numba_solutons.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-29T18:40:32.969964Z",
     "start_time": "2023-06-29T18:40:30.159004Z"
    },
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "import time\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Numba"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " You have some code... you want to make it run fast "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Why do we use python?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "+ Readability and simplicity\n",
    "+ Rapid development and protyping\n",
    "+ Rich eco system of inbuilt libraries and frameworks\n",
    "+ Large and helpful community"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### What are we missing?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "+ Speed?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Compiled code vs Interpreted Code"
   ]
  },
  {
   "attachments": {
    "basicschema-2.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![basicschema-2.png](attachment:basicschema-2.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## How Numba works"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font size = 6> **Just in time (run time) compiler which converts bytecode to machine code** </font>"
   ]
  },
  {
   "attachments": {
    "pythontonumba.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![pythontonumba.png](attachment:pythontonumba.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "<font size = 6> Convenient : To use Numba to compile your code, you just need to apply one of the Numba decorators to your Python function </font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-29T18:40:34.095620Z",
     "start_time": "2023-06-29T18:40:32.974223Z"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import numba"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-29T18:40:34.107796Z",
     "start_time": "2023-06-29T18:40:34.099719Z"
    }
   },
   "outputs": [],
   "source": [
    "def integrate(a, b, n):\n",
    "    s = 0.0\n",
    "    dx = (b - a) / n\n",
    "    for i in range(n):\n",
    "        x = a + (i + 0.5) * dx\n",
    "        y = x ** 4 - 3 * x\n",
    "        s += y * dx\n",
    "    return s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-29T18:40:34.119652Z",
     "start_time": "2023-06-29T18:40:34.113342Z"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "a = 0\n",
    "b = 2\n",
    "n = 1_000_000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-29T18:40:36.870296Z",
     "start_time": "2023-06-29T18:40:34.134514Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "334 ms ± 7.98 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n"
     ]
    }
   ],
   "source": [
    "plaintime = %timeit -o integrate(a, b, n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-29T18:40:37.524407Z",
     "start_time": "2023-06-29T18:40:36.875689Z"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "#Add Numba decorator here\n",
    "@numba.njit \n",
    "def numba_integrate(a, b, n):\n",
    "    s = 0.0\n",
    "    dx = (b - a) / n\n",
    "    for i in range(n):\n",
    "        x = a + (i + 0.5) * dx\n",
    "        y = x ** 4 - 3 * x\n",
    "        s += y * dx\n",
    "    return s\n",
    "\n",
    "#now the decorated function will run entirely without \n",
    "#the involvement of the Python interpreter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-29T18:40:38.410497Z",
     "start_time": "2023-06-29T18:40:37.531842Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The slowest run took 38.53 times longer than the fastest. This could mean that an intermediate result is being cached.\n",
      "12.2 ms ± 24.8 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n"
     ]
    }
   ],
   "source": [
    "jittedtime = %timeit -o -n 10 numba_integrate(a, b, n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-29T18:40:38.792187Z",
     "start_time": "2023-06-29T18:40:38.416751Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "np.testing.assert_almost_equal(numba_integrate(a, b, n), integrate(a, b, n))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-29T18:40:38.808825Z",
