examples/sensitivity_analysis/Sensitivity Analysis Examples.ipynb

{
 "cells": [
  {
   "cell_type": "raw",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## This cell will install the required dependencies in the current environment.\n",
    "## It is only required if you have not installed ttrecipes yet, \n",
    "## but it should not break anything if you had already done so.\n",
    "!pip install -r ../../requirements.txt\n",
    "!pip install -r ../../ttpy_repo.txt\n",
    "!pip install -e ../../"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "# TT recipes: Sensitivity Analysis Examples\n",
    "\n",
    "This notebook shows how to use the __sensitivity analysis__ methods from __TT recipes__. These examples use functions from the built-in library of well-known test functions included in the submodule _models_. Some of these examples have been used for related scientific publications:\n",
    "\n",
    "  - [1] _Sobol Tensor Trains for Global Sensitivity Analysis._\n",
    "    Rafael Ballester-Ripoll, Enrique G. Paredes, Renato Pajarola\n",
    "    [[arXiv](https://arxiv.org/abs/1712.00233)]\n",
    "\n",
    "  - [2] _Tensor Approximation of Advanced Metrics for Sensitivity Analysis._\n",
    "    Rafael Ballester-Ripoll, Enrique G. Paredes, Renato Pajarola\n",
    "    [[arXiv](https://arxiv.org/abs/1712.01633)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "import pprint\n",
    "import random\n",
    "import numpy as np\n",
    "from IPython.display import HTML, display\n",
    "%matplotlib inline\n",
    "\n",
    "# The most important \"import\" statement!\n",
    "import ttrecipes as tr"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's set some general settings for the examples in this tutorial:\n",
    "\n",
    "  - __bins__ will be used as the default number of samples per axis\n",
    "  - __max_order__ indicates the maximum order of the indices reported (all possible orders are always computed, this only affects the report tables)\n",
    "  - __verbose__ sets the _verbose_ mode to __True__ or __False__\n",
    "  - __seed__ is the random seed that will be used by the random generators\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "# Number of samples per axis\n",
    "bins = 100\n",
    "\n",
    "# Maximum order of the shown sensitivity indices \n",
    "max_order = 2\n",
    "\n",
    "# Verbose mode (True/False)\n",
    "verbose = True\n",
    "\n",
    "# Set a seed value (e.g. 9999) if you want to get\n",
    "# always the same results \n",
    "random_seed = None  # 9999\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Piston function\n",
    "\n",
    "We will use as a first example a function modeling the circular motion of a piston within a cylinder with a chain of nonlinear functions:\n",
    "\n",
    "\\begin{equation}\n",
    "f(\\vec{x}) = 2 \\pi \\sqrt{\\frac{M}{k + S^2 \\frac{P_0 V_0}{T_0} \\frac{T_a}{V^2}}}\n",
    "\\end{equation}\n",
    "\n",
    "with:\n",
    "\n",
    "\\begin{equation}\n",
    "\\begin{gathered}\n",
    "V = \\frac{S}{2k} \\left(\\sqrt{A^2 + 4k \\frac{P_0 V_0}{T_0} T_a} - A\\right) \\\\\n",
    "A = P_0 S + 19.62 M - \\frac{k V_0}{S}\n",
    "\\end{gathered}\n",
    "\\end{equation}\n",
    "\n",
    "More details about the function can be found at the [Virtual Library of Simulation Experiments](https://www.sfu.ca/~ssurjano/piston.html) from [Simon Fraser University](https://www.sfu.ca).\n",
    "\n",
    "The first step is to get the function object and the axis definitions from the library of test models included in TT recipes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[{'domain': (30, 60), 'name': 'M'},\n",
      " {'domain': (0.005, 0.02), 'name': 'S'},\n",
      " {'domain': (0.002, 0.01), 'name': 'V_0'},\n",
      " {'domain': (1000, 5000), 'name': 'k'},\n",
      " {'domain': (90000, 110000), 'name': 'P_0'},\n",
      " {'domain': (290, 296), 'name': 'T_a'},\n",
      " {'domain': (340, 360), 'name': 'T_0'}]\n"
     ]
    }
   ],
   "source": [
    "# Get example function and axes definitions from 'ttrecipes.models'\n",
    "f_piston, axes_piston = tr.models.get_piston()\n",
    "pprint.pprint(axes_piston)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The exact meaning of each one of the parameters is explained in the documentation of the function __tr.sensitivity_analysis.var_metrics()__:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function var_metrics in module ttrecipes.sensitivity_analysis:\n",
      "\n",
      "var_metrics(fun=None, axes=None, t=None, default_bins=100, effective_threshold=0.95, dist_fraction=5e-05, fun_mode='array', eps=1e-05, verbose=False, cross_kwargs=None, random_seed=None, max_order=2, show=True)\n",
      "    Variance-based sensitivity analysis.\n",
      "    \n",
      "    User-friendly wrapper that conducts a general variance-based sensitivity\n",
      "    analysis on an N-dimensional black-box function according to the given\n",
      "    marginal distributions.\n",
      "    \n",
      "    Args:\n",
      "        fun (callable): Callable object representing the N-dimensional function.\n",
      "        axes (iterable): A list of axis definitions. Each axis is a `dict` with\n",
      "            the name of the axis variable, its domain and its distribution function.\n",
      "            If the domain and the distribution function are both undefined,\n",
      "            a uniform(0, 1) distribution is assumed for the axis.\n",
      "    \n",
      "            axis: dict(name, domain, dist, display_name=None)\n",
      "                name (str): Variable name. Defaults to x_{i} (i = axis index).\n",
      "    \n",
      "                domain (tuple or np.ndarray): Domain definition.\n",
      "                    Defaults to tuple(None, None) when dist is defined.\n",
      "    \n",
      "                    tuple -> bounds (lower or None, upper or None). None values are\n",
      "                        truncated to (dist.ppf(dist_fraction), dist.ppf(1.0 - dist_fraction))\n",
      "                    np.ndarray -> samples (actual positions in the axis)\n",
      "    \n",
      "                dist (scipy.stats.rv_continuous or np.ndarray): Distribution definition.\n",
      "                    Defaults to a uniform distribution in the defined domain.\n",
      "    \n",
      "                    scipy.stats.rv_continuous-> frozen scipy.stats distribution\n",
      "                    np.ndarray -> values of the marginal PDF at the sampled domain positions.\n",
      "                        In this case, domain must contain a np.ndarray of the same size.\n",
      "    \n",
      "                display_name (str, optional): Variable name using LaTeX fomat. Defaults to None\n",
      "        t: a tensor to compute sensitivity indices of. Either `t` or `fun` must be given (but not both). Unlike `fun`,\n",
