{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Quickstart"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "The best way to get started using `Tweezepy` is to use it for a project. Here's an annotated fully-functional example that demonstrates standard usage. \n",
    "\n",
    "For new Python users, this example is carried out in a Jupyter notebook. If you have Jupyter installed, you can download and run the notebook locally (using the download option in the header above) or run it online using Binder (also in the header above)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load in data\n",
    "\n",
    "Standard usage of ``Tweezepy`` takes in a 1D array of bead positions in nm, trace, collected at a known sampling frequency, fsample. There are many ways to load data into Python depending on its format. [Here](https://cmdlinetips.com/2018/01/how-to-read-a-numerical-data-file-in-python-with-numpy/) is a quick tutorial for how to load in data from csv files."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For this tutorial, we will use an example trajectory that is included with ``Tweezepy``. The sampling frequency for this data was 400 Hz."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-10-27T18:19:26.832591Z",
     "start_time": "2021-10-27T18:19:25.952942Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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2i989P8VzO4Cfdlcundm9p4xz/vlF+QBFb369nM8Xhi7eP27a4VmkW1amvPn1Mkr3lLFsw3bemxW7eHZJCkbTC7VbiL7NPz5ZGDhIxeJ+b1M5cNItb+8deTGyzYdb5Pdq9x6lZPVWZi7bxPptu7jv3e8qlaCFS76+C9CVMdqgWIl8pc/xGVUz3XX6YRb4q5Ya2Tqwqq4AVjiPt4jIXKANMAQ4xtnsBeBj4EZn+Ysa+sVOFpHGItLa2U9WPf7RAt9+uQBPfryQT+avYczVAyqtW7p+O+2a1qs0K5m7qH3bzmBBP/yajXHMurdy0w5GTl7CtSd2rnDT4i4aXL7xJ1o1rENhGq4y4TQvWrONXz/95d7lCQb8eLpL9bztA045uBVP/eawSusiSy4+ijKkslepwJJ12/jy+/X8/KkvWDz81ErrL3j2K6bcfALNG9QuX/afaUu58Y2ZrNu6i398spB1PqU97rRFC25hG7btosk+tXzXx9vY78jhH7Ff47oVFwb4uLwawSXb0r7Up5/+Qx5162HHP/gJ5/VpX/78s5K1nPBQ7OoegA1J5PgB5qzYTLum9ZLaRzmRqGMepLoXg6kacqJOX0SKgEOBL4GWrkC+EmjpPG4DuMsClznLMqI0Stcnr5b2kWZ7zH0NoYZxXjkDdyCJWnTusS6yWDySO57+8d/f8PiEkkr1pe5BT/oP/6hSY7YgoiY7xv3DxAVrGfpS/H3wow3W4uVdZ3CfjREX8+k/bAzetjrGuQzzGW3QPWQtUB7k123b5Rvwi4aN4aEP4msIGO7xkBTXOa7ZsrNCv/W1Ufqwu6tZ3vm28v15aZlyxcsVP+d4hrP+LoHAtmjtNu4eW7ktTDQLVm9l7dadlQbl2VOmMfvwp6vNhxB9oLBZy4ONHBqE5farjkBBX0SaiEh3EekoIim9URCR+sAbwB9VtcK31MnVx/WLEZGhIjJVRKauWZP4IDCR3EXv81Zu5sO5qygaNiahuuPIi8DIyUtYEBH43RN1RA5m467vTzbvHW4UVqbRL06fxWg57SUTY6FD8pMGnfPPLyrNYJbIBEGbtu9m3JxVvPjF4gqNDl+b4l1v/bMnP2eGR+O0KYujtxEIj5kf1Huz9wbbOT9u9uwBESnyuxD5Di/bsLdnRvFd430D9YEt65c/DvfmWL6hYq+O8h4c5ceOmbysuNhjdr+/vT+Pw+4aH2imvFQTyY/BpExu8S3eF5FGwJXAeUAtYA1QB2gpIpOBJ1U1WN8t/2PUJBTwX1bVN53Fq8LF9iLSGgiXqy4H2rle3tZZVoGqjgBGABQXF6flN7F2667yC8Bf/juLGgGLvXeW7qF2jUJudvrBh/kNjhI2cnLFhoO97xznuZ1fkeZpj03ksqMP4LSe+1Va524Eluo3K9r45OXHTPFB+9w9Pu7XfPn9erq0bJDwMYVQY61LXSUTnVrU93+By2cla+nZtnGFZansGgpwz9h51KlZyAX9ihj86EQALj6qQ1z7iHVjtW6rd9BrWq9ytYJXd1i3m9+ayXMX9QmeuAxZv61yjn7c7FA1WLRif/dXPJXfd0FsOl0Tt2i59tcJFacPUNUuqnqUqharajtgODBERC5O9MASuoo8A8xV1Ydcq0YDFzqPLwTedi2/wGnF3xfYlAv1+as27+DDgFPoXvz8VEZ/+yOvxLjoJeobn0GAZi3fzFWvfIOqMnPZJt/gnswFJNHM9q4ERg6Mxm80t3TasXtPhYAPsDFgr4rRrq6R6bx+3/L27ArtHeIdyyGy+iPSIp+R4xIZMyLckHTJum1880Nqb4CSER7BMF7p+lz/762ZlabuTScr4q8afHP6qnpilHXTgGQHPe8PnA/MFJHpzrL/I3RDMcq5oVgC/NJZNxYYDJQA24GLkjx+SgTJzYZ9VrI27qLZWOIp2n5u0mLueGcOR3RoWmndnjLlspFf+75WUZ76OPoFJtpgPJHCqU7XDVC8vIqnz/7HFx5bVhaezCURyVZNxKPLX94rf3