Cost functon for Logistic Regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "416b3a97",
   "metadata": {},
   "source": [
    "# Cost Function for Logistic Regression\n",
    "\n",
    "## Goals\n",
    "In this notebook, we will:\n",
    "- examine the implementation and utilize the cost function for logistic regression."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "274d9c68",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "%matplotlib widget\n",
    "import matplotlib.pyplot as plt\n",
    "from lab_utils_week3 import  plot_data, sigmoid, dlc\n",
    "plt.style.use('./deeplearning.mplstyle')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6e9df521",
   "metadata": {},
   "source": [
    "## Dataset \n",
    "Let's start with the same dataset as was used in the decision boundary notebook."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "a92c9b54",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "X_train = np.array([[0.5, 1.5], [1,1], [1.5, 0.5], [3, 0.5], [2, 2], [1, 2.5]])  #(m,n)\n",
    "y_train = np.array([0, 0, 0, 1, 1, 1])                                           #(m,)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "605157f8",
   "metadata": {},
   "source": [
    "We will use a helper function to plot this data. The data points with label $y=1$ are shown as red crosses, while the data points with label $y=0$ are shown as blue circles."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "0025a3fd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "af1c198e99434651ab040b7fbf4637dd",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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' width=400.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(footer_visible=False, header_visible=False, toolbar=Toolbar(toolitems=[('Home', 'Reset original view', …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax = plt.subplots(1,1,figsize=(4,4))\n",
    "plot_data(X_train, y_train, ax)\n",
    "\n",
    "# Set both axes to be from 0-4\n",
    "ax.axis([0, 4, 0, 3.5])\n",
    "ax.set_ylabel('$x_1$', fontsize=12)\n",
    "ax.set_xlabel('$x_0$', fontsize=12)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b8cbee60",
   "metadata": {},
   "source": [
    "## Cost function\n",
    "\n",
    "In a previous notebook, we developed the *logistic loss* function. Recall, loss is defined to apply to one example. Here you combine the losses to form the **cost**, which includes all the examples.\n",
    "\n",
    "\n",
    "Recall that for logistic regression, the cost function is of the form \n",
    "\n",
    "$$ J(\\mathbf{w},b) = \\frac{1}{m} \\sum_{i=0}^{m-1} \\left[ loss(f_{\\mathbf{w},b}(\\mathbf{x}^{(i)}), y^{(i)}) \\right] \\tag{1}$$\n",
    "\n",
    "where\n",
    "* $loss(f_{\\mathbf{w},b}(\\mathbf{x}^{(i)}), y^{(i)})$ is the cost for a single data point, which is:\n",
    "\n",
    "    $$loss(f_{\\mathbf{w},b}(\\mathbf{x}^{(i)}), y^{(i)}) = -y^{(i)} \\log\\left(f_{\\mathbf{w},b}\\left( \\mathbf{x}^{(i)} \\right) \\right) - \\left( 1 - y^{(i)}\\right) \\log \\left( 1 - f_{\\mathbf{w},b}\\left( \\mathbf{x}^{(i)} \\right) \\right) \\tag{2}$$\n",
    "    \n",
    "*  where m is the number of training examples in the data set and:\n",
    "$$\n",
    "\\begin{align}\n",
    "  f_{\\mathbf{w},b}(\\mathbf{x^{(i)}}) &= g(z^{(i)})\\tag{3} \\\\\n",
    "  z^{(i)} &= \\mathbf{w} \\cdot \\mathbf{x}^{(i)}+ b\\tag{4} \\\\\n",
    "  g(z^{(i)}) &= \\frac{1}{1+e^{-z^{(i)}}}\\tag{5} \n",
    "\\end{align}\n",
    "$$\n",
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e8f6ef10",
   "metadata": {},
   "source": [
    "<a name='ex-02'></a>\n",
    "#### Code Description\n",
    "\n",
    "The algorithm for `compute_cost_logistic` loops over all the examples calculating the loss for each example and accumulating the total.\n",
    "\n",
    "Note that the variables X and y are not scalar values but matrices of shape ($m, n$) and ($𝑚$,) respectively, where  $𝑛$ is the number of features and $𝑚$ is the number of training examples.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "8d9540b1",
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute_cost_logistic(X, y, w, b):\n",
