sigmoid_function_and_logistic_regression.ipynb

{
 "cells":[
  {
   "cell_type":"markdown",
   "source":[
    "**This notebook covers use of sigmoid function and logistic regression for classification ml use cases**"
   ],
   "attachments":{
    
   },
   "metadata":{
    "datalore":{
     "node_id":"Ar4IkAr3OD3ia2NlznTZ3M",
     "type":"MD",
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     "hide_output_from_viewers":true
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  {
   "cell_type":"code",
   "source":[
    "# let's start by importing libraries\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.linear_model import SGDClassifier \n",
    "from sklearn.preprocessing import StandardScaler "
   ],
   "execution_count":51,
   "outputs":[
    
   ],
   "metadata":{
    "datalore":{
     "node_id":"T7LLPYVq5CDPl6CoJZHLQy",
     "type":"CODE",
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     "hide_output_from_viewers":true
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  {
   "cell_type":"markdown",
   "source":[
    "**We start off using the linear regression prediction function fwb = wx + b however, classification results are binary and we need to ensure that our prediction stays within 0 and 1 boundaries inclusive. So we are going to use the logistical regression that uses sigmoid function**\n",
    "\n",
    "**Sigmoid function is denoted by g and uses output of linear regression (z) to compute the logistical regression**\n",
    "\n",
    "z = 1\/1+e^-(fwb)"
   ],
   "attachments":{
    
   },
   "metadata":{
    "datalore":{
     "node_id":"QfSzc7W0IdZz7MRXgk9RhL",
     "type":"MD",
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     "hide_output_from_viewers":true
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  {
   "cell_type":"code",
   "source":[
    "# numpy has a built in function exp to calculate the exponential value like e^z\n",
    "\n",
    "input_array = np.array([1,2,3])\n",
    "exp_array = np.exp(input_array)\n",
    "\n",
    "print(f\"Input array is: {input_array}\")\n",
    "print(f\"Exp array is: {exp_array}\")\n",
    "\n",
    "# let's try when the input is a single number\n",
    "\n",
    "input = -10\n",
    "exp = np.exp(input)\n",
    "\n",
    "print(f\"Input is: {input}\")\n",
    "print(f\"Exp is: {exp}\")"
   ],
   "execution_count":37,
   "outputs":[
    {
     "name":"stdout",
     "text":[
      "Input array is: [1 2 3]\n",
      "Exp array is: [ 2.718  7.389 20.086]\n",
      "Input is: -10\n",
      "Exp is: 4.5399929762484854e-05\n"
     ],
     "output_type":"stream"
    }
   ],
   "metadata":{
    "datalore":{
     "node_id":"HRSoVThOrdsPuFpk0Eate6",
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  {
   "cell_type":"code",
   "source":[
    "# now let's define the implementation of sigmoid function in python\n",
    "\n",
    "def sigmoid_fn(z):\n",
    "\n",
    "    g = 1\/(1+np.exp(-z))\n",
    "\n",
    "    return g"
   ],
   "execution_count":38,
   "outputs":[
    