      "        `t` does not necessarily require `axes`\n",
      "    \n",
      "        default_bins (int, optional): Number of bins for axes without explicit\n",
      "            definition. Defaults to 100.\n",
      "        effective_threshold (float, optional): Threshold (1 - tolerance) for computation of\n",
      "            effective dimensions. Defaults to 0.95\n",
      "        dist_fraction (float, optional): Fraction of the probability distribution\n",
      "            discarded at each side of the sampling space when using 'spatial'\n",
      "            sampling. Defaults to 0.00005\n",
      "        fun_mode (str, optional): ['array' or 'parameters']. If 'array' (default),\n",
      "            the function takes a matrix as input, with one row per evaluation,\n",
      "            and returns a vector. If 'parameters', the function takes one instance\n",
      "            per call (each variable is an argument), and returns a scalar.\n",
      "        eps (float, optional): Tolerated relative approximation error in TT\n",
      "            computations. Defaults to 1e-5.\n",
      "        verbose (bool, optional): Verbose messages. Defaults to False.\n",
      "        cross_kwargs (:obj:`dict`, optional): Parameters for the cross\n",
      "            approximations. Defaults to None.\n",
      "        random_seed: value to initialize random generators to get reproducible results.\n",
      "            Defaults to None.\n",
      "        max_order (int, optional): Maximum order of the collected Sobol indices.\n",
      "            Defaults to 2.\n",
      "        show (bool, optional): Print results. Defaults to True.\n",
      "    \n",
      "    Returns:\n",
      "        tuple(dict, dict): A 'metrics' dictionary containing a structured and\n",
      "            easily accessible collection of sensitivity metrics, and additional\n",
      "            metainfomation with the actual Sobol Tensor Trains (for internal use\n",
      "            of TT recipes routines).\n",
      "    \n",
      "            {\n",
      "                'variables': ``list`` with the names of the model variables\n",
      "                'sobol_indices': ``dict`` with Sobol indices up to ``max_order``\n",
      "                'closed_sobol_indices': ``dict`` with Closed Sobol indices up to ``max_order``\n",
      "                'total_sobol_indices': ``dict`` with Total Sobol indices up to ``max_order``\n",
      "                'superset_sobol_indices': ``dict`` with Superset Sobol indices up to ``max_order``\n",
      "                'dimension_distribution': ``numpy.array`` with shape [N]\n",
      "                'mean_dimension': ``float`` in range [1, N]\n",
      "                'effective_superposition': ``int`` in range [1, N]\n",
      "                'effective_truncation': ``int`` in range [1, N]\n",
      "                'effective_successive': ``int`` in range [1, N]\n",
      "                'shapley_values': ``numpy.array`` with shape [N]\n",
      "                'banzhaf_coleman_values': ``numpy.array`` with shape [N]\n",
      "                '_tr_info': ``dict`` for internal use\n",
      "            }\n",
      "    \n",
      "    Examples:\n",
      "        Call the function with a user-defined function::\n",
      "    \n",
      "            from ttrecipes import sensitivity_analysis\n",
      "    \n",
      "            axes = [dict(name='Q', domain=(500, 3000), dist=sp.stats.gumbel_r(1013.0, 558.0)),\n",
      "                    dict(name='K_s', domain=(15.0, None), dist=sp.stats.norm(loc=30, scale=8)),\n",
      "                    dict(name='Z_m', dist=sp.stats.triang(loc=54.0, scale=2, c=0.5)),\n",
      "                    dict(name='H_d', dist=sp.stats.uniform(loc=7, scale=2)),\n",
      "                    dict(name='B', dist=sp.stats.triang(loc=295.0, scale=10, c=0.5)),\n",
      "                    dict(name='delta', dist=sp.stats.lognorm(scale=np.exp(2.19), s=0.517))]\n",
      "    \n",
      "            metrics = sensitivity_analysis.var_metrics(\n",
      "                my_function, axes, eps=1e-3, verbose=True)\n",
      "            tabulate_metrics(metrics)\n",
      "    \n",
      "    References:\n",
      "        * R. Ballester-Ripoll, E. G. Paredes, R. Pajarola. (2017)\n",
      "            \"Sobol Tensor Trains for Global Sensitivity Analysis\"\n",
      "            arXiv: https://arxiv.org/abs/1712.00233\n",
      "        * R. Ballester-Ripoll, E. G. Paredes, R. Pajarola (2017)\n",
      "            \"Tensor Approximation of Advanced Metrics for Sensitivity Analysis\"\n",
      "            arXiv: https://arxiv.org/abs/1712.01633\n",
      "        * Caflisch, R.E. and Morokoff, W.J. and Owen, A.B. (1997) \"Valuation of Mortgage\n",
      "            Backed Securities Using Brownian Bridges to Reduce Effective Dimension\"\n",
      "        * Pierre L'Ecuyer and Christiane Lemieux. (2000) \"Variance Reduction via Lattice Rules\"\n",
      "        * Owen, Art B. (2003) \"The dimension distribution and quadrature test functions\"\n",
      "        * Owen, Art B. (2014) \"Sobol' Indices and Shapley Value\"\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(tr.sensitivity_analysis.var_metrics)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And now let's compute and show the actual indices. With __TT recipes__ this is as simple as calling the __tr.sensitivity_analysis.var_metrics()__ function with the function object and the axis definitions. In this example we set the parameter __print_results__ to __True__ to get the results tables printed.\n",
    "\n",
    "All the other parameters are optional and control different settings, as the default number of samples per axes when it is not specifically set for every axis, the target relative error of the approximation, and more specific settings for the TT cross approximation algorithm. Check the documentation of the function in the previous cell."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+ Computing tensor approximations of variance-based sensitivity metrics...\n",
      "\n",
      "-> Building surrogate model\n",
      "Cross-approximating a 7D function with target error 1e-05...\n",
      "=multifuncrs= sweep 1{2}, max_dy: 5.983e+11, erank: 5.23723\n",
      "=multifuncrs= sweep 2{1}, max_dy: 2.150e-03, erank: 8.15037\n",
      "=multifuncrs= sweep 2{2}, max_dy: 2.150e-03, erank: 9.59911\n",
      "=multifuncrs= sweep 3{1}, max_dy: 5.017e-05, erank: 11.1739\n",
      "=multifuncrs= sweep 3{2}, max_dy: 5.017e-05, erank: 11.3578\n",
      "=multifuncrs= sweep 4{1}, max_dy: 6.574e-06, erank: 11.1739\n",
      "Function evaluations: 586100 in 1.857342004776001 seconds (time/evaluation: 3.168984823026789e-06)\n",
      "The resulting tensor has ranks [1, 9, 19, 19, 10, 8, 7, 1] and 87400 elements\n",
