FL006_hidden_Markov_models.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# `FL006_hidden_Markov_models` (Frank lab data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Etienne Ackermann, Sat Dec 02 2017 22:56:52 \n",
      "\n",
      "CPython 3.5.4\n",
      "IPython 6.1.0\n",
      "\n",
      "nelpy 0.1.1\n",
      "numpy 1.11.3\n",
      "scipy 0.19.0\n",
      "pandas 0.21.0\n"
     ]
    }
   ],
   "source": [
    "%load_ext watermark\n",
    "%watermark -a \"Etienne Ackermann,\" -n -t -v -p nelpy,numpy,scipy,pandas"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Overview"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see (qualitatively) more remote replay events when we use the idealized position. In some sense, the idealized position is \"more true\" than the actual position, since the rat ultimately did find himself on a particular segment of the track, even when the LED was closer to a different segment. Moreover, the idealized position has more robust firing rate estimation, since the binning leads to more observations per location.\n",
    "\n",
    "It would be awesome if the HMM, which is agnostic to the actual-vs-idealized position considerations, could identify those remote replays that are remote replays in the idealized case, but not in the raw 2D position case. This remains to be seen however, and will take some time to check and quantify comprehensively, so definitely beyond the scope of Asilomar.\n",
    "\n",
    "**Update:** significance was never determined in 2D :/ so it's unclear whether those events that I'm talking about would be significant or not in 1D. Also, there's a decoding ambiguity in the linearized case, so the 2D approach is more principled imo anyway.\n",
    "\n",
    "At any rate, for VTC (LSPF) visualization, it might make sense to use a 20 x 20 grid, or so, and to learn it on the idealized position. This way we will have nice, clean, 2D bins.\n",
    "\n",
    "Using a 50 state model or so is probably better, but 30 states is much faster to train, and since I'm in a time crunch, that is what I'll do initially."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "import warnings\n",
    "\n",
    "import nelpy as nel\n",
    "import nelpy.io\n",
    "import nelpy.plotting as npl\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "warnings.filterwarnings(\"ignore\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Load semi-processed Frank Lab data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "fileroot = '../../../../neoReader/' \n",
    "infile = 'FrankLabData-BonConFra-no-eeg05b.nel' # saved with Pandas=0.21\n",
    "outfile = 'FrankLabData-BonConFra-no-eeg06d.nel' # saved with Pandas=0.21\n",
    "FrankLabData = nel.load_pkl(fileroot + infile) \n",
    "data = FrankLabData.data\n",
    "sessions = FrankLabData.sessions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Train HMM on example Bon Day3 session for initial exploration"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since our goal here is to learn an HMM of E1 run, and then to test E2 SWR sequences, we don't strictly speaking need to use cross validation here. Later on, it might still be good to though."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import nelpy.hmmutils\n",
    "import nelpy.analysis\n",
    "\n",
    "num_states = 30\n",
    "ds_HMM = 0.125 # 500 ms? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "animal, day = 'Bon', 'Day3'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "training HMM...\n",
      "Done!\n"
     ]
    }
   ],
   "source": [
    "run_epochs = data[animal][day]['run_epochs']\n",
    "ripple_epochs = data[animal][day]['ripple_epochs']\n",
    "\n",
    "with warnings.catch_warnings():\n",
    "    warnings.simplefilter(\"ignore\")\n",
    "    st = data[animal][day]['spikes'][[1,3],:] # combine E1a and E1b\n",
    "\n",
    "if st.isempty: # this is true for Fra Day3 epoch 0\n",
    "    pass\n",
    "else:\n",
    "    # get spiketrain during run bouts for epoch\n",
    "    with warnings.catch_warnings():\n",
    "        warnings.simplefilter(\"ignore\")\n",
    "        st_run_no_ripples = st[run_epochs][~ripple_epochs]\n",
    "    bst_training = st_run_no_ripples.bin(ds=ds_HMM)\n",
    "    # train HMM on E1 combined run data [excluding ripples]\n",
    "    hmm = nel.hmmutils.PoissonHMM(n_components=num_states, verbose=False, n_iter=50)\n",
    "    print('training HMM...')\n",
    "    hmm.fit(bst_training)\n",
    "    print('Done!')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "time swap shuffle...\n"
     ]
    },
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-24-45348f3decf4>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      5\u001b[0m \u001b[1;31m# log prob under HMM with time swap\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      6\u001b[0m \u001b[0mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m'time swap shuffle...'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 7\u001b[1;33m \u001b[0mscores_logprob\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mscores_tswap_hmm\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnel\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0manalysis\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mreplay\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mscore_hmm_timeswap_shuffle\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mbst\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mbst\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mhmm\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mhmm\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mn_shuffles\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mn_shuffles\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      8\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      9\u001b[0m \u001b[1;31m# log prob under HMM with transmat shuffle\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32md:\\dropbox\\code\\nelpy\\nelpy\\analysis\\replay.py\u001b[0m in \u001b[0;36mscore_hmm_timeswap_shuffle\u001b[1;34m(bst, hmm, n_shuffles, normalize)\u001b[0m\n\u001b[0;32m    965\u001b[0m         shuffled[ii,:] = score_hmm_logprob(bst=bst_shuffled,\n\u001b[0;32m    966\u001b[0m                                            \u001b[0mhmm\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mhmm\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 967\u001b[1;33m                                            normalize=normalize)\n\u001b[0m\u001b[0;32m    968\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    969\u001b[0m     \u001b[1;32mreturn\u001b[0m \u001b[0mscores\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mshuffled\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32md:\\dropbox\\code\\nelpy\\nelpy\\analysis\\replay.py\u001b[0m in \u001b[0;36mscore_hmm_logprob\u001b[1;34m(bst, hmm, normalize)\u001b[0m\n\u001b[0;32m    