notebook_fitting_dev.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import Score_assignment\n",
    "import Score_cluster\n",
    "import Score_physics\n",
    "from Plotting import *\n",
    "\n",
    "from scipy.optimize import curve_fit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "df = pd.read_csv(\"result_truth.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Library/Python/2.7/site-packages/pandas/core/frame.py:1686: UserWarning: Boolean Series key will be reindexed to match DataFrame index.\n",
      "  \"DataFrame index.\", UserWarning)\n"
     ]
    }
   ],
   "source": [
    "ievent = 0\n",
    "iparticle=6\n",
    "itrack =5\n",
    "\n",
    "df_event=df.loc[df['event']==ievent]\n",
    "df_particle=df_event[df['particle']==iparticle]\n",
    "df_track=df_event[df['track']==itrack]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Unnamed: 0</th>\n",
       "      <th>event</th>\n",
       "      <th>particle</th>\n",
       "      <th>track</th>\n",
       "      <th>hit</th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0 </th>\n",
       "      <td>  0</td>\n",
       "      <td> 0</td>\n",
       "      <td> 0</td>\n",
       "      <td> 0</td>\n",
       "      <td>  20</td>\n",
       "      <td> -4.279116</td>\n",
       "      <td>  3.125760</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1 </th>\n",
       "      <td>  1</td>\n",
       "      <td> 0</td>\n",
       "      <td> 0</td>\n",
       "      <td> 0</td>\n",
       "      <td>  40</td>\n",
       "      <td> -8.049544</td>\n",
       "      <td>  6.430402</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2 </th>\n",
       "      <td>  2</td>\n",
       "      <td> 0</td>\n",
       "      <td> 0</td>\n",
       "      <td> 0</td>\n",
       "      <td>  60</td>\n",
       "      <td>-11.885345</td>\n",
       "      <td>  9.659012</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3 </th>\n",
       "      <td>  3</td>\n",
       "      <td> 0</td>\n",
       "      <td> 0</td>\n",
       "      <td> 0</td>\n",
       "      <td>  80</td>\n",
       "      <td>-15.784986</td>\n",
       "      <td> 12.810297</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4 </th>\n",
       "      <td>  4</td>\n",
       "      <td> 0</td>\n",
       "      <td> 0</td>\n",
       "      <td> 0</td>\n",
       "      <td> 100</td>\n",
       "      <td>-19.746907</td>\n",
       "      <td> 15.882994</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5 </th>\n",
       "      <td>  5</td>\n",
       "      <td> 0</td>\n",
       "      <td> 0</td>\n",
       "      <td> 0</td>\n",
       "      <td> 120</td>\n",
       "      <td>-23.769527</td>\n",
       "      <td> 18.875874</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6 </th>\n",
       "      <td>  6</td>\n",
       "      <td> 0</td>\n",
       "      <td> 0</td>\n",
       "      <td> 0</td>\n",
       "      <td> 140</td>\n",
       "      <td>-27.851236</td>\n",
       "      <td> 21.787738</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7 </th>\n",
       "      <td>  7</td>\n",
       "      <td> 0</td>\n",
       "      <td> 0</td>\n",
       "      <td> 0</td>\n",
       "      <td> 160</td>\n",
       "      <td>-31.990404</td>\n",
       "      <td> 24.617418</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8 </th>\n",
       "      <td>  8</td>\n",
       "      <td> 0</td>\n",
       "      <td> 0</td>\n",
       "      <td> 0</td>\n",
       "      <td> 180</td>\n",
       "      <td>-36.185376</td>\n",
       "      <td> 27.363783</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9 </th>\n",
       "      <td>  9</td>\n",
       "      <td> 0</td>\n",
       "      <td> 0</td>\n",
       "      <td> 0</td>\n",
       "      <td> 200</td>\n",
       "      <td>-40.434475</td>\n",
       "      <td> 30.025731</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td> 10</td>\n",
       "      <td> 0</td>\n",
       "      <td> 0</td>\n",
       "      <td> 0</td>\n",
       "      <td> 220</td>\n",
       "      <td>-44.736003</td>\n",
       "      <td> 32.602196</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td> 11</td>\n",
       "      <td> 0</td>\n",
       "      <td> 0</td>\n",
       "      <td> 0</td>\n",
       "      <td> 240</td>\n",
       "      <td>-49.088240</td>\n",
