maria_mcmc_3.ipynb

{
 "metadata": {
  "name": "",
  "signature": "sha256:20ed39b613af19a0edaa12a2c8353acce499b312d07843f4548341a9b4ec3bda"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Imports\n",
      "%matplotlib inline\n",
      "import numpy as np\n",
      "import matplotlib.pyplot as plt\n",
      "import pandas as pd\n",
      "import pymc as pm\n",
      "import statsmodels.api as sm\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Load \n",
      "f = pd.read_csv('/home/acs/Dropbox/misc/15414007_props.csv')\n",
      "f.hist('times', bins=50)\n",
      "f.hist('intervals', bins=50)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        "array([[<matplotlib.axes.AxesSubplot object at 0x7f5bf6180b50>]], dtype=object)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x7f5bf5ed99d0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x7f5bf5ed9210>"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Peaks, smoothing\n",
      "\n",
      "We want to find the values (bin-centers) of the potential peaks, we'll use these to set the priors for the MCMC processes. We should make sure we don't find > 2 peaks, otherwise something wierd happened. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def savitzky_golay(y, window_size, order, deriv=0, rate=1):\n",
      "    r\"\"\"Smooth (and optionally differentiate) data with a Savitzky-Golay filter.\n",
      "    The Savitzky-Golay filter removes high frequency noise from data.\n",
      "    It has the advantage of preserving the original shape and\n",
      "    features of the signal better than other types of filtering\n",
      "    approaches, such as moving averages techniques.\n",
      "    Parameters\n",
      "    ----------\n",
      "    y : array_like, shape (N,)\n",
      "        the values of the time history of the signal.\n",
      "    window_size : int\n",
      "        the length of the window. Must be an odd integer number.\n",
      "    order : int\n",
      "        the order of the polynomial used in the filtering.\n",
      "        Must be less then `window_size` - 1.\n",
      "    deriv: int\n",
      "        the order of the derivative to compute (default = 0 means only smoothing)\n",
      "    Returns\n",
      "    -------\n",
      "    ys : ndarray, shape (N)\n",
      "        the smoothed signal (or it's n-th derivative).\n",
      "    Notes\n",
      "    -----\n",
      "    The Savitzky-Golay is a type of low-pass filter, particularly\n",
      "    suited for smoothing noisy data. The main idea behind this\n",
      "    approach is to make for each point a least-square fit with a\n",
      "    polynomial of high order over a odd-sized window centered at\n",
      "    the point.\n",
      "    Examples\n",
      "    --------\n",
      "    t = np.linspace(-4, 4, 500)\n",
      "    y = np.exp( -t**2 ) + np.random.normal(0, 0.05, t.shape)\n",
      "    ysg = savitzky_golay(y, window_size=31, order=4)\n",
      "    import matplotlib.pyplot as plt\n",
      "    plt.plot(t, y, label='Noisy signal')\n",
      "    plt.plot(t, np.exp(-t**2), 'k', lw=1.5, label='Original signal')\n",
      "    plt.plot(t, ysg, 'r', label='Filtered signal')\n",
      "    plt.legend()\n",
      "    plt.show()\n",
      "    References\n",
      "    ----------\n",
      "    .. [1] A. Savitzky, M. J. E. Golay, Smoothing and Differentiation of\n",
      "       Data by Simplified Least Squares Procedures. Analytical\n",
      "       Chemistry, 1964, 36 (8), pp 1627-1639.\n",
      "    .. [2] Numerical Recipes 3rd Edition: The Art of Scientific Computing\n",
      "       W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery\n",
      "       Cambridge University Press ISBN-13: 9780521880688\n",
      "    \"\"\"\n",
      "    import numpy as np\n",
      "    from math import factorial\n",
      "    \n",
      "    try:\n",
      "        window_size = np.abs(np.int(window_size))\n",
      "        order = np.abs(np.int(order))\n",
      "    except ValueError, msg:\n",
      "        raise ValueError(\"window_size and order have to be of type int\")\n",
      "    if window_size % 2 != 1 or window_size < 1:\n",
      "        raise TypeError(\"window_size size must be a positive odd number\")\n",
      "    if window_size < order + 2:\n",
      "        raise TypeError(\"window_size is too small for the polynomials order\")\n",
      "    order_range = range(order+1)\n",
      "    half_window = (window_size -1) // 2\n",
      "    # precompute coefficients\n",
      "    b = np.mat([[k**i for i in order_range] for k in range(-half_window, half_window+1)])\n",
      "    m = np.linalg.pinv(b).A[deriv] * rate**deriv * factorial(deriv)\n",
      "    # pad the signal at the extremes with\n",
      "    # values taken from the signal itself\n",
      "    firstvals = y[0] - np.abs( y[1:half_window+1][::-1] - y[0] )\n",
      "    lastvals = y[-1] + np.abs(y[-half_window-1:-1][::-1] - y[-1])\n",
      "    y = np.concatenate((firstvals, y, lastvals))\n",
      "    return np.convolve( m[::-1], y, mode='valid')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# We'd like to find how many peaks are in this distribution\n",
      "# Can assume that it will either be all-tonic, all-burst, or mixed, \n",
      "#  so Npeaks = {1,2}, but not >2\n",
      "\n",
      "# Let's find out how many peaks\n",
      "int_data = f.intervals.dropna()\n",
      "hist, bin_e = np.histogram(int_data, bins=50)\n",
      "bin_cents = (bin_e[:-1]+bin_e[1:])*.5\n",
      "\n",
      "histhat = savitzky_golay(hist, 11, 3)\n",
      "\n",
      "# Find the peaks for the dist\n",
      "def whichPeaks(trace):\n",
      "    peaks = []\n",
      "    df = np.diff(trace)\n",
      "    for t in range(len(df)-4):\n",
      "        if df[t] > 0 and df[t+1] > 0:\n",
      "            if df[t+2] < 0 and df[t+3] < 0: # Potential peak\n",
      "                if trace[t+2] > np.mean(trace):\n",
      "                    peaks.append([t+2, trace[t+2]])\n",
      "    return peaks\n",
      "\n",
      "\n",
      "pks = whichPeaks(histhat)\n",
      "print(pks)\n",
      "print(np.mean(histhat))\n",
      "plt.plot(bin_cents, histhat)\n",
      "print([bin_cents[p[0]] for p in pks])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[7, 177.17249417249411], [23, 50.181818181818187]]\n",
        "32.7008857809\n",
        "[67.327804999999984, 204.70850899999996]\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x7f5bf5d9ec50>"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## MCMC\n",
      "\n",
      "Those are pretty close to the actual peak locations. We'll use these peak values as the priors.\n",
      "\n",
      "The MCMC process will use a stochastic categorical function to assign each value to distribution 0 or 1; these will have means based on the peak values found above."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "type(hist)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 9,
       "text": [
        "numpy.ndarray"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Stochastic categorical assignment\n",
      "p = pm.Uniform('p', 0, 1)\n",
      "assignment = pm.Categorical('assignment', [p, 1-p], \n",
      "                            size=int_data.shape[0])\n",
      "print('Prior assignment with p = %.2f' %p.value)\n",
      "print(assignment.value[:10])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Prior assignment with p = 0.58\n",
