examples/scattering/scattering_reweighting.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Enemble Refinement with SAXS data using BioEn\n",
    "\n",
    "By applying this Jupyter notebook, you can perform ensemble refinement with small-angle X-ray scattering  (SAXS) data using BioEn. The steps of the Jupyer notebook are <br>\n",
    "\n",
    "1. Preparation of the input <br> \n",
    "2. BioEn <br> \n",
    "3. Analysis of the BioEn results<br> \n",
    "\n",
    "You can either use the provided test data or define your own protein of interest and load your scattering data. The part, which can be individualized by the user, is highlighted in green. \n",
    "\n",
    "\n",
    "### Theory and methods applied in this Jupyter notebook are available in:\n",
    "G. Hummer, J. Köfinger, “Bayesian ensemble refinement by replica simulations and reweighting,” J. Chem. Phys. 143, 243150 (2015). \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.interpolate import interp1d\n",
    "import pickle\n",
    "import pandas as pd\n",
    "import os, h5py, sys, math\n",
    "\n",
    "import matplotlib as m\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.mlab as mlab\n",
    "import matplotlib.ticker as ticker\n",
    "\n",
    "import bioen_scattering as bs\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Define paths to the experimental and simulated data and for the output of preparation, BioEn, and analysis of the BioEn runs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%capture\n",
    "! mkdir files/output_preparation\n",
    "! mkdir files/output_bioen\n",
    "! mkdir files/output_analysis\n",
    "\n",
    "# path to experimental data\n",
    "path_experimental_data = \"files/experimental_data/\"\n",
    "\n",
    "# path to simulated data\n",
    "path_simulated_data = \"files/simulated_data/\"\n",
    "\n",
    "# define path to the output of the preparation\n",
    "path_output_preparation = \"files/output_preparation\"\n",
    "\n",
    "# define path to the output of BioEn\n",
    "path_output_bioen = \"files/output_bioen\"\n",
    "\n",
    "# define path to the output of the analysis\n",
    "path_output_analysis = \"files/output_analysis\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1. Preparation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this part of the notebook, we prepare our input for BioEn. The standard output from a scattering experiment is: <br>\n",
    "    \n",
    "    #   q                 I(q)        error/noise                                                         \n",
    "    4.138455E-02        5.904029    1.555333E-01\n",
    "    4.371607E-02        5.652469    1.527037E-01 \n",
    "    4.604759E-02        5.533381    1.521723E-01\n",
    "    4.837912E-02        5.547052    1.474577E-01\n",
    "    5.071064E-02        5.296281    1.436712E-01\n",
    "    \n",
    "For a single modeled structure, predicted scattering intensities will look like this: <br>\n",
    "\n",
    "\t#  q               I(q)\n",
    "\t4.138454e-02 \t2.906550e+06\n",
    "\t4.371607e-02 \t2.865970e+06\n",
    "\t4.604758e-02 \t2.823741e+06\n",
    "\t4.837911e-02 \t2.779957e+06\n",
    "\t5.071064e-02 \t2.734716e+06\n",
    "\n",
    "Since these formats are not always available, this notebook also shows how to edit the simulated data, so that ensemble refinement can easily be performed. Therefore, we consider two possible cases.\n",
    "\n",
    "1. The experimental and simulated data has already the correct format, but the number of data points deviate. However, for the comparison of the experimental and simulated SAXS data, we need the same number of data points in both cases (which might differ using different SAXS data prediction tools). To handle this case of reformating, we interpolate the simulated data for the number of data points provided by the user and save the reformated simulated data in a pkl file, which is subsequently the input for BioEn.\n",
