LinR Reg and polynom reg.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "7864aef3",
   "metadata": {},
   "source": [
    "# a) |x - x̂|³ , Linear Regression\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "3ebcd418",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[7.71320643 0.20751949 6.33648235 7.48803883 4.98507012 2.24796646\n",
      " 1.98062865 7.60530712 1.69110837 0.88339814 6.85359818 9.53393346\n",
      " 0.03948266 5.12192263 8.12620962 6.12526067 7.21755317 2.91876068\n",
      " 9.17774123 7.14575783 5.42544368 1.42170048 3.7334076  6.74133615\n",
      " 4.41833174 4.34013993 6.17766978 5.13138243 6.50397182 6.01038953\n",
      " 8.05223197 5.21647152 9.08648881 3.19236089 0.90459349 3.00700057\n",
      " 1.13984362 8.28681326 0.46896319 6.26287148 5.47586156 8.19286996\n",
      " 1.9894754  8.56850302 3.51652639 7.54647692 2.95961707 8.8393648\n",
      " 3.25511638 1.65015898]\n",
      "[ 9.62182172 -4.79765865  7.33382445 10.28824759  5.53529292 -0.65148735\n",
      " -1.06464804 10.49970845 -2.15766234 -2.5250437   9.54942111 14.27144772\n",
      " -2.52633101  6.16130421 11.14014676  6.88834089  9.20292409  0.33579246\n",
      " 14.4842676   8.59370564  5.76976518 -2.68589513  3.51299806  7.06411627\n",
      "  3.47416431  3.55837418  7.67469599  5.72366775  7.79215375  8.00985153\n",
      " 11.41921772  7.9005941  11.66465613  2.00532244 -4.23594555  0.21599232\n",
      " -0.73522817 13.31844067 -5.91825909  7.30296927  5.88587527  9.2540278\n",
      " -1.06987972 12.53034727  2.25031793  8.09856006  2.02694237 12.92327357\n",
      "  1.44832073 -2.45357501]\n",
      "50\n",
      "[0.53142904]\n",
      "[1.09754474]\n",
      "no of iterations: 0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "no of iterations: 10000\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "no of iterations: 20000\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "no of iterations: 30000\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "no of iterations: 40000\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(array([0.99313331]), array([1.55924901]))"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "%matplotlib inline\n",
    "\n",
    "rng = np.random.RandomState(10)\n",
    "x = 10 * rng.rand(50)\n",
    "y = 2 * x - 5 + rng.randn(50)\n",
    "#plt.scatter(x, y);\n",
    "\n",
    "#print(x)\n",
    "\n",
    "#print(rng)\n",
    "\n",
    "#print(y)\n",
    "\n",
    "#xlen = len(x)\n",
    "#print(xlen)\n",
    "\n",
    "#ylen = len(y)\n",
    "#print(ylen)\n",
    "\n",
    "print(x)\n",
    "print(y)\n",
    "\n",
    "def loss(y_hat, y):\n",
    "    l = (y_hat - y)**3\n",
    "    return l.mean()\n",
    "\n",
    "def forward_pass(x,m,c):\n",
    "    return m*x+c\n",
    "\n",
    "learningrate = 0.01\n",
    "numiter = 50000\n",
    "\n",
    "L=[]\n",
    "N=x.shape[0]\n",
    "print(N)\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "m1 = np.random.randn(1)\n",
    "c1 = np.random.randn(1)\n",
    "\n",
    "print(m1)\n",
    "print(c1)\n",
    "\n",
    "\n",
    "learningrate = 0.01\n",
    "numiter = 50000\n",
    "\n",
    "for i in range(numiter):\n",
    "    \n",
    "    y_hat=forward_pass(x,m1,c1)\n",
    "    \n",
    "   \n",
    "    \n",
    "    dm = (3.0/N) *  -np.sum(np.multiply(x,(y - (m1*x +c1))))\n",
    "   \n",
    "    dc = (3.0/N) * -np.sum(y - (m1*x + c1))\n",
    "    \n",
    "    m1 = m1 -learningrate * dm\n",
    "    c1 = c1 - learningrate * dm\n",
    "    if i%10000==0:\n",
    "        L.append(loss(y_hat,y))\n",
    "        print (\"no of iterations:\",i )\n",
    "        plt.plot(x,y,'go')\n",
    "        plt.plot(x,y_hat,'r*')\n",
    "    #plt.plot(x,m1*x+c1,'r*')\n",
    "        plt.ylabel('Data')\n",
    "        plt.show()\n",
