sin1x.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from math import sin, cos, fsum\n",
    "import numpy as np\n",
    "\n",
    "\n",
    "def sin1x_integrand(b, ns):\n",
    "    \"\"\"\n",
    "    Compute integrand values at nodes\n",
    "\n",
    "    Parameters:\n",
    "        b  - integration limit\n",
    "        ns - nodes\n",
    "\n",
    "    Returns:\n",
    "        Integrand values\n",
    "    \"\"\"\n",
    "    rb = 1.0 / abs(b)\n",
    "    d = rb * rb + ns * ns\n",
    "    return (cos(rb) + 2.0 * rb * sin(rb) * ns / d) / d\n",
    "\n",
    "\n",
    "def integrate_sin1x_from0(b, ns, ws):\n",
    "    \"\"\"\n",
    "    Compute int_0^b \\sin(1/x) dx\n",
    "\n",
    "    Parameters:\n",
    "        b  - integration limit\n",
    "        ns - Gauss-Laguerre nodes\n",
    "        ws - Gauss-Laguerre weights\n",
    "\n",
    "    Returns:\n",
    "        Integral value\n",
    "    \"\"\"\n",
    "    if b == 0.0:\n",
    "        return 0.0\n",
    "    else:\n",
    "        return fsum(sin1x_integrand(b, ns) * ws)\n",
    "\n",
    "\n",
    "def integrate_sin1x(a, b, deg=32):\n",
    "    \"\"\"\n",
    "    Compute int_a^b \\sin(1/x) dx\n",
    "\n",
    "    Parameters:\n",
    "        a   - left integration limit\n",
    "        b   - right integration limit\n",
    "        deg - Gauss-Laguerre quadrature degree\n",
    "\n",
    "    Returns:\n",
    "        Integral value\n",
    "    \"\"\"\n",
    "    ns, ws = np.polynomial.laguerre.laggauss(deg)\n",
    "    return integrate_sin1x_from0(b, ns, ws) - integrate_sin1x_from0(a, ns, ws)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.64031690782597e-07"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = 0\n",
    "b = 0.001\n",
    "\n",
    "integrate_sin1x(a, b, 128)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(5.85139031596554e-07, 4.936575165647834e-09)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.integrate import quad\n",
    "quad(lambda x : sin(1.0 / x), a, b, limit=1000000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x720 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "\n",
    "%matplotlib inline\n",
    "plt.rcParams['figure.figsize'] = [15, 10]\n",
    "\n",
    "x = np.arange(0.0, 10000.0, 1.0)\n",
    "\n",
    "fig, ax1 = plt.subplots()\n",
    "ax2 = ax1.twinx()\n",
    "\n",
    "if a != 0:\n",
    "    ya = sin1x_integrand(a, x)\n",
    "    ax1.plot(x, ya, color=\"tab:red\")\n",
    "    ax1.tick_params(axis='y', labelcolor=\"tab:red\")\n",
    "\n",
    "if b != 0:\n",
    "    yb = sin1x_integrand(b, x)\n",
    "    ax2.plot(x, yb, color=\"tab:blue\")\n",
    "    ax2.tick_params(axis='y', labelcolor=\"tab:blue\")\n",
    "\n",
    "fig.suptitle(\"Instead of original oscillatory function, these are now integrated\", fontsize=24)\n",
    "fig.tight_layout()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.8.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}