    "2. We use HDF5 file format as input. This is a convenient file format, while working with a large number of structures. Here, we convert it to a pkl file, as the input for BioEn. *Not yet in the notebook*."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Reformating SAXS data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# file name of experimental data\n",
    "fn_exp = \"{}/exp-saxs.dat\".format(path_experimental_data)\n",
    "\n",
    "# ids of the models\n",
    "# here: simple range from 0 to 9 \n",
    "model_ids = range(0,100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# get experimental data\n",
    "exp_1 = np.genfromtxt(fn_exp, comments='#')\n",
    "exp_tmp = exp_1[:,0:2]\n",
    "\n",
    "# estimating standard error of the mean \n",
    "error = exp_1.copy()\n",
    "error[:,1] /= error[:,0]\n",
    "error[:,1] = np.sqrt(error[:,1]) \n",
    "exp_err_tmp = exp_1[:,0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# get number of restraints (M)\n",
    "nrestraints = len(exp_tmp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# get simulated data and interpolate (experimental and simulated data have the same number of data points)\n",
    "sim_tmp = dict()\n",
    "for nmodel in model_ids:\n",
    "    fn_sim = \"{}/sim-tau{}-test.dat\".format(path_simulated_data, nmodel)\n",
    "    sim_single = np.genfromtxt(fn_sim, comments='#')\n",
    "    sim_tmp[nmodel] = bs.adapt_q(sim_single, exp_1)[:,1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# let BioEn perform an initial optimization of the coefficient\n",
    "coeff = 'initial-optimization'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# write pkl file as input for BioEn\n",
    "fn_out_pkl = '{}/input-bioen-scattering.pkl'.format(path_output_preparation)\n",
    "with open(fn_out_pkl, 'wb') as fp:\n",
    "    pickle.dump([coeff, nrestraints, exp_tmp, exp_err_tmp, sim_tmp], fp)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Working with HD5F file formats (output from Capriqorn [Köfinger2013])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# needs to be implemented"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# BioEn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Settings and input parameters for BioEn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# define theta series, for which to perform reweighting\n",
    "theta_series = [10e5, 10e4, 10e3, 10e2, 10e1, 10e0, 10e-1, 0]\n",
    "np.savetxt('theta.dat', np.array(theta_series))\n",
    "\n",
    "# number of ensemble members\n",
    "number_of_ensemble_members = len(model_ids)\n",
    "np.savetxt('{}/models_scattering.dat'.format(path_output_preparation), model_ids)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "INFO:root:BioEn weight refinement runs with\n",
      "INFO:root:    optimization method: log-weights\n",
      "INFO:root:    optimization algorithm: bfgs\n",
      "INFO:root:    optimization minimizer: GSL\n",
      "INFO:root:    optimization parameter modification: \n",
      "Note: GSL might require more iterations, please check the parameters of the minimizer.\n",
      "Note: GSL might require more iterations, please check the parameters of the minimizer.\n",
      "Note: GSL might require more iterations, please check the parameters of the minimizer.\n",
      "Note: GSL might require more iterations, please check the parameters of the minimizer.\n",
      "Note: GSL might require more iterations, please check the parameters of the minimizer.\n",
      "Note: GSL might require more iterations, please check the parameters of the minimizer.\n",
      "Note: GSL might require more iterations, please check the parameters of the minimizer.\n",
      "Note: GSL might require more iterations, please check the parameters of the minimizer.\n",