    "        \n",
    "        \n",
    "        \n",
    "        \n",
    "plt.plot(L)\n",
    "\n",
    "m1,c1\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "30140d4e",
   "metadata": {},
   "source": [
    " # b) |x - x̂| , Linear Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "1397e24e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "50\n",
      "[-0.19474148]\n",
      "[1.94254209]\n",
      "no of iterations: 0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "no of iterations: 10000\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "no of iterations: 20000\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "no of iterations: 30000\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "no of iterations: 40000\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(array([0.78407741]), array([2.92136097]))"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rng = np.random.RandomState(10)\n",
    "x = 10 * rng.rand(50)\n",
    "y = 2 * x - 5 + rng.randn(50)\n",
    "\n",
    "def loss(y_hat, y):\n",
    "    l = (y_hat - y)\n",
    "    return l.mean()\n",
    "\n",
    "def forward_pass(x,m,c):\n",
    "    return m*x+c\n",
    "\n",
    "learningrate = 0.01\n",
    "numiter = 50000\n",
    "\n",
    "L=[]\n",
    "N=x.shape[0]\n",
    "print(N)\n",
    "\n",
    "\n",
    "m1 = np.random.randn(1)\n",
    "c1 = np.random.randn(1)\n",
    "\n",
    "print(m1)\n",
    "print(c1)\n",
    "\n",
    "\n",
    "learningrate = 0.01\n",
    "numiter = 50000\n",
    "\n",
    "for i in range(numiter):\n",
    "    \n",
    "    y_hat=forward_pass(x,m1,c1)\n",
    "    \n",
    "   \n",
    "    \n",
    "    dm = (1.0/N) *  -np.sum(np.multiply(x,(y - (m1*x +c1))))\n",
    "   \n",
    "    dc = (1.0/N) * -np.sum(y - (m1*x + c1))\n",
    "    \n",
    "    m1 = m1 -learningrate * dm\n",
    "    c1 = c1 - learningrate * dm\n",
    "    if i%10000==0:\n",
    "        L.append(loss(y_hat,y))\n",
    "        print (\"no of iterations:\",i )\n",
    "        plt.plot(x,y,'go')\n",
    "        plt.plot(x,y_hat,'r*')\n",
    "    #plt.plot(x,m1*x+c1,'r*')\n",
    "        plt.ylabel('Data')\n",
    "        plt.show()\n",
    "        \n",
    "        \n",
    "plt.plot(L)  \n",
    "\n",
    "m1,c1\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ebb59430",
   "metadata": {},
   "source": [
    "# c) |x - x̂|⁴, Polynomial Regression\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "b0dc0f14",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x2024dbe9840>]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "np.random.seed(42)\n",
    "X = np.random.rand(1000,1)\n",
    "y = 5*((X)**(2)) + np.random.rand(1000,1)\n",
    "\n",
    "#ynew = y[-50:] \n",
    "\n",
    "#print(xlen)\n",
    "#print(ylen)\n",
    "\n",
    "#ynewlen = len(ynew)\n",
    "#print(ynewlen)\n",
    "\n",
    "\n",
    "#print(x)\n",
    "#print(y)\n",
    "\n",
    "#plt.scatter(x, ynew)\n",
    "#plt.show\n",
    "\n",
    "\n",
    "def loss(y, y_hat):\n",
    "    loss = np.mean((y_hat - y)**4)\n",
    "    return loss\n",
    "\n",
    "\n",
    "def gradients(X, y, y_hat):\n",
    "    \n",
    "    # X --> Input.\n",
    "    # y --> true/target value.\n",
    "    # y_hat --> hypothesis\n",
    "    # w --> weights (parameter).\n",
    "    # b --> bias (parameter).\n",
    "    \n",
    "    # m-> number of training examples.\n",
    "    m = X.shape[0]\n",
    "    \n",
    "    # Gradient of loss w.r.t weights.\n",
    "    dw = (1/m)*np.dot(X.T, (y_hat - y))\n",
    "    \n",
    "    # Gradient of loss w.r.t bias.\n",
    "    db = (1/m)*np.sum((y_hat - y)) \n",
    "    \n",
    "    return dw, db\n",
    "\n",
    "def x_transform(X, degrees):\n",
    "    \n",
    "    \n",