        "[1 0 0 1 1 1 0 0 0 0]\n"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Tau = the precision of the normal distribution (of the above peaks)\n",
      "# tau = 1/sigma**2\n",
      "taus = 1.0 / pm.Uniform('stds', 0, 100, size=2)**2\n",
      "# Centers are the bin_centers at the peak indices.\n",
      "# Here 'sigma' is 20, but is really tau = 1/sigma**2, so = 0.0025\n",
      "print([bin_cents[p[0]] for p in pks])\n",
      "centers = pm.Normal('centers', [bin_cents[p[0]] for p in pks], \n",
      "                    [.0025, .0025], size=2)\n",
      "\n",
      "# Deterministic functions map assignment (0,1) to a set of params,\n",
      "# either taus[0] and cents[0] or taus[1] and cents[1]\n",
      "\n",
      "@pm.deterministic\n",
      "def center_i(assignment=assignment, centers=centers):\n",
      "    return centers[assignment]\n",
      "@pm.deterministic\n",
      "def tau_i(assignment=assignment, taus=taus):\n",
      "    return taus[assignment]\n",
      "\n",
      "print('Random assignments: ', assignment.value[:10])\n",
      "print('Assigned centers: ', center_i.value[:10])\n",
      "print('Assigned precision: ', tau_i.value[:10])\n",
      "print(np.mean(assignment.value[:]))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[67.327804999999984, 204.70850899999996]\n",
        "('Random assignments: ', array([1, 0, 0, 1, 1, 1, 0, 0, 0, 0]))\n",
        "('Assigned centers: ', array([ 236.65001543,   80.54184122,   80.54184122,  236.65001543,\n",
        "        236.65001543,  236.65001543,   80.54184122,   80.54184122,\n",
        "         80.54184122,   80.54184122]))\n",
        "('Assigned precision: ', array([ 0.00031815,  0.00077196,  0.00077196,  0.00031815,  0.00031815,\n",
        "        0.00031815,  0.00077196,  0.00077196,  0.00077196,  0.00077196]))\n",
        "0.420440636475\n"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Combine it with the observations (histogram)\n",
      "# Use half-rectified yhat (histhat), all (+)\n",
      "# hhat = [i if i > 0 else 0 for i in histhat]\n",
      "observations = pm.Normal('obs', center_i, tau_i, \n",
      "                         value=int_data, \n",
      "                         observed=True)\n",
      "\n",
      "# Create the model\n",
      "model = pm.Model([p, assignment, observations, taus, centers])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Sometimes mcmc = pm.MCMC(model)  throws an error, presumably\n",
      "#   because pm.MCMC tries to wrap everything [] in a container,\n",
      "#   and pm.Model does the same thing.\n",
      "\n",
      "mcmc = pm.MCMC([p, assignment, observations, taus, centers])\n",
      "mcmc.sample(50000)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
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      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# This is the pre-model stats \n",
      "# fig = plt.figure()\n",
      "# ax1 = fig.add_subplot(2,2,1)\n",
      "#ax1.hist(taus.value[:], bins=50)\n",
      "#dir(mcmc.trace.im_self)\n",
      "#mcmc.trace.im_self.summary()\n",
      "\n",
      "# plt.plot(hhat)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "ename": "NameError",
       "evalue": "name 'hhat' is not defined",
       "output_type": "pyerr",
       "traceback": [
        "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
        "\u001b[1;32m<ipython-input-14-29cbfdbf4b7d>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      6\u001b[0m \u001b[1;31m#mcmc.trace.im_self.summary()\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      7\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 8\u001b[1;33m \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mhhat\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
        "\u001b[1;31mNameError\u001b[0m: name 'hhat' is not defined"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "center_trace = mcmc.trace(\"centers\")[:]\n",
      "plt.hist(center_trace[:,0], bins=50, histtype='stepfilled',\n",
      "         color='blue', alpha=0.7)\n",
      "plt.hist(center_trace[:,1], bins=50, histtype='stepfilled',\n",
      "         color='red', alpha=0.7)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 15,
       "text": [
        "(array([  1.00000000e+01,   0.00000000e+00,   0.00000000e+00,\n",
        "          0.00000000e+00,   0.00000000e+00,   0.00000000e+00,\n",
        "          0.00000000e+00,   0.00000000e+00,   0.00000000e+00,\n",
        "          0.00000000e+00,   0.00000000e+00,   0.00000000e+00,\n",
        "          0.00000000e+00,   0.00000000e+00,   0.00000000e+00,\n",
        "          2.04000000e+02,   7.53000000e+02,   7.08000000e+02,\n",
        "          7.35000000e+02,   4.16000000e+02,   6.06000000e+02,\n",
        "          4.61000000e+02,   3.27000000e+02,   7.33000000e+02,\n",
        "          6.47000000e+02,   6.32000000e+02,   7.74000000e+02,\n",
        "          6.80000000e+02,   5.65000000e+02,   6.06000000e+02,\n",
        "          6.47000000e+02,   6.96000000e+02,   5.71000000e+02,\n",
        "          7.25000000e+02,   7.27000000e+02,   9.76000000e+02,\n",
        "          1.24000000e+03,   1.27000000e+03,   1.34600000e+03,\n",
        "          1.16700000e+03,   1.70100000e+03,   5.99700000e+03,\n",
        "          1.29860000e+04,   8.99100000e+03,   1.95700000e+03,\n",
        "          1.40000000e+02,   5.00000000e+00,   0.00000000e+00,\n",
        "          0.00000000e+00,   1.00000000e+00]),\n",
        " array([  94.30415467,   97.15107189,   99.9979891 ,  102.84490632,\n",
        "         105.69182353,  108.53874075,  111.38565796,  114.23257518,\n",
        "         117.07949239,  119.92640961,  122.77332682,  125.62024404,\n",
        "         128.46716125,  131.31407847,  134.16099568,  137.0079129 ,\n",
        "         139.85483011,  142.70174733,  145.54866454,  148.39558176,\n",
        "         151.24249897,  154.08941619,  156.9363334 ,  159.78325062,\n",
        "         162.63016783,  165.47708505,  168.32400226,  171.17091948,\n",
        "         174.01783669,  176.86475391,  179.71167112,  182.55858834,\n",
        "         185.40550555,  188.25242277,  191.09933998,  193.9462572 ,\n",
        "         196.79317441,  199.64009163,  202.48700884,  205.33392606,\n",
        "         208.18084328,  211.02776049,  213.87467771,  216.72159492,\n",
        "         219.56851214,  222.41542935,  225.26234657,  228.10926378,\n",
        "         230.956181  ,  233.80309821,  236.65001543]),\n",
        " <a list of 1 Patch objects>)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ewLwujbtF38Z8FIvT/38vYz6Rezhmf/RTOPM6DcW8U3oR83/WHZZ1e0+vWDWn\nl3N7T5/TPZfzhEzBhAHAEMwv9yZwsVV7Fvg3B/qahdlqA3Ms4wvgHYf6GoY5CARmRRLbQ+M+yzRM\nkH7CsT9mENvXDzBv6e0fCuREX/aeGp1sqzXuS3Wqp9cwrxXAvcCvcP512gP8kzV9DSYcurqngdbP\nsH+xh9PLeryenF7O4/XUyOnlPCl+BWwE/oJ5+3wG5oDkOuA5nDmbqA/wv5gzLNZj9hU61dcwmg8M\ntdbD7TS/htd0cV9uzBbS3zAH2FYAjzrUV2NPR6s52dNJmI2ftcBSmt8FO9nTBMwy7sds8JzkQE9P\nA8U0Lz+NB2r9OLesx/a0CrOLz8nlPN7r1Pjl1sNwdjkXERERERERERERERERERERERERERERERER\nEZGe4v8D4ZVcFy7EJuwAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f5bf5d60d50>"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Fucking nailed it\n",
      "\n",
      "clusts = [center_trace[:,0], center_trace[:,1]]\n",
      "print([np.mean(c) for c in clusts])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[77.638455539961299, 202.01044043427967]\n"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Reverse assignment of bursting/spiking activity\n",