      "\n",
      "-> Computing sensitivity metrics\n",
      "=multifuncrs= sweep 1{2}, max_dy: 1.160e+00, erank: 7.71825\n",
      "=multifuncrs= sweep 2{1}, max_dy: 2.562e-06, erank: 7.71825\n",
      "\n",
      "-> Exporting results\n",
      "\n",
      "\t\t ** SENSITIVITY INDICES **\n",
      " Variable   |    Sobol |    Total |   Shapley |   Banzhaf-Coleman\n",
      "------------+----------+----------+-----------+-------------------\n",
      " M          | 0.039123 | 0.050511 |  0.044658 |          0.044578\n",
      " S          | 0.557384 | 0.599199 |  0.576674 |          0.575866\n",
      " V_0        | 0.321202 | 0.352519 |  0.335278 |          0.334487\n",
      " k          | 0.020616 | 0.066594 |  0.042076 |          0.041311\n",
      " P_0        | 0.001238 | 0.001304 |  0.001266 |          0.001264\n",
      " T_a        | 0.000003 | 0.000007 |  0.000005 |          0.000005\n",
      " T_0        | 0.000026 | 0.000058 |  0.000042 |          0.000042\n",
      "\n",
      "\t\t ** SENSITIVITY INDICES (ORDER 2) **\n",
      " Variable 1   | Variable 2   |     Sobol |    Total |   Closed |   Superset\n",
      "--------------+--------------+-----------+----------+----------+------------\n",
      " M            | S            |  0.004437 | 0.644381 | 0.600945 |   0.005329\n",
      " M            | V_0          |  0.004853 | 0.397490 | 0.365178 |   0.005540\n",
      " M            | k            |  0.001140 | 0.115644 | 0.060880 |   0.001461\n",
      " M            | P_0          | -0.000005 | 0.051812 | 0.040357 |   0.000003\n",
      " M            | T_a          |  0.000000 | 0.050518 | 0.039127 |   0.000000\n",
      " M            | T_0          |  0.000001 | 0.050566 | 0.039150 |   0.000003\n",
      " S            | V_0          |  0.004476 | 0.937827 | 0.883062 |   0.013891\n",
      " S            | k            |  0.023184 | 0.633510 | 0.601184 |   0.032284\n",
      " S            | P_0          |  0.000001 | 0.600498 | 0.558623 |   0.000005\n",
      " S            | T_a          |  0.000002 | 0.599205 | 0.557389 |   0.000001\n",
      " S            | T_0          |  0.000012 | 0.599247 | 0.557422 |   0.000011\n",
      " V_0          | k            |  0.012451 | 0.397774 | 0.354269 |   0.021340\n",
      " V_0          | P_0          |  0.000042 | 0.353784 | 0.322482 |   0.000040\n",
      " V_0          | T_a          |  0.000000 | 0.352527 | 0.321206 |   0.000000\n",
      " V_0          | T_0          |  0.000003 | 0.352577 | 0.321231 |   0.000001\n",
      " k            | P_0          |  0.000008 | 0.067848 | 0.021862 |   0.000050\n",
      " k            | T_a          |  0.000002 | 0.066599 | 0.020622 |   0.000003\n",
      " k            | T_0          |  0.000016 | 0.066633 | 0.020659 |   0.000020\n",
      " P_0          | T_a          |  0.000000 | 0.001311 | 0.001241 |   0.000000\n",
      " P_0          | T_0          |  0.000000 | 0.001362 | 0.001264 |   0.000000\n",
      " T_a          | T_0          |  0.000000 | 0.000065 | 0.000030 |   0.000000\n",
      "\n",
      "\t\t ** DIMENSION METRICS **\n",
      " Dimension Metric          |    Value |   Rel. Variance | Variables\n",
      "---------------------------+----------+-----------------+--------------\n",
      " Mean dimension            | 1.070193 |                 |\n",
      " Effective (superposition) | 2.000000 |        0.990217 |\n",
      " Effective (successive)    | 2.000000 |        0.960965 |\n",
      " Effective (truncation)    | 4.000000 |        0.998631 | M, S, V_0, k\n",
      "\n",
      "\t ** DIMENSION DISTRIBUTION **\n",
      "   Order |   Rel. Variance |   Cumul. Variance\n",
      "---------+-----------------+-------------------\n",
      "       1 |        0.939593 |          0.939593\n",
      "       2 |        0.050623 |          0.990217\n",
      "       3 |        0.009779 |          0.999996\n",
      "       4 |        0.000006 |          1.000001\n",
      "       5 |       -0.000001 |          1.000000\n",
      "       6 |        0.000000 |          1.000000\n",
      "       7 |        0.000000 |          1.000000\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Compute sensitivity indices and print result tables\n",
    "print(\"+ Computing tensor approximations of variance-based sensitivity metrics...\")\n",
    "metrics = tr.sensitivity_analysis.var_metrics(\n",
    "    f_piston, axes_piston, default_bins=bins, verbose=verbose, eps=1e-5,\n",
    "    random_seed=random_seed, cross_kwargs=dict(), max_order=max_order, show=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By default only indices up to second order are collected and printed. If we are interested in higher order interactions, we can collect more indices by simply running again the computation code with a different *max_order* parameter. Actually, since all the Sobol indices have been already computed and encoded in a Sobol Tensor Train, we can also call __tr.sensitivity_analysis.tabulate_metrics()__ (or __tr.sensitivity_analysis.collect_sobol()__) with the previously computed *metrics* object and the desired *max_order* value.\n",
    "\n",
    "Note that we can generate and export tables with different styles by using __tabulate_metrics()__ with the powerful formatting options from the [tabulate](https://bitbucket.org/astanin/python-tabulate) package. For example, we can generate HTML tables in a notebook environment or save individual tables as **TSV/CSV** files. All the examples in the *examples/sensitivity_analysis/piston.py* folder have a command line argument to export the results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead>\n",
       "<tr><th>Variable  </th><th style=\"text-align: right;\">   Sobol</th><th style=\"text-align: right;\">   Total</th><th style=\"text-align: right;\">  Shapley</th><th style=\"text-align: right;\">  Banzhaf-Coleman</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "<tr><td>M         </td><td style=\"text-align: right;\">0.039123</td><td style=\"text-align: right;\">0.050511</td><td style=\"text-align: right;\"> 0.044658</td><td style=\"text-align: right;\">         0.044578</td></tr>\n",
       "<tr><td>S         </td><td style=\"text-align: right;\">0.557384</td><td style=\"text-align: right;\">0.599199</td><td style=\"text-align: right;\"> 0.576674</td><td style=\"text-align: right;\">         0.575866</td></tr>\n",
       "<tr><td>V_0       </td><td style=\"text-align: right;\">0.321202</td><td style=\"text-align: right;\">0.352519</td><td style=\"text-align: right;\"> 0.335278</td><td style=\"text-align: right;\">         0.334487</td></tr>\n",
       "<tr><td>k         </td><td style=\"text-align: right;\">0.020616</td><td style=\"text-align: right;\">0.066594</td><td style=\"text-align: right;\"> 0.042076</td><td style=\"text-align: right;\">         0.041311</td></tr>\n",
