homework_2.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "6d43704b",
   "metadata": {},
   "source": [
    "# import libraries and data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "3c400d73",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import plotly.express as px\n",
    "\n",
    "df=pd.read_csv('housing.csv')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "34dc02a7",
   "metadata": {},
   "source": [
    "# EDA"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5a3e2438",
   "metadata": {},
   "source": [
    "it shows long tail distribution we need to log our target variable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "6eb96c35",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "No artists with labels found to put in legend.  Note that artists whose label start with an underscore are ignored when legend() is called with no argument.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f713d77e2f0>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1300x700 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(13,7))\n",
    "sns.histplot(df['median_house_value'])\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "84a50711",
   "metadata": {},
   "source": [
    "keep only the records where ocean_proximity is either '<1H OCEAN' or 'INLAND'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "35007d51",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(15687, 9)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df=df.query(\"ocean_proximity=='<1H OCEAN' or ocean_proximity=='INLAND'\")\n",
    "features=['latitude',\n",
    "'longitude',\n",
    "'housing_median_age',\n",
    "'total_rooms',\n",
    "'total_bedrooms',\n",
    "'population',\n",
    "'households',\n",
    "'median_income',\n",
    "'median_house_value']\n",
    "\n",
    "\n",
    "df=df[features]\n",
    "df.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0ae649e8",
   "metadata": {},
   "source": [
    "# Question one\n",
    "There's one feature with missing values. What is it? <br>\n",
    "\n",
    "total_rooms <br>\n",
    "total_bedrooms <br>\n",
    "population <br>\n",
    "households"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "d7b7059b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "latitude                0\n",
       "longitude               0\n",
       "housing_median_age      0\n",
       "total_rooms             0\n",
       "total_bedrooms        157\n",
       "population              0\n",
       "households              0\n",
       "median_income           0\n",
       "median_house_value      0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.isnull().sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c7534802",
   "metadata": {},
   "source": [
    "# Question 2\n",
    "What's the median (50% percentile) for variable 'population'?\n",
    "\n",
    "995 <br>\n",
    "1095 <br>\n",
    "1195<br>\n",
    "1295<br>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "ae038eda",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1195.0"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['population'].median()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "af51d299",
   "metadata": {},
   "source": [
    "# Prepare and split the dataset\n",
    "Shuffle the dataset (the filtered one you created above), use seed 42. <br>\n",
    "Split your data in train/val/test sets, with 60%/20%/20% distribution.<br>\n",
    "Apply the log transformation to the median_house_value variable using the np.log1p() function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "b47c1011",
   "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>latitude</th>\n",
       "      <th>longitude</th>\n",
       "      <th>housing_median_age</th>\n",
       "      <th>total_rooms</th>\n",
       "      <th>total_bedrooms</th>\n",
       "      <th>population</th>\n",
       "      <th>households</th>\n",
       "      <th>median_income</th>\n",
       "      <th>median_house_value</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>36.23</td>\n",
       "      <td>-119.14</td>\n",
       "      <td>22.0</td>\n",
       "      <td>2935.0</td>\n",
       "      <td>523.0</td>\n",
       "      <td>1927.0</td>\n",
       "      <td>530.0</td>\n",
       "      <td>2.5875</td>\n",
       "      <td>11.161963</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>34.12</td>\n",
       "      <td>-117.79</td>\n",
       "      <td>16.0</td>\n",
       "      <td>2426.0</td>\n",
       "      <td>426.0</td>\n",
       "      <td>1319.0</td>\n",
       "      <td>446.0</td>\n",
       "      <td>4.8125</td>\n",
       "      <td>12.321635</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>33.68</td>\n",