zwre/H9dpEq2pilWJFc/T9HwOw6J7BDAvSlz5Hub9bqZ5+e9TU+Ed3TEY48Hs1TjX5IVDrfRHpCRS5t3cVxydEVT/Dv0r6eI/tlVB1g3GJJ2SEuxst21A5OD8xwb/3AYRKC6I1DFq8djv9h8c/H3qumO8x6UzQcc+9GsplqjtVukQ2PPXqoZBOt43e2/1uxeYdGQ9u8doTpTuje7hqK4032RazUZ6IPAs8C/wcON35Oy3N6TIBxdOFKNq2kS3J4/XjpviKPuMpFchHmQ6SqRY56qRfb4J0SaaEIFM+L1lbXq0ROd6/n6oygY4V9eevIDn9vs4AOiYHRZvXO1J44Buvuvtki5mX+Exi48evC2N1I4QCQbP6tXKqUZZI7uRKow12k01Pxqju8pKNNifpYkX9+SlI97svnJHyTBXxo8cEI7l6Yc1XscZKCJuzYjPHPvAxPW+PPVlQJkUG/D1lqW1wGY8Ln/0qa8eOJpExAsAmwjHZFSSn/yKhwL8S2Ekoc6Kq2jOtKTOmGsmVXLUfr8mhqrt4h8euqtxF/Zbrz31Bgv4zOK3sgezd7hvjIx/qf4N4IM6R9kx2pWSkwyqmaNgYC/w5LkjQX6Oqo9OeEmMSFGT8eWOMMcGC/jci8grwP0LF+0DyXfaMMcZUPdbAL7cFCfp1CQX7k1zLFLCgb4wxxpNftz67GciumEFfVXNi5DtjjDHGJCdm0BeR5sDvqTwi3+/SlyxjjDFVkTX2y64gxftvAxOB8YD1UTHGGJOUyKJ/uwnInCBBv56q3pj2lBhjjDEmrYIE/XdEZLCqjk17aowxxlQ7lvPPnCBB/xrg/0RkJ7CbvSPyNUxryowxxlRLdhOQPjHH3lfVBqpaoKp1VbWh8zwlAV9EnhWR1SIyy7WsqYiME5EFzv8mznIRkUdFpEREZohI71SkwRhjjKkufHP6IlKkqoujrBegjaomM9H188DjhMb3DxsGfKiqw0VkmPP8RuAUoJPzdwTwlPPfGGNMFWZ9/lMnWk7/fhF5Q0QuEJHuItJCRNqLyHEicicwCTgomYOr6qfA+ojFQ4AXnMcvAGe6lr+oIZOBxiLSOpnjG2OMyV9Fw8b43hAYb745fVU925lS99fA74DWwHZgLjAWuFtVg80fGp+Wqhqee3Il0NJ53AZY6tpumbOswjyVIjIUGArQvn37hBJQVpbjU54ZY4wxCYjakE9V5wA3ZygtXsdXEYkrAqvqCGAEQHFxcULRe0epDUdgjDH5Ilpu36oAKorZkC8LVoWL7Z3/q53ly4F2ru3aOsuMMcYYT1YFUFEuBv3RwIXO4wsJjQgYXn6B04q/L7DJVQ1gjDHGmBiC9NNPGxF5FTgGaCYiy4BbgeHAKBG5GFgC/NLZfCwwGCgh1LbAJgIyxhgTiPUACAkU9EWkDbA/FSfc+TTZg6vqeT6rjvfYVoErkz2mMcYYE1bdbgaCzLJ3H3AOMIe9E+4okHTQN8YYY3KR181AVbgRCJLTPxPooqo705wWY4wxxqRRkKC/CKgJWNA3xhhTbblz//ma6w8S9LcD00XkQ1yBX1WvTluqskyQbCfBGGNMDsvXtgBBgv5o588YY4wxeSxm0FfVF0SkFtDZWfSdqu5Ob7KMMcaY/BMuAcjVHH+Q1vvHEJr4ZjEgQDsRuTAVXfaMMcaYqihXhwYOUrz/IHCSqn4HICKdgVeBw9KZMGOMMcakVpCgXzMc8AFUdb6I1ExjmowxxpgqK7IUIJM5/yBBf6qIPA2MdJ7/GpiaviQZY4wx1UcmuwIGCfqXExr+NtxFbyLwZNpSlAPEeuwZY4ypgoK03t8JPOT8VQuq2U6BMcaY6ijdrf99g76IjFLVX4rITEJj7Vegqj3TkiJjjDGmmovW+t8t3puDaDn9a5z/p8W1xzQTkUHAI0Ah8LSqDs9ykowxxpi84Bv0VXWF8/AKVb3Rvc6Zee/Gyq9KLxEpBJ4ATgSWAVNEZLSqzkntcVK5N2OMMSY1ki32LwiwzYkey05J6qiJ6wOUqOoiVd0FvAYMyVJajDHGmLwSrU7/cuAKoKOIzHCtagBMSnfCfLQBlrqeLwOOyFJajDHGmLwSrU7/FeBd4F5gmGv5FlVdn9ZUJUFEhgJDAdq3b5/l1BhjjDG5I1rxvqrqYkJ99Le4/hCRpulPmqflQDvX87bOsnKqOkJVi1W1uHnz5gkdxLrsGWOMyTWp6MYXK6d/GjCNUJc9d/M2BTomffT4TQE6iUgHQsH+XOBXWUiHMcYYk3d8c/qqeprzv4OqdnT+h/+yEfBR1VLgKuB9YC4wSlVnZyMtxhhjTCYF7bsfTZCpdfsD01V1m4j8BugNPKyqPyR99ASo6lhgbDaObYwxxmRKOkblC9Jl7ylgu4gcAlwHLAReSnlKcsiWnbuznQRjjDEm5YIE/VJVVUL94R9X1ScIddursnaVlmU7CcYYY6qxjI+977JFRG4CzgcGiEgBUDMtqTHGGGOqmXRPp+sWJKd/DrAT+J2qriTUTe7+tKYqy6zLnjHGmKooyNS6K0XkZeBwETkN+EpVX0x/0owxxpj8l8mcfCwxc/oi8kvgK+Bs4JfAlyLyi3QnLJtswh1jjDFVUZA6/ZuBw1V1NYCINAfGA6+nM2HGGGOMSa0gQb8gHPAd6wjWFsAYY4ypFnKpCD+aIEH/PRF5H3jVeX4ONjiOMcYYk3eCNOS7XkTOAo5yFo1Q1bfSmyxjjDHGpFqQnD7A58AeoIzQpDfGGGNy2A2DumQ7CVVGvhTdBxFk7P1LgFuAjwjNtPeYiNyhqs+mO3HGGGNMJlWlAO8lSE7/euBQVV0HICL7Esr5W9A3xpgcJVjfY1NZkKC/Dtjier7FWZYwETkbuA04COijqlNd624CLiZUnXC1qr7vLB8EPAIUAk+r6vBk0mCMMVWZYkOLxlLVc/VeggT9EkID8rwNhCfemSEi1wKo6kMJHHcWcBbwT/dCEekGnAt0B/YDxotIZ2f1E8CJwDJgioiMVtU5CRw7JrHReYwxpkqpjgHeS5Cgv9D5C3vb+Z/wTHuqOhc8g+sQ4DVV3Ql8LyIlQB9nXYmqLnJe95qzbVqCvjHGGFMVBemyd3smEuJoA0x2PV/mLANYGrH8iEwlyhhjTO6z3HxsQbvsxU1ExgOtPFbdrKpveyxP1XGHAkMB2rdvn67DGGOMyQEW6OOTtqCvqick8LLlQDvX87bOMqIsjzzuCGAEQHFxsbVkMcaYKsICfPJybQz90cC5IlJbRDoAnQjN8DcF6CQiHUSkFqHGfqOzmE5jjMlp1mXPePHN6YvIY+Df50NVr070oCLyM+AxoDkwRkSmq+rJqjpbREYRaqBXClypqnuc11wFvE+oy96zqjo70eMbY4zJXZajT59oxfvhvvP9gW7Av53nZ5Nkq3ln7H7P8ftV9W7gbo/lY7GJfowxpsqyYJ9+vkFfVV8AEJHLgaNUtdR5/g9gYmaSZ4wxxphUCdKQrwnQEFjvPK/vLKuyrCbMGJPv6tTMtSZbFVmuPjuCBP3hwDciMoFQPBxIaAjdKsua/Btj8t0+tdPWOSshFuRzQ5DBeZ4TkXfZOxjOjaq6Mr3JMsYYY0yqBS3/2QmsADYAnUVkYPqSZIwxpiqxXH7uiJnTF5FLgGsIDYgzHegLfAEcl9aUZZHV6RtjTOIsyOeuIDn9a4DDgSWqeixwKLAxnYkyxqTfnWcenO0kmDSyzIvxEiTo71DVHQAiUltV5wFd0pssY4zJD/s1qpPtJBgTWJDmnctEpDHwX2CciGwAlqQzUfnmN33bM3LyD0ntY59ahWzbtSdFKcot5x7ejtemLI29YYo1q1+LtVt3Zfy4+aJx3ZrZTkKV8NRvDmPIE5OynYyssaL8/BIzp6+qP1PVjap6G/BX4BngzDSnK6ua1a+d8WPWqVmY8WNmws2DD6Ko2T5ZObZa38uoTuvZOi37LSyoXgXLkqOne/oh+2U7CSYHBWq9LyJHichFqvoJoUZ8bWK9Jp/VqlHA0Z2bB97egou3aX85gd8P7Ji1usWyPP9g2jWtm9b9S5qiVTWL+Tk5sc3i4admJCNhufz8EzPoi8itwI3ATc6imsDIdCYqHzWrXyup1+d3ePIWPqd6tYJdfBqkeDCRsjS/qacc3Cqt+7/jjNQ0tHvlkiN813143dEpOYZbLgTBy44+INtJyJo3rzgy7cdYPPxUC/h5KkhO/2fAGcA2AFX9EWiQzkTlgnhzWZ8POz6p42kWcqVXH3dgSvbT/8B9PZeHT+ncPu2D7SjOWPHIub2irk93Tn/owI5p3X9kMXmiNxnR3oUDmtdPaJ9hAz1KxDo2z051TliDOjUYdkpXurbKzGUqaIFJ031iZwxm3X5yUmk56sBm9G5fpUdJN0kKEvR3aSgiKYCIZPcXnSF/ObVbXNvXqpH6ca6vPzm9nST2a5x88fH1J3ehZYPorZdrFhbw/b2DY+4rnph/+xndOSNGneX++9aLY4+5xx1Mhg7sSPf9Gia0n3Te+3jdrHbfr1H6DpjH/L7fz110ePnj+rVrJJWDfva3h8feKAmWw89/QSLVKBH5J9BYRH4PjAf+lcxBReR+EZknIjNE5C2nd0B43U0iUiIi34nIya7lg5xlJSIyLJnjB1GnZiFz7kjurjuWGimu/PzFYW1jbnPY/t65gLl3DIr7eIUFEjPwholIzGL+Xxa3C3zsIJOJHHVg8HYZ6ZZIwG7ZcO/NVKIBPxuC5nxPTVFDwltOq3iDnunKhaDn67fdsV1apCwt6ch8hFmwrxqCtN5/AHgdeINQ//xbVPWxJI87DjhYVXsC83HaC4hIN+BcoDswCHhSRApFpBB4AjgF6Aac52ybVvVq1eA55865Y5QW6L87qkOg/RVF5DzdxbeHtGtcafs2cebEg1x7hp/VY+/2rhckMiPXwnsG065pPd/iY41YEyvHWTfipuDUHq357ZFFcacrFyXSkrpzy73F00N6tUlbw7tU6tuxaeBtD44oETiwRWJVDakosUrU8LN6xNGGIfc/P1P1BbrSq+o4Vb2e0Ix745M9qKp+oKqlztPJhIb4BRgCvKaqO1X1e6AE6OP8lajqIlXdBbzmbJt2x3ZtweLhp/p2O7v3rB4x60W7tPSuW3Rfw5/4Ve9K64f02i9m4HfXEwaJCelo0Xtc12A5lZqF0RMYuVYEDvAJBEGKrCNvOlLNHYTD9dipLr0J6rMbj/Vc3qlF/bS/D24HNK9f6XO84hjvRnWR6RqcYJuFfgfsS9smlX8nJxzUMu599SkKftMCcOQBzSo8v+b4Ttx2und+JNrv891rBvDG5f3Kn7dqaAP+mPTwDfoi0ldEPhaRN0XkUBGZBcwCVolI/GXB/n4HvOs8bgO4R3FZ5izzW+6V7qEiMlVEpq5ZsyZlifT7vZ4XoJFaOEcfeel1/7C9psEUES6OUYrgvqAGyXHs6/QyuO30bjSqm1yPg7CgudjXLz+Sa47vlJJjKqH3J2q1RAKxLp4SD3d9dvidb+/TjiDITUoyDc/8gkSrRnXSWqcfWRIjUjm4XXtiZ14b2pe/nHoQx0e5QezVvnGlZeGb3hsHdfV9XaO6NfnsxspTgVx7Ymf/hPt46ZI+fHvLSYG3V7TC+bZoWJvf9vf+zUb7dR7UuiGH7R/7hmP6LScGTlsqWdF+1RHtCvc4cA/wKvARcImqtgIGAvfG2rGIjBeRWR5/Q1zb3AyUAi8ndRYuqjpCVYtVtbh58/TW6QYdftPrDv+Rc3vx2tB+lVcEeK2b+4Lu3tavpXC9WqGGQr/t34GTu8efE4pH7RoVSxU6t2zAn07s7NvaP/JkI2NVXY9SisgqgWivD8Lvxun5i7wbSD1/0eGMunTv5zh0QPpa9Ef7LgQt+o8WdOO1ePipHO+Rm458D2sUFtC3475cMqAjjVyjAKqGSkZuPb0bU24+geO67t1X+6ahm6cnf92bly85IqGBhAoSKHWpXaOQRvVq8tLFfSosP7VHsONHu/H2+oj8uqn6fZyN6takt8fNEcDPe8du02NMtKBfwymG/w+wUlUnAzhj78ekqieo6sEef28DiMhvgdOAX+veLNNywN2aq62zzG95xnj9CO921Y9H065JPc7r045/nn9Y+bIhvdrQKsBNgzuoP3reoZXXu0KbO40Tbzg2Zh/sROqI590Zu5DnxG4tef+PAytc4N2e+20fz+WxUhNvcsNfq1j9/z+5/piY+zrG1djqkLaNKizv06EpfTuGbmQiqzoePqcXi+6J3XMBYn8e7oAStY1J/w7c8zPv7+YfT4g/95tOJfcM5qL+HWjewHsUzIZ1a9L/wGae6yI9cPYhcR//30P7epbuDOhUMcNw6xn+TYjcH1vUGzPn87uw3/7lywb73Ez4lc6ICG9e0d9zXes0zQFgufyqJVrQL3M9/iliXVIFhk71wA3AGaq63bVqNHCuiNQWkQ5AJ+ArYArQSUQ6iEgtQo39RieThkwqKIB7z+pJ11aJt8Bu37SeZ72lWzh3f92Jndmndo2k+2B7CdImoE7NQrpEKar2a2Ecubx2xHP39TRIMXz4wlk7xrb777s3gDap5z8e/TMXFvPBnwbuTY/rCn/bGd358LqjaRFRzH7moW1i5jhTPVzqLad34+guoaB1xiH7VegF0KNtI0Zd2o8ZtwUvwo7ljiHdyx8LkpJhaRPZx4kB6vAj28gc0XHfuKs/Fg8/lTcu78dRBzajTeO6gRvyXXNCqGrrpsEHlS/L9baZFvCrnmhXw0NEZLOIbAF6Oo/Dz4Nlcf09TmiAn3EiMl1E/gGgqrOBUcAc4D3gSlXd4zT6uwp4H5gLjHK2zaC9v854huhNlcgc5DHORb1C8X4WWwe7xxRo1TDxuQsWDz+VhfcM5spjD+DW07pXKC0oECkPkAUeV0t38EnUvy/tx3U+dcHHH9SyQot6t5qFBQndZB3SrjGXHe1fJfCLw9qW15uHT3lAp9g53zaN67LonsGcXdyu0g1Ynw5NaVgndZPtXNCvqGLgj/I1dMfXaANSpeub3GSfyucdLqU5s5f/zVfkze5h+zdl5CVHUKOwgH1qB2sce16f9uXD4155bPQRAxO5Gchkg02Tv3yDvqoWqmpDVW2gqjWcx+HnSV0xVPVAVW2nqr2cv8tc6+5W1QNUtYuqvutaPlZVOzvr7k7m+Ilw/wj3dXLUdWr4/9jHXzswbd3NerVrXB58gvzMm9SrydkB+vCPcFU/hB1eFGx0ryuPPZDv7x3MI+f24s8JDioUfo8LC4TrT+5Ko3o1Ob1n6711lTEuhBf0K6rQUPDQ9k24oN/+vPA77+oEL+2a1uP3zkh76ezzHNQDZx/CbWeEAmpzZyKooDedidRpZ1I8OeyGAWYETDTohbv8Hd7BuyHd+GuPpmGdmjz722LGXzuw0vq2TeqVlyD4veORQbxtk/weOMrkr+xf1fLM8LN6cPuQ7tx55sGV+iS/dcWRDOzcnLev7M+BLRpw9fGdaFC7BkMH+t/VP3fR4XwUpe791J6tad6gNue76gFh78Ul1oXz67+eyMQbj+P+sw+JWVR3UvfKXaauPDb4UL0iwpBebSo14PPSs20jfte/A68N7Rtzn+HBV4KEsD+d2Jnv7x3MG5f3Y3CPVtwx5GDPEeKCFFv6HS+R0BItIAUNfmf1bsMTv+rNRf07BAqCyTi4TXxVUUMOacPhRU247JgD6Ngs9dVKfu1DvERrG+FVGhYeP8NvZMnw+AHHdW3JgS28S3qOimh34L5ZvumUroy9ekD0REcIlz64PefRmNRd3WRMEBb0AwpfKhrXq0WDOjU5v+/+lS4uh7Zvwou/61M+0E7TfWox8/aT6eUx8E7YsV1a0NGjWPisQ0M9Els2rMOUm0/ggOb16dmmEWcd2ibUYMk5dKzcTdN9alE/iYlsjunSwrefdTJGX3UUt5zercLFzS/4xZuDExEO279phc9n6l9OYOINFfuyB8nJH9+1he+Y96nIR4vPY89tRTi1Z2sKC4QR5x/Grad3Czyj3YQ/H8P7f/QOEJGNM/t13JezDws+OiJAo3o1+c9lR9KmcV0uPqoDr/zef5KfsGifarirql8Dv1S6ZEBHXrq4Dyd0S7w3S8O6od9YuDdJt9Z7b5ouPfoADmrtfRPl950f/vMe/Dvihthr5L7OLRvw55M6R92XMW6pndbMJOXk7i1ZvHY7Y68Z4Hkxr1FYwEPn9AK8cyy/7V/E1z9s4FdHBJzgJqAbBnXlyY8XpnSfbr8f0IF/Tfzed334YiYiXHnsAUxfuoGBneJrV9GsfuXgMfmm49m+q9Rj672eSdFY5pEX5K6tGjBv5ZaE99eiYR0u6t+BO9+ZE2j7DlFa+4fVqlHA/LtOAeDVr35IOG0FBVJp0Jowdz1+tCB1fr8izu9X5Lu+Wf1arN26K9EkVlBYIJVa68fr2hO70LJhHU7vGWoX0NlpR3Hu4fHdPIXVrlFInw5Nuah/Ec9NWhx123SN1GiN+Komy+nHLX230/88v5j3/zSQwgIJ/EN2Xzib1a/NK7/vy74eAS6X1SiM/jUMn2KBQNdWDZl4w3E0CTBjWSxN96mVlbrVK489gFt8Rm2LV/gGL9WX/V8c1tazsVm8I8VFjq2QzK8n1lwYsXK6g3u0Sltr+bq1CrlkQMfydhRN64W+ny1ilFTEGnvh1tOTb5xqjJsF/YBSdbF47qLDuTdg//5oMtHVJ5561GTEuliHp8jN1NjzNZ2bkKt82jPUctb7JSfW5DjXn9y1QruHcJFwIv2s7zjjYObdOSipRnu1axRwTnE7Xr5kb5F8zcICrj+5K/f9vEfUMQGi+fC6o5noMzwwwBFxjNMPoYGlmtSrWV715cfvc3niV705v+/+3itTbNDBrXj4nF78IUUjUBqTKla8H1B4hLBkh65N1Yxa6Q5/fzyhU+BRyFIlVkzPVFv0wgKJWrT56HmHMnLyEnq08Z5CdszVAygaNqbCsnDxemR3QJHQePWPnncoR3duziG3fxBXWgsKhDoFyc2nICLc94uenuvOObw95xzevvx8fn1Eex4cNz9Qt8FYXRi9GqvF8o0zRG7xXeMA+NcFxYFe16B2DUSEs4vbcXZxO4qGjeH3A6IPcf2vC4pZtGZr3GmE0Ht6Zoybk2SMvXqA76ibxkRjQT+g60/uyhEd9qXfAfFfqNIhHCDLypKrbji/7/68NHlJpeXZGLnNtyFfBhooNW9QmzVbdgbadr/GdbkhyljwXgb3aM1bVxzp26gz6BTF2dbSKY1o4dPSPVl3DunOYx+VBN4+WiPZCiLuGIPUV5/YrSWQ3qGqE9Utj6ZaNrnFgn5AtWoUJNW6N9VSNRDP7Wd056+ndcvqtK0x5xdAA22XjEk3HldejZAuh7YPNuZBPkj0sxjUvRVvT/+xvIokUqwGfGFeH1U9Z5CcSzwmqdqnVm5d6o7t0oJaNQoqdcVNRLg6qWdb75InY9xy65dg4qbA0xcUs2rLjoReX1Ag1IqoD44c/jbbwgGiaN/E6pbdBnRq5hncUz0Qz+uX9WPbrj2+68PTDCfTnTIfhRtOdm6V+r78tWsUVsrB1ygQSsuUlwN0IcykVo3qlPeUiOWkbi0ZFGXa4WO6tGDSsONiTsNtDFjQz1vunFYqSyD+elo3Bgaor82kxvVq8cyFxfSOklP26pLn5aWLM3PxL44xL3uPNo34v8FdOSvfZkbL077g4TY5+WhEgHYLqQ74fu1VTP6zoJ/nUl0ifbFH0SjAb/q2582vMzqxYQVeU7iGTfjzMTTOUE+DVBGRqCM1vnXFkRlMTfxyZYDfXJ+wxphcY0E/TxU6RfKZuujddWYP7joz+a6GXgYf3JqnPl7I8Qcl1rMhyMAz+eKdPxzF5h27E6r/f+rXvcu/F6l2dOfmnF3clu07/ass4pHszWrQl791RX/+N+NHauT4PATGZIoF/Tx1yYCOrN6y0zdnnk96tG1ko385Dk6iWPWUNHaxDE9aNGrK0pTsL1M3qz3aNqKHNXAzplxWWmyJyJ0iMsOZVvcDEdnPWS4i8qiIlDjre7tec6GILHD+LsxGunNJ/do1uOdnPdinmjUEM9k1oHOovcdvMjTIjTEmtbLVTPt+Ve2pqr2Ad4BbnOWnAJ2cv6HAUwAi0hS4FTgC6APcKiJVp/+TMXmidaO6LB5+avmkUtlmhfbGxCcrQV9VN7ue7sPeKrohwIsaMhloLCKtgZOBcaq6XlU3AOOAilODGWOMMSaqrHXIFpG7RWQp8Gv25vTbAO5Kw2XOMr