Almost example.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "############################################################\n",
    "### This file is used to generate Table 1-3, Fig 1 ###\n",
    "############################################################\n",
    "\n",
    "- [Verify Assumption 1](#Verify-Assumption-1)\n",
    "    - [Table 1](#Table-1)\n",
    "    - [Table 2](#Table-2)\n",
    "\n",
    "- [Verify Assumption 2](#Verify-Assumption-2)\n",
    "    - [Table 3](#Table-3)\n",
    "    - [Left plot in Figure 1](#Left-plot-in-Figure-1)\n",
    "    - [Middle plot in Figure 1](#Middle-plot-in-Figure-1)\n",
    "    - [Right plot in Figure 1](#Right-plot-in-Figure-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-01T08:29:49.428145Z",
     "start_time": "2021-07-01T08:29:46.964236Z"
    },
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "import os\n",
    "import numpy as np\n",
    "from scipy.stats import norm\n",
    "from scipy.stats import gaussian_kde as kde \n",
    "import ipywidgets as widgets\n",
    "from ipywidgets import interact, interactive, fixed, interact_manual\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-01T08:29:49.440529Z",
     "start_time": "2021-07-01T08:29:49.431124Z"
    }
   },
   "outputs": [],
   "source": [
    "####### Plot Formatting ######\n",
    "plt.rc('lines', linewidth = 4)\n",
    "plt.rc('xtick', labelsize = 18)\n",
    "plt.rc('ytick', labelsize = 18)\n",
    "plt.rc('legend',fontsize=20)\n",
    "# plt.rcParams[\"font.family\"] = \"serif\"\n",
    "plt.rcParams['axes.labelsize'] = 20\n",
    "plt.rcParams['axes.titlesize'] = 28\n",
    "plt.rcParams['lines.markersize'] = 6\n",
    "plt.rcParams['figure.figsize'] = (7.0, 5.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "An almost example\n",
    "\n",
    "* $\\Lambda=[-1,1]$.\n",
    "\n",
    "* $Q(\\lambda) = \\lambda^p$ for $p=5$.\n",
    "\n",
    "* $\\mathcal{D} = Q(\\Lambda) = [-1,1]$.\n",
    "\n",
    "___\n",
    "\n",
    "* $\\pi_{\\Lambda}^{init} \\sim U([-1,1])$\n",
    "\n",
    "* $\\pi_{\\mathcal{D}}^{obs} \\sim N(0.25,0.1^2)$\n",
    "\n",
    "* $\\pi_{\\mathcal{D}}^{Q(init)}$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-01T08:29:49.461431Z",
     "start_time": "2021-07-01T08:29:49.449985Z"
    },
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def QoI(lam,p): \n",
    "    '''Defing a QoI mapping function'''\n",
    "    q = lam**p\n",
    "    return q\n",
    "\n",
    "def QoI_approx(lam,p,n):\n",
    "    '''Definie a QoI approximation with n+2 knots for piecewise linear spline'''\n",
    "    lam_knots = np.linspace(-1,1,n+2)\n",
    "    q_knots = QoI(lam_knots,p)\n",
    "    q = np.interp(lam, lam_knots, q_knots)\n",
    "    return q"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-01T08:29:49.511564Z",
     "start_time": "2021-07-01T08:29:49.467283Z"
    },
    "scrolled": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "# number of samples from init and observed mean (mu) and std (sigma)\n",
    "N, mus, sigma = int(1E5), [0.5,0.25,1], 0.1 \n",
    "lam = np.random.uniform(low=-1,high=1,size=N) # sample set of the init\n",
    "\n",
    "qvals_nonlinear = QoI(lam,5) # Evaluate lam^5 samples\n",
    "\n",
    "# Estimate the push-forward density for the QoI\n",
    "q_nonlinear_kde = kde(qvals_nonlinear)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Verify Assumption 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-01T08:29:50.217041Z",
     "start_time": "2021-07-01T08:29:49.520392Z"
    }
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#### Use plot to show approximate pushforward #####\n",
    "fig = plt.figure()\n",
    "J = int(1E3)\n",
    "qplot = np.linspace(-1,1, num=100)\n",
    "\n",
    "lam = np.random.uniform(low=-1,high=1,size=J) # sample set of the init\n",
    "\n",
    "# Evaluate the QoI map on this init sample set\n",
    "#qvals_nonlinear = QoI(lam,5) # Evaluate lam^5 samples\n",
    "for n in [1,2,4,8,16]:\n",
    "    qvals_approx_nonlinear = QoI_approx(lam,5,n) # Evaluate lam^5 samples\n",
    "    # Estimate the push-forward density for the QoI\n",
    "    q_nonlinear_kde1 = kde( qvals_approx_nonlinear )\n",
