Relatório de Aprendizado de Máquina - Trabalho 02 (LoadTXT).ipynb

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    "# 1. Regressão Logística com Regularização\n",
    "\n",
    "Nesta parte do trabalho, será implementada a **_Regressão Logística Regularizada_**\n",
    "para prever se os microchips de uma usina de fabricação passam na garantia\n",
    "de qualidade (QA). Durante a QA, cada microchip passa por vários testes para\n",
    "garantir se está funcionando corretamente. Dessa forma, a Gestão de Produto da \n",
    "fábrica terá o resultados de teste para alguns microchips em dois testes diferentes. \n",
    "\n",
    "A partir desses dois testes, será determinado se os microchips deveriam ser \n",
    "aceitos ou rejeitados. Para auxiliar a tomar a decisão, há um conjunto de dados\n",
    "com resultados de testes anteriores sobre microchips, a partir do qual é possível construir\n",
    "um modelo de Regressão Logística.\n",
    "\n",
    "O arquivo {ex2data2.txt} contém os dados a serem usados nessa parte do trabalho. A primeira \n",
    "coluna corresponde aos resultados do primeiro teste, enquanto que a segunda coluna corresponde\n",
    "aos resultados do segundo teste. A terceira coluna contém os valores da classe (y = 0 significa \n",
    "rejeitado no teste, e y = 1 significa aceito no teste).\n",
    "\n",
    "## 1.1 Visualização dos Dados\n",
    "\n",
    "Para a maioria dos conjuntos de dados do mundo real, não é possível criar um gráfico para \n",
    "visualizar seus pontos. Mas, para o conjunto de dados fornecido, isso é possível. Implemente \n",
    "um script em _Python_ que produza um gráfico de dispersão (scatter plot) dos dados fornecidos. \n",
    "Após finalizado, seu script deve produzir um resultado similar ao apresentado na Figura abaixo.\n",
    "\n",
    "![ScatterPlot](scatter_plot2.jpg)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#import os \n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib as plt\n",
    "\n",
    "from numpy import loadtxt, where, append, zeros, ones, array, linspace, logspace\n",
    "from pylab import scatter, show, legend, xlabel, ylabel\n",
    "\n",
    "#%matplotlib inline\n",
    "\n",
    "# Carregando o arquivo gerado pelo MATLAB\n",
    "#import scipy.io\n",
    "#mat = scipy.io.loadmat('file.mat')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
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       "\n",
       "    .dataframe thead th {\n",
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       "\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>QATest1</th>\n",
       "      <th>QATest2</th>\n",
       "      <th>QAcceptance</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",
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      "text/plain": [
       "    QATest1  QATest2  QAcceptance\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": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Construindo um dataset com base num Dataframe, já identificando colunas e exibindo seus primeiros 20 registros.\n",
    "df = pd.read_csv('am-T2-dados/ex2data2.txt', names=['QATest1', 'QATest2', 'QAcceptance'])\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
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oyDcsLEwlJSWuxxUVFZcdhADqPsY84Fk1Kt+uXbsqJydHkvTpp5+qXbt2Hg0FwL8w5gHP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\ngGX/D4893ofOJlrGAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11eafebe0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11ec4a2b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualização da Distribuição dos Dados conforme Histograma\n",
    "\n",
    "df.hist()\n",
    "plt.pyplot.show()\n",
    "\n",
    "df.QATest1.hist(), df.QATest2.hist(), df.QAcceptance.hist()\n",
    "plt.pyplot.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>QATest1</th>\n",
       "      <th>QATest2</th>\n",
       "      <th>QAcceptance</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>118.000000</td>\n",
       "      <td>118.000000</td>\n",
       "      <td>118.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>0.054779</td>\n",
       "      <td>0.183102</td>\n",
       "      <td>0.491525</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.496654</td>\n",
       "      <td>0.519743</td>\n",
       "      <td>0.502060</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>-0.830070</td>\n",
       "      <td>-0.769740</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>-0.372120</td>\n",
       "      <td>-0.254385</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>-0.006336</td>\n",
       "      <td>0.213455</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>0.478970</td>\n",
       "      <td>0.646562</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1.070900</td>\n",
       "      <td>1.108900</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          QATest1     QATest2  QAcceptance\n",
       "count  118.000000  118.000000   118.000000\n",
       "mean     0.054779    0.183102     0.491525\n",
       "std      0.496654    0.519743     0.502060\n",
       "min     -0.830070   -0.769740     0.000000\n",
       "25%     -0.372120   -0.254385     0.000000\n",
       "50%     -0.006336    0.213455     0.000000\n",
       "75%      0.478970    0.646562     1.000000\n",
       "max      1.070900    1.108900     1.000000"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    118.00\n",
       "mean       0.05\n",
       "std        0.50\n",
       "min       -0.83\n",
       "25%       -0.37\n",
       "50%       -0.01\n",
       "75%        0.48\n",
       "max        1.07\n",
       "Name: QATest1, dtype: float64"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.QATest1.describe().round(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    118.00\n",
       "mean       0.18\n",
       "std        0.52\n",
       "min       -0.77\n",
       "25%       -0.25\n",
       "50%        0.21\n",
       "75%        0.65\n",
       "max        1.11\n",
       "Name: QATest2, dtype: float64"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.QATest2.describe().round(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    118.00\n",
       "mean       0.49\n",
       "std        0.50\n",
       "min        0.00\n",
       "25%        0.00\n",
       "50%        0.00\n",
       "75%        1.00\n",
       "max        1.00\n",
       "Name: QAcceptance, dtype: float64"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.QAcceptance.describe().round(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "#df.drop(labels='QATest1', axis=1)\n",
    "#df.drop(labels='QATest2', axis=1)\n",
    "#df.drop(labels='QAcceptance', axis=1)\n",
    "\n",
    "\n",
    "#load the dataset\n",
    "data = np.loadtxt('am-T2-dados/ex2data2.txt', delimiter=',')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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KSsNJb9s2k5QU684HkJOTnegkxJzyZA9Oy5PT8gPNz5Pb7WrR/vHU9DQ9Rs1s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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11f0da390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = data[:, 0:2]\n",
    "y = data[:, 2]\n",
    "\n",
    "pos = where(y == 1)\n",
    "neg = where(y == 0)\n",
    "scatter(X[pos, 0], X[pos, 1], marker='+', c='xkcd:black', label='Not Admitted')\n",
    "scatter(X[neg, 0], X[neg, 1], marker='o', c='xkcd:yellow', label='Admitted')\n",
    "legend(['Admitted', 'Not Admitted'])\n",
    "xlabel('Exam 1 score')\n",
    "ylabel('Exam 2 score')\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1.2 Mapeamento de características (_feature mapping_)\n",
    "\n",
    "Uma maneira de tornar os dados mais apropriados para a classificação é criar\n",
    "mais características a partir das já existentes. Para isso, você deve criar uma\n",
    "função **`mapFeature`**. Essa função deve ser implementada em um arquivo de\n",
    "nome **_`mapFeature.py`_**, que irá mapear as características para todos os termos\n",
    "polinomiais de x1 e x2, até a sexta potência. Como resultado desse mapeamento, nosso \n",
    "vetor de duas características (os escores nos dois testes de QA) será transformado \n",
    "em um **vetor de _28 dimensões_**.\n",
    "\n",
    "Um classificador que usa regressão logística treinado nesse vetor de características \n",
    "de maior dimensão terá uma fronteira de decisão mais complexa e parecerá não-linear \n",
    "quando desenhado em um gráfico bidimensional. \n",
    "\n",
    "Embora o mapeamento de características nos permita construir um classificador mais expressivo, \n",
    "também é mais suscetível a sobreajuste (overfitting). Desse modo, será implementada a \n",
    "**_Regressão Logística Regularizada_** sobre os dados fornecidos e também verá como a regularização pode \n",
    "ajudar a combater o problema do sobreajuste."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def map_feature(X1, X2):\n",
    "    '''\n",
    "    Função que mapeia características p/ os termos polinomiais X1 e X2 até a 6ª potência.\n",
    "    Retorna um novo conjunto com mais características, através do algoritmo de mapping\n",
    "    X1, X2, X1 ** 2, X2 ** 2, X1*X2, X1*X2 ** 2, etc...\n",
    "    Os parâmetros X1, X2 devem ser do mesmo tamanho\n",
    "    '''\n",
    "    # Potência padrão para o mapeamento\n",
    "    potencia = 6\n",
    "    \n",
    "    X1.shape = (X1.size, 1)\n",
    "    X2.shape = (X2.size, 1)\n",
    "    \n",
    "    features = np.ones(shape=(X1.size, 1))\n",
    "\n",
    "    for i in range(1, potencia + 1):\n",
    "        for j in range(i + 1):\n",
    "            r = (X1 ** (i - j)) * (X2 ** j)\n",
    "            features = append(features, r, axis=1)\n",
    "\n",
    "    return features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = data[:, 0:2]\n",
    "y = data[:, 2]\n",
    "\n",
    "pos = where(y == 1)\n",
    "neg = where(y == 0)\n",
    "scatter(X[pos, 0], X[pos, 1], marker='o', c='b')\n",
    "scatter(X[neg, 0], X[neg, 1], marker='x', c='r')\n",
    "xlabel('Microchip Test 1')\n",
    "ylabel('Microchip Test 2')\n",
    "legend(['y = 1', 'y = 0'])\n",
    "\n",
    "\n",
    "m, n = X.shape\n",
    "y.shape = (m, 1)\n",
    "\n",
    "it = map_feature(X[:, 0], X[:, 1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(118, 28)"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "it.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "      0         1         2         3         4         5             6   \\\n",
      "0    1.0  0.051267  0.699560  0.002628  0.035864  0.489384  1.347453e-04   \n",
      "1    1.0 -0.092742  0.684940  0.008601 -0.063523  0.469143 -7.976812e-04   \n",
      "2    1.0 -0.213710  0.692250  0.045672 -0.147941  0.479210 -9.760555e-03   \n",
      "3    1.0 -0.375000  0.502190  0.140625 -0.188321  0.252195 -5.273438e-02   \n",
      "4    1.0 -0.513250  0.465640  0.263426 -0.238990  0.216821 -1.352032e-01   \n",
      "5    1.0 -0.524770  0.209800  0.275384 -0.110097  0.044016 -1.445130e-01   \n",
      "6    1.0 -0.398040  0.034357  0.158436 -0.013675  0.001180 -6.306380e-02   \n",
      "7    1.0 -0.305880 -0.192250  0.093563  0.058805  0.036960 -2.861892e-02   \n",
      "8    1.0  0.016705 -0.404240  0.000279 -0.006753  0.163410  4.661648e-06   \n",
      "9    1.0  0.131910 -0.513890  0.017400 -0.067787  0.264083  2.295267e-03   \n",
      "10   1.0  0.385370 -0.565060  0.148510 -0.217757  0.319293  5.723131e-02   \n",
      "11   1.0  0.529380 -0.521200  0.280243 -0.275913  0.271649  1.483551e-01   \n",
      "12   1.0  0.638820 -0.243420  0.408091 -0.155502  0.059253  2.606967e-01   \n",
      "13   1.0  0.736750 -0.184940  0.542801 -0.136255  0.034203  3.999083e-01   \n",
      "14   1.0  0.546660  0.487570  0.298837  0.266535  0.237725  1.633623e-01   \n",
      "15   1.0  0.322000  0.582600  0.103684  0.187597  0.339423  3.338625e-02   \n",
      "16   1.0  0.166470  0.538740  0.027712  0.089684  0.290241  4.613260e-03   \n",
      "17   1.0 -0.046659  0.816520  0.002177 -0.038098  0.666705 -1.015795e-04   \n",
      "18   1.0 -0.173390  0.699560  0.030064 -0.121297  0.489384 -5.212813e-03   \n",
      "19   1.0 -0.478690  0.633770  0.229144 -0.303379  0.401664 -1.096890e-01   \n",
      "20   1.0 -0.605410  0.597220  0.366521 -0.361563  0.356672 -2.218956e-01   \n",
      "21   1.0 -0.628460  0.334060  0.394962 -0.209943  0.111596 -2.482178e-01   \n",
      "22   1.0 -0.593890  0.005117  0.352705 -0.003039  0.000026 -2.094682e-01   \n",
      "23   1.0 -0.421080 -0.272660  0.177308  0.114812  0.074343 -7.466101e-02   \n",
      "24   1.0 -0.115780 -0.396930  0.013405  0.045957  0.157553 -1.552032e-03   \n",
      "25   1.0  0.201040 -0.601610  0.040417 -0.120948  0.361935  8.125450e-03   \n",
      "26   1.0  0.466010 -0.535820  0.217165 -0.249697  0.287103  1.012012e-01   \n",
      "27   1.0  0.673390 -0.535820  0.453454 -0.360816  0.287103  3.053515e-01   \n",
      "28   1.0 -0.138820  0.546050  0.019271 -0.075803  0.298171 -2.675199e-03   \n",
      "29   1.0 -0.294350  0.779970  0.086642 -0.229584  0.608353 -2.550305e-02   \n",
      "..   ...       ...       ...       ...       ...       ...           ...   \n",
      "88   1.0 -0.403800  0.706870  0.163054 -0.285434  0.499665 -6.584138e-02   \n",
      "89   1.0 -0.380760  0.918860  0.144978 -0.349865  0.844304 -5.520189e-02   \n",
      "90   1.0 -0.507490  0.904240  0.257546 -0.458893  0.817650 -1.307021e-01   \n",
      "91   1.0 -0.547810  0.706870  0.300096 -0.387230  0.499665 -1.643955e-01   \n",
      "92   1.0  0.103110  0.779970  0.010632  0.080423  0.608353  1.096232e-03   \n",
      "93   1.0  0.057028  0.918860  0.003252  0.052401  0.844304  1.854661e-04   \n",
      "94   1.0 -0.104260  0.991960  0.010870 -0.103422  0.983985 -1.133322e-03   \n",
      "95   1.0 -0.081221  1.108900  0.006597 -0.090066  1.229659 -5.358028e-04   \n",
      "96   1.0  0.287440  1.087000  0.082622  0.312447  1.181569  2.374880e-02   \n",
      "97   1.0  0.396890  0.823830  0.157522  0.326970  0.678696  6.251878e-02   \n",
      "98   1.0  0.638820  0.889620  0.408091  0.568307  0.791424  2.606967e-01   \n",
      "99   1.0  0.823160  0.663010  0.677592  0.545763  0.439582  5.577669e-01   \n",
      "100  1.0  0.673390  0.641080  0.453454  0.431697  0.410984  3.053515e-01   \n",
      "101  1.0  1.070900  0.100150  1.146827  0.107251  0.010030  1.228137e+00   \n",
      "102  1.0 -0.046659 -0.579680  0.002177  0.027047  0.336029 -1.015795e-04   \n",
      "103  1.0 -0.236750 -0.638160  0.056051  0.151084  0.407248 -1.326997e-02   \n",
      "104  1.0 -0.150350 -0.367690  0.022605  0.055282  0.135196 -3.398680e-03   \n",
      "105  1.0 -0.490210 -0.301900  0.240306  0.147994  0.091144 -1.178003e-01   \n",
      "106  1.0 -0.467170 -0.133770  0.218248  0.062493  0.017894 -1.019588e-01   \n",
      "107  1.0 -0.288590 -0.060673  0.083284  0.017510  0.003681 -2.403498e-02   \n",
      "108  1.0 -0.611180 -0.067982  0.373541  0.041549  0.004622 -2.283008e-01   \n",
      "109  1.0 -0.663020 -0.214180  0.439596  0.142006  0.045873 -2.914606e-01   \n",
      "110  1.0 -0.599650 -0.418860  0.359580  0.251169  0.175444 -2.156222e-01   \n",
      "111  1.0 -0.726380 -0.082602  0.527628  0.060000  0.006823 -3.832584e-01   \n",
      "112  1.0 -0.830070  0.312130  0.689016 -0.259090  0.097425 -5.719317e-01   \n",
      "113  1.0 -0.720620  0.538740  0.519293 -0.388227  0.290241 -3.742131e-01   \n",
      "114  1.0 -0.593890  0.494880  0.352705 -0.293904  0.244906 -2.094682e-01   \n",
      "115  1.0 -0.484450  0.999270  0.234692 -0.484096  0.998541 -1.136964e-01   \n",
      "116  1.0 -0.006336  0.999270  0.000040 -0.006332  0.998541 -2.544062e-07   \n",
      "117  1.0  0.632650 -0.030612  0.400246 -0.019367  0.000937  2.532156e-01   \n",
      "\n",
      "           7         8             9       ...                 18  \\\n",
      "0    0.001839  0.025089  3.423536e-01      ...       8.998098e-04   \n",
      "1    0.005891 -0.043509  3.213347e-01      ...       2.763825e-03   \n",
