{
 "metadata": {
  "name": "",
  "signature": "sha256:20ef638fc8fb665aa9096a438cfa76c399d3c12e63d6049c7218b49c69314f89"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline\n",
      "import cPickle as pickle\n",
      "\n",
      "import matplotlib.pyplot as plt\n",
      "import pandas as pd\n",
      "import numpy as np\n",
      "from path_helpers import path\n",
      "import matplotlib.mlab as mlab\n",
      "\n",
      "from microdrop.experiment_log import ExperimentLog\n",
      "\n",
      "log_path = path('.').abspath() / path('data')\n",
      "\n",
      "# load the experiment log\n",
      "log = ExperimentLog.load(log_path)\n",
      "\n",
      "# get the start time for each step (in seconds), relative to the beginning of the protocol\n",
      "step_time = log.get('time')\n",
      "\n",
      "# get the FeedbackResults object for each step\n",
      "results = log.get('FeedbackResults', plugin_name='wheelerlab.dmf_control_board')\n",
      "\n",
      "df = pd.DataFrame()\n",
      "for step_number, feedback_result in enumerate(results):\n",
      "    if feedback_result is None:\n",
      "        continue\n",
      "\n",
      "    # get the raw dx/dt and interpolate it to use the same time points as the\n",
      "    # impedance values.\n",
      "    t, dxdt = feedback_result.dxdt()\n",
      "    dxdt_raw = np.interp(feedback_result.time,\n",
      "                         t, dxdt) * 1e3 # multiply by 1000 to convert to mm/s\n",
      "        \n",
      "    # get the smoothed dx/dt and interpolate it to use the same time points as the\n",
      "    # impedance values.\n",
      "    t, dxdt = feedback_result.dxdt(filter_order=3)\n",
      "    dxdt_smoothed = np.interp(feedback_result.time,\n",
      "                              t, dxdt) * 1e3 # multiply by 1000 to convert to mm/s\n",
      "    \n",
      "    # append the fields for this step to a pandas data frame\n",
      "    df = df.append(pd.DataFrame([step_number*np.ones(len(feedback_result.time)),\n",
      "                                 step_time[step_number] + feedback_result.time / 1000.,\n",
      "                                 feedback_result.time / 1000.,\n",