      "\n",
      "Now for each inteval and its associated spikes and times, we can assign it to either bursting or spiking (with almost perfect discriminability).\n",
      "\n",
      "Simple time-based association"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Assign a delta_tms to burst or tonic cluster\n",
      "def assignTms(clusts, tms):\n",
      "    assns = [abs(np.mean(clusts[c])-tms) for c in range(len(clusts))]\n",
      "    #for c in clusts:\n",
      "    #    cp = np.array([i for i in c])\n",
      "    #    fw = float(len([i for i in cp if i < tms]))/len(cp)\n",
      "    #    bw = float(len([i for i in cp if i > tms]))/len(cp)\n",
      "    #    assns.append(np.mean([fw,bw]))\n",
      "    # Whoever is closer to 0.5 wins\n",
      "    return assns.index(min(assns))\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Iterate through spike times, assign each to burst or tonic\n",
      "print(len(f.times.dropna()), len(f.intervals.dropna()))\n",
      "# Since len(ISI) != len(times) -1, must make our own ISIs (on the fly)\n",
      "clust_tms = [[] for c in clusts]\n",
      "\n",
      "tms_clean = f.times.dropna()\n",
      "for t in range(len(tms_clean)-1):\n",
      "    t_clust = assignTms(clusts, tms_clean[t+1]-tms_clean[t])\n",
      "    clust_tms[t_clust].append(tms_clean[t])\n",
      "\n",
      "\"\"\"\n",
      "# Show the times\n",
      "for c in clust_tms:\n",
      "    plt.plot(c, [(clust_tms.index(c)+1) for i in c], \n",
      "             '|', color=['blue', 'red'][clust_tms.index(c)])\n",
      "plt.ylim([0,3])\"\"\"\n",
      "\n",
      "def sort_tms_byClust(df, clusts):\n",
      "    clust_tms = [[] for c in clusts]\n",
      "    tms_clean = df.times.dropna()\n",
      "    for t in range(len(tms_clean)-1):\n",
      "        t_clust = assignTms(clusts, tms_clean[t+1]-tms_clean[t])\n",
      "        clust_tms[t_clust].append(tms_clean[t])\n",
      "    \n",
      "    # Group spikes from same spike type together\n",
      "    type_tms = []\n",
      "    for c in range(len(clust_tms)):\n",
      "        for t in clust_tms[c]:\n",
      "            type_tms.append([t, c]) # [spike tms, clust index]\n",
      "\n",
      "    # Now group these together\n",
      "    clust_id = []\n",
      "    for i in range(df.shape[0]):\n",
      "        if df.iloc[i].times in [k[0] for k in type_tms]:\n",
      "            clust_id.append(type_tms[[k[0] for k in type_tms].index(df.iloc[i].times)][1])\n",
      "        else: # No matching spike found -- this happens w/ isolated spks\n",
      "            clust_id.append(np.nan)\n",
      "    \n",
      "    df['clust_inds'] = clust_id\n",
      "    return df\n",
      "\n",
      "new_df = sort_tms_byClust(new_df, clusts)\n",
      "f = f.dropna()\n",
      "print(new_df['clust_inds'][:10])\n",
      "# Show the times ## np.mean(f[f['clust_ind'] == 0]['maxV'])\n",
      "for c in range(max(f['clust_inds'])):\n",
      "    plt.plot(f[f['clust_ind'] == c][times], \n",
      "             [i+1 for i in f[f['clust_ind'] == c][times]], \n",
      "             '|', color=['blue', 'red'][c])\n",
      "plt.ylim([0,3])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(0, 0)\n"
       ]
      },
      {
       "ename": "AttributeError",
       "evalue": "'DataFrame' object has no attribute 'times'",
       "output_type": "pyerr",
       "traceback": [
        "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
        "\u001b[1;32m<ipython-input-71-e4023336647c>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m     40\u001b[0m     \u001b[1;32mreturn\u001b[0m \u001b[0mdf\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     41\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 42\u001b[1;33m \u001b[0mnew_df\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0msort_tms_byClust\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnew_df\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mclusts\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     43\u001b[0m \u001b[0mf\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mf\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdropna\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     44\u001b[0m \u001b[1;32mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnew_df\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'clust_inds'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;36m10\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
        "\u001b[1;32m<ipython-input-71-e4023336647c>\u001b[0m in \u001b[0;36msort_tms_byClust\u001b[1;34m(df, clusts)\u001b[0m\n\u001b[0;32m     18\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0msort_tms_byClust\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdf\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mclusts\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     19\u001b[0m     \u001b[0mclust_tms\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m[\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0mc\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mclusts\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 20\u001b[1;33m     \u001b[0mtms_clean\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdf\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtimes\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdropna\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     21\u001b[0m     \u001b[1;32mfor\u001b[0m \u001b[0mt\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mtms_clean\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     22\u001b[0m         \u001b[0mt_clust\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0massignTms\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mclusts\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mtms_clean\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mt\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m-\u001b[0m\u001b[0mtms_clean\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mt\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
        "\u001b[1;32m/home/acs/anaconda/lib/python2.7/site-packages/pandas/core/generic.pyc\u001b[0m in \u001b[0;36m__getattr__\u001b[1;34m(self, name)\u001b[0m\n\u001b[0;32m   1841\u001b[0m                 \u001b[1;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mname\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1842\u001b[0m             raise AttributeError(\"'%s' object has no attribute '%s'\" %\n\u001b[1;32m-> 1843\u001b[1;33m                                  (type(self).__name__, name))\n\u001b[0m\u001b[0;32m   1844\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1845\u001b[0m     \u001b[1;32mdef\u001b[0m \u001b[0m__setattr__\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mname\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mvalue\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
        "\u001b[1;31mAttributeError\u001b[0m: 'DataFrame' object has no attribute 'times'"
       ]
      }
     ],
     "prompt_number": 71
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Add contiguous times together to calculate %-ages\n",
      "# Use 2-s as the period of silence (??) 'bouts'\n",
      "def timeInClusters(clust_tms, thresh=2000.):\n",
      "    cluster_bouts = [ [] for c in clust_tms ]\n",
      "    for c in range(len(clust_tms)): # Each new cluster\n",
      "        on = False\n",