       "<tr><td>P_0       </td><td style=\"text-align: right;\">0.001238</td><td style=\"text-align: right;\">0.001304</td><td style=\"text-align: right;\"> 0.001266</td><td style=\"text-align: right;\">         0.001264</td></tr>\n",
       "<tr><td>T_a       </td><td style=\"text-align: right;\">0.000003</td><td style=\"text-align: right;\">0.000007</td><td style=\"text-align: right;\"> 0.000005</td><td style=\"text-align: right;\">         0.000005</td></tr>\n",
       "<tr><td>T_0       </td><td style=\"text-align: right;\">0.000026</td><td style=\"text-align: right;\">0.000058</td><td style=\"text-align: right;\"> 0.000042</td><td style=\"text-align: right;\">         0.000042</td></tr>\n",
       "</tbody>\n",
       "</table>\n",
       "\n",
       "<table>\n",
       "<thead>\n",
       "<tr><th>Variable 1  </th><th>Variable 2  </th><th style=\"text-align: right;\">    Sobol</th><th style=\"text-align: right;\">   Total</th><th style=\"text-align: right;\">  Closed</th><th style=\"text-align: right;\">  Superset</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "<tr><td>M           </td><td>S           </td><td style=\"text-align: right;\"> 0.004437</td><td style=\"text-align: right;\">0.644381</td><td style=\"text-align: right;\">0.600945</td><td style=\"text-align: right;\">  0.005329</td></tr>\n",
       "<tr><td>M           </td><td>V_0         </td><td style=\"text-align: right;\"> 0.004853</td><td style=\"text-align: right;\">0.397490</td><td style=\"text-align: right;\">0.365178</td><td style=\"text-align: right;\">  0.005540</td></tr>\n",
       "<tr><td>M           </td><td>k           </td><td style=\"text-align: right;\"> 0.001140</td><td style=\"text-align: right;\">0.115644</td><td style=\"text-align: right;\">0.060880</td><td style=\"text-align: right;\">  0.001461</td></tr>\n",
       "<tr><td>M           </td><td>P_0         </td><td style=\"text-align: right;\">-0.000005</td><td style=\"text-align: right;\">0.051812</td><td style=\"text-align: right;\">0.040357</td><td style=\"text-align: right;\">  0.000003</td></tr>\n",
       "<tr><td>M           </td><td>T_a         </td><td style=\"text-align: right;\"> 0.000000</td><td style=\"text-align: right;\">0.050518</td><td style=\"text-align: right;\">0.039127</td><td style=\"text-align: right;\">  0.000000</td></tr>\n",
       "<tr><td>M           </td><td>T_0         </td><td style=\"text-align: right;\"> 0.000001</td><td style=\"text-align: right;\">0.050566</td><td style=\"text-align: right;\">0.039150</td><td style=\"text-align: right;\">  0.000003</td></tr>\n",
       "<tr><td>S           </td><td>V_0         </td><td style=\"text-align: right;\"> 0.004476</td><td style=\"text-align: right;\">0.937827</td><td style=\"text-align: right;\">0.883062</td><td style=\"text-align: right;\">  0.013891</td></tr>\n",
       "<tr><td>S           </td><td>k           </td><td style=\"text-align: right;\"> 0.023184</td><td style=\"text-align: right;\">0.633510</td><td style=\"text-align: right;\">0.601184</td><td style=\"text-align: right;\">  0.032284</td></tr>\n",
       "<tr><td>S           </td><td>P_0         </td><td style=\"text-align: right;\"> 0.000001</td><td style=\"text-align: right;\">0.600498</td><td style=\"text-align: right;\">0.558623</td><td style=\"text-align: right;\">  0.000005</td></tr>\n",
       "<tr><td>S           </td><td>T_a         </td><td style=\"text-align: right;\"> 0.000002</td><td style=\"text-align: right;\">0.599205</td><td style=\"text-align: right;\">0.557389</td><td style=\"text-align: right;\">  0.000001</td></tr>\n",
       "<tr><td>S           </td><td>T_0         </td><td style=\"text-align: right;\"> 0.000012</td><td style=\"text-align: right;\">0.599247</td><td style=\"text-align: right;\">0.557422</td><td style=\"text-align: right;\">  0.000011</td></tr>\n",
       "<tr><td>V_0         </td><td>k           </td><td style=\"text-align: right;\"> 0.012451</td><td style=\"text-align: right;\">0.397774</td><td style=\"text-align: right;\">0.354269</td><td style=\"text-align: right;\">  0.021340</td></tr>\n",
       "<tr><td>V_0         </td><td>P_0         </td><td style=\"text-align: right;\"> 0.000042</td><td style=\"text-align: right;\">0.353784</td><td style=\"text-align: right;\">0.322482</td><td style=\"text-align: right;\">  0.000040</td></tr>\n",
       "<tr><td>V_0         </td><td>T_a         </td><td style=\"text-align: right;\"> 0.000000</td><td style=\"text-align: right;\">0.352527</td><td style=\"text-align: right;\">0.321206</td><td style=\"text-align: right;\">  0.000000</td></tr>\n",
       "<tr><td>V_0         </td><td>T_0         </td><td style=\"text-align: right;\"> 0.000003</td><td style=\"text-align: right;\">0.352577</td><td style=\"text-align: right;\">0.321231</td><td style=\"text-align: right;\">  0.000001</td></tr>\n",
       "<tr><td>k           </td><td>P_0         </td><td style=\"text-align: right;\"> 0.000008</td><td style=\"text-align: right;\">0.067848</td><td style=\"text-align: right;\">0.021862</td><td style=\"text-align: right;\">  0.000050</td></tr>\n",
       "<tr><td>k           </td><td>T_a         </td><td style=\"text-align: right;\"> 0.000002</td><td style=\"text-align: right;\">0.066599</td><td style=\"text-align: right;\">0.020622</td><td style=\"text-align: right;\">  0.000003</td></tr>\n",
       "<tr><td>k           </td><td>T_0         </td><td style=\"text-align: right;\"> 0.000016</td><td style=\"text-align: right;\">0.066633</td><td style=\"text-align: right;\">0.020659</td><td style=\"text-align: right;\">  0.000020</td></tr>\n",
       "<tr><td>P_0         </td><td>T_a         </td><td style=\"text-align: right;\"> 0.000000</td><td style=\"text-align: right;\">0.001311</td><td style=\"text-align: right;\">0.001241</td><td style=\"text-align: right;\">  0.000000</td></tr>\n",
       "<tr><td>P_0         </td><td>T_0         </td><td style=\"text-align: right;\"> 0.000000</td><td style=\"text-align: right;\">0.001362</td><td style=\"text-align: right;\">0.001264</td><td style=\"text-align: right;\">  0.000000</td></tr>\n",
       "<tr><td>T_a         </td><td>T_0         </td><td style=\"text-align: right;\"> 0.000000</td><td style=\"text-align: right;\">0.000065</td><td style=\"text-align: right;\">0.000030</td><td style=\"text-align: right;\">  0.000000</td></tr>\n",
       "</tbody>\n",
       "</table>\n",
       "\n",
       "<table>\n",
       "<thead>\n",
       "<tr><th>Variable 1  </th><th>Variable 2  </th><th>Variable 3  </th><th style=\"text-align: right;\">    Sobol</th><th style=\"text-align: right;\">   Total</th><th style=\"text-align: right;\">  Closed</th><th style=\"text-align: right;\">  Superset</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "<tr><td>M           </td><td>S           </td><td>V_0         </td><td style=\"text-align: right;\"> 0.000632</td><td style=\"text-align: right;\">0.978090</td><td style=\"text-align: right;\">0.932108</td><td style=\"text-align: right;\">  0.000622</td></tr>\n",
