Lab3 19Aug2021.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "8f4fffc1",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "26e09aa7",
   "metadata": {},
   "outputs": [],
   "source": [
    "user_data = {\n",
    "                \"Physics\" : np.random.randint(1,100,5),\n",
    "                \"Chemistry\" : np.random.randint(70,75,5),\n",
    "                \"Math\" : np.random.randint(30,80,5)\n",
    "            }"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "64350cac",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   Physics  Chemistry  Math\n",
      "0       57         74    45\n",
      "1       79         71    58\n",
      "2       72         73    52\n",
      "3       58         74    45\n",
      "4       62         70    48\n"
     ]
    }
   ],
   "source": [
    "df = pd.DataFrame(user_data)\n",
    "print(df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "328c5ea9",
   "metadata": {},
   "outputs": [
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      "text/plain": [
       "   Physics  Chemistry  Math\n",
       "0       57         74    45\n",
       "1       79         71    58\n",
       "2       72         73    52"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head(n=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "f57cc4de",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Index(['Physics', 'Chemistry', 'Math'], dtype='object')\n"
     ]
    }
   ],
   "source": [
    "print(df.columns)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "f0e73e9d",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Create a CSV file from this data frame\n",
    "df.to_csv('marks.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "3f6aa64b",
   "metadata": {},
   "outputs": [
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      "text/plain": [
       "   Unnamed: 0  Physics  Chemistry  Math\n",
       "0           0       57         74    45\n",
       "1           1       79         71    58\n",
       "2           2       72         73    52\n",
       "3           3       58         74    45\n",
       "4           4       62         70    48"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Read a CSV file\n",
    "my_data = pd.read_csv('marks.csv')\n",
    "my_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "80184516",
   "metadata": {},
   "outputs": [
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       "      <th>Physics</th>\n",
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      "text/plain": [
       "   Physics  Chemistry  Math\n",
       "0       57         74    45\n",
       "1       79         71    58\n",
       "2       72         73    52\n",
       "3       58         74    45\n",
       "4       62         70    48"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "my_data = my_data.drop(columns = ['Unnamed: 0'])\n",
    "my_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "cb21a2b8",
   "metadata": {},
   "outputs": [
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Physics</th>\n",
       "      <th>Chemistry</th>\n",
       "      <th>Math</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>5.000000</td>\n",
       "      <td>5.00000</td>\n",
       "      <td>5.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>65.600000</td>\n",
       "      <td>72.40000</td>\n",
       "      <td>49.600000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>9.555103</td>\n",
       "      <td>1.81659</td>\n",
       "      <td>5.504544</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>57.000000</td>\n",
       "      <td>70.00000</td>\n",
       "      <td>45.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>58.000000</td>\n",
       "      <td>71.00000</td>\n",
       "      <td>45.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>62.000000</td>\n",
       "      <td>73.00000</td>\n",
       "      <td>48.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>72.000000</td>\n",
       "      <td>74.00000</td>\n",
       "      <td>52.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>79.000000</td>\n",
       "      <td>74.00000</td>\n",
       "      <td>58.000000</td>\n",
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       "  </tbody>\n",
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      ],
      "text/plain": [
       "         Physics  Chemistry       Math\n",
       "count   5.000000    5.00000   5.000000\n",
       "mean   65.600000   72.40000  49.600000\n",
       "std     9.555103    1.81659   5.504544\n",
       "min    57.000000   70.00000  45.000000\n",
       "25%    58.000000   71.00000  45.000000\n",
       "50%    62.000000   73.00000  48.000000\n",
       "75%    72.000000   74.00000  52.000000\n",
       "max    79.000000   74.00000  58.000000"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "my_data.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "8a36554c",
   "metadata": {},
   "outputs": [
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       "      <th></th>\n",
       "      <th>Physics</th>\n",
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       "      <th>Math</th>\n",
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      "text/plain": [
       "   Physics  Chemistry  Math\n",
       "1       79         71    58\n",
       "2       72         73    52\n",
       "3       58         74    45\n",
       "4       62         70    48"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "my_data.tail(n=4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "13d7e9ef",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Physics      58\n",
       "Chemistry    74\n",
       "Math         45\n",
       "Name: 3, dtype: int64"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Access a particular row\n",
    "df.iloc[3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "54fa4634",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "74"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Access a particular row and col\n",
    "df.iloc[3,1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "06331911",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "74"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.iloc[3][1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "6f0a8872",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "74"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "idx = df.columns.get_loc('Chemistry')\n",
    "df.iloc[3][idx]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "eddde8e0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    74\n",
       "1    71\n",
       "2    73\n",
       "Name: Chemistry, dtype: int64"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.iloc[:3,idx]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "ff8b45f1",
   "metadata": {},
   "outputs": [
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      "text/plain": [
       "   Physics  Chemistry  Math\n",
       "1       79         71    58\n",
       "2       72         73    52\n",