   ],
   "metadata":{
    "datalore":{
     "node_id":"xn6DcBzFd8KdncPONNE2LZ",
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     "hide_input_from_viewers":true,
     "hide_output_from_viewers":true
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  },
  {
   "cell_type":"code",
   "source":[
    "# now let's compute output of the sigmoid function with some test data\n",
    "\n",
    "z_tmp = np.arange(-10,11)\n",
    "\n",
    "y = sigmoid_fn(z_tmp)\n",
    "\n",
    "np.set_printoptions(precision=3)\n",
    "\n",
    "print(f\"Input data is: {z_tmp}\\n\")\n",
    "print(f\"Output data is: {y}\\n\")\n",
    "\n",
    "# using _c function to concatenate arrays along columns\n",
    "\n",
    "print(f\"Input and output data is : \\n {np.c_[z_tmp,y]}\")"
   ],
   "execution_count":39,
   "outputs":[
    {
     "name":"stdout",
     "text":[
      "Input data is: [-10  -9  -8  -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4   5   6   7\n",
      "   8   9  10]\n",
      "\n",
      "Output data is: [4.540e-05 1.234e-04 3.354e-04 9.111e-04 2.473e-03 6.693e-03 1.799e-02\n",
      " 4.743e-02 1.192e-01 2.689e-01 5.000e-01 7.311e-01 8.808e-01 9.526e-01\n",
      " 9.820e-01 9.933e-01 9.975e-01 9.991e-01 9.997e-01 9.999e-01 1.000e+00]\n",
      "\n",
      "Input and output data is : \n",
      " [[-1.000e+01  4.540e-05]\n",
      " [-9.000e+00  1.234e-04]\n",
      " [-8.000e+00  3.354e-04]\n",
      " [-7.000e+00  9.111e-04]\n",
      " [-6.000e+00  2.473e-03]\n",
      " [-5.000e+00  6.693e-03]\n",
      " [-4.000e+00  1.799e-02]\n",
      " [-3.000e+00  4.743e-02]\n",
      " [-2.000e+00  1.192e-01]\n",
      " [-1.000e+00  2.689e-01]\n",
      " [ 0.000e+00  5.000e-01]\n",
      " [ 1.000e+00  7.311e-01]\n",
      " [ 2.000e+00  8.808e-01]\n",
      " [ 3.000e+00  9.526e-01]\n",
      " [ 4.000e+00  9.820e-01]\n",
      " [ 5.000e+00  9.933e-01]\n",
      " [ 6.000e+00  9.975e-01]\n",
      " [ 7.000e+00  9.991e-01]\n",
      " [ 8.000e+00  9.997e-01]\n",
      " [ 9.000e+00  9.999e-01]\n",
      " [ 1.000e+01  1.000e+00]]\n"
     ],
     "output_type":"stream"
    }
   ],
   "metadata":{
    "datalore":{
     "node_id":"KvFxwUDiV9j85Zd3rCyHqx",
     "type":"CODE",
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     "hide_output_from_viewers":true
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  {
   "cell_type":"code",
   "source":[
    "# now let's plot these values on a graph\n",
    "\n",
    "plt.plot(z_tmp, y, marker=\"\", color=\"b\")\n",
    "plt.title(\"Plot between linear function output (z) & Sigmoid function output (y)\")\n",
    "plt.xlabel(\"Linear function output (z)\")\n",
    "plt.ylabel(\"Sigmoid function output (y)\")\n",
    "plt.show()"
   ],
   "execution_count":40,
   "outputs":[
    {
     "data":{
      "image\/png":[
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\n"
      ]
     },
     "metadata":{
      "image\/png":{
       