      "                                 feedback_result.V_actuation(),\n",
      "                                 feedback_result.capacitance(),\n",
      "                                 feedback_result.x_position(),\n",
      "                                 dxdt_raw,\n",
      "                                 dxdt_smoothed,\n",
      "                                ],\n",
      "                                index=['step number', 'protocol time (s)', 'step time (s)',\n",
      "                                       'V_actuation (V)', 'capacitance (F)', 'x_position (mm)',\n",
      "                                       'dx/dt (mm/s)', 'smoothed dx/dt (mm/s)'\n",
      "                                ]).T\n",
      "    )\n",
      "    \n",
      "# save the data frame to a csv file\n",
      "df.to_csv(path_or_buf='log.csv', index=False)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Plotting data\n",
      "\n",
      "The following cells show some examples of plotting data."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Plot the velocity of the first 5 steps versus the protocol time\n",
      "plt.figure()\n",
      "filtered_steps = df[df['step number'] < 5]\n",
      "plt.plot(filtered_steps['protocol time (s)'], filtered_steps['smoothed dx/dt (mm/s)'])\n",
      "plt.xlabel('Protocol time (s)')\n",
      "plt.ylabel('dx/dt (mm/s)')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "<matplotlib.text.Text at 0x392ee70>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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rN4GKQ6oYpy+afpA00pFbbvxnmPkfGzkZEa0BMA4Fg7syeS56WX41/TiOyHUH\nNYkDVZ+L13Zh3ZI0RqZz6KoSow+oGUhkKt5c+hK9EzYNT6LCzMO27PP1Js73JwB+0MT36jKdqT8w\ny6FNc0euTl3RGd4OiKbvh/ZUAqcuSeOla7qK22SO3IUxm3OnVa4Vp2/9lzj9YGl25iww81QTX9sA\n4FZYxv+aWju6b87AwEDd9S1btxfX9z6zs+b+J4aOAih5HH6OH+T64OBgqOcrX2e2HjrnN8+0+um4\nf4cOHgRgvT3pLl/U17duf7K43JVOVN3f8fQnpqYjVf6or9eD/MwTS0TXMPNvXOvvZ+bP+T7L/ONd\nDeAoM++u9Hl/fz/39fU1dMxnhmZw585RAMA7L1uBVT1tVfe9d88Yth+cRjpJ+KurVzd0HhP44uaj\nmM0xLlnXhVef0xKBWZFn4LlxbD0whSQBt75yje7iRJqdR6Zx1y6rS/DGK1YW+0rK+cXTo/jt0Rks\n6UjiXb+7Kswitiz9/f3o6+ur2anp19P/HBG9DACI6DoAr262UES0Fpan/