885\u001b[0m     \"\"\"\n\u001b[0;32m    886\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 887\u001b[1;33m     \u001b[0mlogprob\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0matleast_1d\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mhmm\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mscore\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mbst\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    888\u001b[0m     \u001b[1;32mif\u001b[0m \u001b[0mnormalize\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    889\u001b[0m         \u001b[0mlogprob\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0matleast_1d\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mlogprob\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m/\u001b[0m \u001b[0mbst\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mlengths\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32md:\\dropbox\\code\\nelpy\\nelpy\\hmmutils.py\u001b[0m in \u001b[0;36mscore\u001b[1;34m(self, X, lengths, w)\u001b[0m\n\u001b[0;32m    696\u001b[0m             \u001b[1;31m# we have a BinnedSpikeTrainArray\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    697\u001b[0m             \u001b[0mlogprobs\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m[\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 698\u001b[1;33m             \u001b[1;32mfor\u001b[0m \u001b[0mseq\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mX\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    699\u001b[0m                 \u001b[0mwindowed_arr\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mlengths\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_sliding_window_array\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mbst\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mseq\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mw\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mw\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    700\u001b[0m                 \u001b[0mlogprob\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_score\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mX\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mwindowed_arr\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mlengths\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mlengths\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32md:\\dropbox\\code\\nelpy\\nelpy\\core\\_spiketrain.py\u001b[0m in \u001b[0;36m__next__\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m   1242\u001b[0m             \u001b[1;32mfor\u001b[0m \u001b[0mattr\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mattrs\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1243\u001b[0m                 \u001b[0mexec\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"binnedspiketrain.\"\u001b[0m \u001b[1;33m+\u001b[0m \u001b[0mattr\u001b[0m \u001b[1;33m+\u001b[0m \u001b[1;34m\" = self.\"\u001b[0m \u001b[1;33m+\u001b[0m \u001b[0mattr\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1244\u001b[1;33m             \u001b[0mbinindices\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0minsert\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcumsum\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mlengths\u001b[0m \u001b[1;33m+\u001b[0m \u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;31m# indices of bins\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   1245\u001b[0m             \u001b[0mbinstart\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mbinindices\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mindex\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1246\u001b[0m             \u001b[0mbinstop\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mbinindices\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mindex\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\Anaconda3\\lib\\site-packages\\numpy\\lib\\function_base.py\u001b[0m in \u001b[0;36minsert\u001b[1;34m(arr, obj, values, axis)\u001b[0m\n\u001b[0;32m   4906\u001b[0m         \u001b[0mnew\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mempty\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnewshape\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0marr\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdtype\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0marrorder\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   4907\u001b[0m         \u001b[0mslobj\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0maxis\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mslice\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;32mNone\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mindex\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 4908\u001b[1;33m         \u001b[0mnew\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mslobj\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0marr\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mslobj\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   4909\u001b[0m         \u001b[0mslobj\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0maxis\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mslice\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mindex\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mindex\u001b[0m\u001b[1;33m+\u001b[0m\u001b[0mnumnew\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   4910\u001b[0m         \u001b[0mnew\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mslobj\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mvalues\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "n_shuffles = 100\n",
    "# now let's score some events:\n",
    "bst = data[animal][day]['remote_replay_E1_in_E2']['bst_remote_candidates']\n",
    "\n",
    "# log prob under HMM with time swap\n",
    "print('time swap shuffle...')\n",
    "scores_logprob, scores_tswap_hmm = nel.analysis.replay.score_hmm_timeswap_shuffle(bst=bst, hmm=hmm, n_shuffles=n_shuffles)\n",
    "\n",
    "# log prob under HMM with transmat shuffle\n",
    "print('transition matrix shuffle...')\n",
    "scores_logprob, scores_tmat_shuffled = nel.analysis.replay.score_hmm_transmat_shuffle(bst=bst, hmm=hmm, n_shuffles=n_shuffles)\n",
    "\n",
    "print('Done!')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "scores = data[animal][day]['remote_replay_E1_in_E2']['logprobs']\n",
    "tswap = data[animal][day]['remote_replay_E1_in_E2']['scores_tswap_hmm']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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    {
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tVNV24Glgaa8xS4EnPMvPAYtFRFR1s6qeaRhSCkSLSNRwFG7690FlLafaOlky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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d5620e4e48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "evt_idx = 16\n",
    "sns.distplot(tswap[:,evt_idx], hist=False)\n",
