj+4LLWrVtTtmxZu0O0RW5uLuXKldOSQ7DQbqlKeVeZMmVo2bIllSpV4vbbb2fmzJlUqVKFxx9/nCVLlpCamsqcOXPIKtwNLMSVJin6PDkYY+oYYxYaY7YYYzYbY54sZp92xpg0Y8wv7sfLvo5LKRUejDFcd911vPLKK6xfv5527dpx4MABXnnlFWrUqMHAgQNJSkqyO8yA44+SQw7wjIg0AloBjxtjGhez348icoP7MdwPcSmlwlBeslixYgUbN26kZcuWlC1blh07dtCnTx8mTpwYlmMpCvN5chCRQyKy1v37Sax1IGr5+rxKKXU+tWrV4vHHH+eaa67h8ssvp0ePHkyZMoW6desyffp0XC4XR44csTtMW/i1Qdq9mtwSrBXkThTY3g74BtgPHASeFZHNxbx/MDAYoG7dujfu2bPH90ErpcLOyZMnAThy5Ag33nhj/liKu+++myuuuMLm6C5OwM2tZIypjJUAniqYGNzWAvVEpBnwPjC9uGOIyCciEicicbHaequU8pGoqCiioqJo2LAhycnJDB06lPXr17Ny5UoyMzMZNWoUv/76q91h+pRfkoMxJgIrMUwUEWfh10XkhIiku3+fBUQYYy7zR2xKKXUuBcdS3HXXXaSnp7Nv3z46dOhAkyZNmDFjht0h+oQ/eisZYBywRURGl7BPDfd+GGNucsf1u69jU0qp0qpWrRoffPAB+/btY9y4cVx99dUcP36ca665hmeeeYZly5bhcrnsDvOi+aPkcAswAOhQoKvqHcaYR4wxj7j36QNsMsasB94D+kmwjs5THruQqcqVChRlypShVatWNGrUiCpVqvD1118TFRXFY489xogRIwBYtmwZ2dnZNkd6YXSEtLKFv5bWVMoOOTk5ZGdn06FDB3799Vd69OjBX//6V9q2bWt3aIHXIK1UnpQUKzGcPm3NSHv6tPU8lEoQWioKb+XKlSMyMvKssRRHjhxBRPjb3/7GV199RVrB6ZgDkCYH5XehvLIZ6AJO6mx5Yyl69+5Nbm4urVq1YtKkSdSpU4fXXnsNgFOnTtkcZVFaraT8LpSnKg/lz6a868SJE6SmplKvXj0aNmxI3bp186fVrlOnjs/Oq9VKKmD5cqpyu6tzQr1UpLwnOjqa+vXrY4xh8+bNPPPMM6xbt4533nkHgKlTp7Jt2zbb4tOSg7KNt6cqD4RGbi05KG95+umnmTx5MlWrVuXRRx/l8ccf98pxdSU45ZFQ1bUNRQAADMdJREFUWUsikC7K4b7es/Iel8vFzz//TGpqKt27d6dv377Url07f12KMmVKX/mj1UrqvEKp4TSQqnP697eS0rx51k9NDOpClSlThtatW9O9e3cAXnjhBSpXrswjjzxCz549Adi5c6dPxlJoySFMBdKdtjeE2udR6nxOnjxJVFQU/fr1Y+7cufTs2ZN77rmHO+6445zv05KDOqdAutP2Bl2P+9zsbqhX3hcVFQXA5MmTWb9+PXFxcSxduhSAsWPHMmnSJE6cKDzHqec0OYSp+vWtRtuCsrOt7cFKq3OKF0rVh6p4tWvXZsiQIbz++usAxMTEMHHiRGrXrs19990HUOr5nrRaKYxpw2no0+q28HbixAk2b95M69at6d+/P8nJySxatMijaqVy/ghQBab+/aFTp9DoraSKl1d9WDA55FUf6r936IuOjqZ169YAjB8/nqVLl7Jo0SKP3qvJIczFxupFIpSFYvWhujCRkZF07tzZ4/21zUGpEKYN9epCaclBqRCn1YfqQmhyUMotVEaLF0erD1VpabWSUmh3T6UK0+Sgwl44LD6kVGlpclBhL9RGiyvlDZocVNjT7p5KFaXJQYU97e6pVFHaW0kptLunUoVpclDKTbt7KvUHrVZSSilVhCYHpZRSRWhyUEopVYQmB6WUUkVoclBBQ5e6VMp/NDmooBAscx9pAlOhQpOD8gpfXhSDZe6jYElgSnlCk4O6aL6+KAbD3EfBksCU8pQmB3VR/HFRDIa5j4IhgSlVGj5PDsaYOsaYhcaYLcaYzcaYJ4vZxxhj3jPG7DDGbDDGNPd1XMo7/HFRDIa5j4IhgSlVGv4oOeQAz4hII6AV8LgxpnGhfboBV7sfg4GP/BCX8gJ/XRT794c9e2DePOtn//7ePf7FCoYEplRp+HxuJRE5BBxy/37SGLMFqAUkFdjtTuALERHgJ2NMjDGmpvu9KoDlXRQHDbJKDNnZvrsoBvrcR76avC+Uly9VgcuvE+8ZY+oDfwZ+LvRSLWBfgef73dvOSg7GmMFYJQvq1q3rqzBVKemMpn/wdgKbNMlKvOXLWyW0ceMCr9SkQpPfGqSNMZWBb4CnRORE4ZeLeYsU2SDyiYjEiUhcbDhfgQJQbCy0aBHeicHbtAeUspNfkoMxJgIrMUwUEWcxu+wH6hR4Xhs46I/YlApU2gNK2ckfvZUMMA7YIiKjS9htBjDQ3WupFZCm7Q0q3GkPKGUnf7Q53AIMADYaY35xb3sBqAsgIh8Ds4A7gB3AKeBBP8SlVEDzZ2O/UoUZq4NQ8ImLi5PVq1fbHYZSPqe9lZQ3GWPWiEjc+fbTZUKVCnCB3oVXhSadPkMppVQRmhyUUkoVoclBKaVUEZoclFJKFaHJQSmlVBGaHJRSShWhyUEppVQRmhyUUkoVoclBKaVUEZoclFJKFaHJQSmlVBGaHJRSShWhyUEppVQRmhyUUkoVoclBKaVUEZoclFJKFaHJQSmlVBGaHJRSShWhyUEppVQRmhyUUkoVoclBKaVUEZocVFhISYFVq6yfSqnz0+SgQt6kSVCvHnTubP2cNMnuiJQKfJocVEhLSYFBg+D0aUhLs34OGqQlCKXOR5ODCmm7d0P58mdvi4iwtiulSqbJQYW0+vUhK+vsbdnZ1nalVMk0OaiQFhsL48ZBZCRER1s/x42ztiulSlbO7gCU8rX+/aFTJ6sqqX59TQxKeUKTgwoLsbGaFJQqDa1WUkopVYQmB6WUUkX4PDkYY8YbY44YYzaV8Ho7Y0yaMeYX9+NlX8eklFLq3PzR5vAZ8AHwxTn2+VFEevghFqWUUh7weclBRJYAqb4+j1JKKe8JlDaH1saY9caY740xTUrayRgz2Biz2hizOkXnP1BKKZ8JhOSwFqgnIs2A94HpJe0oIp+ISJyIxMVqv0SllPIZ25ODiJwQkXT377OACGPMZTaHpZRSYc325GCMqWGMMe7fb8KK6Xd7o1JKqfDm895KxphJQDvgMmPMfuAVIAJARD4G+gCPGmNygNNAPxERX8ellFKqZD5PDiLS/zyvf4DV1VUppVSAsL1aSSmlVODR5KCUUqoITQ5KKaWK0OSglFKqCE0OSimlitDkoJRSqoj/3969hsh1l3Ec//5oYiupUjRFQxNIwBpJGzaGUEMjEkPVWosKXgtavEAQIkZaUKsvUi/4RijSN0poS70UixLFoqIGjKYhJm3S5mK6VkoMGhqMIsZGwaJ9fHFOnKUns7stTs5u5/uBIbNnzpl59k/2/GbOOfP8DQdJUofhIEnqMBwkSR2GgySpw3CQJHUYDpKkDsNBktRhOEiSOgwHSVKH4SBJ6jAcJEkdhoMkqcNwkCR1GA6SpA7DQZLUYThIkjoMB0lSh+EgSeowHCRJHYaDJKnDcJAkdRgOkqQOw0GS1GE4SJI6DAdJUsfIwyHJPUlOJ/nNkMeT5M4kTyQ5kmTtqGuSJE3vQnxyuBe4fprH3wpc2d42A1+7ADVJkqYx8nCoqt3AX6dZ5R3AN6uxD7gsyZJR1yVJGm4unHO4AvjjlJ9PtsskST1Z0HcBQM6zrM67YrKZ5tATwL+GnccYQ4uBv/RdxBzhWAw4FgOOxcDK2aw0F8LhJLBsys9LgSfPt2JVbQe2AyQ5UFXrRl/e3OdYDDgWA47FgGMxkOTAbNabC4eVHgBubq9aWg+cqapTfRclSeNs5J8cknwH2AgsTnIS2AYsBKiqrwM/AW4AngD+CXx41DVJkqY38nCoqptmeLyALc/jqbc/v4pekByLAcdiwLEYcCwGZjUWafbNkiQNzIVzDpKkOWZehkOS65M83rbc+Ezf9fRlptYk4yTJsiS7kkwmOZZka9819SXJJUkeSnK4HYvP911Tn5JclOTRJD/qu5a+JTmR5GiSQzNdtTTvDisluQj4HfAmmstgHwZuqqrHei2sB0neAJyl+Yb51X3X06f2W/VLquqRJC8BDgLvHNP/FwEWVdXZJAuBPcDWtgPB2ElyC7AOeGlV3dh3PX1KcgJYV1UzfudjPn5yuAZ4oqqOV9XTwP00LTjGzixak4yNqjpVVY+0958CJhnTb9q3rWjOtj8ubG/z613g/0mSpcDbgLv6rmW+mY/hYLsNTSvJcuC1wP5+K+lPeyjlEHAa2FlV4zoWXwU+BTzTdyFzRAE/T3Kw7Tgx1HwMh1m329D4SXIpsAP4ZFX9ve96+lJV/6mqNTQdB65JMnaHHZPcCJyuqoN91zKHbKiqtTTdsLe0h6bPaz6Gw6zbbWi8tMfXdwD3VdX3+65nLqiqvwG/ZPq2+S9UG4C3t8fZ7wc2Jfl2vyX1q6qebP89DfyA5jD9ec3HcHgYuDLJiiQvAt5P04JDY6w9CXs3MFlVd/RdT5+SXJ7ksvb+i4HrgN/2W9WFV1W3VdXSqlpOs5/4RVV9oOeyepNkUXuxBkkWAW8Ghl7pOO/Coar+DXwc+BnNScfvVtWxfqvqR9ua5NfAyiQnk3y075p6tAH4IM27w0Pt7Ya+i+rJEmBXkiM0b6Z2VtXYX8YpXgHsSXIYeAj4cVX9dNjK8+5SVknS6M27Tw6SpNEzHCRJHYaDJKnDcJAkdRgOkqQOw0GS1GE4SJI6DAeNpSSvSnL0WcsuTvL7JKuew/NcO918CUk2JvnWkMeuG/bYlHWcs0O9MBw0ro4Dy5JM/RvYDPxqNnNAtPOKUFV7q2rbNKuuAR4d8tgEcHiGl7qX8eyLpJ4ZDhpLVfUM8AdgOfyvB9GtwO1J3p1kXzuT2p4kl7frfC/JHUl2AbdNWfb6YdvQBMAVSfYnOZ5k45QyJoBD7fOsSPLDJAfaWdxWtnU6Z4d6YThonE0Cr2nvbwEeqKoTwK6qWl9VE8BO4L3tOquBs1X1xqr6UrvsauDoNNusAZ6qqtcBHwO+OOX1J4DDbTfZu4BbqmodcDswttPfam5Y0HcBUo8maZoW7qYJh/Xt8g8leR9wMfBK4LNJLgFeBnzh3MbtsoVVdSbJrefZZgHwcuDL7SaHgMXttgtppq38c5L3AFcBO5rmsiwAHhzh7y3NyHDQOJsENgFbaeaA+FOSm2l63G9q52DeDRyj2Xnvb7sCn3MV8Ng026yimdL26Xb9tQzOMaxqXx+aTxCfq6q7R/abSs+Rh5U0ziZpduofAb7SLlsN7G138u8CrqU5bLQaOPKs7c8tG7bNBLCivQrqUmAbzbSVMOV8A3AKeMu5k+NJVrfzU0i9MRw0zh6n2bFvr6oz7bJvAJ9I8iDwauB4Vf2D6cNh2DYTwH3AXpr++XdW1b5226lXKt1D87c42c77/Olqe+k7Z4f64nwOkqQOPzlIkjoMB0lSh+EgSeowHCRJHYaDJKnDcJAkdRgOkqQOw0GS1PFf3gi5qXVuhLMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#scatter plot with decision boundary on predicted values for different values of C\n",
    "for i in range(len(C)):\n",
    "    fig = plt.figure(figsize = (6, 6))\n",
    "    c = -B[i][0]/W[i][1][0]\n",
    "    slope = -W[i][0][0]/W[i][1][0]\n",
    "    c11 = c + math.sqrt((1 + slope*slope))/math.sqrt((W[i][0][0]*W[i][0][0] + W[i][1][0]*W[i][1][0]))\n",
    "    c12 = c - math.sqrt((1 + slope*slope))/math.sqrt((W[i][0][0]*W[i][0][0] + W[i][1][0]*W[i][1][0]))\n",
    "    yl = slope*xl + c\n",
    "    yl1 = slope*xl + c11\n",
    "    yl2 = slope*xl + c12\n",
    "    plt.plot(xl, yl, \"k\", lw = 1, ls = \"-\")\n",
    "    plt.plot(xl, yl1, \"k\", lw = 1, ls = \"--\")\n",
    "    plt.plot(xl, yl2, \"k\", lw = 1, ls = \"--\")\n",
    "\n",
    "    plt.scatter(*X2[Y_P[i] == (-1)].T, s = 20, color = \"blue\", alpha = 1.0)\n",
    "    plt.scatter(*X2[Y_P[i] == 1].T, s = 20, color = \"red\", alpha = 1.0)\n",
    "    plt.xlim(0.0, 5.0)\n",
    "    plt.ylim(1.0, 5.0)\n",
    "    plt.ylabel(r'$Variable 2$')\n",
    "    plt.xlabel(r'$Variable 1$')\n",
    "    plt.title(\"SVM predicted Data 2 with C = \" + str(C[i])) \n",
    "    #image_name = \"C:\\Me\\sem6\\cll788\\A3\\Data2_scatter\" + str(C[i]) + \".jpeg\"\n",
    "    #plt.savefig(image_name)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}