MSC Revo.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "d0cd6f45",
   "metadata": {},
   "source": [
    "# 1. Import Libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "11091109",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9b7c0f9c",
   "metadata": {},
   "source": [
    "# 2. Load Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "07a02bc5",
   "metadata": {},
   "outputs": [],
   "source": [
    "data = pd.read_csv(\"SLR.csv\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "84237996",
   "metadata": {},
   "source": [
    "### 2.1 Show Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "d7588f71",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SAT</th>\n",
       "      <th>GPA</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1714</td>\n",
       "      <td>2.40</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1664</td>\n",
       "      <td>2.52</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1760</td>\n",
       "      <td>2.54</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1685</td>\n",
       "      <td>2.74</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1693</td>\n",
       "      <td>2.83</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1670</td>\n",
       "      <td>2.91</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1764</td>\n",
       "      <td>3.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>1764</td>\n",
       "      <td>3.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1792</td>\n",
       "      <td>3.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>1850</td>\n",
       "      <td>3.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>1735</td>\n",
       "      <td>3.02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>1775</td>\n",
       "      <td>3.07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>1735</td>\n",
       "      <td>3.08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>1712</td>\n",
       "      <td>3.08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>1773</td>\n",
       "      <td>3.12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>1872</td>\n",
       "      <td>3.17</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>1755</td>\n",
       "      <td>3.17</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>1674</td>\n",
       "      <td>3.17</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>1842</td>\n",
       "      <td>3.17</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>1786</td>\n",
       "      <td>3.19</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     SAT   GPA\n",
       "0   1714  2.40\n",
       "1   1664  2.52\n",
       "2   1760  2.54\n",
       "3   1685  2.74\n",
       "4   1693  2.83\n",
       "5   1670  2.91\n",
       "6   1764  3.00\n",
       "7   1764  3.00\n",
       "8   1792  3.01\n",
       "9   1850  3.01\n",
       "10  1735  3.02\n",
       "11  1775  3.07\n",
       "12  1735  3.08\n",
       "13  1712  3.08\n",
       "14  1773  3.12\n",
       "15  1872  3.17\n",
       "16  1755  3.17\n",
       "17  1674  3.17\n",
       "18  1842  3.17\n",
       "19  1786  3.19"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.head(20)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aa928f61",
   "metadata": {},
   "source": [
    "### 2.2 Describe Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "8cfebfb8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SAT</th>\n",
       "      <th>GPA</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>84.000000</td>\n",
       "      <td>84.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>1845.273810</td>\n",
       "      <td>3.330238</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>104.530661</td>\n",
       "      <td>0.271617</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>1634.000000</td>\n",
       "      <td>2.400000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>1772.000000</td>\n",
       "      <td>3.190000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>1846.000000</td>\n",
       "      <td>3.380000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>1934.000000</td>\n",
       "      <td>3.502500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>2050.000000</td>\n",
       "      <td>3.810000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               SAT        GPA\n",
       "count    84.000000  84.000000\n",
       "mean   1845.273810   3.330238\n",
       "std     104.530661   0.271617\n",
       "min    1634.000000   2.400000\n",
       "25%    1772.000000   3.190000\n",
       "50%    1846.000000   3.380000\n",
       "75%    1934.000000   3.502500\n",
       "max    2050.000000   3.810000"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "baae8770",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "SAT = data[\"SAT\"]\n",
    "GPA = data[\"GPA\"]\n",
    "\n",
    "plt.scatter(SAT, GPA, color=\"g\")\n",
    "plt.xlabel(\"SAT\")\n",
    "plt.ylabel(\"GPA\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "2a5d1334",
   "metadata": {},
   "outputs": [],
   "source": [
    "data.insert(0,\"Ones\",1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "fffe3ffc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(84, 3)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "e5a8a229",
   "metadata": {},
   "outputs": [],
   "source": [
    "cols = data.shape[1]\n",
    "Features = data.iloc[: , 0:cols-1]\n",
    "Results = data.iloc[: , cols-1:cols]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "1599cc79",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Ones</th>\n",
       "      <th>SAT</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>1714</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>1664</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>1760</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>1685</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>1693</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1</td>\n",
       "      <td>1670</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1</td>\n",
       "      <td>1764</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>1</td>\n",
       "      <td>1764</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1</td>\n",
       "      <td>1792</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>1</td>\n",
       "      <td>1850</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Ones   SAT\n",
       "0     1  1714\n",
       "1     1  1664\n",
       "2     1  1760\n",
       "3     1  1685\n",
       "4     1  1693\n",