       "      <td> 35.092146</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td> 12</td>\n",
       "      <td> 0</td>\n",
       "      <td> 0</td>\n",
       "      <td> 0</td>\n",
       "      <td> 260</td>\n",
       "      <td>-53.489446</td>\n",
       "      <td> 37.494583</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td> 13</td>\n",
       "      <td> 0</td>\n",
       "      <td> 0</td>\n",
       "      <td> 0</td>\n",
       "      <td> 280</td>\n",
       "      <td>-57.937861</td>\n",
       "      <td> 39.808544</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td> 14</td>\n",
       "      <td> 0</td>\n",
       "      <td> 1</td>\n",
       "      <td> 1</td>\n",
       "      <td>  40</td>\n",
       "      <td>  5.473631</td>\n",
       "      <td> -4.947957</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td> 15</td>\n",
       "      <td> 0</td>\n",
       "      <td> 1</td>\n",
       "      <td> 1</td>\n",
       "      <td>  60</td>\n",
       "      <td>  7.932295</td>\n",
       "      <td> -7.135807</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td> 16</td>\n",
       "      <td> 0</td>\n",
       "      <td> 1</td>\n",
       "      <td> 1</td>\n",
       "      <td>  80</td>\n",
       "      <td> 10.434247</td>\n",
       "      <td> -9.274071</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td> 17</td>\n",
       "      <td> 0</td>\n",
       "      <td> 1</td>\n",
       "      <td> 1</td>\n",
       "      <td> 100</td>\n",
       "      <td> 12.978486</td>\n",
       "      <td>-11.361892</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td> 18</td>\n",
       "      <td> 0</td>\n",
       "      <td> 1</td>\n",
       "      <td> 1</td>\n",
       "      <td> 120</td>\n",
       "      <td> 15.563996</td>\n",
       "      <td>-13.398435</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td> 19</td>\n",
       "      <td> 0</td>\n",
       "      <td> 1</td>\n",
       "      <td> 1</td>\n",
       "      <td> 140</td>\n",
       "      <td> 18.189743</td>\n",
       "      <td>-15.382884</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td> 20</td>\n",
       "      <td> 0</td>\n",
       "      <td> 1</td>\n",
       "      <td> 1</td>\n",
       "      <td> 160</td>\n",
       "      <td> 20.854678</td>\n",
       "      <td>-17.314443</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td> 21</td>\n",
       "      <td> 0</td>\n",
       "      <td> 1</td>\n",
       "      <td> 1</td>\n",
       "      <td> 180</td>\n",
       "      <td> 23.557736</td>\n",
       "      <td>-19.192340</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td> 22</td>\n",
       "      <td> 0</td>\n",
       "      <td> 1</td>\n",
       "      <td> 1</td>\n",
       "      <td> 200</td>\n",
       "      <td> 26.297836</td>\n",
       "      <td>-21.015822</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td> 23</td>\n",
       "      <td> 0</td>\n",
       "      <td> 1</td>\n",
       "      <td> 1</td>\n",
       "      <td> 220</td>\n",
       "      <td> 29.073882</td>\n",
       "      <td>-22.784159</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td> 24</td>\n",
       "      <td> 0</td>\n",
       "      <td> 1</td>\n",
       "      <td> 1</td>\n",
       "      <td> 240</td>\n",
       "      <td> 31.884767</td>\n",
       "      <td>-24.496642</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td> 25</td>\n",
       "      <td> 0</td>\n",
       "      <td> 1</td>\n",
       "      <td> 1</td>\n",
       "      <td> 260</td>\n",
       "      <td> 34.729364</td>\n",
       "      <td>-26.152586</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td> 26</td>\n",
       "      <td> 0</td>\n",
       "      <td> 1</td>\n",
       "      <td> 1</td>\n",
       "      <td> 280</td>\n",
       "      <td> 37.606539</td>\n",
       "      <td>-27.751325</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td> 27</td>\n",
       "      <td> 0</td>\n",
       "      <td> 2</td>\n",
       "      <td> 2</td>\n",
       "      <td>  40</td>\n",
       "      <td> -7.537927</td>\n",
       "      <td>  1.512603</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td> 28</td>\n",
       "      <td> 0</td>\n",
       "      <td> 2</td>\n",
       "      <td> 2</td>\n",
       "      <td>  60</td>\n",
       "      <td>-10.965578</td>\n",
