solutions.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Jupyter Notebooks - solutions to exercises"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Lesson 1 - introduction to jupyter"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 1.3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from ipywidgets import interact\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "\n",
    "# gaussian function\n",
    "def gauss(x,param):\n",
    "    [a,b,c] = param\n",
    "    return a*np.exp(-b*(x-c)**2)\n",
    "\n",
    "# gaussian array y in interval -5<x-5 \n",
    "nx = 100\n",
    "x = np.linspace(-5.,5.,nx)\n",
    "p = [2.0,0.5,1.5] # some parameters\n",
    "y = gauss(x,p)\n",
    "\n",
    "# add some noise\n",
    "noise = np.random.normal(0,0.2,nx)\n",
    "y += noise\n",
    "\n",
    "@interact\n",
    "def fit(n=(3,30)):\n",
    "    pfit = np.polyfit(x,y,n)\n",
    "    yfit = np.polyval(pfit,x)\n",
    "    plt.plot(x,y,\"r\",label=\"Data\")\n",
    "    plt.plot(x,yfit,\"b\",label=\"Fit\")\n",
    "    plt.legend()\n",
    "    plt.ylim(-0.5,2.5)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 1.4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# %load random_walk.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def step():\n",
    "    import random\n",
    "    return 1. if random.random() > .5 else -1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def walk(n):\n",
    "    x = np.zeros(n)\n",
    "    dx = 1. / n\n",
    "    for i in range(n - 1):\n",
    "        x_new = x[i] + dx * step()\n",
    "        if x_new > 5e-3:\n",
    "            x[i + 1] = 0.\n",
    "        else:\n",
    "            x[i + 1] = x_new\n",
    "    return x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 100000\n",
    "x = walk(n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.plot(x);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "t1 = %timeit -o walk(n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "t1.best"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%prun\n",
    "walk(n)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Lesson 2 - data analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###  *Exercise 2.1* \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "nobels_by_country_of_death = nobel.groupby('diedCountry',sort=True)[\"number\"].sum()\n",
    "nobels_by_country_of_death.sort_values(ascending=False).head(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###  *Exercise 2.2* "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "born_but_not_died_in_sweden = nobel[(nobel[\"bornCountryCode\"] == \"SE\") \n",
    "                                    & (nobel[\"diedCountryCode\"] != \"SE\") \n",
    "                                    ]\n",
    "born_but_not_died_in_sweden.dropna(subset=['diedCountryCode'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 2.3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "toppings_tidy = pd.melt(\n",
    "                        person_toppings, \n",
    "                        id_vars=[\"Person\", \"Pizza\"], \n",
    "                        value_vars=[\"Ingredient 1\", \"Ingredient 2\"], \n",
    "                        var_name=\"Ingredient priority\", \n",
    "                        value_name=\"Ingredient\"\n",
    "                        )\n",
    "toppings_tidy[toppings_tidy[\"Ingredient\"] == \"Ham\"]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Lesson 3 - accelerating python"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "import random\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 3.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# %load random_walk.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def step():\n",
    "    return 1. if random.random() > .5 else -1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def walk(n):\n",
    "    x = np.zeros(n)\n",
    "    dx = 1. / n\n",
    "    for i in range(n - 1):\n",
    "        x_new = x[i] + dx * step()\n",
    "        if x_new > 5e-3:\n",
    "            x[i + 1] = 0.\n",
    "        else:\n",
    "            x[i + 1] = x_new\n",
    "    return x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 100000\n",
    "x = walk(n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.plot(x);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "t1 = %timeit -o walk(n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "t1.best"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 3.2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def primes(kmax):  \n",
    "    p = []\n",
    "    result = []  \n",
    "    if kmax > 1000:\n",
    "        kmax = 1000\n",
    "    k = 0\n",
    "    n = 2\n",
    "    while k < kmax:\n",
    "        i = 0\n",
    "        while i < k and n % p[i] != 0:\n",
    "            i = i + 1\n",
    "        if i == k:\n",
    "            p.append(n)\n",
    "            k = k + 1\n",
    "            result.append(n)\n",
    "        n = n + 1\n",
    "    return result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "t_py = %timeit -o p = primes(100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "%load_ext Cython"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Start with simplest cython"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%cython -a\n",
    "def primes_simplecython(kmax):  \n",
    "    p = []\n",
    "    result = []  \n",
    "    if kmax > 1000:\n",
    "        kmax = 1000\n",
    "    k = 0\n",
    "    n = 2\n",
    "    while k < kmax:\n",
    "        i = 0\n",
    "        while i < k and n % p[i] != 0:\n",
    "            i = i + 1\n",
    "        if i == k:\n",
    "            p.append(n)\n",
    "            k = k + 1\n",
    "            result.append(n)\n",
    "        n = n + 1\n",
    "    return result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "t_cy0 = %timeit -o p = primes_simplecython(100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now for proper cythonization. Add annotation (`-a`) if you want!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%cython -a\n",
    "def primes_cython(int kmax):  # The argument will be converted to int or raise a TypeError.\n",
    "    cdef int n, k, i  # These variables are declared with C types.\n",
    "    cdef int p[1000]  # Another C type\n",
    "    result = []  # A Python type\n",
    "    if kmax > 1000:\n",
    "        kmax = 1000\n",
    "    k = 0\n",
    "    n = 2\n",
    "    while k < kmax:\n",
    "        i = 0\n",
    "        while i < k and n % p[i] != 0:\n",
    "            i = i + 1\n",
    "        if i == k:\n",
    "            p[k] = n\n",
    "            k = k + 1\n",
    "            result.append(n)\n",
    "        n = n + 1\n",
    "    return result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "t_cy = %timeit -o p = primes_cython(100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Factor 20 in speedup"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, let's compare with just-in-time compilation with numba"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numba import jit, vectorize, float64"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "@jit\n",
    "def primes_jit(kmax):  \n",
    "    p = []\n",
    "    result = []  \n",
    "    if kmax > 1000:\n",
    "        kmax = 1000\n",
    "    k = 0\n",
    "    n = 2\n",
    "    while k < kmax:\n",
    "        i = 0\n",
    "        while i < k and n % p[i] != 0:\n",
    "            i = i + 1\n",
    "        if i == k:\n",
    "            p.append(n)\n",
    "            k = k + 1\n",
    "            result.append(n)\n",
    "        n = n + 1\n",
    "    return result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "t_jit = %timeit -o p = primes_jit(100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "print(\" Python: %.3E\\n Simply Cython: %.3E\\n Proper Cython: %.3E\\n Numba-jit: %.3E\"%(t_py.best,t_cy0.best,t_cy.best,t_jit.best))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Just-in-time compilation comes close to Cython"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that the slowest run took much much longer than the fastest.  \n",
    "`cache=True` stores the compiled function in file-based cache and avoids re-compilation on re-running\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "@jit(cache=True)\n",
    "def primes_jit2(kmax):  \n",
    "    p = []\n",
    "    result = []  \n",
    "    if kmax > 1000:\n",
    "        kmax = 1000\n",
    "    k = 0\n",
    "    n = 2\n",
    "    while k < kmax:\n",
    "        i = 0\n",
    "        while i < k and n % p[i] != 0:\n",
    "            i = i + 1\n",
    "        if i == k:\n",
    "            p.append(n)\n",
    "            k = k + 1\n",
    "            result.append(n)\n",
    "        n = n + 1\n",
    "    return result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%timeit\n",
    "p = primes_jit2(100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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