       "<tr><td>M           </td><td>S           </td><td>k           </td><td style=\"text-align: right;\"> 0.000266</td><td style=\"text-align: right;\">0.677486</td><td style=\"text-align: right;\">0.646152</td><td style=\"text-align: right;\">  0.000255</td></tr>\n",
       "<tr><td>M           </td><td>S           </td><td>P_0         </td><td style=\"text-align: right;\"> 0.000002</td><td style=\"text-align: right;\">0.645679</td><td style=\"text-align: right;\">0.602181</td><td style=\"text-align: right;\">  0.000002</td></tr>\n",
       "<tr><td>M           </td><td>S           </td><td>T_a         </td><td style=\"text-align: right;\"> 0.000000</td><td style=\"text-align: right;\">0.644387</td><td style=\"text-align: right;\">0.600950</td><td style=\"text-align: right;\">  0.000000</td></tr>\n",
       "<tr><td>M           </td><td>S           </td><td>T_0         </td><td style=\"text-align: right;\"> 0.000001</td><td style=\"text-align: right;\">0.644427</td><td style=\"text-align: right;\">0.600985</td><td style=\"text-align: right;\">  0.000002</td></tr>\n",
       "<tr><td>M           </td><td>V_0         </td><td>k           </td><td style=\"text-align: right;\"> 0.000063</td><td style=\"text-align: right;\">0.441334</td><td style=\"text-align: right;\">0.399448</td><td style=\"text-align: right;\">  0.000051</td></tr>\n",
       "<tr><td>M           </td><td>V_0         </td><td>P_0         </td><td style=\"text-align: right;\"> 0.000003</td><td style=\"text-align: right;\">0.398753</td><td style=\"text-align: right;\">0.366456</td><td style=\"text-align: right;\">  0.000002</td></tr>\n",
       "<tr><td>M           </td><td>V_0         </td><td>T_a         </td><td style=\"text-align: right;\"> 0.000000</td><td style=\"text-align: right;\">0.397497</td><td style=\"text-align: right;\">0.365182</td><td style=\"text-align: right;\">  0.000000</td></tr>\n",
       "<tr><td>M           </td><td>V_0         </td><td>T_0         </td><td style=\"text-align: right;\"> 0.000000</td><td style=\"text-align: right;\">0.397545</td><td style=\"text-align: right;\">0.365208</td><td style=\"text-align: right;\">  0.000001</td></tr>\n",
       "<tr><td>M           </td><td>k           </td><td>P_0         </td><td style=\"text-align: right;\"> 0.000003</td><td style=\"text-align: right;\">0.116897</td><td style=\"text-align: right;\">0.062124</td><td style=\"text-align: right;\">  0.000002</td></tr>\n",
       "<tr><td>M           </td><td>k           </td><td>T_a         </td><td style=\"text-align: right;\"> 0.000000</td><td style=\"text-align: right;\">0.115649</td><td style=\"text-align: right;\">0.060886</td><td style=\"text-align: right;\">  0.000000</td></tr>\n",
       "<tr><td>M           </td><td>k           </td><td>T_0         </td><td style=\"text-align: right;\"> 0.000000</td><td style=\"text-align: right;\">0.115680</td><td style=\"text-align: right;\">0.060923</td><td style=\"text-align: right;\">  0.000000</td></tr>\n",
       "<tr><td>M           </td><td>P_0         </td><td>T_a         </td><td style=\"text-align: right;\">-0.000000</td><td style=\"text-align: right;\">0.051819</td><td style=\"text-align: right;\">0.040360</td><td style=\"text-align: right;\"> -0.000000</td></tr>\n",
       "<tr><td>M           </td><td>P_0         </td><td>T_0         </td><td style=\"text-align: right;\">-0.000000</td><td style=\"text-align: right;\">0.051867</td><td style=\"text-align: right;\">0.040383</td><td style=\"text-align: right;\"> -0.000000</td></tr>\n",
       "<tr><td>M           </td><td>T_a         </td><td>T_0         </td><td style=\"text-align: right;\"> 0.000000</td><td style=\"text-align: right;\">0.050573</td><td style=\"text-align: right;\">0.039154</td><td style=\"text-align: right;\">  0.000000</td></tr>\n",
       "<tr><td>S           </td><td>V_0         </td><td>k           </td><td style=\"text-align: right;\"> 0.008813</td><td style=\"text-align: right;\">0.959613</td><td style=\"text-align: right;\">0.948126</td><td style=\"text-align: right;\">  0.008815</td></tr>\n",
       "<tr><td>S           </td><td>V_0         </td><td>P_0         </td><td style=\"text-align: right;\">-0.000028</td><td style=\"text-align: right;\">0.939071</td><td style=\"text-align: right;\">0.884315</td><td style=\"text-align: right;\"> -0.000016</td></tr>\n",
       "<tr><td>S           </td><td>V_0         </td><td>T_a         </td><td style=\"text-align: right;\">-0.000001</td><td style=\"text-align: right;\">0.937833</td><td style=\"text-align: right;\">0.883067</td><td style=\"text-align: right;\"> -0.000000</td></tr>\n",
       "<tr><td>S           </td><td>V_0         </td><td>T_0         </td><td style=\"text-align: right;\">-0.000005</td><td style=\"text-align: right;\">0.937871</td><td style=\"text-align: right;\">0.883099</td><td style=\"text-align: right;\"> -0.000003</td></tr>\n",
       "<tr><td>S           </td><td>k           </td><td>P_0         </td><td style=\"text-align: right;\"> 0.000017</td><td style=\"text-align: right;\">0.634788</td><td style=\"text-align: right;\">0.602448</td><td style=\"text-align: right;\">  0.000029</td></tr>\n",
       "<tr><td>S           </td><td>k           </td><td>T_a         </td><td style=\"text-align: right;\"> 0.000000</td><td style=\"text-align: right;\">0.633514</td><td style=\"text-align: right;\">0.601191</td><td style=\"text-align: right;\">  0.000000</td></tr>\n",
       "<tr><td>S           </td><td>k           </td><td>T_0         </td><td style=\"text-align: right;\"> 0.000001</td><td style=\"text-align: right;\">0.633540</td><td style=\"text-align: right;\">0.601240</td><td style=\"text-align: right;\">  0.000002</td></tr>\n",
       "<tr><td>S           </td><td>P_0         </td><td>T_a         </td><td style=\"text-align: right;\">-0.000000</td><td style=\"text-align: right;\">0.600504</td><td style=\"text-align: right;\">0.558628</td><td style=\"text-align: right;\"> -0.000000</td></tr>\n",
       "<tr><td>S           </td><td>P_0         </td><td>T_0         </td><td style=\"text-align: right;\">-0.000000</td><td style=\"text-align: right;\">0.600546</td><td style=\"text-align: right;\">0.558661</td><td style=\"text-align: right;\"> -0.000000</td></tr>\n",
       "<tr><td>S           </td><td>T_a         </td><td>T_0         </td><td style=\"text-align: right;\"> 0.000000</td><td style=\"text-align: right;\">0.599253</td><td style=\"text-align: right;\">0.557427</td><td style=\"text-align: right;\">  0.000000</td></tr>\n",
       "<tr><td>V_0         </td><td>k           </td><td>P_0         </td><td style=\"text-align: right;\"> 0.000010</td><td style=\"text-align: right;\">0.399010</td><td style=\"text-align: right;\">0.355567</td><td style=\"text-align: right;\">  0.000022</td></tr>\n",