       "      <td>  1.987371</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td> 29</td>\n",
       "      <td> 0</td>\n",
       "      <td> 2</td>\n",
       "      <td> 2</td>\n",
       "      <td>  80</td>\n",
       "      <td>-14.402072</td>\n",
       "      <td>  2.393500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td> 30</td>\n",
       "      <td> 0</td>\n",
       "      <td> 2</td>\n",
       "      <td> 2</td>\n",
       "      <td> 100</td>\n",
       "      <td>-17.846035</td>\n",
       "      <td>  2.730825</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td> 31</td>\n",
       "      <td> 0</td>\n",
       "      <td> 2</td>\n",
       "      <td> 2</td>\n",
       "      <td> 120</td>\n",
       "      <td>-21.296091</td>\n",
       "      <td>  2.999212</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td> 32</td>\n",
       "      <td> 0</td>\n",
       "      <td> 2</td>\n",
       "      <td> 2</td>\n",
       "      <td> 140</td>\n",
       "      <td>-24.750858</td>\n",
       "      <td>  3.198550</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td> 33</td>\n",
       "      <td> 0</td>\n",
       "      <td> 2</td>\n",
       "      <td> 2</td>\n",
       "      <td> 160</td>\n",
       "      <td>-28.208955</td>\n",
       "      <td>  3.328758</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td> 34</td>\n",
       "      <td> 0</td>\n",
       "      <td> 2</td>\n",
       "      <td> 2</td>\n",
       "      <td> 180</td>\n",
       "      <td>-31.668999</td>\n",
       "      <td>  3.389784</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td> 35</td>\n",
       "      <td> 0</td>\n",
       "      <td> 2</td>\n",
       "      <td> 2</td>\n",
       "      <td> 200</td>\n",
       "      <td>-35.129607</td>\n",
       "      <td>  3.381602</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td> 36</td>\n",
       "      <td> 0</td>\n",
       "      <td> 2</td>\n",
       "      <td> 2</td>\n",
       "      <td> 220</td>\n",
       "      <td>-38.589393</td>\n",
       "      <td>  3.304213</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td> 37</td>\n",
       "      <td> 0</td>\n",
       "      <td> 2</td>\n",
       "      <td> 2</td>\n",
       "      <td> 240</td>\n",
       "      <td>-42.046974</td>\n",
       "      <td>  3.157647</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td> 38</td>\n",
       "      <td> 0</td>\n",
       "      <td> 2</td>\n",
       "      <td> 2</td>\n",
       "      <td> 260</td>\n",
       "      <td>-45.500967</td>\n",
       "      <td>  2.941961</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td> 39</td>\n",
       "      <td> 0</td>\n",
       "      <td> 2</td>\n",
       "      <td> 2</td>\n",
       "      <td> 280</td>\n",
       "      <td>-48.949990</td>\n",
       "      <td>  2.657240</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td> 40</td>\n",
       "      <td> 0</td>\n",
       "      <td> 3</td>\n",
       "      <td> 3</td>\n",
       "      <td>  40</td>\n",
       "      <td> -3.739851</td>\n",
       "      <td>  5.255006</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>41</th>\n",
       "      <td> 41</td>\n",
       "      <td> 0</td>\n",
       "      <td> 3</td>\n",
       "      <td> 3</td>\n",
       "      <td>  60</td>\n",
       "      <td> -5.609476</td>\n",
       "      <td>  7.617156</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td> 42</td>\n",
       "      <td> 0</td>\n",
       "      <td> 3</td>\n",
       "      <td> 3</td>\n",
       "      <td>  80</td>\n",
       "      <td> -7.525985</td>\n",
       "      <td>  9.941466</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>43</th>\n",
       "      <td> 43</td>\n",
       "      <td> 0</td>\n",
       "      <td> 3</td>\n",
       "      <td> 3</td>\n",
       "      <td> 100</td>\n",
       "      <td> -9.488615</td>\n",
       "      <td> 12.227007</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>44</th>\n",
       "      <td> 44</td>\n",
       "      <td> 0</td>\n",
       "      <td> 3</td>\n",
       "      <td> 3</td>\n",
       "      <td> 120</td>\n",
       "      <td>-11.496579</td>\n",
       "      <td> 14.472863</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45</th>\n",
       "      <td> 45</td>\n",
