Machine Learning Programming Exercise 2.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Logistic Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Exam 1 score</th>\n",
       "      <th>Exam 2 score</th>\n",
       "      <th>Admission Status</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>34.623660</td>\n",
       "      <td>78.024693</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>30.286711</td>\n",
       "      <td>43.894998</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>35.847409</td>\n",
       "      <td>72.902198</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>60.182599</td>\n",
       "      <td>86.308552</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>79.032736</td>\n",
       "      <td>75.344376</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Exam 1 score  Exam 2 score  Admission Status\n",
       "0     34.623660     78.024693                 0\n",
       "1     30.286711     43.894998                 0\n",
       "2     35.847409     72.902198                 0\n",
       "3     60.182599     86.308552                 1\n",
       "4     79.032736     75.344376                 1"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "data=pd.read_csv(\"/Users/natalychacon/Documents/Machine Learning/std coursera/machine-learning-ex/ex2/ex2data1.txt\",header=None)\n",
    "data.columns = ['Exam 1 score', 'Exam 2 score',\"Admission Status\"] \n",
    "data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.1 Visualizing the Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1024d96150>"
      ]
     },
     "execution_count": 134,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtMAAAHgCAYAAABn8uGvAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjEsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy8QZhcZAAAgAElEQVR4nO3dfXRV9Z3v8c9XUdGWohDapaQpabBUx0agacEUgwZL6+3ztEwVqdrhltorw1DaYdrxXvuwxrl9WkpZzC3XGSp2ELQybXVmOh0tKCnESRsejFbK1WMwDVI1qFFb7fjwvX/sc8LJEznZOefsvc9+v9ZinZydk5wvm0Py2b/z/f1+5u4CAAAAMHrHRV0AAAAAkFSEaQAAACAkwjQAAAAQEmEaAAAACIkwDQAAAIREmAYAAABCGhd1AWNRVVXl06ZNi7oMAAAAVLjdu3f3uPuUgccTHaanTZum9vb2qMsAAABAhTOzx4Y6TpsHAAAAEBJhGgAAAAiJMA0AAACElOieaQAAgKR6+eWX1d3drZdeeinqUpBn/Pjxqq6u1gknnFDQ4wnTAAAAEeju7taECRM0bdo0mVnU5UCSu+vIkSPq7u5WbW1tQV9DmwcAAEAEXnrpJU2ePJkgHSNmpsmTJ4/q3QLCNAAAQEQI0vEz2n+TkoVpM/u+mT1pZg/mHZtkZneb2cPZ29Oyx83M1prZI2bWYWazS1UXAAAAjvrxj38sM9NvfvObIT9/5ZVXauvWrQV/v8cff1yf+MQnJEn79u3TT3/6077P3XvvvWptbR11jdOmTVNPT8+ov64cSjkyvVHS+wcc+5Kkbe5+pqRt2fuSdLGkM7N/lkn6XgnrAgAASJT1OzJqzfQPk62ZHq3fkRnz996yZYvmzZunW2+9dczfS5LOOOOMvvBdrDAdZyUL0+7eIunpAYc/Iunm7Mc3S/po3vEfeOA/JZ1qZqeXqjYAAIAkqa+eqOWb9/YF6tZMj5Zv3qv66olj+r4vvPCCdu3apQ0bNvSFaXfX8uXLdfbZZ+sDH/iAnnzyyb7HT5s2TX/zN3+j8847Tw0NDdqzZ4/e9773qa6uTuvXr5ckHTx4UOecc47+67/+S9dee61uu+02zZw5U9/85je1fv163XDDDZo5c6Z+8Ytf6KmnntLHP/5xvetd79K73vUu7dq1S5J05MgRLVy4ULNmzdJnP/tZufuY/p6lVO7VPN7k7oclyd0Pm9kbs8enSvpt3uO6s8cOl7k+AACA2Gmsq9K6xbO0fPNeLZlTo01tXVq3eJYa66rG9H1/8pOf6P3vf7/e9ra3adKkSdqzZ48OHjyoAwcO6IEHHtATTzyhs88+W3/+53/e9zVvfvObdd999+nzn/+8rrzySu3atUsvvfSS/uRP/kRXXXVV3+NOPPFEff3rX1d7e7vWrVsnSXrxxRf1+te/Xl/84hclSYsXL9bnP/95zZs3T11dXXrf+96n/fv362tf+5rmzZuna6+9Vv/2b/+mG2+8cUx/z1KKy9J4Q3V6D3kJYmbLFLSCqKamppQ1AQAAxEZjXZWWzKnR2u2PaEXz9DEHaSlo8Vi5cqUk6ZJLLtGWLVv08ssv69JLL9Xxxx+vM844Q83Nzf2+5sMf/rAk6R3veIdeeOEFTZgwQRMmTND48eP17LPPjur5f/7zn+uhhx7qu//cc8/p+eefV0tLi370ox9Jkj7wgQ/otNNOG8tfs6TKHaafMLPTs6PSp0vKvW/QLenNeY+rlvT4UN/A3W+UdKMkNTQ0xHfMHwAAoIhaMz3a1NalFc3TtamtS3PrJo8pUB85ckTbt2/Xgw8+KDPTq6++KjPTxz72sWOuaHHSSSdJko477ri+j3P3X3nllVHV8Nprr+m+++7TySefPOhzSVnppNxL490p6Yrsx1dIuiPv+OXZVT3mSurNtYMAAACkXa5Het3iWVq1cEZfy8fASYmjsXXrVl1++eV67LHHdPDgQf32t79VbW2tJk2apFtvvVWvvvqqDh8+rHvuuSf0c0yYMEHPP//8sPcXLlzY1wIiBRMWJampqUm33HKLJOnf//3f9cwzz4SuodRKuTTeFkn3SZphZt1mtlTSNyS918welvTe7H1J+qmkRyU9IukfJP2PUtUFAACQNB3dvf16pHM91B3dvaG/55YtW/Sxj32s37GPf/zj+t3vfqczzzxT73jHO/S5z31O8+fPD/0cF154oR566CHNnDlTt912mz70oQ/pxz/+cd8ExLVr16q9vV319fU6++yz+yYxfuUrX1FLS4tmz56tu+66K9atvRbn2ZEjaWho8Pb29qjLKKv1OzKqr57Y722d1kyPOrp7ddX8uggrAwAAo7F//36dddZZUZeBIQz1b2Nmu929YeBj2QExYUq1NA4AAABGLy6reaBApVoaBwAAAKPHyHQC5S+Ns2RODUEaAAAgIoTpBBq4NM5YZvICAAAgPMJ0wpRiaRwAAACEQ5hOmFIsjQMAkdm5Rups6X+ssyU4DgAJQJhOmKvm1w3qkW6sq6qsZfH45Qqkx9TZ0u1XHv0/39kS3J86O8qqgNQwM33hC1/ou/+d73xHX/3qV4/5NT/5yU/6bQE+lHPPPVeXXnrpsJ8/ePCgzjnnnFHVeu211+rnP/+5JGnNmjX6wx/+0Pe5v/u7vxvV95KkjRs3avny5aP+uoEI04gffrkC6VHbJC3aGPwf335dcLtoY3AcwFElGmg66aST9KMf/Ug9PYW3i44Upvfv36/XXntNLS0t+v3vfz+m+vJ9/etf10UXXSSpOGG6WAjTiB9+uQLpUtskNSyVWr4V3PJ/HRisRANN48aN07Jly3TDDTcM+txjjz2mBQsWqL6+XgsWLFBXV5daW1t155136q/+6q80c+ZMZTKZQV+3efNmfepTn9LChQt155139h3fvXu3zj33XJ133nn6+7//+77jGzdu1Ec/+lF96EMfUm1trdatW6frr79es2bN0ty5c/X0009Lkq688kpt3bpVa9eu1eOPP64LL7xQF154ob70pS/pxRdf1MyZM3XZZZdJkjZt2qR3v/vdmjlzpj772c/q1VdflSTddNNNetvb3qb58+dr165dYzp3OYRpxBO/XIH06