      }
     },
     "output_type":"display_data"
    }
   ],
   "metadata":{
    "datalore":{
     "node_id":"homTCQ6MLJwcXgU88uqF4a",
     "type":"CODE",
     "hide_input_from_viewers":true,
     "hide_output_from_viewers":true
    }
   }
  },
  {
   "cell_type":"code",
   "source":[
    "# now let's evaluate some individual examples to draw relation between increasing and decreasing z values\n",
    "# if we predicted values from linear regression as a positive number then the exponential function would negate it and compute a very small exponential result that will produce a sigmoid function output closer to 1\n",
    "# if we predicted values from linear regression as a negative number then the exponential function would make it positive and compute a very large exponential result that will produce a very small close to 0 output\n",
    "\n",
    "inp_tmp = -100\n",
    "exp_tmp = np.exp(-inp_tmp)\n",
    "y_tmp = sigmoid_fn(inp_tmp)\n",
    "\n",
    "print(f\"Input is: {inp_tmp}\\n\")\n",
    "print(f\"Exp is: {exp_tmp:0.6f}\\n\")\n",
    "print(f\"Sigmoid fn is: {y_tmp:0.6f}\\n\")"
   ],
   "execution_count":41,
   "outputs":[
    {
     "name":"stdout",
     "text":[
      "Input is: -100\n",
      "\n",
      "Exp is: 26881171418161356094253400435962903554686976.000000\n",
      "\n",
      "Sigmoid fn is: 0.000000\n",
      "\n"
     ],
     "output_type":"stream"
    }
   ],
   "metadata":{
    "datalore":{
     "node_id":"3i2p1kWYKf3V4gBWoyIMhZ",
     "type":"CODE",
     "hide_input_from_viewers":true,
     "hide_output_from_viewers":true
    }
   }
  },
  {
   "cell_type":"code",
   "source":[
    "# now let's take some training data and compute the logistical regression based on that\n",
    "\n",
    "x_train = np.array([0., 1000, 2000, 3000, 4000, 5000])\n",
    "y_train = np.array([0,  0, 0, 1, 1, 1])\n",
    "\n",
    "scaler = StandardScaler()\n",
    "\n",
    "X_train = scaler.fit_transform(x_train.reshape(-1,1))\n",
    "\n",
    "clf = SGDClassifier(max_iter=1000, alpha=0.0001)\n",
    "\n",
    "clf.fit(X_train, y_train)\n",
    "\n",
    "X_test = np.array([-1500, -500, 0, 500, 1500])\n",
    "\n",
    "y_pred = clf.predict(X_test.reshape(-1,1))\n",
    "\n",
    "print(f\"X train data is: {X_train}\")\n",
    "print(f\"Y predict value is: {y_pred}\")\n",
    "\n",
    "# now let's compute the sigmoid function for the predicted y\n",
    "\n",
    "y_pred_sig = sigmoid_fn(y_pred)\n",
    "print(f\"Y predict value from sigmoid fn is: {y_pred_sig}\")\n",
    "\n",
