Math Fundamental(Pandas & Numpy ).ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "7119f9d0",
   "metadata": {},
   "outputs": [],
   "source": [
    "#suppose we have vector of one dimentional array [1,1]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "id": "d8ce16ee",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 1]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "v = np.array([1,1])\n",
    "print(v)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0d4d62a5",
   "metadata": {},
   "source": [
    "### suppose we have two dimentional vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "id": "ff9284e0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 1],\n",
       "       [1, 0]])"
      ]
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m= np.array([[1,1],\n",
    "             [ 1,0]])\n",
    "m"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5f030100",
   "metadata": {},
   "source": [
    "### plotting vector \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "id": "340de815",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.patches.FancyArrow at 0x1e561051850>"
      ]
     },
     "execution_count": 114,
     "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",
    "plt.xlim(0,3)\n",
    "plt.ylim(0,3)\n",
    "plt.arrow(0,0,v[0],v[1],head_width=0.1,head_length=0.2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "26d6d54f",
   "metadata": {},
   "source": [
    "### now we are calculating the norm of vector ** the norm of vector is the distcance of line from origin to its end we can calculate it by formoula  Xnorm = sqrt(v1^2+v2^2+.....+vn^2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "id": "8152c509",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Length of Vector\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "1.4142135623730951"
      ]
     },
     "execution_count": 115,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# we can caluclate it by numpy\n",
    "print(\"Length of Vector\")\n",
    "np.sqrt(np.sum(v**2))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "id": "9654b997",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 1 1]\n"
     ]
    }
   ],
   "source": [
    "#if we have more than 2 values t=in the array then how we can write code for it and plot our vector in 3d projection\n",
    "v = np.array([0,1,1])\n",
    "print(v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "id": "05838a7d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<mpl_toolkits.mplot3d.art3d.Line3DCollection at 0x1e560e688e0>"
      ]
     },
     "execution_count": 117,
     "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": [
    "fig = plt.figure()\n",
    "ax= fig.add_subplot(111,projection='3d')\n",
    "ax.set_xlim([0,3])\n",
    "ax.set_ylim([0,3])\n",
    "ax.set_zlim([0,3])\n",
    "ax.quiver(0,0,0,v[0],v[1],v[2],length=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "id": "cf0dcea7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.5, 0.5])"
      ]
     },
     "execution_count": 118,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v= np.array([1,1]) * 0.5\n",
    "v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "id": "f2413514",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.patches.FancyArrow at 0x1e5610f6550>"
      ]
     },
     "execution_count": 119,
     "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": [
    "plt.xlim([0,3])\n",
    "plt.ylim([0,3])\n",
    "plt.arrow(0,0,v[0],v[1],head_width=0.1,head_length=0.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "id": "a3332870",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2 1]\n"
     ]
    }
   ],
   "source": [
    "v = np.array([1,1])+ np.array([1,0])\n",
    "print(v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "id": "5d1f9ebe",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.patches.FancyArrow at 0x1e560eda670>"
      ]
     },
     "execution_count": 121,
     "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": [
    "plt.xlim([0,3])\n",
    "plt.ylim([0,3])\n",
    "plt.arrow(0,0,v[0],v[1],head_width=0.1,head_length=0.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "id": "2c2b8fcd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.quiver.Quiver at 0x1e560692340>"
      ]
     },
     "execution_count": 122,
     "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": [
    "v1 = np.array([1,0])\n",
    "v2 = np.array([0,1])\n",
    "\n",
    "plt.xlim(-1, 3)  # set x-axis limits\n",
    "plt.ylim(-1, 3)  # set y-axis limits\n",
    "\n",
    "# Plot the arrows with plt.quiver\n",
    "plt.quiver([0,0], [0,0], [v1[0],v2[0]], [v1[1],v2[1]], angles='xy', scale_units='xy', scale=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "id": "6df82dca",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2, 1])"
      ]
     },
     "execution_count": 123,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v1 = np.array([1,0])\n",
    "v2= np.array([0,1])\n",
    "#2,1\n",
    "2*v1+1*v2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "id": "8372d42f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.quiver.Quiver at 0x1e561138100>"
      ]
     },
     "execution_count": 124,
     "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": [
    "plt.xlim([-1,3])\n",
    "plt.ylim([-1,3])\n",
    "plt.quiver([0,0],[0,0],[v1[0],v2[0]],[v1[1],v2[1]],angles='xy',scale_units='xy',scale=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "56a155c1",
   "metadata": {},
   "source": [
    "## Matrices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "id": "37ea7a8d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1, 2],\n",
       "       [3, 4, 5],\n",
       "       [6, 7, 8]])"
      ]
     },
     "execution_count": 125,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m = np.array([[0,1,2],\n",
    "             [3,4,5],\n",
    "             [6,7,8]])\n",
    "m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "id": "deb55f7b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3, 3)"
      ]
     },
     "execution_count": 126,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# check shape of matrices\n",
    "m.shape\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "id": "c437f35a",
   "metadata": {},
   "outputs": [
    {
     "ename": "SyntaxError",
     "evalue": "invalid syntax (2753873972.py, line 1)",
     "output_type": "error",
     "traceback": [
      "\u001b[1;36m  Cell \u001b[1;32mIn[127], line 1\u001b[1;36m\u001b[0m\n\u001b[1;33m    getting full row\u001b[0m\n\u001b[1;37m            ^\u001b[0m\n\u001b[1;31mSyntaxError\u001b[0m\u001b[1;31m:\u001b[0m invalid syntax\n"
     ]
    }
   ],
   "source": [
    "getting full row\n",
    "m[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "id": "fce18dc9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1, 2],\n",