      "2    0.031616 -0.102412  3.317332e-01      ...       1.515091e-02   \n",
      "3    0.070620 -0.094573  1.266497e-01      ...       1.781011e-02   \n",
      "4    0.122661 -0.111283  1.009603e-01      ...       2.659554e-02   \n",
      "5    0.057775 -0.023098  9.234565e-03      ...       2.543047e-03   \n",
      "6    0.005443 -0.000470  4.055512e-05      ...       6.425385e-06   \n",
      "7   -0.017987 -0.011305 -7.105572e-03      ...      -6.648156e-04   \n",
      "8   -0.000113  0.002730 -6.605685e-02      ...      -1.843363e-05   \n",
      "9   -0.008942  0.034835 -1.357096e-01      ...      -2.361380e-03   \n",
      "10  -0.083917  0.123046 -1.804196e-01      ...      -2.679412e-02   \n",
      "11  -0.146063  0.143806 -1.415837e-01      ...      -3.967786e-02   \n",
      "12  -0.099338  0.037852 -1.442344e-02      ...      -5.886075e-03   \n",
      "13  -0.100386  0.025199 -6.325466e-03      ...      -3.433467e-03   \n",
      "14   0.145704  0.129954  1.159073e-01      ...       3.463742e-02   \n",
      "15   0.060406  0.109294  1.977477e-01      ...       2.050327e-02   \n",
      "16   0.014930  0.048316  1.563643e-01      ...       4.333209e-03   \n",
      "17   0.001778 -0.031108  5.443779e-01      ...       1.185145e-03   \n",
      "18   0.021032 -0.084854  3.423536e-01      ...       1.029255e-02   \n",
      "19   0.145225 -0.192273  2.545629e-01      ...       5.833158e-02   \n",
      "20   0.218894 -0.215933  2.130115e-01      ...       7.807324e-02   \n",
      "21   0.131941 -0.070134  3.727979e-02      ...       1.472410e-02   \n",
      "22   0.001805 -0.000016  1.339819e-07      ...       4.725614e-08   \n",
      "23  -0.048345 -0.031305 -2.027049e-02      ...      -3.594128e-03   \n",
      "24  -0.005321 -0.018242 -6.253768e-02      ...      -8.383181e-04   \n",
      "25  -0.024315  0.072763 -2.177435e-01      ...      -8.800556e-03   \n",
      "26  -0.116362  0.133793 -1.538356e-01      ...      -3.340775e-02   \n",
      "27  -0.242970  0.193332 -1.538356e-01      ...      -6.975737e-02   \n",
      "28   0.010523 -0.041392  1.628161e-01      ...       3.137627e-03   \n",
      "29   0.067578 -0.179069  4.744972e-01      ...       4.111135e-02   \n",
      "..        ...       ...           ...      ...                ...   \n",
      "88   0.115258 -0.201765  3.531983e-01      ...       5.759056e-02   \n",
      "89   0.133215 -0.321477  7.757969e-01      ...       1.124736e-01   \n",
      "90   0.232883 -0.414949  7.393518e-01      ...       1.904172e-01   \n",
      "91   0.212129 -0.273722  3.531983e-01      ...       1.059933e-01   \n",
      "92   0.008292  0.062727  4.744972e-01      ...       5.044699e-03   \n",
      "93   0.002988  0.048149  7.757969e-01      ...       2.523041e-03   \n",
      "94   0.010783 -0.102590  9.760734e-01      ...       1.061006e-02   \n",
      "95   0.007315 -0.099874  1.363569e+00      ...       8.995262e-03   \n",
      "96   0.089810  0.339630  1.284366e+00      ...       1.061165e-01   \n",
      "97   0.129771  0.269368  5.591300e-01      ...       8.807510e-02   \n",
      "98   0.363046  0.505577  7.040664e-01      ...       2.873232e-01   \n",
      "99   0.449251  0.361847  2.914474e-01      ...       1.974826e-01   \n",
      "100  0.290700  0.276752  2.634733e-01      ...       1.194731e-01   \n",
      "101  0.114855  0.010741  1.004507e-03      ...       1.151995e-03   \n",
      "102 -0.001262 -0.015679 -1.947892e-01      ...      -4.240683e-04   \n",
      "103 -0.035769 -0.096416 -2.598895e-01      ...      -1.456695e-02   \n",
      "104 -0.008312 -0.020327 -4.971019e-02      ...      -1.123705e-03   \n",
      "105 -0.072548 -0.044680 -2.751626e-02      ...      -6.612317e-03   \n",
      "106 -0.029195 -0.008360 -2.393736e-03      ...      -5.224276e-04   \n",
      "107 -0.005053 -0.001062 -2.233502e-04      ...      -1.860154e-05   \n",
      "108 -0.025394 -0.002825 -3.141824e-04      ...      -1.173600e-04   \n",
      "109 -0.094153 -0.030415 -9.825095e-03      ...      -4.319068e-03   \n",
      "110 -0.150614 -0.105205 -7.348635e-02      ...      -2.642423e-02   \n",
      "111 -0.043583 -0.004956 -5.636009e-04      ...      -2.973716e-04   \n",
      "112  0.215063 -0.080870  3.040931e-02      ...       2.095251e-02   \n",
      "113  0.279764 -0.209153  1.563643e-01      ...       8.119893e-02   \n",
      "114  0.174547 -0.145447  1.211992e-01      ...       4.274760e-02   \n",
      "115  0.234520 -0.483743  9.978116e-01      ...       2.341782e-01   \n",
      "116  0.000040 -0.006327  9.978116e-01      ...       4.006210e-05   \n",
      "117 -0.012252  0.000593 -2.868634e-05      ...      -1.148159e-05   \n",
      "\n",
      "               19            20            21            22            23  \\\n",
      "0    1.227829e-02  1.675424e-01  1.815630e-08  2.477505e-07  3.380660e-06   \n",
      "1   -2.041205e-02  1.507518e-01  6.362953e-07 -4.699318e-06  3.470651e-05   \n",
      "2   -4.907685e-02  1.589699e-01  9.526844e-05 -3.085938e-04  9.995978e-04   \n",
      "3   -2.385083e-02  3.194040e-02  2.780914e-03 -3.724126e-03  4.987251e-03   \n",
      "4   -2.412849e-02  2.189028e-02  1.827990e-02 -1.658422e-02  1.504584e-02   \n",
      "5   -1.016696e-03  4.064690e-04  2.088401e-02 -8.349308e-03  3.338005e-03   \n",
      "6   -5.546100e-07  4.787141e-08  3.977043e-03 -3.432803e-04  2.963039e-05   \n",
      "7   -4.178462e-04 -2.626224e-04  8.190426e-04  5.147801e-04  3.235467e-04   \n",
      "8    4.460706e-04 -1.079435e-02  2.173096e-11 -5.258619e-10  1.272520e-08   \n",
      "9    9.199376e-03 -3.583858e-02  5.268249e-06 -2.052385e-05  7.995603e-05   \n",
      "10   3.928766e-02 -5.760668e-02  3.275423e-03 -4.802685e-03  7.042077e-03   \n",
      "11   3.906476e-02 -3.846113e-02  2.200925e-02 -2.166916e-02  2.133433e-02   \n",
      "12   2.242867e-03 -8.546362e-04  6.796276e-02 -2.589696e-02  9.867941e-03   \n",
      "13   8.618736e-04 -2.163487e-04  1.599267e-01 -4.014501e-02  1.007726e-02   \n",
      "14   3.089336e-02  2.755401e-02  2.668725e-02  2.380255e-02  2.122966e-02   \n",
      "15   3.709691e-02  6.712007e-02  1.114642e-03  2.016740e-03  3.648921e-03   \n",
      "16   1.402339e-02  4.538330e-02  2.128217e-05  6.887460e-05  2.228960e-04   \n",
      "17  -2.073971e-02  3.629394e-01  1.031840e-08 -1.805693e-07  3.159915e-06   \n",
      "18  -4.152637e-02  1.675424e-01  2.717342e-05 -1.096340e-04  4.423297e-04   \n",
      "19  -7.722912e-02  1.022488e-01  1.203168e-02 -1.592955e-02  2.109020e-02   \n",
      "20  -7.701706e-02  7.597518e-02  4.923768e-02 -4.857159e-02  4.791451e-02   \n",
      "21  -7.826643e-03  4.160278e-03  6.161208e-02 -3.275010e-02  1.740843e-02   \n",
      "22  -4.071624e-10  3.508141e-12  4.387691e-02 -3.780467e-04  3.257278e-06   \n",
      "23  -2.327289e-03 -1.506979e-03  5.574266e-03  3.609479e-03  2.337229e-03   \n",
      "24  -2.874016e-03 -9.853026e-03  2.408803e-06  8.258129e-06  2.831144e-05   \n",
      "25   2.633557e-02 -7.880889e-02  6.602294e-05 -1.975729e-04  5.912348e-04   \n",
      "26   3.841235e-02 -4.416666e-02  1.024169e-02 -1.177593e-02  1.354000e-02   \n",
      "27   5.550631e-02 -4.416666e-02  9.323951e-02 -7.419117e-02  5.903431e-02   \n",
      "28  -1.234189e-02  4.854696e-02  7.156691e-06 -2.815092e-05  1.107320e-04   \n",
      "29  -1.089371e-01  2.886619e-01  6.504056e-04 -1.723448e-03  4.566800e-03   \n",
      "..            ...           ...           ...           ...           ...   \n",
      "88  -1.008149e-01  1.764809e-01  4.335088e-03 -7.588765e-03  1.328447e-02   \n",
      "89  -2.714243e-01  6.550082e-01  3.047249e-03 -7.353700e-03  1.774614e-02   \n",
      "90  -3.392832e-01  6.045310e-01  1.708303e-02 -3.043835e-02  5.423472e-02   \n",
      "91  -1.367692e-01  1.764809e-01  2.702587e-02 -3.487300e-02  4.499859e-02   \n",
      "92   3.816035e-02  2.886619e-01  1.201724e-06  9.090376e-06  6.876365e-05   \n",
      "93   4.065234e-02  6.550082e-01  3.439766e-08  5.542300e-07  8.929996e-06   \n",
      "94  -1.009472e-01  9.604412e-01  1.284418e-06 -1.222033e-05  1.162677e-04   \n",
      "95  -1.228112e-01  1.676725e+00  2.870847e-07 -3.919530e-06  5.351285e-05   \n",
      "96   4.012965e-01  1.517566e+00  5.640054e-04  2.132876e-03  8.065808e-03   \n",
      "97   1.828187e-01  3.794792e-01  3.908597e-03  8.113129e-03  1.684053e-02   \n",
      "98   4.001259e-01  5.572149e-01  6.796276e-02  9.464487e-02  1.318023e-01   \n",
      "99   1.590613e-01  1.281151e-01  3.111040e-01  2.505771e-01  2.018260e-01   \n",
      "100  1.137406e-01  1.082832e-01  9.323951e-02  8.876577e-02  8.450669e-02   \n",
      "101  1.077340e-04  1.007523e-05  1.508320e+00  1.410573e-01  1.319160e-02   \n",
      "102 -5.268521e-03 -6.545481e-02  1.031840e-08  1.281933e-07  1.592643e-06   \n",
      "103 -3.926524e-02 -1.058395e-01  1.760921e-04  4.746566e-04  1.279438e-03   \n",
      "104 -2.748088e-03 -6.720616e-03  1.155103e-05  2.824873e-05  6.908398e-05   \n",
      "105 -4.072252e-03 -2.507931e-03  1.387692e-02  8.546218e-03  5.263261e-03   \n",
      "106 -1.495925e-04 -4.283449e-05  1.039560e-02  2.976689e-03  8.523486e-04   \n",
      "107 -3.910778e-06 -8.221998e-07  5.776804e-04  1.214512e-04  2.553384e-05   \n",
      "108 -1.305404e-05 -1.452010e-06  5.212125e-02  5.797485e-03  6.448585e-04   \n",
      "109 -1.395219e-03 -4.507073e-04  8.494929e-02  2.744177e-02  8.864706e-03   \n",
      "110 -1.845752e-02 -1.289272e-02  4.649294e-02  3.247567e-02  2.268450e-02   \n",
      "111 -3.381630e-05 -3.845500e-06  1.468870e-01  1.670360e-02  1.899488e-03   \n",
      "112 -7.878740e-03  2.962631e-03  3.271058e-01 -1.230011e-01  4.625193e-02   \n",
      "113 -6.070482e-02  4.538330e-02  1.400354e-01 -1.046913e-01  7.826790e-02   \n",
      "114 -3.562096e-02  2.968243e-02  4.387691e-02 -3.656200e-02  3.046659e-02   \n",
      "115 -4.830370e-01  9.963553e-01  1.292688e-02 -2.666414e-02  5.499985e-02   \n",
      "116 -6.317918e-03  9.963553e-01  6.472253e-14 -1.020695e-11  1.609667e-09   \n",
      "117  5.555592e-07 -2.688181e-08  6.411816e-02 -3.102482e-03  1.501196e-04   \n",
      "\n",
      "               24            25            26            27  \n",
      "0    4.613055e-05  6.294709e-04  8.589398e-03  1.172060e-01  \n",
      "1   -2.563226e-04  1.893054e-03 -1.398103e-02  1.032560e-01  \n",
      "2   -3.237900e-03  1.048821e-02 -3.397345e-02  1.100469e-01  \n",
      "3   -6.678793e-03  8.944062e-03 -1.197765e-02  1.604015e-02  \n",
      "4   -1.365016e-02  1.238395e-02 -1.123519e-02  1.019299e-02  \n",
      "5   -1.334515e-03  5.335313e-04 -2.133027e-04  8.527719e-05  \n",
      "6   -2.557560e-06  2.207569e-07 -1.905473e-08  1.644718e-09  \n",
      "7    2.033538e-04  1.278108e-04  8.033094e-05  5.048915e-05  \n",
      "8   -3.079338e-07  7.451610e-06 -1.803196e-04  4.363507e-03  \n",
      "9   -3.114897e-04  1.213490e-03 -4.727468e-03  1.841709e-02  \n",
      "10  -1.032565e-02  1.514029e-02 -2.219989e-02  3.255123e-02  \n",
      "11  -2.100467e-02  2.068010e-02 -2.036055e-02  2.004594e-02  \n",
      "12  -3.760142e-03  1.432788e-03 -5.459587e-04  2.080355e-04  \n",
      "13  -2.529607e-03  6.349853e-04 -1.593949e-04  4.001153e-05  \n",
      "14   1.893489e-02  1.688817e-02  1.506268e-02  1.343451e-02  \n",
      "15   6.602054e-03  1.194521e-02  2.161266e-02  3.910415e-02  \n",
      "16   7.213493e-04  2.334473e-03  7.554959e-03  2.444980e-02  \n",
      "17  -5.529766e-05  9.676943e-04 -1.693439e-02  2.963473e-01  \n",
      "18  -1.784625e-03  7.200257e-03 -2.905018e-02  1.172060e-01  \n",
      "19  -2.792274e-02  3.696881e-02 -4.894550e-02  6.480225e-02  \n",
      "20  -4.726632e-02  4.662690e-02 -4.599613e-02  4.537389e-02  \n",
      "21  -9.253507e-03  4.918732e-03 -2.614569e-03  1.389783e-03  \n",
      "22  -2.806495e-08  2.418097e-10 -2.083450e-12  1.795116e-14  \n",
      "23   1.513415e-03  9.799749e-04  6.345586e-04  4.108928e-04  \n",
      "24   9.706047e-05  3.327536e-04  1.140783e-03  3.910962e-03  \n",
      "25  -1.769264e-03  5.294502e-03 -1.584374e-02  4.741222e-02  \n",
      "26  -1.556835e-02  1.790054e-02 -2.058211e-02  2.366538e-02  \n",
      "27  -4.697391e-02  3.737739e-02 -2.974139e-02  2.366538e-02  \n",
      "28  -4.355654e-04  1.713301e-03 -6.739289e-03  2.650907e-02  \n",
      "29  -1.210113e-02  3.206562e-02 -8.496764e-02  2.251476e-01  \n",
      "..            ...           ...           ...           ...  \n",
      "88  -2.325507e-02  4.070904e-02 -7.126299e-02  1.247491e-01  \n",
      "89  -4.282546e-02  1.033475e-01 -2.494009e-01  6.018608e-01  \n",
      "90  -9.663481e-02  1.721828e-01 -3.067934e-01  5.466411e-01  \n",
      "91  -5.806421e-02  7.492351e-02 -9.667801e-02  1.247491e-01  \n",
      "92   5.201589e-04  3.934714e-03  2.976393e-02  2.251476e-01  \n",
      "93   1.438840e-04  2.318322e-03  3.735381e-02  6.018608e-01  \n",
      "94  -1.106205e-03  1.052476e-02 -1.001356e-01  9.527193e-01  \n",
      "95  -7.306042e-04  9.974846e-03 -1.361853e-01  1.859321e+00  \n",
      "96   3.050214e-02  1.153487e-01  4.362093e-01  1.649595e+00  \n",
      "97   3.495612e-02  7.255891e-02  1.506115e-01  3.126264e-01  \n",
      "98   1.835478e-01  2.556084e-01  3.559600e-01  4.957095e-01  \n",
      "99   1.625597e-01  1.309329e-01  1.054592e-01  8.494161e-02  \n",
      "100  8.045197e-02  7.659179e-02  7.291683e-02  6.941820e-02  \n",
      "101  1.233672e-03  1.153723e-04  1.078956e-05  1.009034e-06  \n",
      "102  1.978660e-05  2.458239e-04  3.054056e-03  3.794285e-02  \n",
      "103  3.448726e-03  9.296047e-03  2.505751e-02  6.754255e-02  \n",
      "104  1.689490e-04  4.131751e-04  1.010445e-03  2.471103e-03  \n",
      "105  3.241424e-03  1.996259e-03  1.229413e-03  7.571443e-04  \n",
      "106  2.440625e-04  6.988513e-05  2.001099e-05  5.729970e-06  \n",
      "107  5.368219e-06  1.128611e-06  2.372786e-07  4.988533e-08  \n",
      "108  7.172808e-05  7.978367e-06  8.874396e-07  9.871056e-08  \n",
      "109  2.863628e-03  9.250579e-04  2.988279e-04  9.653248e-05  \n",
      "110  1.584529e-02  1.106805e-02  7.731118e-03  5.400243e-03  \n",
      "111  2.160048e-04  2.456349e-05  2.793294e-06  3.176460e-07  \n",
      "112 -1.739205e-02  6.539906e-03 -2.459191e-03  9.247260e-04  \n",
      "113 -5.851357e-02  4.374511e-02 -3.270412e-02  2.444980e-02  \n",
      "114 -2.538737e-02  2.115493e-02 -1.762810e-02  1.468924e-02  \n",
      "115 -1.134476e-01  2.340073e-01 -4.826843e-01  9.956280e-01  \n",
      "116 -2.538495e-07  4.003286e-05 -6.313306e-03  9.956280e-01  \n",
      "117 -7.263830e-06  3.514745e-07 -1.700678e-08  8.229060e-10  \n",
      "\n",
      "[118 rows x 28 columns]\n"
     ]
    }
   ],
   "source": [
    "print(pd.DataFrame(it))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1.3 Função de custo e gradiente\n",
    "\n",
    "Agora, você deverá implementar o código para calcular **_a função de custo e\n",
    "o gradiente para a regressão logística regularizada_**. Crie um arquivo de nome\n",
    "costFunctionReg.py que contém uma função de nome costFunctionReg.py\n",
    "e que computa o custo e o gradiente. Lembre-se de que a função de custo\n",
    "regularizada na regressão logística é dada por:\n",
    "    \n",
    "$$J_{regularizado} = \\small \\underbrace{-\\frac{1}{m} \\sum\\limits_{i = 1}^{m} \\large{(}\\small y^{(i)}\\log\\left(x^{(i)}\\right) + (1-y^{(i)})\\log\\left(1- x^{(i)}\\right) \\large{)} }_\\text{Função de Custo} + \\underbrace{\\frac{\\lambda}{2m} \\sum\\limits_{j = 1}^{n}\\ {\\theta}_{j}^{2} }_\\text{Fator Regularização} $$\n",
    "    \n",
    "Depois de concluir a implementação da função **costFunctionReg**, você deve\n",
    "testar a corretude dela usando o valor inicial de ${\\theta}$ (inicializado todo com zeros).\n",
    "Você deve ver que o custo é de cerca de `0.693`.\n",
    "Porém, usando a função **costFunctionReg**, você agora deve computar os valores ótimos para ${\\theta}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from numpy import loadtxt, where, zeros, e, array, log, ones, append, linspace\n",