    "# let's create two plots one from linear regression and one from sigmoid function\n",
    "\n",
    "plt.plot(x_train, y_train, marker=\"x\", color=\"b\")\n",
    "plt.xlabel(\"x training data\")\n",
    "plt.xlabel(\"y predicted value\")\n",
    "plt.title(\"Linear regression prediction\")\n",
    "plt.show() \n",
    "\n",
    "plt.plot(X_test, y_pred_sig, marker=\"x\", color=\"b\")\n",
    "plt.xlabel(\"x training data\")\n",
    "plt.xlabel(\"y predicted value\")\n",
    "plt.title(\"Logistical regression prediction\")\n",
    "plt.show()"
   ],
   "execution_count":75,
   "outputs":[
    {
     "name":"stdout",
     "text":[
      "X train data is: [[-1.464]\n",
      " [-0.878]\n",
      " [-0.293]\n",
      " [ 0.293]\n",
      " [ 0.878]\n",
      " [ 1.464]]\n",
      "Y predict value is: [0 0 1 1 1]\n",
      "Y predict value from sigmoid fn is: [0.5   0.5   0.731 0.731 0.731]\n"
     ],
     "output_type":"stream"
    },
    {
     "data":{
      "image\/png":[
       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bjYI998Pv\/iFz26x0ckJ3WwQ6sW4PH5uo5ETutkg1Gqw\/\/7whjeUHYnZqzmhmzXp8cfhmmu8d26jV1MJXdI8SaskrZZ0ej9tTpB0p6Q7JP1Xa8M0K5+LcdloN3agBpLGAOcC7wbWAcskdUfEnYU2M4AzgN+NiCckvXa4AjYrS70YV1dX2ZGYNdbMHvqhwOqIuC8iXgS+D\/TdR\/kEcG5EPAEQEetbG6ZZuV54Af7nf1yMy0a3Zr6aewJrC\/Pr8rKifYF9JV0n6QZJ8xptSNKpknol9W7YsGHrIjYrQb0Yl4dbbDRr1b7GWGAGcCSwAPiWpF36NoqICyKiKyK6Jk+e3KKXNht+tVoqxvXOd5YdiVn\/mknoDwFTC\/NT8rKidUB3RLwUEfcDd5MSvFnbe+WVdP75vHkuxmWjWzMJfRkwQ9LeksYDJwLdfdr8P9LeOZImkYZg7mtdmGblWb4cfvlLD7fY6DdgQo+IjcBpwGJgJbAoIu6QtFBS\/QLoxcBjku4EeoC\/iIjHhitos5HkYlzWLhQRpbxwV1dX9Pb2lvLaZoPxlrekQlxLl5YdiRlIWh4RDU+e9QlYZltw331w++0ebrH24IRutgUuxmXtxAndbAtqNTjgANhnn7IjMRuYE7pZPx5\/HK691nvn1j6c0M36cemlLsZl7cUJ3awf9WJchxxSdiRmzXFCN2vg+edTMa7jjnMxLmsf\/qqaNdDTA88+6+EWay9O6GYN1Gqw444uxmXtxQndrI9iMa5tty07GrPmOaGb9dHbCw8\/7OEWaz9O6GZ91ItxzZ9fdiRmg+OEbtZHrQZvexvstlvZkZgNjhO6WcG998Idd3i4xdqTE7pZgYtxWTtzQjcrqNVS\/fO99y47ErPBc0I3yx57zMW4rL05oZtll16azkF3Qrd25YRultVq8PrXw+zZZUditnWc0M1IxbgWL3YxLmtv\/uqaAVdf7WJc1v6c0M1Iwy0TJ8LcuWVHYrb1nNCt47kYl1WFE7p1vGXL4Fe\/8nCLtT8ndOt49WJcxxxTdiRmQ+OEbh2vuxve\/nYX47L254RuHc3FuKxKnNCto9Vq6acTulWBE7p1tFoNDjwQpk8vOxKzoXNCt4716KPws59579yqwwndOla9GNdxx5UdiVlrNJXQJc2TtErSakmnb6HdBySFpK7WhWg2PLq7Yc894ZBDyo7ErDUGTOiSxgDnAscAM4EFkmY2aDcR+AxwY6uDNGu1YjEuqexozFqjmT30Q4HVEXFfRLwIfB9oNOr4t8BXgOdbGJ\/ZsFiyxMW4rHqaSeh7AmsL8+vyst+SNBuYGhGXbmlDkk6V1Cupd8OGDYMO1qxV6sW4jjyy7EjMWmfIB0UlbQN8DfjcQG0j4oKI6IqIrsmTJw\/1pc22yiuvwE9+ki71dzEuq5JmEvpDwNTC\/JS8rG4icACwVNIa4HCg2wdGbbS66aZUjMtnt1jVNJPQlwEzJO0taTxwItBdXxkRT0XEpIiYHhHTgRuA4yKid1giNhui7u5UjGv+\/LIjMWutARN6