      "        for t in range(len(clust_tms[c])-1):\n",
      "            if clust_tms[c][t+1] - clust_tms[c][t] > thresh: # 2-s threshold\n",
      "                if on: # If this is a bout, end it\n",
      "                    cluster_bouts[c].append(clust_tms[c][t])\n",
      "                    on = False\n",
      "                # Else, ignore it (too sparse for tonic)\n",
      "            else: # Close enough to be a continuation or new bout\n",
      "                if on is False: # Not an active bout, so start it\n",
      "                    cluster_bouts[c].append(clust_tms[c][t])\n",
      "                    on = True\n",
      "                # Else, ignore it (continue the bout)\n",
      "        if on: # If a bout is active at the end, end it with\n",
      "            cluster_bouts[c].append(clust_tms[c][-1])\n",
      "    \n",
      "    print(cluster_bouts)\n",
      "    # Calculate time spent in each cluster (assumes unit is ms)\n",
      "    timeIn = [sum([cluster_bouts[c][2*i+1]-cluster_bouts[c][2*i]\n",
      "                   for i in range(len(cluster_bouts[c])/2)])\n",
      "              for c in range(len(cluster_bouts))]\n",
      "    percentIn = [i/max([max(cl) for cl in clust_tms]) for i in timeIn]\n",
      "    for t in timeIn: # Dependent on dT\n",
      "        print('Time (percent) spent in cluster %i: %.3f s (%.2f)'\n",
      "              %(timeIn.index(t), t/10000., percentIn[timeIn.index(t)])) \n",
      "        \n",
      "    return timeIn, cluster_bouts\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 19
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "tIn, cBouts = timeInClusters(clust_tms)\n",
      "\n",
      "# Show the times and durations of the bouts\n",
      "for b in range(len(cBouts[0])/2):\n",
      "    plt.plot([cBouts[0][b*2], cBouts[0][b*2+1]], [1,1], \n",
      "             lw=5, color='blue')\n",
      "for b in range(len(cBouts[1])/2):\n",
      "    plt.plot([cBouts[1][b*2], cBouts[1][b*2+1]], [2,2], \n",
      "             lw=5, color='red')\n",
      "plt.ylim([0,3])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[1131.3833, 7897.8500000000004, 215052.7769, 217071.5693, 264723.46629999997, 266720.61180000001, 297653.9179, 372733.74790000002], [1253.127, 15062.544400000001, 214233.2818, 220925.98259999999, 264988.45549999998, 299414.88650000002, 302252.71590000001, 305541.70480000001, 376057.62719999999, 509550.69689999998]]\n",
        "Time (percent) spent in cluster 0: 8.586 s (0.17)\n",
        "Time (percent) spent in cluster 1: 19.171 s (0.38)\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 20,
       "text": [
        "(0, 3)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAX4AAAD/CAYAAAD2Qb01AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f5bf6033d90>"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# This does a decent job of determining bouts\n",
      "# Will compare it to actual trace (see figure in notebook)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 21
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Burst vs tonic: features\n",
      "\n",
      "Last will be to assign every spike to either burst or tonic activity (or neither) so differences between spike types can be examined."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Group spikes from same spike type together\n",
      "type_tms = []\n",
      "for c in range(len(clust_tms)):\n",
      "    for t in clust_tms[c]:\n",
      "        type_tms.append([t, c]) # [spike tms, clust index]\n",
      "\n",
      "# Now group these together\n",
      "clust_id = []\n",
      "for i in range(f.shape[0]):\n",
      "    if f.iloc[i].times in [k[0] for k in type_tms]:\n",
      "        clust_id.append(type_tms[[k[0] for k in type_tms].index(f.iloc[i].times)][1])\n",
      "    else: # No matching spike found -- this happens w/ isolated spks\n",
      "        clust_id.append(np.nan)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 22
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print(len(f), len(clust_id))\n",
      "# Now we have an index for each spike type\n",
      "# Add this to the data frame for easier reference\n",
      "f['clust_ind'] = clust_id"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(1904, 1904)\n"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.mean(f[f['clust_ind'] == 0]['maxV'])\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 24,
       "text": [
        "-18.81371224299064"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Show some sample features\n",
      "def showVs(df, feat1, feat2):\n",
      "    colors = ['blue', 'red', 'green', 'coral']\n",
      "    for u in range(len(cBouts)):\n",
      "        plt.plot(f[f['clust_ind'] == u][feat1],\n",
      "                 f[f['clust_ind'] == u][feat2], 'o', color=colors[u],\n",
      "                 alpha=0.6, markeredgecolor='none')\n",
      "        plt.xlabel(feat1)\n",
      "        plt.ylabel(feat2)\n",
      "\n",
      "# Test it out\n",
      "showVs(f, 'postMinV', 'preMinV')\n",
      "# Actually, the Peirce criterion wouldn't help in this case\n",
      "#   since the outlier is (very) near the best fit"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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QDuFKVq0yDCTNSPYQavX0wKJFI72EffeFzk44+mhciU7STNe2gVAuhxEiCDnQ10f8H8I8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\nJI3h/wEEzp6+PZgKgAAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f5c3421bfd0>"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Instead of guessing, let's find out which variables contribute to most between-cluster and overall variability. Overall variability is determined by eigendecomposition (or singular value decomposition).\n",
      "\n",
      "*Discriminability (sensitivity) index*\n",
      "$d' = (\\mu_A - \\mu_B) / {\\sqrt{1/2(\\sigma_A^2 + \\sigma_B^2)}}$\n",
      "\n",
      "Typically used for signal/noise but we can use it for our purposes.\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def discrim(a, b):\n",
      "    return (np.mean(a)-np.mean(b))/ \\\n",
      "           np.sqrt(0.5*(np.var(a)**2 + np.var(b)**2))\n",
      "\n",
      "# Check discriminability between all variables\n",
      "checks = ['maxV', 'maxDerivV', 'maxDerivdV', 'minDerivV',\n",
      "          'minDerivdV', 'preMinV', 'postMinV', 'preMaxCurveV',\n",
      "          'preMaxCurveK', 'postMaxCurveV', 'postMaxCurveK',\n",
      "          'height', 'repolarizationV', 'intervals', 'frequencies']\n",
      "\n",
      "def a_and_b(f, feat):\n",
      "    return f[f['clust_ind'] == 0][feat], f[f['clust_ind'] == 1][feat]\n",
      "\n",
      "discs = []\n",
      "for ch in checks:\n",
      "    a, b = a_and_b(f, ch)\n",
      "    discs.append(discrim(a,b))\n",
      "\n",
      "# These are the most sensitive factors\n",
      "print('These are the most sensitive factors: ')\n",
      "abdiscs = [abs(i) for i in discs]\n",
      "for u in range(len(abdiscs)):\n",
      "    if abdiscs[u] > np.mean(abdiscs)+np.std(abdiscs):\n",
      "        print(checks[u])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "These are the most sensitive factors: \n",
        "preMinV\n",
        "postMinV\n",
        "preMaxCurveV\n"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Find total variance contribution of each variable\n",
      "new_df = f.copy()\n",
      "for col in new_df.columns:\n",