8pmj1GJKZe8s6jGyEnA\nG72ja3J0nYhWGjwSveMfd2LEatOaAuZMNh81/Br96wC8hoj+CsAsgHc1e0JmPszMNzHzV5o9RiWc\n9LdEtRsSUAoTYwQbA+yXRl7FVKBaf9ZdP9VUqp8TXshASzsSYdw7J7SaqPpE80DJOZF8+sHi1+jv\nB/A0gCsB7ADwgqoCNcuk7ekvqpF3xyHtSa8cP3dXRSKruBNGympTcIx+V51n1TH60kyDxa/R/ymA\nlbA8/j8D8AVlJWoSJylWPWkH8CZ50hGrrztWuDjoRXLvNEWtOH2gtSenCePe+R1E6QT2BOnpm942\n/eDX6D/GzN9iK+zjowDOUlimppiy0992p5N19417Tv2iB9XCxilqJGT8g28cB62e0U+6+klaWTKL\nGn5TK3/ctZwDcK2yEjWJ05FbbZILN+6c+jqMvm5dsSjvSD79pqis6bvTW7SugVJ975gZx6esUc7V\nonYcvHmigjm/6W3TD83G6b8jyEIslEKBS0a/vTFPX9dEKjopJQeLX91V4c1eqq8cUWdirlB0tFZ2\n1zP6pWXJCBscNa86Ed0D4AEAqwD8LoB+WOGaj6svmn+mXCFg3T48fd2To+vWFVWnDNBdP9VUqp+7\nQ7KV7ZPqezc0mS0ur6yRqhpQkxHW9Lbph3oW8gPM/EkAYwCuZOYPAbgCwHHlJWuAKdfE1d0+PP0o\nTI6uk4To+HPVAAAZRUlEQVTEPweOzEjmj91DswCsNnhKjQGUgDciSkdotanUNPrMvMNenLO1fDBz\nFsCo6oI1gtOJC/jT9N3pXGOp6SsOhdNdP9VU1PQNSVmt8t79es8Ydh6dAQCc3puumXcHKJN3Arqo\nprdNP/jV9LvL1pcFXZCFMDZbMvo9vjR91+ToMfT0iyMdW1mHiBgJ15PUyh25KnFkVSLg8tPLTcp8\nPPKOXNPA8Jta+R4i+gSAh2Fp+/eoK1LjjM5YRj+ZAHp8xOm7HYx4xuk7IZtqjq+7fqqpHKdvhqev\n8t5dsb4b47N5XHlGN1Ysqi3tAKV8+kBw0Tumt00/+DL6zHw/ET0O4HwAn2HmCbXFaozRGSsEbElH\nsu5oXMDqdEsXJ0dv4Se0ScTTDx6Ze7g+7akE3viSXt/7Sz+JGnyHbDLzBDM/GjWDDwCjtryztNP3\nnDCliVQ09BDp1hUTitMw6K6faupq+i3c6Rile+eVd4I5ZpTqp4um8+lHBWYuyju9nfX1fAfdUybq\nxOnSEOcpOETTDx4VIZuCAUZ/OlsodsYuacDTdyIH5jQMztKtK6pOuKa7fqqpVD+3gWrl8MIo3TsV\n0TtRqp8uWt7oO14+0Jin76R0nWvlJ7RJEpK9MHBS4pUGjjdOX65pUBhl9Jd0NGL09Xn6unVF1R25\nuuunmkr1c3c6trKBitK986ZhCOaYUaqfLlre6I/YkTtAYx25HeLpy8xZASKefvDINVVDyxv94UnL\n6C/uSHrSK9Qj3pp+aVlFp6Pu+qlGNP1wcEdESZx+cLS80XcSOJ1SJ2NfOY6mny1w7LyIpIKHKe6I\nVxo8KQUduUKLG/25XKGo6a/qrj/Cz40770fY3r5uXVF1eKHu+qmmUv3cBko0/WDwvj1J7p2gaMw9\nDgAi2gTgKgBJAD9m5qebPdb+k3PF5TWLGzP6Ha6ka3O5Arp8JGozBfH0g0diyoPHkw1XrmlghG70\nAZxmp2sGEd0Ca8L1pnj6mJWmNZUATu9tb+i7Oj193bqi6skpdNdPNdXmyCUADNH0gyJBhFTCup5B\nJUaMUv10Ebp7y8zfDeI4B8cy2DNsGf2NKzsa6sQFSpo+EL8IHm/KAPGggoCIirq+5N4JDmdq0zhm\nw1WFNk2DiG4C8LNmv//I/kkAlte6acPihr/f4fL0Z0M2+rp1RRXxz25010811ernXFfR9IMjHXC6\nlKjVTwdajD4RXQ9gKzMfqLaP++YMDAx41u++72HsPWHp+Reu6cLjjzxQc/9K609s21pc3/HbXQ1/\nfyHrg4ODoZ6vfP2ZXbuKywVm4+qn6/45nv6LBw9HqrytvO68wR8+OhSJ8rTCej2IQ34VJaK3AXiB\nmbdU26e/v5/7+vqqHuPXu8fw+KFpEIAbr1iJ3q7GuyZmswV88YFjAIBrzu7BZT4mdTCFPcOz+OlT\nIwCAd1y2ou60dYI/vvLQEMZm83jJ6k684YKluotjBN/ZdhxHxrM4Y1ka1168XHdxIk9/fz/6+vpq\nat2hduQS0ZkArgOwhYiuArCCmd/fyDEKzNhta/nrl6WbMviAd8pEHQO0dCK539VggrwTNRx5RzT9\n4AhV3mHm55n5jcx8m/3XkMEHgBdHM5jKWBr8eas6my5Lwp5IBYifpp9QMCORG931U021+hU7clvY\n6Eft3gWdAj1q9dNBywWnn7o4jTdf2IvzT+nAOSs7FnSsUqbN1n1Im6HNZfTFgwoOJ1ZfPP3gEE8/\neHTE6S+IVJJwzsqFG3zAiuCZmCuEHrKpO1bYM+hFgauvu36qqVa/lAGJ7KJ274IO2Yxa/XTQcp5+\nkMTW00+Kp68C0fSDp008/cCJudF3Mm3GS9NXPbxdd/1UI5p+eLjj9IOINIxa/XQQa6PvDNCajZmn\nnxZPXwkp0fQDJy35dwIn3ka/TU/0jm5dUXVHru76qaaepp/LV/y4JYjavQtaioxa/XQQc6Nfmkgl\nTjloEgkqxuqLpx8cRf05Rm1JNdL/FDyxNvqdnvw74TWoKOiKKjvIolA/ldTT9FtZ3onavXPLO0HE\n6ketfjqItdF3PH0gfIlHN0EPehGscGLA+iENO72JqYinHzwxN/qlBjWTDc/oR0FXVClFRKF+KqlW\nP3dfSavap6jdu7QrJWwQDkrU6qeDWBt9j7wTotGPAmnJUx44KZdXmpPrGgji6QdPrI2+LnknCrqi\naPrNU61+rubUsp25Ubt3QY8ej1r9dBBro9/pekqns635kDZLudGP2+xhKkglxNMPmqA7coWYG/2O\nVCl0cXIuvODqKOiKjv6czTO2vziFf9x8DJv3TgRy7CjUTyVVNX0DBhJF7d61BWz0o1Y/HcTa6BMR\netqTAICJEI1+FChF7xRw77PjAICHX5jUWaSWRzz94BFNP3hibfQBoKfDNvqzoukDkPwmPqiq6Rvg\n6Uft3iWI4MRbBGH0o1Y/HcTe6He3W5cgrp5+uXF6YSSjozhGIJ6+GiTSLFhib/QdeWdyLh/agJoo\n6IqO0S8PiPjh4MnidcgXGD8aPIl/3jqM0ZncvGPMZAsVr1m9+s1W+V6r0Kimv3toBl97eAg7j0wH\nXpZ8IdiBYFFom+U4nblOsEE2z9h7fLah4IPpTAEP75/EBS+/SkkZW4nYG/3FtryTZ2AyE58IFreB\nKmd0xvoB/K/dY3j+5ByOT+WKE6k7PHVkGrc/cAx37xqb9/1aRug/fzuCLz5wDN/edhyZVp5tpAKV\nPH1mxs92jmJkJo+7Klyrahwey+C7247jrqdHMZWp/ha6Z3gWd2w5hp8+NRJqMEKYLCq+jVvt5f69\n4/jxjhH84+ZjuHePv2v6q91j2LxvAj8aPKmsnK1CqEafiM4mos8Q0SeIaGOY567GUtvoA8DYTDgP\nTRR0xXSiutEfnsrhqSMzeOrITHHb0GTOY6QdY7/z6Iwnf/wzQzP4wn0H8eiB+Z3CmXwBTx+zJrU/\nNpHDYwemFlwPHVTNveMenGVfk51HZzz7VBoEODmX91zDfIFx165RHB7PYufRGXxpS/W3hAMjGcxk\nGftOzHrGnTRLFNpmOY5jNj5rPZ/bD5auxfaD076ch93DVrubyhRQaOG3zCAI29N/EzN/iJk/AuAt\nIZ+7Iks7SzNGOhLG4fEM7t87jsdenDJW66/l6Q9PZvHQ/vlGe2hivsQDADsOlx7CO3eOIocU7ntu\nAnfvGvXsd2LK+/2dR2ZaWuYpxx1TPpNlKzJqz7hnn8denPLUeeeRaXz5wSH8+MmSrLb/5BxOTnvb\n3V27xipeqwOjcwCAU5ekPW8aJrHYlmDHZvPY8vz8sOLtL05j64FJDE1k532WyRfwi6e97fDweBa/\neXYcz5+cU1PgiBP2HLnuJ2Cm6l4hssTl6Q9P5fAfO07i2eOlxvDA3gm8+6pVnoFcCyUKumkto7/3\n+BzGZuf/2B0az2Dd0vQ84/OrPeNYtzSN/9rtfdV+6sgM+jYuLs5Qdn/ZOIDR2TxOTOewYlFbs9XQ\nQrX7155KoLMtgZlsAaMz1ptMeWz5Q/snwcx4xYbFKDDjnmesa7Z/JINdQ7