       "       [3, 4, 5]])"
      ]
     },
     "execution_count": 128,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#entire coloumn or row\n",
    "m[:2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "id": "ebc3c3d6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#diagonal element\n",
    "m[2,2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "id": "32f479c8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1, 2],\n",
       "       [3, 4, 5],\n",
       "       [6, 7, 8]])"
      ]
     },
     "execution_count": 130,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# by row and coloumn\n",
    "m[:3,:3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "id": "b6d371f7",
   "metadata": {},
   "outputs": [],
   "source": [
    "m[0,0]=10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "id": "74425f96",
   "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>precipitation</th>\n",
       "      <th>temp_max</th>\n",
       "      <th>temp_min</th>\n",
       "      <th>wind</th>\n",
       "      <th>weather</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2012-01-01</th>\n",
       "      <td>0.0</td>\n",
       "      <td>12.8</td>\n",
       "      <td>5.0</td>\n",
       "      <td>4.7</td>\n",
       "      <td>drizzle</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-01-02</th>\n",
       "      <td>10.9</td>\n",
       "      <td>10.6</td>\n",
       "      <td>2.8</td>\n",
       "      <td>4.5</td>\n",
       "      <td>rain</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-01-03</th>\n",
       "      <td>0.8</td>\n",
       "      <td>11.7</td>\n",
       "      <td>7.2</td>\n",
       "      <td>2.3</td>\n",
       "      <td>rain</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-01-04</th>\n",
       "      <td>20.3</td>\n",
       "      <td>12.2</td>\n",
       "      <td>5.6</td>\n",
       "      <td>4.7</td>\n",
       "      <td>rain</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-01-05</th>\n",
       "      <td>1.3</td>\n",
       "      <td>8.9</td>\n",
       "      <td>2.8</td>\n",
       "      <td>6.1</td>\n",
       "      <td>rain</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            precipitation  temp_max  temp_min  wind  weather\n",
       "date                                                        \n",
       "2012-01-01            0.0      12.8       5.0   4.7  drizzle\n",
       "2012-01-02           10.9      10.6       2.8   4.5     rain\n",
       "2012-01-03            0.8      11.7       7.2   2.3     rain\n",
       "2012-01-04           20.3      12.2       5.6   4.7     rain\n",
       "2012-01-05            1.3       8.9       2.8   6.1     rain"
      ]
     },
     "execution_count": 132,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "data = pd.read_csv(\"C:/Users/MR/Downloads/Compressed/archive/weather.csv\",index_col=0)\n",
    "data=data.ffill()\n",
    "data.head(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "id": "5d6e9263",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'x2=temp_min\\n    x3=wind\\n    w= weights\\n    b=bias'"
      ]
     },
     "execution_count": 133,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# y = w1x1+w2x2+w3x3+b\n",
    "# where x1= temp_max\n",
    "'''x2=temp_min\n",
    "    x3=wind\n",
    "    w= weights\n",
    "    b=bias'''"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "id": "be2039c7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Weather Prediction: 4.69\n"
     ]
    }
   ],
   "source": [
    "w1=.10\n",
    "w2=.20\n",
    "w3=.30\n",
    "b=1\n",
    "prediction = .10*12.8+.20*5.0+.30*4.7+1\n",
    "print(\"Weather Prediction:\",prediction)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d09f12e4",
   "metadata": {},
   "source": [
    "## Matric Multiplication"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "id": "c93c3949",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.4"
      ]
     },
     "execution_count": 135,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x= np.array([1,2,3])\n",
    "y= np.array([.10,.20,.30])\n",
    "np.dot(x,y)+1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "id": "2e1c9ce1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[12.8,  5. ,  4.7],\n",
       "       [10.6,  2.8,  4.5],\n",
       "       [11.7,  7.2,  2.3]])"
      ]
     },
     "execution_count": 136,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x= data[['temp_max','temp_min','wind']].iloc[:3].to_numpy()\n",
    "x\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "id": "b25a2a18",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3, 3)"
      ]
     },
     "execution_count": 137,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "id": "db89399f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3,)"
      ]
     },
     "execution_count": 138,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "id": "0acbaf28",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.1],\n",
       "       [0.2],\n",
       "       [0.3]])"
      ]
     },
     "execution_count": 139,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#now rechape the y into 3by 1\n",
    "Y = y.reshape(3,1)\n",
    "Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "id": "651ffdbc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3, 1)"
      ]
     },
     "execution_count": 140,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y.shape\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "id": "3b30716d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.69],\n",
       "       [3.97],\n",
       "       [4.3 ]])"
      ]
     },
     "execution_count": 141,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b= np.array([1])\n",
    "x@Y+b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "id": "163eb1f4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[12.8, 10.6, 11.7],\n",
       "       [ 5. ,  2.8,  7.2],\n",
       "       [ 4.7,  4.5,  2.3]])"
      ]
     },
     "execution_count": 142,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "id": "b8eaf4fc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1, 3)"
      ]
     },
     "execution_count": 143,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y.T.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "id": "8efa6064",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.69],\n",
       "       [3.97],\n",
       "       [4.3 ]])"
      ]
     },
     "execution_count": 144,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(Y.T @ x.T+b).T"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "459161fa",
   "metadata": {},
   "source": [
    "## Identity Matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "id": "074dcf8f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 0., 0.],\n",
       "       [0., 1., 0.],\n",
       "       [0., 0., 1.]])"