      "    if col not in checks:\n",
      "        new_df = new_df.drop(col, 1)\n",
      "        print('Dropped %s' %col)\n",
      "new_df = new_df.dropna()\n",
      "\n",
      "mat = np.array([new_df[ch] for ch in checks])\n",
      "mat = mat.T\n",
      "print(mat.shape)\n",
      "# print([new_df[j][:4] for j in new_df.columns])\n",
      "u,s,v = np.linalg.svd(mat, full_matrices=False)\n",
      "# print('unitary matrices', np.shape(u)) # Unitary matrices\n",
      "print('singular values', np.shape(s),) # singular values\n",
      "# print('more unitary matrices', np.shape(v)) # unitary matrices\n",
      "# SVD does not converge in some cases"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Dropped times\n",
        "Dropped n1List\n",
        "Dropped n2List\n",
        "Dropped maxVtms\n",
        "Dropped maxVinds\n",
        "Dropped maxDerivtms\n",
        "Dropped maxDerivinds\n",
        "Dropped minDerivtms\n",
        "Dropped minDerivinds\n",
        "Dropped preMintms\n",
        "Dropped preMininds\n",
        "Dropped postMintms\n",
        "Dropped postMininds\n",
        "Dropped preMaxCurvetms\n",
        "Dropped preMaxCurveinds\n",
        "Dropped postMaxCurvetms\n",
        "Dropped postMaxCurveinds\n",
        "Dropped freq\n",
        "Dropped Unnamed: 33\n",
        "Dropped clust_ind\n",
        "(1634, 15)"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "('singular values', (15,))"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Explore variance\n",
      "print(new_df.columns)\n",
      "for g in range(len(new_df.columns)):\n",
      "    if s[g] > np.mean(s):\n",
      "        print(new_df.columns[g], s[g])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Index([u'maxV', u'maxDerivV', u'maxDerivdV', u'minDerivV', u'minDerivdV', u'preMinV', u'postMinV', u'preMaxCurveV', u'preMaxCurveK', u'postMaxCurveV', u'postMaxCurveK', u'height', u'repolarizationV', u'intervals', u'frequencies'], dtype='object')\n",
        "('maxV', 9110.2209507924526)\n",
        "('maxDerivV', 1402.0965719495464)\n"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# This suggests that maxV and maxDerivV are the most\n",
      "#   informative dimensions\n",
      "showVs(new_df, 'maxV', 'maxDerivV')\n",
      "# Should probably remove gross outliers; need some criteria"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x7f5bf5e036d0>"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Removing outliers: Peirce's criterion"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def peirce_dev(N, n, m): # From Wikipedia\n",
      "   \"\"\"\n",
      "   Name:     peirce_dev\n",
      "   Input:    - int, total number of observations (N)\n",
      "             - int, number of outliers to be removed (n)\n",
      "             - int, number of model unknowns (m)\n",
      "   Output:   float, squared error threshold (x2)\n",
      "   Features: Returns the squared threshold error deviation for outlier \n",
      "             identification using Peirce's criterion based on Gould's\n",
      "             methodology\n",
      "   \"\"\"\n",
      "   # Assign floats to input variables:\n",
      "   N = float(N)\n",
      "   n = float(n)\n",
      "   m = float(m)\n",
      "   #\n",
      "   # Check number of observations:\n",
      "   if N > 1:\n",
      "      # Calculate Q (Nth root of Gould's equation B):\n",
      "      Q = (n**(n/N)*(N - n)**((N - n)/N))/N\n",
      "      #\n",
      "      # Initialize R values (as floats)\n",
      "      Rnew = 1.0  \n",
      "      Rold = 0.0  # <- Necessary to prompt while loop\n",
      "      #\n",
      "      # Start iteration to converge on R:\n",
      "      while ( abs(Rnew - Rold) > (N*2.0e-16) ):\n",
      "         # Calculate Lamda \n",
      "         # (1/(N-n)th root of Gould's equation A'):\n",
      "         ldiv = Rnew**n\n",
      "         if ldiv == 0:\n",
      "            ldiv = 1.0e-6\n",
      "         Lamda = ((Q**N)/(ldiv))**(1.0/(N - n))\n",
      "         #\n",
      "         # Calculate x-squared (Gould's equation C):\n",
      "         x2 = 1.0 + (N - m - n)/n*(1.0 - Lamda**2.0)\n",
      "         #\n",
      "         # If x2 goes negative, return 0:\n",
      "         if x2 < 0:\n",
      "            x2 = 0.0\n",
      "            Rold = Rnew\n",
      "         else:\n",
      "            # Use x-squared to update R (Gould's equation D):\n",
      "            Rold = Rnew\n",
      "            Rnew = (np.exp((x2 - 1)/2.0)*\n",
      "                    scipy.special.erfc(np.sqrt(x2)/np.sqrt(2.0)))\n",
      "         #\n",
      "   else:\n",
      "      x2 = 0.0\n",
      "   return x2\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 30
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import scipy.special\n",
      "new_df = f.copy()\n",
      "for col in new_df.columns:\n",
      "    if col not in checks:\n",
      "        new_df = new_df.drop(col, 1)\n",
      "        print('Dropped %s' %col)\n",
      "new_df = new_df.dropna()\n",
      "thing1 = new_df['maxV']\n",
      "thing2 = new_df['maxDerivV']\n",
      "print(len(thing1), len(thing2), new_df.shape)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Dropped times\n",
        "Dropped n1List\n",
        "Dropped n2List\n",
        "Dropped maxVtms\n",
        "Dropped maxVinds\n",
        "Dropped maxDerivtms\n",
        "Dropped maxDerivinds\n",
        "Dropped minDerivtms\n",
        "Dropped minDerivinds\n",
        "Dropped preMintms\n",
        "Dropped preMininds\n",
        "Dropped postMintms\n",
        "Dropped postMininds\n",
        "Dropped preMaxCurvetms\n",
        "Dropped preMaxCurveinds\n",
        "Dropped postMaxCurvetms\n",
        "Dropped postMaxCurveinds\n",
        "Dropped freq\n",
        "Dropped Unnamed: 33\n",
        "Dropped clust_ind\n",
        "(1634, 1634, (1634, 15))\n"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# The problem is that using the Peirce criterion requires a fit\n",
      "#   and I don't want to run so many comparisons...\n",
      "\n",
      "\n",
      "# Linregress\n",
      "beta, alpha, r, p, serr = scipy.stats.linregress(thing1, thing2)\n",
      "res = [(alpha + thing1[i]*beta - thing2[i])**2 \n",
      "       for i in range(len(thing1))]\n",
      "print('Min res: %.3f, max res: %.3f, mean res: %.3f, median res:%.3f'\n",
      "      %(min(res), max(res), np.mean(res), np.median(res)))\n",
      "print('Sum res: %.3f' %sum(res))\n",
      "\n",
      "plt.plot(thing1, thing2, 'o', color='r', markeredgecolor='none', \n",
      "         alpha=0.5)\n",
      "plt.plot(thing1, [alpha+i*beta for i in thing1], 'b', lw=3)\n",
      "\n",
      "# Remove points beyond a threshold\n",
      "# I think there's an easier way to do this if res ~ (dist-mean)\n",
      "mean_res = [(np.mean(thing1)-i)**2 for i in thing1]\n",
      "med_res = [(np.median(thing1)-i)**2 for i in thing1]\n",
      "print(len(med_res))\n",
      "med_res_ix = [i for i in med_res]\n",
      "med_res.sort(reverse=True)\n",
      "print(med_res[:10])\n",
      "\n",
      "# Try removing a few points and see what that does to the mean and std\n",
      "thing_copy = [u for u in thing1]\n",
      "tracks = []\n",
      "for i in range(10):\n",
      "    print('%i th iteration. Mean: %.3f, median: %.3f, std: %.3f'\n",
      "          %(i, np.mean(thing_copy), np.median(thing_copy), \n",
      "            np.std(thing_copy)))\n",
