{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "PointCloud\n",
    "===============\n",
    "Suppose we have `N` data points in `R^k` stored in `X` which is a numpy.ndarray array with shape `N`-by-`k`.\n",
    "In this example, we have loaded some data from the file `tests/circle.npy`, `tests/normal.npy`, and `tests/square.npy`, each of which contains `1000` data points in `R^2`.  Then, we'll shift them around to make an interesting pointcloud with 3000 points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "circ = np.load('../tests/circle.npy') + np.array([5., 5.])\n",
    "norm = np.load('../tests/normal.npy') * np.array([3.,0.5]) + np.array([-5., 0])\n",
    "square = np.load('../tests/square.npy') * np.array([0.9, 1.2]) + np.array([-2, 6.])\n",
    "X = np.concatenate([circ, norm, square])\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A SimplicialComplex with 3000 points, 0 edges, and 0 faces.\n"
     ]
    },
    {
     "data": {
      "image/png": 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6NfX19UQiEUpLS1m4cOGE2xydCrzjjjv41a9+xYEDBygvLycUChEIBPB4PB94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cbGjtmb0nEczZs376qfmc7OTr322msqLy9XTk6OPU/cXQhOnz5t97C8ndx6xJu9H0AQe9uNMhl7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\nBAAA4MH/BwIT8A313G0MAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e2829b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import multidim\n",
    "pc = multidim.PointCloud(X)\n",
    "print(pc)\n",
    "fig, ax = plt.subplots(figsize=(6,6),dpi=100)\n",
    "pc.plot(ax, title='some shapes')\n",
    "ax.set_aspect('equal')\n",
    "ax.set_xlim(-15,15)\n",
    "ax.set_ylim(-15,15)\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Persistence Diagrams\n",
    "-------------------\n",
    "\n",
    "We would like to compute the 0-dimensional persistence of this dataset.  Howevever,\n",
    "if we run `make_pers0()` now, it will fail, because we have not placed any edges between the vertices.\n",
    "Remember, PointCloud is just an embedded form of SimplicialComplex!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "whoops!  See this exception\n",
      "This SimplicialComplex has no 1-stratum (edges).  Persistence is meaningless.\n"
     ]
    }
   ],
   "source": [
    "try: \n",
    "    pc.make_pers0()\n",
    "except ValueError as e:\n",
    "    print(\"whoops!  See this exception\\n{}\".format(e))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To fix the problem, we re-initialize the PointCloud, computing all the edges up to some length.\n",
    "Then, we can compute the persistence diagram up to some maximum distance \"cutoff\".\n",
    "Here, we compute them all the way.  (using -1.0 as the limit, which in this case is shorthand for infinity)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING:root:Examined 4498500 possible edge distances using level 0.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A SimplicialComplex with 3000 points, 4498500 edges, and 0 faces.\n"
     ]
    }
   ],
   "source": [
    "pc = multidim.PointCloud(X, max_length=-1.0)\n",
    "print(pc)\n",
    "pc.make_pers0(cutoff=-1.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>birth_index</th>\n",
       "      <th>death_index</th>\n",
       "      <th>birth</th>\n",
       "      <th>death</th>\n",
       "      <th>pers</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2904</td>\n",
       "      <td>2904</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.000579</td>\n",
       "      <td>-0.999421</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2504</td>\n",
       "      <td>2504</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.000994</td>\n",
       "      <td>-0.999006</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>866</td>\n",
       "      <td>866</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.001142</td>\n",
       "      <td>-0.998858</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2607</td>\n",
       "      <td>2607</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.001476</td>\n",
       "      <td>-0.998524</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2879</td>\n",
       "      <td>2879</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.001672</td>\n",
       "      <td>-0.998328</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>2901</td>\n",
       "      <td>2901</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.001720</td>\n",
       "      <td>-0.998280</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>187</td>\n",
       "      <td>187</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.001997</td>\n",
       "      <td>-0.998003</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>2741</td>\n",
       "      <td>2741</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.002007</td>\n",
       "      <td>-0.997993</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>2936</td>\n",
       "      <td>2936</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.002030</td>\n",
       "      <td>-0.997970</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>2701</td>\n",
       "      <td>2701</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.002293</td>\n",
       "      <td>-0.997707</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>2660</td>\n",
       "      <td>2660</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.002362</td>\n",
       "      <td>-0.997638</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>2839</td>\n",
       "      <td>2839</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.002371</td>\n",
       "      <td>-0.997629</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>2976</td>\n",