      "INFO:root:BioEn finished weight refinement in 21.75 s.\n"
     ]
    }
   ],
   "source": [
    "#%%capture\n",
    "! bash run_bioen_ipynb_scattering.sh $number_of_ensemble_members "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Settings and input parameters for analysis of BioEn outputs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "# output of BioEn is a pkl file (contains all the necessary information)\n",
    "bioen_pkl = \"{}/bioen-scattering.pkl\".format(path_output_bioen)\n",
    "df = pd.read_pickle(bioen_pkl)\n",
    "bioen_data = df.to_dict()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`bioen_data` contains all needed and useful information to analyse the BioEn calculations. <br>\n",
    "For each previously defined confidence value $\\theta$ (defined in the variable `theta_series`) a list of variables are available:\n",
    "\n",
    "**Experimental information**\n",
    "- **`exp`** <br> \n",
    "--> experimental scattering curves<br>\n",
    "- **`exp_err`** <br>\n",
    "--> error/noise of each experimental data point defined in `exp`\n",
    "- **`nrestraints`** <br>\n",
    "--> number of data points ($M$)\n",
    "\n",
    "**Simulated data and parameters**\n",
    "- **`sim_init`** <br> \n",
    "--> initial ensemble averaged simulated scattering curves (see above for exp)\n",
    "- **`sim_wopt`** <br>\n",
    "--> optimized ensemble averaged simulated scattering curves and for a given confidence value $\\theta$\n",
    "- **`coefficient`** <br>\n",
    "--> coefficient of the optimized ensemble averaged simulated SAXS data \n",
    "- **`nmodels_list`** <br>\n",
    "--> list of model ids (extracted e.g. from models_370-292.dat)\n",
    "- **`nmodels`** <br>\n",
    "--> number of models ($N$), which is also the number of ensemble members (relevant in the BioEn context) <br>\n",
    "\n",
    "\n",
    "**Free energy parameters**\n",
    "- **`theta`** <br>\n",
    "--> confidence parameter $\\theta$\n",
    "- **`chi2_init`** <br>\n",
    "--> deviation from the experimental data with the initial weight distribution <br>\n",
    "--> if you use `chi2_init` of the maximal value of $\\theta$, $\\chi^2$ is calculated with the prior weight distribution `w0`\n",
    "- **`chi2`** <br>\n",
    "--> optimal $\\chi^2$ calculated with optimal weight distribution `wopt`\n",
    "- **`S_init`** <br>\n",
    "--> initial relative entropy\n",
    "--> if you use `S_init` of the maximal value of $\\theta$, $S$ is equal to $0$\n",
    "- **`S`** <br>\n",
    "--> relative entropy of optimized weight distribution\n",
    "- **`w0`** <br>\n",
    "--> reference weight distribution\n",
    "- **`winit`** <br>\n",
    "--> initial weight distribution\n",
    "- **`wopt`** <br>\n",
    "--> optimal weight distribution <br>\n",
    "--> optimized for each $\\theta$\n",
    "\n",
    "**Misc**\n",
    "- **`len_sim`** <br>\n",
    "--> seconds it took for BioEn to optimize for a given value of $\\theta$\n",
    "- **`optimization_method`** <br>\n",
    "--> information about the optimization method: log-weights or forces\n",
    "- **`optimization_minimizer`** <br>\n",
    "--> information about the minimer: scipy, GSL, LBFGS\n",
    "- **`optimization_algorithm`** <br>\n",
    "--> information about the inimizer: <br>\n",
    "--> scipy: bfgs, lbfgs, cg <br>\n",
    "--> GSL: conjugate_fr, conjugate_pr, bfgs, bfgs, steepest_descent<br>\n",
    "--> LBFGS: lbfgs <br>\n",
    "\n",
    "\n",
    "Several default plots are provided in the following, so that the analysis is as intuitive as the preparation and running BioEn itself.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### Plot $\\chi^{2} vs. S_{\\mathrm{KL}}$\n",
    "\n",
    "the lower $\\theta$, the closer to experimental data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "def visualize_chi2_skl(bioen_data):\n",