      "    rm = thing1[med_res_ix.index(med_res[i])]\n",
      "    thing_copy.pop(thing_copy.index(rm))\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Min res: 0.008, max res: 14198.797, mean res: 16.195, median res:3.361\n",
        "Sum res: 26462.909\n",
        "1634"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "[16979.301811622503, 15736.686371402502, 15527.116281622497, 14474.8209388225, 52.586427722500019, 50.997451562500039, 48.834240422500066, 47.912007422500039, 47.525167822500059, 46.297818062499992]\n",
        "0 th iteration. Mean: -20.486, median: -19.208, std: 6.819\n",
        "1 th iteration. Mean: -20.567, median: -19.208, std: 5.994\n",
        "2 th iteration. Mean: -20.645, median: -19.208, std: 5.107\n",
        "3 th iteration. Mean: -20.722, median: -19.208, std: 4.044\n",
        "4 th iteration. Mean: -20.797, median: -19.209, std: 2.693\n",
        "5 th iteration. Mean: -20.793, median: -19.208, std: 2.691\n",
        "6 th iteration. Mean: -20.790, median: -19.208, std: 2.688\n",
        "7 th iteration. Mean: -20.786, median: -19.208, std: 2.685\n",
        "8 th iteration. Mean: -20.783, median: -19.208, std: 2.683\n",
        "9 th iteration. Mean: -20.780, median: -19.208, std: 2.681\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x7f5bf5f2aad0>"
       ]
      }
     ],
     "prompt_number": 32
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Once the largest delta std occurs, remove all points beyond that\n",
      "def outlier(arr, as_nan=True, thresh=0.05):\n",
      "    \"\"\"\n",
      "    Return nan instead (more robust) of nothing (loss of index parity).\n",
      "    Median is more robust than mean.\n",
      "    \"\"\"\n",
      "    med_res = [(np.median(arr)-i)**2 for i in arr] \n",
      "    med_res_ix = [u for u in med_res] # Create index\n",
      "    arr_copy = [u for u in arr] # The copy will be edited first\n",
      "    stds = []\n",
      "    med_res.sort(reverse=True) # Largest to smallest\n",
      "    # print(med_res[:10])\n",
      "    numPts = int(len(arr)*thresh)\n",
      "    print('Testing largest %i residuals' %numPts)\n",
      "    \n",
      "    # Pretend to remove 10% of points\n",
      "    for i in range(int(len(arr)*.1)):\n",
      "        stds.append(np.std(arr_copy))\n",
      "        rm_ix = med_res_ix.index(med_res[i])\n",
      "        try:\n",
      "            rm = arr[rm_ix]\n",
      "        except:\n",
      "            print('tried to remove ix %i but arr is len %i'\n",
      "                  %(rm_ix, len(arr)))\n",
      "        try:      \n",
      "            arr_copy.pop(arr_copy.index(rm))\n",
      "        except:\n",
      "            print('tried to remove %f but not in arr_copy' %rm)\n",
      "    \n",
      "    # Find the greatest d(std)\n",
      "    dstd = np.diff(stds)\n",
      "    dstd = [abs(i) for i in dstd]\n",
      "    rm_to = list(dstd).index(max(dstd))+1 # len(diff) = len(arr)-1\n",
      "    print('Mean d(std): %.3f, removing all above %.3f (%i pts)'\n",
      "          %(np.mean(dstd), dstd[rm_to-1], rm_to))\n",
      "    \n",
      "    for i in range(rm_to):\n",
      "        arr[med_res_ix.index(med_res[i])] = np.nan\n",
      "    return arr\n",
      "    \n",
      "    "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 52
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "#print(max([(np.median(thing1)-i)**2 for i in thing1]))\n",
      "new_thing1 = outlier(thing1.dropna())\n",
      "#print(min(thing1), np.median(thing1))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Testing largest 163 residuals\n",
        "Mean d(std): 0.028, removing all above 1.351 (4 pts)\n"
       ]
      }
     ],
     "prompt_number": 34
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.subplot(1,2,1)\n",
      "plt.plot(np.random.random(len(thing1)), thing1, 'o', color='blue',\n",
      "         markeredgecolor='none', alpha=0.4)\n",
      "plt.title('With outliers')\n",
      "plt.subplot(1,2,2)\n",
      "plt.plot(np.random.random(len(new_thing1)), new_thing1, 'o',\n",
      "         color='red', markeredgecolor='none', alpha=0.4)\n",
      "plt.title('Without outliers')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 35,
       "text": [
        "<matplotlib.text.Text at 0x7f5bf5d7b590>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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rMqb64mGINFzLctMmtn3uHGPKJc0AQaesG+ERzqQEosMoFUO/tGR162VZ61g3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\nYRiGYRiGYRhGvfgftpWQFK5Fjx0AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f5bf629a590>"
       ]
      }
     ],
     "prompt_number": 35
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "showVs(new_df, 'maxV', 'maxDerivV')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x7f5bf5f05650>"
       ]
      }
     ],
     "prompt_number": 36
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Let's get rid of all the outliers in the checks list\n",
      "newer_df = new_df.copy()\n",
      "for col in checks:\n",
      "    print('Removing outliers for %s ...' %col)\n",
      "    newer_df[col] = outlier(newer_df[col])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Removing outliers for maxV ...\n",
        "Testing largest 81 residuals"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Mean d(std): 0.028, removing all above 1.351 (4 pts)"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Removing outliers for maxDerivV ...\n",
        "Testing largest 81 residuals"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Mean d(std): 0.013, removing all above 0.981 (1 pts)\n",
        "Removing outliers for maxDerivdV ..."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Testing largest 81 residuals"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Mean d(std): 0.015, removing all above 0.952 (2 pts)\n",
        "Removing outliers for minDerivV ...\n",
        "Testing largest 81 residuals"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Mean d(std): 0.020, removing all above 1.126 (2 pts)"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Removing outliers for minDerivdV ...\n",
        "Testing largest 81 residuals"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Mean d(std): 0.007, removing all above 0.896 (1 pts)\n",
        "Removing outliers for preMinV ...\n",
        "Testing largest 81 residuals"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Mean d(std): 0.004, removing all above 0.318 (1 pts)\n",
        "Removing outliers for postMinV ..."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Testing largest 81 residuals"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Mean d(std): 0.004, removing all above 0.318 (1 pts)\n",
        "Removing outliers for preMaxCurveV ...\n",
        "Testing largest 81 residuals"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Mean d(std): 0.005, removing all above 0.361 (1 pts)"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Removing outliers for preMaxCurveK ...\n",
        "Testing largest 81 residuals"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Mean d(std): 0.018, removing all above 0.925 (2 pts)\n",
        "Removing outliers for postMaxCurveV ...\n",
        "Testing largest 81 residuals"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Mean d(std): 0.018, removing all above 1.319 (2 pts)\n",
        "Removing outliers for postMaxCurveK ...\n",