    "plt.vlines(scores[evt_idx], 0,1)\n",
    "plt.title(evt_idx)\n",
    "npl.savefig('hmm-tswap-{}'.format(evt_idx))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Augment data dict with HMMs, and with scoring results [first remote, then local]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Bon Day2\n",
      "training HMM...\n",
      "time swap shuffle...\n",
      "transition matrix shuffle...\n",
      "Bon Day3\n",
      "training HMM...\n",
      "time swap shuffle...\n",
      "transition matrix shuffle...\n",
      "Bon Day4\n",
      "training HMM...\n",
      "time swap shuffle...\n",
      "transition matrix shuffle...\n",
      "Bon Day5\n",
      "training HMM...\n",
      "time swap shuffle...\n",
      "transition matrix shuffle...\n",
      "Bon Day6\n",
      "training HMM...\n",
      "time swap shuffle...\n",
      "transition matrix shuffle...\n",
      "Bon Day7\n",
      "training HMM...\n",
      "time swap shuffle...\n",
      "transition matrix shuffle...\n",
      "Bon Day8\n",
      "training HMM...\n",
      "time swap shuffle...\n",
      "transition matrix shuffle...\n",
      "Bon Day9\n",
      "training HMM...\n",
      "time swap shuffle...\n",
      "transition matrix shuffle...\n",
      "Con Day0\n",
      "The (animal, day) pair does not have remote replay analysis results; skipping...\n",
      "Con Day1\n",
      "The (animal, day) pair does not have remote replay analysis results; skipping...\n",
      "Con Day2\n",
      "The (animal, day) pair does not have remote replay analysis results; skipping...\n",
      "Con Day3\n",
      "training HMM...\n",
      "time swap shuffle...\n",
      "transition matrix shuffle...\n",
      "Con Day4\n",
      "training HMM...\n",
      "time swap shuffle...\n",
      "transition matrix shuffle...\n",
      "Con Day5\n",
      "training HMM...\n",
      "time swap shuffle...\n",
      "transition matrix shuffle...\n",
      "Fra Day1\n",
      "training HMM...\n",
      "time swap shuffle...\n",
      "transition matrix shuffle...\n",
      "Fra Day2\n",
      "The (animal, day) pair does not have remote replay analysis results; skipping...\n",
      "Fra Day3\n",
      "The (animal, day) pair does not have remote replay analysis results; skipping...\n",
      "Fra Day4\n",
      "The (animal, day) pair does not have remote replay analysis results; skipping...\n",
      "Fra Day5\n",
      "training HMM...\n",
      "time swap shuffle...\n",
      "transition matrix shuffle...\n",
      "Fra Day6\n",
      "The (animal, day) pair does not have remote replay analysis results; skipping...\n",
      "Fra Day7\n",
      "training HMM...\n",
      "time swap shuffle...\n",
      "transition matrix shuffle...\n",
      "Fra Day8\n",
      "training HMM...\n",
      "time swap shuffle...\n",
      "transition matrix shuffle...\n",
      "Fra Day9\n",
      "training HMM...\n",
      "time swap shuffle...\n",
      "transition matrix shuffle...\n",
      "Fra Day10\n",
      "training HMM...\n",
      "time swap shuffle...\n",
      "transition matrix shuffle...\n",
      "Fra Day11\n",
      "training HMM...\n",
      "time swap shuffle...\n",
      "transition matrix shuffle...\n"
     ]
    }
   ],
   "source": [
    "n_shuffles = 10000\n",
    "\n",
    "for animal, day in sessions:\n",
    "    print(animal, day)\n",
    "    \n",
    "    try:\n",
    "        bst = data[animal][day]['remote_replay_E1_in_E2']['bst_remote_candidates']\n",
    "    except KeyError:\n",
    "        print('The (animal, day) pair does not have remote replay analysis results; skipping...')\n",
    "        continue\n",
    "        \n",
    "    run_epochs = data[animal][day]['run_epochs']\n",
    "    ripple_epochs = data[animal][day]['ripple_epochs']\n",
    "    \n",
    "    with warnings.catch_warnings():\n",
    "        warnings.simplefilter(\"ignore\")\n",
    "        st = data[animal][day]['spikes'][[1,3],:] # combine E1a and E1b\n",
    "\n",
    "    if st.isempty: # this is true for Fra Day3 epoch 0\n",
    "        pass\n",
    "    else:\n",
    "        # get spiketrain during run bouts for epoch\n",
    "        with warnings.catch_warnings():\n",
    "            warnings.simplefilter(\"ignore\")\n",
    "            st_run_no_ripples = st[run_epochs][~ripple_epochs]\n",
    "\n",
    "        # train HMM on E1 combined run data [excluding ripples]\n",
    "        bst_training = st_run_no_ripples.bin(ds=ds_HMM)\n",
    "        # train HMM on E1 combined run data [excluding ripples]\n",
    "        hmm = nel.hmmutils.PoissonHMM(n_components=num_states, verbose=False, n_iter=50)\n",
    "        print('training HMM...')\n",
    "        hmm.fit(bst_training)\n",
    "        data[animal][day]['HMM_E1'] = hmm\n",
    "        \n",
    "        # score events\n",
    "        bst = data[animal][day]['remote_replay_E1_in_E2']['bst_remote_candidates']\n",
    "        \n",
    "        print('time swap shuffle...')\n",
    "        scores_logprob, scores_tswap_hmm = nel.analysis.replay.score_hmm_timeswap_shuffle(bst=bst, hmm=hmm, n_shuffles=n_shuffles)\n",
    "\n",
    "        # log prob under HMM with transmat shuffle\n",
    "        print('transition matrix shuffle...')\n",
    "        scores_logprob, scores_tmat_shuffled = nel.analysis.replay.score_hmm_transmat_shuffle(bst=bst, hmm=hmm, n_shuffles=n_shuffles)\n",
    "        \n",
    "        data[animal][day]['remote_replay_E1_in_E2']['logprobs'] = scores_logprob\n",
    "        data[animal][day]['remote_replay_E1_in_E2']['scores_tswap_hmm'] = scores_tswap_hmm\n",
    "        data[animal][day]['remote_replay_E1_in_E2']['scores_tmat_shuffled'] = scores_tmat_shuffled\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Bon Day2\n",
      "training HMM...\n",
      "time swap shuffle...\n",
      "transition matrix shuffle...\n"
     ]
    }
   ],
   "source": [
    "n_shuffles = 10000\n",
    "\n",
    "for animal, day in sessions:\n",
    "    print(animal, day)\n",
    "    \n",
    "    try:\n",
    "        bst = data[animal][day]['remote_replay_E1_in_E2']['bst_local_candidates']\n",
    "    except KeyError:\n",
    "        print('The (animal, day) pair does not have remote replay analysis results; skipping...')\n",
    "        continue\n",
    "        \n",
    "    run_epochs = data[animal][day]['run_epochs']\n",
    "    ripple_epochs = data[animal][day]['ripple_epochs']\n",
    "    \n",
    "    with warnings.catch_warnings():\n",
    "        warnings.simplefilter(\"ignore\")\n",
    "        st = data[animal][day]['spikes'][[5],:] # use E2\n",
    "\n",
    "    if st.isempty: # this is true for Fra Day3 epoch 0\n",
    "        pass\n",
    "    else:\n",
    "        # get spiketrain during run bouts for epoch\n",
    "        with warnings.catch_warnings():\n",
    "            warnings.simplefilter(\"ignore\")\n",
    "            st_run_no_ripples = st[run_epochs][~ripple_epochs]\n",