     "start_time": "2023-06-29T18:40:38.795437Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "171.60698320412175"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plaintime.best/jittedtime.best"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<font size = 6>Why is there a slow run? </font>\n",
    "\n",
    "Numba has to compile your function for the argument types given before it executes the machine code version of your function. This takes time. \n",
    "\n",
    "However, once the compilation has taken place Numba caches the machine code version of your function for the particular types of datatypes presented. \n",
    "\n",
    "If it is called again, it can reuse the cached version, if it sees the same datatypes, instead of having to compile again."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-29T18:40:39.418488Z",
     "start_time": "2023-06-29T18:40:38.823222Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Elapsed (with compilation) = 0.19546s\n",
      "Elapsed (after compilation) = 0.00347s\n",
      "Elapsed (without numba) = 0.38547s\n"
     ]
    }
   ],
   "source": [
    "@numba.njit\n",
    "def numba_integrate(a, b, n):\n",
    "    s = 0.0\n",
    "    dx = (b - a) / n\n",
    "    for i in range(n):\n",
    "        x = a + (i + 0.5) * dx\n",
    "        y = x ** 4 - 3 * x\n",
    "        s += y * dx\n",
    "    return s          \n",
    "\n",
    "# COMPILATION TIME!\n",
    "start = time.perf_counter()\n",
    "numba_integrate(a, b, n)\n",
    "end = time.perf_counter()\n",
    "print(\"Elapsed (with compilation) = %0.5fs\" %(end - start))\n",
    "\n",
    "# NOW THE FUNCTION IS COMPILED, RE-TIME IT EXECUTING FROM CACHE\n",
    "start = time.perf_counter()\n",
    "numba_integrate(a, b, n)\n",
    "end = time.perf_counter()\n",
    "print(\"Elapsed (after compilation) = %0.5fs\" %(end - start))\n",
    "\n",
    "#Original function\n",
    "start = time.perf_counter()\n",
    "integrate(a, b, n)\n",
    "end = time.perf_counter()\n",
    "print(\"Elapsed (without numba) = %0.5fs\" %(end - start))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-29T18:40:39.434501Z",
     "start_time": "2023-06-29T18:40:39.422787Z"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(int64, int64, int64)]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "numba_integrate.signatures"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-29T18:40:39.462166Z",
     "start_time": "2023-06-29T18:40:39.438586Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.39999994666667177"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "numba_integrate(0, 2, 10000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## What can you use numba on?\n",
    "\n",
    "If your code is numerically orientated (does a lot of math), uses NumPy a lot and/or has a lot of loops, then Numba is often a good choice.\n",
    "\n",
    "* Functions with loops\n",
    "* Functions with mathematical operations\n",
    "* Functions using numpy\n",
    "\n",
    "***OK***: tuples, strings\n",
    "\n",
    "***Not good***: objects, Python lists, python dicts"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<font size=8> **Hands on exercise** <font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Function ```estimate_pi``` calculates the value of $pi$\n",
    "\n",
    "Notice that the greater the value of n, the better is the estimate of $pi$\n",
    "\n",
    "You task is to:\n",
    "+ Use time or timeit to benchmark the speed up in execution of the function for different *n* with and without numba\n",
    "+ Plot the difference in time for different *n* with and without numba \n",
    "\n",
    "**(Ensure that the numba function is compiled before timing the function)**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-29T18:40:39.478030Z",
     "start_time": "2023-06-29T18:40:39.468996Z"
    },
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "#This function takes n as input which is the number of total points within the square\n",
    "#It then estimates how many of those points are within the circle\n",