    "    fs = 22\n",
    "    fig = plt.figure(figsize=[6,4])\n",
    "    ax = fig.add_subplot(111)\n",
    "    \n",
    "    for theta in theta_series:\n",
    "        chi2 = bioen_data[theta]['chi2'] / bioen_data[theta]['nrestraints']\n",
    "        skl = - bioen_data[theta]['S']\n",
    "        ax.scatter(skl, chi2, marker='^', s=160, label=theta)  \n",
    "    \n",
    "    #ax.set_xticks(range(-1,6,1))   \n",
    "    #ax.set_xticklabels(range(-1,6,1), fontsize=fs)\n",
    "    #ax.set_xlim(-0.4,5.5)\n",
    "    ax.set_xlabel(r'$S_{\\mathrm{KL}}$', fontsize=fs)\n",
    "\n",
    "    #ax.set_yticks(np.arange(0,10,1))   \n",
    "    #ax.set_yticklabels(np.arange(0,10,1), fontsize=fs)\n",
    "    #ax.set_ylim(-0.2, 4)\n",
    "    ax.set_ylabel(r'$\\chi^{2}$', fontsize=fs)    \n",
    "    \n",
    "    plt.grid()\n",
    "    \n",
    "    ax.legend(ncol=2, fontsize=10)\n",
    "    \n",
    "    plt.tight_layout()\n",
    "    plt.savefig(\"{}/bioen_chi2_skl.png\".format(path_output_analysis), dpi=400)\n",
    "    plt.show()\n",
    "    return"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "visualize_chi2_skl(bioen_data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The elbow plot would suggest that a $\\theta=100000$ would give good trade-off between agreement with experiment and the initial ensemble."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Comparison of scattering curves from experiment and ensemble refinement"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "def visualize_scattering_data(theta, bioen_data):\n",
    "    fs = 22\n",
    "    fig = plt.figure(figsize=[6,4])\n",
    "    ax = fig.add_subplot(111)\n",
    "    \n",
    "    theta_max = np.max(list(bioen_data.keys()))\n",
    "    \n",
    "    exp = bioen_data[theta]['exp']['scattering']\n",
    "    exp_err = bioen_data[theta]['exp_err']['scattering']\n",
    "    \n",
    "    sim_init = bioen_data[theta_max]['sim_init']['scattering']\n",
    "    sim = bioen_data[theta]['sim_wopt']['scattering']\n",
    "    \n",
    "    ax.plot(exp[:,0], exp[:,1], color='black', linewidth=1.5, label='Exp.',zorder=2)\n",
    "    ax.fill_between(exp[:,0], exp[:,1]-exp_err, exp[:,1]+exp_err, color='black', alpha=0.2, label='Error', linewidth=1.0, zorder=1)\n",
    "    ax.plot(exp[:,0], sim_init, color='green', linewidth=2.0, label=r\"w0\",zorder=0)\n",
    "    ax.plot(exp[:,0], sim, color='red', linewidth=2.0, label=r\"BioEn (wopt)\".format(theta),zorder=3)\n",
    "    \n",
    "    #ax.set_xticks(np.arange(0,4.0,1.0))\n",
    "    #ax.set_xticklabels(np.arange(0,4.0,1.0), fontsize=fs)\n",
    "    #ax.set_xlim(0,3.5)\n",
    "    ax.set_xlabel(r'q [${\\AA}^{-1}$]', fontsize=fs)\n",
    "\n",
    "    #ax.set_yticks(np.arange(-0.6,1.4,0.2))\n",
    "    #ax.set_yticklabels(np.arange(-0.6,1.4,0.2), fontsize=fs)\n",
    "    #ax.set_ylim(0.35,1.0)\n",
    "    ax.set_ylabel(r'I(q)', fontsize=fs)\n",
    "\n",
    "    ax.legend(loc=1, ncol=2, fontsize=10)\n",
    "    \n",
    "    plt.grid()\n",
    "    \n",
    "    plt.tight_layout()\n",
    "    plt.savefig(\"{}/bioen_scattering.png\".format(path_output_analysis), dpi=400)\n",
    "    plt.show()\n",
    "    return"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "theta = 1.0\n",
    "visualize_scattering_data(theta, bioen_data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "At $\\theta=1$ we find very good agreement. However the elbow plot above highlights large changes in relative entropy for low values of $\\theta$. Below we are looking at scattering curves from the optimal ensembles at the different values of $\\theta$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "def visualize_scattering_all_thetas(bioen_data):\n",
    "    fs = 22\n",
    "    fig = plt.figure(figsize=[6,4])\n",
    "    ax = fig.add_subplot(111)\n",
    "    \n",
