notebooks/pdLSR_demo.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# pdLSR: Pandas-aware least squares regression\n",
    "\n",
    "*This notebook first appeared as a [blog](https://modernscientist.com/posts/2016/2016-07-17-pdLSR_pandas_aware_least_squares_regression/) post on [themodernscientist](https://modernscientist.com).  \n",
    "License: [BSD](http://opensource.org/licenses/BSD-3-Clause) (C) 2016, Michelle L. Gill. Feel free to use, distribute, and modify with the above attribution.*"
   ]
  },
  {
   "cell_type": "code",
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   "source": [
    "from __future__ import print_function\n",
    "import os\n",
    "import inspect\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "pd.set_option('display.float_format', lambda x: '%.2f' % x)\n",
    "np.set_printoptions(precision=2)\n",
    "\n",
    "import pdLSR\n",
    "from pdLSR import exponential_decay\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "sns.set_context('talk')\n",
    "sns.set_palette('dark')\n",
    "sns.set_style('ticks')\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
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    "ExecuteTime": {
     "end_time": "2016-07-24T18:11:03.825193",
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   "source": [
    "# This will download the demonstration data for those who want to run the demo\n",
    "import requests\n",
    "\n",
    "r = requests.get('https://raw.githubusercontent.com/mlgill/pdLSR/master/pdLSR/demo/GCN4_twofield.tsv')\n",
    "\n",
    "with open('GCN4_twofield.tsv', 'w') as fh:\n",
    "    fh.write(r.text)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Overview\n",
    "\n",
    "`pdLSR` is a library for performing least squares minimization. It attempts to seamlessly incorporate this task in a Pandas-focused workflow. Input data are expected in dataframes, and multiple regressions can be performed using functionality similar to Pandas `groupby`. Results are returned as grouped dataframes and include best-fit parameters, statistics, residuals, and more. The results can be easily visualized using [`seaborn`](https://github.com/mwaskom/seaborn).\n",
    "\n",
    "`pdLSR` currently utilizes [`lmfit`](https://github.com/lmfit/lmfit-py), a flexible and powerful library for least squares minimization, which in turn, makes use of `scipy.optimize.leastsq`. I began using `lmfit` because it is one of the few libraries that supports non-linear least squares regression, which is commonly used in the natural sciences. I also like the flexibility it offers for testing different modeling scenarios and the variety of assessment statistics it provides. However, I found myself writing many `for` loops to perform regressions on groups of data and aggregate the resulting output. Simplification of this task was my inspiration for writing `pdLSR`.\n",
    "\n",
    "`pdLSR` is related to libraries such as [`statsmodels`](http://statsmodels.sourceforge.net) and [`scikit-learn`](http://scikit-learn.org/stable/) that provide linear regression functions that operate on dataframes. However, these libraries don't support grouping operations on dataframes. Supporting `statsmodels` and `scikit-learn` is under consideration. (And pull requests adding this functionality would be welcome.)\n",
    "\n",
    "Some additional 'niceties' associated with the input of parameters and equations have also been incorporated. `pdLSR` also utilizes multithreading for the calculation of confidence intervals, as this process is time consuming when there are more than a few groups."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Minimization setup\n",
    "\n",
    "To demonstrate how to use `pdLSR`, I will be using some sample scientific data. This data is nuclear magnetic resonance (NMR) data acquired at two different magnetic field strengths (14.1 and 18.8 T) on the DNA-binding region of a transcription factor called GCN4. \n",
    "\n",
    "There are six amino acids in the enclosed data set (numbered 51 - 56), so using amino acid residue (`resi`) and magnetic field (`field`) as the `groupby` columns means we will need to perform twelve regressions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-07-24T18:11:04.901349",
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    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "resi\tfield\ttime\tintensity\r\n",
      "51\t14.1\t0.004\t1624.219428\r\n",
      "51\t14.1\t0.008\t1491.46728\r\n",
      "51\t14.1\t0.024\t1022.717456\r\n",
      "51\t14.1\t0.064\t448.038543\r\n",
      "51\t14.1\t0.096\t270.116745\r\n",
      "51\t14.1\t0.144\t148.671651\r\n",
      "51\t14.1\t0.208\t103.322608\r\n",
      "52\t14.1\t0.004\t1614.38584\r\n",
      "52\t14.1\t0.008\t1500.47205\r\n"
     ]
    }
   ],
   "source": [
    "data = pd.read_csv('GCN4_twofield.tsv', sep='\\t')\n",
    "! head GCN4_twofield.tsv"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will be analyzing this data to determine the rate of exponential decay as a function of time for every amino acid residue at each of the two magnetic field strengths. The equation looks like this:\n",
    "\n",
    "$I_{(t)} = I_{(0)} \\space e^{(-R * t)}$  \n",
    "\n",
    "where $I_{(0)}$ is the initial intensity, $I_{(t)}$ is the intensity at time $t$, and $R$ is the exponential decay rate. We have $I_{(t)}$ and $t$ from the data above and will use NLS to determine $I_{(0)}$ and $R$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Regression and prediction\n",