    "# value of pi = 4 * numberofpointsincircle/numberofpointsinsquare\n",
    "\n",
    "def estimate_pi(n):\n",
    "    np.random.seed(1234)\n",
    "    count_inside_circle = 0\n",
    "    for _ in range(n): #Numba likes loops\n",
    "        x = np.random.uniform(-1, 1) #Numba likes numpy functions\n",
    "        y = np.random.uniform(-1, 1)\n",
    "        \n",
    "        if x**2 + y**2 <= 1:\n",
    "            count_inside_circle += 1\n",
    "    \n",
    "    pi_estimate = 4 * count_inside_circle / n #Numba likes math\n",
    "    return pi_estimate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-29T18:40:39.809136Z",
     "start_time": "2023-06-29T18:40:39.484334Z"
    }
   },
   "outputs": [],
   "source": [
    "@numba.njit\n",
    "def numba_estimate_pi(n):\n",
    "    np.random.seed(1234)\n",
    "    count_inside_circle = 0\n",
    "    for _ in range(n): #Numba likes loops\n",
    "        x = np.random.uniform(-1, 1) #Numba likes numpy functions\n",
    "        y = np.random.uniform(-1, 1)\n",
    "        \n",
    "        if x**2 + y**2 <= 1:\n",
    "            count_inside_circle += 1\n",
    "    \n",
    "    pi_estimate = 4 * count_inside_circle / n #Numba likes math\n",
    "    return pi_estimate\n",
    "numba_estimate_pi(2); #Compile"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-29T18:40:54.649889Z",
     "start_time": "2023-06-29T18:40:39.812404Z"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of runs 10, Estimated Pi: 3.60\n",
      "Number of runs 1000, Estimated Pi: 3.06\n",
      "Number of runs 10000, Estimated Pi: 3.12\n",
      "Number of runs 100000, Estimated Pi: 3.14\n",
      "Number of runs 1000000, Estimated Pi: 3.14\n"
     ]
    }
   ],
   "source": [
    "n = [10, 1000, 10000, 100_000, 1_000_000]\n",
    "for i in n:\n",
    "    pi_estimate = estimate_pi(i)\n",
    "    print(\"Number of runs %d, Estimated Pi: %0.2f\" %(i, pi_estimate))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-29T18:43:05.087514Z",
     "start_time": "2023-06-29T18:40:54.661170Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Calculating using n=10\n",
      "Calculating using n=1000\n",
      "Calculating using n=10000\n",
      "Calculating using n=100000\n",
      "Calculating using n=1000000\n"
     ]
    }
   ],
   "source": [
    "#Time functions with and without numba\n",
    "plaintime, jittedtime = [], []\n",
    "for idx, i in enumerate(n):\n",
    "    print('Calculating using n=%d' %i)\n",
    "    temptime = %timeit -o -q estimate_pi(i)\n",
    "    plaintime.append(temptime.best)\n",
    "    \n",
    "    temptime = %timeit -o -q numba_estimate_pi(i)\n",
    "    jittedtime.append(temptime.best)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-29T18:43:05.444269Z",
     "start_time": "2023-06-29T18:43:05.089693Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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bqXeOm6fl+x1Kh4V1odnM/mRmvc2sB8HrCRvM7K7ohiYikjiqauv504odXDR6ICP6dvc7nA4Lt/fROc65o8BVwKsEB7O7MVpBiYgkmkXv7+LQiRq+lgBzJrQm3KSQbmbpBJPCIm8gO02OLCJCsBvqgiWljBrYi2ln9PU7nE4JNyn8FigFegD/NLM84Gi0ghIRSSQrSg6xYfdR5s7IJzjOZ+IK6/K4c+4R4JGQVdvN7MLohCQiklgWFJeS0z2dq8YP9TuUTmvrPoU729j/5xGMRUQk4ZQdPsnr6/dw66fPoFtGqt/hdFpbRwoNE4qOAiYBi7zly4EV0QpKRCRRPLFsO2bGjdPy/A4lItq6T+FHAGb2T2Cic+6Yt3wfcNo9DCIiyeRkTR1PrdjJJecOZGhON7/DiYhwLzQPBGpClmu8dSIiSeuFNbuoqKxl7vQCv0OJmHDvw34cWGFmf/WWrwIWRiUiEZEE4JxjQXEJ5w7pzaT8Pn6HEzHh9j76iZm9BpzvrZrnnFsTvbBEROJb8daDfLT3OA9eMzbhu6GGas+ITWuB3Q37mNkI59yOaAQlIhLv5i8poW+PDC4fN8TvUCIqrKRgZrcTnFN5L1APGME7msdGLzQRkfi0/eAJ/rFpH7ddeCZZ6YnfDTVUuEcK3wJGOecORjMYEZFEsLB4O6lm3DC1a3RDDRVu76OdQEU0AxERSQTHq+t4ZtVOLisczMDeWX6HE3HhHilsAxab2StAdcNK55zuaBaRpPLc6jKOVdcxL8FHQ21JuElhh/fI8B4iIkknEHAsLC5l3PAcJozoOt1QQ4XbJbXhzuae3vLxaAYlIhKP3vl4P9sOnODh68f7HUrUhDvz2hgzWwOsB9ab2WozOze6oYmIxJcFS0oZ0CuTS8cM9juUqAn3QvOjwJ3OuTznXB7wXeCx6IUlIhJftuw7zjsf7eeGqXlkpIX71Zl4wv1kPZxzbzcsOOcWE5xwR0QkKTy+tJSM1BTmTB7hdyhRFXbvIzP7X8AT3vINBHskiYh0eRWVtTy7uozLxw2hf69Mv8OJqnCPFL4G9AeeB54D+nnrRES6vGdW7eRkTX2X7YYaKtzeR4eBO6Ici4hI3KkPOBYuLWVSfh/GDM32O5yoC7f30RtmlhOy3MfMXo9aVCIiceKtTfvYeaiyS82Z0JpwTx/1c84daVjwjhwGdLRSM8sxs2fNbJOZbTSzaR0tS