    "    \"\"\"\n",
    "    Computes cost\n",
    "\n",
    "    Args:\n",
    "      X (ndarray (m,n)): Data, m examples with n features\n",
    "      y (ndarray (m,)) : target values\n",
    "      w (ndarray (n,)) : model parameters  \n",
    "      b (scalar)       : model parameter\n",
    "      \n",
    "    Returns:\n",
    "      cost (scalar): cost\n",
    "    \"\"\"\n",
    "\n",
    "    m = X.shape[0]\n",
    "    cost = 0.0\n",
    "    for i in range(m):\n",
    "        z_i = np.dot(X[i],w) + b\n",
    "        f_wb_i = sigmoid(z_i)\n",
    "        cost +=  -y[i]*np.log(f_wb_i) - (1-y[i])*np.log(1-f_wb_i)\n",
    "             \n",
    "    cost = cost / m\n",
    "    return cost\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "678ade58",
   "metadata": {},
   "source": [
    "Check the implementation of the cost function using the cell below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "4ac12fc7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.36686678640551745\n"
     ]
    }
   ],
   "source": [
    "w_tmp = np.array([1,1])\n",
    "b_tmp = -3\n",
    "print(compute_cost_logistic(X_train, y_train, w_tmp, b_tmp))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ddf675dd",
   "metadata": {},
   "source": [
    "**Expected output**: 0.3668667864055175"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "06283a47",
   "metadata": {},
   "source": [
    "## Example\n",
    "Now, let's see what the cost function output is for a different value of $w$. \n",
    "\n",
    "* In a previous notebook, we plotted the decision boundary for  $b = -3, w_0 = 1, w_1 = 1$. That is, we had `b = -3, w = np.array([1,1])`.\n",
    "\n",
    "* Let's say we want to see if $b = -4, w_0 = 1, w_1 = 1$, or `b = -4, w = np.array([1,1])` provides a better model.\n",
    "\n",
    "Let's first plot the decision boundary for these two different $b$ values to see which one fits the data better.\n",
    "\n",
    "* For $b = -3, w_0 = 1, w_1 = 1$, we'll plot $-3 + x_0+x_1 = 0$ (shown in blue)\n",
    "* For $b = -4, w_0 = 1, w_1 = 1$, we'll plot $-4 + x_0+x_1 = 0$ (shown in magenta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "84ef62a1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "d2ba6b5be87547248681cb133d6ed36c",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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OwEgb9bl3fgkhDJeUlCThkUaRIkWcdjSWPwMEoBMwCjBp6vOAOahTWkIIIbIt/wYIQEdsh8h8JESEECKH8neAAHQAXkMfIgtQ10UkRIQQIlvyf4AAtAdGow+Rr7l7h5YQwuX8+++/FC9enNu3c++bwMiRI6lWrRrVq1cnKCiIRYsW5dp7O4r8dxeWTggqQKZiPSgW3tneH33QCCFy3cPL8+Z9f+6W9X337t1L/fr1MZly7x9/u3btmDx5MoUKFeLQoUM0bNiQp59+Gg+P/PNtN//8SbKiHWrM9S7qVt70Ft3ZPhAJESEMsifW3h2oAClZsiQdOnTgzz//pHr16ixduhQvL68cv2fbtm1T//vw4cPUqVMnX4UHuFqAALS587suRJagRiIvIiEihIuIiIggPj6eVatW4eXlRbt27Zg/fz4vvvgiw4YNY+PGjRleU7duXZYsWWLzfY8cOUKrVq0oUKAAa9asyav27cb1AgRUiJiAKVgPkW9QITIICREhXMDevXtZv3493t7eANSvX5/YWDU0Cg8Pt/naP//8k86dO6d+/c0331CnTh0AatSowd9//81vv/1Ghw4dOHz4MD4+Pnn0pzCeawYIQGvU6az/w3qIfHtn+0tIiAiRj124cIFLly4RFBSUum337t2MGTMGINMRSNWqVTly5IjNYwQHB1OkSBGio6OpX79+7v4B7Mh1AwSg5Z3fdSGy7M7vEiJC5JmHAux7/L1793L16lWOHz9O5cqVmT9/PomJiYSEhACZj0CsuX79OmvXrqVbt264u7uzc+dOLl++TPXq1XO7fbty7QABFSJuwP/Qh0gK8DISIkLkgezcLZUXIiIiGDBgAM8//zxxcXEEBQWxZs2ae5rc0GQyMWfOHEaOHImXlxfFihXju+++y3dTuOS/9UB8fHL2P3478A7WQwTUqoavICEixD06c+YMZcuWtXcbDiXt34msB+KMmgHjAXdNfQXwEfKwoRBC3CEBklYz4G30IbISCEM/ShFCCBciAZJeU2AC+hBZDYQjISKEcHkSINY8igoR3S0Gq5GRiBDC5UmA6DwKTEQfImtQqx5KiAghXJQEiC2PoO7MKqCpr0NCRAjhsiRAMvMwaiRiK0TeR0JECOFyJECy4mFsj0TWA9OQEBFCuBQJkKx6CJiEPkQ2oEIk2bCOhBDCriRAsqMRmYfIe0iICOFk8mJFQrM//viDokWLsnLlylx/b3uTubCyqxFq8sW3gEQr9U2op9VfR/8siRDiriF59L6fZH3XvFiRENRMv88++yz+/v65+r6OQgIkJxqiQmQs1kPkB1SIjEFCRIjMHLZ3A3mzImFiYiJPPfUUU6dOZcqUKbnYreOQU1g51QCYDBTS1DejFqyS01lCOLyIiAhiYmJYunQpR48e5ebNm8yfPx9Q64HUqFEjw6+ePXvafM8BAwbw5JNP0q5dOyP+CHZhlxHI2LFj2bBhAyaTCTc3N1577TW6d++eYb8pU6bw+eefU6JEidRtU6dOpWXLlhn2tYv6qBB5E7hppf4jaiTyJjISEcKB5faKhDt27KBw4cIMHTo075p2AHYJkFatWjF+/HgKFSpEVFQULVu25IknnrC64HzPnj1599137dBlFgWjRhpvYD1EtqBCZCwSIkI4oLxYkfDLL7/kxx9/pEaNGgCcPn2al19+mbNnz/Lyyy/n4Z/GWHYJkLQjiKNHj1KrVi2r4eE06gHvokLkhpX6VtQzIm8hV52ESK+mfQ+fFysSzpgxw+Lr5s2bM3z4cB5//PHcaNlh2O3bWXR0NF27dsXDw4MlS5Zo9/vmm2/YtGkTvr6+vPLKKzzxxBMGdpkNdbk7ErEWItvv/C4hIoSlbNwtlRfyYkVCV2H3FQn37dtH79692bNnDz4+Pha169evp94FcfDgQR5//HHWrVuXOiy0JscrEuaW/ai7r6yFCMBjwDgkRITLkhUJM5IVCXOobt26eHt7c/z48Qy1tLfQ1a5dm7p16xIdHW1ke9lXB/Uwoe7uvx2oaVFuGdaREELkCcMD5Pr166xcuZLkZHV/6+7du4mPj6dKlSpcvHiRM2fOpO67ceNGEhPVgxZRUVEcPHiQ4OBgo1vOvtrAVPQhshMJESGE0zP8RIrJZGLhwoW89dZbeHp64uvry/z58ylSpAgzZsxg165drFu3DoA1a9YwcuRIPD098fb2ZsaMGZQpU8bolnOmNmok8jpwzUp9F2qW37fRT40ihBAOzO7XQHKb3a+BpHcIGI31EAG15sjbQEHDOhLCrrJ8DSQ2FjZsgL599fvMmwchIRAQkHsN2oFcAxHWPYCapddbU9+NWj7X2pQoQriq2Fho0QL69QPdbbTh4areooXaXxhOAsQINVGns3Qh8jNqFCIhIsTd8IiKUl8PH54xRMLD1XZQ+0mI2IUEiFFqYnsksgcYj4SIcG3pw8MsbYikDQ8zO4fIyZMnKVasGPHx8XY5vr1IgBgpCLX8rS5EfkE9IyIhIlzVhg0Zw8Ns+HCoVCljeJhFRanXG2zQoEE0atTI5cIDJECMVwP4ACiiqf+Kfq0RIfK7vn0hLExfP3lSXwsLs33BXeP999/nmWeeSf360qVLlChRgkuXLmXp9Z999hkXLlzI9nHzA3ke2h6qo0JkFGDtZosI1OSLk9BPFy9EfjVsmPpdN9KwJizs7uuyqX///lSsWJHz589TqlQpZs2aRffu3fH09NTOejFx4kR69OiRo+PlJ3Ibrz1Fow8RUGuOSIiIfCbLt/Fau9ZhzT2Eh9lLL72Ev78/48ePp3LlymzatInq1atn6z1MJhOXL1/G19c328eX23hF9lVDjUSKaup7USMR3bxaQuRnw4ZBxYq296lY8Z7DQx1qGF988QWLFi2idu3aVK9enWvXrlldSKpGjRp8880393zM/EBOYdlbVVSIjAT+s1KPRC1INRnwNLAvIewtPNz2NQ9Q9fDwew6R6tWrU7duXV566SVWrVoFQOHChTOs8yEsyQjEEVTB9kjkd1SIXDesIyHsK6unr8D6cyI58Mwzz1C5cmVatWqVrdeNGjWKBg0aANCiRQtGjBhxz704CxmBOIoqwHTUSORfK3VziExGP0mjEPlBdsLDzLz/PYxEli9fzvDsHhd1F5erkhGII6kMfAj4aur7UAtWyUhE5Ffz5tkOD1vXRIYPV6/PgaNHj7Jnzx6L23lF5iRAHE1F1EjEV1M3L1glISLyo5AQSLM2uYWwMDhxQv+cSFCQen0OVK9enfPnz1OokNzymB0SII7IHCLFNPUD6KeJF8KZBQTA1q0ZQyTtrbrDhmUMkaAg9Tonn5XX2UiAOKrMQuQgEiIif0oXIglhn7Cw/TAmRMCYPfDe77CnxzBum0NEwsNu5EFCR3cKGAFc1tQfQK1+qJtfSwgHk9UHCc+evMC7my8y31SDBCurd9YpDsMSfqJvxyq4BTp3eMiDhCJvlAfCAD9N/RBqJHLVqIaEyHu7Y6DO1hJ8kmQ9PAD2X4TnE5vw1L4AricZ259QJECcQTnU3VnFNXXzqodXDOtIiDyzLw7arYVLN7O2/4qT8MxmSE7J275ERhIgzsIcIv6a+mEkRITTS7kNoT/ClXSjDjcTNC8NPatAOSszWa88CV/Z6aHx1atXU7t2bapVq0a3bt1calp3CRBnUhbbIRIFvIaEiHBaW/6GP9LNot6mDJzoDVu7wuI2cPJZ+KYNFC1ouV/4Abht8BXdc+fOMWjQINauXUt0dDQPPPAAb7zxhrFN2JEEiLMpg7omUkJTP4KEiHBaM/+w/LpyUVjdHsr73N3mZoKnq8Ds5pb7HroMu85n/5j3sh7I5s2beeyxxyhfvjwAL7zwAitWrMh+E05KAsQZ3Y8aidgKEVvTxAvhoLads/x62IPgqZlwqVslqJRu/rj0r8+K/v37s379es6fV+mTfj0QW7Pxnj17luLF716cLFWqFP/88w+3bmmu/OczMheWszKHyKvAP1bqR1Hzar2PfpJGIRzI7dsZL5w/Gqjf382k6ifSzGKd1Qvvafn6+tKrVy9mzpzJ+PHjmTlzJps2bcrybLzu7u4WX9++fZtbt25RoECB7DfjZCRAnFnaEIm1Uv8TNRKREBFOopA73Ey++/WFTNbCSV8v5G59v8wMGzaM5s2bU6VKFYv1QIKDg63ub16RsHTp0uzfvz91+/nz5ylWrBiFCxfOWSNORgLE2ZVGhcgI9CFiHoncZ2BfQmSTyaSueRxO89Dsoj+hreaZw5hrsPms5bb0p7SyKqfrgbRu3ZrXX3899UHAOXPm0LFjx5w14YTkGkh+UAp1YV33MO4x9NPEC+FAnq1m+fX8oxlDAiApBV7aAbfSPPvh6Q5PVsr5sXOyHkiZMmX47LPP6NChA9WqVePAgQOE58LaJM5CpjLJT2JQI5EYTb0San4tGYkIO7I1lck/16DMAstgMAH9akCfahBYGH6KgbADGW/37Vcd5rTMeV9PPPEEXbp04bnnnsv5m+SQs05lIgGS38SiQkR3O2Ml1OqHvkY1JISlzObCenMPTPk9e+/pUwB+6w5VcvjD0dGjR2nevDl//fWXXaZ0d9YAceHvtPlUAOqaSGlN/QTqdFa8UQ0JkT3/awTdK2d9f093WNYu5+EBsh5ITkmA5EdZCZFX0c/wK4QdubvB4tYwph54ZPIdqlJR2NJFf6Fd5C27BMjYsWOpX78+DRo0oFGjRixdutTqfrGxsTz11FPUr1+fRx99lB07dhjcqRMribqwfr+mfhJ1qivzh22FMJy7G0x5CE4/C+80VKML051aYQ9oVxZWhsDRXvCwjWdFRN6yyzWQLVu20KRJEwoVKkRUVBQtW7bkzJkzeHhY3lXco0cPWrVqxcCBA4mKiuLxxx9n//79eHp6at/b5a+BpHcBNdqwcicLoKaLn45+unghctn58+fx8fGhSBErsyLakHJbXVzP6bMejurKlSskJCRQqlQpwLmugdj9IvrKlSv55JNP+OGHHyy2JyUlUbp0aU6dOoWXlxcAHTt2ZMSIEbRu3Vr7fovP+DColgSIhQuo6x5nNHXzTL8SIsIAKSkpxMbGkpQki3gAeHh4EBAQkPqDrzMFiN0eJIyOjqZr1654eHiwZMmSDPULFy7g4eGRGh4AgYGBnDtne7Kbt36F68kwok6ut+y8SqBGGa9iPUROo05nTUe/5ogQucTNzS31p23h3Oz2o3q1atWIiopiwYIFPP3001YTN/0cMwCJiYmZvveru2H6/kx3cy3+qFGG7mKjOUQuGtaREMLJ2f1cT926dfH29ub48eMW2/39/bl16xZXr95dqzUmJobSpXW3FlkauRs+2JebneYDxVEX1stp6mdQIRJnVENCCGdmeIBcv36dlStXkpysZkzbvXs38fHxVKlShYsXL3LmjDrHUqBAAZo2bcrChQsB9aDP0aNHadKkSZaPNepnmJbNB5LyPT/USKS8pm4OkQuGdSSEcFKGX0S/ceMGoaGhREVF4enpia+vL5MmTeKhhx5iypQp7Nq1i3Xr1gHqbo0hQ4Zw6tQpPD09mTx5Ms2aNbP5/pW/8+HiTctcfPcheL1env2RnNMl1DWRU5p6ZmuOCCHyhDNdRLf7XVi5zVqAAExpDGOsz8zsui6jQuQvTd08029JoxoSQjhTgNj9GohR3vgFJkfauwsHUwwVEBU19XPop4kXQri8fBcg0x7W18b+CpMkRCz5om7f1U2DLSEihNDIdwHStzp8buMyybhf4X97jevHKfhiO0TOY3uaeCGES8p3AQIwsCbMshEi4yNgYoRx/TiF+1AhopsFVUJECJFOvgwQgAE14cvmdydgS2/CXpggIWLpPtRaIVU09RhgOBIiQgggHwcIwAtBtkNk4l54+1e4na/uQ7tH5hCpqqnHokJEt2CVEMJl5OsAAXg+CGa30IfIO5HqlJaESBpFgffJPERsT0smhMjn8n2AADxXA+bYCJFJkWoSRgmRNIqiRiLVNPV/UCHyt1ENCSEcjUsECEDfGjC3