    "from pylab import scatter, show, legend, xlabel, ylabel, contour, title\n",
    "from scipy.optimize import fmin_bfgs\n",
    "\n",
    "\n",
    "def sigmoid(X):\n",
    "    '''Compute the sigmoid function '''\n",
    "    den = 1.0 + e ** (-1.0 * X)\n",
    "    d = 1.0 / den\n",
    "    return d\n",
    "\n",
    "\n",
    "def cost_function_reg(theta, X, y, l):\n",
    "    '''Compute the cost and partial derivatives as grads\n",
    "    '''\n",
    "\n",
    "    h = sigmoid(X.dot(theta))\n",
    "\n",
    "    thetaR = theta[1:, 0]\n",
    "\n",
    "    J = (1.0 / m) * ((-y.T.dot(log(h))) - ((1 - y.T).dot(log(1.0 - h)))) + (l / (2.0 * m)) * (thetaR.T.dot(thetaR))\n",
    "\n",
    "    delta = h - y\n",
    "    sumdelta = delta.T.dot(X[:, 1])\n",
    "    grad1 = (1.0 / m) * sumdelta\n",
    "\n",
    "    XR = X[:, 1:X.shape[1]]\n",
    "    sumdelta = delta.T.dot(XR)\n",
    "\n",
    "    grad = (1.0 / m) * (sumdelta + l * thetaR)\n",
    "\n",
    "    out = zeros(shape=(grad.shape[0], grad.shape[1] + 1))\n",
    "\n",
    "    out[:, 0] = grad1\n",
    "    out[:, 1:] = grad\n",
    "\n",
    "    return J.flatten(), out.T.flatten()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.3.1 Testando a Função de Custo e o Gradiente"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 0.69314718]),\n",
       " array([  1.87880932e-02,   1.87880932e-02,   7.77711864e-05,\n",
       "          5.03446395e-02,   1.15013308e-02,   3.76648474e-02,\n",
       "          1.83559872e-02,   7.32393391e-03,   8.19244468e-03,\n",
       "          2.34764889e-02,   3.93486234e-02,   2.23923907e-03,\n",
       "          1.28600503e-02,   3.09593720e-03,   3.93028171e-02,\n",
       "          1.99707467e-02,   4.32983232e-03,   3.38643902e-03,\n",
       "          5.83822078e-03,   4.47629067e-03,   3.10079849e-02,\n",
       "          3.10312442e-02,   1.09740238e-03,   6.31570797e-03,\n",
       "          4.08503006e-04,   7.26504316e-03,   1.37646175e-03,\n",
       "          3.87936363e-02]))"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.optimize import fmin_bfgs\n",
    "\n",
    "m, n = X.shape\n",
    "y.shape = (m, 1)\n",
    "it = map_feature(X[:, 0], X[:, 1])\n",
    "\n",
    "#Initialize theta parameters\n",
    "initial_theta = zeros(shape=(it.shape[1], 1))\n",
    "\n",
    "#Set regularization parameter lambda to 1\n",
    "regularizacao = 1\n",
    "\n",
    "# Compute and display initial cost and gradient for regularized logistic regression\n",
    "cost, grad = cost_function_reg(initial_theta, it, y, regularizacao)\n",
    "\n",
    "#def decorated_cost(theta):\n",
    "#    return cost_function_reg(theta, it, y, l)\n",
    "\n",
    "#cost_function_reg(theta, it, y, l)\n",
    "\n",
    "#print fmin_bfgs(decorated_cost, initial_theta, args=(it, y, l), maxfun=400)\n",
    "\n",
    "cost, grad"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1.4 Esboço da fronteira de decisão\n",
    "\n",
    "Nessa parte, você deve esboçar (plotar) a fronteira de decisão que foi aprendida\n",
    "para separar os exemplos positivos dos negativos. Crie uma arquivo de nome\n",
    "**``plotDecisionBoundary.py``**, para criar esse gráfico que traça o limite da decisão\n",
    "não-linear. Seu gráfico deve ser semelhante ao apresentado na **_Figura_** abaixo.\n",
    "\n",
    "![ScatterBoundaryPlot](scatter_boundary.jpg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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vjZCdnYfBg4fDZnOgqqoCu3dvg88X+e2DHY5MzJp1FQoLT8f+/d9ixYpX4PN5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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11f412630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Plot Boundary\n",
    "l = 1\n",
    "m, n = X.shape\n",
    "y.shape = (m, 1)\n",
    "it = map_feature(X[:, 0], X[:, 1])\n",
    "theta = ones(shape=(it.shape[1], 1))\n",
    "\n",
    "u = linspace(-1, 1.5, 50)\n",
    "v = linspace(-1, 1.5, 50)\n",
    "z = zeros(shape=(len(u), len(v)))\n",
    "for i in range(len(u)):\n",
    "    for j in range(len(v)):\n",
    "        z[i, j] = (map_feature(array(u[i]), array(v[j])).dot(array(theta)))\n",
    "\n",
    "z = z.T\n",
    "contour(u, v, z)\n",
    "title('lambda = %f' % l)\n",
    "xlabel('Microchip Test 1')\n",
    "ylabel('Microchip Test 2')\n",
    "legend(['y = 1', 'y = 0', 'Decision boundary'])\n",
    "show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "#load the dataset\n",
    "data2 = np.loadtxt('am-T2-dados/ex2data2.txt', delimiter=',')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [],
   "source": [
    "#y = np.c_[data2[:,2]]\n",
    "y = data2[:,2]\n",
    "y.shape = (y.size, 1)\n",
    "X = data2[:,0:2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(118, 1)\n"
     ]
    }
   ],
   "source": [
    "print(y.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(118, 28)"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#it = map_feature(X[:, 0], X[:, 1])\n",
    "\n",
    "X_feature = map_feature(X[:, 0], X[:, 1])\n",
    "X_feature.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def costFunctionReg(theta, reg, X, y):\n",
    "    m = y.size\n",
    "    h = sigmoid(X.dot(theta))\n",
    "    J = -1*(1/m)*(np.log(h).T.dot(y)+np.log(1-h).T.dot(1-y)) + (reg/(2*m))*np.sum(np.square(theta[1:]))\n",
    "    \n",
    "    if np.isnan(J[0]):\n",
    "        return(np.inf)\n",
    "    return(J[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def gradientReg(theta, reg,  X, y):\n",
    "    m = y.size\n",
    "    h = sigmoid(X.dot(theta.reshape(-1,1)))\n",
    "      \n",
    "    grad = (1/m)*X.T.dot(h-y) + (reg/m)*np.r_[[[0]],theta[1:].reshape(-1,1)]\n",
    "        \n",
    "    return(grad.flatten())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.69314718055994529"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "initial_theta = np.zeros(X_feature.shape[1])\n",
    "costFunctionReg(initial_theta, 1, X_feature, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,\n",
       "        0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,\n",
       "        0.,  0.])"
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "initial_theta"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## 1.3 Visualização de J(ø)\n",
    "\n",
    "Para melhor entender a função de custo, você irá nessa parte do trabalho plotar o custo sobre \n",
    "uma grade bidimensional de valores de 0 e de 1. Para isso, você deve usar sua implementação da função **computarCusto**.\n",
    "\n",
    "O código que você deve implementar deve gerar um array bidimensional de valores de J(ø). Os valores gerados pelo seu código devem estar na faixa a seguir: -10;0;+10 e -1;+4. Utilize incremento de 0.01 para gerar os valores de 0 e de 1.\n",
    "\n",
    "A seguir, usando a função _matplotlib.pyplot.contour_ da biblioteca matplotlib, produza um gráfico de curvas de contorno (contour plot). Também\n",
    "utilizando a biblioteca matplotlib, crie um gráfico da superfície correspondente a J(ø)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from scipy.optimize import minimize\n",
    "\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "\n",
    "pd.set_option('display.notebook_repr_html', False)\n",
    "pd.set_option('display.max_columns', None)\n",
    "pd.set_option('display.max_rows', 150)\n",
    "pd.set_option('display.max_seq_items', None)\n",
    " \n",
    "#%config InlineBackend.figure_formats = {'pdf',}\n",
    "%matplotlib inline\n",
    "\n",
    "import seaborn as sns\n",
    "sns.set_context('notebook')\n",
    "sns.set_style('white')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def predict(theta, X, threshold=0.5):\n",
    "    p = sigmoid(X.dot(theta.T)) >= threshold\n",
    "    return(p.astype('int'))\n",
    "\n",
    "def loaddata(file, delimeter):\n",
    "    data = np.loadtxt(file, delimiter=delimeter)\n",
    "    print('Dimensions: ',data.shape)\n",
    "    print(data[1:6,:])\n",
    "    return(data)\n",
    "\n",
    "def plotData(data, label_x, label_y, label_pos, label_neg, axes=None):\n",
    "    # Get indexes for class 0 and class 1\n",
    "    neg = data[:,2] == 0\n",
    "    pos = data[:,2] == 1\n",
    "    \n",
    "    # If no specific axes object has been passed, get the current axes.\n",
    "    if axes == None:\n",
    "        axes = plt.gca()\n",
    "    axes.scatter(data[pos][:,0], data[pos][:,1], marker='+', c='k', s=60, linewidth=2, label=label_pos)\n",
    "    axes.scatter(data[neg][:,0], data[neg][:,1], c='y', s=60, label=label_neg)\n",
    "    axes.set_xlabel(label_x)\n",
    "    axes.set_ylabel(label_y)\n",
    "    axes.legend(frameon= True, fancybox = True);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "Input z must be a 2D array.",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-99-04dbf6a05529>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m     23\u001b[0m     \u001b[0mh\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msigmoid\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX_feature\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mres2\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     24\u001b[0m     \u001b[0;31m#h = h.reshape(xx1.shape)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 25\u001b[0;31m     \u001b[0maxes\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mflatten\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcontour\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mxx1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mxx2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mh\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;36m0.5\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlinewidths\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcolors\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'g'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m;\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     26\u001b[0m     \u001b[0maxes\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mflatten\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mset_title\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'Train accuracy {}% with Lambda = {}'\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mformat\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mround\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0maccuracy\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdecimals\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mC\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/anaconda/lib/python3.6/site-packages/matplotlib/__init__.py\u001b[0m in \u001b[0;36minner\u001b[0;34m(ax, *args, **kwargs)\u001b[0m\n\u001b[1;32m   1896\u001b[0m                     warnings.warn(msg % (label_namer, func.__name__),\n\u001b[1;32m   1897\u001b[0m                                   RuntimeWarning, stacklevel=2)\n\u001b[0;32m-> 1898\u001b[0;31m             \u001b[0;32mreturn\u001b[0m \u001b[0mfunc\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0max\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1899\u001b[0m         \u001b[0mpre_doc\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0minner\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__doc__\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1900\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mpre_doc\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/anaconda/lib/python3.6/site-packages/matplotlib/axes/_axes.py\u001b[0m in \u001b[0;36mcontour\u001b[0;34m(self, *args, **kwargs)\u001b[0m\n\u001b[1;32m   5823\u001b[0m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcla\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   5824\u001b[0m         \u001b[0mkwargs\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'filled'\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mFalse\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 5825\u001b[0;31m         \u001b[0mcontours\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmcontour\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mQuadContourSet\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   5826\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mautoscale_view\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   5827\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0mcontours\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/anaconda/lib/python3.6/site-packages/matplotlib/contour.py\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, ax, *args, **kwargs)\u001b[0m\n\u001b[1;32m    862\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_transform\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mkwargs\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'transform'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    863\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 864\u001b[0;31m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_process_args\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    865\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_process_levels\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    866\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/anaconda/lib/python3.6/site-packages/matplotlib/contour.py\u001b[0m in \u001b[0;36m_process_args\u001b[0;34m(self, *args, **kwargs)\u001b[0m\n\u001b[1;32m   1427\u001b[0m                 \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_corner_mask\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmpl\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrcParams\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'contour.corner_mask'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1428\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1429\u001b[0;31m             \u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mz\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_contour_args\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1430\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1431\u001b[0m             \u001b[0m_mask\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mma\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mgetmask\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mz\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/anaconda/lib/python3.6/site-packages/matplotlib/contour.py\u001b[0m in \u001b[0;36m_contour_args\u001b[0;34m(self, args, kwargs)\u001b[0m\n\u001b[1;32m   1506\u001b[0m             \u001b[0margs\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1507\u001b[0m         \u001b[0;32melif\u001b[0m \u001b[0mNargs\u001b[0m \u001b[0;34m<=\u001b[0m \u001b[0;36m4\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1508\u001b[0;31m             \u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mz\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_check_xyz\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1509\u001b[0m             \u001b[0margs\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1510\u001b[0m         \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/anaconda/lib/python3.6/site-packages/matplotlib/contour.py\u001b[0m in \u001b[0;36m_check_xyz\u001b[0;34m(self, args, kwargs)\u001b[0m\n\u001b[1;32m   1540\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1541\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mz\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mndim\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1542\u001b[0;31m             \u001b[0;32mraise\u001b[0m \u001b[0mTypeError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Input z must be a 2D array.\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1543\u001b[0m         \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1544\u001b[0m             \u001b[0mNy\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mNx\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mz\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mTypeError\u001b[0m: Input z must be a 2D array."