    "\n",
    "        # train HMM on E2 run data [excluding ripples]\n",
    "        bst_training = st_run_no_ripples.bin(ds=ds_HMM)\n",
    "        # train HMM on E1 combined run data [excluding ripples]\n",
    "        hmm = nel.hmmutils.PoissonHMM(n_components=num_states, verbose=False, n_iter=50)\n",
    "        print('training HMM...')\n",
    "        hmm.fit(bst_training)\n",
    "        data[animal][day]['HMM_E2'] = hmm\n",
    "        \n",
    "        # score events\n",
    "        bst = data[animal][day]['remote_replay_E1_in_E2']['bst_local_candidates']\n",
    "        \n",
    "        print('time swap shuffle...')\n",
    "        scores_logprob, scores_tswap_hmm = nel.analysis.replay.score_hmm_timeswap_shuffle(bst=bst, hmm=hmm, n_shuffles=n_shuffles)\n",
    "\n",
    "        # log prob under HMM with transmat shuffle\n",
    "        print('transition matrix shuffle...')\n",
    "        scores_logprob, scores_tmat_shuffled = nel.analysis.replay.score_hmm_transmat_shuffle(bst=bst, hmm=hmm, n_shuffles=n_shuffles)\n",
    "        \n",
    "        data[animal][day]['remote_replay_E1_in_E2']['logprobs_local'] = scores_logprob\n",
    "        data[animal][day]['remote_replay_E1_in_E2']['scores_tswap_hmm_local'] = scores_tswap_hmm\n",
    "        data[animal][day]['remote_replay_E1_in_E2']['scores_tmat_shuffled_local'] = scores_tmat_shuffled\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Augment data dict with VTCs/LSPFs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "ds_HMM = 0.125\n",
    "ds_25ms = 0.025"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def sub2ind(array_shape, rows, cols):\n",
    "    return rows*array_shape[1] + cols"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def append_ASAs(a, b):\n",
    "    \"\"\"Very dumb append; does not check for overlaps or anything... use at your own risk!\"\"\"\n",
    "    c = nel.AnalogSignalArray(empty=True)\n",
    "    c._ydata = np.hstack((a.ydata, b.ydata))\n",
    "    c._fs = a.fs\n",
    "    c._time = np.hstack((a.time, b.time))\n",
    "    c._support = a.support + b.support\n",
    "    \n",
    "    return c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def get_vtc2d(hmm, bst, pos, nx=20, ny=20):\n",
    "    \n",
    "    num_states = hmm.n_components\n",
    "    xpos, ypos = pos.asarray(at=bst.centers).yvals\n",
    "    \n",
    "    ext_xmin, ext_xmax = np.floor(pos[:,0].min()/10)*10-1, np.ceil(pos[:,0].max()/10)*10+1\n",
    "    ext_ymin, ext_ymax = np.floor(pos[:,1].min()/10)*10-1, np.ceil(pos[:,1].max()/10)*10+1\n",
    "    \n",
    "    xx_left = np.linspace(ext_xmin, ext_xmax, nx+1)\n",
    "    xx_mid = np.linspace(ext_xmin, ext_xmax, nx+1)[:-1]; xx_mid += (xx_mid[1]-xx_mid[0])/2\n",
    "    yy_left = np.linspace(ext_ymin, ext_ymax, ny+1)\n",
    "    yy_mid = np.linspace(ext_ymin, ext_ymax, ny+1)[:-1]; yy_mid += (yy_mid[1]-yy_mid[0])/2\n",
    "\n",
    "    ext_y = np.digitize(ypos, yy_left) - 1 # spatial bin numbers\n",
    "    ext_x = np.digitize(xpos, xx_left) - 1\n",
    "\n",
    "    t = np.zeros(len(xpos), dtype=np.float)\n",
    "\n",
    "    for ii, (x, y) in enumerate(zip(ext_x, ext_y)):\n",
    "        t[ii] = sub2ind((nx, ny), x, y)\n",
    "\n",
    "    t[t==0] = np.nan\n",
    "    t[t>=nx*ny] = np.nan\n",
    "\n",
    "    extern = hmm.fit_ext(X=bst, ext=t, n_extern=nx*ny)\n",
    "    # transform into ratemap shape\n",
    "    tmp = np.reshape(extern, (num_states, nx, ny))\n",
    "    vtc_ratemap = np.transpose(tmp, (0,2,1)) # for images, we have (y,x) <==> (r,c) coordinates\n",
    "\n",
    "    vtc2d = nel.TuningCurve2D(ratemap=vtc_ratemap, min_duration=0, ext_xmin=ext_xmin, ext_xmax=ext_xmax, ext_ymin=ext_ymin, ext_ymax=ext_ymax)\n",
    "#     vtc2d = vtc2d.smooth(sigma=sigma_tc)\n",
    "    vtc2d._initialize_mask_from_extern(pos)\n",
    "    \n",
    "    return vtc2d    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "sigma_spk = 0.3 # 300 ms spike smoothing\n",
    "\n",
    "for animal, day in sessions:\n",
    "    print(animal, day)\n",
    "    \n",
    "    try:\n",
    "        hmmE1 = data[animal][day]['HMM_E1']\n",
    "        hmmE2 = data[animal][day]['HMM_E2']\n",
    "    except KeyError:\n",
    "        print('The (animal, day) pair does not have an HMM; skipping...')\n",
    "        continue\n",
    "        \n",
    "    run_epochs = data[animal][day]['run_epochs']\n",
    "    ripple_epochs = data[animal][day]['ripple_epochs']\n",
    "    \n",
    "    with warnings.catch_warnings():\n",
    "        warnings.simplefilter(\"ignore\")\n",
    "        st = data[animal][day]['spikes'][[1,3],:] # use E1 and E3 combined\n",
    "\n",
    "    if st.isempty: # this is true for Fra Day3 epoch 0\n",
    "        pass\n",
    "    else:\n",
    "        # get spiketrain during run bouts for epoch\n",
    "        with warnings.catch_warnings():\n",
    "            warnings.simplefilter(\"ignore\")\n",
    "            st_run_no_ripples = st[run_epochs][~ripple_epochs]\n",
    "            \n",
    "        # smooth and re-bin:\n",
    "        bst = st_run_no_ripples.bin(ds=ds_25ms).smooth(sigma=sigma_spk, inplace=True).rebin(w=ds_HMM/ds_25ms)\n",
    "\n",
    "        # we use the idealized position (2D) to learn the place fields...\n",
    "        pos = append_ASAs(data[animal][day]['pos_ideal'][1], data[animal][day]['pos_ideal'][3])\n",
    "        \n",
    "        vtc2d = get_vtc2d(hmm=hmmE1, bst=bst, pos=pos)     \n",
    "        data[animal][day]['VTC_E1'] = vtc2d\n",
    "        \n",
    "    with warnings.catch_warnings():\n",
    "        warnings.simplefilter(\"ignore\")\n",
    "        st = data[animal][day]['spikes'][[5],:] # use E2\n",
    "\n",
    "    if st.isempty: # this is true for Fra Day3 epoch 0\n",
    "        pass\n",
    "    else:\n",
    "        # get spiketrain during run bouts for epoch\n",
    "        with warnings.catch_warnings():\n",
    "            warnings.simplefilter(\"ignore\")\n",
    "            st_run_no_ripples = st[run_epochs][~ripple_epochs]\n",
    "            \n",
    "        # smooth and re-bin:\n",
    "        bst = st_run_no_ripples.bin(ds=ds_25ms).smooth(sigma=sigma_spk, inplace=True).rebin(w=ds_HMM/ds_25ms)\n",
    "\n",
    "        # we use the idealized position (2D) to learn the place fields...\n",
    "        pos = data[animal][day]['pos_ideal'][5]\n",
    "        \n",
    "        vtc2d = get_vtc2d(hmm=hmmE2, bst=bst, pos=pos)     \n",
    "        data[animal][day]['VTC_E2'] = vtc2d"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Augment data dict with HMM event p-vals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Bon Day2\n",
      "Bon Day3\n",
      "Bon Day4\n",
      "Bon Day5\n",
      "Bon Day6\n",
      "Bon Day7\n",
      "Bon Day8\n",
      "Bon Day9\n",
      "Con Day0\n",