    "    pf_init_approx_plot = plt.plot(qplot,q_nonlinear_kde1(qplot),'--', linewidth=4, label=\"$n=$\" + str(n))\n",
    "\n",
    "plt.title('J = %1.0E' %(J)) \n",
    "plt.ylim([0,6.6])\n",
    "plt.legend();\n",
    "# fig.savefig(\"images/concept_example_pf_approxes_J_1E3\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-01T08:29:50.845307Z",
     "start_time": "2021-07-01T08:29:50.222039Z"
    },
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 504x360 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "d36fa1ca08fd481aa36fe56dd096923a",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(IntSlider(value=1, description='n'), IntSlider(value=1000, description='J', max=100000, …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<function __main__.plot_func(n, J)>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Failing Lipschitz as a function of approximate map\n",
    "\n",
    "fig = plt.figure()\n",
    "def plot_func(n,J):\n",
    "    fig.clear()\n",
    "    qplot = np.linspace(-1,1, num=100)\n",
    "    #observed_plot = plt.plot(qplot,norm.pdf(qplot, loc=mu, scale=sigma), 'r-', linewidth=4, label=\"$\\pi_\\mathcal{D}^{obs}$\")\n",
    "    pf_init_plot = plt.plot(qplot,1/10*np.abs(qplot)**(-4/5),'b-', linewidth=4, label=\"$\\pi_\\mathcal{D}^{Q(init)}$\")\n",
    "\n",
    "    np.random.seed(123456)\n",
    "    lam = np.random.uniform(low=-1,high=1,size=J) # sample set of the init\n",
    "    # Evaluate the QoI map on this init sample set\n",
    "    qvals_approx_nonlinear = QoI_approx(lam,5,n) # Evaluate lam^5 samples\n",
    "\n",
    "    # Estimate the push-forward density for the QoI\n",
    "    q_nonlinear_kde = kde( qvals_approx_nonlinear )\n",
    "    \n",
    "    pf_init_approx_plot = plt.plot(qplot,q_nonlinear_kde(qplot),'b--', linewidth=4, label=\"$\\pi_{\\mathcal{D},N}^{Q(init)}$\")\n",
    "    \n",
    "    plt.title('Lipschitz const. = %4.2f and Bound = %2.2f' %(np.max(np.abs(np.gradient(q_nonlinear_kde(qplot), qplot))),\n",
    "                                                                             np.max(q_nonlinear_kde(qplot))));\n",
    "interact(plot_func, \n",
    "         n = widgets.IntSlider(value=int(1),min=int(0),max=int(1E2),step=1),\n",
    "         J = widgets.IntSlider(value=int(1E3), min=int(1E3), max=int(1E5), step=int(1E3)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-01T08:29:55.504769Z",
     "start_time": "2021-07-01T08:29:50.850324Z"
    }
   },
   "outputs": [],
   "source": [
    "##### Generate data in Table 1 and 2 #####\n",
    "def assumption1(n, J):\n",
    "    np.random.seed(123456)\n",
    "    x = np.linspace(-1, 1, 100)\n",
    "    lam = np.random.uniform(low=-1, high=1, size=J)  # sample set of the init\n",
    "    qvals_approx_nonlinear = QoI_approx(lam, 5, n)  # Evaluate lam^5 samples\n",
    "    q_nonlinear_kde = kde(qvals_approx_nonlinear)\n",
    "    return np.round(np.max(np.abs(np.gradient(q_nonlinear_kde(x), x))), 2), np.round(np.max(q_nonlinear_kde(x)), 2)\n",
    "\n",
    "\n",
    "size_J = [int(1E3), int(1E4), int(1E5)]\n",
    "degree_n = [1, 2, 4, 8, 16]\n",
    "Bound_matrix, Lip_Bound_matrix = np.zeros((3, 5)), np.zeros((3, 5))\n",
    "for i in range(3):\n",
    "    for j in range(5):\n",
    "        n, J = degree_n[j], size_J[i]\n",
    "        Lip_Bound_matrix[i, j] = assumption1(n, J)[0]\n",
    "        Bound_matrix[i, j] = assumption1(n, J)[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Table 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-01T08:29:55.527800Z",
     "start_time": "2021-07-01T08:29:55.512715Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Table 1\n",
      "Bound under certain n and J values\n",
      "[[0.54 1.52 2.5  2.94 3.19]\n",
      " [0.53 2.09 3.42 4.1  4.43]\n",
      " [0.51 3.03 4.44 5.63 6.12]]\n"
     ]
    }
   ],
   "source": [
    "###########################################\n",
    "############## Table 1 ##################\n",
    "###########################################\n",
    "print('Table 1')        \n",
    "print('Bound under certain n and J values')\n",
    "print(Bound_matrix)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Table 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-01T08:29:55.564947Z",