     ]
    },
    {
     "data": {
      "image/png": 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JJEuozS7HbiuJdWtF831pbVWBFWcEAAAAABAeU7votwWR6krekhLqWOwr2lwuV70KDkSH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\nAAAA4AD/H4U0fwPMzM4gAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x120026be0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(1,3, sharey = True, figsize=(17,5))\n",
    "\n",
    "# Decision boundaries\n",
    "# Lambda = 0 : No regularization --> too flexible, overfitting the training data\n",
    "# Lambda = 1 : Looks about right\n",
    "# Lambda = 100 : Too much regularization --> high bias\n",
    "\n",
    "for i, C in enumerate([0, 1, 100]):\n",
    "    # Optimize costFunctionReg\n",
    "    res2 = minimize(costFunctionReg, initial_theta, args=(C, X_feature, y), method=None, jac=gradientReg, options={'maxiter':3000})\n",
    "    \n",
    "    # Accuracy\n",
    "    accuracy = 100*sum(predict(res2.x, X_feature) == y.ravel())/y.size    \n",
    "\n",
    "    # Scatter plot of X,y\n",
    "    plotData(data2, 'Microchip Test 1', 'Microchip Test 2', 'y = 1', 'y = 0', axes.flatten()[i])\n",
    "    \n",
    "    # Plot decisionboundary\n",
    "    x1_min, x1_max = X[:,0].min(), X[:,0].max(),\n",
    "    x2_min, x2_max = X[:,1].min(), X[:,1].max(),\n",
    "    xx1, xx2 = np.meshgrid(np.linspace(x1_min, x1_max), np.linspace(x2_min, x2_max))\n",
    "    \n",
    "    h = sigmoid(X_feature.fit_transform(np.c_[xx1.ravel(), xx2.ravel()]).dot(res2.x))\n",
    "    h = h.reshape(xx1.shape)\n",
    "    axes.flatten()[i].contour(xx1, xx2, h, [0.5], linewidths=1, colors='g');       \n",
    "    axes.flatten()[i].set_title('Train accuracy {}% with Lambda = {}'.format(np.round(accuracy, decimals=2), C))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2. Regressão Linear com Múltiplas Variáveis\n",
    "\n",
    "\n",
    "Nessa parte do trabalho, você irá implementar a regressão linear com múltiplas variáveis para predizer \n",
    "o preço de venda de imóveis. O arquivo ex1data2.txt contém informações acerca de preços de imóveis. \n",
    "A primeira coluna corersponde ao tamanho do imóvel (em _pés quadrados_). A segunda coluna corresponde à\n",
    "quantidade de dormitórios no imóvel em questão. A terceira coluna corresponde ao preço do imóvel.\n",
    "\n",
    "## Visualização dos dados"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Carregando o dataset na forma de txt, porque tem melhor desempenho p/ representação gráfica e \n",
    "# principalmente na vertorização, se comparado ao Dataframe, utilizado na primeira seção deste trabalho.\n",
    "\n",
    "data = np.loadtxt('am-T1-dados/ex1data2.txt', delimiter=',')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Inicializando visualização gráfica\n",
    "plano = plt.figure()\n",
    "plano = plano.add_subplot(111, projection='3d')\n",
    "\n",
    "# Criação dos pontos ('x' vermelhos) para o gráfico\n",
    "for c, m in [('red', 'x')]:\n",
    "    tamanho = data[:, 0] \n",
    "    quartos = data[:, 1] \n",
    "    valor   = data[:, 2] \n",
    "    plano.scatter(tamanho, quartos, valor, c=c, marker=m)\n",
    "\n",
    "\n",
    "# Plotando o Gráfico\n",
    "plano.set_xlabel('Tamanho')\n",
    "plano.set_ylabel('Nº de Quartos')\n",
    "plano.set_zlabel('Valor do Imóvel')\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## 2.1 Normalização das características\n",
    "\n",
    "Se você inspecionar os valores do conjunto de dados fornecido, irá notar que os tamanhos dos imóveis são \n",
    "aproximadamente 1000 vezes maiores que as quantidades encontradas na coluna de quantidade de dormitórios. \n",
    "Sua tarefa nessa parte é implementar uma função denominada normalizarCaracteristica em um arquivo denominado \n",
    "normalizarCaracteristica.py. Essa função deve:\n",
    "\n",
    " - subtrair o valor médio de todas as características do conjunto de dados.\n",
    " - após subtrair a média, dividir cada característica pelos seus respectivos desvios padrões.\n",
    "\n",
    "A sua função **normalizarCaracteristica** deve a matriz de dados X de dados como parâmetro (na forma de um numpy array). Além disso, essa função deve funcionar com conjuntos de dados de variados tamanhos (qualquer quantidade\n",
    "de características / exemplos). Repare que cada coluna da matriz de dados X passada para a função **normalizarCaracteristica** deve corresponder a um característica.\n",
    "\n",
    "**Nota de Implementação**: Ao normalizar as características, é importante armazenar os valores utilizados para a normalização - o valor médio e o desvio padrão utilizados para a normalização. Depois de aprender os parâmetros do modelo, muitas vezes queremos prever os preços das casas que não temos visto antes. Dado um novo valor x (área da sala de estar e número de quartos), devemos normalizar x usando a média e o desvio padrão que nós previamente\n",
    "calculamos a partir do conjunto de treinamento."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def normalizarCaracteristica(X):\n",
    "    '''\n",
    "    Retorna uma versão normalizada de X onde o valor médio de cada característica é 0 \n",
    "    e o desvio padrão é 1. Este é frequentemente um bom passo de pré-processamento \n",
    "    a ser feito ao trabalhar com algoritmos de aprendizado.\n",
    "    '''\n",
    "    valormedio = []\n",
    "    desviopadrao = []\n",
    "    X_Normalizado = X\n",
    "\n",
    "    for i in range(X.shape[1]):\n",
    "        m = np.mean(X[:, i])\n",
    "        s = np.std(X[:, i])\n",
    "        valormedio.append(m)\n",
    "        desviopadrao.append(s)\n",
    "        X_Normalizado[:, i] = (X_Normalizado[:, i] - m) / s\n",
    "\n",
    "    return X_Normalizado, valormedio, desviopadrao"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.2 Gradiente descendente\n",
    "\n",
    "Anteriormente, você implementou o GD em uma regressão linear univariada. A única diferença agora é que há mais uma característica na matriz de dados X. A função de hipótese h(x) e a atualização dos gradientes em lote permanecem inalteradas. Você deve implementar código nos arquivos denominados **computarCustoMulti.py** e **gdmulti.py** para implementar a função de custo e o algoritmo GD para regressão linear com múltiplas variáveis, respectivamente. Se o seu código na parte anterior (variável única) já provê suporte a múltiplas variáveis, você também pode reusá-lo aqui. Se assegure de que o seu código dá suporte a qualquer número de características e está bem vetorizado."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def computarCustoMulti(X, y, theta):\n",
    "    '''\n",
    "    Função que computa o custo para Regressão Linear com múltiplas variáveis.\n",
    "    '''\n",
    "    # Número do conjunto de treinamento\n",
    "    m = y.size\n",
    "    J = (1 / (2 * m)) * (X.dot(theta) - y).T.dot(X.dot(theta) - y)\n",
    "    return J"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def gradienteDescendenteMulti(X, y, theta, alpha, iteracoes):\n",
    "    '''\n",
    "    Essa função calcula o gradiente descendente conforme o Theta, e com\n",
    "    etapas de iteracoes gradiente mediante a taxa de aprendizado em Alpha.\n",
    "    '''\n",
    "    m = y.size\n",
    "    J = np.zeros(shape=(iteracoes, 1))\n",
    "\n",
    "    for i in range(iteracoes):\n",
    "        hipotese = X.dot(theta)\n",
    "        \n",
    "        for it in range(theta.size):\n",
    "            temp = X[:, it]\n",
    "            temp.shape = (m, 1)\n",
    "\n",
    "            errors_x1 = (hipotese - y) * temp\n",
    "            theta[it][0] = theta[it][0] - alpha * (1.0 / m) * errors_x1.sum()\n",
    "\n",
    "        J[i, 0] = computarCustoMulti(X, y, theta)\n",
    "\n",
    "    return J"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X = data[:, :2]\n",
    "y = data[:, 2]\n",
    "\n",
    "# Tamanho do conjunto de treinamento\n",
    "m = y.size\n",
    "y.shape = (m,1)\n",
    "\n",
    "# Normalizando X, obtendo Média e Desvio-padrão\n",
    "x, media, desviopadrao = normalizarCaracteristica(X)\n",
    "\n",
    "# Adicionando uma coluna de 1's ao novo X\n",
    "Xnovo = np.ones(shape=(m, 3))\n",
    "Xnovo[:, 1:3] = x\n",
    "\n",
    "# Atributos para a função GradienteDescendenteMulti\n",
    "iteracao = 100           # Número de repeticões p/ o algoritmo\n",
    "alpha = 0.01             # Taxa de aprendizado\n",
    "\n",
    "# Inicializando o Theta p/ execução da função GradienteDescendenteMulti\n",
    "theta = np.zeros(shape=(3, 1))\n",
    "J = gradienteDescendenteMulti(Xnovo, y, theta, alpha, iteracao)\n",
    "\n",
    "plot(np.arange(iteracao), J)\n",
    "xlabel('Iteracões')\n",
    "ylabel('Função de Custo')\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3. Regressão Logística\n",
    "\n",
    "Nessa parte do trabalho, você irá implementar a regressão logística. Em particular,\n",
    "você irá criar uma classificador para predizer se um estudante será admitido em uma \n",
    "universidade, com base nos resultados de duas avaliações. Suponha que estão disponíveis \n",
    "dados históricos acerca de realizações passadas dessas avaliações, e que esses dados \n",
    "históricos podem ser usados como conjunto de treinamento. Para cada exemplo desse conjunto \n",
    "de treinamento, temos as notas das duas avaliações e a decisão acerca do candidato \n",
    "(aprovado ou reprovado). \n",
    "\n",
    "Sua tarefa é construir um modelo de classificação que provê uma estimativa da probabilidade \n",
    "de admissão de um candidato, com base na notas que ele obteve nas duas avaliações. \n",
    "\n",
    "O arquivo **ex2data1.txt** contém os dados a serem usados nessa parte do trabalho."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.1 Visualização dos dados\n",
    "\n",
    "Antes de começar a implementar qualquer algoritmo de aprendizado, é adequado\n",
    "visualizar os dados, quando possível. Nessa parte do trabalho, você deve\n",
    "carregar o arquivo com o conjunto de treinamento e plotar (i.e., produzir um\n",
    "gráfico) os pontos de dados. O resultado dessa tarefa deve ser um gráfico similar\n",
    "ao apresentado na _Figura_ abaixo.\n",
    "\n",
    "![Boundary.png](Boundary.png)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# carregando os dados \n",
    "data = np.loadtxt('am-T1-dados/ex2data1.txt', delimiter=',', usecols=(0,1,2), unpack=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Transportando matriz\n",
    "X = np.transpose(np.array(data[:2]))\n",
    "y = np.transpose(np.array(data[2:]))\n",
    "\n",
    "# Tamanho do conjunto de treinamento\n",
    "m = y.size\n",
    "\n",
    "# Adicionando uma coluna de 1's ao novo X\n",
    "X = np.insert(X,0,1,axis=1)\n",
    "\n",
    "# Classificando a amostra em Positiva (data[:, 2]=1) e Negativa(data[:, 2]=0)\n",
    "X_Admitted  = np.array([X[i] for i in range(X.shape[0]) if y[i] == 1])\n",
    "X_Nadmitted = np.array([X[i] for i in range(X.shape[0]) if y[i] == 0])\n",
    "\n",
    "plt.figure(figsize=(16,8))\n",
    "plt.plot(X_Admitted[:, 1], X_Admitted[:, 2],'k+',label='Admitted')\n",
    "plt.plot(X_Nadmitted[:, 1], X_Nadmitted[:, 2],'yo',label='Not admitted')\n",