    "    theta_max = np.max(list(bioen_data.keys()))\n",
    "    \n",
    "    exp = bioen_data[theta_max]['exp']['scattering']\n",
    "    ax.plot(exp[:,0], exp[:,1], color='black', linewidth=1.5, label='Exp.',zorder=2)\n",
    "    \n",
    "    a = np.linspace(0.1, 0.7, num=len(theta_series))\n",
    "    for i, theta in enumerate(theta_series):\n",
    "        sim = bioen_data[theta]['sim_wopt']['scattering']\n",
    "        ax.plot(exp[:,0], sim, color='red', alpha=a[i], linewidth=2.0,\n",
    "                label=r\"BioEn ($\\theta={}$)\".format(theta), zorder=3)\n",
    "    \n",
    "    #ax.set_xticks(np.arange(0,4.0,1.0))\n",
    "    #ax.set_xticklabels(np.arange(0,4.0,1.0), fontsize=fs)\n",
    "    #ax.set_xlim(0,3.5)\n",
    "    ax.set_xlabel(r'q [${\\AA}^{-1}$]', fontsize=fs+2)\n",
    "\n",
    "    #ax.set_yticks(np.arange(-0.6,1.4,0.2))\n",
    "    #ax.set_yticklabels(np.arange(-0.6,1.4,0.2), fontsize=fs)\n",
    "    #ax.set_ylim(0.35,1.0)\n",
    "    ax.set_ylabel(r'I(q)', fontsize=fs)\n",
    "\n",
    "    ax.legend(loc=1, ncol=2, fontsize=10)\n",
    "    \n",
    "    plt.grid()\n",
    "    \n",
    "    plt.tight_layout()\n",
    "    plt.savefig(\"{}/bioen_theta_series.png\".format(path_output_analysis), dpi=400)\n",
    "    plt.show()\n",
    "    return"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "visualize_scattering_all_thetas(bioen_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Cummulative weights"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "def visualize_cum_dist(theta, bioen_data):\n",
    "    fs = 22\n",
    "    fig = plt.figure(figsize=[6,4])\n",
    "    ax = fig.add_subplot(111)\n",
    "    \n",
    "    nmodels = bioen_data[theta][\"nmodels\"]\n",
    "    a = np.vstack((bioen_data[theta][\"nmodels_list\"], np.array(bioen_data[theta][\"wopt\"]).reshape(1,-1)))\n",
    "    \n",
    "    models = []\n",
    "    for i, id in enumerate(np.argsort(a[1,:])[::-1]):\n",
    "        if i == 0: models.append([a[:,id][0], float(a[:,id][1]), float(a[:,id][1])])\n",
    "        else: models.append([a[:,id][0], float(a[:,id][1]), models[-1][2]+float(a[:,id][1])])\n",
    "\n",
    "    models = np.array(models)\n",
    "    ax.scatter(range(1,nmodels+1), models[:,2], s=20, color='green', zorder=2)\n",
    "    ax.plot(range(1,nmodels+1), models[:,2], color='black', zorder=1)\n",
    "\n",
    "    ax.set_xticks([0.0, 10.0, 100.0, 1000.0, 10000.0])\n",
    "    ax.set_xticklabels([r'$10^{0}$', r'$10^{1}$', r'$10^{2}$', r'$10^{3}$', r'$10^{4}$'], fontsize=fs)\n",
    "    ax.set_xlabel(\"Number of configurations\", fontsize=fs)\n",
    "    ax.semilogx()\n",
    "    ax.set_yticklabels(np.arange(0,1.2,0.2), fontsize=fs)\n",
    "    ax.set_ylim(0,1)\n",
    "    ax.set_ylabel(\"Cumulative distribution\", fontsize=fs)\n",
    "    \n",
    "    ax.grid()\n",
    "    \n",
    "    plt.savefig('{}/bioen_cum_weights.png'.format(path_output_analysis), dpi=600, bbox_inches='tight')\n",
    "    return"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "theta = 10000.0\n",
    "visualize_cum_dist(theta, bioen_data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "At $\\theta=10$ about 40% of weight is concentrated in a single structure. This is indicative of overfitting and would suggest to use a larger $\\theta$ value. This highlights the importance to look at the distribution of weights before performing further analysis of the optimized BioEn ensembles."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "theta = 100000.0\n",
    "visualize_cum_dist(theta, bioen_data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "At $\\theta=100000$ about ten structures out of a 100 structures account for 40% of the weights. This is more reasonable and also agrees with the elbow plot above. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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