regularized logistic regression.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import scipy.optimize as opt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "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>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.051267</td>\n",
       "      <td>0.69956</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.092742</td>\n",
       "      <td>0.68494</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-0.213710</td>\n",
       "      <td>0.69225</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-0.375000</td>\n",
       "      <td>0.50219</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-0.513250</td>\n",
       "      <td>0.46564</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          0        1  2\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": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_csv('E:\\Mat_Work\\machine-learning-ex2\\ex2\\ex2data2.txt', header = None)\n",
    "X = data.iloc[:,:-1]\n",
    "y = data.iloc[:,2]\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZQAAAEKCAYAAAA1qaOTAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4zLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvnQurowAAIABJREFUeJzt3XuUXGWZ7/Hvj5CrFxIgIEmICWeYKIaeBJuIgggBTBwUMoAQlCMoriyvKB7RsHSQgeOhRY854uBghoky6oCIAq0IIRACiwBKkBACDCSEWyco10SBALk854+9i1Qqu+77WvV81qpVXbt21X57d1c9+709r8wM55xzrl07ZV0A55xzncEDinPOuVh4QHHOORcLDyjOOedi4QHFOedcLDygOOeci4UHFOecc7HwgOKccy4WHlCcc87FYuesC5Cm3Xff3SZMmJB1MZxzrlDuueee58xsdL39uiqgTJgwgWXLlmVdDOecKxRJTzSynzd5Oeeci4UHFOecc7HwgOKccy4WXdWH4pxzAJs2bWJgYIBXX30166LkyrBhwxg3bhyDBw9u6fUeUJxzXWdgYIC3vOUtTJgwAUlZFycXzIznn3+egYEBJk6c2NJ7eJOXc67rvPrqq+y2224eTMpIYrfddmur1uYBxTnXlTyY7Kjdc+IBxTnnXCw8oLjutuJKmDcZzh0Z3K+4MusSuS4waNAgpkyZwuTJk/noRz/KK6+8kurxDzvssEQmeXtAcd1rxZXw2zNgw1OABfe/PcODikvc8OHDWb58OStXrmTIkCFccsklWRcpFh5QXPe6+TzYtHH7bZs2Bts7kdfGWnbNvWs5uG8xE+dex8F9i7nm3rWxvff73/9+Vq9eDcCsWbN497vfzbve9S7mz58PwJYtWzjttNOYPHky+++/P/PmzQPgoosuYr/99qOnp4fZs2cD8PLLL/OpT32KAw88kKlTp3LttdcCsHHjRmbPnk1PTw8nnXQSGzdujChJ+3zYsOteGwaa215kpdpYKYCWamMAPSdmV64CuObetZz9m/vZuGkLAGvXb+Ts39wPwKypY9t6782bN3P99dczc+ZMABYsWMCuu+7Kxo0bOfDAAzn++ON5/PHHWbt2LStXrgRg/fr1APT19fHYY48xdOjQN7Z9+9vfZvr06SxYsID169czbdo0jjzySH784x8zYsQIVqxYwYoVKzjggAPaKnc1XkNx3WuXcc1tL7Juq43F6LsLH34jmJRs3LSF7y58uOX33LhxI1OmTKG3t5fx48dz+umnA0Gt4x/+4R846KCDeOqpp1i1ahX77LMPa9as4Ytf/CI33HADb33rWwHo6enh4x//OD//+c/ZeeegbnDjjTfS19fHlClTOOyww3j11Vd58sknue222zjllFPeeF1PT0/LZa/Fayiuex1xzvZX7QCDhwfbO0031cZitm59dPNQte2NKPWhlFuyZAk33XQTd955JyNGjHgjIIwaNYr77ruPhQsXcvHFF3PllVeyYMECrrvuOm677Tb6+/s5//zzeeCBBzAzfv3rXzNp0qQdjpnGMGmvobju1XMifOQi2GVvQMH9Ry7qzCagbqqNxWzMyOFNbW/Vhg0bGDVqFCNGjOC///u/ueuuuwB47rnn2Lp1K8cffzznn38+f/rTn9i6dStPPfUUhx9+OBdeeCHr16/npZdeYsaMGfzwhz/EzAC49957ATj00EP5xS9+AcDKlStZsWJFrGUv8RqK6249J3ZmAKnUTbWxmJ01Y9J2fSgAwwcP4qwZO9YC2jFz5kwuueQSenp6mDRpEgcddBAAa9eu5ZOf/CRbt24F4IILLmDLli2ccsopbNiwATPjzDPPZOTIkfzzP/8zX/7yl+np6cHMmDBhAr/73e/47Gc/yyc/+Ul6enqYMmUK06ZNi7XsJSpFsm7Q29trvsCW61orrgz6TDYMBDWTI87pjmAa4aGHHuKd73xnw/tfc+9avrvwYdat38iYkcM5a8aktjvk8yrq3Ei6x8x6673WayjOdYtuqY0lYNbUsR0bQOKUaR+KpAWSnpG0ssrzknSRpNWSVkg6oOy5UyWtCm+npldq55xzUbLulP8pMLPG8x8C9g1vc4B/A5C0K/At4D3ANOBbkkYlWtJO5hPeGufnyrmqMg0oZnYb8EKNXY4F/tMCdwEjJe0FzAAWmdkLZvYisIjagclV043pR1oNCt14rpxrQtY1lHrGAk+VPR4It1Xb7prVbRPe2gkK3XaunGtS3gNK1Ewcq7F9xzeQ5khaJmnZs88+G2vhOkK3TXhrJyh027lyrkl5DygDwN5lj8cB62ps34GZzTezXjPrHT16dGIFLawcTXhLMgHfG9oJCjk6V67YSunrS7fHH3+86r7r1q3jhBNOAILZ9B/+8IebOlZSqeqj5D2g9AOfCEd7HQRsMLOngYXAByWNCjvjPxhuc8064pxgglu5DCa8lRLwrV2/EWNbAr7Yg0o7QSEn58oVXyn1Suk2YcKEqvuOGTOGq666Kr3CtSHrYcOXA3cCkyQNSDpd0mckfSbc5ffAGmA18O/A5wDM7AXgfODu8HZeuM01KyfpR5JIwBepnaCQk3PlMpDC6L7HH3+c97///RxwwAEccMAB3HHHHW9snzx58g77Z52qPkqmExvN7OQ6zxvw+SrPLQAWJFGurpODCW9JJOCLVPo9W50xntW58lnu2Ukg9X8p2zDAxIkTufrqq9ljjz1YtGgRw4YNY9WqVZx88sk1m6qyTlUfxWfKu/bF8GU3ZuRw1kYEj7gT8AHpBIU4A4CvZZKtWgM5Wjz/UdmGN23axBe+8AWWL1/OoEGDeOSRR2q+x4033kh/fz/f+973ALZLVX/GGcH/R5Kp6qN4QHHtienLLq0EfKmIOwAk8IXmmpDS6L558+ax5557ct9997F161aGDRtWc/+sU9VHyXunvEtCnO3BMc3NmDV1LBcctz9jRw5HwNiRw7nguP2LmT8p7vkqPlw5WymN7tuwYQN77bUXO+20Ez/72c/YsmVLzf2zTlUfxWso3Sbuq+cYv+w6JgFf3AFgl3HhRMyI7S6QZB9TSqn/P/e5z3H88cfzq1/9isMPP5w3velNNffPOlV9FE9f323mTa7y5bQ3nBmZozPd9+sEcZ+TyosACL7QfIRZoIXz02z6+m4aFNFO+npv8uo2cV89+9yMHcV9Tny4cm1ppMTpOTG4GDh3fXDv5z6SN3l1m7ibT9odhtuJkjgnORjanVvex5QbHlC6TRLtwf5ltyM/J+lp8SLJzDIbDZVX7XaBeJNXt/HmE9dpWmhiHDZsGM8//3zbX6CdxMx4/vnn6w5XrsVrKN3Ir55dJ2mhiXHcuHEMDAzgGci3N2zYMMaNa330oAcU51zj8jraqcmLpMGDBzNx4sQEC9SdPKA4F+Gae9fy3YUPs279RsaMHM5ZMyZ1xhyZdngKGFeHBxTXUeIIBKVU+qU0MKVU+kB3BxVPAePq8E551zHiWlMltVT6RePDc10dHlBcZuJeoTGuQJB4Kv2419ZIYa0OwFesdHV5QHGZSGKFxrgCQbWU+bGk0i/1Q2x4CrBt/RCtBoG4368Wz4rg6vCA4jKRRLNSXIHgrBmTGD540HbbYkulH3eakDTSjpT4HCZXR6ad8pJmAj8ABgGXmllfxfPzgMPDhyOAPcxsZPjcFuD+8LknzeyYdErt4pBEs1Jca6qUOt4TGeUVdz9E2v0accxhyuvQY9e2zAKKpEHAxcBRwABwt6R+M3uwtI+ZnVm2/xeBqWVvsdHMpqRVXhevJFZojDMQJJZKP+5cakVLbe9Djztalk1e04DVZrbGzF4HrgCOrbH/ycDlqZTMJS6pZqVZU8eydO50Hus7mqVzp+dvmG/c/RBF69dIs4nOpS7LgDIWKL+0Ggi37UDS24GJwOKyzcMkLZN0l6RZyRXTJaGjVmhsRtz9EEXr14iriS6tkW2uKVn2oUSl+ayWqW02cJWZlffijjezdZL2ARZLut/MHt3hINIcYA7A+PHj2y2zi1HHrNDYrLhzqRUpN1scTXTebJZbWdZQBoC9yx6PA9ZV2Xc2Fc1dZrYuvF8DLGH7/pXy/eabWa+Z9Y4ePbrdMhdLUldxfnXoWhVHE503m+VWljWUu4F9JU0E1hIEjY9V7iRpEjAKuLNs2yjgFTN7TdLuwMHAhamUuiiSuorL8OqwVlqVPOXeylNZ6km9rHEsPuYz9nMrs4BiZpslfQFYSDBseIGZPSDpPGCZmfWHu54MXGHbL1zwTuDHkrYS1LL6ykeHFUaSwyeTyruUUT6nWvm1gJZybyXxZVqkPGCZlbXdJrqijWzrIpnOQzGz3wO/r9h2TsXjcyNedwewf6KFS1rSV/pJXcVldHVYbyJkteeqfTEm9WVaq5x5CyhFKut2klh11MXCZ8pnJel24KTyLmWUz6nWRMhWJkkmlQAy8TxgMYq7rHHnZqsqLyPbvC9xBx5QspL0lX5S8xMymvdQK61KKylXkvriTzQPWMziLGsSudlq6jkRzlwJ564P7rMIJmnlUCsQDyhZSfpKP6mruIyuDmtNhDxrxiQG77T9KPTBO6nmJMmkvvgTzQMWszjL2nUp/32kWSRfYCsrabQDN9H52VQHdQbzHmqlVbnm3rU7zmqKmuVUJq68X82UM2/iLGtum/qSGvjiI80ieUDJShzDJ2NSlJFJ1SZCfnfhw2zasv2c2E1brGbncpJf/EWasBlXWZPIzda2JAe++EizSB5QspSTGc6FHe0TavXquEhf/LFJ6Io9qRpfW5Ic4u4jzSJ5QHH5ba5oUC6vjvMowSv2XDb1JdkslaMWhjzxgFJQcU7KK/oXci6vjvMo4UmpqdX4Gq1lJd0slZMWhjzxUV4FFPcQzSKNTIrStZmLm9UJHcnNDNctWmr/DqDtM5p0tt7eXlu2bFnWxWjbwX2LI2sUY0cOZ+nc6S29Z5HyT3WqxP8G8yZHXrH/mdG899UfFOPvXuV3YJe9g/kolXx1yFhIusfMeuvt501eBZREn0dXdlDnSCoj7SI6kjfaEP7Ppo9uV9ON9Zhxa7aW5c1SqfImrwIq0mxs15hUJgZWTEr9M6P5+qZP07/1kOSOGbeMUv+4xngNpYC8E7ox9ZqQ8tTMl9pIu7Ir9vfOvS5yRbtcj+7z4bq55jWUNMWUTM47oeurN3Ah9dxTdVSrXe4kJZZssZA13bwkhnSRvFM+LZVzACC4svIPQyLqDVxIYmBDOyr7UKIMHzwo1guHqGPGfQzXGRrtlPcaSlo8mVyq6jUh5W0yZ2Wtc5B2TEZWrX+j1bTxXtN1cfM+lLR0whyAAqk3WTOPkznLR9pNnHtd5D6VAa/d0WE+us/FqWoNRdJYST+XdIukr0nauey5X8dxcEkzJT0sabWkuRHPnybpWUnLw9uny547VdKq8HZqHOVJVIePTkltcaUG1ZusmffJnI32b3Rd2vi0+OJZLanV5LUAuAs4C5gI3CJpVPjcPu0eWNIg4GLgQ8B+wMmS9ovY9ZdmNiW8XRq+dlfgW8B7gGnAt8rKlk9JzNrNyT993jq4oX5zTt6bexoNeHlrumtXLi5MfPGsltVq8trDzP41/HlZWAu4TdIxEDnasFnTgNVmtgZA0hXAscCDDbx2BrDIzF4IX7sImAlcHkO5khF3Mrmk16RvQl6zFddrzslzc0+jyRbz2HTXqtwso5BwzrNOViugDJU01MxeAzCzyyT9BVgEjIjh2GOB8hwKAwQ1jkrHSzoUeAQ408yeqvLayP84SXOAOQDjx4+PodhtiHPWbo7+6du9Ss7TfJA8aSTgddKcpNxcmHh/Z8tqNXn9BHhv+QYzuwGYDcTRQBu1pl5lzee3wAQz6wFuAi5r4rXBRrP5ZtZrZr2jR49uubC50+I/fRJNCu3MZ8hjc1mR5L3prhm5ab7r8P7OJFUNKGb2XTNbIumgiu3LgLNjOPYAsHfZ43HAuopjPV+qIQH/Dry70dd2vBb+6ZP68m6ng9s7lds3a+pYls6dzmN9R7N07vRCBhPI0URLz1LcskbmofwoYtvFMRz7bmBfSRMlDSGo+fSX7yBpr7KHxwAPhT8vBD4oaVTYGf/BcFv3aOGfPqkv73auknNzVeoyl8XIu8gau8/Gb1nVPhRJ0wiavEZLOqPsqbcCg9s9sJltlvQFgkAwCFhgZg9IOg9YZmb9wBnhIIDNwAvAaeFrX5B0PkFQAjiv1EHfNVro5E/yy7vVDu5O6lR27Ul71cfagwA8S3ErqqZekXQ4MB34NHBp2VN/A641s8K1SXTKeiitylu6EfD0Hy47efw85FXb66GY2S0Ec09+Uja0V8AIM3s5vqK6tORxRFAu1yJ3XcGbW+PXSOqVc8Omqc3AMmB3SX1m9v1ki+biltcv7zzPB6nkQ5w7hze3xq+RgLK/mf1V0seAG4GvEQQWDygFVKQv77zJzcQ7F4s81tiLrpFRXkPCPF7HAteY2evA1mSL5Vz++BDnztJJc3jyopEayqXAk8BK4FZJ44GXEi2Vcznkbe6dx2vs8apbQzGzeWY2xsw+aMGQsAGC0V/OdZXcTLxznSMnCV7jUjegSBot6ceSfhduegfwsWSL5Vy0LLPR5j3lvSuYDsxq3Egfyk+BW9mW6mQV8L+SKpBz1WSd98vb3F2sOnAV10b6UPYws/+SdBaAmW2SVH3ha5cIH66aj2y03ubuYtOBWY0bqaG8HC5oZQCSDiSYLe9SkvWVeV54p7jrKB2Y1biRgPJVgjTy+0i6lWARqy8mWqo8yrDzrEjDVZPs4/BOcddROjCrca015Q+CN9LVHw58APgSsJ+ZLU+neDmRcedZUa7Mk65Jeae46ygdmNW4Vh/Kj4ADAMLJjPelUqI8ynh1xKKkiEi6jyOvqWOca1mcq7jmQCOd8q6VzrMVV8a2fnxRUkSkUZPyTnHn8qtWQNlHUn+1J83smATKk0+7jAubuyK2Ryk1kZVqNaUmMmgpqBTlyrwoNSnnYhHjRWOnqBVQngX+b1oFybUjztk+QEDtzrMEmsiKcGVelJqUK47cDpeP+aKxU9QKKH8zs1uTPLikmcAPCFZsvNTM+iqe/wrBAl+bCQLcp8zsifC5LcD94a5PJlpjanZ1xA4cX96IotSkXDHkOrtzxv2qeVUroDye5IElDSJYm/4ogvxgd0vqN7MHy3a7F+g1s1ckfRa4EDgpfG6jmU1JsozbaabzrNkmsg5ShJqUK4Y8TGStqksvGuupOmzYzI5L+NjTgNVmtiYcRXYFQYr88jLcYmavhA/vAorxjdyB48udS1uuh8t34KTEODQysTEpY4Hyy/iBcFs1pwPXlz0eJmmZpLskzUqigC3rwPHlzqUt1xNZ/aIxUpbDhhWxzSJ3lE4BegkmV5aMN7N1kvYBFku638wejXjtHGAOwPjx49svdaM6ZHx5bjtFXcfL9SCPZvtVu0RDAUXSccAhBF/4t5vZ1TEce4BtGYwhaM5aF3HsI4FvAB8ws9dK281sXXi/RtISYCqwQ0Axs/nAfIDe3t7IgNUNWgkMue4UdR0v94M8OuSiMU4K1syqsYP0I+DvCHJ4QdAp/qiZfb6tAwfLCj8CHAGsBe4GPmZmD5TtMxW4CphpZqvKto8CXjGz1yTtDtwJHFvRob+D3t5eW7ZsWTvFLqTKwADBlV691OsH9y2OnFcyduRwls71Ndac6xaS7jGz3nr7NVJD+QAwOVytEUmXsW24bsvMbLOkLwALCYYNLzCzBySdBywzs37gu8CbgV9Jgm3Dg98J/FjSVoJ+oL56waSbtTpaJtedos653GkkoDwMjAeeCB/vDayI4+Bm9nvg9xXbzin7+cgqr7sD2D+OMnSDVgODz3x3zjWjkVFeuwEPSVoS9lU8CIyW1F8rNYvLj1ZHy+Qxu2+WSwA752prpIbS3ePgOkCro2Xy1inqgwRcJR+FmC91O+U7Sbd2ykNnfPB8kIAr1+pgE9e8tjvlJd1uZodI+hvbzw8RYGb21hjK6VLSCSlRfJCAK5fr1CxdqmpAMbNDwvu3pFcc56rzQQKunF9g5E9DqVckDZI0RtL40i3pgjlXKY+DBFx2cp2apUvVDSiSvgj8BVgEXBfefpdwuZzbwaypY7nguP0ZO3I4Iug78fby7uUXGPnTyCivLwGTzOz5pAvjXD2d0Bfk4pG3UYi5ktFqko0ElKeADUkXxDnnmuUXGBEyXE2y1iivr4Q/rgGWSLoOKE/O+P1ES+acc92o3dpFhqtJ1qqhlEZ3PRnehoQ355xzSYijdpHhapK1hg3/S+JHd845t00ctYsMlyBvZJTXIkkjyx6PkrQw2WI551wXiqN2keFqko3MQxltZutLD8zsRWCP5IrURVZcCfMmw7kjg/sVV2ZdIudcluJYqz7DJcgbGeW1RdJ4M3sSQNLbqbJUr2tChiMx4tAJucGcy50jztn+ewFaq11ktJpkIwHlG8Dtkm4NHx9KuEa7a0OGIzHaFUfWXw9IzkUo+Fr1dQOKmd0g6QDgoHDTmWb2XLLF6gIZjsRoV7tJ+TwNfefzC4YmRA0TPnNl1qVqSUO5vID3AYeFt4Nq7tkESTMlPSxptaS5Ec8PlfTL8Pk/SJpQ9tzZ4faHJc2Iq0ypiaGtNKvFptpNylcrILniK10wrF2/EWPbBYMvhhah1PS94SnAtjV9F7Q/tZFRXn0E6VceDG9fknRBuweWNAi4GPgQsB9wsqT9KnY7HXjRzP4OmAd8J3ztfsBs4F3ATOBH4fsVR5sjMbL80LablM+zxHY2v2BoQq2m7wJqpIbyj8BRZrbAzBYQfIEfHcOxpwGrzWyNmb0OXAEcW7HPscBl4c9XAUdIUrj9CjN7zcweA1aH71ccbY7EyPJD225SvlYDki//Wwx+wdCEAjd9R2mkUx5gJPBC+PMuMR17LEGesJIB4D3V9jGzzZI2EKxxPxa4q+K1kQ20kuYQDiIYPz5nWffbGImR5Ye23aR8rSxJ7P0uxeHr1jQhw0mISWgkoFwA3CvpFoLVGg8Fzo7h2IrYVjkcudo+jbw22Gg2H5gPwRLAzRQwz7L+0LaTlK+VgOSr8xVHKxcMbckos24s4homnBM1A0rYvHQ7QUf8gQRf5F83sz/HcOwBYO+yx+OAdVX2GZC0M0Ht6IUGX9vRUv/QxqzZgOTNKMWRalr5gs/nKvow4Uo1A4qZmaRrzOzdQH/Mx74b2FfSRGAtQSf7xyr26QdOBe4ETgAWh2XqB/5L0veBMcC+wB9jLl+uddtaEFnXyFxzUksrX+D5XG/IaBJiEhpp8rpL0oFmdnecBw77RL4ALAQGAQvM7AFJ5wHLzKwf+A/gZ5JWE9RMZoevfUDSlQSjzjYDnzezLZEH6kRhFX/WhgFm7TIOPnYO9MQxTiIDDTZXFL1G5hLSYZ3aRSez2t0Kkh4E/h54AniZoNnLzKwn+eLFq7e315YtW5Z1MdpTWcWHoM01pVw9sWryd/HJcm4H8yZX6dTeu7CTA/NI0j1m1lt3vwYCytujtpvZEy2WLTOZB5Q4Og876QPUSb+Ly0ZeL7CKPFAgQqMBpZEmr72AB8zsb+Ebv4VgImLhAkqm4uo87KQqfif9Li4beezULvpAgTY0ElD+DTig7PHLEdtcPXF1HnbSuPVO+l1cdvLWqd0JAwVa1MhMeVlZu5iZbaXxCZGuJK6r8QwXz4ldJ/0uzpV0cc27kYCyRtIZkgaHty8Ba5IuWMeJY+EcyHTxnNh10u/iXElcn/UCaqRTfg/gImA6wWz0m4Evm9kzyRcvXpl2yue187Bch3UkOpeJInzWmxRbp3wYOGbHUqpulsfOw3Jd3JHoOkNuhpXn/bOeoKo1FElfM7MLJf2QiDxZZnZG0oWLW+bDhvPMh/C6AqtMHgrBxNcLjtvf5yrFII4aykPhvX8Dd4Mu7khMSm6umLuAJw/Nh6oBxcx+G95fVm0f10F8CG+sPN1+ujx5aD5UDShhAsaqzOyY+IvjMtNhabRbEWeNwq+Yt5d0ba3d5KFem4xHrSav9xIsbnU58Aei1yBxnSLFjsQ8fnjjrlH4FfM2adTW2kke6rXJ+NQKKG8DjgJOJkgrfx1wuZk9kEbBXAZSmHGc1w9v3DUKT7e/TRq1tXaWc/DaZHxq9aFsAW4AbpA0lCCwLJF0npn9MK0CdqUOng/S7Ic3rdpM3DUKT7e/TVq1tVbXYEmtNtnBn+uSeis2DgWOJggmEwgmOP4m+WJ1sQ6fD9LMhzfN2kzcNYpuWwCtlrzX1lIpX4d/rkuqpl6RdBlwB0ESyH8xswPN7HwzW5ta6bpRrcRyHaDahzRqe63aTNzOmjGJ4YMHbbet3RrFrKljWTp3Oo/1Hc3SudMzDybX3LuWg/sWM3HudRzct5hr7k3no5zEuY1TKuXr8M91Sa1cXv+TYGGtLwF3SPprePubpL+2c1BJu0paJGlVeD8qYp8pku6U9ICkFZJOKnvup5Iek7Q8vE1ppzy50uHzQZr58KbZsT1r6lguOG5/xo4cjoCxI4d31KS4Um1v7fqNGNtqe2kElTTObTvBMpW/fYd/rktq9aE0kjiyVXOBm82sT9Lc8PHXK/Z5BfiEma2SNAa4R9JCM1sfPn+WmV2VYBmz0eHzQZppCkq7qSS1ddAzkHXHc5LnNo6m0cT/9h3+uS5JMmjUcixQmjB5GTCrcgcze8TMVoU/rwOeAUanVsK4rLgySGty7sjgfsWVtfcvUkr3Zn+3UKNNQXlvKimSTh7GnGbTaMuK9LluQ1brmuxpZk8DmNnTYUbjqiRNA4YAj5Zt/rakcwiyH881s9cSK22rWumIy3FiufIRV6e++Y980y5h5y2vBk8m0MnYbsd2Hue7ZCXvHePtKESwzPHnOk5109e3/MbSTQRzWSp9A7jMzEaW7fuime3QjxI+txewBDjVzO4q2/ZngiAzH3jUzCJ7tyTNAeYAjB8//t1PPJHiysUdlHCxslnh9iFnMG6n53bcMSe/mycL3F4nn4+D+xZHBsuxI4ezdO70DErUeRpNDplYk5eZHWlmkyNu1wJ/CYNCKThErq0i6a0EEyq/WQom4Xs/bYHXgJ8A02qUY76Z9ZpZ7+jRKbeYdVAv+X2FAAARfUlEQVRHXGWzwhhFBBPIze9WiGaQFHXyoANvGs2PrJq8+oFTgb7w/trKHSQNAa4G/tPMflXx3F5hU5kI+l+yvySOUoSOuAYnW1U2H6yz3RkXFVRy8rsVohkkZZ066MDn/ORHVgGlD7hS0unAk8BHAST1Ap8xs08DJwKHArtJOi183Wlmthz4haTRBPnFlgOfSbn8jcl7wsUm+ngq2+Av3HwifYMvZYRe37ZTjn63Tu4zcDvq1GBZNIn1oeRRJgts5TndQhN9PFFt8CcMuYPz3vRrRmz8c+5+t07uM3AubbEtAezalELCxZY10ccT1axwyIzPMWLqt5MsYcu8GcS59HlA6WZN9vEUrVmhaOV1ruiymtjo8qBLJls559LhAaWb9ZwIH7ko6DNBwf1HLspvE51zLte8yavb5bmPp1V5HgjhOluX/+95QHGdpUvWnXA55P973uTlOkyXrDvhcsj/97yG4jpMjaHQnizSJaqDUi21ygOK6yxVhkK/MvxtiSwn7EHKvaEIqZYS5k1eRdbieiSFPW4jqgyFvnDTSbEni8xyFcTKcmSxtG9def4/SYIPw/eAUlilDsANTwG2rQMw6Q9tVsdtVJWh0Je9FJ2Qup1kkXnIaJyXoLaDvP+fJMGH4XuTV2HV6gBM8h84q+M2I2Io9JjfR6+Z0U6yyDxkNM56ad+qivB/koROHIbfBK+hFFVWHYBF63gMm11uf/U4lg49g2N2uv2Np9pdM6NaMEozo3Eeglqkov2fuFh4QCmqah19SXcAZnXcVpQ1uwhjrJ7jO0P+g2N3uj2WBabysLBTHoJapCL9n7jYeEApqqw6AIvU8RjR7DKc1/jB6N+ydO70tpuE8rAKYh6CWqQi/Z+42HgfSlGV2mnTTvOQ1XFbkUKzS9YZjXObpr9I/ycuNr7AlutcTSwg5pyrrtEFtjJp8pK0q6RFklaF96Oq7LdF0vLw1l+2faKkP4Sv/2W4/rxz2/NmF+dSlVUfylzgZjPbF7g5fBxlo5lNCW/HlG3/DjAvfP2LwOnJFtcVks8LcC5VmTR5SXoYOMzMnpa0F7DEzHboRZT0kpm9uWKbgGeBt5nZZknvBc41sxn1jutNXi6vPIWLy7O8rym/p5k9DRAGlT2q7DdM0jJgM9BnZtcAuwHrzWxzuM8A4J88V1il2e5x5xkrikIH0y5f/6RSYgFF0k3A2yKe+kYTbzPezNZJ2gdYLOl+4K8R+1WtZkmaA8wBGD9+fBOHdi4duZ3t3qZGAkXSwTTRYOXrn+wgsT4UMzvSzCZH3K4F/hI2dRHeP1PlPdaF92uAJcBU4DlgpKRSMBwHrKtRjvlm1mtmvaNHj47t93MuLrmd7d6GRnOMJZkPLfE8Z77+yQ6y6pTvB04Nfz4VuLZyB0mjJA0Nf94dOBh40IJOn1uAE2q93rmiyO1s9zY0GiiSDKaJJ+/09DI7yCqg9AFHSVoFHBU+RlKvpEvDfd4JLJN0H0EA6TOzB8Pnvg58RdJqgj6V/0i19M7FKLez3cs0myK/0UCRZDCNPVhVpuMfHjnboavTy2TSKW9mzwNHRGxfBnw6/PkOYP8qr18DROcjd65gcjvbPdRKP8eYkcMbyu581oxJ2703xBdMGy1DQ6L6SwYNgZ0Gw9ZN2/br8nlOnsvLuSgpLw41a+pYls6dzmN9R7P0H59j1pIZ2S1MVfG7L79uftNNR43WupLMhxZrzS+qv2TL6zD0LT7PqYzn8nKuUpajd7IeORRx/K/Zj3hhp9fp33rIdrvWajpqqNYVDrmdtWGAWbuMg4+dAz1Hx/arxFrzq9YvsvFF+PpjbZSys3guL+cqZZkDrIFjJzoUtsrxB7buziGvX7TdtrEjh7N07vTWjlMZuCBoLsrrFX6X54XLdS4v53Ity9E7dY6d+FDYKscfo+e3e9x2P0fRhtx6XriGeEBxrlKWi0PVOXbiQ2GrHP/VEW+Lt5+jaENuPS9cQ7wPxblKR5wT3RyTxtVonWMnPgmyyvFHfOg8lva02LwVZZdxVZqQcjzktsvXi2+E11BcvqU82grI9mq0zrETnwSZ1u/uTUgdyTvlXX4VreM2BZVzQiDoz0h76eFYeGLFwsh7tmHn6qvVcdulXzx5nwTZFG9C6jgeUFx+Fa3jNiVZr2PvXDXeh+LyK8vRVs65pnlAcfnlHbfOFYoHFJdfPvbfuULxPhSXb95x61xheA3FOedcLDygOOeci4UHFOdcMWSRNcE1JZOAImlXSYskrQrvd1hLU9LhkpaX3V6VNCt87qeSHit7bkr6v4VzLjWlrAkbngJs2zoxHlRyJasaylzgZjPbF7g5fLwdM7vFzKaY2RRgOvAKcGPZLmeVnjez5amU2rl2+BV264qW7r5LZRVQjgUuC3++DJhVZ/8TgOvN7JVES+VcUvJwhV3kgOZZEwohq4Cyp5k9DRDe71Fn/9nA5RXbvi1phaR5koZWe6GkOZKWSVr27LPPtldq51qV9RV2HgJaOzxrQiEkFlAk3SRpZcTt2CbfZy9gf2Bh2eazgXcABwK7Al+v9nozm29mvWbWO3r06BZ+E+dikPUVdtYBrV2eNaEQEpvYaGZHVntO0l8k7WVmT4cB45kab3UicLWZbSp776fDH1+T9BPgq7EU2rmkZL2gVNYBrV2lya2e7j7Xspop3w+cCvSF99fW2PdkghrJG8qCkQj6X1YmVVDnYpHlKpCQfUCLg2dNyL2s+lD6gKMkrQKOCh8jqVfSpaWdJE0A9gZurXj9LyTdD9wP7A787xTK7Fzrss5L5k1GLgW+YqNz3cJXSHQt8hUbnXPb8yYjlzBPveKccy4WHlCcc87FwgOKc865WHhAcc45FwsPKM4552LhAcU551wsPKA455yLhQcU55xzseiqmfKSngWeyODQuwPPZXDcRuS5bJDv8uW5bJDv8uW5bJDv8mVRtrebWd107V0VULIiaVkjaQuykOeyQb7Ll+eyQb7Ll+eyQb7Ll+eyeZOXc865WHhAcc45FwsPKOmYn3UBashz2SDf5ctz2SDf5ctz2SDf5ctt2bwPxTnnXCy8huKccy4WHlBiImlXSYskrQrvR0Xsc7ik5WW3VyXNCp/7qaTHyp6bkmbZwv22lB2/v2z7REl/CF//S0lD4ipbo+WTNEXSnZIekLRC0kllz8V+7iTNlPSwpNWS5kY8PzQ8F6vDczOh7Lmzw+0PS5rRbllaKNtXJD0YnqebJb297LnIv3HK5TtN0rNl5fh02XOnhv8HqySdmkHZ5pWV6xFJ68ueS/TcSVog6RlJkUuaK3BRWPYVkg4oey7R89YwM/NbDDfgQmBu+PNc4Dt19t8VeAEYET7+KXBClmUDXqqy/UpgdvjzJcBn0y4f8PfAvuHPY4CngZFJnDtgEPAosA8wBLgP2K9in88Bl4Q/zwZ+Gf68X7j/UGBi+D6DUi7b4WX/V58tla3W3zjl8p0G/GvEa3cF1oT3o8KfR6VZtor9vwgsSPHcHQocAKys8vw/AtcDAg4C/pDGeWvm5jWU+BwLXBb+fBkwq87+JwDXm9kriZYq0GzZ3iBJwHTgqlZe36C65TOzR8xsVfjzOuAZoO5EqxZNA1ab2Rozex24IixjtTJfBRwRnqtjgSvM7DUzewxYHb5famUzs1vK/q/uAsbFePy2y1fDDGCRmb1gZi8Ci4CZGZbtZODyGI9fk5ndRnCRWc2xwH9a4C5gpKS9SP68NcwDSnz2NLOnAcL7PersP5sd/1m/HVZl50kamkHZhklaJumuUlMcsBuw3sw2h48HgLExlq2Z8gEgaRrBFeajZZvjPHdjgafKHkf9zm/sE56bDQTnqpHXJl22cqcTXNWWRP2N49Ro+Y4P/15XSdq7ydcmXTbCZsKJwOKyzUmfu3qqlT/p89YwX1O+CZJuAt4W8dQ3mnyfvYD9gYVlm88G/kzwRTkf+DpwXsplG29m6yTtAyyWdD/w14j9mh4aGPO5+xlwqpltDTe3de6iDhOxrfJ3rrZPI69tR8PvL+kUoBf4QNnmHf7GZvZo1OsTLN9vgcvN7DVJnyGo6U1v8LVJl61kNnCVmW0p25b0uasnq/+5hnlAaYKZHVntOUl/kbSXmT0dfuk9U+OtTgSuNrNNZe/9dPjja5J+Anw17bKFTUmY2RpJS4CpwK8JqtY7h1fi44B1zZQtrvJJeitwHfDNsMpfeu+2zl2EAWDvssdRv3NpnwFJOwO7EDRXNPLapMuGpCMJgvUHzOy10vYqf+M4vxTrls/Mni97+O/Ad8pee1jFa5ekWbYys4HPl29I4dzVU638SZ+3hnmTV3z6gdLoilOBa2vsu0PbbPhFWuqzmAVEjvRIqmySRpWaiiTtDhwMPGhBr98tBH0+VV+fQvmGAFcTtCH/quK5uM/d3cC+Cka3DSH4cqkc1VNe5hOAxeG56gdmKxgFNhHYF/hjm+VpqmySpgI/Bo4xs2fKtkf+jWMsW6Pl26vs4THAQ+HPC4EPhuUcBXyQ7WvxiZctLN8kgs7tO8u2pXHu6ukHPhGO9joI2BBeTCV93hqXxUiATrwRtJ/fDKwK73cNt/cCl5btNwFYC+xU8frFwP0EX4Y/B96cZtmA94XHvy+8P73s9fsQfCmuBn4FDE373AGnAJuA5WW3KUmdO4IRNY8QXIF+I9x2HsGXNMCw8FysDs/NPmWv/Ub4uoeBDyXwv1avbDcBfyk7T/31/sYpl+8C4IGwHLcA7yh77afCc7oa+GTaZQsfnwv0Vbwu8XNHcJH5dPh/PkDQ//UZ4DPh8wIuDst+P9Cb1nlr9OYz5Z1zzsXCm7ycc87FwgOKc865WHhAcc45FwsPKM4552LhAcU551wsPKC4riLJJP2s7PHOCjLf/i58fIwistDGePxzJUVOvJR0RxPvc3WY9Xa1pA3algX3fU2WZ3o4p6H0+HBJ90ranFF6EVdgPlPedZuXgcmShpvZRuAognlBAJhZPxGT3aKEEyll21LAtMXMGg4GZvZPYRkOA75qZh9u8bDTgecIkkgCPA58giCdjXNN8RqK60bXA0eHP2+XtUDBWh3/Gv68Z1gTuC+8vU/SBEkPSfoR8Cdgb0knS7pf0kpJ3yl7r5mS/hS+9uay4+8naYmkNZLOKNv/pfD+MEm3hcd+UNIlkhr+rEo6UNKtku6RdL2kPcPtZ4bvd5+kn0v6H8CngbNKtRsze8zM7gdiCZKuu3gNxXWjK4BzwmauHmAB8P6I/S4CbjWzf5I0CHgzQUqOSQSzkT8naQxBLqp3Ay8CN4ZNRUsJ8lQdamaPSdq17H3fQbBmyVuAhyX9m5XldQtNI1hb5QngBuA4ti0hUFWYHuQHBDO/n5P0ceB8YA7wNeDtZva6pJFmtl7SpcBzZvb/6r23c/V4QHFdx8xWKFhh8WTg9zV2nU7Q/IMFWWc3hLmSnrBtySkPBJaY2bMAkn5BsFDSFuA2C9ZEwczK17m4zoKEja9JegbYkyDVRrk/mtma8D0vBw6hgYACvBN4F3BT0CLHoLL3fgD4uaRrgWsaeC/nmuIBxXWrfuB7BFlad2vytS+X/RyVOry0vVpeo9fKft5C9Oew8rWN5kgSsMLMompcMwhS2R8LfFPS5Abf07mGeB+K61YLgPPC/oJqbiZYQhdJgxSkz6/0B+ADknYPm8VOBm4lyFT7gTDjMBVNXo2YFmbF3Qk4Cbi9wdc9CIxVsAgZkoZIeldYtnFmthg4i2C1yxHA3wia3pxrmwcU15XMbMDMflBnty8BhytYaOwegqakyvd5mmBE1C0EmWj/ZGbXhk1gc4DfSLoP+GWTRbwT6CPIoPwYQer+usKmtBOA74fHvRd4D0Et6L8krSAYTPAdM/sbwVIBJ4ZDhd8n6b2SBoB/Ai4N93euIZ5t2LmciWEosHOZ8BqKc865WHgNxTnnXCy8huKccy4WHlCcc87FwgOKc865WHhAcc45FwsPKM4552LhAcU551ws/j/hZ0oQoOhEUQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mask = y == 1\n",
    "passed = plt.scatter(X[mask][0].values, X[mask][1].values)\n",
    "failed = plt.scatter(X[~mask][0].values, X[~mask][1].values)\n",
    "plt.xlabel('Microchip Test1')\n",
    "plt.ylabel('Microchip Test2')\n",
    "plt.legend((passed, failed), ('Passed', 'Failed'))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "def mapFeature(X1, X2):\n",
    "    degree = 6\n",
    "    out = np.ones(X.shape[0])[:,np.newaxis]\n",
    "    for i in range(1, degree+1):\n",
    "        for j in range(i+1):\n",
    "            out = np.hstack((out, np.multiply(np.power(X1, i-j),np.power(X2, j))[:,np.newaxis]))\n",
    "    return out\n",
    "X = mapFeature(X.iloc[:,0], X.iloc[:,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sigmoid(x):\n",
    "    return 1/(1+np.exp(-x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "def costFunction(theta,X,y,lambda_t):\n",
    "    m = len(y)\n",
    "    J = (-1/m) * (y.T @ np.log(sigmoid(X@theta)) + (1-y.T)@np.log(1 - sigmoid(X@theta)))\n",