    "plt.title('Gráfico Decision Boundary p/ admissão de candidato', fontsize=18, fontweight='bold')\n",
    "plt.xlabel('Exam 1 Score', fontweight='bold')\n",
    "plt.ylabel('Exam 2 Score', fontweight='bold')\n",
    "plt.legend()\n",
    "plt.grid(False)    \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.2 Implementação\n",
    "\n",
    "### 3.2.1 Função sigmoide\n",
    "\n",
    "Como primeiro passo nessa parte, implemente a função em Python que calcula\n",
    "o valor da função **sigmoide**. Defina essa função em um arquivo denominado\n",
    "**_sigmoide.py_**, de tal forma que ela possa ser chamada de outras parte do seu\n",
    "código. Após finalizar sua implementação, você pode verificar sua corretude:\n",
    "\n",
    " - Para a sigmoide(0), o valor retornado deve ser 0.5. \n",
    " - Para valores muito grandes positivos (ou negativos), ela retornará um valor muito próximo de 1 (ou de 0). \n",
    "\n",
    "O seu código também deve funcionar com vetores (i.e., **o seu código deve estar vetorizado**). Em particular, se\n",
    "uma matriz for passada, o seu código deve aplicar a função sigmoide a cada componente."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def sigmoid(x):\n",
    "    '''\n",
    "    A função sigmoid\n",
    "    '''\n",
    "    g = np.array([x]).flatten()\n",
    "    s = 1 / (1 + np.exp(-g))\n",
    "    return s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "print('\\t ###########################  Teste para função sigmoid(0)  ###########################\\n')\n",
    "print('\\t O Valor da Sigmoid(0) é', sigmoid(0))\n",
    "print('\\t O Valor da Sigmoid([0,1,2,3000]) é', sigmoid(np.array([0,1,2,3000])))\n",
    "print('\\t ######################################################################################\\n')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Exibindo o gráfico da função Sigmoid\n",
    "X_teste = np.arange(-6,6,.5)\n",
    "plt.plot(X_teste, sigmoid(X_teste))\n",
    "plt.title(\"Função Sigmoid\", fontsize=18, fontweight='bold')\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.2.2 Função de custo e gradiente\n",
    "\n",
    "Agora, você deverá implementar a função de custo para a regressão logística.\n",
    "Essa função deve retornar o valor de função de custo e o gradiente. Implemente\n",
    "esse código em um arquivo denominado funcaoCustoRegressaoLogistica.py.\n",
    "Lembre-se de que o gradiente é um vetor com o mesmo número de elementos que ø.\n",
    "\n",
    "Uma vez que tenha implementado essa função, realize uma chamada usando\n",
    "o valor inicial de ø. Você deve confirmar que o valor produzido é aproximadamente 0.693."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def custoJ(theta, X, y):\n",
    "    '''\n",
    "    A função custoJ retorna o valor de função de custo:\n",
    "        X é uma matrix com n-colunas e m-linhas\n",
    "        y é um vetor com m-linhas\n",
    "        theta é um vetor n-dimensional\n",
    "        \n",
    "    Obs.: Será utilizada para facilitar o cálculo de minimização. \n",
    "    '''\n",
    "    m = len(y)\n",
    "    H = sigmoid(X.dot(theta).T)\n",
    "    J = -np.sum( y* np.log(H) + (1-y) * np.log(1-H))/m\n",
    "    return J"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def custoRegressaoLogistica(theta, X, y):\n",
    "    '''\n",
    "    A função funcaoCustoRegressaoLogistica retorna o valor de função de custo e o gradiente.\n",
    "        Returna J, gradiente:\n",
    "        \n",
    "        X é uma matrix com n-colunas e m-linhas\n",
    "        y é um vetor com m-linhas\n",
    "        theta é um vetor n-dimensional\n",
    "    '''\n",
    "    \n",
    "    # Calcula o Custo\n",
    "    m = len(y)\n",
    "    H = sigmoid(X.dot(theta).T)\n",
    "    J = -np.sum( y* np.log(H) + (1-y) * np.log(1-H))/m\n",
    "\n",
    "    # Calcula o Gradiente\n",
    "    erro = H-y\n",
    "    gradiente = []\n",
    "    for i in range(len(X.columns)):\n",
    "        gradiente.append(np.sum(erro*(X.iloc[:,i]))/m)\n",
    "    \n",
    "    return J, gradiente"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.2.3 Aprendizado dos parâmetros\n",
    "\n",
    "Para a regressão logística, o objetivo é minimizar J(ø) com relação ao vetor\n",
    "de parâmetros ø. Sendo assim, nessa parte você deve implementar uma função\n",
    "em Python para encontrar o vetor ø que minimiza a função de custo. Utilize a\n",
    "função **funcaoCustoRegressaoLogistica** que você implementou previamente."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from scipy import optimize\n",
    "\n",
    "def minimizar(theta, X, y):\n",
    "    '''\n",
    "    A função minimizar J(ø) com relação ao vetor de parâmetros ø\n",
    "    '''\n",
    "    minimo = optimize.fmin(func=custoJ, x0=theta, args=(X, y), maxiter=1000, full_output=True)\n",
    "    return minimo[0], minimo[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Exame1</th>\n",
       "      <th>Exame2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.051267</td>\n",
       "      <td>0.69956</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.092742</td>\n",
       "      <td>0.68494</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-0.213710</td>\n",
       "      <td>0.69225</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-0.375000</td>\n",
       "      <td>0.50219</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-0.513250</td>\n",
       "      <td>0.46564</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     Exame1   Exame2\n",
       "0  0.051267  0.69956\n",
       "1 -0.092742  0.68494\n",
       "2 -0.213710  0.69225\n",
       "3 -0.375000  0.50219\n",
       "4 -0.513250  0.46564"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Utilizando uma segunda estrutura de dados\n",
    "import pandas as pd\n",
    "\n",
    "dfQA = pd.read_csv('am-T2-dados/ex2data2.txt', names=['Exame1', 'Exame2', 'Admissao'])\n",
    "\n",
    "X = dfQA.iloc[:, :2]\n",
    "y = dfQA.iloc[:, 2]\n",
    "X.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>theta0</th>\n",
       "      <th>Exame1</th>\n",
       "      <th>Exame2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.051267</td>\n",
       "      <td>0.69956</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.0</td>\n",
       "      <td>-0.092742</td>\n",
       "      <td>0.68494</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.0</td>\n",
       "      <td>-0.213710</td>\n",
       "      <td>0.69225</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.0</td>\n",
       "      <td>-0.375000</td>\n",
       "      <td>0.50219</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.0</td>\n",
       "      <td>-0.513250</td>\n",
       "      <td>0.46564</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   theta0    Exame1   Exame2\n",
       "0     1.0  0.051267  0.69956\n",
       "1     1.0 -0.092742  0.68494\n",
       "2     1.0 -0.213710  0.69225\n",
       "3     1.0 -0.375000  0.50219\n",
       "4     1.0 -0.513250  0.46564"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#add a column of ones to the feature matrix X to account for theta 0\n",
    "m = len(y)\n",
    "X.insert(0, \"theta0\",value=pd.Series(np.ones([m])))\n",
    "X.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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NYwPgvOM8B2sP8I+yv3Pq/BkUpxa9NxlZAY2kQq3uX+Qv1LJdSSVx2Ygp/P3E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\n266jO8LptHuo/lO2Vm4JhMt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tQyv5vBMUeOnw/wQNhfa3dfpQ+jvpKafx3nvvUV5ezsiR\nI6mpqWHZsmWsXr2akpISLrzwQg4ePMiGDRu44447mDBhAidPnuSaa67h+PHjHD58mO9973tcf/31\nAY/k+9//PrW1tXg8HlatWgX4WjapVCrGjBnDs88+y+eff86aNWvweDzIssxLL72Ex+Ph0UcfxeFw\noNFoWLVqFbm5ub2eW0iexvDhw0lLG7yTqASho5W0aCUtyfjaVvtnZ7hlNw5PxzyEf+54e9488UZg\ndXos0Kg1zBoxi1kjZtHgaGBr5RY2V26iyupLnp+nkvPaSrQZf2fmRbO4Nnc+l2Tmo1a1hWEDeR2b\nz6PxC4tfVDoWELgD2x0OLy0WX7jN7Q6t/1jf8zpdMRqlViHRkmSUSE3Vo9Oquy0q8Hs8nfM6t41f\nhNVt5ZPagzy06ZuoVCqmZE7l21MeFjmTMHjvvfdYvnw5mZmZ3HHHHVx99dVUVFTw1ltvcfToUQ4e\nPAjA+fPn+da3vsWwYcOYN28e27Zt48yZM/zmN7/h+uuvB3zTVU+dOsWf/vQnKioqsFqtfPrppxQW\nFvLtb3+bDz74AKvVypdffsmqVavIyclh+fLlHDhwgF27dnHrrbdy8803s3PnTn7+85/zy1/+slf7\nQ/qfz87O5qabbmL69OlotW1/7IlcPSWIDRq1pu0CoofUFANnnfU0OZt59dgfgs4df/3YazEVDj/p\nhnRuveA2bsm7lWMNRymu2MTu6l0B0dtZtYOdVTsYZsyiMKeIwtxChhmzUKlUbXmd9J4rldrT/g7f\n5fK2ei3eNuGxe7BZPW2/2zxYrG7srY/9RQdWW295nY7Y7V7sdi/nzjv7/BkB6HTq1oWhGozGizjr\nNiLp3Kj1HiaMm8bvj+8nKUlDiklPsslAmtlIqjmJ9JQk0sxJ6HWRCbENRmpqajh8+HBgAqrVauWL\nL77g4osvBmDy5MkYDL5O21qtlvHjfeOjhw8fjslkwmw243S2/b8mJyfz8MMP81//9V/IssyyZcu4\n4447WLt2Lf/2b//GuHHjuPrqq8nKymLNmjUYjUa+/PJLrrrqKkpLS7nvvvsAX4unZ599NqRzCEk0\nCgsLKSwsDO1TEQxpJLWESWvmUP0hTjWVMnXYVJZMvBdUdMhxRKthYiioVComZ1zE5IyLeOCir7O7\nehfFFRs50egbO1pvr+Odk2/xfyffZuqwSynKnd8lIdxXdDoJnU4ire+9FwFfXsdu97YVC7TL7QTz\ndtoLkm+/0NfruFwyrg55nbbmex9+Xtnr/hpJhcmkbe27pvV1lTbpGZZhau3R5m+Vo2/rx9b6+mST\nDqNB2yXENlh47733eOihh1i6dCkAxcXF/OEPfwiMhPjyyy8DohCK8NbU1HDs2DFeeukljhw5wtq1\na7nuuuuYM2cO3/ve91i1ahW7d+/m17/+Na+88gqpqak8+OCDKIrCuHHjKCkpITc3lwMHDjB6dGjz\n4EMSjUWLFtHY2Ijdbvd1bPV6qaioCOkAgqFJ56S9y+vC6rbywOR/49P6krgJRmeStEnMH72A+aMX\ncKblDJsri9lasZkWdwsKCofqP+VQ/aeYtWbmjiqgKHcBY1NiX4MvSWrMZjVmsxboW04oNdVIQ4MN\nh8PbFkKztXkxHQsL/KXVbirO12CzecBtQHZpQs7reLwKTc0umpr7V0ygVqswJWlDaPYZvCmoyahF\nkhKzyvP999/n5ZdfDjwuKCjgiSeeYP78+dx5553k5eWRlJQU8vsNHz6cysrKQG++7373u2RlZfH4\n44+j1+sxmUzMnDmTG2+8ka997WukpKRgMpmora3loYce4rHHHuONN95ApVLx05/+NKRjhpQI/8Uv\nfsGf//xnPB4P6enp1NTUMGXKFN5+++2QTy7WiER44trh9Dp9JaIeO27ZHRU7wllY55HdHKg9wOaK\nTZTUlaB0alqfl3oBhTlFfGXUXExaU1RsiCT9scPfIXli+iTunXQfklqDze7ktc/WcbKunMLh15Oj\nzwuIjdXmwW7zdPCE2le4WfuQ14kEScau4wzMSVqGZZrQSqpWkdF3GHvgH4dgTtKi1Ya3IHTIL+77\n4IMP2LJlCz/96U95+OGHOXv2LK+88kq0bRMMUvx9ldL0aXhlb6Cc1+6192lWe7TQqLVcMWI2V4yY\nzTn7ObZWbqa4ophaew0ApU1fUtr0Ja8d/SNXjJhNUe58Lsq4uEPyfKDj9wTbt+E3JRl4cMY9/Q4t\nGpN0VFdbWj2bdl0I2hUU+ASn1SOyun2hNasHm92NvQ95HZvdjc3upqa+fzdSep0U1JNp7+n4f5I7\nj0Mw9W043UAj5Oops9nMhAkTOHr0KNdeey1r1qyJtm2CIYCkljCpTYE7dqfHN1rV7rEFnScSazKN\nmSy68HZuvWARX5z/guKKjeyp3h1YA7H97Da2n93GcGM2RblFzMstJMOQGW+zI0IwYdBI2n6HFnVa\nic9nUuUAACAASURBVNQUHakp/buo+vM6lvaejLWtPNpu9+VvbDZvu9CbOxB2s/Qhr+N0eXG67NQ3\n9M9TVM6s6Nd+A4GQRMNsNvO3v/2NSy65hNdff53hw4d3aV4oEEQCvcbXnC9Nn4ZH9mDz2LB77K1t\nM+KHWqXmksxLuCTzEr5+8TfYcXY7myuLKW36EoBaew3rTrzJWyfWcVlWPkW58ykyz42rzYONjnmd\nviPLCjq9luoqS1uxQKunY7fL2OxeTp1u4lR5E1abG40kYTLqUBQVVqsbi80Vs/U6iUxIOY2amho+\n/PBDli5dyjPPPMPOnTt56KGHuPHGG2NhY78QOY3BZYcvjGXH5rHj8Nh7HY0bq3xCeXM5mys2se3s\nVixuS0cb9KnMHVlAYe58RieHVpkSDQZybiWWNpR8XsO69Ye7bL/7linkX5wdWK/jtPs8Hpu1nUfT\n2pHA7+l88Mr90T6VuBGSaBw9erTL/IwNGzYEFpgkIkI0Bq8dXtmLxW2hxd3SbQ4k1hcof0+m4opN\nfFZ/qEvy/MLUCRTmFnHlyK+QpA29OiYSJMLFOpZ2lHxew5ZdZdTUW8keZmLenHHkX5zdqw2//v0e\nqussXbaPGG7mu0uv6JMNdxUV9NnugUJI4anvfOc73HPPPTz44IM0NjayYsUKysvLE1o0BIMXSS2R\nqk8lRZeC3WMPeCDxTKL7+3nNGXkl9fY6tlRsZmvVFmqsvuT5yaYTnGw60S55voDJ6ZPFIrgI09lb\nqK6zBB77haM7ukua9zeZPlgJqdzjr3/9K0ePHmXx4sXceeedXHbZZbzzzjvRtk0g6BGVSkWSNokM\nQya55lyGG4dj0phQE98L8TBjFrdPuJM/3PQyP565nCtHfsXXzwlfufHWyi08uWc5/7n1u7z35bs0\nOBp6eUdBqGzZVRZ8++7g29uTPSx4+XR32wcasiyzfPly7r77bu677z7Ky/sXjQnJ01AUBa1WG1jc\np1KpRIt0QcJh0BgwaAwoSgZao4ylubrLdL9YolapmTpsKlOHTcXiamF71XY2n9lEWUsZANW2Kt44\n/hfWnXiTaVnTKMpdQH7