    "\n",
    "Parameters for `pdLSR` are entered as a list of dictionaries with the format being similar to that used by [`lmfit`](https://lmfit.github.io/lmfit-py/parameters.html).\n",
    "\n",
    "Performing the regression is quite simple--just call the class `pdLSR` with input parameters set. The `fit` method performs the regression and `predict` calculates a best-fit line at higher resolution for plotting."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
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     "end_time": "2016-07-24T18:11:12.136577",
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   "source": [
    "params = [{'name':'inten', \n",
    "           'value':np.asarray(data.groupby(['resi', 'field']).intensity.max()), \n",
    "           'vary':True},\n",
    "          {'name':'rate', \n",
    "           'value':20.0, \n",
    "           'vary':True}]\n",
    "\n",
    "minimizer_kwargs = {'params':params,\n",
    "                    'method':'leastsq',\n",
    "                    'sigma':0.95,\n",
    "                    'threads':None}\n",
    "\n",
    "fit_data = pdLSR.pdLSR(data, exponential_decay, \n",
    "                       groupby=['resi', 'field'],\n",
    "                       xname='time', yname='intensity',\n",
    "                       minimizer='lmfit',\n",
    "                       minimizer_kwargs=minimizer_kwargs)\n",
    "fit_data.fit()\n",
    "fit_data.predict()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Results\n",
    "\n",
    "From these simple commands, five output tables are created:\n",
    "\n",
    "* **data** for the input data, calculated data, and residuals\n",
    "* **results** that contains the best-fit parameters and estimation of their error\n",
    "* **stats** for statistics related to the regression, such as chi-squared and AIC\n",
    "* **model** that contains a best-fit line created by the `predict` method\n",
    "* **covar** that contains the covariance matrices"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's take a look at a couple of these tables. The **results** table contains best-fit parameters, their standard errors, and confidence intervals."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-07-24T18:11:13.813646",
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       "  <thead>\n",
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       "      <th></th>\n",
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       "      <td>21.64</td>\n",
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       "      <td>22.39</td>\n",
       "      <td>24.36</td>\n",
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       "      <td>23889.26</td>\n",
       "      <td>232.87</td>\n",
       "      <td>23351.24</td>\n",
       "      <td>24329.26</td>\n",
       "      <td>29.96</td>\n",
       "      <td>0.79</td>\n",
       "      <td>28.27</td>\n",
       "      <td>31.59</td>\n",
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       "              inten                             rate                   \\\n",
       "              value stderr ci0.95_lo ci0.95_hi value stderr ci0.95_lo   \n",
       "resi field                                                              \n",
       "51   14.10  1714.80  37.87   1656.39   1833.26 19.65   1.02     17.91   \n",
       "     18.80 24122.68 689.03  22988.09  25953.74 21.64   1.58     18.83   \n",
       "52   14.10  1778.90  17.87   1746.80   1814.00 23.35   0.49     22.39   \n",
       "     18.80 23889.26 232.87  23351.24  24329.26 29.96   0.79     28.27   \n",
       "\n",
       "                      \n",
       "           ci0.95_hi  \n",
       "resi field            \n",
       "51   14.10     22.46  \n",
       "     18.80     25.55  \n",
       "52   14.10     24.36  \n",
       "     18.80     31.59  "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fit_data.results.head(n=4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The **stats** table contains the following statistics for each of the regression groups:\n",
    "\n",
    "* Number of observations (`nobs`)\n",
    "* Number of fit parameters (`npar`)\n",
    "* Degrees of freedom (`dof`)\n",
    "* Chi-squared (`chisqr`)\n",
    "* Reduced chi-squared (`redchi`)\n",
    "* Akaike information criterion (`aic`)\n",
    "* Bayesian information criterion (`bic`)"
   ]
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       "            nobs  npar  dof           chisqr         r_chisqr    aic    bic\n",
       "resi field                                                                 \n",
       "51   14.10     7     2    5      46189329.09       9237865.82 116.27 116.16\n",
       "     18.80     7     2    5 5181283778043.33 1036256755608.67 197.67 197.56\n",
       "52   14.10     7     2    5       2013267.84        402653.57  94.34  94.23\n",
       "     18.80     7     2    5  184908562051.39   36981712410.28 174.34 174.23"
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     "execution_count": 7,
     "metadata": {},
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   "source": [
    "fit_data.stats.head(n=4)"
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  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is also easy to access the covariance matrix for calculations."