    "    # degrees --> A list, We add X^(value) feature to the input\n",
    "    #             where value is one of the values in the list.\n",
    "    \n",
    "    \n",
    "    t = X.copy()\n",
    "    \n",
    "    # Appending columns of higher degrees to X.\n",
    "    for i in degrees:\n",
    "        X = np.append(X, t**i, axis=1)\n",
    "            \n",
    "    return X\n",
    "\n",
    "def train(X, y, bs, degrees, epochs, lr):\n",
    "    \n",
    "   \n",
    "    # bs --> Batch Size.\n",
    "    \n",
    "    # degrees --> A list, We add X^(value) feature to the input\n",
    "    #             where value is one of the values in the list.\n",
    "    \n",
    "    \n",
    "    # Adding features to input X.\n",
    "    x = x_transform(X, degrees)\n",
    "    \n",
    "    # m-> number of training examples\n",
    "    # n-> number of features \n",
    "    m, n = x.shape\n",
    "    \n",
    "    # Initializing weights and bias to zeros.\n",
    "    w = np.zeros((n,1))\n",
    "    b = 0\n",
    "    \n",
    "    \n",
    "    y = y.reshape(m,1)\n",
    "    \n",
    "    \n",
    "    losses = []\n",
    "    \n",
    "    # Training loop.\n",
    "    for epoch in range(epochs):\n",
    "        for i in range((m-1)//bs + 1):\n",
    "            \n",
    "            # Defining batches.\n",
    "            start_i = i*bs\n",
    "            end_i = start_i + bs\n",
    "            xb = x[start_i:end_i]\n",
    "            yb = y[start_i:end_i]\n",
    "            \n",
    "            # Calculating hypothesis\n",
    "            y_hat = np.dot(xb, w) + b\n",
    "            \n",
    "            \n",
    "            dw, db = gradients(xb, yb, y_hat)\n",
    "            \n",
    "            \n",
    "            w -= lr*dw\n",
    "            b -= lr*db\n",
    "        \n",
    "        \n",
    "        l = loss(y, np.dot(x, w) + b)\n",
    "        losses.append(l)\n",
    "        \n",
    "   \n",
    "    return w, b, losses\n",
    "\n",
    "\n",
    "# Predicting function.\n",
    "def predict(X, w, b, degrees):\n",
    "    \n",
    "    \n",
    "    # b --> bias (parameter).\n",
    "    #degrees --> A list, We add X^(value) feature to the input\n",
    "    #             where value is one of the values in the list.\n",
    "    \n",
    "    # Adding degrees to input X.\n",
    "    x1 = x_transform(X, degrees)\n",
    "    \n",
    "    \n",
    "    return np.dot(x1, w) + b\n",
    "\n",
    "\n",
    "w, b, l = train(X, y, bs=100, degrees=[2], epochs=1000,\n",
    "                lr=0.01)\n",
    "# Plotting\n",
    "fig = plt.figure(figsize=(8,6))\n",
    "plt.plot(X, y, 'y.')\n",
    "plt.plot(X, predict(X, w, b, [2]), 'r.')\n",
    "plt.legend([\"Data\", \"Polynomial predictions\"])\n",
    "plt.xlabel('X - Input')\n",
    "plt.ylabel('y - target / true')\n",
    "plt.title('Polynomial Regression')\n",
    "plt.show()\n",
    "\n",
    "\n",
    "plt.plot(l)  \n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e50ddfaf",
   "metadata": {},
   "source": [
    "# d) |x - x̂|7, Polynomial Regression\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "a7d56375",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x2024de53670>]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "np.random.seed(42)\n",
    "X = np.random.rand(1000,1)\n",
    "y = 5*((X)**(2)) + np.random.rand(1000,1)\n",
    "\n",
    "#ynew = y[-50:] \n",
    "\n",
    "#print(xlen)\n",
    "#print(ylen)\n",
    "\n",
    "#ynewlen = len(ynew)\n",
    "#print(ynewlen)\n",
    "\n",
    "\n",
    "#print(x)\n",
    "#print(y)\n",
    "\n",
    "#plt.scatter(x, ynew)\n",
    "#plt.show\n",
    "\n",
    "\n",
    "def loss(y, y_hat):\n",
    "    loss = np.mean((y_hat - y)**7)\n",
    "    return loss\n",
    "\n",
    "\n",