       "      <td>2976</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.002413</td>\n",
       "      <td>-0.997587</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>2841</td>\n",
       "      <td>2841</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.002413</td>\n",
       "      <td>-0.997587</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>2917</td>\n",
       "      <td>2917</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.002433</td>\n",
       "      <td>-0.997567</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>2634</td>\n",
       "      <td>2634</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.002457</td>\n",
       "      <td>-0.997543</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>313</td>\n",
       "      <td>313</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.002471</td>\n",
       "      <td>-0.997529</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>2838</td>\n",
       "      <td>2838</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.002609</td>\n",
       "      <td>-0.997391</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>2725</td>\n",
       "      <td>2725</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.002652</td>\n",
       "      <td>-0.997348</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>629</td>\n",
       "      <td>629</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.002670</td>\n",
       "      <td>-0.997330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>167</td>\n",
       "      <td>167</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.002766</td>\n",
       "      <td>-0.997234</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>2821</td>\n",
       "      <td>2821</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.002858</td>\n",
       "      <td>-0.997142</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>2880</td>\n",
       "      <td>2880</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.002936</td>\n",
       "      <td>-0.997064</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>2623</td>\n",
       "      <td>2623</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.003015</td>\n",
       "      <td>-0.996985</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>2596</td>\n",
       "      <td>2596</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.003338</td>\n",
       "      <td>-0.996662</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>2704</td>\n",
       "      <td>2704</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.003350</td>\n",
       "      <td>-0.996650</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>620</td>\n",
       "      <td>620</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.003405</td>\n",
       "      <td>-0.996595</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>1896</td>\n",
       "      <td>1896</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.003420</td>\n",
       "      <td>-0.996580</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>1237</td>\n",
       "      <td>1237</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.003619</td>\n",
       "      <td>-0.996381</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>2923</td>\n",
       "      <td>2923</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.003648</td>\n",
       "      <td>-0.996352</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2970</th>\n",
       "      <td>1225</td>\n",
       "      <td>1794</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.366748</td>\n",
       "      <td>-0.633252</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2971</th>\n",
       "      <td>1109</td>\n",
       "      <td>1923</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.367097</td>\n",
       "      <td>-0.632903</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2972</th>\n",
       "      <td>1043</td>\n",
       "      <td>1043</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.369048</td>\n",
       "      <td>-0.630952</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2973</th>\n",
       "      <td>1022</td>\n",
       "      <td>1789</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.371620</td>\n",
       "      <td>-0.628380</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2974</th>\n",
       "      <td>1654</td>\n",
       "      <td>1654</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.380318</td>\n",
       "      <td>-0.619682</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2975</th>\n",
       "      <td>1739</td>\n",
       "      <td>1739</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.388628</td>\n",
       "      <td>-0.611372</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2976</th>\n",
       "      <td>1004</td>\n",
       "      <td>1912</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.403299</td>\n",
       "      <td>-0.596701</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2977</th>\n",
       "      <td>1273</td>\n",
       "      <td>1919</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.404921</td>\n",
       "      <td>-0.595079</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2978</th>\n",
       "      <td>1385</td>\n",
       "      <td>1385</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.440238</td>\n",
       "      <td>-0.559762</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2979</th>\n",
       "      <td>1162</td>\n",
       "      <td>1162</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.461514</td>\n",
       "      <td>-0.538486</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2980</th>\n",
       "      <td>1866</td>\n",