      "The (animal, day) pair does not have remote replay analysis results; skipping...\n",
      "Con Day1\n",
      "The (animal, day) pair does not have remote replay analysis results; skipping...\n",
      "Con Day2\n",
      "The (animal, day) pair does not have remote replay analysis results; skipping...\n",
      "Con Day3\n",
      "Con Day4\n",
      "Con Day5\n",
      "Fra Day1\n",
      "Fra Day2\n",
      "The (animal, day) pair does not have remote replay analysis results; skipping...\n",
      "Fra Day3\n",
      "The (animal, day) pair does not have remote replay analysis results; skipping...\n",
      "Fra Day4\n",
      "The (animal, day) pair does not have remote replay analysis results; skipping...\n",
      "Fra Day5\n",
      "Fra Day6\n",
      "The (animal, day) pair does not have remote replay analysis results; skipping...\n",
      "Fra Day7\n",
      "Fra Day8\n",
      "Fra Day9\n",
      "Fra Day10\n",
      "Fra Day11\n"
     ]
    }
   ],
   "source": [
    "from scipy import stats\n",
    "\n",
    "for animal, day in sessions:\n",
    "    print(animal, day)\n",
    "    \n",
    "    try:\n",
    "        bst = data[animal][day]['remote_replay_E1_in_E2']['bst_local_candidates']\n",
    "    except KeyError:\n",
    "        print('The (animal, day) pair does not have remote replay analysis results; skipping...')\n",
    "        continue\n",
    "        \n",
    "    scores = data[animal][day]['remote_replay_E1_in_E2']['logprobs']\n",
    "    shuffle_dists = data[animal][day]['remote_replay_E1_in_E2']['scores_tswap_hmm'].T\n",
    "        \n",
    "    pvals = []\n",
    "    for score, shuffle_dist in zip(scores, shuffle_dists):\n",
    "        pval = (100 - stats.percentileofscore(shuffle_dist, score)) / 100\n",
    "        pvals.append(pval)\n",
    "    \n",
    "    data[animal][day]['remote_replay_E1_in_E2']['pvals_remote_hmm'] = np.array(pvals)\n",
    "    \n",
    "    try:\n",
    "        scores = data[animal][day]['remote_replay_E1_in_E2']['logprobs_local']\n",
    "        shuffle_dists = data[animal][day]['remote_replay_E1_in_E2']['scores_tswap_hmm_local'].T\n",
    "\n",
    "        pvals = []\n",
    "        for score, shuffle_dist in zip(scores, shuffle_dists):\n",
    "            pval = (100 - stats.percentileofscore(shuffle_dist, score)) / 100\n",
    "            pvals.append(pval)\n",
    "\n",
    "        data[animal][day]['remote_replay_E1_in_E2']['pvals_local_hmm'] = np.array(pvals)\n",
    "    except:\n",
    "        pass\n",
    "    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "270 of 623 (43.3%) candidate replay events showed statistically significant replay (P < 0.05) of environment 1 when rats were located in environment 2.\n",
      "\n",
      "As expected, there were also many replays of environment 2; 101 of 424 (23.8%) candidate events were significant.\n"
     ]
    }
   ],
   "source": [
    "n_sig_local = 0\n",
    "n_tot_local = 0\n",
    "\n",
    "n_sig_remote = 0\n",
    "n_tot_remote = 0\n",
    "\n",
    "for animal, day in sessions:\n",
    "    try:\n",
    "        # local\n",
    "        x = data[animal][day]['remote_replay_E1_in_E2']['pvals_local_candidates']\n",
    "        n_sig_local += np.count_nonzero(x<0.05)\n",
    "        n_tot_local += len(x)\n",
    "        # remote\n",
    "        x = data[animal][day]['remote_replay_E1_in_E2']['pvals_remote_candidates']\n",
    "        n_sig_remote += np.count_nonzero(x<0.05)\n",
    "        n_tot_remote += len(x)\n",
    "    except KeyError:\n",
    "        continue\n",
    "\n",
    "print('{} of {} ({:1.1f}%) candidate replay events showed statistically significant replay (P < 0.05) of environment 1 when rats were located in environment 2.'.format(n_sig_remote, n_tot_remote, n_sig_remote/n_tot_remote*100))\n",
    "print('\\nAs expected, there were also many replays of environment 2; {} of {} ({:1.1f}%) candidate events were significant.'.format(n_sig_local, n_tot_local, n_sig_local/n_tot_local*100))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "188 of 623 (30.2%) candidate replay events showed statistically significant replay (P < 0.05) of environment 1 when rats were located in environment 2.\n",
      "\n",
      "As expected, there were also many replays of environment 2; 85 of 424 (20.0%) candidate events were significant.\n"
     ]
    }
   ],
   "source": [
    "n_sig_local = 0\n",
    "n_tot_local = 0\n",
    "\n",
    "n_sig_remote = 0\n",
    "n_tot_remote = 0\n",
    "\n",
    "for animal, day in sessions:\n",
    "    try:\n",
    "        # local\n",
    "        x = data[animal][day]['remote_replay_E1_in_E2']['pvals_local_hmm']\n",
    "        n_sig_local += np.count_nonzero(x<0.05)\n",
    "        n_tot_local += len(x)\n",
    "        # remote\n",
    "        x = data[animal][day]['remote_replay_E1_in_E2']['pvals_remote_hmm']\n",
    "        n_sig_remote += np.count_nonzero(x<0.05)\n",
    "        n_tot_remote += len(x)\n",
    "    except KeyError:\n",
    "        continue\n",
    "\n",
    "print('{} of {} ({:1.1f}%) candidate replay events showed statistically significant replay (P < 0.05) of environment 1 when rats were located in environment 2.'.format(n_sig_remote, n_tot_remote, n_sig_remote/n_tot_remote*100))\n",
    "print('\\nAs expected, there were also many replays of environment 2; {} of {} ({:1.1f}%) candidate events were significant.'.format(n_sig_local, n_tot_local, n_sig_local/n_tot_local*100))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### correlate events statistically significant by both methods..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "all_remote_pvals_hmm = []\n",
    "all_remote_pvals_r2 = []\n",
    "\n",
    "for animal, day in sessions:\n",
    "    try:\n",
    "        # remote\n",
    "        x = data[animal][day]['remote_replay_E1_in_E2']['pvals_remote_hmm']\n",
    "        all_remote_pvals_hmm = np.append(all_remote_pvals_hmm,x)\n",
    "        x = data[animal][day]['remote_replay_E1_in_E2']['pvals_remote_candidates']\n",
    "        all_remote_pvals_r2 = np.append(all_remote_pvals_r2,x)\n",
    "    except KeyError:\n",