    "def gradients(X, y, y_hat):\n",
    "    \n",
    "    # X --> Input.\n",
    "    # y --> true/target value.\n",
    "    # y_hat --> hypothesis\n",
    "    # w --> weights (parameter).\n",
    "    # b --> bias (parameter).\n",
    "    \n",
    "    # m-> number of training examples.\n",
    "    m = X.shape[0]\n",
    "    \n",
    "    # Gradient of loss w.r.t weights.\n",
    "    dw = (1/m)*np.dot(X.T, (y_hat - y))\n",
    "    \n",
    "    # Gradient of loss w.r.t bias.\n",
    "    db = (1/m)*np.sum((y_hat - y)) \n",
    "    \n",
    "    return dw, db\n",
    "\n",
    "def x_transform(X, degrees):\n",
    "    \n",
    "    \n",
    "    # degrees --> A list, We add X^(value) feature to the input\n",
    "    #             where value is one of the values in the list.\n",
    "    \n",
    "    \n",
    "    t = X.copy()\n",
    "    \n",
    "    # Appending columns of higher degrees to X.\n",
    "    for i in degrees:\n",
    "        X = np.append(X, t**i, axis=1)\n",
    "            \n",
    "    return X\n",
    "\n",
    "def train(X, y, bs, degrees, epochs, lr):\n",
    "    \n",
    "   \n",
    "    # bs --> Batch Size.\n",
    "    \n",
    "    # degrees --> A list, We add X^(value) feature to the input\n",
    "    #             where value is one of the values in the list.\n",
    "    \n",
    "    \n",
    "    # Adding features to input X.\n",
    "    x = x_transform(X, degrees)\n",
    "    \n",
    "    # m-> number of training examples\n",
    "    # n-> number of features \n",
    "    m, n = x.shape\n",
    "    \n",
    "    # Initializing weights and bias to zeros.\n",
    "    w = np.zeros((n,1))\n",
    "    b = 0\n",
    "    \n",
    "    \n",
    "    y = y.reshape(m,1)\n",
    "    \n",
    "    \n",
    "    losses = []\n",
    "    \n",
    "    # Training loop.\n",
    "    for epoch in range(epochs):\n",
    "        for i in range((m-1)//bs + 1):\n",
    "            \n",
    "            # Defining batches.\n",
    "            start_i = i*bs\n",
    "            end_i = start_i + bs\n",
    "            xb = x[start_i:end_i]\n",
    "            yb = y[start_i:end_i]\n",
    "            \n",
    "            # Calculating hypothesis\n",
    "            y_hat = np.dot(xb, w) + b\n",
    "            \n",
    "            \n",
    "            dw, db = gradients(xb, yb, y_hat)\n",
    "            \n",
    "            \n",
    "            w -= lr*dw\n",
    "            b -= lr*db\n",
    "        \n",
    "        \n",
    "        l = loss(y, np.dot(x, w) + b)\n",
    "        losses.append(l)\n",
    "        \n",
    "   \n",
    "    return w, b, losses\n",
    "\n",
    "\n",
    "# Predicting function.\n",
    "def predict(X, w, b, degrees):\n",
    "    \n",
    "    \n",
    "    # b --> bias (parameter).\n",
    "    #degrees --> A list, We add X^(value) feature to the input\n",
    "    #             where value is one of the values in the list.\n",
    "    \n",
    "    # Adding degrees to input X.\n",
    "    x1 = x_transform(X, degrees)\n",
    "    \n",
    "    \n",
    "    return np.dot(x1, w) + b\n",
    "\n",
    "\n",
    "w, b, l = train(X, y, bs=100, degrees=[2], epochs=1000,\n",
    "                lr=0.01)\n",
    "# Plotting\n",
    "fig = plt.figure(figsize=(8,6))\n",
    "plt.plot(X, y, 'y.')\n",
    "plt.plot(X, predict(X, w, b, [2]), 'r.')\n",
    "plt.legend([\"Data\", \"Polynomial predictions\"])\n",
    "plt.xlabel('X - Input')\n",
    "plt.ylabel('y - target / true')\n",
    "plt.title('Polynomial Regression')\n",
    "plt.show()\n",
    "\n",
    "\n",
    "plt.plot(l)  \n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8cf26f32",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.10.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}