      ]
     },
     "execution_count": 145,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.eye(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "id": "4739b92a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-3.57956944,  3.07302659,  1.24806529],\n",
       "       [ 3.82861967, -3.38117349, -1.15801323],\n",
       "       [ 5.964542  , -4.83748417, -2.19361193]])"
      ]
     },
     "execution_count": 146,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.inv(x+.1*np.eye(3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "id": "6ad5300b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[12.9,  5. ,  4.7],\n",
       "       [10.6,  2.9,  4.5],\n",
       "       [11.7,  7.2,  2.4]])"
      ]
     },
     "execution_count": 147,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(x+.1*np.eye(3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "id": "b65b2c48",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.00000000e+00, -4.58965917e-15, -3.43923879e-17],\n",
       "       [-1.77635684e-15,  1.00000000e+00, -1.77635684e-15],\n",
       "       [-1.95084322e-15, -5.25468698e-15,  1.00000000e+00]])"
      ]
     },
     "execution_count": 148,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ridge = (x+.1*np.eye(3))\n",
    "inverse= np.linalg.inv(ridge)\n",
    "ridge @ inverse\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "id": "05eba452",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 149,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.allclose(ridge@inverse,np.eye(3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "id": "65ce7fa0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.84190241],\n",
       "       [0.17320122],\n",
       "       [0.25531186]])"
      ]
     },
     "execution_count": 150,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y= data[[\"temp_max\"]].iloc[:3].to_numpy()\n",
    "Y= np.linalg.inv(x.T@x+.1*np.eye(x.shape[0])) @x.T@y\n",
    "Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "id": "a5363811",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[12.84232277],\n",
       "       [10.5580324 ],\n",
       "       [11.68452435]])"
      ]
     },
     "execution_count": 151,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x@Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "id": "20873f04",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[12.8],\n",
       "       [10.6],\n",
       "       [11.7]])"
      ]
     },
     "execution_count": 154,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "id": "c82a0715",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[22.84232277],\n",
       "       [20.5580324 ],\n",
       "       [21.68452435]])"
      ]
     },
     "execution_count": 157,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b= np.array([10])\n",
    "x@Y+b"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0a19c233",
   "metadata": {},
   "source": [
    "# Derivative"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "id": "2b727190",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1e55d29c130>]"
      ]
     },
     "execution_count": 163,
     "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",
    "xs = np.arange(-10,10,.1)\n",
    "ys= xs**2\n",
    "plt.plot(xs,ys)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "id": "5b0d2ef8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10.0"
      ]
     },
     "execution_count": 164,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Find 2 x points close to 5\n",
    "x1 = 5 - 1e-8\n",
    "x2 = 5 + 1e-8\n",
    "\n",
    "# Calculate the corresponding y values\n",
    "y1 = x1 ** 2\n",
    "y2 = x2 ** 2\n",
    "\n",
    "# Calculate the slope (or derivative)\n",
    "# This will equal 2 times the midpoint of the x values (5)\n",
    "(y2 - y1) / (x2 - x1)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "id": "4f4114d6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1e561348ca0>]"
      ]
     },
     "execution_count": 166,
     "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": [
    "ys = xs * 2\n",
    "\n",
    "# Plot the derivative\n",
    "plt.plot(xs, ys)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a4a71828",
   "metadata": {},
   "source": [
    "As you can see, the derivative is an upward-sloping line. This tells us that the rate of change of the function increases as x increases.\n",
    "\n",
    "Derivatives are important for training neural networks. They allow us to determine how much to increase or decrease our network parameters. We'll learn more about this in the next lesson.\n",
    "\n",
    "You usually don't need to know how to find the equation of the derivative yourself, since you'll be given it beforehand. In a later lesson, we'll discuss how to find the derivative if you need to.\n",
    "\n",
    "Wrap-up\n",
    "In the next lesson, we'll build on what we learned here to automatically calculate the correct \n",
    "  W and  B\n",
    " values for linear regression using gradient descent. Gradient descent is a foundational concept of neural networks. I hope to see you there!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "debb281c",
   "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": "3.8.16"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}