    "        continue"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "hmmsig = set(np.argwhere(all_remote_pvals_hmm < 0.05).squeeze()) # maybe should consider 0.15"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "r2sig = set(np.argwhere(all_remote_pvals_r2 < 0.05).squeeze())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "131"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(hmmsig.intersection(r2sig))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "270"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(r2sig)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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7gWvl3r17jT/N2TiOWbF+/Xr279/f9famtkqSJEmSarFFco7KJuvqkOYTExOc\ncsopTExMMDU11XXqV+O+RqUZXP3RLpWwTG8FWLJkyYx0HakXGsurxjTExpRE0xRV19TUFJs3bwYO\nLce89qkXvFaqn5pd96oxd+GFFzIxMcHpp59+IOZGLdW1EyuSc1Q2WZfphdXfN95444z0iU7N2437\nGpVmcPVHu1TC8kfql8byyikZ1GtljAEzUvRNO1SveK1UPzWLrWo6a7P7+VFLde3E1FZJkiRJUi22\nSM5R2axdTW2t/q6T+tW4L1PEFrZOqYRSP5mqqn4z7VDSOGp3Pz9u11Yrkk20Grq3Wd/FOs3Spoap\njnbxMG459uq9OuVYM8aV+qmMx2p/yHJZ4zaWc+q1VtM2lH127aerbjWLpYV0bbUi2USroXvtu6hh\nMW459uo9yzENs3EcNl+jo138gf101b2FXk7ZR1KSJEmSVMvIt0i2St9qTIVplcbQbNtqbvNll13G\nypUrDzwu+3BUp/WQ6upF2uE45dir9xpjpG4fbKdmUD+1Gja/2bV3+fLlph2qpzpN2zCs/XQ3bdrE\nhg0bBn0aqmh1P7ZQ0qfHoiLZTSpMN2k0pfLvjRs3cs0117B27VrOOeecA8u2bNli2oPmZK5ph8ae\nOmmMkbox49QM6qdWw+ZD+2svGIOau1bxN+xxZUVy+LSKmYWSPm1qqyRJkiSplpFvkWyVvtXYxNwu\njabTdBzjPGyv5k81fXViYoLTTz+ddevWMTU1deDxkiVLnPpFQ6HfUzM0pvgATVN+pqam2Lp1KytW\nrGD9+vU9ObaG26imHWo0tOtKMuwjBVsGjo6FUo5FSqnrjaenp9OiRXOve+7fv5+lS5fOeT9qb3p6\nml58XgCLFy+Onuyog17FGAxfnJWpWdX01YsuuujA8vLxqOlVnBljC0s1VXHt2rUAMx6X/wvldmvW\nrOGCCy6Y0zGNMbViObZwYqzVtbi6rh/XY2Ns4cTYoPQqxvLn1VWcmdoqSZIkSarFiqQkSZIkqZaR\n7yPZK61y5oc9X17918spZhqnX6j2jyzz5Y05LQTN+oo06zsyOTnJ6tWrWbFixfyfpFSDI2qOhnZT\nITkOxsLhfX9vWJHMWk2/0GqKEC0cvZpipll/i2p/jE7T0kjjpNlQ+62G5O9lf2+pX6xIjgan1hJ4\n398rprZKkiRJkmrxK96sVaqDaQ5yihlJGj7DloLm1AzjZ9hiTL0zLPf9ox5jTv8xxpz+wzibDw5p\nboz1mzFmjDXTy6kajDFjrBljzBjrt2GMMaf/kCRJkiT1jamtkiRp5NgNQP1mjKnfRj3GrEhKfTTq\nue/qL+NDOqj6/wB0nE7J/xmhgpEMAAAC+UlEQVRVNU7n0Pi7XSx12pdGU6spPhrXD/IaPOrlmBVJ\nqY8cRlrtGB/SQdX/B8CpkVRL43QOjb/rxFKrqSE0Wjp9jpYpc2cfSUmSJElSLQuqRbJu2ow0V6Oe\n+67+Mj6kgxr/H5waSXU0TufQLLW1cdtOU3M1e25Vs3Ta3bt3A7Bu3boZ95dbt25lxYoVThMzjzp9\njpYpc7fgKpKmzWg+GUdqx/iQDur0/+D/i9qpEx+9irVW6bQAe/fuPeT+cs2aNVYk55FlSv+Z2ipJ\nkiRJqmVkWyRnk4Zq2owkddasfG1cZleA0dLt59fNZ99p3908RxoHzdJpq6mt1e1Wr17NihUrBnWq\nC55lUn+MdEWybhqqTdyS1Fmz8rVxmV0BRku3n183n32nfXfzHGkc1Ln/nJ6eZtGikb3tHnmWSf1h\naqskSZIkqRYrkpIkSZKkWka2jb0X/RnNl5akQzUrXxuX2ad8tHT7+XXz2XfadzfPmQ9OzSCpNAxl\n0jiKlFLXG09PT6de5Hfv37+fpUuXznk/c7Vx48YD+dIXXXTRoE+n53qZj7948eLoyY466FWMwfDE\n2bjrVZwZY2rFGDPGZqO8xjebmqF63S+3W7NmDRdccMGcjmmMqRXLMWOs33oVY/nz6irOTG2VJEmS\nJNUysqmtvWAztyRJ48mpGaTxUmcaqrpTVjmN0ews+IqkJEkaP07NII2XOtNQ1Z2yymmMZsfUVkmS\nJElSLX79JkmSJGmo1Rk9vO5I48M6+vSwsyIp9VA1nx4w316SJKkHGu+b2t1H1dm21Xrv0zqzIin1\nUDWfHjDfXpIkSWPJPpKSJEmSpFpskZRamE0aamM+vfn2kiRJGkdWJKUWZpOGOpscfEmSJGnUmNoq\nSZIkSaolUkqDPgdJkiRJ0gixRVKSJEmSVIsVSUmSJElSLVYkJUmSJEm1WJGUJEmSJNViRVKSJEmS\nVIsVSUmSJElSLVYkJUmSJEm1WJGUJEmSJNViRVKSJEmSVIsVSUmSJElSLf8fvrDqdxwhOVsAAAAA\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d500837d68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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5Tbl5lOijVD1lh8QIssh7X4neNt+xUa1xVesxVifHKaWtAAAAAIBMOCNZxnxl\npY2WnTZaXgbUqzT2iEVkwYiaqAdlhwA6SV7HRr1wjOUQQs0LT05OhkWL8s09p6enNTAwkGubvW5y\nclJ5f09Llixxrg1WQIzVr5W3mCHGZuuVGGslYmy2bomxdho2nxibq1PjbL59XB5l/fWML0CMzdWp\nMZZFpx+PSbXHGWckgS7BLWYAtDuGzUczzLePy+v6cMYXQC166XiMayQBAAAAAJlwRrKCRspl2nld\n6F5cv4Z6cGsGNFtpKVf6VlgnnXSS1q9fL6m+PmhkZET9/f2amJjQ4OCg1q9fz22NelAt+7g82++F\na98wW5by6XqOx/r7+yVJS5cunXntpk2b2r4fI5GsoJXlMpTmIA9Zh5YmxiBxawY0X7psa+PGjZL2\n3Qar0Xgqxuq2bdvU19enkZGR3NpG52j2Pq60LeKq92Qpn67neCzd1kUXXaQNGzZo8+bNbd+PUdoK\nAAAAAMiEM5IVVDst3cnrApCvsbEx7dixQ0NDQ7mMwFZNpZEDayk7zVqCw60ZkBfKDpGnvEqXKYFG\nFvRj5ZFIVtDKToUODOhcY2NjGh8fb8kIbJVGDqyl7DRrCQ79EvJC2SHylNeIqYy8iizox8qjtBUA\nAAAAkAmJJAAAAAAgE0pbgQXCLWa6Q6FQ0OrVqzU0NDQzrVm3Vql0DUUt1y92yvUWAFBNXn0ZfSLQ\nOBJJYIFwi5nuUCgUND09rYGBgZlpzfpsG7mGgu8bQDfIqy+jTwQaR2krAAAAACATzkgCC4RbzADo\nFdxqAc1GjKHZiLG5SCSBBcItZgD0Cm61gGYjxtBsxNhclLYCAAAAADLhjCQAAGgqRshEsxFjaDZi\nbC4SSQA9Z2xsTBMTExocHFShUJgzb8uWLbKtE088cc78TsL1HGi1SjGXNf6IXUiz40DSnJgond9I\n+8QZ5kOMzEUiCaDnjI2NaXx8XMPDw2UTyfHxcUnS1NRUxyeSXM+BVsor5ohdSLPjQNKcmJhvfpb2\niTMgO66RBAAAAABkwhlJAD2nUChoeHhYg4ODZectXrx4prS1k3E9B1otr5gjdlurWO6/bNkynXHG\nGZLmLyutV2k5afF5+vZUxXWUxkF/f/9MGyMjI3PmZ40Z4gxoDIkkgJ5TrVy1UCh0dDlrGqVaaLW8\nYo7Yba1iSf+aNWtmJZKNlI1WUlpOWnze19enqampWesoXVdx2T179swkko0gzoDGUNoKAAAAAMgk\n8xlJRjsEgO5UqZQt/ThLf1itZA3doZXfMfHUPMVy/2XLls1Ma7RstJLSdovP099rra8FsLDqSiQZ\n7RAAuk+lUrb046yJZKWSNXSFxb52AAABzElEQVSHVn7HxFPzFI/XpqenZ6Y167MtbTfLevi+gfZC\naSsAAAAAIBMSSQAAAABAJplLWxk2HwC6U7VrourpD7Nc+4TKxsbGtGPHDg0NDc26EftC35pBmv0d\n33///TNtNKMEkXgCgPZSVyJZbV4nXxeZRh0+gF6Td79HP5qP4vgD6WsC2+HWDNLs73jDhg2zbs2Q\nN+IJANoLpa0AAAAAgEwyn5EEAACtUygUtHr1ag0NDc1M49YMAJAPbmNUPxJJAADaWKFQ0PT0tAYG\nBmamcWsGAMgHtzGqH6WtAAAAAIBMOCMJAAAAoCe1ckTobht9mkQSAAAAQE9qZWlpJ5exlkNpKwAA\nAAAgExJJAAAAAEAmlLai7YyNjWliYkKDg4MqFApz5m3ZskW2deKJJ86Z30mKQ0B3+tDPAAAA6D0k\nkmg7Y2NjGh8f1/DwcNlEcnx8XJI0NTXV8Ynk1q1bO37oZwAAAPQeSlsBAAAAAJk4hLDQ2wAAAAAA\n6CCckQQAAAAAZEIiCQAAAADIhEQSAAAAAJAJiSQAAAAAIBMSSQAAAABAJiSSAAAAAIBMSCQBAAAA\nAJmQSAIAAAAAMiGRBAAAAABkQiIJAAAAAMjk/wPtpWrETKRxeQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d507380d30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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boNi9vXr16t2Wl6VQSLPRzXiq7Xt4eLhj+1R3OaOmOs0YktRPGp0Py9YNSj0W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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d56ca04da0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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C/qlrjEdJg8Z6a3TNN67fa/7OMrVVkiRJklTJ0PdI1qcJNkoZbKdMs7IaHd5i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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d588f52e48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d500d3ae80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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1xxhrzxjrjjHW3iBjLH8fHcWZqa2SJEmSpEpGOrVVGhamUUiSJGmY2JCUZkGj\nW9PURn31th+aDcadJEmqwoakNAsa3ZqmdvLubT80G4w7SZJUhX0kJUmSJEmVeEVSmgXNbk1TLrO/\npAbJuJMkSVXYkJRmQavUQdMKNRuMO0mSVIWprZIkSZKkSrwi2QOOdigNr8nJSTZu3MghhxwCsHN6\nYmKi6XL1Za1YP2jQ6mOuXQx2W15lXyRpLmk0in558EPrr9ZsSPaAox1Kw2tycpIbb7yRFStWAOyc\nbtSQbFbWivWDBq0+5trFYLflVfZFkuYSR9HvjqmtkiRJkqRKbEhKkiRJkioxtbWBqvnSDpuvXmuV\nl9+orDwPaFluesZ0ExMTrFixYmcfyfJ0q+U6NUr1g3E0HOpjrl0MdlteZV+k2WY9pjJvx9YdG5IN\nVM2XtiJSr7XKy29UVp4HtCw3XqfrtL9jlX6RZaP0eRtHw6H+u2n3XXVb3q/XSv1gPaYyb8fWHVNb\nJUmSJEmVeEWygXaXuRcsWAAUv2qZdqh+aJVO0aisfl67cmkmjCP1m8dD9Zv12HCoehujRq/ptKzq\nvmgXG5INtLvMXUuL2Lp1q2mH6ouqqRb9TE2Taowj9ZvHQ/WbcTUcqt7GqNFrOi2rui/axdRWSZIk\nSVIlXpGcAdMOJUnqPY+HkqD66NPtlnH06f6IlFLHC09NTaWxscG0PXfs2MGiRYsGsq1hNTU1xaC+\nj4ULF8YgtmOMzS3GWHeMsfaMse4YY+0ZY90xxtozxrpjjLU3yBjL30dHcWZqqyRJkiSpEhuSkiRJ\nkqRK7CMpDQGHnpYkSdJcYkNSGgIOPS1JkqS5xNRWSZIkSVIllUZtlSRJkiTJK5KSJEmSpEpsSEqS\nJEmSKrEhKUmSJEmqxIakJEmSJKkSG5KSJEmSpEpsSEqSJEmSKrEhKUmSJEmqxIakJEmSJKkSG5KS\nJEmSpEpsSEqSJEmSKvn/ZVXOTT9Tz18AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d550289f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d507375eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d56d4e1c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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z1+lerXrf1a4uMF/vvyKl1PXCmzdvTosW9abuuX37dpYtW9aTbam1zZs306vz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\nFiuSkiRJkqRa/j8CnOPv74T61wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d528cb54e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