{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Covariant Lyapunov Vectors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "ndarray-odeint has calculator of Covariant Lyapunov Vector (CLV).\n",
    "The algorithm of CLV has introduced in [Ginelli et al. PRL(2007)] to analyze collective motions.\n",
    "\n",
    "[Ginelli et al. PRL(2007)]:http://link.aps.org/doi/10.1103/PhysRevLett.99.130601"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A sample script for calculate CLV of Lorenz 63 model is placed at `examples/clv.rs`"
   ]
  },
  {
   "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 release [optimized] target(s) in 0.0 secs\n",
      "\u001b[m\u001b[32m\u001b[1m     Running\u001b[m `target/release/examples/clv`\n",
      "exponents = [0.9056117985793435, -0.0007306233624250147, -14.572558554870295] shape=[3], strides=[1], layout=C | F (0x3)\n"
     ]
    }
   ],
   "source": [
    "! cargo run --release --example clv > clv.csv"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Tangency of CLVs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/lib/python3.6/site-packages/ipykernel/__main__.py:1: RuntimeWarning: invalid value encountered in arccos\n",
      "  if __name__ == '__main__':\n"
     ]
    }
   ],
   "source": [
    "df = np.arccos(pd.read_csv(\"clv.csv\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f2647e62c18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f26777aab38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f2646ef63c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for col in df.columns:\n",
    "    plt.figure()\n",
    "    plt.title(col)\n",
    "    df[col].hist(bins=100)\n",
    "    plt.xlim(0, np.pi)\n",
    "    plt.yscale(\"log\")"
   ]
  }
 ],
 "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": "3.6.2"
  },
  "toc": {
   "colors": {
    "hover_highlight": "#DAA520",
    "running_highlight": "#FF0000",
    "selected_highlight": "#FFD700"
   },
   "moveMenuLeft": true,
   "nav_menu": {
    "height": "48px",
    "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
}