/lxpg8Eu80yX7+dEJoTPsGdfKr14Yx2Za2oC8i40VklsffEABVvVlV2wEvA1el8LhDRWSqiExds2ZNqnZrjEmhZEeUPL9fEYuHn5ryQZWMqerS1gpMVU8IuOnLwFhCdfbLAfcE1G2dZcuBYyKWf+xz3BHACIDi4uI8HUrEGGOMSb1std53zzc5BJjnPB4NXOC04u8LbFLVFcD7wEki0sRpwHeSs8wYY4wxAWWrv9dwEekClAFLgMuc5WOBwUAJsB24CEBV14vIncAUZ7s7VHV9ZpNsjElWJmZMNMb4y0rQV9Wf+yxX4Eqfdc8Cz6YzXcaYzLDhc43JDmsFY+LWtVWDbCfBGGNMAmw4NxO3N684kq07S7OdDGOMMXGyoG/iVq9WDerVsq+OMcbkGyveN8ZkzH7OvO9nHLJfllNiTPVk2TVjTMY0b1Cb7+4aRK1Cy28Ykw0W9I0xGVW7RmG2k2BMtWW328YYY0w1YUHfGGOMqSYs6BtjjDHVhAV9Y4wxppqwoG+MMcZUE6JVeAYMEVlDaEKfRDUD1qYoObmuOp0rVK/ztXOtutJ1vr2Br9OwX5MZ+6tqc68VVTroJ0tEpqpqcbbTkQnV6Vyhep2vnWvVVd3O1yTPiveNMcaYasKCvjHGGFNNWNCPbkS2E5BB1elcoXqdr51r1VXdztckyer0jTHGmGrCcvrGGGNMNWFB34OIDBKR70SkRESGZTs96SAii0VkpohMF5GpzrKmIjJORBY4/5tkO52JEJFnRWS1iMxyLfM8Nwl51PmsZ4hI7+ylPDE+53ubiCx3Pt/pIjLYte4m53y/E5GTs5PqxIhIOxGZICJzRGS2iFzjLK9yn2+Uc62Sn63JDAv6EUSkEHgCOAXoBpwnIt2ym6q0OVZVe7m6/AwDPlTVTsCHzvN89DwwKGKZ37mdAnRy/oYCT2Uojan0PJXPF+DvzufbS1XHAjjf5XOB7s5rnnS+8/miFLhOVbsBfYErnXOqip+v37lC1fxsTQZY0K+sD1CiqotUdRfwGjAky2nKlCHAC87jF4Azs5eUxKnqp8D6iMV+5zYEeFFDJgONRaR1RhKaIj7n62cI8Jqq7lTV74ESQt/5vKCqK1T1a+fxFmAu0IYq+PlGOVc/ef3ZmsywoF9ZG2Cp6/kyov/Q8pUCH4jINBEZ6ixrqaornMcrgZbZSVpa+J1bVf68r3KKtJ91VdVUmfMVkSLgUOBLqvjnG3GuUMU/W5M+FvSrr6NUtTeh4s8rRWSge6WGunVUya4dVfncXJ4CDgB6ASuAB7OamhQTkfrAG8AfVXWze11V+3w9zrVKf7YmvSzoV7YcaOd63tZZVqWo6nLn/2rgLULFgKvCRZ/O/9XZS2HK+Z1blfy8VXWVqu5R1TLgX+wt5s378xWRmoSC4Muq+qazuEp+vl7nWpU/W5N+FvQrmwJ0EpEOIlKLUMOY0VlOU0qJyD4i0iD8GDgJmEXoPC90NrsQeDs7KUwLv3MbDVzgtPLuC2xyFRPnrYh6658R+nwhdL7nikhtEelAqIHbV5lOX6JERIBngLmq+pBrVZX7fP3Otap+tiYzamQ7AblGVUtF5CrgfaAQeFZVZ2c5WanWEngrdE2hBvCKqr4nIlOAUSJyMaHZCX+ZxTQmTEReBY4BmonIMuBWYDje5zYWGEyo0dN24KKMJzhJPud7jIj0IlTMvRi4FEBVZ4vIKGAOodbhV6rqniwkO1H9gfOBmSIy3Vn2f1TNz9fvXM+rop+tyQAbkc8YY4ypJqx43xhjjKkmLOgbY4wx1YQFfWOMMaaasKBvjDHGVBMW9I0xxphqwoK+McYYU01Y0DcmIBHZ1zWd6UrX9KZbReTJNB3zjyJyQZT1p4nIHek4tjGm6rF++sYkQERuA7aq6gNpPEYN4Gugt6qW+mwjzjb9VXV7utJijKkaLKdvTJJE5BgRecd5fJuIvCAiE0VkiYicJSJ/E5GZIvKeM5Y6InKYiHzizHL4vs90r8cBX4cDvohcLSJznNnVXoPyyWU+Bk7LyMkaY/KaBX1jUu8AQgH7DGAkMEFVewA/Aac6gf8x4BeqehjwLHC3x376A9Ncz4cBh6pqT+Ay1/KpwICUn4UxpsqxsfeNSb13VXW3iMwkNH/De87ymUAR0AU4GBjnzH9QSGiK1Eitgbmu5zOAl0Xkv8B/XctXA/ulLvnGmKrKgr4xqbcTQFXLRGS37m04U0boNyfAbFXtF2M/PwF1XM9PBQYCpwM3i0gPp+i/jrOtMcZEZcX7xmTed0BzEekHoTnTRaS7x3ZzgQOdbQqAdqo6AbgRaATUd7brzN7pVY0xxpcFfWMyTFV3Ab8A7hORb4HpwJEem75LKGcPoSqAkU6VwTfAo6q60Vl3LDAmnWk2xlQN1mXPmBwmIm8BN6jqAp/1LYFXVPX4zKbMGJOPLOgbk8NEpAvQUlU/9Vl/OLBbVadnNGHGmLxkQd8YY4ypJqxO3xhjjKkmLOgbY4wx1YQFfWOMMaaasKBvjDHGVBMW9I0xxphq4v8BH7z5CmcTkSgAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 576x216 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np # Loads the numpy package\n",
    "import matplotlib.pyplot as plt # Loads the matplotlib package for plotting\n",
    "from tweezepy import load_trajectory # Loads in the exampled trajectory in tweezepy\n",
    "fsample = 400 # sampling frequency in Hz\n",
    "trace = load_trajectory() # load in trajectory in nm\n",
    "N = len(trace) # number of points in trajectory\n",
    "time = np.arange(N)/fsample # time in s\n",
    "fig,ax = plt.subplots(figsize=(8,3), # Figure size\n",
    "                      ncols=2, # number of columns in figure\n",
    "                      gridspec_kw={'width_ratios':[3,1], # width ratio of columns\n",
    "                                   'wspace':0}) # space between columns\n",
    "ax[0].plot(time, trace) # Plot bead positions as a function of time\n",
    "ax[1].hist(trace, bins=100, orientation = 'horizontal') # Plot histogram of bead positions\n",
    "ax[0].set_xlabel('Time (s)') # Label x axis\n",
    "ax[0].set_ylabel('Bead position (nm)') # Label yaxis\n",
    "ax[1].set_xticks([]) # Remove xticks on histogram axis\n",
    "ax[1].set_yticks([]); # Remove yticks on historgram axis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The plot above shows the bead positions at each time point in the example trajectory and a histogram of the bead positions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Using the power spectral density (PSD) method\n",
    "The power spectral density (PSD) method is used via the `PSD` class. Use Python's built-in help function to see the class's docstring, including all its expected inputs (parameters) and available methods. To do so, type the following:\n",
    "\n",
    "```python\n",
    "help(PSD)\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Estimating the PSD of a trajectory\n",
    "To estimate the PSD of a trajectory, input the trajectory (in nm) and sampling frequency (in Hz) into the `PSD` class. By default, it uses Welch's method, splitting the trajectory into three half-overlapping bins, calculating the PSD values for each bin, and averaging them together to reduce noise. The resulting PSD values are stored in a dictionary that can be directly accessed via the data attribute."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x  :  [7.81250000e-03 1.56250000e-02 2.34375000e-02 ... 1.99976562e+02\n",
      " 1.99984375e+02 1.99992188e+02]\n",
      "shape  :  [3. 3. 3. ... 3. 3. 3.]\n",
      "y  :  [2.36022201e+02 3.37331831e+02 2.30037921e+02 ... 2.84133014e-01\n",
      " 5.72460759e-01 8.58512762e-01]\n",
      "yerr  :  [1.36267481e+02 1.94758624e+02 1.32812456e+02 ... 1.64044272e-01\n",
      " 3.30510373e-01 4.95662574e-01]\n"
     ]
    }
   ],
   "source": [
    "from tweezepy import PSD # Load in PSD class\n",
    "psd = PSD(trace,fsample) # Estimate PSD values\n",
    "for key, value in psd.data.items():\n",
    "    print(key, ' : ', value)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fitting a model to the estimated PSD using maximum likelihood estimation (MLE)\n",
    "\n",
    "To fit a model to the estimated PSD and estimate parameters, use the mlefit method in the `PSD` class. By default, it uses the analytical function from Eq. 7 in Morgan and Saleh (2021) and Lansdorp and Saleh (2012) which assumes zero dead-time and accounts for aliasing and motion blur. As with the data, the resulting parameters and their associated uncertainties are stored in a dictionary, which can be accessed directly through the results attribute."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "chi2  :  208597.91145770502\n",
      "redchi2  :  8.1493109136893\n",
      "g  :  1.0010433861570223e-05\n",
      "g_error  :  5.533212958186353e-08\n",
      "k  :  0.0006333567283668794\n",
      "k_error  :  8.130228755790806e-06\n",
      "support  :  1.0\n",
      "p-value  :  0.0\n",
      "AIC  :  89948.62650857156\n",
      "AICc  :  89948.62697739482\n"
     ]
    }
   ],
   "source": [
    "psd.mlefit() # Perform MLE fit on data\n",
    "for key, value in psd.results.items():\n",