GyR2jdITauD24GjbwBKOtB09dVX65ZbblFvb//5V8uXL9fll1+ujo4OXXbZZVqxYoUaGxv14Q9/WN/+9re1b98+1dUNbjO97bbb9MlPflKXXnqptmzZ0nf805/+tNauXav77rtv0Nc8+OCD2rx5s375y1/qmmuu0SmnnKK9e/fqvPPO0w9+8IN+j12xYoXOOOMM3XPPPbrnnnv0jW98QyeffLL27dunW265Rfv379dtt92mXbt2ad++fTr++ON1yy236PDhw/rKV76iXbt26e677x6xVaVQhGnEE79cgXTIja4t2ig1X3M0LPB/HhisRANNb3jDG3T55Zdr7dq1/Y7fd999Wrx4sSTpU5/6lHbu3Dni9/rVr36lKVOm6C1veYsWLFigPXv26JlnnlFvb6+effZZzZ8/v+/75bvwwgs1YcIETZkyRRMnTtSHPvQhSdI73vEOHTx4cFR/n23btmn37t1617vepZkzZ2rbtm169NFH1dbWpgsuuEBTpkzRiSeeqE9+8pOj+r7DIUwjfvjlirRJ86TbQ3v6j67lRt8O7YmyKiCeSjjQtHLlSm3YsOGYPc5mNuL32bJli37zm99o2rRpqqur03PPPad//ud/lrsf8+tPOumkvo+PO+64vvvHHXecXnnllVH8TSR31xVXXKF9+/Zp3759OnDgQN+kykL+DqNFmEb88MsVlaSQoJzmSbfzVg4eXattCo6jMGm+GEuTEg80TZo0SX/2Z3+mDRs29B1rbGzUrbfeKkm65ZZbNG/ePEnShAkT9Pzzzw/6Hq+99ppuv/12dXR06ODBgzp48KDuuOMObdmyRaeeeqomTpzYN7p9yy23jKnegTWccMIJevnllyVJCxYs0NatW/Xkk09Kkp5++mk99thjmjNnju69914dOXJEL7/8sm6//fYx1ZBDmEb88MsVlaSQoMykW4xFmi/G0qQMA01f+MIX+q3qsXbtWt10002qr6/XP/3TP+m73/2uJOmSSy7Rt7/9bc2aNavfBMSWlhZNnTpVU6dO7TvW1NSkhx56SIcPH9ZNN92kq6++Wuedd55OPvnkMdW6bNkyXXzxxbrwwgv77tfX1+uyyy7T2Wefrb/927/VwoULVV9fr/e+9706fPiwTj/9dH31q1/Veeedp4suukizZxfn/4i5e1G+URQaGhq8vb096jIA4Nhy4aZhafDW7HBBeft1QS9k0+pg5AnFs3NNEC7zz3tnSxBEKuFCvdDXGGJl//79Ouuss6IuA0MY6t/GzHa7e8PAxzIyDQClVsikISbdllalj96yAhIQGcI0AJTaSEGZSbelV+mtNFyMAZEhTANAKRUSlJl0Wx6VOnrLxRgQKcJ0xNbvyKg1038Lz9ZMj9bvGLyjEIAEKiQoM+m2PCp19JaLsURL8ty1SjXafxPCdMTqqydq+ea9fYG6NdOj5Zv3qr56YsSVASgKgnI8VPLoLa+xxBo/fryOHDlCoI4Rd9eRI0c0fvz4gr+G1TxiIBegl8yp0aa2Lq1bPEuNdVVRlwUAlaPSV/NAIr388svq7u7WSy+9FHUpyDN+/HhVV1frhBNO6Hd8uNU8CNMxcf1dB7R2+yNa0TxdqxbOiLocAAAA5GFpvBhrzfRoU1uXVjRP16a2rkE91AAAAIgnwnTEci0e6xbP0qqFM7Ru8ax+PdQAAACIL8J0xDq6e/v1SDfWVWnd4lnq6O6NuDIAAACMhJ5pAAAAYAT0TAMAAABFRpgGAAAAQiJMAwAAACERpgEAAICQCNMAAABASIRpAAAAICTCNAAAABASYRoAkBw710idLf2PdbYExwEgAoRpAEByTJ0t3X7l0UDd2RLcnzo7yqoApNi4qAsAAKBgtU3Soo1BgG5YKrVvCO7XNkVcGIC0YmQaAJAstU1BkG75VnBLkAYQIcI0ACBZOluCEemm1cHtwB5qACgjwjQAIDlyPdKLNkrN1xxt+SBQh8OETmDMCNMAgOQ4tKd/j3Suh/rQniirSi4mdAJjZu4edQ2hNTQ0eHt7e9RlAACQXLkAzYRO4JjMbLe7Nww8zsg0AABpxoROYEwI0wAApBkTOoExIUwDAJBWTOgExowwDQBAWu1aK81b1X9C57xVwXEABSFMAwCQVu9ZIe28vv9qHjuvD44DKAjbiQMAkFZszw6MGSPTAACkGat5AGNCmAYAoNiStLMgq3kAYxJJmDazvzSzB83s12a2MntskpndbWYPZ29Pi6I2AADGLCk7C7KaBzBmZQ/TZnaOpM9IerekcyV90MzOlPQlSdvc/UxJ27L3AQBInvxe5O3XHQ2scWuhYHt2YMyimIB4lqT/dPc/SJKZ7ZD0MUkfkXRB9jE3S7pX0l9HUB8AAGOX34vctDp+QVqS5q0cfKy2KZ61AjEVRZvHg5KazGyymZ0i6b9JerOkN7n7YUnK3r4xgtoAACgOepGBVCj7yLS77zezb0q6W9ILku6X9EqhX29myyQtk6SampqS1AgAQEF2rgn6oPNHcjtbpAf/Wdr/L0dbKGrPj2+rB4AxiWQCortvcPfZ7t4k6WlJD0t6wsxOl6Ts7ZPDfO2N7t7g7g1TpkwpX9EAAAw03ERDF73IQEpEsmmLmb3R3Z80sxpJfyrpPEm1kq6Q9I3s7R1R1AagRIYbwTu0Z+i+TSAJRrPpCb3IQEWKap3pfzazhyT9i6Sr3f0ZBSH6vWb2sKT3Zu8DqBRJWSoMGC02PQFSLZKRaXc/f4hjRyQtiKAcAOXAtsWoVAMnGtaez+saSBF2QARQPozgodKw6QmKIUk7ZmIQwjQQtTT9EGWpMFQaNj1BMdAGl2iEaSBqafkhyggeKtG8lYPfYaltYlItRicpO2ZiSIRpIGpp+SHKCB4ADI82uMSKZAIigAGSsO3wWLFtMQAMj4msicXINBAH9BIDQHrRBpdohGkgavwQBYDKVOgEc9rgEo0wDUSNH6JAOqRp5R4ECp1gzkTWRCNMA1HjhyiQDmlZuQdHpWWCecoRplF5GP0BEEcEq3RilY6KR5hG5WH0B0BcEazShwnmFY8wjcrD6A+AuCJYpUvaJ5in5J1iwjQqE6M/AOIm7cEqjdI+wTwl7xSbu0ddQ2gNDQ3e3t4edRmIo9x/2IalwegPI9MolZ1rgl8M+a+vzpbglyWTSJGP1wrSqIJ+H5vZbndvGHickWlUHkZ/UE4pGXlBEbByD9IoBe8UE6ZRedL+thrKix59ABheCuYJjIu6AKDohhrlqW0i3KB08kdemlbzWgMAqf87xbVNUu35FTngwMg0AIxVCkZeMAopWcEAGFFK3ikmTAPAWNCjP7K0hUv66IFASuYJEKYBYCxSMvIyJmkLl/TRA6nC0ngAgNKroOWxCrb9uqN99M3XRF0NgDFiaTwAQHRSsDxWP/TRA6lBmAYAlF4lhcuResDpowdShTANACitSguXI/WA00cPpAo90wCA0qrEbbTT2AMOpNxwPdNs2gIAKK1K3EiJjXoAZNHmAQDAaFVSDziAMSFMAwAwGpXWAw5gTAjTAACMBhMMAeShZxoAgNGoxB5wAKExMg0AAACERJgGAAAAQiJMAwAAACERpgEAAICQCNMAAABASIRpAAAAICTCNAAAABASYRoAAAAIiTANAAAAhESYBgAAAEIiTAMAAAAhEaYBAACAkAjTAAAAQEiEaQAAACAkwjQAAAAQEmEaACrFzjVSZ0v/Y50twXEAQEkQpgGgUkydLd1+5dFA3dkS3J86O8qqAKCijYu6AABAkdQ2SYs2BgG6YanUviG4X9sUcWEAULkYmQaASlLbFATplm8FtwRpACipSMK0mX3ezH5tZg+a2RYzG29mtWbWZmYPm9ltZnZiFLUBQKJ1tgQj0k2rg9uBPdQAgKIqe5g2s6mSVkhqcPdzJB0v6RJJ35R0g7ufKekZSUvLXRsAJFquR3rRRqn5mqMtHwRqACiZqNo8xkk62czGSTpF0mFJzZK2Zj9/s6SPRlQbACTToT39e6RzPdSH9kRZFQBUtLJPQHT3Q2b2HUldkl6UdJek3ZKedfdXsg/rljS13LUBQKLNWzn4WG0TfdMAUEJRtHmcJukjkmolnSHpdZIuHuKhPszXLzOzdjNrf+qpp0pXKAAAADCCKNo8LpLU6e5PufvLkn4kqVHSqdm2D0mqlvT4UF/s7je6e4O7N0yZMqU8FQMAAABDiCJMd0maa2anmJlJWiDpIUn3SPpE9jFXSLojgtoAAACAgpU9TLt7m4KJhnskPZCt4UZJfy1plZk9ImmypA3lrg0AAAAYjUh2QHT3r0j6yoDDj0p6dwTloEKs35FRffVENdZV9R1rzfSoo7tXV82vi7AyAABQqdgBERWjvnqilm/eq9ZMj6QgSC/fvFf11RMjrgwAAFQqwjQqRmNdldYtnqXlm/fq+rsOaPnmvVq3eFa/kWoAKbFzzeDNajpbguMAUESEaVSUxroqLZlTo7XbH9GSOTUEaSCtps7uv/tjbnfIqbOjrApABSJMV4j1OzJ97Q05rZkerd+RiaiiaLRmerSprUsrmqdrU1vXoHMCVCxGYvvL7f54+5XS9uuObrPOBjYAiowwXSHoFz76d163eJZWLZzR1/JBoEYqMBI7WG2T1LBUavlWcEuQBlAC5j7kRoOJ0NDQ4O3t7VGXERu5MLlkTo02tXWlrl+Y1TyQerkA3bBUat/ASCznA0ARmdlud28YeDySpfFQGvn9wiuap6cqSEsaMjA31lWl7jwgxfJHYptWpzs45oJ0LkDXnk+rB4CSoM2jgtAvDKRcZ0swAtu0Orgd2EOdJof29A/OuR7qQ3uirApABWJkukLk9ws31lVpbt1kloYD0oSR2P7mrRx8rLYpnecC6bVzTTBvIv9139kSXFQO9X8EoTAyXSE6unv7Befcmssd3b0RVwagLBiJBTAQE5PLggmIAAAAlYqJuEUz3ARERqYBAAAqFUtElhxhGgAAhMeGQfHGxOSSI0wDAIDw6MuNr/yJyc3XHN0VlEBdVIRpAAAQHlu3xxcTk8uCMI2yW78jM2gN7NZMj9bvyERUEQBgTOjLjad5Kwf/W9Q2sSxekRGmUXb11RO1fPPevkCdWyO7vnpixJWlAL2NheE8AaNDXy5SjDCNssutgb18815df9cBNpcpJ3obC8N5AgpHXy5SjnWmEZnr7zqgtdsf0Yrm6Vq1cEbU5aQHa44WhvMEFIZd9pASrDONWGnN9GhTW5dWNE/XprauQT3UKCF6GwvDeUJSlbtNib5cpBxhOqGSPIkv1yO9bvEsrVo4o6/lg0BdJvQ2FobzhKSiTQkoK8J0QiV5El9Hd2+/HulcD3VHd2/ElaUAvY2F4TwhyViqDigreqYTLBegl8yp0aa2LibxYWT0NhaG84RKsP26oE2paXVwUQhgTIbrmSZMJxyT+AAAgzCBFig6JiBWICbxAQAGoU0JKCvCdEIxiQ8AMCS2kAbKijaPhFq/I6P66on9eqRbMz3q6O7VVfPrIqwMABBrzAkAQqHNo8JcNb9u0GTDxroqgjQA4NhYOg8oqnFRFwAAAMoof+k8JigCY8bINAAAacMOn0DREKYBAEgbdvgEioYwDQBAmrB0HlBUhGkAKJadawYHks6W4DgQFyydBxQVYTqF1u/IDFqPujXTo/U7MhFVBFQIVklAEsxbObhHuraJZfGAkAjTKVRfPbHfBi+5DWDqqydGXBmQcPmrJGy/7uhb6bngwsg1AFQcwnQKNdZV9e2YeP1dB/p2Uhy4bjWAEI61SgIj1wBQcQjTKdVYV6Ulc2q0dvsjWjKnhiANFMuxVkkYaeQaADBYzN/VI0ynVGumR5vaurSiebo2tXUN6qEGEEIhqySwvi8AjE7M39UjTKdQrkd63eJZWrVwRl/LB4EaGKNCVklgfV8AGJ2Yv6tn7h51DaE1NDR4e3t71GUkzvodGdVXT+zX2tGa6VFHd6+uml8XYWVAhcsfua5tGnwfADC87dcF7+o1rQ7e/SszM9vt7g2DjhOmAaBMdq4J3pbMD86dLcHINcuSAcDwcoMPDUuDd/UiGIQYLkyPK2sVAJBmQwXm2iZGpQHgWAa+i1d7fqze1aNnGgAAAPEV8107CdOIDXZmBAAAg8R8107CNGKDnRkBAEDS0DON2MjfmXHJnBptautiZ0YAABBrjEwjVtiZEQAAJAlhGrHCzowAUi/mWycD6I8wjdhgZ0YAUOy3TgbQX9nDtJnNMLN9eX+eM7OVZjbJzO42s4ezt6eVuzZEq6O7t1+PdK6HuqO7N+LKAKCMYr51MoD+It0B0cyOl3RI0hxJV0t62t2/YWZfknSau//1sb6eHRABVBR2SES+iLdOBtDfcDsgjjgybWZvM7NtZvZg9n69mf3PItW1QFLG3R+T9BFJN2eP3yzpo0V6DgBIBt7ej7dy9jJ3tgRbJjetDm4HPi/Kj152DKOQNo9/kPRlSS9Lkrt3SLqkSM9/iaQt2Y/f5O6Hs89xWNIbi/QcAJAMvL0fb+W62MnfOrn5mqOvCQJ1tLjYxTAKCdOnuPsvBxx7ZaxPbGYnSvqwpNtH+XXLzKzdzNqfeuqpsZYBoBCMyJRPbZPUsDR4e79hKUE6Tsp1sRPzrZNTi4tdDKOQMN1jZnWSXJLM7BOSDhfhuS+WtMfdn8jef8LMTs8+x+mSnhzqi9z9RndvcPeGKVOmFKEMACNiRKZ8eHs/3spxsRPzrZNTjYtdDKGQMH21pP8r6e1mdkjSSklXFeG5L9XRFg9JulPSFdmPr5B0RxGeA0AxMCJTHry9H39c7KQb//4YwjHDtJkdJ6nB3S+SNEXS2919XnbCYGhmdoqk90r6Ud7hb0h6r5k9nP3cN8byHACKjBGZ0uPt/XiL+mKHdqtoRf3vnzQper0eM0y7+2uSlmc//r27P1+MJ3X3P7j7ZHfvzTt2xN0XuPuZ2duni/FcAIqEEZnS4+39eIv6Yod2q2hF/e+fNGN5vSYsiI+4zrSZ/S9JL0q6TdLvc8fjEHZZZxook/wRmdqmwfcBlEfu/17D0uCilv+DiLOwr9eY/s4Zbp3pcQV87Z9nb6/OO+aS3lqMwgAkwLFGZPhFDpRPfrtV02r+/yHewr5e8+fpJODCccQw7e615SgEQIwN1WZQ2xTbH2xAxRrYblV7Pv8PEV9jeb0m6MKxkB0QTzCzFWa2NftnuZmdUI7iAABAFhPgkCRjfb0maJ5OIUvjfU/SOyX9n+yfd2aPAQCAcmECHJJkLK/XhF04FjIB8X53P3ekY1FgAiIAAECF2bkmWPUjv7WjsyUI4hGubjSWCYivmlmdu2ey3+itkl4tdoEAAABA0ubpFBKm/0rSPWb2qCST9BZJny5pVQAAAEACFLKaxzYzO1PSDAVh+jfu/seSVwYAAADEXCGreVwt6WR373D3+yWdYmb/o/SlAQAAAPFWyGoen3H3Z3N33P0ZSZ8pXUkAAABAMhQSpo8zM8vdMbPjJZ1YupIAAACAZCgkTP+HpB+a2QIza5a0RdLPSlsWEC/rd2TUmunpd6w106P1OzIRVQTEwM41g9d97WwJjgNAShQSpv9a0jZJn5N0dfbj1aUsCoib+uqJWr55b1+gbs30aPnmvaqvnhhxZUCEps7uv5FCbqOFqbOjrAoAymrETVv6PdhskqRqd+8oXUmFY9MWlFMuQC+ZU6NNbV1at3iWGuuqoi4LiFYuQDcsDbb8zd/xDAAqyHCbthSymse9ZvaGbJDeJ+kmM7u+FEUCcdZYV6Ulc2q0dvsjWjKnhiANSEFwblgqtXwruCVIA0iZQto8Jrr7c5L+VNJN7v5OSReVtiwgflozPdrU1qUVzdO1qa1rUA81kEqdLcGIdNPq4HZgDzWQBswfSLVCwvQ4Mztd0p9J+tcS1wPEUq7FY93iWVq1cIbWLZ7Vr4caSKVci8eijVLzNcFtfg81kBbMH0i1QsL01xWs6PGIu//KzN4q6eHSlgXES0d3b78e6ca6Kq1bPEsd3V5L4AcAAB+MSURBVL0RVwZE6NCe/j3StU3B/UN7oqwKKL/ca//2K6Xt1x29yIxT2xOj5yUzqgmIccMERAAAEBvbrwvmDzStDt6tiZP8d5Jqmwbfx4hCT0AEAADACOI+fyAJo+cJRZhGybDRCcaEtyQBJEVS5g+w+k5JEKZRMmx0gjFhQg+ApEjK/IG4j54n1DF7ps3s7ZKmSmpz9xfyjr/f3SPfUpye6fhjoxOMCRuCAEBx0DM9ZqPumTazFZLukPQXkh40s4/kffrvil8iKhEbnWBMeEsSAIojKaPnCTTuGJ/7jKR3uvsLZjZN0lYzm+bu35Vk5SgOyTdwo5O5dZMJ1CjcwLcka88nUANAGPNWDj5W28TP1CI4Vpg+Ptfa4e4HzewCBYH6LSJMowD5G5001lVpbt3kfveBYxr4FmTt+bwlCQCInWNNQPydmc3M3ckG6w9KqpL0jlIXhuRjoxOMCW9JAgASYNgJiGZWLekVd//dEJ97j7vvKnVxI2ECIgAAAMphuAmIw7Z5uHv3MT4XeZAGAAAAosY60wAAAEBIhGkAAAAgpILDtJm9wcwm5f6UsigA8cP28AAADDZimDazz5rZE5I6JO3O/mHWH5AybA8PAMBgx1pnOueLkv7E3XtGfCSAipVb2pDt4QEAOKqQNo+MpD+UuhAA8cf28AAA9FfIyPSXJbWaWZukP+YOuvuKklUFIJbYHh4AgP4KCdP/V9J2SQ9Ieq205QCIK7aHBwBgsELC9CvuvqrklQCItWNtD0+YBgCk1bDbifc9wOw6SY9J+hf1b/N4urSljYztxAEAAFAOo95OPM/i7O2X8465pLcWozAAAAAgqUYM0+5eW45CAAAAgKQpZGRaZnaOpLMljc8dc/cflKooAAAAIAlGDNNm9hVJFygI0z+VdLGknZII0wAAAEi1QjZt+YSkBZJ+5+6flnSupJNKWhUAIF52rpE6W/of62wJjgNAsSTwZ00hYfpFd39N0itm9gZJT4rJh0Bqrd+RUWump9+x1kyP1u/IRFQRymLqbOn2K4/+kutsCe5PnR1lVQAqTQJ/1hQSptvN7FRJ/yBpt6Q9kn5Z0qoAxFZ99UQt37y3L1DnNnOpr54YcWUoqdomadHG4Jfa9uuC20Ubg+MAUCwJ/Fkz4jrT/R5sNk3SG9y9o1QFjQbrTAfW78iovnpiv40zWjM96uju1VXz6yKsDJUqF6CXzKnRprYudkFMk+3XSS3fkppWS83XRF0NgEoVw581w60zPeLItJktzX3s7gcl/To7KRExwUghyq2xrkpL5tRo7fZHtGRODUE6LTpbpPYNwS+39g2D+xoBoBgS9rOmkDaPBWb2UzM7PbtE3n9KmjCWJzWzU81sq5n9xsz2m9l5ZjbJzO42s4ezt6eN5TnSJLet8/LNe3X9XQe0fPNeRgpRUq2ZHm1q69KK5una1NY1qIcaFSjXt7hoYzBKlHsbNua/5AAkTAJ/1owYpt19saSbJT2gYGm8le7+xTE+73cl/czd365gdZD9kr4kaZu7nylpW/Y+CsRIIcol987HusWztGrhjL4LOQJ1hTu0p3/fYq6v8dCeKKsCUGkS+LNmxJ5pMztTR8P0WZIekrTK3f8Q6gmDFUHul/RWz3tyMzsg6QJ3P2xmp0u6191nHOt70TN9FD2syCl1Dz09+gCANArdMy3pXyT9L3f/rKT5kh6W9Ksx1PJWSU9JusnM9prZP5rZ6yS9yd0PS1L29o1jeI5UYaQQ+UrdQ3/V/LpBF2qNdVUEaQBAKhUyMv0Gd39uwLEz3f3hUE9o1qCg7/o97t5mZt+V9Jykv3D3U/Me94y7D+qbNrNlkpZJUk1NzTsfe+yxMGVUFEYKMRDvVGTtXBOsTZq/pFJnS/B24byV0dUFAEicUY9Mm9lqSXL358xs0YBPf3oMtXRL6nb3tuz9rZJmS3oi296h7O2TQ32xu9/o7g3u3jBlypQxlFE5GCnEQPTQZyVw8X8AQLIcq83jkryPvzzgc+8P+4Tu/jtJvzWzXD/0AgV92HdKuiJ77ApJd4R9DiDtWG0jK4GL/wMAkmXcMT5nw3w81P3R+gtJt5jZiZIeVTDSfZykH2bXte6SNHA0HEAB8nvoG+uqNLducrqXS6xtkhqWHl38nyANACiiY4VpH+bjoe6PirvvkzSo50TBKDWAMejo7u0XnHPrkHd096YzTA9c/L/2fAI1AKBohp2AaGavSvq9glHokyXllsIzSePd/YSyVHgMLI0H4JjyF/+vbRp8HwCAAg03AXHYkWl3P760JQFAiR1r8X/CNACgCI7V5gEAyTbU8ne1TQRpAEDRFLJpCwAAAIAhEKYBAACAkAjTAAAAQEiEaQAAACAkwjQAAAAQEmEaAAAACIkwDQAAkmHnmmDzpXydLcFxICKEaQAAkAxTZwe7mOYCdW5X06mzo6wKKcemLQAAIBlyu5jefqXUsFRq39B/l1MgAoxMAwCA5KhtCoJ0y7eCW4I0IkaYBkJYvyOj1kxPv2OtmR6t35GJqCIASJiw/c+dLcGIdNPq4Hbg9wDKjDANhFBfPVHLN+/tC9StmR4t37xX9dUTI64MABIiTP9z7jGLNkrN1xxt+SBQI0Lm7lHXEFpDQ4O3t7dHXQZSKhegl8yp0aa2Lq1bPEuNdVVRlwUAyZELx4X2P+9cE4Tt/Md0tkiH9kjzVpa6WqScme1294aBx5mACITUWFelJXNqtHb7I1rRPJ0gDQCjld//3LR65P7noQJzbRN904gUbR5ASK2ZHm1q69KK5una1NY1qIcaADAC+p9RAQjTQAi5Fo91i2dp1cIZWrd4Vr8eagDACOh/RoUgTAMhdHT39uuRbqyr0rrFs9TR3RtxZQCQEIf29O+Rzq0hfWhPlFUBo8YERAAAAGAEw01AZGQaAAAACIkwDQAAAIREmAYAAABCIkwDAAAAIRGmAQAAgJAI0wAAAEBIhGkAAAAgJMI0AAAAEBJhGgAAAAiJMA0AAACERJgGAAAAQiJMAwAAACERpgEAAICQCNMAgPLbuUbqbOl/rLMlOA4ACUKYBgCU39TZ0u1XHg3UnS3B/amzo6wKAEZtXNQFAABSqLZJWrQxCNANS6X2DcH92qaICwOA0WFkGkCk1u/IqDXT0+9Ya6ZH63dkIqoIZVPbFATplm8FtwRpAAlEmAYQqfrqiVq+eW9foG7N9Gj55r2qr54YcWXllcqLis6WYES6aXVwO7CHGgASgDANJFglBLDGuiqtWzxLyzfv1fV3HdDyzXu1bvEsNdZVRV1aWaXuoiLXI71oo9R8zdGWDwI1gIQhTAMJVikBrLGuSkvm1Gjt9ke0ZE5N6oK0lMKLikN7+vdI53qoD+2JsioAGDUmIAIJlh/Alsyp0aa2rkQGsNZMjza1dWlF83RtauvS3LrJifs7FEP+RcWK5umVfQ7mrRx8rLaJvmkAicPINJBwSR/VzY2mr1s8S6sWzui7OBjYvpIGAy8q0ngOACBpCNNAwiU9gHV09/YbTc+Ntnd090ZcWXlxUQEAyWTuHnUNoTU0NHh7e3vUZQCRyQ9gjXVVg+4jOdbvyKi+emK/f7fWTI86unt11fy6CCsDAEiSme1294ZBxwnTQHIRwAAAKA/CNAAAABDScGGanmkAAAAgJMI0AESkEjbdAYC0iyRMm9lBM3vAzPaZWXv22CQzu9vMHs7enhZFbQBQLpWy6Q4ApFmUI9MXuvvMvN6TL0na5u5nStqWvQ8AFSt1ux4CQAWKU5vHRyTdnP34ZkkfjbAWoOLQUhBPSd90BwDSLqow7ZLuMrPdZrYse+xN7n5YkrK3b4yotmERRpBktBTEU9I33QGAtIsqTL/H3WdLuljS1WbWVOgXmtkyM2s3s/annnqqdBUOgTCCJKOlIH7Y9RAAki/ydabN7KuSXpD0GUkXuPthMztd0r3uPuNYXxvFOtO5X35L5tRoU1sXYQSJc/1dB7R2+yNa0TxdqxYe878YSoxNdwAgOWKzzrSZvc7MJuQ+lrRQ0oOS7pR0RfZhV0i6o9y1FYL+RiQZLQXxctX8ukE/QxrrqgjSAJAg4yJ4zjdJ+rGZ5Z5/s7v/zMx+JemHZrZUUpekRRHUNqKBYWRu3WQCNRIh967K+/7kTZpbN1lz6yb3tRhIYjQUAIAQyh6m3f1RSecOcfyIpAXlrmc08vsbG+uq+oURAjXirqO7ty8451636xbP0r/c/7j+49dP9H0OAAAULvKe6bEod880/Y2oFPT+AwAwOsP1TEfR5pFYQwXmxroqQggSJ7/3f0XzdF7DAMpj5xpp6mypNm8Rr84W6dAead7K6OoCxiBOm7YAKBMmIgKIxNTZ0u1XBgFaCm5vvzI4DiQUI9NAytD7DyAytU3Soo1BgG5YKrVvCO7XFrzdBBA7jEwDKZObiJgLzrnNXDq6eyOuDEAq1DYFQbrlW8EtQRoJx8g0kDL0/gOIVGdLMCLdtDq4rT2fQI1EY2QaAIA42LnmaC9xTmdLcLxS5HqkF22Umq852vIx8O8NJAhhGgCAOEjD5LxDe/r3SOd6qA/tibIqYExYZxoAgLjIBWgm5wGxM9w604xMV7j1OzKDlj1rzfRo/Y5MRBUBAIbF5DwgcQjTFa6+eqKWb97bF6hzy6LVV0+MuDLEGRdhQEQGTs6jlxiIPcJ0hcste7Z8815df9cB1hNGQbgIQ1hciI0Bk/OARCJMp0D+1tFL5tQQpDEiLsIQVmovxIqxEgeT84BEIkynAFtHIwwuwhBGai/EirESx7yVg3uka5uC4wBiizBd4fK3jl61cEbfLzkCNUbCRRjCSuWFWP422duvO9quwQRCoOIRpiscW0cjDC7CMBapvRBjJQ4glQjTFe6q+XWDRoUa66qG3FIa6TVw0lhHd68+d8Fb+y66uAhDoVJ9IcZKHEAqEaYBDJo0Vl89Ud+799F+k8a4CEMhUvtuGCtxIGnSsH19mbADIgBJR0cUl8yp0aa2rnRMGgOKZeeaYLJhfmtHZ0uwEgcTCBFH+ReAtU2D72OQ4XZAJEwD6HP9XQe0dvsjWtE8XasWzoi6HABIjiReULF9/aiwnTiAY0rtpDEAKIZiLI9YbkyaLQrCNIB0TxoDgGJI4vKITJotCsI0gPROGgPSjAloxZekkV4mzRYNYRoASygCaZTEtoS4S9JIL9vXFw0TEAEASCsmoBUPq2NUPCYgVqCBG21IQe/r+h2ZiCoCACRKktoS4o6R3tQiTCfYwI02cpPI8jfaAABgWElqS4i7eSsHX4zUNsV3WTwUDWF6lOI0GpybJLZ8815df9eBvtUY2GgDADAiJqABRUGYHqW4jQY31lVpyZward3+iJbMqSFIAwAKQ1sCUBRMQAwhTtsux6kWAADGJIm7CCI1mIBYRKUYDQ7TPsJGGwCAilKJy/WxnnfFI0yHUIptl8O0j7DRBgCgoiRxF8GRVOIFAvqhzWOU8keDG+uqBt0vxvemZQMAkGrbrwuW62taHUyOTDrW864ItHkUSSlHg5lMCCBJ4rS6ESpIJS7Xx3reFY0wPUql3Ha5FO0jAFAqcVvdCNEo6kVVpS7XV4kXCOhDmI4JJhMCyZe2kVrWuodU5IuqSlyur1IvENCHMB0TTCYEki+NI7W0p6GoF1WVuItgJV4goB8mIAJAEaVtInHa/r4Y3vV3HdDa7Y9oRfN0rVo4I+pygKJjAiIAlEGaRmppT0MOc36QZoRpACiiNIUK2tMgcVEF0OYBAEVSynXogbhavyOj+uqJ/V7jrZkedXT3FmWlKyAuhmvzIEwDQJEQKtKHf3MgPeiZBoASK+U69IinNK7gAqA/wjQAYFhpWzt7tFhrGwBhGgAwLEZeR5amFVwADDYu6gIAAPGVP/LKWtJDG7iCy9y6yZwfIEUYmQYAHBMjr8NjWbgA7UBIM8I0AOCY0rR29mix1naAdiCkGUvjAQCGxdrZKBRby6PSxW5pPDM73sz2mtm/Zu/XmlmbmT1sZreZ2YlR1QYACDDyikLRDoS0irLN4y8l7c+7/01JN7j7mZKekbQ0kqoAAH1YOxuFoh0IaRVJmDazakkfkPSP2fsmqVnS1uxDbpb00ShqAwAAo8NETKRZVCPTayStlvRa9v5kSc+6+yvZ+92SpkZRGAAAGB3agZBmZV9n2sw+KOlJd99tZhfkDg/x0CFnRprZMknLJKmmpqYkNQIAgMIN1fbTWFdF3zRSIYqR6fdI+rCZHZR0q4L2jjWSTjWzXLivlvT4UF/s7je6e4O7N0yZMqUc9QKIIda1BQDEQdnDtLt/2d2r3X2apEskbXf3yyTdI+kT2YddIemOctcGIDlY1xYAEAdx2k78ryXdamZ/K2mvpA0R1wMgxtjmGgAQB5HugOju97r7B7MfP+ru73b36e6+yN3/GGVtAOKPdW0BpBntbvHAduIAEot1bQGkGe1u8RCnNg8AKNjAba3n1k1mm2sAqUK7WzwwMg0gkVjXFgBK2+5GG0lhCNMAEoltrgGgtO1utJEUhjYPAACABCp1uxttJIVhZBoAACCBytHuxqpJI2NkGgAAIIHKsY37wDaSuXWTCdQDMDINAACAQfLbSFYtnNHX8sEypP0RpgEAADAIqyYVxtw96hpCa2ho8Pb29qjLAAAAQIUzs93u3jDwOCPTAAAAQEiEaQAAACAkwjQAAAAQEmEaAAAACIkwDQAAAIREmAYAAABCIkwDAAAAIRGmAcTW+h2ZQTtttWZ6tH5HJqKKAADojzANILbqqyf227o2t7VtffXEiCsDACAwLuoCAGA4ua1rl2/eqyVzarSpravf1rYAAESNkWkAsdZYV6Ulc2q0dvsjWjKnhiANAIgVwjSAWGvN9GhTW5dWNE/XprauQT3UAABEiTANILZyPdLrFs/SqoUz+lo+CNQAgLggTAOIrY7u3n490rke6o7u3ogrAwAgYO4edQ2hNTQ0eHt7e9RlAAAAoMKZ2W53bxh4nJFpAAAAICTCNAAAABASYRoAAAAIiTANAAAAhESYBgAAAEIiTAMAAAAhEaYBAACAkAjTAAAAQEiEaQAAACAkwjQAAAAQEmEaAAAACIkwDQAAAIREmAYAAABCIkwDAAAAIRGmAQAAgJAI0wAAAEBIhGkAAAAgJMI0AAAAEBJhGgAAAAiJMA0AAACERJgGAAAAQiJMAwAwRut3ZNSa6el3rDXTo/U7MhFVBKBcCNMAAIxRffVELd+8ty9Qt2Z6tHzzXtVXT4y4MgClNi7qAgAASLrGuiqtWzxLyzfv1ZI5NdrU1qV1i2epsa4q6tIAlFjZR6bNbLyZ/dLM7jezX5vZ17LHa82szcweNrPbzOzEctcGAEBYjXVVWjKnRmu3P6Ilc2oI0kBKRNHm8UdJze5+rqSZkt5vZnMlfVPSDe5+pqRnJC2NoDYAAEJpzfRoU1uXVjRP16a2rkE91AAqU9nDtAdeyN49IfvHJTVL2po9frOkj5a7NgAAwsj1SK9bPEurFs7oa/kgUAOVL5IJiGZ2vJntk/SkpLslZSQ96+6vZB/SLWlqFLUBADBaHd29/Xqkcz3UHd29EVcGoNQimYDo7q9Kmmlmp0r6saSzhnrYUF9rZsskLZOkmpqaktUIAEChrppfN+hYY10VfdNACkS6NJ67PyvpXklzJZ1qZrlwXy3p8WG+5kZ3b3D3hilTppSnUAAAAGAIUazmMSU7Ii0zO1nSRZL2S7pH0ieyD7tC0h3lrg0AAAAYjSjaPE6XdLOZHa8gzP/Q3f/VzB6SdKuZ/a2kvZI2RFAbAAAAULCyh2l375A0a4jjj0p6d7nrAQAAAMJiO3EAAAAgJMI0AAAAEBJhGgAAAAiJMA0AAACERJgGAAAAQiJMAwAAACERpgEAAICQCNMAAABASIRpAAAAICTCNAAAABASYRoAAAAIydw96hpCM7OnJD0WwVNXSeqJ4HnTgHNbOpzb0uL8lg7ntnQ4t6XDuS2tKM7vW9x9ysCDiQ7TUTGzdndviLqOSsS5LR3ObWlxfkuHc1s6nNvS4dyWVpzOL20eAAAAQEiEaQAAACAkwnQ4N0ZdQAXj3JYO57a0OL+lw7ktHc5t6XBuSys255eeaQAAACAkRqYBAACAkAjTx2Bm483sl2Z2v5n92sy+lj1ea2ZtZvawmd1mZidGXWtSmdnxZrbXzP41e59zWyRmdtDMHjCzfWbWnj02yczuzp7fu83stKjrTCIzO9XMtprZb8xsv5mdx7kdOzObkX295v48Z2YrObfFY2afz/4+e9DMtmR/z/FztwjM7C+z5/XXZrYye4zXbghm9n0ze9LMHsw7NuS5tMBaM3vEzDrMbHa56yVMH9sfJTW7+7mSZkp6v5nNlfRNSTe4+5mSnpG0NMIak+4vJe3Pu8+5La4L3X1m3vJBX5K0LXt+t2XvY/S+K+ln7v52SecqeA1zbsfI3Q9kX68zJb1T0h8k/Vic26Iws6mSVkhqcPdzJB0v6RLxc3fMzOwcSZ+R9G4FPxM+aGZnitduWBslvX/AseHO5cWSzsz+WSbpe2WqsQ9h+hg88EL27gnZPy6pWdLW7PGbJX00gvISz8yqJX1A0j9m75s4t6X2EQXnVeL8hmJmb5DUJGmDJLn7f7n7s+LcFtsCSRl3f0yc22IaJ+lkMxsn6RRJh8XP3WI4S9J/uvsf3P0VSTskfUy8dkNx9xZJTw84PNy5/IikH2Qz239KOtXMTi9PpQHC9AiybQj7JD0p6W5JGUnPZv+zSFK3pKlR1ZdwayStlvRa9v5kcW6LySXdZWa7zWxZ9tib3P2wJGVv3xhZdcn1VklPSbop26L0j2b2OnFui+0SSVuyH3Nui8DdD0n6jqQuBSG6V9Ju8XO3GB6U1GRmk83sFEn/TdKbxWu3mIY7l1Ml/TbvcWV/DROmR+Dur2bfcqxW8PbNWUM9rLxVJZ+ZfVDSk+6+O//wEA/l3Ib3HnefreAtsKvNrCnqgirEOEmzJX3P3WdJ+r1467aosj27H5Z0e9S1VJJsj+lHJNVKOkPS6xT8fBiIn7uj5O77FbTL3C3pZ5Lul/TKMb8IxRJ5diBMFyj7Nu69kuYqeAthXPZT1ZIej6quBHuPpA+b2UFJtyp4m3GNOLdF4+6PZ2+fVNB3+m5JT+Te/srePhldhYnVLanb3duy97cqCNec2+K5WNIed38ie59zWxwXSep096fc/WVJP5LUKH7uFoW7b3D32e7epKBF4WHx2i2m4c5lt4J3AXLK/homTB+DmU0xs1OzH5+s4AfRfkn3SPpE9mFXSLojmgqTy92/7O7V7j5Nwdu52939MnFui8LMXmdmE3IfS1qo4G3IOxWcV4nzG4q7/07Sb81sRvbQAkkPiXNbTJfqaIuHxLktli5Jc83slOwcldxrl5+7RWBmb8ze1kj6UwWvYV67xTPcubxT0uXZVT3mSurNtYOUC5u2HIOZ1Stocj9ewYXHD93962b2VgWjqZMk7ZW0xN3/GF2lyWZmF0j6ort/kHNbHNnz+OPs3XGSNrv7dWY2WdIPJdUo+MW6yN0HTvLACMxspoKJsydKelTSp5X9GSHO7Zhk+01/K+mt7t6bPcbrtkgsWOL1kwpaEPZK+u8K+kv5uTtGZvYLBXN/Xpa0yt238doNx8y2SLpAUpWkJyR9RdJPNMS5zF4YrlOw+scfJH3a3dvLWi9hGgAAAAiHNg8AAAAgJMI0AAAAEBJhGgAAAAiJMA0AAACERJgGAAAAQiJMA0AZmdmrZrYv70/Zdk80s++b2ZNm9mC5nhMAKh1L4wFAGZnZC+7++oieu0nSC5J+4O7nlOk5j3f3V8vxXAAQBUamASBiZjbRzA7kdlU0sy1m9pnsx98zs3Yz+3V2w43c1xw0s78zs/uyn59tZv9hZhkzu2qo53H3FgXbHB+rlkVm9qCZ3W9mLdljx5vZd8zsATPrMLO/yB5fYGZ7s8e/b2Yn5dV2rZntlLTIzOrM7GdmttvMfmFmby/GeQOAOBgXdQEAkDInm9m+vPv/291vM7Plkjaa2Xclnebu/5D9/DXZXb6Ol7TNzOrdvSP7ud+6+3lmdoOkjZLeI2m8pF9LWh+yvmslvc/dD5nZqdljyyTVSprl7q+Y2SQzG599zgXu/v/M7AeSPidpTfZrXnL3eZJkZtskXeXuD5vZHEn/R1JzyPoAIFYI0wBQXi+6+8yBB939bjNbJOnvJZ2b96k/M7NlCn5eny7pbEm5MH1n9vYBSa939+clPW9mL5nZqe7+bIj6dikI9T+U9KPssYskrXf3V7K1Pm1m50rqdPf/l33MzZKu1tEwfZskmdnrJTVKuj3Y9VeSdFKIugAglgjTABADZnacpLMkvShpkqRuM6uV9EVJ73L3Z8xso4KR55w/Zm9fy/s4dz/Uz3d3vyo7evwBSfvMbKYkkzRwgo0N+uL+fp+9PU7Ss0NdQABAJaBnGgDi4fOS9ku6VNL3zewESW9QEEp7zexNki4udRFmVufube5+raQeSW+WdJekq8xsXPYxkyT9RtI0M5ue/dJPSdox8Pu5+3OSOrOj7rLAuQMfBwBJRZgGgPI6ecDSeN8ws7dJ+u+SvuDuv5DUIul/uvv9kvYq6IH+voIWjNDMbIuk+yTNMLNuM1s6xMO+nZ1Q+GC2jvsl/aOkLkkdZna/pMXu/pKkTyto33hAwWj4cH3al0lamv3aX0v6yFj+HgAQJyyNBwAAAITEyDQAAAAQEmEaAAAACIkwDQAAAIREmAYAAABCIkwDAAAAIRGmAQAAgJAI0wAAAEBIhGkAAAAgpP8PWR5D2EckoW0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.pyplot import figure\n",
    "\n",
    "groups= data.groupby(\"Admission Status\")\n",
    "fig, ax = plt.subplots(figsize=(12,8))\n",
    "for name, group in groups:\n",