       "      <td> 0</td>\n",
       "      <td> 3</td>\n",
       "      <td> 3</td>\n",
       "      <td> 140</td>\n",
       "      <td>-13.549077</td>\n",
       "      <td> 16.678136</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>46</th>\n",
       "      <td> 46</td>\n",
       "      <td> 0</td>\n",
       "      <td> 3</td>\n",
       "      <td> 3</td>\n",
       "      <td> 160</td>\n",
       "      <td>-15.645288</td>\n",
       "      <td> 18.841942</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47</th>\n",
       "      <td> 47</td>\n",
       "      <td> 0</td>\n",
       "      <td> 3</td>\n",
       "      <td> 3</td>\n",
       "      <td> 180</td>\n",
       "      <td>-17.784374</td>\n",
       "      <td> 20.963415</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>48</th>\n",
       "      <td> 48</td>\n",
       "      <td> 0</td>\n",
       "      <td> 3</td>\n",
       "      <td> 3</td>\n",
       "      <td> 200</td>\n",
       "      <td>-19.965480</td>\n",
       "      <td> 23.041705</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>49</th>\n",
       "      <td> 49</td>\n",
       "      <td> 0</td>\n",
       "      <td> 3</td>\n",
       "      <td> 3</td>\n",
       "      <td> 220</td>\n",
       "      <td>-22.187736</td>\n",
       "      <td> 25.075981</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50</th>\n",
       "      <td> 50</td>\n",
       "      <td> 0</td>\n",
       "      <td> 3</td>\n",
       "      <td> 3</td>\n",
       "      <td> 240</td>\n",
       "      <td>-24.450253</td>\n",
       "      <td> 27.065428</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>51</th>\n",
       "      <td> 51</td>\n",
       "      <td> 0</td>\n",
       "      <td> 3</td>\n",
       "      <td> 3</td>\n",
       "      <td> 260</td>\n",
       "      <td>-26.752126</td>\n",
       "      <td> 29.009250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>52</th>\n",
       "      <td> 52</td>\n",
       "      <td> 0</td>\n",
       "      <td> 3</td>\n",
       "      <td> 3</td>\n",
       "      <td> 280</td>\n",
       "      <td>-29.092437</td>\n",
       "      <td> 30.906667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>53</th>\n",
       "      <td> 53</td>\n",
       "      <td> 0</td>\n",
       "      <td> 4</td>\n",
       "      <td> 4</td>\n",
       "      <td>  80</td>\n",
       "      <td>  6.330006</td>\n",
       "      <td> -1.077910</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>54</th>\n",
       "      <td> 54</td>\n",
       "      <td> 0</td>\n",
       "      <td> 4</td>\n",
       "      <td> 4</td>\n",
       "      <td> 100</td>\n",
       "      <td>  7.959852</td>\n",
       "      <td> -1.258202</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>55</th>\n",
       "      <td> 55</td>\n",
       "      <td> 0</td>\n",
       "      <td> 4</td>\n",
       "      <td> 4</td>\n",
       "      <td> 120</td>\n",
       "      <td>  9.592993</td>\n",
       "      <td> -1.405865</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>56</th>\n",
       "      <td> 56</td>\n",
       "      <td> 0</td>\n",
       "      <td> 4</td>\n",
       "      <td> 4</td>\n",
       "      <td> 140</td>\n",
       "      <td> 11.228777</td>\n",
       "      <td> -1.520839</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>57</th>\n",
       "      <td> 57</td>\n",
       "      <td> 0</td>\n",
       "      <td> 4</td>\n",
       "      <td> 4</td>\n",
       "      <td> 160</td>\n",
       "      <td> 12.866549</td>\n",
       "      <td> -1.603077</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>58</th>\n",
       "      <td> 58</td>\n",
       "      <td> 0</td>\n",
       "      <td> 4</td>\n",
       "      <td> 4</td>\n",
       "      <td> 180</td>\n",
       "      <td> 14.505655</td>\n",
       "      <td> -1.652546</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>59</th>\n",
       "      <td> 59</td>\n",
       "      <td> 0</td>\n",
       "      <td> 4</td>\n",
       "      <td> 4</td>\n",
       "      <td> 200</td>\n",
       "      <td> 16.145439</td>\n",
       "      <td> -1.669225</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>114 rows × 7 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "    Unnamed: 0  event  particle  track  hit          x          y\n",
       "0            0      0         0      0   20  -4.279116   3.125760\n",
       "1            1      0         0      0   40  -8.049544   6.430402\n",
       "2            2      0         0      0   60 -11.885345   9.659012\n",
       "3            3      0         0      0   80 -15.784986  12.810297\n",
       "4            4      0         0      0  100 -19.746907  15.882994\n",
       "5            5      0         0      0  120 -23.769527  18.875874\n",
       "6            6      0         0      0  140 -27.851236  21.787738\n",
       "7            7      0         0      0  160 -31.990404  24.617418\n",
       "8            8      0         0      0  180 -36.185376  27.363783\n",
       "9            9      0         0      0  200 -40.434475  30.025731\n",
       "10          10      0         0      0  220 -44.736003  32.602196\n",
       "11          11      0         0      0  240 -49.088240  35.092146\n",
       "12          12      0         0      0  260 -53.489446  37.494583\n",
       "13          13      0         0      0  280 -57.937861  39.808544\n",
       "14          14      0         1      1   40   5.473631  -4.947957\n",
       "15          15      0         1      1   60   7.932295  -7.135807\n",
       "16          16      0         1      1   80  10.434247  -9.274071\n",
       "17          17      0         1      1  100  12.978486 -11.361892\n",
       "18          18      0         1      1  120  15.563996 -13.398435\n",
       "19          19      0         1      1  140  18.189743 -15.382884\n",
       "20          20      0         1      1  160  20.854678 -17.314443\n",
       "21          21      0         1      1  180  23.557736 -19.192340\n",
       "22          22      0         1      1  200  26.297836 -21.015822\n",
       "23          23      0         1      1  220  29.073882 -22.784159\n",
       "24          24      0         1      1  240  31.884767 -24.496642\n",
       "25          25      0         1      1  260  34.729364 -26.152586\n",
       "26          26      0         1      1  280  37.606539 -27.751325\n",
       "27          27      0         2      2   40  -7.537927   1.512603\n",
       "28          28      0         2      2   60 -10.965578   1.987371\n",
       "29          29      0         2      2   80 -14.402072   2.393500\n",
       "30          30      0         2      2  100 -17.846035   2.730825\n",
       "31          31      0         2      2  120 -21.296091   2.999212\n",
       "32          32      0         2      2  140 -24.750858   3.198550\n",
       "33          33      0         2      2  160 -28.208955   3.328758\n",
       "34          34      0         2      2  180 -31.668999   3.389784\n",
       "35          35      0         2      2  200 -35.129607   3.381602\n",
       "36          36      0         2      2  220 -38.589393   3.304213\n",
       "37          37      0         2      2  240 -42.046974   3.157647\n",
       "38          38      0         2      2  260 -45.500967   2.941961\n",
       "39          39      0         2      2  280 -48.949990   2.657240\n",
       "40          40      0         3      3   40  -3.739851   5.255006\n",
       "41          41      0         3      3   60  -5.609476   7.617156\n",
       "42          42      0         3      3   80  -7.525985   9.941466\n",
       "43          43      0         3      3  100  -9.488615  12.227007\n",
       "44          44      0         3      3  120 -11.496579  14.472863\n",
       "45          45      0         3      3  140 -13.549077  16.678136\n",
       "46          46      0         3      3  160 -15.645288  18.841942\n",
       "47          47      0         3      3  180 -17.784374  20.963415\n",
       "48          48      0         3      3  200 -19.965480  23.041705\n",
       "49          49      0         3      3  220 -22.187736  25.075981\n",
       "50          50      0         3      3  240 -24.450253  27.065428\n",
       "51          51      0         3      3  260 -26.752126  29.009250\n",
       "52          52      0         3      3  280 -29.092437  30.906667\n",
       "53          53      0         4      4   80   6.330006  -1.077910\n",
       "54          54      0         4      4  100   7.959852  -1.258202\n",
       "55          55      0         4      4  120   9.592993  -1.405865\n",
