{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true,
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.patches import Ellipse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# https://github.com/joferkington/oost_paper_code/blob/master/error_ellipse.py\n",
    "def plot_cov_ellipse(cov, pos, nstd=2, ax=None, **kwargs):\n",
    "    \"\"\"\n",
    "    Plots an `nstd` sigma error ellipse based on the specified covariance\n",
    "    matrix (`cov`). Additional keyword arguments are passed on to the \n",
    "    ellipse patch artist.\n",
    "    Parameters\n",
    "    ----------\n",
    "        cov : The 2x2 covariance matrix to base the ellipse on\n",
    "        pos : The location of the center of the ellipse. Expects a 2-element\n",
    "            sequence of [x0, y0].\n",
    "        nstd : The radius of the ellipse in numbers of standard deviations.\n",
    "            Defaults to 2 standard deviations.\n",
    "        ax : The axis that the ellipse will be plotted on. Defaults to the \n",
    "            current axis.\n",
    "        Additional keyword arguments are pass on to the ellipse patch.\n",
    "    Returns\n",
    "    -------\n",
    "        A matplotlib ellipse artist\n",
    "    \"\"\"\n",
    "    def eigsorted(cov):\n",
    "        vals, vecs = np.linalg.eigh(cov)\n",
    "        order = vals.argsort()[::-1]\n",
    "        return vals[order], vecs[:,order]\n",
    "\n",
    "    if ax is None:\n",
    "        ax = plt.gca()\n",
    "\n",
    "    vals, vecs = eigsorted(cov)\n",
    "    theta = np.degrees(np.arctan2(*vecs[:,0][::-1]))\n",
    "\n",
    "    # Width and height are \"full\" widths, not radius\n",
    "    width, height = 2 * nstd * np.sqrt(vals)\n",
    "    ellip = Ellipse(xy=pos, width=width, height=height, angle=theta, **kwargs)\n",
    "\n",
    "    ax.add_artist(ellip)\n",
    "    return ellip"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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tMNuiMg5U1GdT3ARcYGbnmFlf4Hdk33M7I+J5pYl69jyIROJN3zEkJxyZzBv07NnTdxDZ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\nVMYiIgFQGYuIBEBlLCISAJWxiEgA/g/0Aw9qrnliowAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f2367f9a850>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cov = np.array([[1, 0],\n",
    "                [0, 0.5]])\n",
    "\n",
    "axes = plt.subplot(111, aspect=1)\n",
    "plot_cov_ellipse(cov, [0,0])\n",
    "axes.set_xlim([-5, 5])\n",
    "axes.set_ylim([-5, 5])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.13"
  }
 },
 "nbformat": 4,
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