   ]
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  {
   "cell_type": "code",
   "execution_count": 8,
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       "            row  col   covar\n",
       "resi field                  \n",
       "51   14.10    0    0 1434.41\n",
       "     14.10    0    1   25.19\n",
       "     14.10    1    0   25.19\n",
       "     14.10    1    1    1.04"
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     "metadata": {},
     "output_type": "execute_result"
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   "source": [
    "fit_data.covar.loc[(51, 14.1)]"
   ]
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  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
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    {
     "data": {
      "text/plain": [
       "array([[  1.43e+03,   2.52e+01],\n",
       "       [  2.52e+01,   1.04e+00]])"
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     "metadata": {},
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   ],
   "source": [
    "fit_data.pivot_covar().loc[(51, 14.1)].values"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualization\n",
    "\n",
    "The results can be visualized in facet plots with Seaborn. To make it easier to view the data, all intensities have been normalized.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-07-24T18:11:26.507388",
     "start_time": "2016-07-24T18:11:26.502624"
    },
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "fit_itensities = fit_data.results.loc[:,('inten','value')]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-07-24T18:11:27.225666",
     "start_time": "2016-07-24T18:11:27.213383"
    },
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "fit_data.data['intensity'] = fit_data.data.intensity.div(fit_itensities)\n",
    "fit_data.model['ycalc'] = fit_data.model.ycalc.div(fit_itensities)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-07-24T18:11:29.596605",
     "start_time": "2016-07-24T18:11:28.190262"
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   },
   "outputs": [
    {
     "data": {
      "image/png": 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Av4A/0zuec5tDE2zLiPqsxfLva7mdngoUKJBoeWxsLIMHD2bnzp389ddfbN++nblz5yZa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+cU5lfsZkDdOwaye/lTfPLGAKbP3k6HwfP48++TFdorLSyHSfcgm1N1/hUd0aElKadOlry+3R6s\nA0cTuO+Jhfz33+FMerST7L2qvSzqi6/O+Xfd1cREFg/oRdtnptDxX8/fsX1ubgHT3lvLms1nWfL1\nKDq0rvgeKVEtSe5VcylnTrN52nNkxl+g38w5BIb1rvA8tFotf61XeWvGFqysNLzzYm+G9Gsm2+Sq\nVz33IIvKSTt75qbX5fWBBOjQ2p9tS8cz58e9jJm6VPZeCWEkdfz8GLlqA/tnzWTflzPuuFfI3t6G\n2e8PYfpr/Rj06M989dM/sidJiGrAs2kzhi9fQ48332fN04+z6omxt715UFk0Gg33D2zO/tXP8J9n\nw/i/jzfSdei3rNl8RtYD1YQUyNVA6Wsz+rRtf9v2TRp68c/KZ/D2dKLdoK/ZHhlbleEJUWu4BjZg\n9PptnFi4gL+ffpz8a3f+AfrQ0Fbs/ONJ5v2yjzFTl8qZ7kJUAxqNhqbDHmT8wZO4BTeqdLcLKysr\nHhzcgkNrJ/HypB68+uF6Wvefy3eL9nPt2s3zio5NIXxkBLYN3yV8ZIRcncrMpECuBu6ZF0FAzzCs\nbGzwaNqMzLgLpEVH3XYaR0dbZr8/hNnv3cuoyb/x5mebKCgoNFHEQtRcrg2CGLNpJ4X5+Szu34uM\nuDtfsaJpQy92//kUbq4OdLx3Hv8cijdBpEKIu2Xr5ETPt99n7ObdxG5cz09d23L6j6VoK3ilCisr\nK0bdF8LhdZP58t3BrFinEtR9Jv/5ZCMJl3Q3GRo/bTnbImMpKChiW2Qs46ctr4qPJAwkBXI14N6w\nEQ+v28oLGflMOKwS+sbbLB6guzbrndzXX+HgmklEHownbGQEMedTTRCxEDWbrZMTQ35YiDJqNAvD\nuhqUi46Otsz7aCjvTuvD/U8uYvLrK0lJzb7jdEII8/No0pThy9cQ/uFn/DPjk0oXyhqNhr49GrEi\nYiw7/3iS9MxcWvWfyyPP/c7Ofedvartrv1wu0pykQK6G2j41kYFfzeevRx5i7+cf3zFB6/m5sGbB\nOEYNCaHL0G/5ednhm8bLYR0hKk6j0dD5+ZcY9M0P/PXIKA7Nm2tQ38LRw1pzYuNUrK01NOs9CyV8\nluSeENWARqOh0aB7Gbstkl7vfXxXhTLojizNeu9eonf+m/Yh9bCxvrkkC+0YaKzQRSVIgVxNNRw4\niHE7/iFq1Qr+GDGUa1eu3La9lZUVLzzdnfULH+WDWdsZPWUJcRfTATmsI8TdCO4/kDGbdnH4u69Y\nN+VpCnLv3MfYw92R2e8PIcjfndPRVyT3hKhGShfKez//+K4KZXc3R6ZNDOXI+sm0bOaDRgPW1hp8\nPJ3YuvucnNRnJlIgV2OuAYE8tHYLXi1asiC0Awl799xxmnYh9di/+hkaNfCg7cCveevzzbccxpHD\nOkJUjHujxozZvJvc9DR+GxhOxoXzd54IOHIq8abXO/aelyvPCFFNXC+Ux23fS693PyoplI98/y35\nV69WeH7NGnlzfONUis6/Tfw/0+jeMZCp/1lFk55f8t4XWzkfn1YFn0KURwrkas7a1pbwDz+l72df\n8ueo+9k/a+Ydf206Odrx4Wv9ObBmImfPpWBV6rqMclhHiIqzc3Zm6C9LaDJsOAtCO7B3xicU5uXd\ndprSuebnU4cWfecw54e9t5zhLoSwTBqNhkaDhzBu+17Cp39O9JqVfKM0YPMrL5By5nSl5unn48y0\niaEc3TCFxXNHcik5iw6D59F/zI9888s+ki5nGflTiNKkQK4hmgwdxritkZxcvJAVY0aQk3bnX5pB\nAe78MmsEC2cPx8XZDoA2LfyI+HxYVYcrRI2k0Wjo8uIrjNsaSdy2LfzUrR0Xtm0pt33E58MI6xqE\njY0VYV2D2LFsAisjxrJ261ka9/wfn329k6yrclk4IaoDjUZDcP+BPLBkOY/uOoCNgwO/9u/J0qED\nOfvXcooKK34lKY1GQ6e29ZnzwRDi9r7IpEc6sXnXOZqFz6LPQz8w54e9JVfBEMYld9KrYQpyc9n6\n+ktErVxOr/c+ovmo0WgMuBe8VqtlycrjvDp9A22a+/HJGwNQGnubIGJRRSzqdk21Jf/0abVazq74\nk82vPE9Aj16Ef/gZderWNXj6wycu8eGs7WzeHcO/nujCs090xcPdsQojFkYiuSdKFOTkcPqPpRya\nN4esiwm0fXIiLcY8gmtgg7uab05OPuu2RbF09QlWbjhNi6Y+jLy3JcMHtyAowN1I0VdLcic9UTYb\ne3v6zZjFvRG/sH/WTBb27k787p13nE6j0fDQ0Fac3DSVHp0D6fHgfIY//SvbI2PlBAEhKqHkRgMH\nTuBcP4Afu7TmwNwvKSooKGmTFhPN4oHhzHS1ZfHAcNJiokvGtW1Zl8VfjWL77xM4dyGNJr2+5LXp\n60lMlkOrQlQXNg4OtBzzCGO37GbYr3+QcT6WBaEdWNSvJwe/nkN2UlJJ29utD0pzcLDl/oHN+emL\n4Vw68BL/eS6M46eT6DTkG1r1m8NL761l445ocnMLyp2HuD3Zg1yDaYuKOLl4ITve+j/qde5Kr/c/\nxr1hI4Omzbqay49LDvPF/D24udjzwtPdeei+EGxtras4amEkshfLwlw5dZKNL0wlJzWVsPc/Jqjf\nAH67p/dN11AO6BnGw+u2ljl9bFwan3y1k0XLjzJ8cAueHN2Bbh0C0Ggs6qsWknviDgrz8ji3YR2n\nliwi5u9V1OvcjeYPjeHI99+SsOfGDq3brQ/KnXdhEfuPJLBmy1n+3nKW46eTCO8WzKDwJgzq3YTG\nwZ7G/jiWxmj5JwVyLZCfnc3+WTPZP2sGrR6bQNdX3sDB/cYhmLSYaNZOHE/Cnl34dwvlnnkRJYV0\nUVERKzecZuZ3ezgTc4V/PdGFZ8Z2xNPDyVwfRxhGNtIWSKvVoi5dzJ6P38fK2obLJ46h1euXaGVj\nwwsZtz85LzE5ix+XHmL+rwexstIw4eH2PDq8DXV9Xao6fGEYyT1hsPyrV4las5JTixcStWrFTeMM\nWR/cyZXUbDZsj+bvLWf5e+tZ6jja0ie0IWFdgwjrGlQTu2NIgVxRspKAq5cusfPd/xK1egVdpr1G\nq8efxN7VlcUDww3ai3Xw2EW+mL+HFetVHrovhEeHtyG0UyBWBvRxFiYnG2kLptVqiVm7htXjx5Kb\nnl4yvCJ7jLRaLbv2XWD+rwf4Y+0pwrsGMeHh9gzu01SO9JiX5J6olEV9e5CwZ1fJa1tnZzo++yKN\n7rkXv46dsLK+u7wuKirimJrE1j2xbIvUPRzsbQjvFlRSMDdt6FXdj0pJgVxRspK4IfnoEfZ89B6x\nmzfQfORojkR8h7bwRj+lO/1qTbiUQcRvh1i0/CgZWbmMvr8VY4a1pl1I3eqeWDWJRX0Rkn9lS4uJ\n5q+xI0k6cgiNtTWtn3iK7q+/iXO9ehWaT2ZWLktWHmf+4oNEn09l1JCW3D9AIbxbsBTLpie5JypF\n/2huva7dafvUJJKOHCJm7Wqyk5NoOGAQwQMHE9ird4XXEWXRarWcjr7C1j3n2BYZy9Y9seQXFNK1\nXQBd2tWnS7v6dGrjb/DJwdGxKYyftpxd+y8Q2jGQiM+H0SjI5F06pECuKFlJ3CozPp6jEd8S+el0\nivJvXK+1Inuxjp5MZNHyoyxacQx7O2vGDGvNmGGtaNZIroBhZrKRrmbSYqLZP2smpxb/QoO+A2g+\nagwNBw7CxsGhQvNRoy7z++oTrFivokZfYVB4E+4foDC4TxPc3eQqGCYguSeMLj32HDFr1xCzbg0J\nu3fg6OVN/R5hBPTUPdyCgu/6PbRaLefj09l7KL7kceDYRfz9XOjc1p8u7erTuW192rTwo46T3S3T\nh4+MYFtkbMnrsK5BbF06/q7jqiApkCtKVhLlSzmtsnz0g6Sop7CysaHNkxPp/OIruAYYfsMQrVZL\n5ME4Fv55lN9WHqeerwuDejdhYFhjQjsGYm9vU4WfQJRBNtLV1LWUFE4vW4K69FeSjhyiyX3DaD5q\nDIG9+2Jta1uheV1MzGTlxtOsWK+ydc85urSrz/0DFO4Jb0KzRtX+UKqlsqiFKrlX82iLirh8/Bhx\nO7YRt3MbcTu2YW1vryuWQ3vh17Ez3iGtKry+KEthYREnzyTrCubD8fxzOIGTZ5KpX9eVti39aNPC\njzbNdc9K79kUFNy41baNjRX5MW/edQwVJAVyRclKwjCXTxzn8Ldfceq3hbg3akLj+4bR5L5heLUM\nMXhjWlBQyO79cazbFsW6bVGcPJtMry5BDAxrzMCwxjRv4i0b5qpnUQtY8q9yshISUJf9hrrkV9LO\nRdNs2AiUUaOpH9qzwv0Rr2bnsX5bFMvXqWzcGU1efiFhXYMI7xpMeLcgWjbz4dyFNEs4RFrdSe4J\nk9JqtaSePUPcjm3E79pO4oF9pMeew7tlK/w6dMKvfUfqduiEV4uWWNnc/c6qgoJCzsSkcPjEJY6c\nTOTIqUQOn0jkYmImhUU3akrZg1xNyEqiYgrz84nbsY2olcs5u3I51ra2NB5yP43vG0b97j0qlGQp\nqdls2hXDum1RrN0aRVGRln49GtKtQwBd2wfQurkvNjY3NvYW0o+pupONdA2Tfi6GU0sXoy75lcy4\n8wT06k2D3v1o0Kcfns2UCv/oPHchteRkna17zpGWkQPAldRrJW3MtIGr7iT3hNnlZWWRdPggiQf3\nk3hgH5cO7CMz7gI+rdrg3bIV3iGt8GoRgleLEOrUNc75QweOJjDxtZUcOnFJ+iBXJ7KSqDytVkvy\nkcOcXbmcqJXLyYg7T8MBg6gf2gv/bqF4twwx6G591+d1JuYKm3bGEHkwnshDcVxIyKB9SF26tg+g\na/v6fDZvF5EH40umkY10pchGugbLSkjg/NZNnN+yifNbNqItKCCwd19dwdy7b6Xu0hV/MYOgbjNv\n2gME8OiINnRoVY8OrerRLqQuri4V6xNdC0nuCYuUm5FB8pFDXD5+jMsnj3PlhO4ZrRavFiF4FxfM\nHk2b4d64Ca6BDSq0M+x2l4w1ISmQK0pWEsaTceE859avJWHPLhL27CQ7OYl6nbvh370H/t1Cqde5\nK3bOzgbPLz0jh38OxxN5MJ49B+NYueH0TeOtrDRs/308Ic18cXOVjbOBZCNdS2i1WtKio7iwZROx\nWzZyYesmrO0d8GvXAb/2HfFt1wG/dh1w9ve/47xKn2TToVU9pjzemQNHL3Lg2EWOnEykfl0XWjf3\no3ljb5TGXsXP3pKbN0juiWpDq9WSnZTElZPHuXziGFdOniAt+ixpUWe5mngJ18AGuDdqgnvj4kfD\nxrg2CMK1QRB2Ljdfe93QS8ZWsepbICuK0h74GggBTgOTVVWNLKPdGOB9wBfYDDylqmpS6XYVeN9g\nZCVRJbKTk3XFcuQu4nfvJOnwQTwaN8E7pLXuV2nLVni1DMEtKNigPc2lN9J+3nVoUN+NE2eS8XBz\nJKSZDy2a+NA42INGDXSP4AB3HBzu/oSEGkQ20rWUVqsl/VwMiQf3k3ToAImHDpB4cD/WNrYlxbJX\nSCs8mjTDo0nTm37MHt1xgIWjx+CRcpZUzyaM/XURrXt2KBlfUFCIGnWF46eTUKOucCrqMqeiLqNG\nXcbV2Z7mTbxRGnnTJNiT4EB3ggPcCQ50x9PdsTadd2BRH1RyT1RWQW4u6ediSIs6S1rUGVKjzpIe\nHUVG3HkyzsdibWeHa2ADXAIa4BLYgCPffY226MZJesa40UklVM8CWVEUe+As8B4wH3gM+AhoqKpq\ntl67NsA2oD9