RGwETgMWAyuBRRFxh6SFkryPY22nVoN3vAN23bXsSMxaa2wzjSLiMuCyPsu+0E\/bI4celtnwWL0a7rwTPvnJsiMxaz1fKWodxcW4rMqc0K2j1Gpw0EGw115lR2LWek7o1jEefRSuu85nt1h1OaFbx6gX4\/Jwi1WVE7p1jFoNpkyB2bPLjsRseDihW0f4zW9cjMuqzwndOsKSJfDccx5usWpzQreO4GJc1gmc0K3yisW4xo8vOxqz4eOEbpV3003wyCMebrHqc0K3yqvVYOxYF+Oy6nNCt8qrF+PaZZeyIzEbXk7oVmn33AMrV3q4xTqDE7pVWr0Yly\/3t07ghG6V5mJc1kmc0K2yNmyAn\/\/cwy3WOZzQrbJcjMs6jRO6VVatBlOnwqxZZUdiNjKc0K2SfvMbuOIKF+OyzuKEbpV01VUuxmWdxwndKqlWg512ShcUmXUKJ3SrHBfjsk7lhG6Vc+ONsH69h1us8zihW+XUi3Edc0zZkZiNLCd0q5xaLd3IwsW4rNM4oVul3H033HWXh1usMzmhW6XUi3Ede2y5cZiVwQndKqW7Gw4+2MW4rDM5oVtluBiXdTondKuMSy5xMS7rbE0ldEnzJK2StFrS6Q3W\/5mkOyXdJmmJJP\/DayOuVoNp09KQi1knGjChSxoDnAscA8wEFkia2afZCqArIg4Efgic0+pAzbbkuedcjMusmT30Q4HVEXFfRLwIfB\/Y7J\/aiOiJiOfy7A3AlNaGabZlV12VKiz6VnPWyZpJ6HsCawvz6\/Ky\/pwCXN5ohaRTJfVK6t2wYUPzUZoNwMW4zFp8UFTSR4Au4KuN1kfEBRHRFRFdkydPbuVLWwd7+eVUjGv+fBfjss42tok2DwFTC\/NT8rLNSDoK+Dzwjoh4oTXhmQ3sxhvTKYs+u8U6XTN76MuAGZL2ljQeOBHoLjaQNAs4HzguIta3Pkyz\/tVqMG6ci3GZDZjQI2IjcBqwGFgJLIqIOyQtlFQ\/BPVVYEfgB5JukdTdz+bMWq5ejGvnncuOxKxczQy5EBGXAZf1WfaFwvRRLY7LrCmrVqXHaaeVHYlZ+XylqLW1ejEun65o5oRuba67G2bNSleImnU6J3RrW+vXuxiXWZETurWtSy6BCCd0szondGtb9WJcBx1UdiRmo4MTurWl556DK690MS6zIid0a0tXXpmKcXm4xWwTJ3RrS93d6UIiF+My28QJ3dpOsRjXuHFlR2M2ejihW9u54QYX4zJrxAnd2o6LcZk15oRubadWg7lz0w0tzGwTJ3RrK3fdBXff7dotZo04oVtb6c6FmZ3QzV7NCd3aSq0Gs2fD1KkDtzXrNE7o1jYeeQSuv95nt5j1xwnd2oaLcZltmRO6tY1aDfbaCw48sOxIzEYnJ3RrC88+62JcZgNxQre2cNVV8PzzHm4x2xIndGsLtRrssgu8\/e1lR2I2ejmh26j38svpgKiLcZltmRO6jXrXX+9iXGbNcEK3Ua9ejGvevLIjMRvdnNBtVItwMS6zZjmh26i2ahXcc4+HW8ya4YRuo1qtln66GJfZwJzQbVSr1eCQQ2DKlLIjMRv9nNBt1HrkkXS7OQ+3mDXHCd1GrZ\/8xMW4zAbDCd1GrXoxrre8pexIzNpDUwld0jxJqyStlnR6g\/XbSro4r79R0vRWB3rOOdDTs\/mynp60vKo6uc\/PPpvqtxx\/PCxdWu0+m7XKgAld0hjgXOAYYCawQNLMPs1OAZ6IiDcC\/wR8pdWBzpkDJ5ywKcH19KT5OXNa\/UqjRyf3+WtfS8W4pk2rfp\/NWkURseUG0hHA2RHxnjx\/BkBEfKnQZnFuc72kscCvgMmxhY13dXVFb2\/voILt6Umnr02YAE88kc582GGHQW2i7Tz7LKxbB7vu2ll9fvBBGD8eJk6ERYvShUVmBpKWR0RXo3Vjm3j+nsDawvw64LD+2kTERklPAa8BHu0TyKnAqQDTpk1rKviiuXNTgaZFi2C\/\/WD\/\/Qe9iba0\/fawcmVn9vkv\/9LJ3KxZzST0lomIC4ALIO2hD\/b5PT1w9dVw1llw3nnw6U9X\/5e9PszSyX2eO7f6fTZrhWYOij4EFO+xPiUva9gmD7nsDDzWigDr6r\/kixbBwoXpZ3F8uYrc587os1mrNJPQlwEzJO0taTxwItDdp003cFKe\/n3g6i2Nn2+NZcs2H0udOzfNL1vWylcZXdznzuizWasMeFAUQNJ84J+BMcB3IuKLkhYCvRHRLWkC8D1gFvA4cGJE3LelbW7NQVEzs0431IOiRMRlwGV9ln2hMP088MGhBGlmZkPjK0XNzCrCCd3MrCKc0M3MKsIJ3cysIpo6y2VYXljaADywlU+fRJ+rUDuA+9wZ3OfOMJQ+7xURkxutKC2hD4Wk3v5O26kq97kzuM+dYbj67CEXM7OKcEI3M6uIdk3oF5QdQAnc587gPneGYelzW46hm5nZq7XrHrqZmfXhhG5mVhFtl9AHumF1O5H0HUnrJd1eWLabpCsl3ZN\/7pqXS9LXc79vkzS78JyTcvt7JJ3U6LVGA0lTJfVIulPSHZI+k5dXuc8TJN0k6dbc57\/Jy\/fON1RfnW+wPj4v7\/eG65LOyMtXSXpPSV1qmqQxklZIuiTPV7rPktZI+oWkWyT15mUj+92OiLZ5kMr33gvsA4wHbgVmlh3XEPrzdmA2cHth2TnA6Xn6dOAreXo+cDkg4HDgxrx8N+C+\/HPXPL1r2X3rp797ALPz9ETgbtKNx6vcZwE75ulxwI25L4tIZaYBvgn8UZ7+NPDNPH0icHGenpm\/79sCe+ffgzFl92+Avv8Z8F\/AJXm+0n0G1gCT+iwb0e926W\/CIN+wI4DFhfkzgDPKjmuIfZreJ6GvAvbI03sAq\/L0+cCCvu2ABcD5heWbtRvND6AGvLtT+gxsD9xMuifvo8DYvPy332tgMXBEnh6b26nvd73YbjQ+SHc2WwK8E7gk96HqfW6U0Ef0u91uQy6Nbli9Z0mxDJfdI+LhPP0rYPc83V\/f2\/I9yf9WzyLtsVa6z3no4RZgPXAlaU\/zyYjYmJsU49\/shutA\/YbrbdVn0g1x\/hJ4Jc+\/hur3OYArJC2XdGpeNqLf7RG9SbQNTkSEpMqdVyppR+BHwGcj4mlJv11XxT5HxMvAwZJ2AX4MvLnciIaXpPcB6yNiuaQjSw5nJL01Ih6S9FrgSkl3FVeOxHe73fbQm7lhdbt7RNIeAPnn+ry8v7631XsiaRwpmf9nRPx3XlzpPtdFxJNAD2m4YRelG6rD5vH3d8P1durz7wLHSVoDfJ807PIvVLvPRMRD+ed60h\/uQxnh73a7JfRmbljd7oo33D6JNM5cX\/7RfHT8cOCp\/K\/cYuBoSbvmI+hH52WjjtKu+LeBlRHxtcKqKvd5ct4zR9J2pGMGK0mJ\/fdzs759bnTD9W7gxHxGyN7ADOCmEenEIEXEGRExJSKmk35Hr46ID1PhPkvaQdLE+jTpO3k7I\/3dLvtAwlYceJhPOjviXuDzZcczxL5cBDwMvEQaKzuFNHa4BLgHuArYLbcVcG7u9y+ArsJ2Pg6szo+Pld2vLfT3raRxxtuAW\/JjfsX7fCCwIvf5duALefk+pOS0GvgBsG1ePiHPr87r9yls6\/P5vVgFHFN235rs\/5FsOsulsn3Ofbs1P+6o56aR\/m770n8zs4potyEXMzPrhxO6mVlFOKGbmVWEE7qZWUU4oZuZVYQTulWWpCMLlf6O0xaqc0raRdKnt+I1zpb050OJs5Xbsc7mhG5tR9KYwT4nIroj4stbaLILqeqfWdtyQrcRIWmhpM8W5r+oXA+9sGy6pLsk\/aeklZJ+KGn7vG6NpK9Iuhn4oKSjJV0v6WZJP8j1Yer18u\/K7X6vsO2TJX0jT+8u6cdKNcpvlfQ7wJeBN+Ra1l\/N7f5C0rJcr\/pvCtv6vKS7Jf0MeFODvu4s6QFJ2+T5HSStlTRO0ifyNm+V9KN6\/\/o8f6mkrjw9KV9CXy\/y9dVCTJ\/cqg\/DKssJ3UbKd4CPAuREdyJwYYN2bwL+NSL2A55m873mxyJiNumKuzOBo\/J8L\/BnkiYA3wKOBQ4BXtdPLF8HfhoRB5Hq0d9BqlV9b0QcHBF\/Ielo0qXmhwIHA4dIerukQ3LsB5Oucp3Td+MR8RTpKth35EXvI5WKfQn474iYk197Jenq4GadQrpEfE5+3U\/kS+LNACd0GyERsQZ4TNIsUn2KFRHxWIOmayPiujx9IalcQN3F+efhpJsfXKdUlvYkYC9SFcP7I+KeSJdAN\/qDAalY1Hk5rpdzAu7r6HqcpBrmbyYl+LcBP46I5yLiafqvJXQx8KE8fWIh9gMkXSvpF8CHgf37eX4jR5Pqf9xCKjv8mhyTGeDyuTay\/g04mbTn\/J1+2vStRVGcfzb\/FHBlRCwoNpR08NBD3LQ54EsRcX6f1\/hsk8\/vBv5e0m6k\/xauzsu\/C7w\/Im6VdDKp1klfG9m0szWhT0x\/EhGjshCZlc976DaSfgzMIw0X9JeUpkk6Ik\/\/b+BnDdrcAPyupDfCb8eo9wXuAqZLekNut6DBcyEVS\/qj\/NwxknYGniHdFq9uMfDxwtj8nkp1rq8B3i9pu1xd79hGLxARvyZVB\/0XUnGql\/OqicDDSmWEP9xPfGtIfwRgU3XCekx\/lJ+LpH1zZT8zwAndRlBEvEgqobqokOD6WgX8saSVpHsqntdgOxtIe\/oXSboNuB54c0Q8D5wKXJoPiq7v+9zsM8DcPOyxnHRf2sdIQzi3S\/pqRFxBuh\/m9bndD4GJEXEzafjkVtI9IZdtocsXAx9h03ALwFmk4ZLrSH+AGvkHUuJeAUwqLP834E7gZqUbi5+P\/8u2AldbtBGTD4beDHwwIu5psH46aW\/2gJGOzawKvIduI0LSTFJ95yWNkrmZDZ330M3MKsJ76GZmFeGEbmZWEU7oZmYV4YRuZlYRTuhmZhXx\/wGfUAyTvq03\/wAAAABJRU5ErkJggg==\n"
      ]
     },
     "metadata":{
      "image\/png":{
       