     "start_time": "2021-07-01T08:29:55.542566Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Table 2\n",
      "Lipschitz bound under certain n and J values\n",
      "[[ 1.41  6.08 13.68 17.98 20.81]\n",
      " [ 2.19 13.89 27.26 38.35 44.06]\n",
      " [ 3.48 33.14 46.45 75.08 89.42]]\n"
     ]
    }
   ],
   "source": [
    "###########################################\n",
    "############## Table 2 ##################\n",
    "###########################################\n",
    "print('Table 2')\n",
    "print('Lipschitz bound under certain n and J values')\n",
    "print(Lip_Bound_matrix)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Verify Assumption 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-01T08:29:57.976814Z",
     "start_time": "2021-07-01T08:29:55.581698Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 504x360 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "68984d7546bb44149800a50336b70f2f",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(IntSlider(value=1, description='n'), IntSlider(value=10000, description='J', max=100000,…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<function __main__.plot_func(n, J, m)>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#### Use plot to show the difference between the observed and approximate pushforward #####\n",
    "#### m: case number; n: approximate map index; J: sample size ####\n",
    "fig = plt.figure()\n",
    "\n",
    "def plot_func(n, J, m):\n",
    "    fig.clear()\n",
    "    \n",
    "    qplot = np.linspace(-1,1, num=100)\n",
    "    observed_plot = plt.plot(qplot,norm.pdf(qplot, loc=mus[m], scale=sigma), 'r-', linewidth=4, label=\"$\\pi_\\mathcal{D}^{obs}$\")    \n",
    "\n",
    "    np.random.seed(123456)   \n",
    "    lam = np.random.uniform(low=-1,high=1,size=J) # sample set of the init\n",
    "    \n",
    "    # Evaluate the QoI map on this init sample set\n",
    "    qvals_approx_nonlinear = QoI_approx(lam,5,n) # Evaluate lam^5 samples\n",
    "    # Estimate the push-forward density for the QoI\n",
    "    q_nonlinear_kde = kde(qvals_approx_nonlinear)  \n",
    "    # Plot Aproximate push forward\n",
    "    pf_init_approx_plot = plt.plot(qplot,q_nonlinear_kde(qplot),'b--', linewidth=4, label=\"$\\pi_{\\mathcal{D}}^{Q_n(init)}$\")    \n",
    "    obs_vals_nonlinear = norm.pdf(qvals_approx_nonlinear, loc=mus[m], scale=sigma)\n",
    "    \n",
    "    # Compute r\n",
    "    r = np.divide(obs_vals_nonlinear,q_nonlinear_kde(qvals_approx_nonlinear))    \n",
    "    plt.title('$\\mathbb{E}(r) =$ %3.2f' %(np.mean(r)))    \n",
    "    plt.legend();\n",
    "    \n",
    "interact(plot_func, \n",
    "         n = widgets.IntSlider(value=int(1),min=int(0),max=int(1E2),step=1),\n",
    "         J = widgets.IntSlider(value=int(1E4), min=int(1E3), max=int(1E5), step=int(1E3)),\n",
    "         m = widgets.IntSlider(vlaue=int(0),min=int(0),max=int(2), step=1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-01T08:30:23.805290Z",
     "start_time": "2021-07-01T08:29:57.982499Z"
    }
   },
   "outputs": [],
   "source": [
    "# The expected r value\n",
    "def Meanr(n, J, m):\n",
    "    '''\n",
    "    n: index of approximating mapping\n",
    "    J: sample size of sample generated from parameter space\n",
    "    m: index of mu\n",
    "    '''\n",
    "    np.random.seed(123456)\n",
    "    lam = np.random.uniform(low=-1, high=1, size=J)  # sample set of the init\n",
    "    qvals_approx_nonlinear = QoI_approx(lam, 5, n)  # Evaluate lam^5 samples\n",
    "    q_nonlinear_kde = kde(qvals_approx_nonlinear)\n",
    "    obs_vals_nonlinear = norm.pdf(qvals_approx_nonlinear, loc=mus[m], scale=sigma)\n",
    "    r = np.divide(obs_vals_nonlinear, q_nonlinear_kde(qvals_approx_nonlinear))\n",
    "    return np.round(np.mean(r), 2)\n",
    "\n",
    "\n",
    "meanr_matrix = np.zeros((3, 5))\n",
    "for i in range(3):\n",
    "    for j in range(5):\n",
    "        J = int(1E4)\n",
    "        meanr_matrix[i, j] = Meanr(degree_n[j], J, i)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Table 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-01T08:30:23.815955Z",