wFJgN+KuqOuQu3jsYWUmYREFuLpePHtEdwjl5nMvHj3Hl5HFyUlPwVFrg3TIET6UF\nbsENcW0QjFtwQxy9b5y4V95GuqioiNi4dI6fTuLk2ctEx6YSfV73OJ+Qjq9XnRsFc6A79eu6UL+u\nK/XruuDv54KXh5NspM1E8s+8tFotmfFxJB7QFc1XTp0g9exp0qLO4uDugUfTZng0aUbs5g2kx0SX\nTFe/ZxijDdgDVFRURPylTNSoyyW5GRufxrm4NM5dSCMvv7CkWA4OcCegniv1fEpPcmMAAA6jSURB\nVF2o5+tMPV8X/Ou6GKWItpDzFyT3RI2n1WrJSUkh48J5Mi+cJyPuPP/M+ISs+LiSNrIHuQIURRkE\nfK2qarDesCPAu6qqLtUb9hFQV1XVJ4pfewLJxcOSK/newchKwqxy09O5cuoEl08cJ+X0KTJiz5ER\ne4702BgKcnJwCwrGtUEwSUcOcfViQsl0vu07MnzZKhy9vcs9c7+wsIi4ixklBfO5C2nEX8og/lIm\nCYmZxF/KIDsnH38/l5KHj2cdfLyc8PGsg6/3jb99vJzw8nDC2rridwi0kA00yEZaGEBbVERmfByp\nZ06TeuY0G6c9C3p7gAA8lea4BATi7B+AS0AgLvUDqFO3Hk4+vjj5+ODk44ttnTq3fZ/0jBxi49OI\njUsn5kJqSV5eTMrkYlIWCYmZZF/Lp66PM/5+Lvh66fLQ29MJbw/ds49XnZLXnu6OuLrY35KjNe06\nrMYguSdMpab1QTb1xWmbAydKDVOLh5duV3K/RVVVUxRFSQEUdIWyqIbs3dzw79od/67dbxmXm5FB\nxvlYMmLPsfzhB24al3RwPz92bkVuWhqOXt44+dXFydcXR08v7N09cPTwxMHTE3t3DwI9PGka6IFD\na1/sXBpj6+yCnYsL1ra2ZF/LI6F4w5yQmElySjbJV65yTE0iefdVkq9kk5yie05Nv0YdJzs83Bxw\nd3XAw82x+Fn32t3NAZc69rg42930/Pw7f3Pg6EUAtkXGMn7acjnBUFgsjZUVroENcA1sQFDf/qi/\nL76pD6F/t1AGzP6GzLgLukd8HAmRu8lOvET25WSyk5O4lpwEGg1OPr44eusKZgdPTxzcPbB3c8fe\n3R17N3cc3T1o6+5Olw7u2Lv6YOfsgq2zMzaOuj3H167lcylZVywnXb7K5dRsLqdkk5CYyZFTiVxO\nyS7J0dT0HLKu5uHibKfLx+LH8d2HmJy5nOCCC5yzCeT3yAdu8+mFEMbk3rCROfYYVxlTF8h1gOxS\nw7IBp0q2EzWEvasrPq1a49OqNfVDe5bZ0b8wP59ryclcTbxEdlIiOWmp5KSkkJOWSsaF8+QcOURO\naio5qSnkpqWSl5lJXlYmeZmZWNnYYOfigl1xwWzr7EI9JycCHRyxcXLC1tEJmwZO2CiO2Do6Ye3g\nQL7WmtyiInKKcsgpyCU7H67mwdV0yEyCi3lFnM3VkpVbRFaOlqzcQmKPXGJylmygRfV0z7yIMvcA\nebcMKXcarVZL/tWrxcWyrmjOSU0hNz2NnLQ0MuMucPnYEXLS0shNT7uRm1ezyM/MpDAvD9s6dUoK\nZts6ztg6OeHh5ISPgyOtHR2xcXDE1ssJmwDd3zYODmhs65CvtSK3SENOYT7XCgrYvXkF9Qp0e5Ab\nF8QyQbsG+MJES08IUZOYukDOBkrf69QJyKpkuzIpiuIFeJUaXN/AGIWZlbWRBrC2tcXZ39+gs/H1\nabVaCnJyyC8umHMzMsi/mkXBtWvkZ2dTcC1b95xzjYJs3d85qSkU5uZSlJODdV4u9rm52OTmUic3\nl8K8XN24/HwK8/IoKsinMD+forw8WmXl4F+g24NcWzfQkn/VV2X2AGk0GuycnbFzdq7U4dSiggLy\nr14lLyuLvKxM8jMzyb+WTcG1a7pHju5Zf1heViaFubkU5Opykbxc7HJzqXct9qZ5+2REl/OuNZPk\nnhDGY+oC+SQwtdQwBfiljHZKSQNF8QY8iocb4lngrUrGKMzM2IdpNBoNto6O2Do64uTra7T5lmWG\nqy36vfpr2wa6mOSfMJiVjQ32bm7Yu7nd9bxKX2aqfrfQu55nNSO5J4SRVPwspLuzCbBXFGWqoig2\niqJMQHcZt7Wl2i0CRiiKEqooigMwHVitqmqqge8zC12Brf/oa5RPIMRtlN4g18INNEj+CTO5Z14E\nAT3DsLKxIaBnWMnRp1pEck8IIzHHdZBbAfOAVugu+TZJVdV/FEX5CtCqqjqluN1I4APAD9gOjFdV\n9fJdvG8wciavqGIWchYvyJn0QpiL5J4Q5lNtr2KBqqrHgB5lDJ9c6vVSYGnpdkJYspp2Fq8QQghR\nG5m6i4UQQgghhBAWTQpkIYQQQggh9EiBLIQQQgghhB4pkIUQQgghhNAjBbIQQgghhBB6pEAWQggh\nhBBCjxTIQgghhBBC6JECWQghhBBCCD1SIAshhBBCCKFHCmQhhBBCCCH0SIEshBBCCCGEHhtzB2BC\n1gCXLl0ydxxCVLl+/foFA3GqqhaYO5Zikn+iVpDcE8J8jJl/talArgcwbtw4c8chhCnEAO2BQ+YO\npJjkn6gtJPeEMB+j5V9tKpD/AXoBF4FCM8eiryGwCeiL7ou1BBKTYSwxJrgRV665A9Fjiflnid+f\nJcYElhmXJcckuXdnlvz9SUx3ZolxGTX/ak2BrKpqLrDD3HGUpiiKXfGf8aqqnjNnLNdJTIaxxJjg\nprgsZmNoiflnid+fJcYElhmXhcckuXcHFv79SUx3YIlxGTv/5CQ9IYQQQggh9EiBLIQQQgghhB4p\nkIUQQgghhNAjBbL5XQHeKX62FBKTYSwxJrDcuCyNJS4nS4wJLDMuial6s8RlJTEZzhLjMmpMGq1W\na4z5CCGEEEIIUSPIHmQhhBBCCCH0SIEshBBCCCGEHimQhRBCCCGE0CMFshBCCCGEEHqkQBZCCCGE\nEEKPFMhCCCGEEELokQJZCCGEEEIIPTbmDqAmUhSlPfA1EAKcBiarqhpZRrsxwPuAL7AZeEpV1aTi\ncdOAD4FcQANogcGqqu6s6rj02r8AhKqqOqqy8zBRTEZdVhX4/p4GXkb3/anANFVVd1Tmc5kwLqP/\nX1kaS8w/S8w9I8ZV4/NPcs9wkn8mjanG554R46rwspI9yEamKIo9sAKYD7gBs4AViqI4lWrXBvgK\neBjwBhKBCL0m7YHXVFV1VVXVpfj5bopjg+IqbuukKMonwGfo/okqPA9TxVTMaMuqAt9fb+ADYISq\nqu7AHOAvRVE8jL2cjBVXcROj/l9ZGkvMP0vMPWPFVaxG55/knuEk/0wXU7EanXvGiqu4SYWXlRTI\nxtcHKFRV9RtVVQtVVY1Al/z3lmo3FvhTVdV9qqrmAq8CgxRF8Ske3x44bIa4AP4AGqP7xVbZeZgq\nJjDusjI0pgDgE1VVjwKoqvoTUIjuF66xl5Ox4gLj/19ZGkvMP0vMPWPFBTU//yT3DCf5Z7qYoObn\nnrHigkosKymQja85cKLUMLV4eLntVFVNAVIARVEUR0AB/q0oykVFUY4rijLeRHEBPK6q6ggg6S7m\nYZKYqmBZGRSTqqo/q6r6mV4cPQDn4mmNvZyMEdfxKvq/sjSWmH+WmHtGiauW5J/knuEk/0wUUy3J\nPWPEVen8kwLZ+OoA2aWGZQOlDzHcrp0fsB2YCwQCE4EZiqLcY4K4UFX10t3Ow4QxGXtZVfgzKorS\nElgK/Ld4RW/s5WSMuFKpmv8rS2OJ+WeJuWesuGpD/knuGU7yz3Qx1YbcM0Zclc4/OUnP+LIBx1LD\nnIAsQ9upqnoO3WGF63YoirIAeABYW8VxVfU8jDq/KlhWFYpJUZSBwK/Ap6qqflqZeZgqrir6v7I0\nlph/lph7RpmnuZeVifJPcs9wkn8mmp+5l1Nt2PbJHmTjO4luV74+hVsPEdzUTlEUb8ADOKkoSntF\nUV4t1d4ByDFBXFU9D6POrwqWlcExFR+i+Q2YpKrq9MrMw5RxVdH/laWxxPyzxNwzyjxrSf5J7hlO\n8s9E86sluWeUuCq7rGQPsvFtAuwVRZkKzAMeQ3fJkdK/UhYBWxRF+R44AEwHVquqmlq8snhLUZQz\n6Dro90V3tm+YCeKq6nkYe35ZGHdZGRSToij90J0lO0C99UxYYy8nY8Vl7GVliSwx/ywx94w1z9qQ\nf5J7hpP8M938akPuGSuuSi0r2YNsZKqq5gGD0Z2lewWYCgxVVfWaoihfKYoyt7jdYeBpdJe2uQTU\nBSYUjzsDjALeAjKA2cATxdNUaVyVnYcZYzLqsqpATK8AtsAaRVEyFEXJLH4eaOzlZMS4jP5/ZWks\nMf8sMfeMGFeNzz/JPcNJ/pk0phqfe0aMq1LLSqPVlr6snhBCCCGEELWX7EEWQgghhBBCjxTIQggh\nhBBC6JECWQghhBBCCD1SIAshhBBCCKFHCmQhhBBCCCH0SIEshBBCCCGEHimQhRBCCCGE0CN30hMV\noihKG8AdiAVigOaqqp42b1RC1A6Sf0KYh+Re7SN7kEVF/Qk0B86ju/vRGfOGI0StIvknhHlI7tUy\nsgdZVJQGQFVVLZBk5liEqG0k/4QwD8m9WkZuNS0MpijKZiAc0AI/AY9TfJhJUZQY4APgCaADcAQY\nBzwLjAfSgZdVVV1cPC8X4AvgQaAAWA88r6pqsik/kxDVheSfEOYhuVc7SRcLURHDgTjgFWAmupWF\nvg+KHx0BT+AfIA/oBKwC5imKYl3cdj5QH+gD9AXqACuqOH4hqjPJPyHMQ3KvFpICWRhMVdVUoBDI\nRPerWFOqyS+qqq5RVfUk8AeQq6rqK6qqngH+B7gAAYqiNAJGAI+oqnpYVdVjwCNAB0VRQk31eYSo\nTiT/hDAPyb3aSfogC2OK0vs7G93ZvtddK362B5qiW8FEK4qiv6KxBhRgV1UGKUQNJfknhHlI7tVA\nUiALY8ov9bqonHY26FYabbn1l7j0wxKiciT/hDAPyb0aSLpYiIoyxlmdJwEHwFFV1WhVVaOBVHQn\nLjQwwvyFqKkk/4QwD8m9WkYKZFFRWeiuBelZiWmvXybnNPAX8LOiKKGKooQAi4CWyLUlhbgdyT8h\nzENyr5aRLhaiomYDnwLB3PyL2pBf1/ptHkN3NvAKdP+H24GBqqrmGSdMIWokyT8hzENyr5aR6yAL\nIYQQQgihR7pYCCGEEEIIoUcKZCGEEEIIIfRIgSyEEEIIIYQeKZCFEEIIIYTQIwWyEEIIIYQQeqRA\nFkIIIYQQQo8UyEIIIYQQQuiRAlkIIYQQQgg9UiALIYQQQgih5/8BJEFYuGXFGo4AAAAASUVORK5C\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1046b9b90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_data = pd.concat([fit_data.data, \n",