    "    reg = (lambda_t/2*m)*(theta[1:].T@theta[1:])\n",
    "    J = J+reg\n",
    "    return J"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradientDescent(theta,X,y,lambda_t):\n",
    "    m = len(y)\n",
    "    grad = np.zeros([m,1])\n",
    "    grad = (1/m) * X.T @ (sigmoid(X @ theta) - y)\n",
    "    grad[1:] = grad[1:] + (lambda_t / m) * theta[1:]\n",
    "    return grad"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.69314718]]\n"
     ]
    }
   ],
   "source": [
    "(m,n) = X.shape\n",
    "y = y[:,np.newaxis]\n",
    "theta = np.zeros((n,1))\n",
    "lambda_t = 1\n",
    "J = costFunction(theta,X,y,lambda_t)\n",
    "print(J)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 2.49640504e-04  1.37411664e-04  2.77015264e-04 -4.35864523e-04\n",
      " -1.62448946e-04 -2.48689519e-04  3.40749794e-05 -7.16770320e-05\n",
      " -7.34919150e-05 -2.03237594e-05 -3.10561369e-04 -1.49837678e-05\n",
      " -1.31827480e-04 -4.36565248e-05 -2.29977884e-04 -3.43138390e-05\n",
      " -4.33024117e-05 -1.87923601e-05 -5.59544625e-05 -5.21231445e-05\n",
      " -9.08338038e-05 -2.10980729e-04  2.17307928e-06 -6.54197890e-05\n",
      " -8.84386569e-07 -6.91289403e-05 -1.78749503e-05 -1.85529268e-04]\n"
     ]
    }
   ],
   "source": [
    "output = opt.fmin_tnc(func = costFunction, x0 = theta.flatten(), fprime = gradientDescent, args = (X, y.flatten(), lambda_t))\n",
    "theta = output[0]\n",
    "print(theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "80.50847457627118"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pred = [sigmoid(np.dot(X, theta)) >= 0.5]\n",
    "np.mean(pred == y.flatten()) * 100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "u = np.linspace(-1, 1.5, 50)\n",
    "v = np.linspace(-1, 1.5, 50)\n",
    "z = np.zeros((len(u), len(v)))\n",
    "def mapFeatureForPlotting(X1, X2):\n",
    "    degree = 6\n",
    "    out = np.ones(1)\n",
    "    for i in range(1, degree+1):\n",
    "        for j in range(i+1):\n",
    "            out = np.hstack((out, np.multiply(np.power(X1, i-j), np.power(X2, j))))\n",
    "    return out\n",
    "for i in range(len(u)):\n",
    "    for j in range(len(v)):\n",
    "        z[i,j] = np.dot(mapFeatureForPlotting(u[i], v[j]), theta)\n",
    "mask = y.flatten() == 1\n",
    "X = data.iloc[:,:-1]\n",
    "passed = plt.scatter(X[mask][0], X[mask][1])\n",
    "failed = plt.scatter(X[~mask][0], X[~mask][1])\n",
    "plt.contour(u,v,z,0)\n",
    "plt.xlabel('Microchip Test1')\n",
    "plt.ylabel('Microchip Test2')\n",
    "plt.legend((passed, failed), ('Passed', 'Failed'))\n",
    "plt.show()"
   ]
  }
 ],
 "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": "3.7.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}