WNNHXKQzC8RbmzRkXNKcxb/a4cM3qFx9tOckf1n1C6ekG8saks/TuaVw7\n78J+v9/HH3+My+Vi3bp1lJSU8Mwzz/Diiy/2+X1C+nbedNNNLFmyhKeeeorm5mZWrlzJBx98ILwN\nQUKiUqlI0acwyqTG6rbS5GqKq3gAmHXJXD/2Bq4fewOnmkoprtjEjrPbsXqsyIrMgdoDHKg9QKou\nlaty5lGUO59R5pze31jQgexhpqB5iVC8BX/4asvudvmQ2eN6DWtFg4+2nOTxZzcGHp8sOx943F/h\nOHDgAAUFvlxLfn4+hw93FchQ6FE0/vKXv3DPPffw8ssvo9Vq0Wg0ZGRk8Ktf/YqFCxf264ACQaxQ\nqVSYdWZMWhMtrmaaXc3IvdZdRZ/xqXmMT83j3sn3sa9mH5sqNnLknO8PuMnVxPun1vP+qfVMSp9E\nUe4CZo+YjUET/Xbyg4FwvYX8i7PjIhKd+cO6T4Juf+Wtkn6LhsViwWw2Bx5LkoTH40Gj6Ztn2+Or\n3377be655x4uvvhiFi1axLvvvht4Tqcb3KseBYMHn+eRiklrxuq20OK2xN3zAN+s76+MmstXRs2l\nxlbD5opitlRu5rzjHADHGo5xrOEYr37+B+aMvJKi3PlMSJsokuc9kEjeQjiUng6e5+pueyiYzWas\n1rYwnSzLfRYM6EU02lfjhlCZK2jH7k8q+XDjCSprWsjJTmbhggnMnpYY4YahOsZTUkuk6FNJ1qVg\n89hodjVHrfdVX8lOyubuiYu5c8KdHKo/xOaKYvbV7MWr+NqsFFdsorhiEzmmHApz51OQcxVpejHj\nJhiJ4i2EQ96YdE6WnQ+6vb9Mnz6d4uJibrzxRkpKSpg4cWK/3idkmRF3N6Gz+5NK1r5+IPC4oqo5\n8DjewtHfMZ6DSWhUKhUmra91icPjoNnVhCPOK879qFUS+VnTyM+aRrOrme2V2yiu2MgZyxkAKq2V\n/PnYa7x5/C9MHz6dwtwF5A/LR1KH12BPkFgsvXtah5yGn6/fld/v97zmmmvYsWMHixcvRlEUVq9e\n3a/36VE0hFD0jw83ngi+fdOJuIvGjOEz2T1sF5/VH+L5Q7/pMsZzxvCZXfaJxLxolUqFRqNGI6mR\n1Cqk1t81kjowO8Hvy6pVvvbYapUKlUqF/2vY/ndF8Xm/3TnAw4aZMRk0XV7j8cp4PDJuj4yiKJhl\nHZmkYHfbaXQ0YffYA8cCX+sJRQGFtvdRZAU5Bp53ii6FG8cv5IZxN1La9KUveV61HbvHjlfxsq9m\nH/tq9pGuT+eqnHkU5s5npKl/86YFiYU/b/HKWyWB6qmv35UfVvWUWq1m5cqVYdvW44rwKVOmkJ3t\nc/NqamoCvyuKQl1dHZ999lnYBkSLeK4IX/ro+yhy149VLan4/c9ujokNPdH5gg/0OPe5/eunDruU\nh6Z+h5ePvMSh+k+Zlp3Pj658lCS9b6JdZoaJujoLKhWoWwVCI6kDI0RjRVZWMnV1LX3ez+Fx0uho\nxOqy9fpaj1fG65XxehXcHi9uj2/WjMcj45WVqKyAdnqd7KneTXHFJr44/3mX5y9Kv4ii0Qu4POty\nTjQeJ3/49CG3IjwRbBjMK8J7FI3Kyp6ndOXkJEaMPhjxFI2fPLeZiqquDR1zR6Xw1PcLu32fcEJA\nfhv8d/Tqdl6iWq1CrfbdtUuS7w7eIdu5b71vephKBW/f8SdSDObA6/zIsoIsK7i8LlZtW8P+swcD\nz83Mmc4ThT9EJ7UVRfT3Yh1pwrXD7XXT6GimxdXSr3yex+NFb9BxtroJl9sbcnfVvlBtrWLd8TfY\n25r7aI9GpcGoMbLogq+y+LI7aG7u37zxSBLNC3ZPrUNiZUN7BrNoSCtWrFjR3ZMpKSk9/iQyFWeb\nYnYso1GH3d6WUE0yajlwqKrL65bcOoXckcE/N38IqLyljBnDZyKpJdxeNy8c+i3/KP87o8wjuTBz\nPAadBr1eQ5JBG+jtn5JsIHdkKgadRGZ6EqnJBlKS9YGfZLM+MBcgyahF0iqs2f1LqizVgRBQefNp\nrhp3ZZeFZb6FnCq0Gg2zc2ew7vD/b+/M45uq0v//SW6Wplm6UejeUnaoWmkFqhTEOggDIyIWqAJ+\nlQFHf3W+X1FkRF8sDgMD6CwKiNsoMiMIKMoi20BpQQqUTaFSoJSWUqCULrRNmqRJ7u+PkNC0aZuk\nNzdp+rz/as7Nvee5J7fnuec5z/Kd9djqcSshE9u6gsrlUmg0rlVs45KOysEIGcgl/lBI5DCyRuiN\nzm2YC4VCBAX6gxEIEKD0g9xfAj+pGCJGAONdRdxRFBIlkrsno66xDmq92rxHY9SCBQsTTNCb9Pj5\n9s/46doR6A2N6CEPg5RxvMY51/j5iaHTcZ/u3pI6pP7u712v0SP/wi10C5YjLFRh8113ydCcQT19\ntwhTm0qDa0wmExYuXIi1a9di27ZtSEpKQmDgPQ+QAwcO4I033sB3330HlmUxaNCgds9pDU8qjahw\nFcK6K1B+W416jR6R4SpkTEhAyuAoiMUMpBIR/CQi+PmJIfMTQe4vQa9uMSiuK8HZyl9QYbiOJwY8\ngjVnV+OX278gJSYZL6dMR6DS31zO8u7k7ycVQSoRQSxmoFLJbGRoDb1Rj8UHlyOv7BQeihyM1eNW\noqi6GHllp3CpqgipsSl2N1X1Rj2W5LyH63X3lGFRdXGL7/uK0rDACBkoJHIoJHKwgFPeVk2fC7Pi\nFcJPKr5bMc78G/r7SeDvJwYjEoA1wWllIhQyuC/kPtzS3kKdvhZKsRKMgIFQKLTKWqO7g59vn8GP\nxTtxta4EMpEM3f27Q8Bz0Sh3TdjfbMu3KoymVFZrMOzBKF5kaA4pDY7Yt28fCgsL8fHHHyM+Ph7/\n/Oc/MX78eABAY2MjXn75ZfznP//B5MmTsXjxYqSlpeGnn35q9Zy28KTSAIDoiAD8dlQfPDshAROf\n6I8HBvRAt2DzKsDy5i+Xia2Tv7+fBCN7PozCqiKcuH4am37diut1N+yagOzh6CR5sPgwNuVvtV5X\nJpYhNTYFl6qKkFd2CtEBUYgPirM5xxlFI5dLsf3cPkSpImyUid6ox8Hiwy2u7S64Vl6WlYdKqoRA\nIIDeqG+RybY59p4LC8K7ez1ikRBiMQOZ1Fx2VCmXWqu/+fuJIZEw1pQ9rZnJhEIG/QP7I7vsIIQC\nIfxEflj+8Eok9UiGAALc1NyEwWQACxZl9ddw+PohZF3LQn1jPUJloVCIFXavyzXumrC37btot13d\n0Ii0R3ryIkNzfFlp8Jrkpq0w9suXLyMmJgYBAQEAgKSkJOTl5eHMmTOchL67E6FAANndf3A/iQhS\nCeNSjWEJI8H81DmYuHGatW1+6px2FYYzpMWPBACkxqZYrythJFj46DwcKsm1Hm/KoZJcq8KwKLCF\nj86zKpKm5+0q2I/lh/+BA1dyrN9tqnSaytAZYYQMgmVBCJCqUKO9gzu6Wk5jmIRCgTXholgE+ElF\nUDbJgGE0mb2/LB5gBoMJ9VotNl7aYHOdbwo3Ylq/6eh7Xz9kDv0D9l7MQta1/bhQfQEAUKWtxNbL\n32Lr5W8xKCQBo6Iew5AeQyDxoPnKVTqSOoRwHl6VRlth7PX19VAqldZjcrkc9fX1Loe+q1Qyzj12\nBALz26FEzEAqvWtmkoo6XITegt6gx5Kdy23k/vuJVVg5bgEkovYVR2iost3vAMDUUPsrtalhrbSH\njkdAgAxpvVNt5Fj1zBLsLzyEsf3TrG1pQakY0TsLR4qPY8Wxv+MvY97Ckt1/x+nyMxjRexieThrt\n0L1wgaPj4SphCITBaMBtTRVqtfY33YOD3TtxNRobsfzgalxtKMKQ2ES8mPg81hz7HOcq8rH5ygbM\nTJwJMSPChEG/xYRBv8W12mvYU7QP+4v3o1pbAwDIrzyH/MpzUIjlGBX3KEb3/A16B7vu2tkWAQHc\np0MZ93hffLHpTMv2tL52+3OHDFyzq2B/i/83vUHf4v/NFX7++We89957WL9+vUvn86o02gpjb35M\nrVZDqVS6HPpeW9u2h4TZk0gIEWNWBAKhAMxdLyOhUABGaG6zxAwwQlu3UdZogrZBD22DnhOPoeYm\noPmpc7D00N+QU3gUmVveaddE5W6vpeSQIbhTrQOga9HetN/QUCXeHPoaFjcsR07hUaSumgDA7Gn1\n5tDX7F7DHfDpxcVABn+DELc1VdAa7nkp8VGQKrf0OE6UnMF9PQbh5eSZEAvFeO2Rl7Dq2Kf4pTwf\nF2vOYux9j6Lidh0MRiBKEYHp/adhYtwzOH3rNLKuHcDpilMwsSbUN6qx/dJObL+0E3HKODwa9RiG\nRwxHYaHGIc+k9nCX51Lv2CCkjxvYInVI79igFv15g9tve+wq2I8Fe5Zj94Us6wuj3qDH3J3v4kjx\ncQBwWXF8+umn2LZtG2Qy1xUnr0qjrTD2Xr16oaSkBDU1NfD398eJEycwc+ZMCASCDoe+CwQCiEXm\n1YHZ+4iBRMx4VfCiMyYgb4cPM5u3IRVJEakKR52uDpUN1TCa+MltlRI9BACQHPmgtWaHWChG5tBZ\nOFF2GinRQ8AwQkjEIkjEAPzM//LdWH+EhTyKUb0eQVl1BbKuZiHr2gHc1JgdHYrrivHl+X9h/fmv\n4FcdB2VDf/ixkU4VNeITX0gdYiGtdyp2XzCv1ufufBd/GfMW3t69DEeKj+PhuCFI6+26O29MTAw+\n/PBDvPnmmy5fw6Fyr1xhMpmwaNEiXLx40RrG/uuvv0Kj0WDKlCk4cOAAVq9eDZZlMWnSJDz33HN2\nz+nVq1e7fV26XGENKpNK3KsguHqr3V+UbbPXAJhXII4oDG+Kjyi7WWmzhwHYj+lwtxyeGg8Ta0JV\nQzVE/iZUVrW0tfONIysek4mFTm/AmRtnsatoLw6V/gRds9QqIr0Ciqr+UFT1Q3RQuNMlUL3hLb+z\nxGk0X1kAwMNxQxw2VbfFtWvXMGfOHGzatMml83lVGnzC54ThDRO2N8gAAAFBUmRueaeFma35Ksrd\neMN4BARJcf5qMRoaPRtY54qZTK1XY/+VHPxj39fQysptD7KAvzoa/2/UFCSFPgQhGIfSqpDScI56\nnRqj1k60fs76w1YopB3fI+uo0qDyewSn7C88ZKMg5BI5Fj46Dw9FDraa2boKEpEEEcpwRKoioJQq\nIeQ5LqIjyCVyPNlvLB7Rvoi4yxkIqkwEY7hrBxcAGkUpVua9h9n7f4/Nxf+GVlKBHt3kUCmkd1f2\nnpW/s6M36PH27mU2bW/vXga9wfMxULzGafAJnwFm3hDQxqcMWbnFWLb6MFaty8Oh41ehkEvQM9oc\ncPlAbH8EMsGYkTjVuqJghAxSY1MQHRDF276MN/0mIqEIcok/AvzM2QB0Rn7laitepD38/SU4c7oG\ncnUMgqoegFQXCpOwEQaJOU2OzqjHrxUF+P7CThy7fhxiiRD9w3oiRKW8G2MigIk1R8DzFSPRFp0h\nTqOpaerhuCH4auoqXLp9BUeKj6OgohBpvYd3KKtxbW0t9uzZg/T0dJfOJ6XBAR2doNqahPmSwVGy\ncouxdNVh1NRqwbJATa0Wh45fRXSECj2jAyGXS9FDGt7ioWaEDG+BfYB3KQ0LAoEA/mIZFBI5TKwJ\nep6UR0eURlSYObvBrYp61Gsa0Ss4Fi+NmoRXRk5GgFSFm/W3UKc3mwFva6pwpPQ4NuVvxdU71xDs\nr0LPbpFQKcxpVAKUftBpDTAa2wuLdB+dQWnsvXgQX53cZN3DkElkSOs9HAUVhThSfBxxwdHo0y3e\n5eurVCqXFQZAexqc0BH7uWUSbs78zOEYlRLHiwzOMPtPO3CltKZFe3xMID5eNt4r9hIA79jTaE8G\nnUGHqoZqaBrda2N3p+uviTXhzM2z2H5hNw4WH26xeR6hDMe4PqMxru9o9I+Os8rRaDBCpzNC12iE\nXm9Eo4Efb7POsqfhzjiNjsKry60vk5VbjA0/nENJ2R3ERgYgY0KCQ5P+hh/sR7hv3HbOKaXBFyVl\n9tOztNZOtI5UJEW4Mgxagw5VDVUe3zB3BaFAiMHhD2Bw+AN4XZ+JfZezsP3ibhTcNqf2uF53A5+e\nWofPT6/H8LgheKLnbzA8ZhjEIjHEIgaWsF2jyQSdzogGnQFanQFGowmA49lrfQ17ikEiknhcYQCk\nNDhhb3ahzWrhSmmN9XN7E39nm4RjIwPsrjRiIwM8II1v4CeSIkIZjoZGLaq11Z1SeQCAQiLHxAHj\nMXHAeBRWFWHHxT3YXfhf1OrqYGJNyLlyFDlXjiLQLwBjej+O8X2fsJosGaEQ/jIh/GXmWBODwYhD\neaXYtD3fnOOLhdfGiHQ1Oo87hxfzr29O223fuK39PFmtTbbeOglnTEiw2z71SfvthOPIxH6IUIYj\nXBkGqajz5YBqSu/gePzfsJexLWMD/jzqbQyNNCdPBIAa7R1sPPctpn03G7O2/RE/FPwItd7WfCYS\nMTjw0xWIxQzEIgaMyJyhAQIg+2ixB+6IsEArDQ4oulptt92R1ULGhAS7exreOglbVk4bt90zxU19\n0jFTHOEY/mIZ/MUyqPUaVGtroDN4R/1yV5AwEqTFj0Ra/EhoRXX4Ou8H7Li4BzfrzbEf+RUFyK8o\nwD+PfYTHeo7A+L5j8ECPBAgEApSVm/eDBAIBGIEAzN1X3OoaLQJVftDqDNDpDW4pcEW0DikNDoiP\nCUJB4e0W7Y6sFjrjJDwqJc6r5fMV5BJ/yCX+0DQ2oLqhxiavVWckQhWGFx+chv9JfBYnr5/Bjot7\nkF1yGHpjI7QGHX68tA8/XtqHmIAojOvzBLqF+aPiRkuNEBWuhEohhUohhcnEQqs3oEFrgFbbCCMH\nxa2ItiGlwQEvTnkQb/5lX4t2R1cLNAkTbWFZeWgaG1DVUN2pVx6AefP8ocjBeChyMGp1tdh7OQvb\nL+zGparLAICrd67hoxOfQxgohIyJQUDNQCjqYyGA2Y37t2n38s8JhQL4+4nh7ycGIEOjwYgGrQF6\nvREGozl1vCPR6oTjkNLggNEje6PmTkOnWi0QnQ+L8qjX1+O2uhJG1uRpkTqMSqrCMwMn4JmBE3Dh\ndiF2XNyNvZcPoE5fDxNMUCuLoVYWgzH4I8pwH6YmTcCwxMhWrycWMRArbGOEDAYjtDojtHojRAxt\n43YUitPgAG+LCXDV/ZdrOTyJN8jhThmMJiMqNVWo07efELGjcRq5pcdtsugC5rK3liy6juKoHDqD\nHtklP2HHxd04cb2lk8l93Qfid/3G4LGeI+Evdi7Fd3CwHOW3aqHVGaDVGqB1054IF7mnvBVaafgY\nzYMFnXH/JToPjJBBd0UoFI0KVKhvw2ByT5RzbulxfHpyHY5eO4HMobMgForRaGrEqmOf4mx5PgA4\npTgcQSqSYHSvURjdaxSu193Azot7sfPSHtxSm/cNz976FWdv/Yp/HP0IaT1HYnzfMUjoPsDhTNZi\nkdkjSymXgmVZ6PRG66a6vtFIG+vtQGlEOMCbUlYsW21O8dGcspu1+N3jztcicVUOT+MNcvAhg5gR\nI0CqggmmVvc6OpJGJEzZHSU1pThbno+SmlI8EJaAj/I+x9nyfNzXYxCeGjAOjMCxPEiuyKGUKpEU\nkYj0gU/hvh6D0GhqxLXa6zCxJjSaDLhYaTZpHbiSA51Rh0hVBGRtrD6ayyAQCCASCeEnFUHhb67R\nLhEzYAFrgKEr+HKNcDJPcYA3mUKemP4fmOx4kDCMALu/eo43OTyNN8jBtwx6ox7VDTWobxbz0FHz\nVPOVBQDc12OQdeXhKFylM6nR3sGewgPYcXE3LldfsTnGCBg8EjMUv+s7BkOjHoKoWQ40Z2QwmVg0\naBuhbmiE1sl8Vb5snqJdIR+jswUL8sn+ouwWSQL1Rj32F2V7SCJukTAS9FB0R5QqAnKJP2fXFQvF\neCn5BZu2l5JfcEphcEmgXwCmJEzEVxPX4rMnP8TE/uMhF5vv18gakVNyBHP3LcDT30zD2hP/wrXa\nMpf6EQoFkPtL0D1EjogeSnQL8odCLoFY5HqGWV+AzFMc4E2mEIVcgkPHr7Y4/vL0ZKcz53ZEDk/T\nXI79RdlYfvgfuFRVhNTYFDBCxlqXfVP+VkQowznPwuupsRAJRVBIFPAX+8NgaoRYKnTZPAWYVxof\n5X2OW+oKa1tpbRmSIxMdNk0BHTOT2UMgECBU3g2PxAzF5EFPISYgGvX6ety4GzioaWzAz+XnsPnX\nH3Dqxs8QCgTo0yMOBr3zxhWhUACxmIHMTwylXAKFXAKJiIEAAhjsmLF82TxFSoMDvGGitMjQMzoQ\n0REqlN2sRW29Dj2jA/Hy9GTeNsG9YSzsyRGlisClqiLklZ3CpaoiDItKxpKc96wFo2YkTu1QjQJH\nZOAbkVAEpVSJkAAlquvqYXLBRbepaeq+HoOw4NF5KK0ts+5xOKM4uFYaTREJRegTEo/f9hmNJ3o/\nBpnYH2V1N6wZhG/WlyOn5Aj+fWoLbtTdRLAsEN38Q1wuAy0UCCARM/CXie8WnhJBKBTAaDSBZX1b\nadCeBgd0Rfs533I4Wz/dnhyWlQVftcs98ZvYG6eAICm+PbEHSRGJqNHecUp5WLynmu5hNFUks5Ke\nt+s9Zc9NVxkgwd5zhzn3tmoNg8mIY9dOYOelPThUkgsja5t+PT4oDr/rOwZP9E5DoB935lud3oCR\n9w3m7HreBq00OMDTb5R8yLC/KBtRqgibt3G9UY+DxYdtzDrukMMV05I9ORghg2FRyfjm3HfWttXj\nVrbpbdMR+H4uWhunRVnL8fXP36JXcE/cHzYIRpMReqNjb/zRAZHoLg/FUwPGWRUAI2CQHJmIcEWP\nVhXGpyfX2axEGk2N+ODYp9hxfg+6y0MRHdB6gB5XCAVCxNytFvlU/3EIlgWjUluJ6gZzluZqbQ2O\nlZ3AN/lbUVhVBLnEH+GKsA6X5RUxQkR1890svKQ0OMDXlYYzk7Y75HDFtGRPDr1RjyU57+F63Q1r\nW1F1sfWeuIbv56L1cTqJpPAHMSNxKsSMGAqJHDKRDFqjzqFVR3RAZAsTFCNgWp34W3XTvZmPhO4D\nnXLT5QqZWIb7egzEzJQpuD/4fggAXKstQ6PJABNrQnHNVey5fAA7L+1Bra4OYYoeUEmVLvdHSqMT\nQkqDO5yZtN0hh6XGuEWGb859h+t1N9o0LTWXo6lp6qHIwVg9biWKqout9+QOxcH3c9HaOA2PH4q3\nh79hM05iRgSVVAkWLOc1yy0rEYvi+PHSXtxSVyAp5gG8nDTTY15XgLnmuYoJRGpsCp4Z+BSiVVGo\n1dWiXH0LAKBu1ODMzbPY/Ov3OHPzLBiBENGqSIiEzsVB+7LSoD0NDvCG/QR3y+DIfsD+omw8nTQa\nd6p1Nue1tu/gLGq9GhM3TrN+3jr135BL5Ha/23w8LKulpjI3vad5w/+PExnbkoEvmo/Tocwf0FDb\n+opCZ9ChQlPJeSJETWMDMne+Yf38n2kfQVffsXxZR8+UYed/L6KsvA6RPZQY93jfNnNRNae1OI2S\nmlLsuLgHuwr3oarBttSBUqLAb3qNwu/6jkG/bn0c6mdYv/sdlqmzQSsNDnD0jTIrtxjLVh/GqnV5\nOHT8KhRyCWdusO5+q21vP8AyKV+svIxhEUM4d2l11rTUfDzig+IQoQzHjMSpViVneTOPvmv35hpP\nrEDtjdPlqmLrb2IPkdC86mAEDLQGnblSXgex56Z79U4ZEnvc77Jp6uiZMnz875OorTePaW29Hid/\nuYGw7gpEhakcukZrHlyBfgEYEjkYkwdNRP9ufaE16FBWex0sWOiNepy/fRE/XPgROSVHYDAZEB0Q\n0WahLF9eaZDS4ABHJgdLTqiaWi1YFqip1eLQ8auIjlBxojjcPUG1N2nfM2GdxIXblzl1aXXFMZGZ\nYgAAIABJREFUtGRvPOKD4lp8jxEynMdn2JPBUUeCjtD6OJl/k/ZMcH4iKZRShVMb5fZo1U33Zj6u\nVF91Or7DQlOF0ZRbFfUY9XBPh67RntuvUCBEbGA0ftNrFJ7sNxZBsiCUq2/hjq4WAFDVUI2j1/Lw\nzbmtKKouhkIiR7gyrIXrLimNToi3KQ1354Ryp9JwZNKWMBKkxqbgqroUuSV5Du07OMrB4sPYlL/V\nei2ZWGZju48OiHLIe4pvLDLwFVjY2jhZfhN749QcoUAIhUQOP5EftAatS7Edx6+dxK5L+6xuun4i\nKZIjE3G94QbOlJ1FuKKHS95T/9561m57vUaPCb/p59A1nIkV8Rf74/4egzBpwJN4KMLsQltaew0G\nkxEm1oQrNSXYXbgfP17ah3q9GuGKMCilCgCkNDol3qY0Vq3Ls5s9s7Zeh2kTO27/dOck6eikzQgZ\nPDFoBL44vtF6Lhcura6YlrxJafAVWNjaOP3u/jSEiEOdMsE5kgixNVpz032sfwoCRcEux2mc+OW6\n3ZVGVJiSs5WGPQQCAcIU3TEi9mE8M/ApRKrCUd1wBxUac9bder0ap2/+gs353+OX8nyIGRFG9Bnq\nVB+dCdoI5wBHNjxn/2kHrpTWtGiPjwnEx8vG8yJDR3AkuE5v1GPFsb8jp/Co9TvuDJ5rC29zTuA7\nsLA1OVxh16X/ol+33mg6VbiznkZrWPY0mvPStCSHN8O5SpoImM2zOy/uxa7CfajR3rE5Zlpxk5M+\nvBFeExZqtVq8+uqrePbZZzFr1ixUVVW1+M6XX36J9PR0pKenY9WqVQAAlmWRmpqK6dOnY/r06Xj/\n/ff5FJsTMibYL/3qaElYT5MWP7LF5CZhJDYKY/HB5ThSfBwPRQ7G1qn/xkORg5FXdgqLDy5vkSiw\nqyFhJJifOsembX7qHN6VqbPsL8rG33NX4/NT6xHoFwBGyFj3LD49uQ65pcd5k2VYYiRempaE6HAl\nhEIgOlzplMLgmvigOLw6dDZ+mPo1lqYtwMPRQzscGNgZ4LUI04YNG9C3b1+8+uqr2LlzJ9asWYN3\n3nnHery0tBTbtm3D5s2bIRQKkZGRgccffxwymQyDBg3C2rVr+RSXUyy5n3y1JOyhklzklZ3CiN7D\n8ObQ1yBhJFj46Dzr2zVXbredFb1Rj6WH/mbTtvTQ3zyyCnOG1NgUHLiSg7yyU/hb7mq8Nfw1LDr4\nV+smd3Lkg7zKMywx0mNKojXEjBiPxg3Ho3HDUaG+jQNXDnlaJLfCq3kqMzMTv//975GYmIi6ujpM\nnToVO3futB5vbGxEXV0dgoODAQDPPPMMVq5cifPnz+PTTz+FQqGAn58f3nrrLcTHx7fZF1+miazc\nYny3uwAXiyp5L63aFFdMEFyXhXV3nIYzeJN5qrkjwfzUOVh66G/Wz+5WHB0dC3umteSIB/G/w/4A\nTWODw5vlXJqGXIUvGXw5TsNtSmPz5s1Yt26dTVtISAgWLFiAXr16wWQy4dFHH0VOTk6Lc1mWxYoV\nK6BWq/Huu+8iLy8Pt2/fxtixY3HixAksW7YM3377bZv9GwxGiNyc935vdiHmL9/fon3pvDSMHtnb\nrX07y66C/UjrnQqJyDw57c0uxJ9W7EGd/AoC6u8FLPEte3O5AEBv0GN/4SGM7Z/GmxzuZFfBfizY\nsxwPxw3BynELIBFJoDfoMXfnuzhSfBzvPjHP6++1XqfGqLUTrZ+z/rAVCqkcBqMBFepK1Onar1Xe\nlegb2svTIrgNt5mnLPsSTcnMzIRabdbyarUaKlXLgBydTof58+dDLpdj4cKFAICEhAQwjFkBJCcn\n49atW2BZts20xtXVGq5upVU++ioPBoMJIpEQBsO9t6216/Pw4EB+Xe7aepu8Fw29x/pWu/qrXJR2\n3wONvBRGowmqOrPi6KjszrzV2pOr6VvtnTsNLq9QvGmlkRwyBK8P+yNSY1PursLMK7E3h76GQ2G5\nSA4Z4lZZuVppNH3G52xdbP3NRPCHX6MQFZrbaGwjvqMrrTQQ6v4uPAWvuzaDBw9Gdra5SlpOTg6S\nkpJsjrMsi1deeQX9+vXDu+++a1UUq1atsq5aCgoKEB4e7nIefC4pKbvjVLunSI1NsdmUVuvVyGW3\nQCMvhb86Gor6e6Y+PmW3J1dTM05qbApvsrib9hwJvJXmprXWHBxkYj9EqyI5TTFOeCe8boRnZGRg\n3rx5yMjIgFgstnpBffHFF4iJiYHJZMLx48eh1+tx6JB5M2nOnDmYPXs25s6di+zsbDAMg2XLlvEp\ndqvERgbYdaP1ttKqzTelJ26chsbAGvhXRyP8+mgI2XtmPD5ltycX4Dk3XaIlFgeHpr9Jaw4OAoEA\nIf7BkEvkuKWuaHPVQXReKE6jA1hSgzQ3T83PHM77ZrgjJoimiezq1DrIjjwDxmQ7MXdUdldMIc4k\nInSnHFzjDTJwIYezBbAAs9WgqqHaJn6hK5mnfHkjnNeVhq9hmVy37rmAi0W3PepGuze7EB99ldeq\nJ1Rzl0+lXIrwJ85Dkv8ISsvUHpO9s7qidiXsKYb2TGu06vBdSGl0kFEpcZj85H0efaPMyi3GirVH\nrKudK6U1WLrqsFW+Nl0+H1dhtYcm6LbkWnxwOSkOH8BPJEW0KvJuunGDp8UhOMD3wxe7ABt+OGe3\nfeM2c3tzu7RcIsfCR+dZNzQPleTyKa4Vb5WL4BbLqiMmMBJixnMFmAhuoJWGD1BSdgdCYUtvMosn\nlMWM0NQubdnQ9GSktrfKRbgHv7seVpUNVbijrfW0OISL0ErDB2jN46lpu7e6fHqrXIR7EAgE6OYf\ngnBlmNMlVAnvgJSGD9DZkyESXQ9/sQwxAVEI8HOs4h7hPZCq9wFGpcQhMECGtevzfDIZIuGbWFYd\nComCPKw6EaQ0fITRI3vznrqEILigqYdV87oUhPdB5imCIDyOxcMqUhVBbtZeDikNgiC8Bj+RFFGq\nCATLgrwivxzREjJPER6D63oehG8gEAhw5kwN/vPDGVwuv4HwcCnGPd7X64ovdVVIaRAewZK3y0Lz\nKHai69L02RBBiZulenyy/jQAkOLwAsg8RXiE9qLYia5L82eDMUkg1gfiv/8tI5OVF0BKg/AI9up2\n1Cov4cr1Sps2vVGP/UXZfIlFeAH2ng0BBLhxzYBoVST8xTIPSEVYIKVBeITmUey1yksoD89CXe9s\na2EfS0LD5Yf/4ZTi2F+UDb1Bb9NGyqfz0FaGAzEjRrgyDGGKHhRR7iFIaRAeoXkUu6I+Hv7qaKDb\nzQ5V8bOUkJ27890OKx9n2F90T9lZ0BtIUbmCIxkO5BJ/xAREkZeVB2AWLVq0yNNCuAONRt/+lzhC\nLpfy2l9HZcjKLcay1Yexal0eDh2/CoVcgp7RgbzK0TM6ENERKpTdrEVtvQ7xUUF4/clnIAi4g7yy\nU/jm3He4XnfD6Sp+UaoIXKoqQl7ZSVy4fRnDopKxJOc9q/KZkTgVjJBp/0JOYFFUl6qKkBqbAkbI\nQG/UY1HWcnx9ZgsilOGID4rjtE9n8Ibn0xk5mj8bPaMD8fL05BYOEgKBADKxHxQSOQyswaGIcplM\ngoYG90eeR3Xz3UBbqtzHAVxVaOuIC6qjMjT3WrLAVbXBjo4FF1X89EY9Vhz7O3IKj1rb3FlCtrW6\nIKfLz+DBHom81AVp69nxlQqC7aHWa3BbUwmDqfW6HVS5r+OQecpLsEzmV0prYDKxVhfUrNxiTvvx\nZq+l1qr4NTf7tIeEkeAvY96yaZufOsdtE7clnbulDsjEjdOQV3YKD8cN4U1h8PHseDsWk1WgXwCZ\nrNwIKQ0vga/J3J5nSlvtfNH8bX3r1H9bJ+HFB5c7pTj0Rj3e3r3Mps0V5eMMEkaC+alzbNr+MuYt\nXlJiePOLAN9Y0pFEqSLgJ/LztDg+CSkNL4GvydyR2huegKsqfhblc6T4eIeVjzPYWyW9vXuZWxWV\nBW99EfAkEkaCSFU4usu7cb6H1dUhpeEl8DWZe2vtjbT4kZg3/P9szDkWs8+84f/ncFEmi/KxmIb4\nKCHb2irpSPFxtyoqC976IuANKKVKa90OMllxA3lPcQAX3ikKuQSHjl9t0f7y9GSHPJu49kxxFVfH\nIiu3GBu/voaP1p+y8ehihIxTnkfxQXGIUIbjf0e+CIPO3MYIGaTGpiA6IMotFQEPFh/Gpvyt1lWS\nTCxDamwKrqpLkVuSh+iAKLd6T7X37HQ27ymuEQgE8Bf7Qy7xh1gqQK1a4/Y+yXuqE9JZvac2bjvn\nUiGlzuwh4w6PLr7HY39Rtk2tcwAICJLiu5N7eSld29az05mfDXfIUHTtOiobqmE0Gd3Wjy97T1FI\npRcxKiWuSybra2sjt7OMhz3FIBHxV+u8qz47rqCUKiGXyFHVUI1aXR189L3ZbdCeBuFxaCOX4Buh\nQIhu/iGIVkVCLvH3tDidClIahMehjVzCU4gZMcIUPRCuDKOKgQ5CSoPwON7q0UV0HfzFMkQHRCJU\n3g2MgKbFtqA9DcLjWGzxrjoBEARXqKRKyMX+qGqoQa2u1tPieCW8Kg2tVou5c+eisrIScrkcy5cv\nR3BwsM13lixZglOnTkEuN+cbWrNmDcRicbvnEZ0b2sglvAVGyCBUHgKVVIHbmipoDVpPi+RV8LoO\n27BhA/r27Yuvv/4aTz31FNasWdPiO/n5+fjss8+wfv16rF+/Hkql0qHzCIIL7KY4p1ocXRKpSHov\nqpxMVlZ4HYmTJ08iNTUVADBixAjk5tpG55pMJpSUlGDBggWYOnUqtmzZ4tB5BMEFlhTnTaO4+ajF\nwQekDF1HKVUiJjCaosrv4jbz1ObNm7Fu3TqbtpCQECiVSgCAXC5HXZ1toI9Go8G0adPwwgsvwGg0\nYsaMGUhISEB9fX2b59kjKMgfIhF/OWdCQ5W89eXNMgCdV46ng0Yj9+ZRHCk+jhXH/o6/jHkLS3b/\nHafLz2BE72F4Omk0JCLnPGy8YSx2FezH+0c/QO7No1g5bgEkIgn0Bj3m7jTn6AoIkGFs/zReZGlr\nPPZmF+Jf35xG0dVqxMcE4cUpD2L0yN68ytAWPRAAvUGPW/W3oWls4FiqzoPblEZ6ejrS09Nt2jIz\nM6FWm3PZq9VqqFQqm+MymQwzZsyATGauATxs2DAUFBRAoVC0eZ49qqvdnyrAgrdEunpaBl+Q482h\nr2Fxw3LkFB5F6qoJAMy1ON4c+hruVOsA6NwuA9ek9U7F1jN7kFN4FJlb3rHW+7Dkyro/MJEXOdsa\nj+ZZAQoKb+PNv+xDzZ0GTve6uPhNpFCiUS/AbU1V61HloR3qwqvh1Tw1ePBgZGebl8M5OTlISkqy\nOV5cXIyMjAwYjUY0Njbi1KlTGDRoULvnEQRX2Etx7s5aHFzQnulJIrJf78PVwlTuMHV1tvTuComi\ny9bu4FVpZGRk4NKlS8jIyMA333yDzMxMAMAXX3yB/fv3o1evXpgwYQImT56M6dOnY8KECejTp0+r\n5xEE13BVCIovHN2H4UoZumvfpzNmBRAKhNbaHTJx16ndQQkLOcAbzBDeIENnl6O1sq2uvpXzMRaO\nyBwZFoKym5XW71lw5Z46MkZtjcfsP+3AldKaFu3xMYH4eNl4h+VrD3f+Jmq9GhWaShhNRp9OWEh+\nZARxF64KQfFJa6Vmm07gegN3VREd6c8VfCErgFwiR2xANAL9fDv9DSkNgrgLV4WguMCZfYP2TE/7\nCw9xqgy5MHVl5RZj9p924Inp/8HsP+0wXyNzOOJjAsEwAsTHBHYoNb6nsJSb9WWoCBMHeEORG2+Q\nwRfkiA+Ka1Ee1NlCUB2VwbJvcKmqCKmxKWCEjNUstCl/KyKU4Tby6I16LMl5D9frbljbiqqLrec+\nENsfgUwwZiROtU7sHSlM1V5/rWEZD4unVE2tFiwL1NRqcej4VaQOicGr/zME0ybej9893teh4mPO\nwtfzKZdL3d6Hp6CVBkF4GamxKTbmI7VebWNeSo1NsX63tVKzzU1PafEjW6wEJIzz9T4c7a8tOpun\nFGELJSwkOh1ZucXY8MO95IYZE9yX3NBTfUVH3ofwhFrrvgFgf+O6+T6MxZxmmdgPleRiahh3G8mO\n9NeeIuqMnlLEPUhpEJ2K5kFgV0prrJ+5nsw92VdJaT2MZQPQ8HA+lHdNHfb2DSwTdNNSs5aJ3JEJ\n3Fm46C82MsCupxTVT+kckHmK6FTwadpoqy+uA9ya92USGHEzfD+qau6lq2gtXqQ909Pe7EKbTees\n3GKXZHS0v/bwBU+prgwpDaJTwadpo7Vr/nLnBOcBbk37MgmMuBGxFxp5KcQ1kR1ykc3KLcb85ftx\npbQGJhNrXS11VHF0hFEpcT7hKdVVIaVBdCr4LA3b2jUTAhId3qh2pa96RRE08lL4q6ORInymQy6y\n3rrpPColDh8vG4/dXz2Hj5eNJ4XRiSClQXQq+DRttNbXs08mch7g1rQvVV0f9LgxCuHXR+PZJxMB\nuB4vQpvOBNfQRjjRqeCzNGx7fc1PnWP1bLJ8djUiunlfiUEPYerztvfliotsbGQASm+0LFtKm86E\nq5DSIDodfJaGba2v1hIbdiSVhjvuK2NCAlasPdKinTadCVch8xRBOAkXAW58MSolDkvnpdGmM8EZ\ntNIgOGVvdiE++iqPl2A4T8FFgBufjB7ZGw8O7OFpMQgfgZQGwRlZucVYsfYIDAYTAPcGw3kSvgPq\nCMKbIPMUwRne6t7pDrjK5UQQnQ1SGgRnkHsnQfg+pDQIzuAz8I4gCM9ASoPgDMopRBC+D22EE5wx\nKiUOgQEyrF2f5/bAO4IgPAMpDYJTyL2TIHwbMk8RBEEQDkNKgyAIgnAYUhoEQRCEw5DSIAiCIByG\nlAZBEAThMKQ0CIIgCIchpUEQBEE4DMVpEAQBwJyleMMP53w6rT3RcXhVGlqtFnPnzkVlZSXkcjmW\nL1+O4OBg6/Hz589j6dKl1s9nzpzB6tWrkZqaihEjRiAuLg4AkJiYiNdff51P0QnCp8nKLbamsQd8\nN6090XF4VRobNmxA37598eqrr2Lnzp1Ys2YN3nnnHevxAQMGYP369QCAXbt2oXv37hgxYgRKSkow\naNAgrF27lk9xCR+H3qzv0VZa+646JoR9eN3TOHnyJFJTUwEAI0aMQG5urt3vaTQafPjhh3j77bcB\nAPn5+SgvL8f06dMxa9YsFBUV8SYz4ZtY3qyvlNbAZGKtb9ZZucUelswzUFp7wlHcttLYvHkz1q1b\nZ9MWEhICpVIJAJDL5airq7N77pYtWzBmzBir6So0NBSzZ8/G2LFjceLECcydOxfffvttm/0HBflD\nJGI4uBPHCA1V8taXN8sAdA45vttdAJGo5TvT1j0XMPnJ+ziXYW92If71zWkUXa1GfEwQXpzyIEaP\n7M1ZP47K0Rp940NQWFzVor1PzxBOf09veDa8QYbOjNuURnp6OtLT023aMjMzoVarAQBqtRoqlcru\nudu3b8cHH3xg/ZyQkACGMSuA5ORk3Lp1CyzLQiAQtNp/dbWmo7fgMKGhSlRU2FeAXUmGziTHxaJK\nmEysnfbbnMlvkaH5fkFB4W28+Zd9qLnTwIvpx5Hf5Okx/W1ktDDxiX6cj4cn4UsGX1ZMvJqnBg8e\njOzsbABATk4OkpKSWnynrq4Oer0e4eHh1rZVq1ZZVy0FBQUIDw9vU2EQRHvwWTCqM5TBHZUSh/mZ\nwxEfEwiGESA+JhDzM4fTfgbRAl43wjMyMjBv3jxkZGRALBbj/fffBwB88cUXiImJQVpaGq5cuYLI\nyEib82bPno25c+ciOzsbDMNg2bJlfIpN+CAZExLsvlm7o2BUZ9kvGJUSR0qCaBdelYZMJrMxO1l4\n4YUXrH/ff//9WLNmjc3xgIAAfPLJJ26Xj+g6WCbHjdvOub1gVGxkAK6U1thtJ4jOBgX3EV0Wvt6s\n+VzVEIS7IaVBEG6Gz1UNQbgbUhoEwQO0X0D4CpSwkCAIgnAYUhoEQRCEw5DSIAiCIByGlAZBEATh\nMKQ0CIIgCIchpUEQBEE4DCkNgiAIwmFIaRAEQRAOQ0qDIAiCcBgBy7ItiwoQBEEQhB1opUEQBEE4\nDCkNgiAIwmFIaRAEQRAOQ0qDIAiCcBhSGgRBEITDkNIgCIIgHIaKMDmIVqvF3LlzUVlZCblcjuXL\nlyM4ONh6/Pz581i6dKn185kzZ7B69WqkpqZixIgRiIuLAwAkJibi9ddfd4sMALBkyRKcOnUKcrkc\nALBmzRqIxeJ2z+Naji+//BI7d+4EAIwcORKZmZlgWbbDY2EymbBo0SJcuHABEokES5YsQWxsrPX4\ngQMHsHr1aohEIkyaNAmTJ09u9xxXaO+aO3bswLp168AwDPr27YtFixZBKBRi4sSJUCgUAICoqCgs\nW7bMbTJ8+eWX2Lx5s/W3Wbx4MeLi4ngdi4qKCsyZM8f63fPnz+P1119HRkYGp2Nh4eeff8Z7772H\n9evX27Tz9Vx0CVjCIf71r3+xH3zwAcuyLLtjxw72z3/+c6vf/fHHH9k5c+awLMuyxcXF7EsvvcSb\nDFOnTmUrKytdlp0LOa5evcpOnDiRNRgMrMlkYqdMmcKeP3+ek7HYs2cPO2/ePJZlWfb06dPsH/7w\nB+sxvV7PPv7442xNTQ2r0+nYp59+mq2oqGjzHHfI0dDQwKalpbEajYZlWZZ97bXX2P/+97+sVqtl\nJ0yY0OG+HZGBZVn29ddfZ8+ePevUOe6Qw8KpU6fY6dOnswaDgfOxYFmW/eSTT9jx48ez6enpNu18\nPhddATJPOcjJkyeRmpoKABgxYgRyc3Ptfk+j0eDDDz/E22+/DQDIz89HeXk5pk+fjlmzZqGoqMht\nMphMJpSUlGDBggWYOnUqtmzZ4pTsXMkRFhaGzz77DAzDQCAQwGAwQCqVcjIWTftOTEzEuXPnrMcu\nX76MmJgYBAQEQCKRICkpCXl5eW2e4yptXVMikWDjxo2QyWQAYL3/goICNDQ04MUXX8SMGTNw5swZ\nt8kAmJ+9Tz75BBkZGfj4448dOscdcgAAy7L485//jEWLFoFhGM7HAgBiYmLw4Ycftmjn87noCpB5\nyg6bN2/GunXrbNpCQkKgVCoBAHK5HHV1dXbP3bJlC8aMGWM1CYSGhmL27NkYO3YsTpw4gblz5+Lb\nb791iwwajQbTpk3DCy+8AKPRiBkzZiAhIQH19fUOyc6VHGKxGMHBwWBZFitWrMDAgQPRs2dP3L59\n26WxaEp9fb3VpAEADMPAYDBAJBLZ3KdFtvr6+jbPcZW2rikUCtGtWzcAwPr166HRaPDII4/g4sWL\nmDlzJtLT01FcXIxZs2Zh9+7dLsvR3n2NGzcOzz77LBQKBTIzM5GVlcX7WFg4cOAA+vTpg/j4eACA\nn58fp2MBAE888QSuXbtmVz6+nouuAI2OHdLT05Genm7TlpmZCbVaDQBQq9VQqVR2z92+fTs++OAD\n6+eEhAQwDAMASE5Oxq1bt8CyLAQCAecyyGQyzJgxw/qGO2zYMBQUFEChUDgkO1dyAIBOp8P8+fMh\nl8uxcOFCAK6PRVOa3gtgXl1Z/smbH1Or1VAqlW2e4yrtXdNkMmHlypW4cuUKPvzwQwgEAvTs2ROx\nsbHWvwMDA1FRUYHw8HDOZWBZFs8//7x1shw5ciR+/fVXj4wFAGzbtg0zZsywfuZ6LJyRz53PRVeA\nzFMOMnjwYGRnZwMAcnJykJSU1OI7dXV10Ov1Ng/+qlWrrG/qBQUFCA8Pd2qSdEaG4uJiZGRkwGg0\norGxEadOncKgQYMckp1LOViWxSuvvIJ+/frh3XfftSoKLsZi8ODByMnJAWB2Nujbt6/1WK9evVBS\nUoKamhro9XqcOHECDz74YJvnuEp711ywYAF0Oh3WrFljVeJbtmzBX//6VwBAeXk56uvrERoa6hYZ\n6uvrMX78eKjVarAsi2PHjiEhIcEjYwEA586dw+DBg62fuR6LtuDzuegKUMJCB2loaMC8efNQUVEB\nsViM999/H6Ghofjiiy8QExODtLQ0/PLLL1i7di3WrFljPe/OnTuYO3cuNBoNGIbBggUL0KtXL7fJ\n8Nlnn2HXrl0Qi8WYMGECMjIyWj3PXWNhMpkwZ84cJCYmWs+ZM2cO4uPjOzwWFo+XixcvgmVZLF26\nFL/++is0Gg2mTJli9ZJhWRaTJk3Cc889Z/ccV38DR+RISEjApEmTkJycbFWKM2bMwMiRI/HWW2/h\n+vXrEAgEeOONN2wmUi5lmDJlCr7//nusX78eEokEKSkp+OMf/8j7WEyZMgVVVVV44YUX8MMPP1jP\n0ev1nI6FhWvXrmHOnDnYtGkTtm/fzvtz0RUgpUEQBEE4DJmnCIIgCIchpUEQBEE4DCkNgiAIwmFI\naRAEQRAOQ0qDIAiCcBiKZCF8hmvXrmHMmDEt3CYnT56M5557jnd55s2bh6FDh+Lpp5/mvW+CcBek\nNAifonv37jbxAJ6gvLwcCxcuRG5uLoYOHepRWQiCa0hpED5Pfn4+Zs2ahR07dljTk69ZswbBwcGY\nP38+6urqUFFRgXHjxuGNN97Ad999h4MHD+LWrVu4efMmnn/+eVy/fh1Hjx5FYGAgPvvsM0ilUnz/\n/fdYt24dTCYTBg0ahIULF0IqlWL79u1IS0tDYGCgp2+dIDiHlAbhU9y6dQsTJkywaVuxYgWmTp2K\nFStWoLGxERkZGRgwYAA+//xzjB8/HhMnTkRdXR1GjhyJF198EQBw9uxZbN++HXfu3MFjjz2Gzz77\nDG+//TamT5+OQ4cOITY2Fps2bcLGjRshlUrx/vvv4/PPP8crr7yC3//+9wDM2V8JwtcgpUH4FK2Z\np+Lj4zFp0iT4+flh5cqVAICZM2fi6NGj+Pzzz3Hp0iU0NjaioaEBgDmfkkKhsGZBTUlJAQBERkai\ntrYWx44dQ0lJCSZPngwAaGxsxMCBA/m4RYLwKKQ0iC5BXV0d1Go11Go1ampqEBwcjL/FP+vmAAAB\nD0lEQVT+9a8oLS3F+PHj8fjjj+PIkSOwZNURi8U25zfPfmo0GjF27Fi88847AMyZU41GIz83QxAe\nhFxuiS7B4sWLMW3aNDz77LNYvHgxAOCnn37CzJkzMXbsWNy4cQPl5eUwmUwOXW/o0KHYt28fKisr\nwbIsFi1a1KLuCEH4IrTSIHwKe3sajY2N8PPzw9/+9jdrltMff/wRL730Et58802oVCqEhIQgISHB\nbhEfe/Tv3x+ZmZl4/vnnYTKZMGDAAMyePdsdt0QQXgVluSUIgiAchsxTBEEQhMOQ0iAIgiAchpQG\nQRAE4TCkNAiCIAiHIaVBEARBOAwpDYIgCMJhSGkQBEEQDkNKgyAIgnCY/w9xdJNq8Q/fVwAAAABJ\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b59b358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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FNm3a8M477+Dr68uuXbuYNm0acXFxJCYmEhAQgDGGRo0asW/fPgD27NnDvffe63a8ax4y\n6tixI61bty7zdZnBwcGsXr2aLVu2uF2xiMidZsOGDWVu6G3bti1xcXE89thj9OrVi5CQEO66664b\nXl+dOnX44YcfiI6OxuFw8Je//IXg4GDGjRtHlSpV8Pf357e//S3//u//Tv/+/QkKCsLf358zZ84w\nZMgQxo4dy7vvvovD4bihp1Q7zC/whEBmZrZtYwUHB9o6nifn8IQMyuF5GTwlh10ZgoMDK32M20X3\nIYiICKBCEBERi9tCKCwsZMGCBYwePZqcnBzmzp1LYWGhHdlERMRGbgshPj6e/Px8Dh48iLe3NydP\nnmT8+PF2ZBMRERu5LYTU1FRGjBiBj48P1apVY/r06Rw6dMiObCIiYiO3heBwOCgsLHRdM5uVlaUb\n00REfoXcfh/CwIEDefbZZ8nMzCQxMZHNmzfzpz/9yY5sIiJyg0pLS5k0aRLffvstfn5+TJ48mYYN\nG97UOtwWwpNPPklYWBgpKSmUlJSwYMECmjVrVu7QIiJ3us++OMyb73/F0ZNZhDSoyXN9HuL/tbvP\n/YLXsXnzZgoLC3n//ffZt28f06ZNY8GCBTe1