       "5     1  1670\n",
       "6     1  1764\n",
       "7     1  1764\n",
       "8     1  1792\n",
       "9     1  1850"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Features.head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "da74d32b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>GPA</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2.40</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2.52</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2.54</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2.74</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2.83</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>2.91</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>3.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>3.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>3.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>3.01</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    GPA\n",
       "0  2.40\n",
       "1  2.52\n",
       "2  2.54\n",
       "3  2.74\n",
       "4  2.83\n",
       "5  2.91\n",
       "6  3.00\n",
       "7  3.00\n",
       "8  3.01\n",
       "9  3.01"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Results.head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "e2c0c951",
   "metadata": {},
   "outputs": [],
   "source": [
    "Features = np.matrix(Features.values)\n",
    "Results = np.matrix(Results.values)\n",
    "theta = np.matrix( np.array([0 , 0]) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "1572a9d0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(84, 2)\n",
      "(84, 1)\n",
      "(1, 2)\n"
     ]
    }
   ],
   "source": [
    "print(Features.shape)\n",
    "print(Results.shape)\n",
    "print(theta.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f3b9ff01",
   "metadata": {},
   "source": [
    "# 3. Cost Fuction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "6639d805",
   "metadata": {},
   "outputs": [],
   "source": [
    "def CalcCost(x,y,t):\n",
    "    z = np.power( ((x * t.T) - y),2)\n",
    "    return np.sum(z) / (2 * len(x))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9a5770fd",
   "metadata": {},
   "source": [
    "### 3.1 Testing Cost Function "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "41dd0a63",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5.581691666666667\n"
     ]
    }
   ],
   "source": [
    "print( CalcCost(Features , Results , theta) )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "621b64de",
   "metadata": {},
   "source": [
    "# 4.Gradiant Descent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "2f3374b0",
   "metadata": {},
   "outputs": [],
   "source": [
    "def GradiantDescent(x, y, theta, alpha, iters):\n",
    "    temp = np.matrix( np.zeros(theta.shape) )\n",
    "    parameters = int( theta.ravel().shape[1] )\n",
    "    cost = np.zeros(iters)\n",
    "    \n",
    "    for i in range(iters):\n",
    "        error = (x * theta.T) - y\n",
    "        \n",
    "        for ii in range(parameters):\n",
    "            term = np.multiply(error, x[ : , ii])\n",
    "            temp[0,ii] = theta[0,ii] - ( (alpha / len(x)) * np.sum(term))\n",
    "            \n",
    "        theta = temp\n",
    "        cost[i] = CalcCost(x, y, theta)\n",
    "        \n",
    "    return theta,cost"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "d131588a",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "g = [[9.76197377e-07 1.80384464e-03]]\n",
      "cost = [2.43206581 1.06666347 0.47474442 0.21814009 0.10689889 0.05867443\n",
      " 0.03776852 0.02870555 0.02477664 0.02307341 0.02233503 0.02201494\n",
      " 0.02187617 0.02181602 0.02178994 0.02177863 0.02177373 0.02177161\n",
      " 0.02177069 0.02177029]\n",
      "CalcCost = 0.021770288812162756\n"
     ]
    }
   ],
   "source": [
    "alpha = 0.0000001\n",
    "iters = 20\n",
    "\n",
    "g,cost = GradiantDescent(Features, Results, theta, alpha, iters)\n",
    "\n",
    "print(\"g =\", g)\n",
    "print(\"cost =\", cost[0:20])\n",
    "print(\"CalcCost =\", CalcCost(Features, Results, g))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "94c4b1d7",
   "metadata": {},
   "source": [
    "# 5. Best Fit Line"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "bfbe672b",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2.94748313 2.95506292 2.96264271 2.9702225  2.97780229 2.98538208\n",
      " 2.99296188 3.00054167 3.00812146 3.01570125 3.02328104 3.03086083\n",
      " 3.03844063 3.04602042 3.05360021 3.06118    3.06875979 3.07633958\n",
      " 3.08391938 3.09149917 3.09907896 3.10665875 3.11423854 3.12181833\n",
      " 3.12939812 3.13697792 3.14455771 3.1521375  3.15971729 3.16729708\n",
      " 3.17487687 3.18245667 3.19003646 3.19761625 3.20519604 3.21277583\n",
      " 3.22035562 3.22793542 3.23551521 3.243095   3.25067479 3.25825458\n",
      " 3.26583437 3.27341417 3.28099396 3.28857375 3.29615354 3.30373333\n",
      " 3.31131312 3.31889292 3.32647271 3.3340525  3.34163229 3.34921208\n",
      " 3.35679187 3.36437167 3.37195146 3.37953125 3.38711104 3.39469083\n",
      " 3.40227062 3.40985042 3.41743021 3.42501    3.43258979 3.44016958\n",
      " 3.44774937 3.45532917 3.46290896 3.47048875 3.47806854 3.48564833\n",
      " 3.49322812 3.50080792 3.50838771 3.5159675  3.52354729 3.53112708\n",
      " 3.53870687 3.54628667 3.55386646 3.56144625 3.56902604 3.57660583\n",
      " 3.58418562 3.59176541 3.59934521 3.606925   3.61450479 3.62208458\n",
      " 3.62966437 3.63724416 3.64482396 3.65240375 3.65998354 3.66756333\n",
      " 3.67514312 3.68272291 3.69030271 3.6978825 ]\n"
     ]
    }
   ],
   "source": [
    "x = np.linspace( data[\"SAT\"].min() , data[\"SAT\"].max() , 100)\n",
    "f = g[0 , 0] + ( g[ 0 , 1] * x)\n",
    "print(f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "eb30ab03",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x , f , \"r\", label=\"Prediction\")\n",
    "plt.scatter(data[\"SAT\"], data[\"GPA\"], label=\"Training Data\")\n",
    "plt.legend(loc=\"upper left\")\n",
    "plt.xlabel(\"SAT\")\n",
    "plt.ylabel(\"GPA\")\n",
    "plt.title(\"SAT vs. GPA\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "8f1243ff",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.subplots(figsize=(5,5))\n",
    "plt.plot(np.arange(iters), cost, 'r')\n",
    "plt.xlabel('Iterations')\n",
    "plt.ylabel('Cost')\n",
    "plt.title('Error vs. Training Epoch')\n",
    "\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}