       "<tr><td>V_0         </td><td>k           </td><td>T_a         </td><td style=\"text-align: right;\"> 0.000000</td><td style=\"text-align: right;\">0.397779</td><td style=\"text-align: right;\">0.354275</td><td style=\"text-align: right;\">  0.000000</td></tr>\n",
       "<tr><td>V_0         </td><td>k           </td><td>T_0         </td><td style=\"text-align: right;\"> 0.000001</td><td style=\"text-align: right;\">0.397814</td><td style=\"text-align: right;\">0.354315</td><td style=\"text-align: right;\">  0.000002</td></tr>\n",
       "<tr><td>V_0         </td><td>P_0         </td><td>T_a         </td><td style=\"text-align: right;\"> 0.000000</td><td style=\"text-align: right;\">0.353791</td><td style=\"text-align: right;\">0.322485</td><td style=\"text-align: right;\">  0.000000</td></tr>\n",
       "<tr><td>V_0         </td><td>P_0         </td><td>T_0         </td><td style=\"text-align: right;\"> 0.000000</td><td style=\"text-align: right;\">0.353841</td><td style=\"text-align: right;\">0.322511</td><td style=\"text-align: right;\">  0.000000</td></tr>\n",
       "<tr><td>V_0         </td><td>T_a         </td><td>T_0         </td><td style=\"text-align: right;\"> 0.000000</td><td style=\"text-align: right;\">0.352584</td><td style=\"text-align: right;\">0.321235</td><td style=\"text-align: right;\">  0.000000</td></tr>\n",
       "<tr><td>k           </td><td>P_0         </td><td>T_a         </td><td style=\"text-align: right;\">-0.000000</td><td style=\"text-align: right;\">0.067853</td><td style=\"text-align: right;\">0.021867</td><td style=\"text-align: right;\"> -0.000000</td></tr>\n",
       "<tr><td>k           </td><td>P_0         </td><td>T_0         </td><td style=\"text-align: right;\">-0.000000</td><td style=\"text-align: right;\">0.067887</td><td style=\"text-align: right;\">0.021904</td><td style=\"text-align: right;\"> -0.000000</td></tr>\n",
       "<tr><td>k           </td><td>T_a         </td><td>T_0         </td><td style=\"text-align: right;\"> 0.000000</td><td style=\"text-align: right;\">0.066638</td><td style=\"text-align: right;\">0.020664</td><td style=\"text-align: right;\">  0.000000</td></tr>\n",
       "<tr><td>P_0         </td><td>T_a         </td><td>T_0         </td><td style=\"text-align: right;\">-0.000000</td><td style=\"text-align: right;\">0.001369</td><td style=\"text-align: right;\">0.001267</td><td style=\"text-align: right;\"> -0.000000</td></tr>\n",
       "</tbody>\n",
       "</table>\n",
       "\n",
       "<table>\n",
       "<thead>\n",
       "<tr><th>Variable 1  </th><th>Variable 2  </th><th>Variable 3  </th><th>Variable 4  </th><th style=\"text-align: right;\">    Sobol</th><th style=\"text-align: right;\">   Total</th><th style=\"text-align: right;\">  Closed</th><th style=\"text-align: right;\">  Superset</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "<tr><td>M           </td><td>S           </td><td>V_0         </td><td>k           </td><td style=\"text-align: right;\">-0.000011</td><td style=\"text-align: right;\">0.998733</td><td style=\"text-align: right;\">0.998631</td><td style=\"text-align: right;\"> -0.000012</td></tr>\n",
       "<tr><td>M           </td><td>S           </td><td>V_0         </td><td>P_0         </td><td style=\"text-align: right;\"> 0.000001</td><td style=\"text-align: right;\">0.979336</td><td style=\"text-align: right;\">0.933362</td><td style=\"text-align: right;\"> -0.000001</td></tr>\n",
       "<tr><td>M           </td><td>S           </td><td>V_0         </td><td>T_a         </td><td style=\"text-align: right;\"> 0.000000</td><td style=\"text-align: right;\">0.978096</td><td style=\"text-align: right;\">0.932113</td><td style=\"text-align: right;\">  0.000000</td></tr>\n",
       "<tr><td>M           </td><td>S           </td><td>V_0         </td><td>T_0         </td><td style=\"text-align: right;\"> 0.000001</td><td style=\"text-align: right;\">0.978133</td><td style=\"text-align: right;\">0.932147</td><td style=\"text-align: right;\">  0.000001</td></tr>\n",
       "<tr><td>M           </td><td>S           </td><td>k           </td><td>P_0         </td><td style=\"text-align: right;\"> 0.000001</td><td style=\"text-align: right;\">0.678765</td><td style=\"text-align: right;\">0.647416</td><td style=\"text-align: right;\"> -0.000001</td></tr>\n",
       "<tr><td>M           </td><td>S           </td><td>k           </td><td>T_a         </td><td style=\"text-align: right;\"> 0.000000</td><td style=\"text-align: right;\">0.677489</td><td style=\"text-align: right;\">0.646159</td><td style=\"text-align: right;\">  0.000000</td></tr>\n",
       "<tr><td>M           </td><td>S           </td><td>k           </td><td>T_0         </td><td style=\"text-align: right;\"> 0.000000</td><td style=\"text-align: right;\">0.677515</td><td style=\"text-align: right;\">0.646209</td><td style=\"text-align: right;\">  0.000000</td></tr>\n",
       "<tr><td>M           </td><td>S           </td><td>P_0         </td><td>T_a         </td><td style=\"text-align: right;\">-0.000000</td><td style=\"text-align: right;\">0.645685</td><td style=\"text-align: right;\">0.602186</td><td style=\"text-align: right;\"> -0.000000</td></tr>\n",
       "<tr><td>M           </td><td>S           </td><td>P_0         </td><td>T_0         </td><td style=\"text-align: right;\">-0.000000</td><td style=\"text-align: right;\">0.645725</td><td style=\"text-align: right;\">0.602221</td><td style=\"text-align: right;\"> -0.000000</td></tr>\n",
       "<tr><td>M           </td><td>S           </td><td>T_a         </td><td>T_0         </td><td style=\"text-align: right;\">-0.000000</td><td style=\"text-align: right;\">0.644433</td><td style=\"text-align: right;\">0.600990</td><td style=\"text-align: right;\"> -0.000000</td></tr>\n",
       "<tr><td>M           </td><td>V_0         </td><td>k           </td><td>P_0         </td><td style=\"text-align: right;\"> 0.000000</td><td style=\"text-align: right;\">0.442573</td><td style=\"text-align: right;\">0.400747</td><td style=\"text-align: right;\"> -0.000001</td></tr>\n",
       "<tr><td>M           </td><td>V_0         </td><td>k           </td><td>T_a         </td><td style=\"text-align: right;\"> 0.000000</td><td style=\"text-align: right;\">0.441339</td><td style=\"text-align: right;\">0.399454</td><td style=\"text-align: right;\">  0.000000</td></tr>\n",
       "<tr><td>M           </td><td>V_0         </td><td>k           </td><td>T_0         </td><td style=\"text-align: right;\"> 0.000000</td><td style=\"text-align: right;\">0.441372</td><td style=\"text-align: right;\">0.399496</td><td style=\"text-align: right;\">  0.000000</td></tr>\n",
       "<tr><td>M           </td><td>V_0         </td><td>P_0         </td><td>T_a         </td><td style=\"text-align: right;\">-0.000000</td><td style=\"text-align: right;\">0.398760</td><td style=\"text-align: right;\">0.366460</td><td style=\"text-align: right;\"> -0.000000</td></tr>\n",
