py4ds-Session7-drafts.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "a0182b97",
   "metadata": {},
   "source": [
    "## Session 7 (numpy part c)\n",
    "\n",
    "### Universal Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "3169569d",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "fe8d1387",
   "metadata": {},
   "outputs": [],
   "source": [
    "# when you use numpy package it's best practice not to loop !"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "f68c5a5f",
   "metadata": {},
   "outputs": [],
   "source": [
    "a = np.random.randint(0, 100, size=10000000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "a440529e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "495015991\n",
      "CPU times: user 1.88 s, sys: 0 ns, total: 1.88 s\n",
      "Wall time: 1.88 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "sum = 0\n",
    "for n in a :\n",
    "    sum += n\n",
    "\n",
    "print(sum)    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "400ebb4d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "495015991\n",
      "CPU times: user 12.1 ms, sys: 0 ns, total: 12.1 ms\n",
      "Wall time: 9.55 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "sum = np.sum(a)\n",
    "print(sum)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "714f4c79",
   "metadata": {},
   "outputs": [],
   "source": [
    "# you may ask why ?\n",
    "# well, because python generic code interperet the code while numpy package uses the compiled code (machine code)\n",
    "# we have to use vector operation for vector calculations \n",
    "# do not use loops for vector operations"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a4a81578",
   "metadata": {},
   "source": [
    "### vector operations in numpy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "b20e7ea8",
   "metadata": {},
   "outputs": [],
   "source": [
    "a = np.array([1, 6, 3, 8, 9])\n",
    "b = np.array([6, 3, 6, 2, 1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "de8a64c8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 7,  9,  9, 10, 10])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a+b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "ef30b84b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 7,  9,  9, 10, 10])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.add(a, b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "acd4f592",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.16666667, 2.        , 0.5       , 4.        , 9.        ])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a/b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "3bae2054",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 2, 0, 4, 9])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a//b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "9173f44a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 0, 3, 0, 0])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a%b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "4054fcd5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.84147098, -0.2794155 ,  0.14112001,  0.98935825,  0.41211849])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sin(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "65e9616c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.        , 1.79175947, 1.09861229, 2.07944154, 2.19722458])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.log(a) # in e base, use log10 and log2 for 10, 2 log base"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "524e7a3f",
   "metadata": {},
   "source": [
    "### aggreation in numpy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "95d56779",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "27"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "61a0cb62",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.4"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "95ef12d2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.max(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "0f9043db",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.min(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "4b5e821c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2, 4, 3],\n",
       "       [7, 2, 1],\n",
       "       [3, 1, 3],\n",
       "       [6, 9, 9]])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c = np.array([[2, 4, 3], [7, 2, 1], [3, 1, 3], [6, 9, 9]])\n",
    "c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "6fdb976d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "50"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "a88123c9",
   "metadata": {},
   "outputs": [],
   "source": [
    "# aggregation over a specific dimension"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "37ab455b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 9, 10,  7, 24])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(c, axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "202fc392",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([18, 16, 16])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(c, axis=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8db9c67e",
   "metadata": {},
   "source": [
    "### missing values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "e166ff69",
   "metadata": {},
   "outputs": [],
   "source": [
    "a = 123\n",
    "name = \"amir\"\n",
    "b = None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "8a7ccd7e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4, 3, 9, None, 1], dtype=object)"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d = np.array([4, 3, 9, None, 1])\n",
    "d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "e5409b79",
   "metadata": {},
   "outputs": [],
   "source": [
    "# np.sum(d)  would raise error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "a187c23d",
   "metadata": {},
   "outputs": [],
   "source": [
    "# as you see, the data type for array d has changed to object\n",
    "# we could avoid that by using np.nan instead of None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "5802840d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 4.,  3.,  9., nan,  1.])"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "e = np.array([4, 3, 9, np.nan, 1])\n",
    "e"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "2583b801",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "nan"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# adding nan to the calculations will result to nan value\n",
    "np.sum(e)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "237faf63",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "17.0"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# we could ignore nan values in the calculations by using alternative numpy method for\n",
    "# arrays with nan values\n",
    "np.nansum(e)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "6309024f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 3., inf,  1.,  5.])"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# for infinite values we could use np.inf in numpy\n",
    "f = np.array([3, np.inf, 1, 5])\n",
    "f"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "6f687a13",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.33333333, 0.        , 1.        , 0.2       ])"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1/f"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "f196f6ea",
   "metadata": {},
   "outputs": [],
   "source": [
    "# 1/0 will raise error in python"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "f145ea29",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_6399/2975533412.py:3: RuntimeWarning: divide by zero encountered in true_divide\n",
      "  b/a\n",
      "/tmp/ipykernel_6399/2975533412.py:3: RuntimeWarning: invalid value encountered in true_divide\n",
      "  b/a\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([       nan, 1.        ,        inf, 1.33333333])"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.array([0, 2, 0, 3])\n",
    "b = np.array([0, 2, 3, 4])\n",
    "b/a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "7528f716",
   "metadata": {},
   "outputs": [],
   "source": [
    "# but with numpy, the result will be an inf (infinite) number\n",
    "# also 0/0 will result in nan"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "665e1ea8",
   "metadata": {},
   "source": [
    "### President heights dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "20deb46c",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "f6ece042",
   "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>order</th>\n",
       "      <th>name</th>\n",
       "      <th>height(cm)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>George Washington</td>\n",
       "      <td>189</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>John Adams</td>\n",
       "      <td>170</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>Thomas Jefferson</td>\n",
       "      <td>189</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>James Madison</td>\n",
       "      <td>163</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>James Monroe</td>\n",
       "      <td>183</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   order               name  height(cm)\n",
       "0      1  George Washington         189\n",
       "1      2         John Adams         170\n",
       "2      3   Thomas Jefferson         189\n",
       "3      4      James Madison         163\n",
       "4      5       James Monroe         183"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv('president_heights.csv')\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "id": "3f93f5f7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([189, 170, 189, 163, 183, 171, 185, 168, 173, 183, 173, 173, 175,\n",
       "       178, 183, 193, 178, 173, 174, 183, 183, 168, 170, 178, 182, 180,\n",
       "       183, 178, 182, 188, 175, 179, 183, 193, 182, 183, 177, 185, 188,\n",
       "       188, 182, 185])"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# h = df['height(cm)']  returns data series (i.e. index  height)\n",
    "h = df['height(cm)'].values # returns np array\n",
    "h"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "id": "8267b327",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "179.73809523809524"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(h)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "id": "86227654",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "182.0"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.median(h)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "id": "10df9d10",
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "id": "31032cea",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'histogram of US president heights')"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(h)\n",
    "plt.xlabel('heights (cm)')\n",
    "plt.ylabel('number')\n",
    "plt.title(\"histogram of US president heights\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "756c08d3",
   "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": "3.8.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}