ndarray-odeint 0.2.1

solve ODE using rust-ndarray
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Accuracy test for ndarray-odeint"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## generate data for accuracy test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[m\u001b[32m\u001b[1m    Finished\u001b[m debug [unoptimized + debuginfo] target(s) in 0.0 secs\n",
      "\u001b[m\u001b[32m\u001b[1m     Running\u001b[m target/debug/accuracy-0a4a353313c014e8\n",
      "\n",
      "running 3 tests\n",
      "test euler ... \u001b[32mok\u001b[m\n",
      "test heun ... \u001b[32mok\u001b[m\n",
      "test rk4 ... \u001b[32mok\u001b[m\n",
      "\n",
      "test result: \u001b[32mok\u001b[m. 3 passed; 0 failed; 0 ignored; 0 measured\n",
      "\n",
      "\u001b[m\u001b[32m\u001b[1m     Running\u001b[m target/debug/main-b5557b9ac13b38b4\n",
      "\n",
      "running 0 tests\n",
      "\n",
      "test result: \u001b[32mok\u001b[m. 0 passed; 0 failed; 0 ignored; 0 measured\n",
      "\n",
      "\u001b[m\u001b[32m\u001b[1m     Running\u001b[m target/debug/deps/ndarray_odeint-33490c74c9fab310\n",
      "\n",
      "running 0 tests\n",
      "\n",
      "test result: \u001b[32mok\u001b[m. 0 passed; 0 failed; 0 ignored; 0 measured\n",
      "\n",
      "\u001b[m\u001b[32m\u001b[1m   Doc-tests\u001b[m ndarray-odeint\n",
      "\n",
      "running 0 tests\n",
      "\n",
      "test result: \u001b[32mok\u001b[m. 0 passed; 0 failed; 0 ignored; 0 measured\n",
      "\n"
     ]
    }
   ],
   "source": [
    "! cargo test"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "euler = pd.read_csv(\"euler.csv\").dropna().set_index(\"dt\")\n",
    "heun = pd.read_csv(\"heun.csv\").dropna().set_index(\"dt\")\n",
    "rk4 = pd.read_csv(\"rk4.csv\").dropna().set_index(\"dt\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7efc8bc43e80>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Fi5YBA+D++9W9v79+b7QWr74KDRqoEvV8zp9XYb0HHrBMqv3pJxUOMqduXVUxZIskXUni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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7efc8bc43d30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(euler, \"b\", label=\"Euler\")\n",
    "plt.plot(heun, \"g\", label=\"Heun\")\n",
    "plt.plot(rk4, \"r\", label=\"RK4\")\n",
    "plt.plot(euler.index, 200*euler.index, \"b:\", label=r\"$\\propto dt^1$\")\n",
    "plt.plot(heun.index, 1000*heun.index**2, \"g:\", label=r\"$\\propto dt^2$\")\n",
    "plt.plot(rk4.index, 5000*rk4.index**4, \"r:\", label=r\"$\\propto dt^4$\")\n",
    "plt.xscale(\"log\")\n",
    "plt.yscale(\"log\")\n",
    "plt.xlabel(\"dt\")\n",
    "plt.ylabel(\"accuray (deviation from truth)\")\n",
    "plt.axis(\"tight\")\n",
    "plt.legend(loc=4, ncol=2)"
   ]
  }
 ],
 "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": "3.5.2"
  },
  "toc": {
   "colors": {
    "hover_highlight": "#DAA520",
    "running_highlight": "#FF0000",
    "selected_highlight": "#FFD700"
   },
   "moveMenuLeft": true,
   "nav_menu": {
    "height": "66px",
    "width": "252px"
   },
   "navigate_menu": true,
   "number_sections": true,
   "sideBar": true,
   "threshold": 4,
   "toc_cell": false,
   "toc_section_display": "block",
   "toc_window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}