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H1KnnaEnjkvpqrPuKpFcUXu+mlOWwMr8OSccU1l8t6a8KMfedwjpL2i7pUVXb3pCfH5vj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\nCQAAAAAohY4kAAAAAKCU/wK7T6znacjD+wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d50107dda0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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22bjvN7VVkiRJklSJqa1SH5lvKROSJEnqTVYkpT5RHlIaaPmYj5GREbZs2QLA\n0NDQvBg5bK5pNoR4bX65P+xsfb+thjmfb0OgS5JmVy9dH+vLVCtLszL26zXTiqTUJ8pDSgMth5eu\nrQuwe/fuvjopqdBsCPHa/EWLFjExMTGrQ4z72CNJUq/opetjfZlqZWlWxn69ZtpHUpIkSZJUyZxu\nkeyHJu5W5ezXZm51R6vHgjRat/aokKGhoRkrozqnWX/YXnrUi0OgS5J6RS9dH+vLVCtLszL26zVz\nTj/+o/aohHLz8Ww/MqHR4xualXO6j3rw8R8ONz0THNLcGOs2Y8wY6zZjzBjrNmPMGOs2H/8hSZIk\nSep5czK1tZYSOjg4uF/z8djYGOeddx4weyNZlpu0y6Nu1pdz48aNe8vfb83ckqT5o1WXjdr1q9F0\ns5F+e6k7iiTVa3Z+azb44Vw+r83ZimQtJXTDhg1759dSRWH2RrKsHXP9+vVs2rSpYdpqeVm5/JIk\n9ZpGow02G2W6PN1spN9eGnFRkupNZRT9uXpeM7VVkiRJklSJFUlJkiRJUiVzMrW11bD53XokQtV8\n6YmJCVauXMng4GDb5VdvaqcvEMCWLVuAff1zq8SMJPWqRtesVo8rmuyRMb00dL+kwubNm9mxYwfL\nly9n3bp1s12cWVX1cWxz+bw2ZyuSzeZ36ya9ar70DTfcAMBRRx3VsJzqH+30BapNw77+uVViRpJ6\nVaNz1lTOY577pN61efNmrr32WlavXm1FssK5aq6f10xtlSRJkiRVMidbJMumknZYXlafgtiqtbNK\nM3e3Umw189pN4ar/zqvEjCRJzZh2qG5bt24dq1evZvny5bNdlK7wMUZTMy8qklXTDsvL6lMQW1Uk\n29XNFFvNvHa/y/r1jAFJUieYdqhum+tx5WOMpsbUVkmSJElSJXO+RXKqaYflZY6iKkmSetVcTzuU\nus3Rp6cmUkptrzw+Pp4WLJh+3XPPnj0sXbp02vtRa+Pj43Ti+wJYvHhxdGRHk+hUjMHMxdnIyMgB\nj/aYTa3y/Otz9tvp/zuZTsWZMaZm+j3GptN/zRibGf0eY9NhjM0MY8wY67bZuO+f8y2SUrfV8uFh\n36M9eqE8jfL863P22+n/K2l67L8mSZqL7CMpSZIkSarEFklpCupTQmt9bJcsWcLGjRtnddjncn7+\nxo0b95ahnLNfWzY4OGj/X6nL7L8mSZqLrEhKU1BOCb3ooov2VhbXr1/Ppk2bZnXY5/qy1MpYVl62\nYcOGGS2fNN+YzipJmotMbZUkSZIkVVJp1FZJkiRJkmyRlCRJkiRVYkVSkiRJklSJFUlJkiRJUiVW\nJCVJkiRJlViRlCRJkiRVYkVKbURiAAAALklEQVRSkiRJklSJFUlJkiRJUiVWJCVJkiRJlViRlCRJ\nkiRVYkVSkiRJklTJfwDYpvwxNJWU0AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d528d3fef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d58e1f0cc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d500c8f0b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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SW9uZa/+1bocn1uhrd4uZlStXsnr1ar73ve8xOTnJPffcw+rVqxkfH+8YM/Yr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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d500cc7dd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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9SdK4pH1rrOdgSeslDVWZ901J78p8nqGY5bAkfQ6SDs3Mv1nSn2Ri7s7MPEvaLGnvim0/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\npooCRd8j6IUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d592158e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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VjONPzAEAUFk7nysZIwkAAAAAyIUeySZp525uNAfjIztbM44/MQcAQGXtfK4k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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d528cd54a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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dSsjhhuaXXsRYtW1tSon9+/dz6qmnMjIyckSZUW/dQbtOU+d0+rdvVI/o9n5n\nqtvX/ANfkex2u4+5mJPvxVf3lYmD2piErMt6eCjeLrvssqbrVmNvEOJPvdNoGITamKstD3t5PM3K\n8UYVSdt4l1P7PbbyG5cdMqidbWrw9SLGqm1si+fKZcuWHZq+evVqNm7cWHfdQbtOU+d0+rdvVI/o\n9n5nqtvnSVNbJUmSJEmlDPQTyV6mUtR2ab5p06ZDyw4PD3P++ed3vZvxRmlq6h8zSWUoxmRtaut0\naWCmig2+bqboV7vYn5iYYHh4mEqlAjxUZi1ZsuRQams19iqVStfKlnrDMkxXjtcyNb8/TZei36xM\n7JcUMPU3z5WaiVZ+++magVTX3bJlC1NTU4edPxttt52Y60QzkM2bN3P33Xd3vRnIwFckm/3dyjrT\nTa/XpfnQ0BDf+c53WhqOoZMapampf8wklaGd39EYGHzdTNGvvjZs2MBNN910RMr0W9/61kPb3LBh\nA1u3bu1q2VIv/bpsOW46a39qJUW/WUWyH1LA1N88V2omWvntp2sGUjwfAwwNDR12/pzpfsscT9lm\nIDfccAM333xz15uBmNoqSZIkSSploJ9I9kK9dNnatNhepUvUSwtTfzF9RmXZo6bmAtMOJQ2qRtfX\ntWVTr67BO9EM5IlPfCJnn31215uBREqp5YUnJyfTwoUzr3sePHiQpUuXznh9zdzk5CTt/HaLFy+O\nDh5OQ/0WYw4x0zpjTN1mjPVWJ8udVsq5buy3LGNssJRtN1Z2e9NNn6l24my+xlivr8caLTcI12PQ\nu7LMJ5JSEw4xI2m+6mS500o51439am4r226s7Pamm67e6fX1WKPljIXD2UZSkiRJklSKTyRLavWR\n9qA8+lZztl/TXODQDJqJdruvrzcUDcCSJUuabrfRfnuVdqjBUbbdWNntTTe9XePj40xMTHR9iIa5\nYDaux4rlVnVorHrDApYx18oxK5IltfpI20ffc0MvhphpZ5tSKxyaQTPRie7ri0PRFKdddtllpfdr\n2qFqzeQcXWZ7ndpuI+Pj42zbtq3rQzTMBbNxPVYst6rDcNQOC1jWXCvHTG2VJEmSJJXiE8mSWk1v\nMBVRUr9waAb1Wr246UXaYaNeGltRqVS45ZZbmJyc5MQTTzTdsE9UKhW2bNkCZOVWvd4zgbrL9Op4\nyvYeu3nzZu6++25OOukkRkdHuz5Eg2Zu0NOnu82KZEmtFk6D9Fha0tzWTnlkWaaZqBc3vUg73LBh\nQ91eGltRTS1btGgR+/fvN92wT1R/F+BQemFxerHXztplenU8ZXuPveGGG7j55psZHR3l0ksv7dqx\nqn2Dnj7dbaa2SpIkSZJKsSKcp9mwAAADmElEQVQpSZIkSSrF1FapzzjEjCTNTKPu/ltd98wzzzzU\nRvKee+7huuuus63kLCsOwVBt212dXmxTVm+ZbhgZGeHee+/lwIEDDA8PHxoWopV2dNXz9oMPPshZ\nZ53FSSed1NVjlbrNiqTUZxxiRpJmpt32wJOTkyxcmF0aXX755Xz+85+3reQsqw4fU296s7+75Y47\n7mDHjh0MDQ1x0003sW/fPjZu3NjSsdS2w42IXhyy1DWmtkqSJEmSSvGJpNRnHGJGkqbXaKiPdoYA\nKVq3bp1DM8xzjWJpeHiYiYkJgMPSW6dTPW/v3LmT5cuXG1vqejnWbVYkpT7jEDOSNL1qmmDtUB+N\nppdlOqvqxdLGjRupVCps376doaEhtm/f3vKQI9VliinUmt+6XY51m6mtkiRJkqRSvB0iSZIGTqMe\nWtvpuVUqMsbUbYMeY1YkJUnSjFQqFbZs2QJkwy5UU6+KwxMBdZdpV73t1DueSqXCpk2bjmh71KjN\n0fj4OBMTEw770WdqY6pZu7JOtSdrto3t27cDcPbZZ/dlyqEGQ6PYGZSYsiIpSZJmpNqOBzisnVhx\neCKg7jK9Op7aoZKmGzppfHycbdu2OexHn6kXU43alXW7PVmjuJfmG9tISpIkSZJK8YmkJEmakepQ\nCJClkhanF4cnqrdMr46n9limGzrJYT/6U+3v1qxdWbfbkzWKe2m+iZRSywtPTk6mdrorPnjwIEuX\nLp3x+pq5druaXrx4cXTwcBoyxgaXMaZuM8bUbcaYeqGdODPG1IpelWWmtkqSJEmSSjG1VZIGUCd7\nJ6zXG2Kj7Xa6V0TNTa3GifEkSYPLiqQkDaBO9k5YrzfERtvtVa+IGmytxonxJEmDy9RWSZIkSVIp\nViQlSZIkSaWY2ipJA6iT3dzX61a/0XZ71b2+BlurcWI8SdLgsiIpSQOok+3JymzLdmxqRatxYjxJ\n0uAytVWSJEmSVIpPJCVJkiSpwGGMpmdFUpIkSZIKHMZoeqa2SpIkSZJK8YmkJEmSJBXY+/T0rEhK\nkiRJUoG9T0/P1FZJkiRJUilWJCVJkiRJpViRlCRJkiSVYkVSkiRJklSKFUlJkiRJUimRUprtY5Ak\nSZIkDRCfSEqSJEmSSrEiKUmSJEkqxYqkJEmSJKkUK5KSJEmSpFKsSEqSJEmSSrEiKUmSJEkqxYqk\nJEmSJKkUK5KSJEmSpFKsSEqSJEmSSrEiKUmSJEkq5f8DCu/Bj3m9YrMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d58c88ddd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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v1q5dy4YNG0Z9BIEkSVKVjzGau0xtlSRJkiTVYovkJKibdthunTRZJnsk4VWr\nVrFs2bJRR46UJEmqcvTpuStSSmMuvHnz5tTT093Yc8eOHRx00EFdPcZ0a5ezXZ2u0+x+7bXXdr3/\n2v777x9d2XET69jMtHnzZrr9d7GOzW/WsXqsY/VZx+qxjtVnHavHOlbfVNQxGHs9s0VyGrTL2a5O\n239NkiRJ0kxlH0lJkiRJUi22SE4D+6+prk5DWE90eGxJkiSpLgPJaTDZX/ZXr149JfnSmj6dhrCe\n6PDYkiRJUl2mtkqSJEmSaqk1aqskSZIkSbZISpIkSZJqMZCUJEmSJNViIClJkiRJqsVAUpIkSZJU\ni4GkJEmSJKkWA0lJkiRJUi0GkpIkSZKkWgwkJUmSJEm1GEhKkiRJkmoxkJQkSZIk1fL/AaTH66x+\nvYPQAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d5921514a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d557a17e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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2u8VyvRo2X4uj7muW10OpOlNbJUmSJEmV2JCUJEmSJFViTkefmZOvbtr1/enU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\nYkNSkiRJklSJDUlJkiRJUiX/H9LtWssvTXIAAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d518003ef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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8aCfmynrPALYAj5pgO08CNgMLWiz7CvCyyuu9yFkOK8rrBKyuLP8M8EeVmLu2siyAceDo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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d56cad8ef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d501054048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Dw+rp6dGRRx6po446ShIxhqk32Wt+GpIdqN5xH0WnYebiDHnTmVfDmFq0EvGG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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d56cb33cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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KpFLkDbVPCg+qyYuPbKrNunXriB00FWUWGo17NMxHedz0allFRbIONm/erI0b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\no7bP33hkAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d528ccf8d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d58c937d68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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IclienydgZWn5ZcCflWLumtKyADYBBzVt+5b8+Kgc97vM92frNKfHzauA00rPnwD8Jq/7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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d588ec1e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sig_thresh = 0.05\n",
    "\n",
    "E1a, E1b, E2 = 1, 3, 5\n",
    "animal = 'Bon'\n",
    "day = 'Day3'\n",
    "\n",
    "def plot_all_significant_linearized_E2_remote_events(data, animal, day):\n",
    "    try:\n",
    "        bst = data[animal][day]['remote_replay_E1_in_E2']['bst_remote_candidates']\n",
    "    except KeyError:\n",
    "        raise UserWarning('The (animal, day) pair does not have remote replay analysis results...')\n",
    "        return\n",
    "    \n",
    "    tc_E1a_co = data[animal][day]['tuning_curves1D_center'][E1a]\n",
    "    tc_E1b_co = data[animal][day]['tuning_curves1D_center'][E1b]\n",
    "    tc_E2_co = data[animal][day]['tuning_curves1D_center'][E2]\n",
    "    \n",
    "    tc_E1a_oo = data[animal][day]['tuning_curves1D_outer'][E1a]\n",
    "    tc_E1b_oo = data[animal][day]['tuning_curves1D_outer'][E1b]\n",
    "    tc_E2_oo = data[animal][day]['tuning_curves1D_outer'][E2]\n",
    "    \n",
    "    pvals = data[animal][day]['remote_replay_E1_in_E2']['pvals_remote_hmm']\n",
    "    sig_idx = np.argwhere(pvals < sig_thresh).squeeze().tolist()\n",
    "    \n",
    "    for evt_idx in sig_idx:\n",
    "        fig, (ax1, ax2, ax3, ax4, ax5, ax6) = plt.subplots(1, 6, figsize=(16, 2))\n",
    "        axes = (ax1, ax2, ax3, ax4, ax5, ax6)\n",
    "        \n",
    "        evt = bst[evt_idx]\n",
    "        evt_extent = evt.support\n",
    "        plot_extent = evt_extent.expand(0.05)\n",
    "        \n",
    "        st = data[animal][day]['remote_replay_E1_in_E2']['st_placecells_remote'][plot_extent]\n",
    "        \n",
    "        peak_order = tc_E1a_co._unit_subset(st.unit_ids).get_peak_firing_order_ids()\n",
    "        npl.rasterplot(st.reorder_units_by_ids(peak_order), vertstack=True, lw=2.5, ax=ax1)\n",
    "        npl.epochplot(plot_extent-evt_extent, hatch='', color='0.9', ax=ax1)\n",
    "        ax1.set_xlim(*st.support.time)\n",
    "        ax1.set_title('E1a center')\n",
    "\n",
    "        peak_order = tc_E1b_co._unit_subset(st.unit_ids).get_peak_firing_order_ids()\n",
    "        npl.rasterplot(st.reorder_units_by_ids(peak_order), vertstack=True, lw=2.5, ax=ax2)\n",
    "        npl.epochplot(plot_extent-evt_extent, hatch='', color='0.9', ax=ax2)\n",
    "        ax2.set_xlim(*st.support.time)\n",
    "        ax2.set_title('E1b center')\n",
    "        \n",
    "        peak_order = tc_E2_co._unit_subset(st.unit_ids).get_peak_firing_order_ids()\n",
    "        npl.rasterplot(st.reorder_units_by_ids(peak_order), vertstack=True, lw=2.5, ax=ax3)\n",
    "        npl.epochplot(plot_extent-evt_extent, hatch='', color='0.9', ax=ax3)\n",
    "        ax3.set_xlim(*st.support.time)\n",
    "        ax3.set_title('E2 center')\n",
    "\n",
    "        peak_order = tc_E1a_oo._unit_subset(st.unit_ids).get_peak_firing_order_ids()\n",
    "        npl.rasterplot(st.reorder_units_by_ids(peak_order), vertstack=True, lw=2.5, ax=ax4)\n",
    "        npl.epochplot(plot_extent-evt_extent, hatch='', color='0.9', ax=ax4)\n",
    "        ax4.set_xlim(*st.support.time)\n",
    "        ax4.set_title('E1a outer')\n",
    "        \n",
    "        peak_order = tc_E1b_oo._unit_subset(st.unit_ids).get_peak_firing_order_ids()\n",
    "        npl.rasterplot(st.reorder_units_by_ids(peak_order), vertstack=True, lw=2.5, ax=ax5)\n",
    "        npl.epochplot(plot_extent-evt_extent, hatch='', color='0.9', ax=ax5)\n",
    "        ax5.set_xlim(*st.support.time)\n",
    "        ax5.set_title('E1b outer')\n",
    "        \n",
    "        peak_order = tc_E2_oo._unit_subset(st.unit_ids).get_peak_firing_order_ids()\n",
    "        npl.rasterplot(st.reorder_units_by_ids(peak_order), vertstack=True, lw=2.5, ax=ax6)\n",
    "        npl.epochplot(plot_extent-evt_extent, hatch='', color='0.9', ax=ax6)\n",
    "        ax6.set_xlim(*st.support.time)\n",
    "        ax6.set_title('E2 outer')\n",
    "        \n",
    "        fig.suptitle('{} {} remote candidate #{}'.format(animal, day, evt_idx), y=1.1)\n",
    "        \n",
    "        for ax in axes:\n",
    "            npl.utils.clear_left_right(ax)\n",
    "            npl.utils.clear_top_bottom(ax)\n",
    "            \n",
    "        plt.show()\n",
    "\n",
    "plot_all_significant_linearized_E2_remote_events(data=data, \n",
    "                         animal=animal,\n",
    "                         day=day)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notes: 13 ran back and forth on center arm (good to show trajectory, since local is all messed up)\n",
    "\n",
    "14 truly messed up\n",
    "\n",
    "15 _could_ make sense\n",
    "\n",
    "20 seems plausible\n",
    "\n",
    "22 is good in ONLY E1a-raw\n",
    "\n",
    "29, 30 are fails\n",
    "\n",
    "33 only bad in E1a-ideal\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Save augmented data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "FrankLabData = nel.ResultsContainer(data=data,\n",
    "                                    sessions=FrankLabData.sessions,\n",
    "                                    cellinfo=FrankLabData.cellinfo,\n",
    "                                    taskinfo=FrankLabData.taskinfo,\n",
    "                                    tetinfo=FrankLabData.tetinfo,\n",
    "                                    description=FrankLabData.description)\n",
    "\n",
    "FrankLabData.save_pkl(fileroot + 'FrankLabData-BonConFra-no-eeg06d.nel')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To try:\n",
    "- different training ds\n",
    "- E1a and E1b seperately\n",
    "- scaling of E2 SWR sequences?\n",
    "- scaling Lambda mat?"
   ]
  }
 ],
 "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": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}