        "Testing largest 81 residuals"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Mean d(std): 0.012, removing all above 0.707 (1 pts)\n",
        "Removing outliers for height ...\n",
        "Testing largest 81 residuals"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Mean d(std): 0.031, removing all above 1.461 (3 pts)\n",
        "Removing outliers for repolarizationV ...\n",
        "Testing largest 81 residuals"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "tried to remove -9.207200 but not in arr_copy\n",
        "tried to remove -9.048500 but not in arr_copy\n",
        "tried to remove -9.036300 but not in arr_copy\n",
        "tried to remove -9.036300 but not in arr_copy\n",
        "tried to remove -9.036300 but not in arr_copy\n",
        "tried to remove -8.996600 but not in arr_copy\n",
        "tried to remove -8.960000 but not in arr_copy\n",
        "tried to remove -6.338500 but not in arr_copy\n",
        "Mean d(std): 0.025, removing all above 1.565 (2 pts)\n",
        "Removing outliers for intervals ...\n",
        "Testing largest 81 residuals"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Mean d(std): 0.096, removing all above 0.329 (1 pts)\n",
        "Removing outliers for frequencies ...\n",
        "Testing largest 81 residuals"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Mean d(std): 0.096, removing all above 0.329 (1 pts)\n"
       ]
      }
     ],
     "prompt_number": 53
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# We can see that in general very few points are removed\n",
      "# Make a new df without the nans (returned from outliers)\n",
      "print(newer_df.shape)\n",
      "newest_df = newer_df.dropna()\n",
      "print(newest_df.shape)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(1634, 15)\n",
        "(1629, 15)\n"
       ]
      }
     ],
     "prompt_number": 54
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 54
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Can also try PCA\n",
      "from sklearn.decomposition import RandomizedPCA\n",
      "pca = RandomizedPCA(n_components=mat.shape[1])\n",
      "pca.fit(mat)\n",
      "expvar = pca.explained_variance_ratio_\n",
      "for g in range(len(new_df.columns)):\n",
      "    if expvar[g] > np.median(expvar):\n",
      "        print(new_df.columns[g], expvar[g])\n",
      "\n",
      "# PCA agreed that the dimension of most variability are maxV and maxDerivV"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "('maxV', 0.98156862392118094)\n",
        "('maxDerivV', 0.01337453063723807)\n",
        "('maxDerivdV', 0.0033491095298337136)\n",
        "('minDerivV', 0.0010872437716173498)\n",
        "('minDerivdV', 0.00049859440333851611)\n",
        "('preMinV', 6.868202925442514e-05)\n",
        "('postMinV', 2.7881099228157944e-05)\n"
       ]
      }
     ],
     "prompt_number": 48
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 48
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Putting it all together\n",
      "\n",
      "Run a cell from start to finish using just the .csv file.\n",
      "\n",
      "*Data flow: *\n",
      "1. load csv, dropna()\n",
      "2. identify number and location of peaks (savitsky-golay)\n",
      "3. run MCMC to get intervals\n",
      "4. reverse assign rows of df to each cluster type\n",
      "5. calculate bout on/off times and percentages\n",
      "6. remove outliers and characterize clusters"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# 0. imports\n",
      "%matplotlib inline\n",
      "import numpy as np\n",
      "import matplotlib.pyplot as plt\n",
      "import pandas as pd\n",
      "import pymc as pm\n",
      "import statsmodels.api as sm\n",
      "\n",
      "# 1. Load CSV and dropna()\n",
      "F = pd.read_csv('/home/acs/data/maria/15305000_props.csv')\n",
      "# Clean -- keep only the checks columns\n",
      "for col in F.columns:\n",
      "    if col not in checks:\n",
      "        F = F.drop(col, 1)\n",
      "F = F.dropna()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 58
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# 2. Identify number of location of peaks\n",
      "plt.subplot(1,2,1)\n",
      "plt.hist(F['intervals'], bins=50, histtype='stepfilled', alpha=0.6)\n",
      "plt.title('Raw Intervals')\n",
      "int_hist, bin_es = np.histogram(F['intervals'], bins=50)\n",
      "bin_cents = (bin_es[:-1]+bin_es[1:])*.5\n",
      "int_hat = savitzky_golay(int_hist, 11, 3)\n",
      "\n",
      "pks = whichPeaks(int_hat)\n",
      "print([bin_cents[p[0]] for p in pks])\n",
      "plt.subplot(1,2,2)\n",
      "plt.plot(bin_cents, int_hat)\n",
      "plt.title('Smoothed peaks')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[35.238303000000002]\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 68,
       "text": [
        "<matplotlib.text.Text at 0x7f5bcbc8cf90>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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L1+uN4O2VEvn5+eTn59s55AHr3+ZIgb8H+FvA447L7XnzYP9+OPPMuLxdQhky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\n1QAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f5bcbd5a110>"
       ]
      }
     ],
     "prompt_number": 68
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "bin_cents[pks[0][0]]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 62,
       "text": [
        "35.238303000000002"
       ]
      }
     ],
     "prompt_number": 62
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# 3. Run MCMC\n",
      "# Don't need a p assignment variable\n",
      "tau = 1. / pm.Uniform('stds', 0, 100)**2\n",
      "center = pm.Normal('center', bin_cents[pks[0][0]], 0.0025)\n",
      "observations = pm.Normal('obs', value=int_hist, observed=True)\n",
      "mcmc = pm.MCMC([tau, center, observations])\n",
      "mcmc.sample(50000)\n",
      "\n",
      "center_trace = mcmc.trace(\"center\")[:]\n",
      "plt.hist(center_trace, bins=50, histtype='stepfilled',\n",
      "         color='blue', alpha=0.7)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-------          20%                  ] 10484 of 50000 complete in 0.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---------------- 42%                  ] 21222 of 50000 complete in 1.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------63%----              ] 31750 of 50000 complete in 1.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------84%------------      ] 42285 of 50000 complete in 2.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------100%-----------------] 50000 of 50000 complete in 2.4 sec"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 67,
       "text": [
        "(array([  7.00000000e+00,   4.00000000e+00,   8.00000000e+00,\n",
        "          1.20000000e+01,   1.50000000e+01,   3.80000000e+01,\n",
        "          6.30000000e+01,   7.90000000e+01,   1.36000000e+02,\n",
        "          1.66000000e+02,   2.71000000e+02,   3.86000000e+02,\n",
        "          5.01000000e+02,   6.50000000e+02,   9.08000000e+02,\n",
        "          1.20300000e+03,   1.44700000e+03,   1.70200000e+03,\n",
        "          2.04500000e+03,   2.25700000e+03,   2.48800000e+03,\n",
        "          2.88400000e+03,   3.12100000e+03,   3.10000000e+03,\n",
        "          3.14900000e+03,   3.07200000e+03,   3.09500000e+03,\n",
        "          2.77600000e+03,   2.59800000e+03,   2.28100000e+03,\n",
        "          1.99600000e+03,   1.73200000e+03,   1.40600000e+03,\n",