       "56          56      0         4      4  140  11.228777  -1.520839\n",
       "57          57      0         4      4  160  12.866549  -1.603077\n",
       "58          58      0         4      4  180  14.505655  -1.652546\n",
       "59          59      0         4      4  200  16.145439  -1.669225\n",
       "           ...    ...       ...    ...  ...        ...        ...\n",
       "\n",
       "[114 rows x 7 columns]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_event"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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TSyryZgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x105ed7290>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x=df_track['x'].values\n",
    "y=df_track['y'].values\n",
    "\n",
    "plt.scatter(x,y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([-0.51643181, -0.51381024, -0.43859625, -0.29081848, -0.07053458,\n",
       "         0.22216879,  0.58717599,  1.02434247,  1.53349482,  2.11443081,\n",
       "         2.76691951,  3.49070137,  4.28548831]),\n",
       " array([ -8.03604995, -11.66590266, -15.2950133 , -18.92193022,\n",
       "        -22.54520266, -26.16338127, -29.77501871, -33.37867023,\n",
       "        -36.97289424, -40.5562529 , -44.12731268, -47.68464495, -51.22682652]))"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x,y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p[0]x+p[1]x+p[2]x+x\n"
     ]
    }
   ],
   "source": [
    "def rotateToQuadrant(x,y):\n",
    "    seedx=x[1]-x[0]\n",
    "    seedy=y[1]-y[0]\n",
    "    phi0=np.arctan2(y[0],x[0])\n",
    "    phi1=np.arctan2(seedy,seedx)\n",
    "    phi=phi1\n",
    "    c, s = np.cos(-phi), np.sin(-phi)\n",
    "    xr=c*x-s*y\n",
    "    yr=s*x+c*y\n",
    "    print phi\n",
    "    return xr,yr\n",
    "\n",
    "def func(x, r, vx, vy):\n",
    "    return r - np.sqrt(r**2-(x-vx)**2) + vy\n",
    "\n",
    "\n",
    "from formulate import *\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-1.57007410199\n"
     ]
    },
    {
     "data": {
      "image/png": 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ssjpAdk6+QxVJc1Nwi7iItfb4SPtURfUcl/Cj4BZxiarqAL9YsLben6cmxjdjNeIkBbeI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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1053e7250>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xr,yr=rotateToQuadrant(x,y)\n",
    "plt.scatter(xr,yr)\n",
    "plt.plot(xr,yr)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "popt, pcov = curve_fit(func, xr, yr, p0=[200.,0.,0.], bounds=([5.,-25.,-25.], [1000., 25, 25]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 181.50577883,    9.85019937,   -0.53131378])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "popt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([-0.51643181, -0.51381024, -0.43859625, -0.29081848, -0.07053458,\n",
       "         0.22216879,  0.58717599,  1.02434247,  1.53349482,  2.11443081,\n",
       "         2.76691951,  3.49070137,  4.28548831]),\n",
       " array([ -8.03604995, -11.66590266, -15.2950133 , -18.92193022,\n",
       "        -22.54520266, -26.16338127, -29.77501871, -33.37867023,\n",
       "        -36.97289424, -40.5562529 , -44.12731268, -47.68464495, -51.22682652]))"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x,y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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xKnSRABUfH0+HDh0oUaIEq1at4te//rXTkcRNGkMXCUBLliwhIiKCihUrsn79epW5n1Ch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\niJ9QoYuI+AkVuoiIn1Chi4j4if8Hlz2nQOvzJk8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a512190>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xp=np.arange(5.,80.,5.)\n",
    "plt.plot(xp,func(xp,popt[0],popt[1],popt[2]),'k')\n",
    "plt.scatter(xr,yr)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 181.50577883,    9.85019937,   -0.53131378])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "popt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 294,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 219,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 220,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 221,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "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": "2.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}