       "      <td>-117.97</td>\n",
       "      <td>26.0</td>\n",
       "      <td>3653.0</td>\n",
       "      <td>568.0</td>\n",
       "      <td>1930.0</td>\n",
       "      <td>585.0</td>\n",
       "      <td>5.7301</td>\n",
       "      <td>12.471896</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>34.10</td>\n",
       "      <td>-118.03</td>\n",
       "      <td>32.0</td>\n",
       "      <td>2668.0</td>\n",
       "      <td>609.0</td>\n",
       "      <td>1512.0</td>\n",
       "      <td>541.0</td>\n",
       "      <td>2.9422</td>\n",
       "      <td>12.359227</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>37.34</td>\n",
       "      <td>-121.87</td>\n",
       "      <td>39.0</td>\n",
       "      <td>2479.0</td>\n",
       "      <td>541.0</td>\n",
       "      <td>1990.0</td>\n",
       "      <td>506.0</td>\n",
       "      <td>2.4306</td>\n",
       "      <td>12.574531</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9407</th>\n",
       "      <td>33.92</td>\n",
       "      <td>-118.02</td>\n",
       "      <td>35.0</td>\n",
       "      <td>2075.0</td>\n",
       "      <td>424.0</td>\n",
       "      <td>1312.0</td>\n",
       "      <td>396.0</td>\n",
       "      <td>3.7969</td>\n",
       "      <td>12.012494</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9408</th>\n",
       "      <td>34.44</td>\n",
       "      <td>-119.15</td>\n",
       "      <td>33.0</td>\n",
       "      <td>2005.0</td>\n",
       "      <td>392.0</td>\n",
       "      <td>1043.0</td>\n",
       "      <td>351.0</td>\n",
       "      <td>5.3080</td>\n",
       "      <td>12.604516</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9409</th>\n",
       "      <td>36.13</td>\n",
       "      <td>-119.13</td>\n",
       "      <td>28.0</td>\n",
       "      <td>1673.0</td>\n",
       "      <td>385.0</td>\n",
       "      <td>1434.0</td>\n",
       "      <td>371.0</td>\n",
       "      <td>2.0586</td>\n",
       "      <td>10.618910</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9410</th>\n",
       "      <td>34.13</td>\n",
       "      <td>-118.08</td>\n",
       "      <td>46.0</td>\n",
       "      <td>1238.0</td>\n",
       "      <td>147.0</td>\n",
       "      <td>377.0</td>\n",
       "      <td>145.0</td>\n",
       "      <td>8.4546</td>\n",
       "      <td>13.122367</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9411</th>\n",
       "      <td>34.29</td>\n",
       "      <td>-118.46</td>\n",
       "      <td>24.0</td>\n",
       "      <td>3668.0</td>\n",
       "      <td>890.0</td>\n",
       "      <td>3151.0</td>\n",
       "      <td>810.0</td>\n",
       "      <td>3.0526</td>\n",
       "      <td>12.118885</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>9412 rows × 9 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      latitude  longitude  housing_median_age  total_rooms  total_bedrooms  \\\n",
       "0        36.23    -119.14                22.0       2935.0           523.0   \n",
       "1        34.12    -117.79                16.0       2426.0           426.0   \n",
       "2        33.68    -117.97                26.0       3653.0           568.0   \n",
       "3        34.10    -118.03                32.0       2668.0           609.0   \n",
       "4        37.34    -121.87                39.0       2479.0           541.0   \n",
       "...        ...        ...                 ...          ...             ...   \n",
       "9407     33.92    -118.02                35.0       2075.0           424.0   \n",
       "9408     34.44    -119.15                33.0       2005.0           392.0   \n",
       "9409     36.13    -119.13                28.0       1673.0           385.0   \n",
       "9410     34.13    -118.08                46.0       1238.0           147.0   \n",
       "9411     34.29    -118.46                24.0       3668.0           890.0   \n",
       "\n",
       "      population  households  median_income  median_house_value  \n",
       "0         1927.0       530.0         2.5875           11.161963  \n",
       "1         1319.0       446.0         4.8125           12.321635  \n",
       "2         1930.0       585.0         5.7301           12.471896  \n",
       "3         1512.0       541.0         2.9422           12.359227  \n",
       "4         1990.0       506.0         2.4306           12.574531  \n",
       "...          ...         ...            ...                 ...  \n",
       "9407      1312.0       396.0         3.7969           12.012494  \n",
       "9408      1043.0       351.0         5.3080           12.604516  \n",
