Integration/riemann_sums.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import libraries\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.patches as patches\n",
    "import matplotlib.animation as animation\n",
    "\n",
    "# ignore warnings\n",
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")\n",
    "\n",
    "# set a random seed\n",
    "np.random.seed(42)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Integral Calculation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def calculate_integral(f, a, b, n):\n",
    "    '''Calculates the integral based on the composite trapezoidal rule\n",
    "    relying on the Riemann Sums.\n",
    "    \n",
    "    :param function f: the integrand function\n",
    "    :param int a: lower bound of the integral\n",
    "    :param int b: upper bound of theintergal\n",
    "    :param int n: number of trapezoids of equal width\n",
    "    :return float: the integral of the function f between a and b\n",
    "    '''\n",
    "    w = (b - a)/n\n",
    "    result = 0.5*f(a) + sum([f(a + i*w) for i in range(1, n)]) + 0.5*f(b)\n",
    "    result *= w\n",
    "    return result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "f = lambda x: 4.0/(1 + x**2)  # specify a function to integrate\n",
    "a, b = 0, 1  # the intervals of integration\n",
    "N = 400  # number of points to generate\n",
    "factor = 5  # increase num of trapezoids every iteration\n",
    "\n",
    "X = np.linspace(a, b, N + 1)  # generate more points on the x-axis\n",
    "Y = f(X)  # generate more function values"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Animation of the Riemann Sums"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1512x1008 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(21, 14))  # make a new figure\n",
    "\n",
    "# animation function \n",
    "def animate(i):\n",
    "    plt.cla()  # clear all previous axes objects\n",
    "    ax = plt.axes(xlim=(a, b), ylim = (0, 4))  # make a new axes object\n",
    "    \n",
    "    ax.set_xticks(np.linspace(a, b, 11))  # format the x-axis\n",
    "    ax.set_xlabel('X-axis', fontsize=30)\n",
    "    \n",
    "    ax.set_yticks(np.linspace(0, 4, 11))  # format the y-axis\n",
    "    ax.set_ylabel('Y-axis', fontsize=30)\n",
    "    \n",
    "    ax.tick_params(labelsize=22)  # make the ticks larger\n",
    "    \n",
    "    num_trapezoids = (i + 1) * factor  # calculate the number of trapezoids\n",
    "    \n",
    "    x = np.linspace(a, b, num_trapezoids + 1)  # generate the intervals on the x-axis\n",
    "    y = f(x)  # generate the function values\n",
    "    \n",
    "    y_int = calculate_integral(f, a, b, num_trapezoids)  # calculate the integral\n",
    "    err = np.abs(np.pi - y_int)  # calculate the absolute error\n",
    "    \n",
    "    # take the left end-points\n",
    "    x_left = x[:-1]\n",
    "    y_left = y[:-1]\n",
    "    \n",
    "    ax.plot(x_left,y_left, c='#2CBDFE', marker='.', markersize=10)  # plot the left points\n",
    "    ax.plot(X, Y, c='#2CBDFE')  # plot the smoother line\n",
    "    \n",
    "    bar = ax.bar(x, y, width=1.0*(b-a)/num_trapezoids, alpha=0.3, align='edge', color='#47DBCD', edgecolor='#2CBDFE', lw=2)\n",
    "    ax.set_title('Riemann Sum for $\\pi = \\int_{{0}}^{{1}} \\\\frac{{4}}{{1 + x^2}}dx$. \\n' + \n",
    "                 '{0} trapezoids: Value: {1:.9f} Approx. err. {2:.9f}'.format(num_trapezoids, y_int, err), fontsize=30)\n",
    "    \n",
    "    return bar\n",
    "\n",
    "# call the animator\t \n",
    "anim = animation.FuncAnimation(fig, animate, frames=40, interval=120, blit=True)\n",
    "anim.save('riemann_sum.gif',writer=\"imagemagick\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "file_extension": ".py",
  "kernelspec": {
   "display_name": "Python (tf21)",
   "language": "python",
   "name": "myenv"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.0"
  },
  "mimetype": "text/x-python",
  "name": "python",
  "npconvert_exporter": "python",
  "pygments_lexer": "ipython3",
  "version": 3
 },
 "nbformat": 4,
 "nbformat_minor": 2
}