        "          1.18800000e+03,   8.46000000e+02,   7.10000000e+02,\n",
        "          4.75000000e+02,   3.50000000e+02,   2.85000000e+02,\n",
        "          2.02000000e+02,   1.18000000e+02,   9.00000000e+01,\n",
        "          4.20000000e+01,   3.50000000e+01,   3.00000000e+01,\n",
        "          1.50000000e+01,   8.00000000e+00,   6.00000000e+00,\n",
        "          1.00000000e+00,   3.00000000e+00]),\n",
        " array([ -42.6430077 ,  -39.4623786 ,  -36.2817495 ,  -33.10112041,\n",
        "         -29.92049131,  -26.73986222,  -23.55923312,  -20.37860403,\n",
        "         -17.19797493,  -14.01734583,  -10.83671674,   -7.65608764,\n",
        "          -4.47545855,   -1.29482945,    1.88579965,    5.06642874,\n",
        "           8.24705784,   11.42768693,   14.60831603,   17.78894513,\n",
        "          20.96957422,   24.15020332,   27.33083241,   30.51146151,\n",
        "          33.6920906 ,   36.8727197 ,   40.0533488 ,   43.23397789,\n",
        "          46.41460699,   49.59523608,   52.77586518,   55.95649428,\n",
        "          59.13712337,   62.31775247,   65.49838156,   68.67901066,\n",
        "          71.85963975,   75.04026885,   78.22089795,   81.40152704,\n",
        "          84.58215614,   87.76278523,   90.94341433,   94.12404343,\n",
        "          97.30467252,  100.48530162,  103.66593071,  106.84655981,\n",
        "         110.0271889 ,  113.207818  ,  116.3884471 ]),\n",
        " <a list of 1 Patch objects>)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x7f5bcbf36790>"
       ]
      }
     ],
     "prompt_number": 67
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# 4. Assign clusters\n",
      "# Looks like all spikes are part of this cluster\n",
      "clusts = [center_trace] # Could be several, just one here\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Explore the clusters, as a function\n",
      "\"\"\"\n",
      "def exploreTrace(mcmc):\n",
      "    plt.figure(figsize=(11., 4.))\n",
      "    std_trace = mcmc.trace('stds')[:]\n",
      "    \n",
      "    things = [mcmc.trace('centers', chain=0), std_trace[:,0],\n",
      "              mcmc.trace('centers', chain=1), std_trace[:,1]]\n",
      "    cols = ['red', 'red', 'blue', 'blue']\n",
      "    \n",
      "    for i in range(4):\n",
      "        plt.subplot(2, 2, i+1)\n",
      "        plt.hist(thing[i], color=cols[i], bins=30,\n",
      "                 histtype='stepfilled')\n",
      "    plt.tight_layout()\n",
      "    return\n",
      "\"\"\"\n",
      "\n",
      "#plt.hist(mcmc.trace('centers', chain=0))\n",
      "\n",
      "center_trace = mcmc.trace(\"centers\")[:]\n",
      "#center1_trace = mcmc.trace(\"centers\", chain=1)[:]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 20
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "center_trace.shape\n",
      "print(np.mean(center0_trace[:,0]), np.mean(center0_trace[:,1]))\n",
      "plt.hist(center0_trace[:,0], bins=30, color='blue', \n",
      "         histtype='stepfilled')\n",
      "# print(np.mean(center1_trace[:,0]), np.mean(center1_trace[:,1]))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(21.001844797260585, 49.603721968953998)\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 22,
       "text": [
        "(array([  1.00000000e+00,   0.00000000e+00,   0.00000000e+00,\n",
        "         0.00000000e+00,   3.12000000e+02,   4.94000000e+02,\n",
        "         2.82600000e+03,   9.32300000e+03,   1.83250000e+04,\n",
        "         1.39580000e+04,   4.11500000e+03,   5.96000000e+02,\n",
        "         2.80000000e+01,   0.00000000e+00,   0.00000000e+00,\n",
        "         0.00000000e+00,   1.00000000e+00,   0.00000000e+00,\n",
        "         7.00000000e+00,   3.00000000e+00,   0.00000000e+00,\n",
        "         0.00000000e+00,   0.00000000e+00,   0.00000000e+00,\n",
        "         0.00000000e+00,   0.00000000e+00,   0.00000000e+00,\n",
        "         0.00000000e+00,   0.00000000e+00,   1.10000000e+01]),\n",
        " array([  7.47607066,   9.04344155,  10.61081245,  12.17818334,\n",
        "        13.74555424,  15.31292513,  16.88029602,  18.44766692,\n",
        "        20.01503781,  21.5824087 ,  23.1497796 ,  24.71715049,\n",
        "        26.28452139,  27.85189228,  29.41926317,  30.98663407,\n",
        "        32.55400496,  34.12137586,  35.68874675,  37.25611764,\n",
        "        38.82348854,  40.39085943,  41.95823032,  43.52560122,\n",
        "        45.09297211,  46.66034301,  48.2277139 ,  49.79508479,\n",
        "        51.36245569,  52.92982658,  54.49719747]),\n",
        " <a list of 1 Patch objects>)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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BAIysIV8ptLa2avny5ZKknp4ePf3001q4cKHy8vJUUlKiQCAgj8ejnTt3SpJ8Pp9KSkrk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\ngg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f525a792750>"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.hist(center0_trace[:,1], bins=30, color='red',\n",
      "         histtype='stepfilled')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 23,
       "text": [
        "(array([  1.71000000e+02,   4.35000000e+02,   1.31580000e+04,\n",
        "         3.04220000e+04,   5.75400000e+03,   4.00000000e+01,\n",
        "         0.00000000e+00,   0.00000000e+00,   0.00000000e+00,\n",
        "         0.00000000e+00,   6.00000000e+00,   0.00000000e+00,\n",
        "         0.00000000e+00,   0.00000000e+00,   0.00000000e+00,\n",
        "         5.00000000e+00,   0.00000000e+00,   0.00000000e+00,\n",
        "         0.00000000e+00,   1.00000000e+00,   0.00000000e+00,\n",
        "         0.00000000e+00,   0.00000000e+00,   1.00000000e+00,\n",
        "         0.00000000e+00,   0.00000000e+00,   0.00000000e+00,\n",
        "         0.00000000e+00,   0.00000000e+00,   7.00000000e+00]),\n",
        " array([  14.10181968,   24.76491358,   35.42800748,   46.09110138,\n",
        "         56.75419528,   67.41728919,   78.08038309,   88.74347699,\n",
        "         99.40657089,  110.06966479,  120.7327587 ,  131.3958526 ,\n",
        "        142.0589465 ,  152.7220404 ,  163.3851343 ,  174.04822821,\n",
        "        184.71132211,  195.37441601,  206.03750991,  216.70060381,\n",
        "        227.36369772,  238.02679162,  248.68988552,  259.35297942,\n",
        "        270.01607333,  280.67916723,  291.34226113,  302.00535503,\n",
        "        312.66844893,  323.33154284,  333.99463674]),\n",
        " <a list of 1 Patch objects>)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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88MPLlhuGMafGNlG9s20sVVVV9PT00NXVxeLFi9m2bds1150ttZ85c4bCwkJ2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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f525a93cd50>"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "list(hist).index(hist.max())"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 28,
       "text": [
        "7"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.diff(hist)[:10]\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 29,
       "text": [
        "array([  -2,    0,    0,    0,   13,  224,  241, -337, -124,  -11])"
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    },
    {
     "cell_type": "code",
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   ],
   "metadata": {}
  }
 ]
}