    "    ax.plot(group[\"Exam 1 score\"], group[\"Exam 2 score\"], marker=\"x\", linestyle=\"\")\n",
    "ax.set_xlabel('Exam 1 score')\n",
    "ax.set_ylabel('Exam 2 score')\n",
    "categories = data[\"Admission Status\"].apply(lambda z: 'Admitted' if z == 0 else 'Not Admitted')\n",
    "ax.legend(categories.unique())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.2 Implementation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.2.1 Warmup exercise: sigmoid function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sigmoid(z):\n",
    "    return 1 / (1 + np.exp(-z))   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Provide input values to the sigmoid function below and run to check your implementation\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sigmoid(0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.2.2 Cost function and gradient"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = data.loc[:,['Exam 1 score','Exam 2 score']] #Access to features\n",
    "X.insert(0,\"1\",1) #Add intercept therm to X\n",
    "y = data.loc[:,[\"Admission Status\"]]#Access to target variable\n",
    "X = np.matrix(X)#From data frame to numpy matrix\n",
    "y = np.matrix(y)#From data frame to numpy matrix\n",
    "theta = np.zeros(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def cost(theta, X, y):#si sirve\n",
    "    m = np.size(y,0)\n",
    "    theta = np.matrix(theta)\n",
    "    sig = sigmoid(X * theta.T)\n",
    "    j = 1/m * np.sum(np.multiply(-y,np.log(sig))-np.multiply((1-y),np.log(1-sig)))\n",
    "    return j"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost at initial theta (zeros): \n",
      " 0.6931471805599453\n"
     ]
    }
   ],
   "source": [
    "cost1 = cost(theta, X, y)\n",
    "print('Cost at initial theta (zeros): \\n', cost1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradient(theta,X,y):\n",
    "    theta = np.matrix(theta)\n",
    "    m = np.size(y,0)\n",
    "    sig = sigmoid(X * theta.T)\n",
    "    grad = np.multiply(1/m,X.transpose()*(sig-y)) \n",
    "    return grad"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Gradient at initial theta (zeros):\n",
      " [[ -0.1       ]\n",
      " [-12.00921659]\n",
      " [-11.26284221]]\n"
     ]
    }
   ],
   "source": [
    "gradient1 = gradient(theta, X, y)\n",
    "print(\"Gradient at initial theta (zeros):\\n\",gradient1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that instead of having one cost function as in the Matlab code, here we need separete functions for gradient and cost to use the Scipy's \"optimize\" that does the same thing as Matlab \"fminunc\".\n",
    "Scipy's \"optimize\" seeks better values for theta."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([-25.16131869,   0.20623159,   0.20147149]), 36, 0)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import scipy.optimize as opt\n",
    "new_theta = opt.fmin_tnc(func=cost, x0=theta, fprime=gradient, args=(X, y))\n",
    "new_theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost at theta found by fminunc:\n",
      " 0.2034977015894743\n"
     ]
    }
   ],
   "source": [
    "cost_new_theta = cost(new_theta[0], X, y)\n",
    "print('Cost at theta found by fminunc:\\n',cost_new_theta)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " #### 1.2.3 Evaluating logistic regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The predict function will produce '1' or '0' predictions given a dataset and a learned parameter vector. This function also helps compute accuracy on our training data set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {},
   "outputs": [],
   "source": [
    "def predict(theta,X):\n",
    "    p = np.zeros(np.size(X,0))\n",
    "    for i in range(len(X)):\n",
    "        if sigmoid(X[i]*theta.T)>= 0.5:\n",
    "            p[i]=1\n",
    "        else:\n",
    "            p[i]=0\n",
    "    return(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Predict probability for a student with score 45 on exam 1  and score 85 on exam 2 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For a student with scores 45 and 85, we predict an admission probability of 0.7762906242704579\n"
     ]
    }
   ],
   "source": [
    "nt = np.matrix(new_theta[0])\n",
    "prob = sigmoid([1,45,85] * nt.T)\n",
    "print(\"For a student with scores 45 and 85, we predict an admission probability of\",prob[0,0] )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compute the accuracy of our data set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train Accuracy:89%\n"
     ]
    }
   ],
   "source": [
    "import statistics\n",
    "nt = np.matrix(new_theta[0])\n",
    "p = predict(nt,X)\n",
    "accu=[]\n",
    "\n",
    "for i in range(len(p)):\n",