pT5EJv8GY3+RELHggwqRGpr6BdSFdQkRIVySywQIQJ/qML8VuGlSZMrv6oFDCZE0igDTsB0iw9EvWCWEyLdcKkAAnq0G81vqQ2Tq7/D6HgkRC+YQCdLU41AjEd2CVUKIfMnlAgSgdzVYYCNEpu2D0T9LiFgoArwH1NTUzSFy2rCOhBB25pIBAvBMNVho43TW+/vVdPASImmYQ+QBTf0ianJGCREhXILLBghAz6qwqDW4a0Jk+n61uqGESBrewFRsh4iMRIRwCS4dIAA9qsDiNvoQCTsAI36SELHgjRqJ1NLUL6EurOvWGhFC5AsuHyAA3SvDEhshEn4QhkmIWCqMGonU1tQvo0YifxnVkBDCaBIgdzxVGb5pAx6av5EZB2HoLgkRC+YQeVBTN4fIScM6EkIYSAIkjScrw7c2QuTjP+DlnRIiFryAd9GHSDzqwrqEiBD5jgRIOk9UgqVt9SHy6SEYshNSJETuModIXU09HjUSOWFQP0IIQ0iAWPF4RVjWFgpo/nZmHoKXdkiIWPACJgP1NPV/USFy3LCOhBB5TAJEo2tF+K6dPkQ+PwyDJUQsZRYi/6FOZx0zrCMhRB6SALGhcwVY3g4Kav6WZh2GF7dLiFjwRIVIsKb+HzASCREh8gEJkEx0qgDLQ/Qh8mUUDNwmIWLBHCINNHXzSORPwzoSQuQBCZAs6FgeVtgIkdlHoP82CRELhYBJ6EMkATUSiTasIyFELpMAyaIO5WFVeyjkbr0+5wi8sBWSU4zty6GZQ6Shpm4OkaOGdSSEyEUSINkQUg5WhehDZO5ReF5CxJI5RBpp6leAUUiICOGEJECyqV05WN0ePDUhMj8annPUEImNhXnzbO8zb57aLzcVBP4HNNbUr6BGIkdy97BCiLwlAZIDbcvaDpEF0dB3i4OFSGwstGgB/fpBeLj1fcLDVb1Fi7wJkXeAhzT1q6iRyOHcPawQIu9IgORQm7KwtgN4eVivL/wT+myBJEcIEXN4REWpr4cPzxgi4eFqO6j98ipEJgIPa+pXgdFIiAjhJCRA7kGrMrC2vT5EFv0JfX60c4ikDw+ztCGSNjzM8jJEJgCPaOpXgdeAQ7l7WCFE7rNLgPTv3586derQsGFDQkJCOHzY+o+cgwcPpmrVqjRs2DD1V1T6b4R21rIMrLMxEll8DJ61Z4hs2JAxPMyGD4dKlTKGh1lUlHp9bjOHSBNN/RpqJPJH7h9aCJF77BIgXbp0ITIykoiICHr37s3QoUO1+44YMYKIiIjUX0FBQQZ2mjUt7ofvO0BhTYh8cwx6b7ZTiPTtC2Fh+vpJG9PkhoWp1+eFAsDbwKOaujlEDubN4YUQ985uAeLhob7b1q1bl5iYGHu0kaua3w/fd9SHyLfH4ZnNcCvZ2L4AGDbMdohYExamXpeXzCHSVFO/DryOhIgQDsru10Dmzp1L27ZttfUPP/yQevXq0b59e7Zv325gZ9nXrDSs7wjemhBZehx6OUOIGBEeZh7AeOAxTf06aiRywJh2hBBZZ4qPj7fbBByzZ8/mq6++Yv369RQtWjRD/fr163h5eQGwfft2QkNDOXDgAL6+vtr39PHxwc3Nvrm46zy0XwdXblmvd6uoltAtoLkNOE9VqmT7tFXFinDCDgt3JKEeONT9jOCJWnOkjmEdCWEXKSkpJCQk2LuNLLHbd9qPPvqIBQsWsGrVKqvhAaSGB0CzZs0ICAjgr7/+MqjDnHu0FGzoCEUKWK8vPwk9foBEo0ci4eG2wwNUXfecSF7yAN4CmmnqN4AxwD6jGhJCZMbwAElOTmbUqFFs376dNWvW4O/vn1qLiYmxuB6ybt06UlLUleedO3eSkJBAtWrVjG45R5qUgo2dwEcTIitOwtObDAwRa7fq6lh7TsQIHsA4oIWmfgN4A/jdsI6EEDYYfgrr1KlT1KlTh0qVKuHufvcczieffMKcOXMAmDlzJgDdunUjOjoaLy8v/Pz8mDRpEg0b6mbmUxzhFFZaP8dAu7WQoDmd1aWCWkK3YF6ezspOeKRl5LWQtJJR08Fv0dQLYXvNESGcmDOdwrLrNZC84GgBArAnBtqtg/8Srdc7l4el7fSTNN6TefPU9CQ6FSvaPq01d27e3cprSzIwBfhRUy8E/B9Q37COhDCEMwWIY32nzaceCoRNnaBoQev1NafgyY1wMy9OZ4WEgO7ZmbAwdcFcd3dWUJB6vT24o05XtdbUbwJvApGGdSSESEcCxCCNA+CHTnCfJkTWnYJuG+BGUi4fOCAAtm7NGCJpT09Zu8U3KEi9LiAglxvKBnfUhfM2mnoiKkQiDOtICJGGBIiBGgXAD531IfL9aei20YAQsXZtI22IOEJ4mLmjHibUPSqUCIwFfjWsIyHEHXINxA72/gNt1kC85ppIu7KwMgQ8NQ8k5lhsrJrbytY1jXnz1GkrRwiPtJKBacBGTb0AtheuEsJJONM1EAkQO/ntArReA5dvWq+3vRMiukkaXVIy8D6gm9+xALYXrhLCCThTgDj+d9p8KrgEbO4MxQpZr286A13Xw/XcPp3lzNxRU72319RvoZ4j2WNYR0K4NAkQOwouAT92Bj9NiPxwFrqsh2uaZ0hckhtq5cKOmvot1NxaPxvWkRAuSwLEzuqVgC1doLin9frms9BZQsSSG/AqmYfIbsM6EsIlSYA4gDr+aiSiC5Etf0On7+GqhMhd5hDprKknoaaK/8mwjoRwORIgDqKOvxqJ+GtCZOs5CZEM3IDhQBdNPQm18uEug/oRwsVIgDiQB4vD1i5QQhMi285BRwkRS+YQ6aqpm0Nkp0H9COFCJEAcTK3iaiSiC5Ht56CDjbVGXJIJGAY8rqknAxOBHUY1JIRrkABxQLWKw9auUNLLen3HeWi/FhI0DyK6JBMwFHhCUzeHiGMvaimEU5EAcVAP+KnTWQGaENkVo1Y9lBBJwwS8AjypqacA7wDbjGpIiPxNAsSB1fRTIxFdiPwUAyE2pol3SSZgCPCUpp6Celp9q2EdCZFvSYA4uKBisK0rBBa2Xt8dAyFrJUQsmICXsB0ik9AvWCWEyBIJECdQoxhs6wKlNCHyc6xa9fBfzbxaLskcIk9r6imoBal0C1YJITIlAeIkqt8ZiZT2tl7fIyGSkQkYBPTQ1FNQS+NuNqwjIfIVCRAnUs1XjUTu14TIL/9A27UQLyFylwl4Eeipqaegls79wbCOhMg3JECcTFVfNRIpowmRXyVEMjIBA4FnNHVziGwyrCMh8gUJECdU5T7bIRJxZ8Eq3VojLskE9Ad6a+q3gXfRrzUihMhAAsRJVb4TImWLWK/vvSAhkoEJeAF4VlO/DbyHhIgQWSQB4sTMIVJOEyKRF6D1arh0w9i+HJoJeB4I1dTNIbLesI6EcFoSIE6uUlEVIuV9rNd/i4NWa+CihMhd5hDRLQ1/G7X++jrDOhLCKUmA5AMVi6q7s3Qhsi9Orb8uIZJOvzu/rLmNWn9dQkQIrXsOkJSUFBYvXpwbvYh7UKEobO8KFWyESKvVEHfd2L4cXl/0IQIqRN7MZGnDefMgNjb3ehLCSdxzgNy6dYshQ4bkRi/iHpX3USFSURMi+y9Cy9VwQULEUl/UKS2dnx+B4ZpH1sPDoV8/aNFCQkS4HFN8fPztzHaaOnWqtnbr1i2mT5/OpUuXcrWxnPLx8cHNzbXPzJ1OgBar4cR/1uu1/eDHLlBCM0mjy/oamG2jXmcLhLW8+3V4OAwffvfroCDYuhUCAvKoQeEKUlJSSEhIsHcbWZKlAClRogRdu3alaNGiGWrJycksWLBAAsTBnLkCLVbBcU2I1PJT67CX1Myv5bIWAl/aqD+4FcJbZAwPMwkRcY/yXYA0a9aMN954g5CQkAy1GzduUKpUKS5fvpzlg/bv35+IiAgKFixI8eLFmT59OjVr1syw37Fjx3j55Ze5cOECxYoVIzw8nAceeMDme0uA3HX2ihqJHPvXer1mMbX6YYCEiKVRkRBZX1+/9DYceEdfnzsX+upu8RLCNmcKkCx9p+3bty8pKSlWawUKFOD111/P1kG7dOlCZGQkERER9O7dm6FDh1rdLzQ0lOHDhxMZGcm4ceN4/nlbJ6pFemWKqLuzqt5nvX74sromEnvN2L4c3vv14YFd+rrfRLj/Zeu1sDAJD+EysjQCyUsHDx6kV69e/PHHHxbbz5w5Q6tWrYiOjk7dVrt2bb777