       "<tr><td>M           </td><td>V_0         </td><td>P_0         </td><td>T_0         </td><td style=\"text-align: right;\">-0.000000</td><td style=\"text-align: right;\">0.398809</td><td style=\"text-align: right;\">0.366486</td><td style=\"text-align: right;\"> -0.000000</td></tr>\n",
       "<tr><td>M           </td><td>V_0         </td><td>T_a         </td><td>T_0         </td><td style=\"text-align: right;\"> 0.000000</td><td style=\"text-align: right;\">0.397552</td><td style=\"text-align: right;\">0.365212</td><td style=\"text-align: right;\">  0.000000</td></tr>\n",
       "<tr><td>M           </td><td>k           </td><td>P_0         </td><td>T_a         </td><td style=\"text-align: right;\">-0.000000</td><td style=\"text-align: right;\">0.116901</td><td style=\"text-align: right;\">0.062129</td><td style=\"text-align: right;\"> -0.000000</td></tr>\n",
       "<tr><td>M           </td><td>k           </td><td>P_0         </td><td>T_0         </td><td style=\"text-align: right;\">-0.000000</td><td style=\"text-align: right;\">0.116933</td><td style=\"text-align: right;\">0.062167</td><td style=\"text-align: right;\"> -0.000000</td></tr>\n",
       "<tr><td>M           </td><td>k           </td><td>T_a         </td><td>T_0         </td><td style=\"text-align: right;\"> 0.000000</td><td style=\"text-align: right;\">0.115685</td><td style=\"text-align: right;\">0.060929</td><td style=\"text-align: right;\">  0.000000</td></tr>\n",
       "<tr><td>M           </td><td>P_0         </td><td>T_a         </td><td>T_0         </td><td style=\"text-align: right;\">-0.000000</td><td style=\"text-align: right;\">0.051874</td><td style=\"text-align: right;\">0.040387</td><td style=\"text-align: right;\"> -0.000000</td></tr>\n",
       "<tr><td>S           </td><td>V_0         </td><td>k           </td><td>P_0         </td><td style=\"text-align: right;\"> 0.000013</td><td style=\"text-align: right;\">0.960846</td><td style=\"text-align: right;\">0.949427</td><td style=\"text-align: right;\">  0.000011</td></tr>\n",
       "<tr><td>S           </td><td>V_0         </td><td>k           </td><td>T_a         </td><td style=\"text-align: right;\"> 0.000000</td><td style=\"text-align: right;\">0.959617</td><td style=\"text-align: right;\">0.948133</td><td style=\"text-align: right;\">  0.000000</td></tr>\n",
       "<tr><td>S           </td><td>V_0         </td><td>k           </td><td>T_0         </td><td style=\"text-align: right;\"> 0.000001</td><td style=\"text-align: right;\">0.959640</td><td style=\"text-align: right;\">0.948181</td><td style=\"text-align: right;\">  0.000001</td></tr>\n",
       "<tr><td>S           </td><td>V_0         </td><td>P_0         </td><td>T_a         </td><td style=\"text-align: right;\">-0.000000</td><td style=\"text-align: right;\">0.939077</td><td style=\"text-align: right;\">0.884320</td><td style=\"text-align: right;\"> -0.000000</td></tr>\n",
       "<tr><td>S           </td><td>V_0         </td><td>P_0         </td><td>T_0         </td><td style=\"text-align: right;\">-0.000000</td><td style=\"text-align: right;\">0.939114</td><td style=\"text-align: right;\">0.884351</td><td style=\"text-align: right;\"> -0.000000</td></tr>\n",
       "<tr><td>S           </td><td>V_0         </td><td>T_a         </td><td>T_0         </td><td style=\"text-align: right;\"> 0.000000</td><td style=\"text-align: right;\">0.937876</td><td style=\"text-align: right;\">0.883103</td><td style=\"text-align: right;\">  0.000000</td></tr>\n",
       "<tr><td>S           </td><td>k           </td><td>P_0         </td><td>T_a         </td><td style=\"text-align: right;\"> 0.000000</td><td style=\"text-align: right;\">0.634792</td><td style=\"text-align: right;\">0.602455</td><td style=\"text-align: right;\"> -0.000000</td></tr>\n",
       "<tr><td>S           </td><td>k           </td><td>P_0         </td><td>T_0         </td><td style=\"text-align: right;\"> 0.000000</td><td style=\"text-align: right;\">0.634818</td><td style=\"text-align: right;\">0.602503</td><td style=\"text-align: right;\"> -0.000000</td></tr>\n",
       "<tr><td>S           </td><td>k           </td><td>T_a         </td><td>T_0         </td><td style=\"text-align: right;\"> 0.000000</td><td style=\"text-align: right;\">0.633544</td><td style=\"text-align: right;\">0.601247</td><td style=\"text-align: right;\">  0.000000</td></tr>\n",
       "<tr><td>S           </td><td>P_0         </td><td>T_a         </td><td>T_0         </td><td style=\"text-align: right;\">-0.000000</td><td style=\"text-align: right;\">0.600552</td><td style=\"text-align: right;\">0.558666</td><td style=\"text-align: right;\"> -0.000000</td></tr>\n",
       "<tr><td>V_0         </td><td>k           </td><td>P_0         </td><td>T_a         </td><td style=\"text-align: right;\">-0.000000</td><td style=\"text-align: right;\">0.399015</td><td style=\"text-align: right;\">0.355573</td><td style=\"text-align: right;\"> -0.000000</td></tr>\n",
       "<tr><td>V_0         </td><td>k           </td><td>P_0         </td><td>T_0         </td><td style=\"text-align: right;\">-0.000000</td><td style=\"text-align: right;\">0.399050</td><td style=\"text-align: right;\">0.355613</td><td style=\"text-align: right;\"> -0.000000</td></tr>\n",
       "<tr><td>V_0         </td><td>k           </td><td>T_a         </td><td>T_0         </td><td style=\"text-align: right;\"> 0.000000</td><td style=\"text-align: right;\">0.397819</td><td style=\"text-align: right;\">0.354321</td><td style=\"text-align: right;\">  0.000000</td></tr>\n",
       "<tr><td>V_0         </td><td>P_0         </td><td>T_a         </td><td>T_0         </td><td style=\"text-align: right;\"> 0.000000</td><td style=\"text-align: right;\">0.353848</td><td style=\"text-align: right;\">0.322514</td><td style=\"text-align: right;\">  0.000000</td></tr>\n",
       "<tr><td>k           </td><td>P_0         </td><td>T_a         </td><td>T_0         </td><td style=\"text-align: right;\"> 0.000000</td><td style=\"text-align: right;\">0.067892</td><td style=\"text-align: right;\">0.021910</td><td style=\"text-align: right;\"> -0.000000</td></tr>\n",
       "</tbody>\n",
       "</table>\n",
       "\n",
       "<table>\n",
       "<thead>\n",
       "<tr><th>Dimension Metric         </th><th style=\"text-align: right;\">   Value</th><th style=\"text-align: right;\">  Rel. Variance</th><th>Variables   </th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "<tr><td>Mean dimension           </td><td style=\"text-align: right;\">1.070193</td><td style=\"text-align: right;\">               </td><td>            </td></tr>\n",
       "<tr><td>Effective (superposition)</td><td style=\"text-align: right;\">2.000000</td><td style=\"text-align: right;\">       0.990217</td><td>            </td></tr>\n",