0QkmuYvKWFwdhaXnJsc84qFmxQCZtZ4yd3M8giOktpRDwOvOedGA+OAjZ0oS0QkKjbvOUbx1oPcOC2PtNSu2w01VLi9j/4DeNfM3iE4bPYFwK0dqdDMsoFPA3MBnHM1nDrVp4hIXFhQXEJmWgpzJnXtbqihwr3Q/JqZTQSmequ+7Zw70ME6C4D9wHwzGwesBr7lnDvRwfJERCLu8Ika/rqmnC9OGEqfHskz5Fu4F5oNmAVMdM69DHQ3s8kdrDMNmAj8P+fcBOAEcE8zdd5qZqvMbNX+/fs7WJWISMc8tXInVbUB5iZBN9RQ4Z4k+7/ANGCOt3wM+HUH6ywDypxzy73lZwkmiVM45x51zhU554r69+/fwapERNqvrj7AE0tLmTayL6MH9fY7nJgKNylMcc79D6AKGnsfdeh4yjm3B9hpZqO8VRcBGzpSlohINPx9w152VVQlxc1qTYV7obnWzFLxehyZWX8g0Il6bweeNLMMgsNlzOtEWSIiEbVgSSnDc7tx0aeSoxtqqHCTwiPAX4EBZvYT4Brg3o5W6pxbCxR1dH8RkWj5sLyCFaWHuPcLnyI1xfwOJ+bC7X30pJmtJniqx4CrnHO6t0BEupwFxaV0z0jl2qLhfofii3B7H50BlDjnfg18CHw+dNgLEZGu4MDxahat3cWXJg4ju1u63+H4ItwLzc8B9WZ2JvBbYDjwp6hFJSLigz8v30FNfYCbp+f7HYpvwh7mwjlXB1wN/Mo5dxfQdeejE5GkU1MX4Ill2/n02f05c0BPv8PxTbhJodbM5gA3AS9765Lz2EpEuqRXP9zNvmPVzEviowQIPynMI3jz2k+ccyVmVsAns7CJiCS8+UtKKejXg8+cndw3y4bb+2gDIZPsOOdKgJ9FKygRkVhas+Mwa3ce4b7LzyElCbuhhkqOsWBFRFqxoLiUnplpXJOk3VBDKSmISFLbe7SKVz7YzbVFw+iZGe79vF2XkoKIJLUnl22n3jlunpbvdyhxIay0aGZnA3cBeaH7OOc+G6W4RESirrqunieX7+CzowaQ36+H3+HEhXCPlZ4BfgM8BtRHLxwRkdh56f3dHDxRw7wZBX6HEjfCTQp1zrn/F9VIRERiyDnH/CUlnDWgJzPO7Ot3OHEj3GsKL5nZN81ssJnlNjyiGpmISBSt2n6Y9buOMndGPsHJJQXCP1K42Xu+K2SdA0ZGNhwRkdhYsKSU3llpfHHCUL9DiSvh3rymE24i0mXsOlLJa+v3cMv5BXTPUDfUUK22hpl91jn3lpld3dz7zrnnoxOWiEj0PLFsO845bpyW53cocaetFPkZ4C3g8mbec4CSgogklMqaev68YgcXnzOIYX26+x1O3Gk1KTjnfug9aw5lEekSXlxbzpGTtcydke93KHGp1d5HZnaDmbW4jZmdYWbnRz4sEZHIC3ZDLeVTg3szpUAdKJvT1umjvsAab37m1cB+IAs4k+CppQPAPVGNUEQkQpZuO8jmvcd44Etj1Q21BW2dPnrYzH4FfBaYAYwFKoGNwI3OuR3RD1FEJDLmLyklt0cGV4wf4ncocavNvljOuXrgDe8hIpKQdh46yZsb9/LNmWeQlZ7qdzhxS6OkikhSWFhcSooZN07N9zuUuKakICJd3onqOv6yaieXjhnEoOwsv8OJa0oKItLlPf9eGceq6jQaahjCnU8hE/gSkM+p8yn8ODphiYhERiDgWFBcythh2UwckeN3OHEv3COFF4ErgTrgRMhDRCSu/WvLAbbuP8E8jYYalnBHghrmnJsV1UhERKJgwZIS+vXM5LLCwX6HkhDCPVIoNrPCqEYiIhJh2/Yf5+3N+7lh6ggy09QNNRzhHimcD8w1sxKgGjDAOefGRi0yEZFOenzpdtJTja9MGeF3KAkj3KRwaVSjEBGJsKNVtTyzaieXjx3CgF7qhhqusE4fOee2A8OBz3qvT4a7b0vMLNXM1pjZy50pR0SkOc+uKuNETb1GQ22nsL7YzeyHwP8Evu+tSgf+2Mm6v0VwDCURkYiqDzgWLi3lvLw+jB2W43c4CSXc//a/CFyB1w3VObcL6NXRSs1sGPAF4HcdLUNEpCWLN+9j+8GTzJ2e73coCSfcpFDjnHMEZ1vDzHp0st5fAncDgU6WIyJymvlLShnUO4tZYwb5HUrCCTcpPG1mvwVyzOwbwJt08L98M5sN7HPOrW5ju1vNbJWZrdq/f39HqhKRJPTx3mO8u+UAN07LIz1VI/m0V7i9jx4CPgccBUYBPwD+2cE6ZwBXmNllBCfs6W1mf3TO3RC6kXPuUeBRgKKiItfBukQkycwvLiUjLYU5k9UNtSPCTQq/d859DW9OBTPrCfwNuKi9FTrnvo93wdrMZgLfa5oQREQ6ouJkLc+/V8ZV44eQ2yPD73ASUrjHVuVm9n8BzKwP8Hc63/tIRCSinlq5g6raAHOnazTUjgr3PoX/BRw3s98QTAgPOefmd7Zy59xi59zszpYjIlJXH+DxpduZUpDLOUN6+x1Owmo1KZjZ1Q0PYDkwFVgDOG+diEhceHPjXsqPVGrOhE5q65rC5U2W1xC8ce1ygt1Tn49GUCIi7TV/SSlDc7rx+XMG+h1KQms1KTjn5sUqEBGRjlq/q4LlJYf498tGk5qiORM6I9yZ17KArwPnEuxGCoDXI0lExFcLi0vplp7KdUXqhtpZ4fY+egIYBFwCvAMMA45FKygRkXAdPF7NC2t3cfXEoWR3T/c7nIQXblI40+uBdMI5t5DguEVToheWiEh4nlq5k5q6gMY5ipBwk0Kt93zEzMYA2cCA6IQkIhKe2voATyzdzgVn9eOsgR0eo1NChJsUHvVuWrsXWARsAH4WtahERMLw2od72HO0SkcJERTuMBf/cM4dJjje0UgAM1NnYBHx1fwlJeT17c6Fo3TiIlLCPVJ4rpl1z0YyEBGR9nh/5xHe23GEm6flk6JuqBHT6pGCmY0m2A01u8kdzL0J6ZoqIhJrC4pL6ZGRyrVFw/wOpUtp6/TRKGA2kMOpdzcfA74RpZhERFq171gVL3+wi69OyaNXlrqhRlJbdzS/CLxoZtOcc0tjFJOISKueXLaD2nrHzbrAHHHhjpKqhCAicaG6rp4nl+/gwlH9KejX2ZmBpSnNVSciCeWVD3Zz4Hi1RkONEiUFEUkYzjnmLynljP49uOCsfn6H0yWFlRTMbKCZ/d7MXvWWzzGzr0c3NBGRU7234zDryiuYO6MAM3VDjYZwjxQWAK8DQ7zlj4BvRyEeEZEWzV9SSq+sNK6eMNTvULqscJNCP+fc00AAwDlXB9RHLSoRkSZ2V1Ty6od7uH7ScHpkhjsYg7RXuEnhhJn1JTjbGmY2FaiIWlQiIk38cdl2nHPcNC3f71C6tHDT7Z0EB8I7w8yWAP2Ba6IWlYhIiKraev60fAef+9RAhud29zucLi2spOCce8/MPkPwDmcDNjvnatvYTUQkIhat3cXhk7XMnZHvdyhdXrjTcaYClwH53j4XmxnOuZ9HMTYREZxz/GFJCaMH9WLayL5+h9PlhXv66CWgCliHd7FZRCQWlpccYtOeY9x/daG6ocZAuElhmHNubFQjERFpxvwlJeR0T+cqdUONiXB7H71qZhdHNRIRkSZ2HjrJGxv2MmfyCLLSU/0OJymEe6SwDPirmaUQnK/ZAOec6x21yEQk6T2xbDtmxo1T8/wOJWmEmxR+DkwD1jnnXBTjEREB4GRNHU+t2MGscwcxJKeb3+EkjXBPH+0EPlRCEJFYef69co5W1TFP3VBjKtwjhW3AYm9AvOqGleqSKiLR4JxjQXEpY4b25ry8Pn6Hk1TCTQol3iPDe4iIRM27Ww6wZd9xHrp2nLqhxli4dzT/KNqBiIg0WLCklH49M5g9brDfoSSdVpOCmf3KOXebmb2ENxheKOfcFVGLTESSUumBE7y1eR+3f/YsMtPUDTXW2jpSuAm4DfjPSFVoZsOBx4GBBBPNo865hyNVvogktoVLS0lLMW6YMsLvUJJSW0lhK4Bz7p0I1lkHfNcbZK8XsNrM3nDObYhgHSKSgI5V1fLMqjK+UDiYAb2z/A4nKbWVFPqb2Z0tvdmR3kfOud3Abu/1MTPbCAwFlBREktxzq8s4Xl3H3BkFfoeStNpKCqlAT4J3MEecmeUDE4Dl0ShfRBJHIOBYuHQ7E0bkMH54jt/hJK22ksJu59yPo1GxmfUEngO+7Zw72sz7twK3AowYoXOLIl3dOx/tp+TACR6+frzfoSS1tu5ojtYRQjrBhPCkc+755rZxzj3qnCtyzhX1798/GmGISBz5w5ISBvbO5LJCdUP1U1tJ4aJIV2jBO1F+D2zUHdEiArBl3zH+9fEBbpiSR3pquKPvSDS02vrOuUNRqHMGcCPwWTNb6z0ui0I9IpIgFhSXkpGWwlfUDdV34Q5zETHOuXeJ0mkpEUk8FZW1PLe6nCvGDaFvz0y/w0l6Ok4TEV89vXInlbX1zJ2e73cogpKCiPioPuBYuLSUyfm5jBma7Xc4gpKCiPjozY17KTtcqTkT4oiSgoj4ZsGSUobmdOPz5wz0OxTxKCmIiC827j7K0m0HuXFaHmnqhho39JMQEV8sLC4lKz2F6ycN9zsUCaGkICIxd+hEDX9dU84XJwwjp7smc4wnSgoiEnNPrdxBdV1A3VDjkJKCiMRUbX2AJ5ZuZ8aZfRk1qJff4UgTSgoiElN/X7+X3RVVzJ2uORPikZKCiMTU/CUljMjtzmdHD/A7FGmGkoKIxMy6sgpWbT/MTdPySE3REGjxKOYD4olI8nlhTTkPvr6Z8iOVGNAjM9XvkKQFSgoiElUvrCnn+8+vo7K2HgAH/PiljXRLT+OqCUP9DU5Oo9NHIhIVR07W8Pf1e7j3hU8SQoPK2noefH2zT5FJa3SkICIRceB4NStKDrF820GWlxxi895jONfy9ruOVMYuOAmbkoKIdMjeo1Us8xLAipJDbNl3HIBu6amcl9eHLxQOZsrIvnz7qTXsqqg6bf8hOd1iHbKEQUlBRMJSdvgky7cdYnnJQVaUHKL04EkAemamUZTfhy9NHMaUkbkUDs0+ZZ7lu2eNPuWaAgQTx12XjIr5Z5C2KSmIyGmcc2w/eJLlJQe9RHCIcu90T3a3dCbl53LD1DymFPTlU4N7tTrKacPF5Adf38yuI5UMyenGXZeM0kXmOGWutZN+caKoqMitWrXK7zBEuiznHFv2HWd5ySHvdNBB9h6tBqBvjwwmF+QypSCXKSP7MmpgL1J0j0GiaPcPSkcKIkkoEHBs2nOMFSWfXBM4eKIGgIG9M5lS0JfJBblMHZnLGf17YqYkkCyUFESSQF19gA27jzaeClpZeoiKyloAhuZ04zOj+gePBAr6kte3u5JAElNSEOmCausDfFBW0XhReFXpYY5X1wGQ37c7s84dxJSRuUwuyGVYn+4+RyvxRElBpAuoqq3n/Z1HGk8Frd5+uLG3z5kDenLl+CFMGdmXKQW5DOyd5XO0Es+UFEQSUGVNPe/tONx4o9ianUeoqQtgBqMG9uK6ScOZUpDLpIJc+vXM9DtcSSBKCiIJ4Hh1HatKg9cDlm87yLryCmrrHSkG5w7J5qapeUwZ2ZdJ+X00vaV0ipKCSByqOFnLytLgjWLLSw7xYXkFAQdpKUbhsGy+fv5IpozMpSivD72y0v0OV7oQJQWROHDweDUrSw+xzOsdtGnPUZyDjNQUxo/I4X9ceCZTCvoyMS+H7hn6s5Xo0W+XiA/2Ha1imXeT2PJth/jYGzcoKz2F8/L68O2LzmbKyFzGD88hK11zD0jsKCmIxED5kUqWbwt2D11ecoiSAycA6JGRSlF+LldNGMrUkbkUDs0hI00j2ot/lBREOqBhJrHmxvJxzrHjUHDwuGXefQJlh4PjBvXOSmNyQS5fmTyCyQW5nDukd6vjBonEmsY+EmmnpjOJAWSmpXDF+CFU1wZYUXKIPUeDQ0Xn9shgcn5u441iowf11tzEEkuJMfaRmc0CHgZSgd855+73Iw5JXs45ausd1XX1VNUGmn2ubmH9f7215bSZxKrrAjyzqoz+vTIbB46bWpDLmQM0bpB0wAdPwz9+DBVlkD0MLvoBjP1yTKqOeVIws1Tg18DngTJgpZktcs5tiGQ9Kxf9luHvPcgAt5991p+dE+9i0hX/FskquhS/2ss5R019oM0v4uraAFUNz7X1VNcFWvwyb6ushudAJw6Sr0h5l7vTnmaIHWCX68cDdV/mpcD5rPj3i5QEmuPjl1zC+eBpeOkOqPVmpqvYGVyGmLSZH0cKk4EtzrltAGb2FHAlELGksHLRbxmz+l66WQ0YDGI/2avvZSV02cTgnGuc+tA1LDe+Bw53ytSIn2zreP+Vxxi/9gentdeblTUMnHFTq1+sHf1CbtyuLtDqlI1tSU81MtNSyUpPITMtlUzvObicQp8eGWSmpZCVntrqc2bT5ZAys9KD72d52z344P/mf9b+ju4WHFV0mB3g/vTfkZuegdkXOv5huqpYfsk5By7g/YI3fe0tN/s6ZJvT9mutvDDKbnW/ZuJ7/d8/aasGtZXBpBqDpBDzawpmdg0wyzl3i7d8IzDFOXdbS/u095rCnvvOZBD7T1tf61IpTxnc4n6ttoRr9mWLG7e4TTNvhPsTcO3ZuB3ybQ/pVn/a+lqXynY3MKwyzMDMsJDXKXjrDG+9kdLMdmaQgredgTW+9rYPKSel6b6Ra4awBQ5uI8XVnb7eUknJHRmypo0fVpt/e62879e+bb7dzJtHd4E7/fcLS4Ee/Vv50qWVL/FmvnS7PIP7jnRgp/aJ295HZnYrcCvAiBEj2rXvALe/2aZIo55DPc887S1rduH0Lxw7bePm9226pzWz8Wllt3DKoWn5p29lYZbf8n5p+8qbrTuNenrmjSPVjJQUC3mmybI1U37XlXLgo+bXu3oYVHjqyjYbpo33W93fr33b2L/pvmufbH47F4BRlwbLMvOeU1p43dI23nKzry3Msluqp5Wyoxnfs1+DE6f/U0v2sDZ+JpHhR1IoB4aHLA/z1p3COfco8CgEjxTaU8E+69/skcJe68/E777YrmCTQUtHVnutP4O+/pQPEcW5slXBUyBNZQ+Ha+fHPp54V/LPltvr8odjH0+8u+Snp55uA0jvFrwOEwN+dJBeCZxlZgVmlgFcDyyKZAU7J95FpTt1ULBKl8HOiXdFspouQ+3VThf9IPhHGiqGf7QJR+3VPmO/DJc/EkyamJc8H+m6vY+cc3VmdhvwOsEuqX9wzq2PZB2Trvg3VoLXm+YA+6wfO89T76OWqL3aqeGPU71pwqP2ar+xX/atfXTzmohI19Xuq326v15ERBopKYiISCMlBRERaaSkICIijZQURESkUUL0PjKz/cD2Du7eDzgQwXC6OrVX+6i92kft1T6dba8DzrlZ7dkhIZJCZ5jZKudckd9xJAq1V/uovdpH7dU+frSXTh+JiEgjJQUREWmUDEnhUb8DSDBqr/ZRe7WP2qt9Yt5eXf6agoiIhC8ZjhRERCRMXSopmNkfzGyfmX0Ysi7XzN4ws4+95z5+xuiH9rSLBT1iZlvM7AMzmxiyz83e9h+b2c1+fJZoiXYbmdl5ZrbO2+cRS8CJnP1qo0T6G463NmqtjhYF5/btGg/g08BE4MOQdQ8A93iv7wF+5nec8dwuwGXAqwRHV5wKLPfW5wLbvOc+3us+fn+2RGkjYIW3rXn7Xur3Z06UNkqkv+F4a6OW6mj1M/jdiFH4oeQ3+YFsBgZ7rwcDm/2OMZ7bBfgtMKfpdsAc4Lch60/Zris8otVG3nubQtafsl0iPfxoo0T7G46nNmqpjtbi71Knj1ow0Dm323u9BwhvJvqur6V2GQqEzp1Y5q1raX1XFqk2Guq9brq+K4hFGyX637CfbdTuv9tkSAqNXDBVqrtVE2qXtqmN2haLNkr0n0MitFEyJIW9ZjYYwHve53M88aKldikHhodsN8xb19L6rixSbVTuvW66viuIRRsl+t+wn23U7r/bZEgKi4CGq/c3Ay/6GEs8aaldFgE3eb0WpgIV3mHp68DFZtbH69lwsbeuK4tIG3nvHTWzqV5vkZvoOr+HsWijRP8b9rONWqqjZX5flInwBZ4/A7uBWoLnzr4O9AX+AXwMvAnk+h1nPLcLwV4Kvwa2AuuAopByvgZs8R7z/P5cidRGQBHwobfPr/BuHE2kh19tlEh/w/HWRq3V0dJDdzSLiEijZDh9JCIiYVJSEBGRRkoKIiLSSElBREQaKSmIiEgjJQWJS2bmzOyhkOXvmdl9ESp7gZldE4my2qjnWjPbaGZvR6Csv5lZThvbzDWzIZ2tS5KbkoLEq2rgajPr53cgocwsrR2bfx34hnPuws7W65y7zDl3pI3N5gJKCtIpSgoSr+oITkX4naZvNP1P38yOe88zzewdM3vRzLaZ2f1m9lUzW+GNQX9GSDGfM7NVZvaRmc329k81swfNbKU39vy/hZT7LzNbBGxoJp45XvkfmtnPvHU/AM4Hfm9mDzbZfqaZ/dPMXjGzzWb2GzNLaaksb32pmfUzs3zv6OMxM1tvZn83s25eexQBT5rZWm/d/Wa2wfss/9mxH4MkHb/vANRDj+YewHGgN1AKZAPfA+7z3lsAXBO6rfc8EzhCcOjgTIJjvPzIe+9bwC9D9n+N4D9FZxG88zQLuBW419smE1gFFHjlngAKmolzCLAD6A+kAW8BV3nvLaaZO0i98qqAkUAq8AZwTRtllQL9CA7LXAeM99Y/DdzQtD6Cd7hu5pM7XnP8/pnqkRgPHSlI3HLOHQUeB+5ox24rnXO7nXPVBG/t/7u3fh3BL9QGTzvnAs65jwlOYjKa4BgzN5nZWmA5wS/Ws7ztVzjnSpqpbxKw2Dm33zlXBzxJcKKVtqxwzm1zztUTHBrh/HaUVeKcW+u9Xt3kczWoIJh4fm9mVwMnw4hJRElB4t4vCZ6b7xGyrg7vd9c77ZIR8l51yOtAyHKA4H/fDZqO7+IIjhNzu3NuvPcocM41JJUTnfkQzWiu/nCFfsZ6Tv1cwcKCSWUy8Cwwm+CRkUiblBQkrjnnDhE8RfL1kNWlwHne6yuA9A4Ufa2ZpXjXGUYSPNXyOvDfzSwdwMzONrMerRVCcHrEz3jn+1MJzob1Thj1TzazAi+pXQe824myGhwDenmx9wSynXN/I3hdZlw7ypEk1p6eFCJ+eQi4LWT5MeBFM3uf4H/AHfkvfgfBL+HewH9zzlWZ2e8Inop5zxuaeD9wVWuFOOd2m9k9wNsEjzRecc6FM7TzSoKjXJ7p7ftX51ygg2U1WAD8xswqgUsJtlGWV9ad7ShHkphGSRWJMTObCXzPOTfb51BETqPTRyIi0khHCiIi0khHCiIi0khJQUREGikpiIhIIyUFERFppKQgIiKNlBRERKTR/wfqIOJFZIqwBwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Plot the results\n",
    "fs, ax = plt.subplots(1)\n",
    "ax.plot(np.arange(len(n)), plaintime, marker='o', label='Without numba')\n",
    "ax.plot(np.arange(len(n)), jittedtime, marker='o', label='With numba')\n",
    "ax.set_xticks(np.arange(len(n)))\n",
    "ax.set_xticklabels(n)\n",
    "ax.set_xlabel('Number of points')\n",
    "ax.set_ylabel('Time taken (in seconds)')\n",
    "# ax.set_yscale('log')\n",
    "ax.legend()\n",
    "sns.despine()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## What does numba *not* do? : Choose wisely!\n",
    "* Magically make individual numpy functions faster, or speed up code that just has nice array operations\n",
    "* Convert aribitrary python data types\n",
    "* Translate entire programs\n",
    "* Compile third party libraries\n",
    "* Numba cannot help speed up algorithms that are not primarily numerical"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Example 1 : Numba does not work on pandas dataframes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-29T18:43:05.914915Z",
     "start_time": "2023-06-29T18:43:05.449627Z"
    }
   },
   "outputs": [
    {
     "ename": "TypingError",
     "evalue": "Failed in nopython mode pipeline (step: nopython frontend)\nnon-precise type pyobject\nDuring: typing of argument at <ipython-input-18-52bead916339> (7)\n\nFile \"<ipython-input-18-52bead916339>\", line 7:\ndef use_pandas(a): # Function will not benefit from Numba jit\n    df = pd.DataFrame.from_dict(a) # Numba doesn't know about pd.DataFrame\n    ^ \n\nThis error may have been caused by the following argument(s):\n- argument 0: Cannot determine Numba type of <class 'dict'>\n",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypingError\u001b[0m                               Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-18-52bead916339>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      9\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mdf\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcov\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m                \u001b[0;31m# or this!\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     10\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 11\u001b[0;31m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0muse_pandas\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m/opt/anaconda3/envs/noreward/lib/python3.8/site-packages/numba/core/dispatcher.py\u001b[0m in \u001b[0;36m_compile_for_args\u001b[0;34m(self, *args, **kws)\u001b[0m\n\u001b[1;32m    466\u001b[0m                 \u001b[0me\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpatch_message\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmsg\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    467\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 468\u001b[0;31m             \u001b[0merror_rewrite\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0me\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'typing'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    