       "      <td>1866</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.477656</td>\n",
       "      <td>-0.522344</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2981</th>\n",
       "      <td>1566</td>\n",
       "      <td>1918</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.482202</td>\n",
       "      <td>-0.517798</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2982</th>\n",
       "      <td>1227</td>\n",
       "      <td>1881</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.483737</td>\n",
       "      <td>-0.516263</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2983</th>\n",
       "      <td>1555</td>\n",
       "      <td>1894</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.497714</td>\n",
       "      <td>-0.502286</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2984</th>\n",
       "      <td>1067</td>\n",
       "      <td>1124</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.499897</td>\n",
       "      <td>-0.500103</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2985</th>\n",
       "      <td>1309</td>\n",
       "      <td>1309</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.508137</td>\n",
       "      <td>-0.491863</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2986</th>\n",
       "      <td>1025</td>\n",
       "      <td>1254</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.535581</td>\n",
       "      <td>-0.464419</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2987</th>\n",
       "      <td>1655</td>\n",
       "      <td>1655</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.574817</td>\n",
       "      <td>-0.425183</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2988</th>\n",
       "      <td>1922</td>\n",
       "      <td>1922</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.598688</td>\n",
       "      <td>-0.401312</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2989</th>\n",
       "      <td>1431</td>\n",
       "      <td>1431</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.607588</td>\n",
       "      <td>-0.392412</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2990</th>\n",
       "      <td>1701</td>\n",
       "      <td>1701</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.609191</td>\n",
       "      <td>-0.390809</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2991</th>\n",
       "      <td>1151</td>\n",
       "      <td>1151</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.630529</td>\n",
       "      <td>-0.369471</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2992</th>\n",
       "      <td>1272</td>\n",
       "      <td>1272</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.650418</td>\n",
       "      <td>-0.349582</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2993</th>\n",
       "      <td>1190</td>\n",
       "      <td>1701</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.675568</td>\n",
       "      <td>-0.324432</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2994</th>\n",
       "      <td>1070</td>\n",
       "      <td>1272</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.687459</td>\n",
       "      <td>-0.312541</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2995</th>\n",
       "      <td>1589</td>\n",
       "      <td>1589</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.948313</td>\n",
       "      <td>-0.051687</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2996</th>\n",
       "      <td>1370</td>\n",
       "      <td>1809</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.992536</td>\n",
       "      <td>-0.007464</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2999</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2997</th>\n",
       "      <td>1000</td>\n",
       "      <td>1385</td>\n",
       "      <td>1.0</td>\n",
       "      <td>2.963614</td>\n",
       "      <td>1.963614</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2998</th>\n",
       "      <td>2000</td>\n",
       "      <td>2989</td>\n",
       "      <td>1.0</td>\n",
       "      <td>4.330230</td>\n",
       "      <td>3.330230</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>3000 rows × 5 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      birth_index  death_index  birth     death      pers\n",
       "0            2904         2904    1.0  0.000579 -0.999421\n",
       "1            2504         2504    1.0  0.000994 -0.999006\n",
       "2             866          866    1.0  0.001142 -0.998858\n",
       "3            2607         2607    1.0  0.001476 -0.998524\n",
       "4            2879         2879    1.0  0.001672 -0.998328\n",
       "5            2901         2901    1.0  0.001720 -0.998280\n",
       "6             187          187    1.0  0.001997 -0.998003\n",
       "7            2741         2741    1.0  0.002007 -0.997993\n",
       "8            2936         2936    1.0  0.002030 -0.997970\n",
       "9            2701         2701    1.0  0.002293 -0.997707\n",
       "10           2660         2660    1.0  0.002362 -0.997638\n",
       "11           2839         2839    1.0  0.002371 -0.997629\n",
       "12           2976         2976    1.0  0.002413 -0.997587\n",
       "13           2841         2841    1.0  0.002413 -0.997587\n",
       "14           2917         2917    1.0  0.002433 -0.997567\n",
       "15           2634         2634    1.0  0.002457 -0.997543\n",
       "16            313          313    1.0  0.002471 -0.997529\n",
       "17           2838         2838    1.0  0.002609 -0.997391\n",
       "18           2725         2725    1.0  0.002652 -0.997348\n",