       "4       62         70    48\n",
       "3       58         74    45\n",
       "0       57         74    45"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "my_data.sort_values(by = ['Physics'], ascending= False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "fbb26463",
   "metadata": {},
   "outputs": [
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       "      <th>3</th>\n",
       "      <td>58</td>\n",
       "      <td>74</td>\n",
       "      <td>45</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Physics  Chemistry  Math\n",
       "4       62         70    48\n",
       "1       79         71    58\n",
       "2       72         73    52\n",
       "0       57         74    45\n",
       "3       58         74    45"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "my_data.sort_values(by = ['Chemistry'], ascending= True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "4ffe790c",
   "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>Physics</th>\n",
       "      <th>Chemistry</th>\n",
       "      <th>Math</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>62</td>\n",
       "      <td>70</td>\n",
       "      <td>48</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>79</td>\n",
       "      <td>71</td>\n",
       "      <td>58</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>72</td>\n",
       "      <td>73</td>\n",
       "      <td>52</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>57</td>\n",
       "      <td>74</td>\n",
       "      <td>45</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>58</td>\n",
       "      <td>74</td>\n",
       "      <td>45</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Physics  Chemistry  Math\n",
       "4       62         70    48\n",
       "1       79         71    58\n",
       "2       72         73    52\n",
       "0       57         74    45\n",
       "3       58         74    45"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "my_data.sort_values(by = ['Chemistry', 'Physics'], ascending= True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "f08d9015",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "(5, 3)\n"
     ]
    }
   ],
   "source": [
    "print(type(my_data))\n",
    "print(my_data.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "c2e5d8c2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'numpy.ndarray'>\n",
      "(5, 3)\n"
     ]
    }
   ],
   "source": [
    "# Coverting Data Frame to Numpy Array\n",
    "data_array = my_data.values\n",
    "print(type(data_array))\n",
    "print(data_array.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "9f155b86",
   "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>P</th>\n",
       "      <th>C</th>\n",
       "      <th>M</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>57</td>\n",
       "      <td>74</td>\n",
       "      <td>45</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>79</td>\n",
       "      <td>71</td>\n",
       "      <td>58</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>72</td>\n",
       "      <td>73</td>\n",
       "      <td>52</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>58</td>\n",
       "      <td>74</td>\n",
       "      <td>45</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>62</td>\n",
       "      <td>70</td>\n",
       "      <td>48</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    P   C   M\n",
       "0  57  74  45\n",
       "1  79  71  58\n",
       "2  72  73  52\n",
       "3  58  74  45\n",
       "4  62  70  48"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Convert Numpy Array to data frame\n",
    "new_df = pd.DataFrame(data_array, dtype = 'int32', columns = ['P','C','M'])\n",
    "new_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "45b6d0ee",
   "metadata": {},
   "outputs": [],
   "source": [
    "#new_df.to_csv(\"PCM.csv\")\n",
    "new_df.to_csv(\"PCM.csv\", index = False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "7a2beb43",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    P   C   M\n",
      "0  57  74  45\n",
      "1  79  71  58\n",
      "2  72  73  52\n",
      "3  58  74  45\n",
      "4  62  70  48\n"
     ]
    }
   ],
   "source": [
    "pcm = pd.read_csv('PCM.csv')\n",
    "print(pcm)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "82306da1",
   "metadata": {},
   "source": [
    "# GRADIENT DESCENT (GENERAL)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "9f93d9a4",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "3528b22c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 1 2 3 4 5 6 7 8 9] [25 16  9  4  1  0  1  4  9 16]\n"
     ]
    }
   ],
   "source": [
    "X = np.arange(10)\n",
    "Y = (X-5) ** 2\n",
    "print(X,Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "3254970c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x396 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Visualization\n",
    "plt.style.use('seaborn')\n",
    "plt.plot(X,Y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "b4b9f2df",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0\n",
      "1.8\n",
      "2.4400000000000004\n",
      "2.9520000000000004\n",
      "3.3616\n",
      "3.68928\n",
      "3.9514240000000003\n",
      "4.1611392\n",
      "4.32891136\n",
      "4.4631290880000005\n",
      "4.570503270400001\n",
      "4.65640261632\n",
      "4.725122093056\n",
      "4.7800976744448\n",
      "4.82407813955584\n",
      "4.859262511644672\n",
      "4.8874100093157375\n",
      "4.90992800745259\n",
      "4.927942405962073\n",
      "4.942353924769658\n",
      "4.953883139815726\n",
      "4.9631065118525814\n",
      "4.9704852094820655\n",
      "4.976388167585652\n",
      "4.981110534068522\n",
      "4.984888427254818\n",
      "4.987910741803854\n",
      "4.990328593443083\n",
      "4.992262874754466\n",
      "4.993810299803573\n",
      "4.995048239842858\n",
      "4.996038591874287\n",
      "4.996830873499429\n",
      "4.9974646987995435\n",
      "4.997971759039634\n",
      "4.9983774072317075\n",
      "4.998701925785366\n",
      "4.998961540628293\n",
      "4.999169232502634\n",
      "4.999335386002107\n",
      "4.999468308801686\n",
      "4.9995746470413485\n",
      "4.999659717633079\n",
      "4.9997277741064625\n",
      "4.99978221928517\n",
      "4.999825775428136\n",
      "4.999860620342509\n",
      "4.999888496274007\n",
      "4.999910797019206\n",
      "4.999928637615365\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x396 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = 0 \n",
    "lr = 0.1\n",
    "\n",
    "plt.plot(X,Y)\n",
    "\n",
    "for i in range(50) :\n",
    "    \n",
    "    grad = 2 * (x-5)\n",
    "    x = x - lr * grad\n",
    "    y = (x-5) ** 2\n",
    "    \n",
    "    plt.scatter(x,y)\n",
    "    print(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "308f8bfe",
   "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": "3.8.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}