469\u001b[0m         \u001b[0;32mexcept\u001b[0m \u001b[0merrors\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mUnsupportedError\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0me\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    470\u001b[0m             \u001b[0;31m# Something unsupported is present in the user code, add help info\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/opt/anaconda3/envs/noreward/lib/python3.8/site-packages/numba/core/dispatcher.py\u001b[0m in \u001b[0;36merror_rewrite\u001b[0;34m(e, issue_type)\u001b[0m\n\u001b[1;32m    407\u001b[0m                 \u001b[0;32mraise\u001b[0m \u001b[0me\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    408\u001b[0m             \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 409\u001b[0;31m                 \u001b[0;32mraise\u001b[0m \u001b[0me\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mwith_traceback\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    410\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    411\u001b[0m         \u001b[0margtypes\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mTypingError\u001b[0m: Failed in nopython mode pipeline (step: nopython frontend)\nnon-precise type pyobject\nDuring: typing of argument at <ipython-input-18-52bead916339> (7)\n\nFile \"<ipython-input-18-52bead916339>\", line 7:\ndef use_pandas(a): # Function will not benefit from Numba jit\n    df = pd.DataFrame.from_dict(a) # Numba doesn't know about pd.DataFrame\n    ^ \n\nThis error may have been caused by the following argument(s):\n- argument 0: Cannot determine Numba type of <class 'dict'>\n"
     ]
    }
   ],
   "source": [
    "import pandas as pd\n",
    "\n",
    "x = {'a': [1, 2, 3], 'b': [20, 30, 40]}\n",
    "\n",
    "@numba.njit\n",
    "def use_pandas(a): # Function will not benefit from Numba jit\n",
    "    df = pd.DataFrame.from_dict(a) # Numba doesn't know about pd.DataFrame\n",
    "    df += 1                        # Numba doesn't understand what this is\n",
    "    return df.cov()                # or this!\n",
    "\n",
    "print(use_pandas(x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "> @njit stands for @jit(nopython=True) and it means that numba should throw an exception instead of falling back to the python version, in cases where it cannot generate the optimized version."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Example 2 : Numba will not speed up a single numpy function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-29T18:43:47.479794Z",
     "start_time": "2023-06-29T18:43:47.438430Z"
    }
   },
   "outputs": [],
   "source": [
    "n_a = 100_000\n",
    "a = np.random.normal(0, 1,n_a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-29T18:43:47.739766Z",
     "start_time": "2023-06-29T18:43:47.664199Z"
    }
   },
   "outputs": [],
   "source": [
    "def just_sum(a):\n",
    "    result = 0\n",
    "    for i in range(a.shape[0]):\n",
    "        result += a[i]\n",
    "    return result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-29T18:43:47.886331Z",
     "start_time": "2023-06-29T18:43:47.864535Z"
    }
   },
   "outputs": [],
   "source": [
    "def numpy_sum(a):\n",
    "    return np.sum(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-29T18:43:50.276615Z",
     "start_time": "2023-06-29T18:43:48.084654Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "43.5 ms ± 10.1 ms per loop (mean ± std. dev. of 5 runs, 10 loops each)\n",
      "95.3 µs ± 50.8 µs per loop (mean ± std. dev. of 5 runs, 10 loops each)\n"
     ]
    }
   ],
   "source": [
    "forlooptime = %timeit -n 10 -r 5 -o just_sum(a)\n",
    "numpytime = %timeit -n 10 -r 5 -o numpy_sum(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-29T18:43:50.325673Z",
     "start_time": "2023-06-29T18:43:50.281971Z"
    }
   },
   "outputs": [],
   "source": [
    "np.testing.assert_allclose(just_sum(a), numpy_sum(a))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-29T18:43:50.529691Z",