    "                       fit_data.model], axis=0).reset_index()\n",
    "\n",
    "colors = sns.color_palette()\n",
    "\n",
    "palette = {14.1:colors[0], 18.8:colors[2]}\n",
    "\n",
    "grid = sns.FacetGrid(plot_data, col='resi', hue='field', palette=palette,\n",
    "                     col_wrap=3, size=2.0, aspect=0.75, \n",
    "                     sharey=True, despine=True)\n",
    "\n",
    "\n",
    "grid.map(plt.plot, 'xcalc', 'ycalc', marker='', ls='-', lw=1.0)\n",
    "grid.map(plt.plot, 'time', 'intensity', marker='o', ms=5, ls='')\n",
    "\n",
    "grid.set(xticks=np.linspace(0.05, 0.25, 5),\n",
    "         ylim=(-0.1, 1.05))\n",
    "\n",
    "ax = grid.axes[0]\n",
    "legend = ax.get_legend_handles_labels()\n",
    "ax.legend(legend[0][2:], legend[1][2:], loc=0, frameon=True)\n",
    "\n",
    "f = plt.gcf()\n",
    "f.set_size_inches(12,8)\n",
    "f.subplots_adjust(wspace=0.2, hspace=0.25)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Just for fun, here's a bar graph of the decay rates determined from NLS."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-07-24T18:11:31.785986",
     "start_time": "2016-07-24T18:11:30.941522"
    },
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Cz2fmeZn5fGb+EFgAvK/kuiRJKl27h/g2wL192rLWLknSmNbuIb4esKRP2xLA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\nSaooQ1ySpIr6/4AG52g9TIvoAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1046b9cd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_data = (fit_data.results\n",
    "             .sort_index(axis=1)\n",
    "             .loc[:,('rate',['value','stderr'])]\n",
    "             )\n",
    "plot_data.columns = plot_data.columns.droplevel(0)\n",
    "plot_data.reset_index(inplace=True)\n",
    "\n",
    "fig = plt.figure()\n",
    "fig.set_size_inches(7,5)\n",
    "ax = plt.axes()\n",
    "\n",
    "palette = [colors[0], colors[2]]\n",
    "\n",
    "for pos, (field, dat) in enumerate(plot_data.groupby('field')):\n",
    "    _ = dat.plot('resi', 'value', yerr='stderr',\n",
    "                 kind='bar', label=field, color=palette[pos],\n",
    "                 position=(-pos)+1, ax=ax, width=0.4)\n",
    "    \n",
    "ax.set_ylabel('decay rate (s$^{-1}$)')\n",
    "ax.set_xlabel('residue')\n",
    "ax.set_xlim(ax.get_xlim()[0]-0.5, ax.get_xlim()[1])\n",
    "plt.xticks(rotation=0)\n",
    "\n",
    "sns.despine()\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-07-24T18:11:38.369926",
     "start_time": "2016-07-24T18:11:38.240834"
    },
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "! rm ./GCN4_twofield.tsv"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}