      }
     },
     "output_type":"display_data"
    },
    {
     "data":{
      "image\/png":[
       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\n"
      ]
     },
     "metadata":{
      "image\/png":{
       
      }
     },
     "output_type":"display_data"
    }
   ],
   "metadata":{
    "datalore":{
     "node_id":"9C65gj7BGBqFdGSjYeQsBA",
     "type":"CODE",
     "hide_input_from_viewers":true,
     "hide_output_from_viewers":true
    }
   }
  },
  {
   "cell_type":"code",
   "source":[
    
   ],
   "execution_count":null,
   "outputs":[
    
   ],
   "metadata":{
    "datalore":{
     "node_id":"HO1HolGGk6MHMfMKRNckKL",
     "type":"CODE",
     "hide_input_from_viewers":true,
     "hide_output_from_viewers":true
    }
   }
  },
  {
   "cell_type":"code",
   "source":[
    
   ],
   "execution_count":null,
   "outputs":[
    
   ],
   "metadata":{
    "datalore":{
     "node_id":"KoBzy9dTWQEoYI2JJ4H0Ya",
     "type":"CODE",
     "hide_input_from_viewers":true,
     "hide_output_from_viewers":true
    }
   }
  }
 ],
 "metadata":{
  "kernelspec":{
   "display_name":"Python",
   "language":"python",
   "name":"python"
  },
  "datalore":{
   "computation_mode":"JUPYTER",
   "package_manager":"pip",
   "base_environment":"default",
   "packages":[
    
   ],
   "report_row_ids":[
    
   ],
   "version":3
  }
 },
 "nbformat":4,
 "nbformat_minor":4
}