    "    if y[i,0] == p[i]:\n",
    "        accu.append(1)\n",
    "    else:\n",
    "        accu.append(0)\n",
    "\n",
    "x = int(statistics.mean(accu)*100)\n",
    "print('Train Accuracy:{0}%'.format(x))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our logistic regression classifer correctly predicted if a student was admitted or not 89% of the time.  :)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Regularized logistic regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this part of the exercise, it was implement regularized logistic regression to predict whether microchips from a fabrication plant passes quality assurance (QA). During QA, each microchip goes through various tests to ensure it is functioning correctly. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2.1 Visualizing the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Microship Test 1</th>\n",
       "      <th>Microship Test 2</th>\n",
       "      <th>Results</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>0.051267</td>\n",
       "      <td>0.69956</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>-0.092742</td>\n",
       "      <td>0.68494</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>-0.213710</td>\n",
       "      <td>0.69225</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>-0.375000</td>\n",
       "      <td>0.50219</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>-0.513250</td>\n",
       "      <td>0.46564</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Microship Test 1  Microship Test 2  Results\n",
       "0          0.051267           0.69956        1\n",
       "1         -0.092742           0.68494        1\n",
       "2         -0.213710           0.69225        1\n",
       "3         -0.375000           0.50219        1\n",
       "4         -0.513250           0.46564        1"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data2 = data=pd.read_csv(\"/Users/natalychacon/Documents/Machine Learning/std coursera/machine-learning-ex/ex2/ex2data2.txt\",header=None)\n",
    "data2.columns = ['Microship Test 1', 'Microship Test 2',\"Results\"] \n",
    "data2.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1148d2a50>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.pyplot import figure\n",
    "\n",
    "groups= data2.groupby(\"Results\")\n",
    "fig, ax = plt.subplots(figsize=(12,8))\n",
    "for name, group in groups:\n",
    "    ax.plot(group[\"Microship Test 1\"], group[\"Microship Test 2\"], marker=\"x\", linestyle=\"\",label= name)\n",
    "ax.set_xlabel(\"Microship Test 1\")\n",
    "ax.set_ylabel(\"Microship Test 2\")\n",
    "ax.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As is not a linear decision boundary one way to fit the data better is to create more features from each data point, that are derived from polynomials of the original features."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Results</th>\n",
       "      <th>Ones</th>\n",
       "      <th>F10</th>\n",
       "      <th>F20</th>\n",
       "      <th>F21</th>\n",
       "      <th>F30</th>\n",
       "      <th>F31</th>\n",
       "      <th>F32</th>\n",
       "      <th>F40</th>\n",
       "      <th>F41</th>\n",
       "      <th>F42</th>\n",
       "      <th>F43</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.051267</td>\n",
       "      <td>0.002628</td>\n",
       "      <td>0.035864</td>\n",
       "      <td>0.000135</td>\n",
       "      <td>0.001839</td>\n",
       "      <td>0.025089</td>\n",
       "      <td>0.000007</td>\n",
       "      <td>0.000094</td>\n",
       "      <td>0.001286</td>\n",
       "      <td>0.017551</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-0.092742</td>\n",
       "      <td>0.008601</td>\n",
       "      <td>-0.063523</td>\n",
       "      <td>-0.000798</td>\n",
       "      <td>0.005891</td>\n",
       "      <td>-0.043509</td>\n",
       "      <td>0.000074</td>\n",
       "      <td>-0.000546</td>\n",
       "      <td>0.004035</td>\n",
       "      <td>-0.029801</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-0.213710</td>\n",
       "      <td>0.045672</td>\n",
       "      <td>-0.147941</td>\n",
       "      <td>-0.009761</td>\n",
       "      <td>0.031616</td>\n",
       "      <td>-0.102412</td>\n",
       "      <td>0.002086</td>\n",
       "      <td>-0.006757</td>\n",
       "      <td>0.021886</td>\n",
       "      <td>-0.070895</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-0.375000</td>\n",
       "      <td>0.140625</td>\n",
       "      <td>-0.188321</td>\n",
       "      <td>-0.052734</td>\n",
       "      <td>0.070620</td>\n",
       "      <td>-0.094573</td>\n",
       "      <td>0.019775</td>\n",