       "9409      1434.0       371.0         2.0586           10.618910  \n",
       "9410       377.0       145.0         8.4546           13.122367  \n",
       "9411      3151.0       810.0         3.0526           12.118885  \n",
       "\n",
       "[9412 rows x 9 columns]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n=len(df)\n",
    "idx=np.arange(n)\n",
    "np.random.seed(42)\n",
    "np.random.shuffle(idx)\n",
    "\n",
    "n_train=int(.6*n)\n",
    "n_val=int(.2*n)\n",
    "n_test=int(.2*n)\n",
    "n,n_test+n_train+n_val\n",
    "\n",
    "df['median_house_value']=np.log1p(df['median_house_value'])\n",
    "\n",
    "train=df.iloc[idx[:n_train]].reset_index()\n",
    "val=df.iloc[idx[n_train:n_train+n_val]].reset_index()\n",
    "test=df.iloc[idx[n_train+n_val:]].reset_index()\n",
    "\n",
    "\n",
    "del train['index']\n",
    "del test['index']\n",
    "del val['index']\n",
    "train"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7160c12c",
   "metadata": {},
   "source": [
    "# Question 3\n",
    "We need to deal with missing values for the column from Q1.<br>\n",
    "We have two options: fill it with 0 or with the mean of this variable.<br>\n",
    "Try both options. For each, train a linear regression model without regularization using the code from the lessons.<br>\n",
    "For computing the mean, use the training only!<br>\n",
    "Use the validation dataset to evaluate the models and compare the RMSE of each option.<br>\n",
    "Round the RMSE scores to 2 decimal digits using round(score, 2)<br>\n",
    "Which option gives better RMSE?<br>\n",
    "Options:<br>\n",
    "\n",
    "With 0<br>\n",
    "With mean<br>\n",
    "Both are equally good"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a3186915",
   "metadata": {},
   "source": [
    "### OPTION ONE FILL WITH O"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "3cd4cdea",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.3409235996349079"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def linear_regression(train,val):\n",
    "    \n",
    "    # ols function and train on training set\n",
    "    train['total_bedrooms']=train['total_bedrooms'].fillna(0)\n",
    "    y_train=train.iloc[:,-1].values\n",
    "    x_train=train.iloc[:,:-1].values\n",
    "\n",
    "    ones=np.ones(x_train.shape[0])\n",
    "    x_train=np.column_stack([ones,x_train])\n",
    "\n",
    "    xtx_train=x_train.T.dot(x_train)\n",
    "    xtx_inv_train=np.linalg.inv(xtx_train)\n",
    "    beta=xtx_inv_train.dot(x_train.T).dot(y_train)\n",
    "    \n",
    "    # prediction on validation set\n",
    "    val['total_bedrooms']=val['total_bedrooms'].fillna(0)\n",
    "    y_val=val.iloc[:,-1].values\n",
    "    x_val=val.iloc[:,:-1].values\n",
    "    \n",
    "    ones=np.ones(x_val.shape[0])\n",
    "    x_val=np.column_stack([ones,x_val])\n",
    "    \n",
    "    y_pred=np.dot(x_val,beta)\n",
    "    \n",
    "    # rmse\n",
    "    error=y_val-y_pred\n",
    "    rmse=np.sqrt((error**2).mean())\n",
    "    return rmse\n",
    "\n",
    "linear_regression(train,val)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2f19b3fd",
   "metadata": {},
   "source": [
    "# option two fill with the mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "77a75277",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def linear_regression_mean(train,val):\n",
    "    \n",
    "    # ols function and train on training set\n",
    "    train['total_bedrooms']=train['total_bedrooms'].fillna(train.total_bedrooms.mean())\n",
    "    y_train=train.iloc[:,-1].values\n",
    "    x_train=train.iloc[:,:-1].values\n",
    "\n",
    "    ones=np.ones(x_train.shape[0])\n",
    "    x_train=np.column_stack([ones,x_train])\n",
    "\n",
    "    xtx_train=x_train.T.dot(x_train)\n",
    "    xtx_inv_train=np.linalg.inv(xtx_train)\n",
    "    beta=xtx_inv_train.dot(x_train.T).dot(y_train)\n",
    "    \n",
    "    # prediction on validation set\n",
    "    val['total_bedrooms']=val['total_bedrooms'].fillna(0)\n",
    "    y_val=val.iloc[:,-1].values\n",
    "    x_val=val.iloc[:,:-1].values\n",
    "    \n",
    "    ones=np.ones(x_val.shape[0])\n",
    "    x_val=np.column_stack([ones,x_val])\n",
    "    \n",
    "    y_pred=np.dot(x_val,beta)\n",
    "    \n",
    "    # rmse\n",
    "    mse=((y_val-y_pred)**2).mean()\n",
    "    rmse=np.sqrt(mse)\n",
    "    return rmse\n",
    "\n",
    "linear_regression_mean(train,val)==linear_regression(train,val)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fb1fec02",
   "metadata": {},
   "source": [
    "# Question 4\n",
    "Now let's train a regularized linear regression. <br>\n",
    "For this question, fill the NAs with 0.<br>\n",