juqVaumfT8ZgWT09xUVFNGakUgNX7VwlW7NEZf18k441FRf/3MY/P3R3a/DwmDYsDxvS+RvTj8CGTt2rGENzJ07l7Zt22bYfu7cOfz8/Cy2BQYGcv78eaNayzfuL6ICoppmJHIkXl0vOX/V0LYc38dNodYOfb1qOJQZrv5bwkO4IKsBMmvWLHr37s316/r7PU+fPn3PB589ezZ79uxhwoQJ1puzMpK4eVMmd8qJ0t7qifXqvtbrR+LV9RIJkXRmPAaXJunrVT6EBydJeAiXZDVAli5dyk8//UT79u2JTXdv++nTpxk2bBgNGza8pwN/9NFHLFiwgFWrVlm9uyswMJC4uDiLbTExMZQuXfqejuvKSt0JkRq+1utH46H5KjgnIXJXeDgcGKdOV+n4jYWXbYxUhMinrAZI8+bN2bRpE//++y8tW7bkwIEDFsHxzTffEBqqm43OtuTkZEaNGsX27dtZs2YN/v7+qbWYmBhiYmIAKF++PMWKFWPDBjU16o4d6h+otbu1RNYFFlYhElTMej36XxUif18xti+HlPZW3b8/gj+t3+wBwKHH1DUTIVyIzYvoly9f5umnn+bw4cMkJSXh7u5O3759GTZsGIGBgTk64KlTp6hTpw6VKlXC3d09dfsnn3zCnDlzAJg5cyYA0dHRvPLKK8TFxeHr60tYWBi1a9e2+f5yET1rYq+pC+uHNXdfV7kPtnZRd3K5JN1zHvcPgaof619Xcxd88mietSXyP2e6iK4NkLNnzxIeHs6CBQu4efMmJpOJadOm8cILLxjdY7ZIgGTdP3dC5JAmRCoXVRffdWuO5Fvz5qnpSXRqj4fiE/X14Ej4wMZzJELY4EwBYvU77SuvvEL9+vVZsGABffr04cCBA4SGhjJ69Gg+/PBDo3sUeaRkYRUQtfys14//p05nnXaOz3LuCQlRT5RbExYGByaqaU10fquvpkURIp+zOgIJDAwkNDSUV199lVKlSqVu/+ijj5g4cSI9evQgPDycAgUKGNpsVsgIJPsuXFcz9R7UzEZT0efOwlWaSRrzpdhYNUFiVNTdbelv1R2+Bfa3zPDSVLYWrhJCw5lGIFYD5Pz58xbBkdbatWt58cUXqVOnDt9//32eN5hdEiA5E3ddLTx14KL1ekUfNVrRrTmSL6UNEd1zHiN+hH2t9O/xHNAnrxoU+ZHTB0hm9u3bR69evYhK+9OZg5AAybmLN9RIZL8mRCr4qAvrFTLedZ1/xcbChg22pycZuxt2P6Kv90O/+qEQ6eT7AAH1pLgjPpMhAXJvLt5Qqxfui7NeL++j5tdyqRDJinXAB6iVDK3JbOEqIe5wpgDJ8XdaRwwPce+Ke6pp3uv5W6+fSoBmq+CkZpp4l9URGIVab92aecAc9AEjhBOSH9VFBn6esLkzBGtC5PQVFSK6BatcVgdgNPoQmY+EiMhXJECEVX6esLkL1C9hvX7mCjRbCcc1M/y6rBBsh8gC1KqHEiIiH5AAEVrFCqmRSMOS1utnr6rnRHQLVrmsEGAM+hAxr3ooISKcnASIsMm3EGzqBI0yCZE/4w1ty/G1Bd5A/y9sEfAFEiLCqUmAiEyZQ6SxJkT+vgrNV0N0vKFtOb42qJGI7l/ZYuBzJESE05IAEVlyXyHY2AkeCrBeP3dnJHJUM6+Wy2qD7ZHIN0iICKclASKyzBwiD2tC5Pw1tSjVEQkRS62BsdgOkZlIiAinIwEisqVoQdjQCR7RzOYvIaLREtshshT4FAkR4VQkQES2FS0IGzpCE02IxFxTp7OiJEQstQTGof9Xtwz4BAkR4TQkQESO+BSE9R3hUU2IxF5XIXJYM8Ovy2oOjEf/L+87YAYSIsIpSICIHPMpCOs7QVPrEzfzz50QOSQhYqkZKkTcNfUVSIgIpyABIu5JkQLwfUd4TBMiF25Ai1Xwh2aGX5fVDHgb2yESjoSIcGgSIOKemUOkuWZ+zQs31IX1gxIilpoCE9CHyCogDEgxqB8hskkCROQK7wKwtgO00IRI3J0Q0S1Y5bIeRYWIh6a+GgkR4bAkQESuMYdIy/ut1y/egJarYb9mrRGX9SgwEX2IrAE+REJEOBwJEJGrCheANe2hVSYholuwymU9ArwDFNDU1wLTkRARDkUCROS6wgVgTQdoU8Z6/dJNFSK/XzC2L4f3MGokogsR86qHEiLCQUiAiDzh5QGr2kPbstbrl29CqzXwm4SIpYexPRL5HpiGhIhwCBIgIs94ecDKEGhnK0RWQ6SEiKWHgEnoQ2QDKkSSDetICKtM8fHx+epOcx8fH9zc7JuLcddhzhHYdk6drinkDpWLwrPV1K2uJt1CQ/nUjSR4YgNsOGO97lsQfugMDTTTxbusX4G3gFuaelvU6oe624CFU0pJSSEhIcHebWSJBEguunQDRv8MC6IhUXOKoYYvvPsQdK1oaGt2dyMJntwI35+2Xr/vTojoVj90WRGoEEnU1NsAryMhko84U4DIKaxccuYKPLICZh/RhwfAkXh4fANM+92w1hyCpwcsD4GO5a3X/02E1mvgl1hj+3J4DYH/Awpq6j8A7yKns4RdSIDkgqu3oMM6OBqf9deM3gPzj+ZZSw6pkDt81w46aULkv0Rouxb2xBjbl8NrAEwGCmnqm4EpSIgIw9ktQK5cuUK7du1Yu3atdp8pU6ZQoUIFGjZsmPpry5YtBnaZNR8egD/STRhYwA2eqQozH4N3GkJ134yvG7oLrujOb+dThdxhWTvonEmI/CwhYqk+tkPkxzt1CRFhILsEyMKFCwkODiYyMjLTfXv27ElERETqr5YtWxrQYdYlpcBnhyy3Vb0PjvSCha1h0AMwrgFE9YT/a2S537+JsOhP43p1FOYQ6VrBej3hFrRbC7slRCwFo0YauhDZgjrdJSEiDGKXAOnduzfR0dE0btzYHofPVRvPwN9XLbfNbwmVilpuM5ngzfoZn4v4Mipv+3NUBd3h27bwuOZmAnOI/HTe2L4cXj3UNQ9PTX0r6hZgCRFhAIe/BvLNN98QHBxMy5YtWbFihb3byeD3dFNy1CkOD2kWWQIYVDPj62/nq/vgsq6gO3zbBp7QhMiVWxCyDnZJiFiqixqJ6EJkG/A/IMmgfoTLcugAGT58OCdPnuS3334jPDycUaNGceTIEXu3ZSH9NYwH/GzvXytdPSkFbrrwT4sF3OGbNvBkJev1K7cgZC3sPGdsXw6vLrZHItuREBF5zqEDxMvLK/W/a9euTd26dYmOjrZjRxkVSfe0cGar76W/2O7hpq4JuLIC7rC4NTylCZGrSdB+HeyQELFUB3gP8NLUd6CmRZEQEXnEoQLk4sWLnDlz93HljRs3kpionqCKiori4MGDBAcH26s9q+r5W369/6Lt21A/O5zx9a72ZLo1BdxhUWvoXtl63Rwi2yVELNUGpqIPkZ2oEHGxu/2EMewSIMuWLaN58+bs37+fcePG0b59ewBmzZrFoEGDUvdbs2YNwcHBNGjQgEGDBjFjxgzKlNFM8Won7crC/d6W2/psgRP/WW67fRsmR8KmdNN59A/K2/6ciTlEelSxXr+WpJ632fq3sX05vNqokUhhTX0napZfCRGRy2Qqk1wwKRLG/Wq5rYCbOiXTtJRa0nXRnxkfNLyvIJztk/E0mKtLSoHQH2HJMet1Lw9Y2x5aOtbPEvZ3CDU31jVN/RHU6ofyeXNozjSViQRILrh6Cx5anvH6RmbmtYQ+1fOmJ2eXlAJ9t+ifk/HyuLNwlYSIpcOoELmqqT8CvI1+ahRhd84UIA51DcRZeReA9R2tP22u895DEh62eLipgO1d1Xr9ehJ0+h42nzW2L4dXE3U6y1tT340KEN3kjEJkgwRILilTBHY/AS/UsH1XVVAxtUbGa/WM681ZmUMktJr1+o1k6Px9xutKLq8mar0QXYjsAcYjISLumZzCygNx12HuUbUeyMUbd9cDCa0GzVxwPZB7lZwCz2+F+Zo7uAu5w6oQaFfO2L4c3hFgFPrTWY1Rd2jJ6SyH4kynsCRAhFNIToEXtsE8zQzGhdzVyC5EQsTSUVSIXNHUG6KmPpEQcRjOFCDynVY4BXc3mN0cnqthvX4zGbquh/WnDG3L8VUHPgB8NPUIYCxw07CORD4iASKchrsbfNkcnteESGKKWqzrewkRS9WA99GHyF7UqocSIiKbJECEU3EzwRfN9Q9gJqao9dfX/mVkV06gGmokUlRT34saidwwrCORD0iACKfjZoLPm8EAGyHSbSOs+cvQthxfVWyHSCTwJhIiIsskQIRTcjPBZ83gxZrW67dS4MmNsPqksX05vCrYDpHfUSFy3bCOhBOTABFOy80Enz6WcY0Vs1sp8NQmWCkhYqkKMB24T1OXEBFZJAEinJo5RF56wHr9Vgp03wQrThjbl8OrDHwI+Grq+4A3kBARNkmACKdnMsHHTWFILev1pBR4+gdYLiFiqSJqJOKrqe8HxiAhIrQkQES+YDLBjEfhldrW60kp8PQmWHbc2L4cnjlEimnqB4DX0c/wK1yaBIjIN0wmCG8CwzQhknwbev4ASyVELGUWIgeREBFWSYCIfMVkgg+bwPAHrdeTb0OvH+BbzVojLqsC6pqILkT+wPY08cIlSYCIfMdkgumPwAgbIfLMZliiWWvEZZUHwgA/Tf0QaiQiISLukAAR+ZLJBB88AiPrWK8n34beP8JiCRFL5VAjkeKaunnVQ93kjMKlSICIfMtkgmkPw2t1rddTbsOzP8IizTTxLsscIv6aunnVQwkRlycBIvI1kwmmPgSj61qvp9yG0C3wtYSIpbLYDpEo4DUkRFycBIjI90wmePchGKNZBTLlNvT5ERZo1hpxWWVQ10RKaOpHkBBxcRIgwiWYTDC5MbwZbL1+G+i7BeYdMbQtx3c/aiRiK0RGAc6x/pHIZRIgwmWYTDCpEYy1ESLPbYW5EiKWzCFSUlM3r3ooIeJyJECESzGZ4H+NYFx96/XbqPXX50iIWDKHSICmHg2MBP4zrCPhACRAhMsxmeCdRvB2A+v128ALW2F2lKFtOb7S2A6RP1Eh8q9hHQk7kwBxQZdvwq7zsOG0+v2yiy5lOqEhTLARIv23wZeHjezICZRCXVjXhcgx1OksCRGXYIqPj79t7yZyk4+PD25ukovW7DoPn/wB351Q05ybFXCDJyup2WwfLWW//uzlnb3wdoS+/nkzGKhZc8RlxQAj7vxuTWXUwlW6NUeEVkpKCgkJznFBSQLEBSQmw6AdWTuv/1wN+OwxKOie9305kkmRMO5Xff2zx+BFzZojLisWFSLnNfVKqBDxNaqh/MGZAkS+0+ZzySnQ44esXxSec0TNWJuckvm++clb9dUdWjqDdsDMP4zrxykEoK6JlNbUT6CuicQb1ZAwmgRIPvfePutLupqA0t7q9/RWnFSvczVj66tnRXRe2gmfSohYykqIvApcNqwjYSC7BciVK1do164da9eu1e4TGxvLU089Rf369Xn00UfZsWOHgR06vxtJMH2/5TYvD5jSGOKeg7/7qN+nNFbb05q+H24mG9ero3gjWD21rjNkJ3x80Lh+nEJJ1IX1+zX1k6hTXZeMakgYxS4BsnDhQoKDg4mMjLS539ChQ2nbti2RkZF88cUXDBgwgBs3bhjUpfNbdgLi0v11rQyBMcHg56m+9vNUX68Msdwv7obrLrz0ej01f5bOK7tghoSIpRKokUgZTf0UaiQiIZKv2CVAevfuTXR0NI0b688XJCUlsXXrVkJDQwEICgqiSpUq7Nq1y6g2nd6qdKeuWpSGtmWt79u2LDRPdxoi/etdyeh6aiZfnaG7IPyAcf04hRKolQ01nzFOISORfMZhr4FcuHABDw8PvLy8UrcFBgZy7tw5O3blXM6nW4K0cwXb+3dJV0//elczqq5aU0Rn+E/w4X593SVlFiKnUSFy0bCORB5y2AABcHfPeC9pYmKiHToRrurVOmp1Q219d8brTC7PH3U6S0Ik33PYAPH39+fWrVtcvXp3/cyYmBhKl9bd7iHSK1XY8us1f9nef3W6evrXu6oRdSCsib4+cjd8sM+wdpxDcdSF9XKa+hlUiMQZ1ZDICw4VIBcvXuTMmTMAFChQgKZNm7Jw4UIAjh49ytGjR2nSxMa/ZGGha0XLr7eeg01nrO+76QxsS3d2MP3rXdmwByHcxkdv1M8w7Xfj+nEKfqiRSHlN3RwiFwzrSOQyuzyJvmzZMj7++GOOHTtGiRIlCAwMZP369UyZMoVdu3axbt06AM6fP8+QIUM4deoUnp6eTJ48mWbNmtl8b3kS/a4bSVB2geWdWF4eaibaF2uqO7Au3oBZh+F/kXA96e5+/p5wtg8UcrEn0jPz8UF1F5bOuw+pu7hEGpdQd2Cd0tQzW3PExTjTk+gylUk+N+U3ePOXjNtNQClvOH9VTRyY3uTG6pkIkdEnf8DLO/X1KY3VrdEijcuoEPlLUzfP9Ktbc8SFOFOAyHfafG50XXjcyqmo28A5TXg8UVG/hrhQk05+2lRff+MXmGz7ESfXUwwVELrToudQp7NiDetI5AIJkHzO3Q2+aaMmScyK52rAkjbqdUJvcC2Y+Zi+PvZXNUGjSMMXdYtvJU1dQsTpyCksF/LTnencl1mZzv2pO9O5N3HB6dzvxazD8OJ2ff2dhjBOs+aIy/oXdTrrhKZeChU0gYZ15FCc6RSWBIgLunwTDl+ChFvgUwBq+kGxQvbuynl9cRgG2giRCQ3g7YbG9eMU/kXN1KubLicQdcrLBUNEAsSOJECEPcyOggHbrF9TArV87gQJEUv/olYvPKapB6CeJXGxEHGmAJHvtELkgheC4Mvm1qfHB5i4F97+FW7nqx/X7tF9qAWnqmrqscBw9AtWCbuTABEilzwfBLNb6EPknUgYHyEhYqEo8D6Zh4hMgeeQJECEyEXP1YA5NkJkUiS8JSMRS0VRI5Fqmvo/qBD526iGRFZJgAiRy/rWgLkt9SEy+TcY+4uEiAUfVIhU19QvoG7xlRBxKBIgQuSBPtVhfitw06TIlN/VA4cSImkUQZ3O0j2zdAE1EjlrVEMiMxIgQuSRZ6vB/Jb6EJn6O7y+R0LEQhFgGhCkqcehRiKaSUGFsSRAhMhDvavBAhshMm0fjP5ZQsRCEeA9oKambg6R04Z1JDQkQITIY89Ug4U2Tme9v19NBy8hkoY5RB7Q1C+inmaXELErCRAhDNCzKixqDe6aEJm+X61uKCGShjcwFdshIiMRu5IAEcIgParA4jb6EAk7ACN+khCx4I0aidTS1C+hLqzr1hoReUoCRAgDda98Z7ZjTYiEH4RhEiKWCqNGIrU19cuokchfRjUkzCRAhDDYU5XVFPsemn99Mw7C0F0SIhbMIfKgpm4OkZOGdSSQABHCLp6sDN/aCJGP76x6KCGShhfwLvoQiUddWJcQMYwEiBB28kQlWNpWHyKfHoIhOyFFQuQuc4jU1dTjUSMR3VojIldJgAhhR49XhGVt1aJe1sw8BC/tkBCx4AVMBupp6v+iQkS31ojINRIgQthZ14rwXTt9iHx+GAZLiFjKLET+Q53O0q01InKFBIgQDqBzBVjeDgpq/kWal86VEEnDExUiwZr6f6hVDyVE8owEiBAOolMFWB6iD5Evo2DgNgkRC+YQ0a07bx6J/GlYRy5FAkQIB9KxPKywESKzj0D/bRIiFgoBk9CHSAJqJBJtWEcuQwJECAfToTysag+F3K3X5xyBF7ZCcoqxfTk0c4jo1p03h8hRwzpyCab4+Ph89bOMj48Pbm6Si87m9m3Y+jcs/BOO/wc3k8GvEDQvrVb58/eyd4fG23gaum5QfxfW9KkGX7UAd/m435UIjAN+1dTNa47oFq5yACkpKSQkJNi7jSyRABF2t+okjNkDR+Kt1wu5w7NV4b2Hwc/T0NbsbtMZ6LoebmhCJLSaWkLX4UIkNhY2bIC+ffX7zJsHISEQEJC7x04ExgO/aOre2F64ys6cKUAc7WMnXMy03+HxDfrwAPUT+Owj8MgKOHvFsNYcQtuysLo9eGpOZy2Ihr5bHOx0VmwstGgB/fpBeLj1fcLDVb1FC7V/bioIvAM8pKlfBUYBh3P3sK5IAkTYzbwjMHpP1vc/Gg/t18HVW3nWkkNqUxbWdNCHyMI/oc8WSHKEEDGHR1SU+nr48IwhEh6utoPaL69CZCLwsKZ+FRiNhMg9kgARdnHllpp1Nr3qvvBOQ5j5GDxTNePDdX9cUtOeu5rWZWBtB/DysF5f9Cf0+dHOIZI+PMzShkja8DDLyxCZADyiqV8FXgMO5e5hXYldAuTYsWOEhIRQv359WrduzaFD1v8PDh48mKpVq9KwYcPUX1HpP5zCKS2Mhn8TLbdNbgxRPWFcAxj0ACxsDUd6QdX7LPf77JCD/LRtsFZlYJ2NEFl