DreFUFhYyMmTJ/H39wcgLS2NtLQ0nnzyyfKlFhG5\ng332xWHGTU9yTR8+ft41fSulsGfPHtq2bQvAgw8+WK6nUrsthEGDBmGMoV69emXmqxBERG7em+9/\nddX5b63ad0uFkJOTQ0BAgGva29ub4uJifHxu/JuS3b4zKyuLDz/8sHwJRUSkjKMns25q/o0KCAgg\nNzfXNV1aWnpTZQA3cJVR69at2bFjB6WlpTefUEREyghpUPOm5t+oVq1akZycDMC+ffto2rTpTa/D\nbX3UrVuX5557znWpqTEGh8OhexFERMrhuT4PlTmHcNmzvR+8pfV26tSJ7du307dvX4wxTJky5abX\n4bYQ/va3v7Flyxbq1q1brpAiIvJPl88TvLVqn+sqo2d7P3jLVxl5eXkRHx9/S+twWwh16tShRo0a\ntzSIiIj80/9rd98tF0BlcFsI//Iv/0LXrl1p1aoVvr6+rvlTp06t1GAiImIvt4XQvn172rdvX2ED\nLlq0iC1btlBUVER0dDQRERGMGTMGh8NBaGgocXFxeHnpqdwiInZzWwhPPfUUFy5cID8/H2MMJSUl\npKenl2uwlJQUvvrqK959913y8/N58803mTp1KjExMURGRuJ0OklKSqJTp07lWr+IiJSf26/QnDVr\nFn//+98pLi6mZs2aZGRkEBYWxgcffHDTg82cOROHw8H3339PTk4Oo0ePZtiwYSQnJ+NwONi8eTPb\nt28nLi7uuuspLi7Bx8f7pscXEZFrc7uHsHHjRr744gsSExMZOnQop0+f5q233irXYFlZWZw+fZqF\nCxeSnp7O0KFDXZexAvj7+5Od7f47UbOy8so1fnl4wnfFekoOT8igHJ6XwVNy6DuVb53bg/V16tQh\nICCA0NBQ0tLSaN26NWfPni3XYDVq1OCRRx7Bz8+PkJAQqlSpUqYAcnNzCQoKKte6RUR+CTalJVFY\nXPZbJwuLC9mUduW9CeWxf/9+BgwYUK5l3RZCQEAA69ato0WLFmzYsIF9+/bx008/lWuwhx9+mG3b\ntmGMISMjg/z8fNq0aUNKSgoAycnJhIeHl2vdIiKeblNaEs5PpzPqo3hXKRQWFzLqo3icn06/5VJY\nsmQJEyZMoKCgoFzLuy2ExMREzp8/T2RkJPXq1cPpdPLSSy+Va7BHH32U+++/n549ezJ06FCcTiex\nsbHMmTOHPn36UFRUROfOncu1bhERT9fhvrb8rlEEO47/N6M+iienIJdRH8Wz4/h/87tGEXS4r+0t\nrb9BgwbMmTOn3Mu7PamclpZ2xfcffPLJJ3Tp0qXcg94qO49VesKxUU/J4QkZlMPzMnhKjl/KOYTL\newQ7jv+3a97vGkUw4wknfj5+txqP9PR0RowYwapVq256Wbd7CMOGDWPp0qUAXLhwgZiYGBYtWnTz\nKUVEBD8fPxK7jC0zL7HL2Aopg1vlthDWrl1LWloaffv2pVevXrRs2ZLVq1fbkU1E5FensLiQ8Z+U\nfdLD+E+mXnGi+XZwWwjGGHx9fV03pjkcDt1JLCJSDj8/XPS7RhFsHfKPMucUbncpuP3N3rVrV+rV\nq8eaNWtYtWoV+/bto2fPnnZkExH5VUk6vM1VBjOecBJQxZ8ZTzhdpZB0eNstj1G/fv1ynT+AG7gx\nbcmSJTRv3hyAWrVq8frrr7Np06ZyDSYicid7vFkH4NLVRpfPGfj5+DHjCSdJh7e5Xr9drrmHsHLl\nSgCaN2/O999/X+a1vXv3Vm4qEZFfqcebdbjiBLKfj99tLwO4TiH8/FlFo0ePLvPa7t27Ky+RiIjc\nFtcshJ/fnvB/b1Vwc+uCiIj8At3Q5UKXHz53rWkREfnlu2Yh6Je+iMid5ZpXGX3//fd06HDpJEdG\nRobrZ2MMmZmZ9qQTERHbXLMQPv30UztziIjIbXbNQqhXr56dOURE5DbTMyhERARQIYiIiEWFICIi\ngApBREQsKgQREQFUCCIiYlEhiIgIoEIQERGLCkFERAAVgoiIWFQIIiICqBBERMSiQhAREUCFICIi\nFhWCiIgAKgQREbGoEEREBFAhiIiIRYUgIiKACkFERCwqBBERAVQIIiJi8bF7wKeeeoqAgAAA6tev\nz5AhQxgzZgwOh4PQ0FDi4uLw8lJPiYjYzdZCKCgowBjD8uXLXfOGDBlCTEwMkZGROJ1OkpKS6NSp\nk52xREQEmw8ZpaWlkZ+fz3PPPcfAgQPZt28fqampREREABAVFcWOHTvsjCQiIhZb9xCqVq3K888/\nT69evTh+/DiDBg3CGIPD4QDA39+f7Oxst+upWfMufHy8KzuuS3BwoG1jXY8n5PCEDKAcnpYBPCOH\nJ2T4JbO1EBo3bkzDhg1xOBw0btyYGjVqkJqa6no9NzeXoKAgt+vJysqrzJhlBAcHkpnpvqTuhBye\nkEE5PC+Dp+SwK8OvuXRsPWS0evVqpk2bBkBGRgY5OTn8/ve/JyUlBYDk5GTCw8PtjCQiIhZb9xB6\n9uzJ2LFjiY6OxuFwMGXKFGrWrMnEiROZNWsWISEhdO7c2c5IIiJisbUQ/Pz8mDlz5hXzV6xYYWcM\nERG5Cl3wLyIigApBREQsKgQREQFUCCIiYlEhiIgIoEIQERGLCkFERAAVgoiIWFQIIiICqBBERMSi\nQhAREUCFICIiFhWCiIgAKgQREbGoEEREBFAhiIiIRYUgIiKACkFERCwqBBERAVQIIiJiUSGIiAig\nQhAREYsKQUREABWCiIhYVAgiIgKoEERExKJCEBERQIUgIiIWFYKIiAAqBBERsagQREQEUCGIiIhF\nhSAiIoAKQURELCoEEREBVAgiImK5LYVw7tw52rVrx5EjRzhx4gTR0dH069ePuLg4SktLb0ckEZE7\nnu2FUFRUhNPppGrVqgBMnTqVmJgYVq5ciTGGpKQkuyOJiAjgY/eA06dPp2/fvixevBiA1NRUIiIi\nAIiKimL79u106tTpuuuoWfMufHy8Kz3rZcHBgbaNdT2ekMMTMoByeFoG8IwcnpDhl8zWQli7di21\natWibdu2rkIwxuBwOADw9/cnOzvb7XqysvIqNefPBQcHkpnpPtOdkMMTMiiH52XwlBx2Zfg1l46t\nhbBmzRocDgc7d+7k0KFDxMbGcv78edfrubm5BAUF2RlJREQsthbC3//+d9fPAwYMYNKkScyYMYOU\nlBQiIyNJTk6mdevWdkYSERHLbb/sNDY2ljlz5tCnTx+Kioro3Lnz7Y4kInJHsv2k8mXLly93/bxi\nxYrbFUNERCy3fQ9BREQ8gwpBREQAFYKIiFhUCCIiAqgQRETEokIQERFAhSAiIhYVgoiIACoEERGx\nqBBERARQIYiIiEWFICIigApBREQsKgQREQFUCCIiYlEhiIgIoEIQERGLCkFERAAVgoiIWFQIIiIC\nqBBERMSiQhAREUCFICIiFhWCiIgAKgQREbGoEEREBFAhiIiIRYUgIiKACkFERCwqBBERAVQIIiJi\nUSGIiAigQhAREYsKQUREABWCiIhYfOwcrKSkhAkTJnDs2DEcDgevvPIKVapUYcyYMTgcDkJDQ4mL\ni8PLSz0lImI3Wwth69atALz33nukpKTw17/+FWMMMTExREZG4nQ6SUpKolOnTnbGEhERbD5k1LFj\nRxISEgA4ffo0QUFBpKamEhERAUBUVBQ7duywM5KIiFhs3UMA8PHxITY2ls8//5w33niD7du343A4\nAPD39yc7O9vtOoKDAys75m0d71o8IYcnZADl8LQM4Bk5PCHDL9ltOVg/ffp0Pv30UyZOnEhBQYFr\nfm5uLkFBQbcjkojIHc/WQli3bh2LFi0CoFq1ajgcDsLCwkhJSQEgOTmZ8PBwOyOJiIjFYYwxdg2W\nl5fH2LFjOXv2LMXFxQwaNIgmTZowceJEioqKCAkJYfLkyXh7e9sVSURELLYWgoiIeC5d8C8iIoAK\nQURELCoEEREBbsN9CJ7o4sWLjBo1inPnzuHv78/06dOpVauW6/VDhw4xZcoU1/S+ffuYN28ebdu2\nJSoqikaNGgHw4IMPMnLkyErLATB58mT27t2Lv78/APPnz8fX19ftchWZ4e233+ajjz4CoF27dgwf\nPhxjTIVsi9LSUiZNmsS3336Ln58fkydPpmHDhq7Xt2zZwrx58/Dx8aFHjx707t3b7TIVnWHjxo28\n8847eHt707RpUyZNmoSXlxdPPfUUAQEBANSvX5+pU6eWO8ON5Hj77bf54IMPXP99XnnlFRo1amTb\ntsjMzGTEiBGu9x4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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11eaff0f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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FNm3a8M477+Dr68uuXbuYNm0acXFxJCYmEhAQgDGGRo0asW/fPgD27NnDvffe63a8ax4y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\n4mR1gJWpbQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11ea2af98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Apresentando uma visualização gráfica com base na classificação\n",
    "from seaborn import lmplot\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "g = lmplot(\"Exame1\", \"Exame2\", hue=\"Admissao\", data=dfQA, fit_reg=True, palette = \"dark\", markers = [\"o\",\"x\"], legend = True)\n",
    "plt.xlabel(\"Exame 1 Score\")\n",
    "plt.ylabel(\"Exame 2 Score\")\n",
    "plot_x = np.array([min(X.iloc[:,2])-2,  max(X.iloc[:,2])+2])\n",
    "plt.ylim(30,100)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'sigmoid' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-19-c0e412851592>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0mtheta0\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mzeros\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0mhypothesis\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msigmoid\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtheta0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mT\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      3\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mhypothesis\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'sigmoid' is not defined"
     ]
    }
   ],
   "source": [
    "theta0 = np.zeros([X.shape[1], 1])\n",
    "hypothesis = sigmoid(X.dot(theta0).T)\n",
    "print(hypothesis)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "print(custoRegressaoLogistica(theta0, X, y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# \n",
    "print(custoJ(theta0, X, y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Avaliando a minimização\n",
    "X_min, theta_min = minimizar(theta0, X, y)\n",
    "print(X_min, theta_min)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.2.4 Avaliação do modelo\n",
    "\n",
    "Após o aprendizado dos parâmetros, você pode usar o modelo correspondente\n",
    "para predizer se um candidato qualquer será aprovado. Para um candidato\n",
    "com **_notas 45 e 85 na primeira e segunda avaliações_**, respectivamente, você deve\n",
    "esperar que ele seja aprovado com **probabilidade de 77.6%**.\n",
    "\n",
    "Outro modo de avaliar a qualidade dos parâmetros é verificar o quão bem o\n",
    "modelo aprendido prediz os pontos de dados do conjunto de treinamento. Nessa\n",
    "parte, você deve implementar uma função denominada predizer. Essa função\n",
    "deve produzir os valores 0 ou 1, dados um exemplo do conjunto de treinamento\n",
    "o vetor de parâmetros ø. Use essa função para produzir a porcentagem de\n",
    "acertos do seu classificador sobre o conjunto de treinamento."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def predizer(theta, X):\n",
    "    P = sigmoid(X.dot(theta))\n",
    "    return (P >= 0.5).astype(int)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Predição de Admissão do candidato\n",
    "A = np.array([1,45,85])\n",
    "H = sigmoid(A.dot(X_min))\n",
    "\n",
    "# Efetuando predição p/ Admissão de um candidato com notas 45 e 85 na primeira e segunda avaliações \n",
    "print('\\t ######################################  ALUNO TESTE  #################################\\n')\n",
    "print('\\t Para as notas 45 e 85 no 1º e 2º Exame prevê a probabilidade de admissão de %f' % H)\n",
    "print('\\t ######################################################################################\\n')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2 - L2 Regularization\n",
    "\n",
    "The standard way to avoid overfitting is called **L2 regularization**. It consists of appropriately modifying your cost function, from:\n",
    "$$J = -\\frac{1}{m} \\sum\\limits_{i = 1}^{m} \\large{(}\\small  y^{(i)}\\log\\left(a^{[L](i)}\\right) + (1-y^{(i)})\\log\\left(1- a^{[L](i)}\\right) \\large{)} \\tag{1}$$\n",
    "To:\n",
    "$$J_{regularized} = \\small \\underbrace{-\\frac{1}{m} \\sum\\limits_{i = 1}^{m} \\large{(}\\small y^{(i)}\\log\\left(a^{[L](i)}\\right) + (1-y^{(i)})\\log\\left(1- a^{[L](i)}\\right) \\large{)} }_\\text{cross-entropy cost} + \\underbrace{\\frac{1}{m} \\frac{\\lambda}{2} \\sum\\limits_l\\sum\\limits_k\\sum\\limits_j W_{k,j}^{[l]2} }_\\text{L2 regularization cost} \\tag{2}$$\n",
    "\n",
    "Let's modify your cost and observe the consequences.\n",
    "\n",
    "**Exercise**: Implement `compute_cost_with_regularization()` which computes the cost given by formula (2). To calculate $\\sum\\limits_k\\sum\\limits_j W_{k,j}^{[l]2}$  , use :\n",
    "```python\n",
    "np.sum(np.square(Wl))\n",
    "```\n",
    "Note that you have to do this for $W^{[1]}$, $W^{[2]}$ and $W^{[3]}$, then sum the three terms and multiply by $ \\frac{1}{m} \\frac{\\lambda}{2} $."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "# função de custo\n",
    "def loss_function(theta, X, y, Lambda):\n",
    "    \n",
    "    m = y.size\n",
    "    H = np.subtract(X,y)\n",
    "    J = 1/(2*m) * np.sum(H**2)\n",
    "    custo = J + (1/(2*m) * np.multiply(Lambda,np.sum(theta**2)))\n",
    "    return custo\n",
    "\n",
    "def prints(self, epoch):\n",
    "    print(\"--epoca %s: \" % epoch)\n",
    "    print(\"loss: \", self.loss[epoch])\n",
    "    print(\"theta: \", self.theta_0.reshape(theta[0].shape[0]), self.theta_n.reshape(theta[1].shape[0]))\n",
    "\n",
    "def gradient_descent(self, epochs, X, Y, learning_rate, Lambda, m, print_results):\n",
    "    for i in xrange(epochs):\n",
    "        # calcula H\n",
    "        H = np.dot(self.theta_n.T, X) + self.theta_0\n",
    "\n",
    "        # calcula gradientes\n",
    "        gH = H - Y\n",
    "\n",
    "        gTheta_n = np.dot(X, gH.T)/m\n",
    "        gTheta_0 = np.sum(gH)/m\n",
    "\n",
    "        # calcula função de custo\n",
    "        loss = self.loss_function(Y, gH, Lambda, m)\n",
    "        self.loss.append(loss)\n",
    "\n",
    "        # atualiza pesos\n",
    "        self.theta_0 -= learning_rate*gTheta_0\n",
    "        self.theta_n = self.theta_n*(1-(learning_rate*Lambda/m)) - learning_rate*gTheta_n\n",
    "\n",
    "        if print_results:\n",
    "            self.prints(i)\n",
    "\n",
    "    # calcula função de custo final\n",
    "    # calcula H\n",
    "    H = np.dot(self.theta_n.T, X) + self.theta_0\n",
    "\n",
    "    # calcula gradientes\n",
    "    gH = H - Y\n",
    "    loss = self.loss_function(Y, gH, Lambda, m)\n",
    "    self.loss.append(loss)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
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