    "    print(key, ' : ', value)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The PSD values and MLE fit can also be plotted via the built-in plotting method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 360x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax = psd.plot(data_label='data',fit_label = 'MLE fit') # Plot PSD values and MLE fit\n",
    "ax[0].legend() # Add legend to upper axis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lastly, when using the `PSD` class there is an optional ``bins`` parameter, which determines the number of half-overlapping bins to use. More bins reduces noise at the cost of low frequency resolution. For example, here is the estimated PSD values using 5, 15, or 25 half-overlapping bins."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "bins = [5,15,25] # number of half-overlapping bins\n",
    "fig = plt.figure() # figure setup\n",
    "for b in bins:\n",
    "    psd = PSD(trace,fsample = fsample,  bins=b) # estimate PSD values\n",
    "    fig, ax = psd.plot(fig=fig,data_label=b) # plot PSD values\n",
    "ax[0].legend(title = '# of bins') # add legend to axis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Using the Allan variance (AV) method\n",
    "The Allan Variance (AV) method is used via the `AV` class. You can use the built-in help() function to print the class's docstring, which includes a description of all its inputs (parameters) and methods. To do so, type the following:\n",
    "\n",
    "```python\n",
    "help(AV)\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Estimating the AV of a trajectory\n",
    "To estimate AV values, input the trajectory (in nm) and sampling frequency (in Hz) into the `AV` class. The estimated AV values are stored in a dictionary that can be accessed via the data attribute. By default, the `AV` class uses the overlapping AV, octave spaced samples, and calculates the type of noise and equivalent degrees of freedom. Because the AV method uses logarithmically spaced bins, there is no optional bins parameter, somewhat simplifying its use for force calibration. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-10-27T18:22:17.252054Z",
     "start_time": "2021-10-27T18:22:17.183240Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x  :  [2.500e-03 5.000e-03 1.000e-02 2.000e-02 4.000e-02 8.000e-02 1.600e-01\n",
      " 3.200e-01 6.400e-01 1.280e+00 2.560e+00 5.120e+00 1.024e+01 2.048e+01\n",
      " 4.096e+01]\n",
      "shape  :  [3.90583820e+04 2.19038208e+04 1.12664407e+04 5.67381938e+03\n",
      " 2.14800855e+03 1.06986415e+03 5.32777801e+02 2.66111158e+02\n",
      " 1.32777871e+02 6.61112985e+01 3.27781570e+01 1.61118881e+01\n",
      " 7.77941176e+00 3.78125000e+00 1.78571429e+00]\n",
      "y  :  [ 607.28884303 1081.44344278 1725.8873072  2295.80653154 2362.37579231\n",
      " 1791.55502062 1134.34404209  657.39308939  354.5921528   158.06307178\n",
      "   62.49896924   29.20585681   15.19484232   10.18525082    5.95160116]\n",
      "yerr  :  [ 3.07282748  7.30708017 16.25994484 30.47877682 50.97191858 54.77291233\n",
      " 49.14413936 40.29893717 30.77274727 19.43983499 10.91642887  7.27606773\n",
      "  5.44782086  5.23786176  4.45377049]\n"
     ]
    }
   ],
   "source": [
    "from tweezepy import AV # Load in AV class\n",
    "av = AV(trace,fsample) # Estimate AV values\n",
    "for key, value in av.data.items():\n",
    "    print(key, ' : ', value)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fitting a model to the estimated AV using maximum likelihood estimation (MLE)\n",