8DJ61Z4hs2JAxPMyGD4dKlTKGh1lUlHp9bjOHSBNN/RpqJPJH7h/aFdglQEJDQxk+fDiRkZGMGzeO559/XrvviBEjiIiISP0VFBRkYKcir3yZ7vtMu7LwRjCY0q2TUakozGtpue3sVXVx2RW1uB++7wCFNSHyzTHovdlOIdK3L4SF6esnbUyTGxZm+4L7vSgAvA08qqmbQ+Rg3hw+PzM8QM6cOcPFixcJCQkBoFmzZly7do3oaHnKx1Xcvg37LlpuG6RbthR4OBAeLG657fe43O/LWTS/H77vqA+Rb4/DM5vhlubOrTw1bJjtELEmLEy9Li8VQN2Z1VRTvw68joRINhkeIOfOncPPz89iW2BgIOfPn7e6/4cffki9evVo374927dvN6JFkcduJmf8CfmBYrZfU8vyI0OCi11IT69ZaVjfEbw1IbL0OPRyhhAxIjzMzCHymKZ+HTUSccFrbDlll1NY1p7TuHnzZoZt06dP588//+T3339nzJgxhIaGEh8fb0CHIi8Vcs+4Bsahy7Zf88cly699CuRuT87osUxC5LsT0PMHO4ZIxYq296lY0bjwMPNAPWjYTFO/gRqJ7DesI6dmeIAEBgYSF2d5/iEmJobSpUtn2NfL6+7jx82aNSMgIIC//vorr1sUecxkgrrpTkl9ZuNOmJ9j4EC6U171/HO/L2fUtDRs6ARFNIG6/CT0+AESjQ6R8HDb1zxA1XXPieQlD+AtbIfIGGCfUQ05L8MDpHz58hQrVowNd+642LFjBwA1a9YkJiaGmJiY1H3XrVtHSoo617Fz504SEhKoVq2a0S2LPNA/3b0QG8/A5MiMS7ie+E89KJdWGW/1gJ1QHi0FGzvpR2UrTsLTmwwMEWu36upYe07ECOaRSAtN/QbwBvC7YR05JbtMZRIdHc0rr7xCXFwcvr6+hIWFUbt2bQYPHgzAzJkzAejWrRvR0dF4eXnh5+fHpEmTaNhQN1uaIlOZOIcrt6DM/Iy38lb3Vc9/lPCEnedh2Qm4le56yaRGMLa+Ya06jZ9joN1a/fWhLhXUEroFNQ8k5orshEdaRl4LSSsZNR38Fk29ELbXHMkDzjSVicyFJexm/tGMo4vM1PKDPd3AW66BWLUnBtqtg/8Srdc7l4el7fQz/d6TefPU9CQ6FSvaPq01d27e3cprS1ZC5P8Ag35ocaYAke+0wm76VIf3dPMVWVHd985FYwkPrYcCYVMnKFrQen3NKXhyo36G33sSEgK657TCwuDECf3dWUFB6vX24A68CbTW1G/eqUca1pHTkAARdvVaPVgZAkE2buMt5A4v1IDdT0CZIsb15qwaB8APneA+TYisOwXdNsCNpFw+cEAAbN2aMUTSnp6ydotvUJB6XW7Pypsd7qgL52009URUiEQY1pFTkFNYwiHcvg3bzsHX0XfXAynuqdYD6VfdNdcDuVcR/0CbNRmvM5m1L6fWYffU3AacY2nnxNJd2zBfK3GE8EgrGZgK/KCpF0AtXNUo71pwplNYEiBC5GN774RIvCZE2pVVI8A8CRF7rQdyr5KBacBGTT2PQ0QCxI4kQISwFHlBhcjljM/qAuqW6JUh+kkaXVIyatEp3fyOBYD/AY1z/9DOFCDynVaIfK5+CdjcGYoVsl43r3p4PbeviTgzd9RU7+019Vuo50iysZ5NfiQBIoQLCC4BP3ZW68xb88NZ6LIerrn4HGMW3FArF3bU1G+h5tb62bCOHI4EiBAuol4J+LGLPkQ2n4XOEiKW3IBXyTxEdhvWkUORABHChdT1hy1d1B1u1mz5Gzp973rLBttkDpFOmnoSar0RKyts5ncSIEK4mDp3QsRfEyJbz0mIZOAGjAC6aOpJqJUPdxnVkGOQABHCBT1Y3HaIbDsHHSVELLkBw8g8RHYa1ZD9SYAI4aJqF4etXdTEldZsPwcd1qmJL8UdbsBw4HFNPRmYCOwwqB87kwARwoXVKg5bu0JJzZP+O85D+7WQoHkQ0SWZgKHAE5q6OURcYAFVCRAhXNwDfmokEqAJkV0x0H6dhIgFE/AK0E1TTwHeAbYZ1ZB9SIAIIajpp0YiuhD5KQZCbEwT75JMwMvAk5p6Cupp9a2GdWQ4CRAhBKBmRN7WFQILW6/vjoGQtRIiFkzAEOApTT0FNW9WNte9cRYSIEKIVDWKwbYuUEoTIj/HqlUP/9XMq+WSTMBLQHdNPQW1INWPhnVkGAkQIYSF6ndGIqW9rdf3SIhkZAIGAz009RTUqoebDevIEBIgQogMqvmqkYguRH75B9quhXgJkbtMwItAT009BZiCfq0RJyQBIoSwqqqvCpH7NSHyq4RIRiZgINBLUzeHyCbDOspTEiBCCK2qvup0VhlNiJhXPdStNeKSTMAA4BlN/TbwLvq1RpyIBIgQwqYq96kQKatZj35vJgtWuSQT0B94VlO/DbyH04eIBIgQIlOV74RIOU2IRF6A1qvh0g1j+3JoJuB5IFRTN4fI94Z1lOskQIQQWVKpqAqR8j7W67/FQas1cFFC5C4T8BzQR1O/jVo6d51hHeUqCRAhRJZVLKourOtCZF8ctJYQsWQOkb6aujlE1hrWUa6RABFCZEuFOyFSwUaItFoNcdeN7cvh9bvzS+cDYI0hneQaCRAhRLZVuHM6q6ImRPZfhJar4YKEiKW+qNGIznRgo0G95AIJECFEjpT3USFSqaj1+sFLaiQiIZJOH+AFG/XPjGrk3kmACCFyrFwWQqTlavjnmrF9ObxnsR0iTsIuAXLs2DFCQkKoX78+rVu35tChQ/e0nxDCfsoWge1dobImRP64BC1WQ6yEiKVnUQ8cOjFTfHz8baMP+vDDD/P2228TEhLC9u3bGT16NL/88kuO90vL29sbNzcZWAlhtPNX4fGNcPI/6/XqvrC8HZTQrDnislYA8+9+meKTwtVPrtqtnewwPEDOnDlDq1atiI6OTt1Wu3ZtvvvuO6pVq5bt/YQQQtiH4T+qnzt3Dj8/P4ttgYGBnD9/Pkf7CSGEsA+7nOuxdorp5s2ME+lkdT8hhBDGMzxAAgMDiYuLs9gWExND6dKlc7SfEEII+zA8QMqXL0+xYsXYsEFNQ7ljxw4AatasSUxMDDExMZnuJ4QQwv7schdWdHQ0r7zyCnFxcfj6+hIWFkbt2rUZPHgwADNnzrS5nxBCCPuzS4AIIYRwfk71wISjPoCY1eMNHjyYqlWr0rBhw9RfUVFRedobwJUrV2jXrh1r1+qn+4yNjeWpp56ifv36PProo6mnDB2htylTplChQgWLv7ctW7bkaV/9+/enTp06NGzYkJCQEA4fPmx1P3s87JrV3oz+vI0dO5b69evToEEDGjVqxNKlS63uZ4/PWlZ7s8dnDeDw4cOULVtW++/AUR+qdqoACQ0NZfjw4URGRjJu3Dief/75e9rP6L4ARowYQUREROqvoKCgPO1t4cKFBAcHExkZaXO/oUOH0rZtWyIjI/niiy8YMGAAN27k7ZzcWe0NoGfPnhZ/by1btszT3rp06UJkZCQRERH07t2boUOHWt3P6M9adnoDYz9vrVq1Yvfu3ezdu5d58+YxdOhQkpKSMuxnj89aVnsD4z9rcXFxDBw4MMNjC2nZ43OWFU4TIGfOnOHixYuEhIQA0KxZM65du2bxoGF29jO6L3vp3bs30dHRNG7cWLtPUlISW7duJTRULZ0WFBRElSpV2LVrl917s5cuXbrg4eEBQN26dVNv7kjLXv/vs9KbPbRs2ZJChQoBcPToUWrVqpXap5m9PmtZ6c0eEhMT6dOnDxMnTqRMmTJW93Hk7zFOEyCO+gBido/34YcfUq9ePdq3b8/27dvzpKfsunDhAh4eHnh53Z1jIjAwkHPnztmxK0vffPMNwcHBtGzZkhUrVhh67Llz59K2bdsM2x3hYVddb2ZGf96io6MJCgpi3LhxhIWFZajb87OWWW9mRn7Whg4dSpcuXWjVqpV2H0f4nOnYP4KzwVEfQMzq8aZPn576D2f79u2EhoZy4MABfH1986y3rHJ3d8+wLTEx0Q6dZDR8+HDeeOMNAA4ePMjjjz9OUFAQNWrUyPNjz549mz179rB+/XqrdXs+7JpZb/b4vFWrVo2oqCj27dvH008/zZ49e/DxsVw0xF6ftaz0ZuRn7fPPP6dw4cIMGjQo030d9aFqpxmBOOoDiNk5Xtqfupo1a0ZAQAB//fVXnvSVHf7+/ty6dYurV+9O4OZID22m/XurXbs2devWNWT4/tFHH7FgwQJWrVpF0aIZp5q158OumfUG9v281a1bF29vb44fP26x3RE+a7rewNjP2rFjx9i+fXvqxfrffvuN0aNHM2vWLIv9HPmhaqcJEEd9ADGrfQGsW7eOlJQUAHbu3ElCQoLdJoa8ePEiZ86cAaBAgQI0bdqUhQsXAuoc8dGjR2nSpIndewPYuHFj6k+oUVFRHDx4kODg4Dw7fnJyMqNGjWL79u2sWbMGf3//1Jq9H3bNam9g7Oft+vXrrFy5kuTkZAB2795NfHw8VapUsftnLau9gbGftWnTpqXeDBEREUFwcDDvvfceAwcOtPvnLKuc6jkQR30AMat9devWjejoaLy8vPDz82PSpEk0bNgwz/oCWLZsGR9//DHHjh2jRIkSBAYGsn79eqZMmcKuXbtYt24dAOfPn2fIkCGcOnUKT09PJk+eTLNmzRyit5dffplt27bh6emJt7c3b775Ju3atcuzvk6dOkWdOnWoVKmSxemWTz75hDlz5gD2+6xlpzcjP283btwgNDSUqKgoPD098fX1ZdKkSTz00EN2/6xlpzejP2tpdezYkcGDB9OpUye7f0/LKqcKECGEEI7DaU5hCSGEcCwSIEIIIXJEAkQIIUSOSIAIIYTIEQkQIYQQOSIBIoQQIkckQIQQQuSIBIgQQogckQARQgiRIxIgQlhx7tw5AgICGDJkiMX2bdu24e/vnzpjqxCuTAJECCtKly5Nnz59+Pbbbzl9+jSg5iPq27cvrVu35v/+7//s3KEQ9icBIoTGiBEjcHNzIzw8nEuXLtGjRw/KlSvH7Nmzra7PIISrcaoFpYQwknkUMn/+fPbv38+NGzdYt24d3t7e9m5NCIcgP0YJYcMrr7zCzZs3OXToEIsXL86wiE9cXBxPP/00pUuXpkGDBg6zTLEQRpARiBA2fPDBBwAkJSVZXQp21KhRlCxZkmPHjrFt2zb69evHb7/9RrFixQzuVAjjyQhECI2PPvqI+fPnM23aNDw8PFLDxOzKlSusW7eON954g8KFC9OhQwdq1qyZujiREPmdBIgQVqxdu5YJEyYwduxYBgwYQN++fVmyZInFmuLHjx/H29ub+++/P3VbzZo1OXLkiB06FsJ4EiBCpLNv3z4GDhxI9+7dGTVqFADDhg3Dzc3NYhRy9epVfHx8LF5btGhRrl69ami/QtiLBIgQafz999/07NmTBx98kI8++ih1e6lSpXj22WctRiHe3t4kJCRYvP6///6Tu7SEy5A10YXIoStXrlCxYkX279+fendWp06d6NmzJ88++6yduxMi78kIRIgcKlKkCB06dGDKlClcv36dDRs2cOjQITp27Gjv1oQwhNzGK8Q9+OCDDxg8eDCVKlWidOnSzJkzR27hFS5DTmEJIYTIETmFJYQQIkckQIQQQuSIBIgQQogckQARQgiRIxIgQgghckQCRAghRI5IgAghhMiR/wewtEwckkk++AAAAABJRU5ErkJggg==",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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' width=400.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(footer_visible=False, header_visible=False, toolbar=Toolbar(toolitems=[('Home', 'Reset original view', …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Choose values between 0 and 6\n",
    "x0 = np.arange(0,6)\n",
    "\n",
    "# Plot the two decision boundaries\n",
    "x1 = 3 - x0\n",
    "x1_other = 4 - x0\n",
    "\n",
    "fig,ax = plt.subplots(1, 1, figsize=(4,4))\n",
    "# Plot the decision boundary\n",
    "ax.plot(x0,x1, c=dlc[\"dlblue\"], label=\"$b$=-3\")\n",
    "ax.plot(x0,x1_other, c=dlc[\"dlmagenta\"], label=\"$b$=-4\")\n",
    "ax.axis([0, 4, 0, 4])\n",
    "\n",
    "# Plot the original data\n",
    "plot_data(X_train,y_train,ax)\n",
    "ax.axis([0, 4, 0, 4])\n",
    "ax.set_ylabel('$x_1$', fontsize=12)\n",
    "ax.set_xlabel('$x_0$', fontsize=12)\n",
    "plt.legend(loc=\"upper right\")\n",
    "plt.title(\"Decision Boundary\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b1fded41",
   "metadata": {},
   "source": [
    "You can see from this plot that `b = -4, w = np.array([1,1])` is a worse model for the training data. Let's see if the cost function implementation reflects this."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "54f768a3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost for b = -3 :  0.36686678640551745\n",
      "Cost for b = -4 :  0.5036808636748461\n"
     ]
    }
   ],
   "source": [
    "w_array1 = np.array([1,1])\n",
    "b_1 = -3\n",
    "w_array2 = np.array([1,1])\n",
    "b_2 = -4\n",
    "\n",
    "print(\"Cost for b = -3 : \", compute_cost_logistic(X_train, y_train, w_array1, b_1))\n",
    "print(\"Cost for b = -4 : \", compute_cost_logistic(X_train, y_train, w_array2, b_2))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "440591d0",
   "metadata": {},
   "source": [
    "**Expected output**\n",
    "\n",
    "Cost for b = -3 :  0.3668667864055175\n",
    "\n",
    "Cost for b = -4 :  0.5036808636748461\n",
    "\n",
    "\n",
    "You can see the cost function behaves as expected and the cost for `b = -4, w = np.array([1,1])` is indeed higher than the cost for `b = -3, w = np.array([1,1])`"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "af365585",
   "metadata": {},
   "source": [
    "## Lessons Learnt!\n",
    "In this notebook we examined and utilized the cost function for logistic regression."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "55613a31",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
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