O44JROPHt8tuLxj0/l\nsLK7dK3GZ/PFH4fTe9MB1CwabbOcxa5n9MHn5zsjm/dZ7WoAEzh3ZQeuWN+N1YvbcGwii3957Pi8\n/b+//QQA6wf4DRcsxUtWdyoqeTQJ29N3W5rKLTtkUklCj60ZPnpgymPwAatD7vYHjuFXtr49beur\nzIzRmRx2HZvBXU+PzvNio05b0nvr1/S04ZRuywc44vKYbrxiZfGH8bdHLc98uoJE8c1Hj+PQ2HxP\n644tx/DM0AyGJrMVI4MOjpoVLbS007pWO47MYIttoDrbCNddvKwYKbb1wBSmMnls2TfpScz2hC1b\nONeptzMJN4fHvdf3OdePw5nL2oOtSIRwO2b12D08i29vO44DI3P4j7J+qEr8avcYpmPUlweEb/Td\nLl1k3utPXeL1kpZ1JfHqcxZ7tj1xaBo/GjyJO7YM4XP3HcFn7zuKrz48jJ//dhQ7j854HsB6REE3\nTZd5+m+/dDm6270PV2dbAr2dSVy01vKEhidz2PbiFI6Mzzfu1cgXLMnH3T9w9Yae4vmPVngljzq1\n7l+5oba2pbB+WTted95SAECBgV/tHp83GO7gWAZHxjMYtfuWLjilE+9/5eri6OnHD06h/9nxouS4\n65h1TXvaE1jdE8zbUhTaZjmn9abnXddTl9Su778+cbLYB1CLTJ6x7WBr9i01S9hGvwcAiIic5Wq4\nG9/AwIDS9dnhFzznbp8ewvhzj+GtF/VizeI2dGAO7t+o8nE3CRSwZ+/zvs83ODgYav0qrT/5xHZP\nHTZvvh+L0t7msLgjASLCyPM7i9t+89wE7twxDMD64fBrbJ540VL21i1pw+zz29Cetx60oxNZLfVf\nyHqt+7esa75i2j7xIgYGBjyGas+wy0uno8Xl72w7UVxe1dOGBBHaC9YbwJD9o/tPDw7hp/c9hoP2\nm1X33HHcf//92q6H6vWHHtiMs2afQW9nEkTABfQC1k3sxNsvXY7TlvqTtVZiFK85d3HFz7btH8F9\n90WnvgtdrweF2ZFGROcAuAHWj81XmXl/pf36+/u5r68vtHJNzuXxrUePYzpbQHuK8LZLlnu0U8CK\nST80lsGJ6RxmswUrhUM6gZU9bVjd09ZynWgnp3P4+iPDxfUPXrMG9+8dxyMvlLyes1e04y0XLUOh\nwPjcwNF5x7hwTSeSCcLgoVJHbm9nEqf3pvHk4cpdNpeu68KrzlmCe/eMYfvBaSQTwHuvXo0Etdb1\nq8bEXB53PT2KXIGxuqcNi9JJXL5+UbF+X3t4CCOuKLEr1y/CKzYsxve2z5fHbrpyJZZ2pnDfc+N4\ntEqkE8GS4Hor/NiYxlyugFyBsShd8voLzPjpUyMYmc7j4lO70P/seMXvvueqVehpTyKbZ/z4yZMo\nMOO8VZ3FFCTXXrwMZxggkfX396Ovr6/mwxRqS2HmPQA+HOY5/dDdnsSfX7kSw1M5rOhKVQx962xL\n4OwVHThbQ/lU4FZ3nOiI2bJMo0nbUCUShI0r2uf1d5zR245jk15DlS8Arz1vKZgtXbucFYusJrfc\n/p8vABOzeSzpNMNo9bQncd3vLK/6+dkrOvDYi5YBv+w0y+ADwH87vXveWAhHyz53VUdVo/8767pi\nYfABq6O83CwniPCWi5YBQMXoHQB42drO4iDMtiThf11i3Z+ZbAH9z42D2eofMcHo+yH2g7Mc2lMJ\nrFuSDiTWuR6NvIqpoqcjWex0/MOXWlrzWcu9jd49qvQ15y3xfEZkaa0vW9vl2f7SNZ0YGBjAa89b\nYvcTeK/ncjtSxy2DnJhurbDYhdy/V2zowUVrOnH2inZcdWZ3cfvGFe04Y5lXqiD7R3dNT1vFvoLz\nT+nAKzdUliyaJQpts1lW9bThFWf14JJTu/COy1YUt5+3qhSd465fZ5v1zAOIVfhmPFwEYR4JIrzz\nshWYzXExJO7sFe146erO4oCi01166aJ0Epeu6yoOjHn1xsVF7+lPL12OXUOzSBBw+fpFeOiAZbBO\nXZLG/7iwt6hTn740jbWL5xv9kekcsDweXlYqQXjd+UvnbScivP78pfinB4cAeMMUiSzv9J5nxrDv\nxBx6O5N426XLPTKHYHHlGaUf0jdf2IuZbAHra4Szru9N48XRDE5O5zGdyaMrBtdUjL4GohILnU4l\nkHa1ACLCH1ywFMu6UhiZyeHSdYs8+1+xvhtEhLOWt3tCBNcuSWOtKwLKXb81i9P44DVr5p27O51A\nW4KQLTBGKuT1iTKq7l93OoF1S9pwaDyL15/vfbPqaU/ij19m9a8Qld4CgiYqbTMIzlnZMW9bef3W\nuRybg2NZnLNSjL4QQ9zekpvu9iT6NgYjJxARFnckcWI65yu0Lg44Hn0mx1VlxkSLBQxEnTWL20AE\nMAOHxjIVfyhMQzR9DbSybuoHv/Urz6nSKqi8fwmiUPqVqhG3tplOJrDajtQzbaBgNcToC9pwolMq\npXwQhLA41ZZ4jk5kYzEPghh9DZikm1bCb/0cT382x8i00MTsJt8/k+sGVK7fGnuAYYGt/EamI0Zf\n0IY7p4p4+4IuVvWUujbLx52YiBh9DcRNN63GmsVtuPqsHrzxgqXF8M9WwOT7Z3LdgMr1W9aVKuY3\nOtaCuaAaRaJ3BG30dqVwRZVIIUEIiwQRVnancHQiG4t5eEPNveOXsHPvCIIQb8Zn8+hKJ1ouh1Y5\nkcu9IwiCEEUWN5Czv9URTV8DcdRNTcLk+plcN8D8+vlBjL4gCEKMEE1fEATBEPxo+uLpC4IgxAgx\n+howXVeU+rUuJtcNML9+fhCjLwiCECNE0xcEQTAE0fQFQRAED6EafSLaREQfJqKPEtEFYZ47Spiu\nK0r9WheT6waYXz8/hD0i9zRm/iQAENEtAJ4O+fyCIAixRpumT0S3MPPtlT4TTV8QBKFxIqvpE9FN\nAH6m49yCIAhxRonRJ6LTieibRPQt+++bRPRS+7PrAWxl5gMqzt0KmK4rSv1aF5PrBphfPz+EKu8Q\n0dsAvMDMW2rt19/fH704UkEQhBagnrwTmtEnorMAfBGAY/BXMPP7Qzm5IAiCACCig7MEQRAENcjg\nLEEQhBghRl8QBCFGiNEPGSJKEJFMUykIghYiZXyI6GwAfwYgB+DbzPys5iIFChHdDOASALcB2K25\nOEogok0ArgKQBPBjZjZq1DUR/U8AG+zVp5j5FzrLEzRE1APghwD+ipmNaaNE9D6U7N02Zu7XWR4V\nENGlAN4AYBrAHcw8W2m/SBl9AG9i5g8BABF9CMBnNJcnUJj5S0R0te5yKMboVBvM/CNnmYjerbMs\nirgewJd1F0IBk8z8Vd2FUAURnQJgIzN/vN6+UZN3xl3LM9pKITQNM39XdxlUQ0QXE9GPAWzVXZYg\nIaI1sJ7BSd1lUUCKiP6GiD5CRH+guzAKeB2AEbuOV9baMWpG3z2ooOKridAamJxqg5kHAbwDwJs0\nFyVo/gTAD3QXQgXM/GVm/hQzfwLAWbrLo4AzAaxh5k8BuJyIktV2jJq80+ZalgEELUocUm0w8yQR\nHdddjoDZAOBWWEZxEIb2O8FMh5IBfMde3gVgLYAXK+0YNaPfAwBERM6y0FrYqTb22d6wcRDRqcx8\nyF6N2pvygmDm9wCA3e90VHNxAoWILmLmHfaqibblEQAvB/AoLIM/UG3HqBn9nxDRJ2E9TMZ1uhDR\njbBuzAQRDTLz93SXKUiI6EwA1wHYQkRXwcxUG9cRURcsKfJO3YUJGiJaC0vmeQJmefoXEdGb7eV7\ntJZEAcx8jz05VR+s/GZz1faVNAyCIAgxwqjXU0EQBKE2YvQFQRBihBh9QRCEGCFGXxAEIUaI0RcE\nQYgRYvQFQRBihBh9QRCEGCFGXwgEIrqZiH5NRB8kog8Q0a0BHXctEV0bxLEaOOcmux5faOK7763z\n+Q1EdEPzpWseIvr7BvY9pV5dhNYkaiNyhRbFThu9nJlvAwAiegURvY6Zf7nAQ6cBdCy8hP5h5gEA\nA0T0sSa+Xm+I/382ccwFQ0SvhZVPxxfMfIyIzrDv6QmFRRNCRoy+oIodAG4A8EsiehmA9wD4NYCX\nwUp4tY+Z/xUo5qXvhTV5TjuAzzPzNBGdAeBdAM4iotX2cf+dmffZ39sIK//7JKwfhgeZ+V77sxSA\n/4NS5tZeWJOe/Futcy6kwkT0dgC/R0QftDcdYebvuD6/AcD5sBJifdveloaVKGsOwH4AKwCctMt2\nCzMXiOh3AbwWwASARQB+zsyPN1i8/w3gT8vKey2Ac2FNupECMMPMX3TtciesbKKfb/BcQpRhZvmT\nv0D+AHzMtXwLgHNd61fDMm6dZd+5FsAVrvVeAH/jWl8P4IYq5/tC2fpfAjjdXr4ZwKmuz9YBuMrP\nOSvVp5lrUOXzefWB9eN4rr18m2vbmQCWONtc+38UQHuD5fplhW2fBdBrLycAvKTs8yUAfqC7Xclf\nsH/i6QtB4ni5BKCf50+39w1mLp8c5zxm/qGzwswjdpbVmhDRMgD7yjbfC+BSAAcALONSNkww80EA\nBxdyTsU46X6diYRysAzxWQBWud4eAKAbVibF5xs4fqX+u48DeCsRdcOSpcqluBmYmZEy1ojRF4Jk\nC9uafgWqGdWniehKZn4YKBpzN1l451kAADDzSTurp5tXA/ipvTxBRGuZ+bB93CSAS5j5MR/nVEmj\nPy5PA9jrvq5ElGjiOHlPIYjaAFzOzN92bfsUgCddu50JYE+D5xEijmTZFALBnvT9j2B5279ml+Zs\np7R9rb26D8AzzHyn63NHX8/D0uY/xy59nYg+AiBT9nmGiM6GJYNMAuiEpen/2v5OGsAHYP1opOy/\n7zPzc7XOSUQdsKShJIBX2fU56jaOda7DFQBeA0snJwCPM/O9RLQBwFvtc54FYDus3OcPwtL3H2Sr\nM/zfAHwI1uTyq5j5H4joJfa1zdqnWQbg77mBDla7U/qnbOeUt737bwHYBmsCjkUA7mLmR13feS+A\nh50fR8EMxOgLQgyw32b+lplv8bl/CsD/Y+Yb1ZZMCBsx+oIQE4joMlve8rPvcgA9zLxfbamEsBGj\nLwiCECNkRK4gCEKMEKMvCIIQI8ToC4IgxAgx+oIgCDFCjL4gCEKM+P/MQs4L1ouIYQAAAABJRU5E\nrkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10ed7c50>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Plot of the drop velocity versus the protcol time (i.e., time since the protocol started)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Plot the velocity of the first 5 steps versus the relative step time\n",
      "plt.figure()\n",
      "filtered_steps = df[df['step number'] < 5]\n",
      "for step_number, feedback_result in filtered_steps.groupby(['step number']):\n",
      "    plt.plot(feedback_result['step time (s)'],\n",
      "             feedback_result['smoothed dx/dt (mm/s)'],\n",
      "             label='step %d' % step_number)\n",
      "plt.xlabel('Step time (s)')\n",
      "plt.ylabel('dx/dt (mm/s)')\n",
      "plt.legend()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 8,
       "text": [
        "<matplotlib.legend.Legend at 0x392e230>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ocAKZ3j6elVJeBKallMPA1Go7KCyklIzOWcVmzRVNl25QnRY0DgzkfJ6Ui0hf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\nrkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x11a35a90>"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "You can also plot versus the step time (i.e., time since the step started)."
     ]
    }
   ],
   "metadata": {}
  }
 ]
}