    "To fit a model to the estimated AV values, use the mlefit method of the `AV` class. By default, it performs MLE using the analytical function from Eq. 9 in Morgan and Saleh (2021) or Eq. 17 in Lansdorp and Saleh (2012). After fitting, the parameters and their associated uncertainties can be accessed directly from the results attribute. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "chi2  :  14.346818631382492\n",
      "redchi2  :  1.1036014331832686\n",
      "g  :  1.0041155314204818e-05\n",
      "g_error  :  6.688028898070111e-08\n",
      "k  :  0.0006360035178028457\n",
      "k_error  :  7.325143945228793e-06\n",
      "support  :  0.999911671324171\n",
      "p-value  :  3.1085352224861228e-61\n",
      "AIC  :  126.52377592444978\n",
      "AICc  :  127.52377592444978\n"
     ]
    }
   ],
   "source": [
    "av.mlefit() # Perform MLE fit on AV data\n",
    "for key, value in av.results.items():\n",
    "    print(key, ' : ', value)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also plot the AV values and MLE fit using the built-in plotting method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 360x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax = av.plot(data_label='data',fit_label = 'MLE fit')  # Plot AV values and MLE fit\n",
    "ax[0].legend() # Add legend to upper axis\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, the `AV` class has a few extra optional parameters. These should not be used for MLE fitting or calibration, but they may be useful in visualizing some types of parasitic noise. For example, in addition to octave sampling, the AV values can be estimated and plotted for all observation times and decade spaced observation times. Note that calculating AV values for all observation times can be slow."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x231f1ddd820>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
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    {
     "data": {
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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "for taus in ['octave','decade']:\n",
    "    av = AV(trace,fsample=fsample,taus=taus)\n",
    "    fig,ax = av.plot(fig=fig,data_label=taus)\n",
    "ax[0].legend(title='taus')\n",
    "fig = plt.figure()\n",
    "av = AV(trace,fsample=fsample,taus='all')\n",
    "fig,ax = av.plot(fig=fig, data_label = 'all')\n",
    "ax[0].legend(title='taus')"
   ]
  }
 ],
 "metadata": {
  "interpreter": {
   "hash": "f94fc5ffea663767ae62903b10257b44f00e90761e17ce479a3f3bec4d89dc46"
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  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.3"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": false
  },
  "varInspector": {
   "cols": {
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   "kernels_config": {
    "python": {
     "delete_cmd_postfix": "",
     "delete_cmd_prefix": "del ",
     "library": "var_list.py",
     "varRefreshCmd": "print(var_dic_list())"
    },
    "r": {
     "delete_cmd_postfix": ") ",
     "delete_cmd_prefix": "rm(",
     "library": "var_list.r",
     "varRefreshCmd": "cat(var_dic_list()) "
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   },
   "types_to_exclude": [
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    "_Feature"
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