    "Try different values of r from this list: [0, 0.000001, 0.0001, 0.001, 0.01, 0.1, 1, 5, 10].<br>\n",
    "Use RMSE to evaluate the model on the validation dataset.<br>\n",
    "Round the RMSE scores to 2 decimal digits.<br>\n",
    "Which r gives the best RMSE?<br>\n",
    "If there are multiple options, select the smallest r.<br>\n",
    "\n",
    "Options:<br>\n",
    "\n",
    "0<br>\n",
    "0.000001<br>\n",
    "0.001\n",
    "0.0001"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "efc13240",
   "metadata": {},
   "outputs": [],
   "source": [
    "def linear_regression_reg(train,val,r):\n",
    "    \n",
    "    # ols function and train on training set\n",
    "    train['total_bedrooms']=train['total_bedrooms'].fillna(0)\n",
    "    y_train=train.iloc[:,-1].values\n",
    "    x_train=train.iloc[:,:-1].values\n",
    "\n",
    "    ones=np.ones(x_train.shape[0])\n",
    "    x_train=np.column_stack([ones,x_train])\n",
    "\n",
    "    xtx_train=x_train.T.dot(x_train)\n",
    "    xtx_train=xtx_train+r*np.eye(xtx_train.shape[0])\n",
    "    xtx_inv_train=np.linalg.inv(xtx_train)\n",
    "    beta=xtx_inv_train.dot(x_train.T).dot(y_train)\n",
    "    \n",
    "    # prediction on validation set\n",
    "    val['total_bedrooms']=val['total_bedrooms'].fillna(0)\n",
    "    y_val=val.iloc[:,-1].values\n",
    "    x_val=val.iloc[:,:-1].values\n",
    "    \n",
    "    ones=np.ones(x_val.shape[0])\n",
    "    x_val=np.column_stack([ones,x_val])\n",
    "    \n",
    "    y_pred=np.dot(x_val,beta)\n",
    "    \n",
    "    # rmse\n",
    "    error=y_val-y_pred\n",
    "    rmse=np.sqrt((error**2).mean())\n",
    "    return rmse,r\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "3debd185",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(0.3409235996349079, 0)\n",
      "(0.3409236024241936, 1e-06)\n",
      "(0.34092387856510203, 0.0001)\n",
      "(0.3409264112964711, 0.001)\n",
      "(0.34095384832072456, 0.01)\n",
      "(0.34136358989088444, 0.1)\n",
      "(0.3449756916797438, 1)\n",
      "(0.3478195844881851, 5)\n",
      "(0.3483946973484849, 10)\n"
     ]
    }
   ],
   "source": [
    "\n",
    "for r in [0, 0.000001, 0.0001, 0.001, 0.01, 0.1, 1, 5, 10]:\n",
    "    print(linear_regression_reg(train,val,r))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "541e904b",
   "metadata": {},
   "source": [
    "# Question 6\n",
    "Split the dataset like previously, use seed 9.<br>\n",
    "Combine train and validation datasets.<br>\n",
    "Fill the missing values with 0 and train a model with r=0.001.<br>\n",
    "What's the RMSE on the test dataset?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "e0942942",
   "metadata": {},
   "outputs": [],
   "source": [
    "n=len(df)\n",
    "idx=np.arange(n)\n",
    "np.random.seed(9)\n",
    "np.random.shuffle(idx)\n",
    "\n",
    "n_train=int(.8*n)\n",
    "n_test=int(.2*n)\n",
    "\n",
    "\n",
    "df['median_house_value']=np.log1p(df['median_house_value'])\n",
    "\n",
    "train=df.iloc[idx[:n_train]].reset_index()\n",
    "\n",
    "test=df.iloc[idx[n_train:]].reset_index()\n",
    "\n",
    "\n",
    "del train['index']\n",
    "del test['index']\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "f49da2dd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.3304954548672377"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def linear_regression_reg(train,val,r):\n",
    "    \n",
    "    # ols function and train on training set\n",
    "    train['total_bedrooms']=train['total_bedrooms'].fillna(0)\n",
    "    y_train=train.iloc[:,-1].values\n",
    "    x_train=train.iloc[:,:-1].values\n",
    "\n",
    "    ones=np.ones(x_train.shape[0])\n",
    "    x_train=np.column_stack([ones,x_train])\n",
    "\n",
    "    xtx_train=x_train.T.dot(x_train)\n",
    "    xtx_train=xtx_train+r*np.eye(xtx_train.shape[0])\n",
    "    xtx_inv_train=np.linalg.inv(xtx_train)\n",
    "    beta=xtx_inv_train.dot(x_train.T).dot(y_train)\n",
    "    \n",
    "    # prediction on validation set\n",
    "    val['total_bedrooms']=val['total_bedrooms'].fillna(0)\n",
    "    y_val=val.iloc[:,-1].values\n",
    "    x_val=val.iloc[:,:-1].values\n",
    "    \n",
    "    ones=np.ones(x_val.shape[0])\n",
    "    x_val=np.column_stack([ones,x_val])\n",
    "    \n",
    "    y_pred=np.dot(x_val,beta)\n",
    "    \n",
    "    # rmse\n",
    "    error=y_val-y_pred\n",
    "    rmse=np.sqrt((error**2).mean())\n",
    "    return rmse\n",
    "linear_regression_reg(train,test,r=0.001)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "env",
   "language": "python",
   "name": "env"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}