       "      <td>-0.026483</td>\n",
       "      <td>0.035465</td>\n",
       "      <td>-0.047494</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-0.513250</td>\n",
       "      <td>0.263426</td>\n",
       "      <td>-0.238990</td>\n",
       "      <td>-0.135203</td>\n",
       "      <td>0.122661</td>\n",
       "      <td>-0.111283</td>\n",
       "      <td>0.069393</td>\n",
       "      <td>-0.062956</td>\n",
       "      <td>0.057116</td>\n",
       "      <td>-0.051818</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Results  Ones       F10       F20       F21       F30       F31       F32  \\\n",
       "0        1     1  0.051267  0.002628  0.035864  0.000135  0.001839  0.025089   \n",
       "1        1     1 -0.092742  0.008601 -0.063523 -0.000798  0.005891 -0.043509   \n",
       "2        1     1 -0.213710  0.045672 -0.147941 -0.009761  0.031616 -0.102412   \n",
       "3        1     1 -0.375000  0.140625 -0.188321 -0.052734  0.070620 -0.094573   \n",
       "4        1     1 -0.513250  0.263426 -0.238990 -0.135203  0.122661 -0.111283   \n",
       "\n",
       "        F40       F41       F42       F43  \n",
       "0  0.000007  0.000094  0.001286  0.017551  \n",
       "1  0.000074 -0.000546  0.004035 -0.029801  \n",
       "2  0.002086 -0.006757  0.021886 -0.070895  \n",
       "3  0.019775 -0.026483  0.035465 -0.047494  \n",
       "4  0.069393 -0.062956  0.057116 -0.051818  "
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "degree = 5\n",
    "x1 = data2[\"Microship Test 1\"]\n",
    "x2 = data2[\"Microship Test 2\"]\n",
    "\n",
    "data2.insert(3, 'Ones', 1)\n",
    "for i in range(1, degree):\n",
    "    for j in range(0, i):\n",
    "        data2['F' + str(i) + str(j)] = np.power(x1, i-j) * np.power(x2, j)\n",
    "\n",
    "data2.drop(\"Microship Test 1\", axis=1, inplace=True)\n",
    "data2.drop(\"Microship Test 2\", axis=1, inplace=True)\n",
    "\n",
    "data2.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2.3 Cost function and gradient"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we need to modify the cost and gradient functions from part 1 to include the regularization term. Note that you should not regularize the theta(0) parameter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "X2 = data2.iloc[:,1:np.size(data2,1)]#Access to features\n",
    "y2 = data.loc[:,[\"Results\"]]#Access to target variable\n",
    "X2 = np.matrix(X2)#From data frame to numpy matrix\n",
    "y2 = np.matrix(y2)#From data frame to numpy matrix\n",
    "initial_theta = np.zeros(np.size(X2,1))\n",
    "learning_rate = 1 #lambda"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [],
   "source": [
    "def costFunctionReg(theta, X, y, learning_rate):\n",
    "    m = np.size(y,0)\n",
    "    theta = np.matrix(theta)\n",
    "    sig = sigmoid(X * theta.T)\n",
    "    j = 1/m * np.sum(np.multiply(-y,np.log(sig))-np.multiply((1-y),np.log(1-sig))) + (((learning_rate)/(2*m))*np.sum(np.power(initial_theta[i:np.size(initial_theta)],2)))\n",
    "    return j"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost at initial theta (zeros):\n",
      " 0.6931471805599454\n"
     ]
    }
   ],
   "source": [
    "cost2=costFunctionReg(initial_theta, X2, y2, learning_rate)\n",
    "print('Cost at initial theta (zeros):\\n', cost2);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradientReg(theta,X,y,learning_rate):\n",
    "    theta = np.matrix(theta)\n",
    "    m = np.size(y,0)\n",
    "    sig = sigmoid(X * theta.T)\n",
    "    grad1 = 1/m * (X.T*(sig-y)) \n",
    "    grad2 = learning_rate/m * np.power(theta,2)\n",
    "    grad2[0,0]=0\n",
    "    return grad1.T+grad2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[0.00847458, 0.01878809, 0.05034464, 0.01150133, 0.01835599,\n",
       "         0.00732393, 0.00819244, 0.03934862, 0.00223924, 0.01286005,\n",
       "         0.00309594]])"
      ]
     },
     "execution_count": 132,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gradientReg(initial_theta,X2,y2,learning_rate)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 0.95693149,  0.77829086, -3.44260859, -2.05735766,  1.00410602,\n",
       "        -0.34518113, -1.73376852, -2.51273792,  0.11744237, -2.94756349,\n",
       "        -0.17632232]), 107, 4)"
      ]
     },
     "execution_count": 138,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import scipy.optimize as opt\n",
    "result = opt.fmin_tnc(func=costFunctionReg, x0=initial_theta, fprime=gradientReg, args=(X2, y2, learning_rate))\n",
    "result"
   ]
  },
  {
   "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": []
  },
  {
   "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": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}