       "19            629          629    1.0  0.002670 -0.997330\n",
       "20            167          167    1.0  0.002766 -0.997234\n",
       "21           2821         2821    1.0  0.002858 -0.997142\n",
       "22           2880         2880    1.0  0.002936 -0.997064\n",
       "23           2623         2623    1.0  0.003015 -0.996985\n",
       "24           2596         2596    1.0  0.003338 -0.996662\n",
       "25           2704         2704    1.0  0.003350 -0.996650\n",
       "26            620          620    1.0  0.003405 -0.996595\n",
       "27           1896         1896    1.0  0.003420 -0.996580\n",
       "28           1237         1237    1.0  0.003619 -0.996381\n",
       "29           2923         2923    1.0  0.003648 -0.996352\n",
       "...           ...          ...    ...       ...       ...\n",
       "2970         1225         1794    1.0  0.366748 -0.633252\n",
       "2971         1109         1923    1.0  0.367097 -0.632903\n",
       "2972         1043         1043    1.0  0.369048 -0.630952\n",
       "2973         1022         1789    1.0  0.371620 -0.628380\n",
       "2974         1654         1654    1.0  0.380318 -0.619682\n",
       "2975         1739         1739    1.0  0.388628 -0.611372\n",
       "2976         1004         1912    1.0  0.403299 -0.596701\n",
       "2977         1273         1919    1.0  0.404921 -0.595079\n",
       "2978         1385         1385    1.0  0.440238 -0.559762\n",
       "2979         1162         1162    1.0  0.461514 -0.538486\n",
       "2980         1866         1866    1.0  0.477656 -0.522344\n",
       "2981         1566         1918    1.0  0.482202 -0.517798\n",
       "2982         1227         1881    1.0  0.483737 -0.516263\n",
       "2983         1555         1894    1.0  0.497714 -0.502286\n",
       "2984         1067         1124    1.0  0.499897 -0.500103\n",
       "2985         1309         1309    1.0  0.508137 -0.491863\n",
       "2986         1025         1254    1.0  0.535581 -0.464419\n",
       "2987         1655         1655    1.0  0.574817 -0.425183\n",
       "2988         1922         1922    1.0  0.598688 -0.401312\n",
       "2989         1431         1431    1.0  0.607588 -0.392412\n",
       "2990         1701         1701    1.0  0.609191 -0.390809\n",
       "2991         1151         1151    1.0  0.630529 -0.369471\n",
       "2992         1272         1272    1.0  0.650418 -0.349582\n",
       "2993         1190         1701    1.0  0.675568 -0.324432\n",
       "2994         1070         1272    1.0  0.687459 -0.312541\n",
       "2995         1589         1589    1.0  0.948313 -0.051687\n",
       "2996         1370         1809    1.0  0.992536 -0.007464\n",
       "2999            0            0    1.0  1.000000  0.000000\n",
       "2997         1000         1385    1.0  2.963614  1.963614\n",
       "2998         2000         2989    1.0  4.330230  3.330230\n",
       "\n",
       "[3000 rows x 5 columns]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pc.pers0.diagram"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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lMGBAagUYAiQVgEFAas4+/BAOPTRtFQwwdmzaN6Bnz2zrklQybA1IzdWMGTBm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\nOWYQkCQpx/4PXLB6o9WAmX8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111723f28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(6,6),dpi=100)\n",
    "pc.pers0.plot(ax)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Severing a PointCloud \n",
    "---------------------\n",
    "\n",
    "Suppose we want to sever the connected components of our pointcloud, up to some persistence."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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c47333mPatGk0NDSQm+vXgHfOcfToUVpaWqiuruall17ij3/8I3v27PGurf/72ktLS8nJ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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c2d7fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pc.reset()  # reset the persistence diagram, but don't both re-comptuing all the edges\n",
    "pc.make_pers0(cutoff=2.0)\n",
    "\n",
    "fig,ax = plt.subplots(3, figsize=(4,12),dpi=100)\n",
    "for i, (sub_index, sub_pc) in enumerate(pc.sever()):\n",
    "    sub_pc.plot(ax[i], title=\"Part {}\".format(i)) \n",
    "    ax[i].set_aspect('equal')\n",
    "    ax[i].set_xlim(-15,15) \n",
    "    ax[i].set_ylim(-15,15)\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Efficiency\n",
    "----------\n",
    "\n",
    "In the example above, we wanted to see *all* of the edges, but if you know _a priori_ that you only want edges up to some small length, then there is a more efficient way.  (This is because the CoverTree can be computed to find small edges.) Initialize the `PointCloud` with the `max_length` option."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING:root:Examined 673353 possible edge distances using level 4.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A SimplicialComplex with 3000 points, 17620 edges, and 0 faces.\n"
     ]
    }
   ],
   "source": [
    "pc = multidim.PointCloud(X, max_length=0.1)\n",
    "print(pc)\n",
    "pc.make_pers0()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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PVdUnq+rKqvqVqrrHKvsMAOxjs84gHJXkkCQ7l5TvTPKwZdo8KMnjk9yW5Onja/zvJF+R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\nAB0BAQDoCAgAQOf/A201+Xm6jQoOAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b458630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(6,6),dpi=100)\n",
    "pc.pers0.plot(ax)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.6.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