     "start_time": "2021-07-01T08:30:23.808022Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Table 3\n",
      "Expected ratio for verifying Assumption 2\n",
      "[[1.   1.   1.   0.98 0.99]\n",
      " [0.99 0.88 0.85 0.92 0.92]\n",
      " [0.69 0.66 0.63 0.61 0.61]]\n"
     ]
    }
   ],
   "source": [
    "###########################################\n",
    "############## Table 3 ##################\n",
    "###########################################\n",
    "print('Table 3')\n",
    "print('Expected ratio for verifying Assumption 2')\n",
    "print(meanr_matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-01T08:30:23.847026Z",
     "start_time": "2021-07-01T08:30:23.827250Z"
    }
   },
   "outputs": [],
   "source": [
    "#### To make it cleaner, create Directory \"images\" to store all the figures ####\n",
    "imagepath = os.path.join(os.getcwd(),\"images\")\n",
    "os.makedirs(imagepath,exist_ok=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-01T08:30:23.876759Z",
     "start_time": "2021-07-01T08:30:23.853134Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 504x360 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "\n",
    "def plot_all(i):\n",
    "    fig.clear()\n",
    "    case = ['Case I', 'Case II', 'Case III']\n",
    "    qplot = np.linspace(-1, 1, num=100)\n",
    "    observed_plot = plt.plot(qplot, norm.pdf(\n",
    "        qplot, loc=mus[i], scale=sigma), 'r-.', label=\"$\\pi_\\mathcal{D}$\")\n",
    "    pf_init_plot = plt.plot(qplot, 1/10*np.abs(qplot)**(-4/5), 'b-',\n",
    "                             label=\"$\\pi_\\mathcal{D}^{Q}$\")\n",
    "    pf_init_plot = plt.plot(qplot, q_nonlinear_kde(qplot), 'b--',\n",
    "                             label=\"$\\pi_{\\mathcal{D},m}^{Q}$\")\n",
    "    plt.xlim([-1, 1])\n",
    "    plt.xlabel(\"$\\mathcal{D}$\")\n",
    "    plt.legend()\n",
    "    plt.title(case[i]);\n",
    "    loc = ['Left','Mid','Right']\n",
    "    if loc[i]:\n",
    "        filename = os.path.join(os.getcwd(), \"images\", \"Fig1(%s).png\"%(loc[i])) \n",
    "        plt.savefig(filename)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Left plot in Figure 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-01T08:30:24.562573Z",
     "start_time": "2021-07-01T08:30:23.888493Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "###########################################\n",
    "####### The left plot of Fig 1 ##########\n",
    "###########################################\n",
    "plot_all(0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Middle plot in Figure 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-01T08:30:25.191828Z",
     "start_time": "2021-07-01T08:30:24.565331Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#############################################\n",
    "####### The middle plot of Fig 1 ##########\n",
    "#############################################\n",
    "plot_all(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Right plot in Figure 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-01T08:30:25.845807Z",
     "start_time": "2021-07-01T08:30:25.196022Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "############################################\n",
    "####### The right plot of Fig 1 ##########\n",
    "############################################\n",
    "plot_all(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
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   "eqNumInitial": 1,
   "hotkeys": {
    "equation": "Ctrl-E",
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   "labels_anchors": false,
   "latex_user_defs": false,
   "report_style_numbering": false,
   "user_envs_cfg": false
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  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
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   "toc_position": {
    "height": "482.913px",
    "left": "126px",
    "top": "174.923px",
    "width": "494px"
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   "toc_section_display": false,
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     "delete_cmd_postfix": "",
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