     "start_time": "2023-06-29T18:43:50.334567Z"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "@numba.njit\n",
    "def just_sum(a):\n",
    "    result = 0\n",
    "    for i in range(a.shape[0]):\n",
    "        result += a[i]\n",
    "    return result\n",
    "just_sum(a); #Compile"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-29T18:43:50.548459Z",
     "start_time": "2023-06-29T18:43:50.533990Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "146 µs ± 55 µs per loop (mean ± std. dev. of 5 runs, 10 loops each)\n"
     ]
    }
   ],
   "source": [
    "jittedforlooptime = %timeit -n 10 -r 5 -o just_sum(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-29T18:43:50.964632Z",
     "start_time": "2023-06-29T18:43:50.556314Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "@numba.njit\n",
    "def numpy_sum(a):\n",
    "    return np.sum(a)\n",
    "numpy_sum(a);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-29T18:43:50.987593Z",
     "start_time": "2023-06-29T18:43:50.970949Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "113 µs ± 11.8 µs per loop (mean ± std. dev. of 5 runs, 10 loops each)\n"
     ]
    }
   ],
   "source": [
    "jittednumpytime = %timeit -n 10 -r 5 -o numpy_sum(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-29T18:43:51.012550Z",
     "start_time": "2023-06-29T18:43:50.991680Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For loop sum: 34.86 ms\n",
      "Numpy sum: 0.06 ms\n",
      "For loop sum with numba: 0.11 ms\n",
      "Numpy sum with numba: 0.10 ms\n"
     ]
    }
   ],
   "source": [
    "labels = ['For loop sum', 'Numpy sum', 'For loop sum with numba', 'Numpy sum with numba']\n",
    "for idx, i in enumerate([forlooptime, numpytime, jittedforlooptime, jittednumpytime]):\n",
    "    print('%s: %0.2f ms' %(labels[idx], i.best*1000))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Example 3 : you get more benefits if you had more numpy functions and loops"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-29T18:43:51.085492Z",
     "start_time": "2023-06-29T18:43:51.080266Z"
    }
   },
   "outputs": [],
   "source": [
    "n_obs = 100_000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-29T18:43:51.112748Z",
     "start_time": "2023-06-29T18:43:51.091790Z"
    }
   },
   "outputs": [],
   "source": [
    "observation = np.random.rand(n_obs, 2)\n",
    "clusters = np.random.rand(1000, 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-29T18:43:51.129602Z",
     "start_time": "2023-06-29T18:43:51.122437Z"
    }
   },
   "outputs": [],
   "source": [
    "def many_numpy_functions(x, y):\n",
    "    closest = np.zeros(x.shape[0])\n",
    "    for count, i in enumerate(x):\n",
    "        diff = i-y\n",
    "        dist = np.sqrt(np.sum(diff**2, axis=1))\n",
    "        closest[count] = np.argmin(diff)\n",
    "    return closest"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-06-29T18:43:50.513Z"
    }
   },
   "outputs": [],
   "source": [
    "numpytime = %timeit -o many_numpy_functions(observation, clusters) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-06-29T18:43:50.744Z"
    }
   },
   "outputs": [],
   "source": [
    "@numba.njit\n",
    "def jitted_numpy_functions(x, y):\n",
    "    closest = np.zeros(x.shape[0])\n",
    "    for count, i in enumerate(x):\n",
    "        diff = i-y\n",
    "        dist = np.sqrt(np.sum(diff**2, axis=1))\n",
    "        closest[count] = np.argmin(diff)\n",
    "    return closest\n",
    "jitted_numpy_functions(np.array([30.0, 99.0]), clusters); #Compile"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-06-29T18:43:50.965Z"
    }
   },
   "outputs": [],
   "source": [
    "numbatime = %timeit -o jitted_numpy_functions(observation, clusters)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-06-29T18:43:51.745Z"
    }
   },
   "outputs": [],
   "source": [
    "numpytime.best/numbatime.best"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<font size=6> There are other things numba cannot do </font>\n",
    "* Does not give fine grained control : everything is magic\n",
    "* If you need to interface to C++"
   ]
  }
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