       "<tr><td>Effective (successive)   </td><td style=\"text-align: right;\">2.000000</td><td style=\"text-align: right;\">       0.960965</td><td>            </td></tr>\n",
       "<tr><td>Effective (truncation)   </td><td style=\"text-align: right;\">4.000000</td><td style=\"text-align: right;\">       0.998631</td><td>M, S, V_0, k</td></tr>\n",
       "</tbody>\n",
       "</table>\n",
       "\n",
       "<table>\n",
       "<thead>\n",
       "<tr><th style=\"text-align: right;\">  Order</th><th style=\"text-align: right;\">  Rel. Variance</th><th style=\"text-align: right;\">  Cumul. Variance</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "<tr><td style=\"text-align: right;\">      1</td><td style=\"text-align: right;\">       0.939593</td><td style=\"text-align: right;\">         0.939593</td></tr>\n",
       "<tr><td style=\"text-align: right;\">      2</td><td style=\"text-align: right;\">       0.050623</td><td style=\"text-align: right;\">         0.990217</td></tr>\n",
       "<tr><td style=\"text-align: right;\">      3</td><td style=\"text-align: right;\">       0.009779</td><td style=\"text-align: right;\">         0.999996</td></tr>\n",
       "<tr><td style=\"text-align: right;\">      4</td><td style=\"text-align: right;\">       0.000006</td><td style=\"text-align: right;\">         1.000001</td></tr>\n",
       "<tr><td style=\"text-align: right;\">      5</td><td style=\"text-align: right;\">      -0.000001</td><td style=\"text-align: right;\">         1.000000</td></tr>\n",
       "<tr><td style=\"text-align: right;\">      6</td><td style=\"text-align: right;\">       0.000000</td><td style=\"text-align: right;\">         1.000000</td></tr>\n",
       "<tr><td style=\"text-align: right;\">      7</td><td style=\"text-align: right;\">       0.000000</td><td style=\"text-align: right;\">         1.000000</td></tr>\n",
       "</tbody>\n",
       "</table>\n",
       "\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Collect sensitivity indices of a different order from the \n",
    "# already computed Sobol Tensor Train\n",
    "output = tr.sensitivity_analysis.tabulate_metrics(\n",
    "    metrics, max_order=4, show_titles=False, output_mode='string', tablefmt='html')\n",
    "display(HTML(output))\n",
    "\n",
    "# # Export results as CSV tables \n",
    "# tables = tr.sensitivity_analysis.tabulate_metrics(\n",
    "#     metrics, max_order=2, tablefmt='tsv', output_mode='dict', show_titles=False)\n",
    "# for key, value in tables.items():\n",
    "#     with open(\"piston_\" + key + \".csv\", 'w') as f:\n",
    "#         f.write(value)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Querying Sobol indices\n",
    "\n",
    "The function **tr.sensitivity_analysis.query_sobol()** can answer a range of sensitivity queries. It takes a Sobol Tensor Train as an input and produces a) a tuple and b) the variance attained by that tuple. It works on Sobol, Total/Closed Sobol, and Superset indices. See some examples below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "** Model variables: ['M', 'S', 'V_0', 'k', 'P_0', 'T_a', 'T_0'] **\n",
      "\n",
      "Highest order-2 total index: (['S', 'V_0'], 0.93782556608208945)\n"
     ]
    }
   ],
   "source": [
    "print(\"** Model variables: {} **\\n\".format(metrics['variables']))\n",
    "print(\"Highest order-2 total index:\",\n",
    "      tr.sensitivity_analysis.query_sobol(metrics, max_order=2,\n",
    "                                          index_type='total'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Lowest order-1 closed index: (['T_a'], 4.3633457070813009e-06)\n"
     ]
    }
   ],
   "source": [
    "print(\"Lowest order-1 closed index:\",\n",
    "      tr.sensitivity_analysis.query_sobol(metrics, min_order=1,\n",
    "                                          index_type='closed', mode='lowest'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Highest order-2 superset index, other than ['T_a'} (or [5]): (['S'], 0.59919876389999815)\n"
     ]
    }
   ],
   "source": [
    "print(\"Highest order-2 superset index, other than ['T_a'} (or [5]):\",\n",
    "      tr.sensitivity_analysis.query_sobol(metrics, exclude=['T_a'], max_order=2,\n",
    "                                          index_type='superset', mode='highest'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Single variable that interacts the most with ['S'] (or [1]): (['S', 'k'], 0.032283593997117693)\n"
     ]
    }
   ],
   "source": [
    "print(\"Single variable that interacts the most with ['S'] (or [1]):\",\n",
    "      tr.sensitivity_analysis.query_sobol(metrics, include=['S'],\n",
    "                                          min_order=2, max_order=2,\n",
    "                                          index_type='superset', mode='highest'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Plotting sensitivity metrics\n",
    "\n",
    "The module **tr.sensitivity_analysis** also provides basic plotting functionality (require Matplotlib) to give a visual overview of the computed sensitivity metrics. See some examples below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1032d1940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = tr.sensitivity_analysis.plot_indices(metrics)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c1714e828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = tr.sensitivity_analysis.plot_dim_distribution(metrics, max_order=5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sobol __G__ function\n",
    "\n",
    "Let's try now a more challenging example using the __Sobol _G_ __ function, which is a well-known synthetic model that can be tune for generating low or high-order interactions depending on the vector of coefficients __a_i__. A much more detailed description of this function can be also found at the [Virtual Library of Simulation Experiments](https://www.sfu.ca/~ssurjano/gfunc.html).\n",
    "\n",
    "In this case, we will run the example with the same function parameters used in [2]:\n",
    "  - **dimensions**: 20\n",
    "  - **a_i**: 0 _[for i in range(n)]_\n",
    "\n",
    "Again, the first step is to get the function object and the axis definitions from models library:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[{'name': 'X_00'},\n",
      " {'name': 'X_01'},\n",
      " {'name': 'X_02'},\n",
      " {'name': 'X_03'},\n",
      " {'name': 'X_04'},\n",
      " {'name': 'X_05'},\n",
      " {'name': 'X_06'},\n",
      " {'name': 'X_07'},\n",
      " {'name': 'X_08'},\n",
      " {'name': 'X_09'},\n",
      " {'name': 'X_10'},\n",
      " {'name': 'X_11'},\n",
      " {'name': 'X_12'},\n",
      " {'name': 'X_13'},\n",
      " {'name': 'X_14'},\n",
      " {'name': 'X_15'},\n",
      " {'name': 'X_16'},\n",
      " {'name': 'X_17'},\n",
      " {'name': 'X_18'},\n",
      " {'name': 'X_19'},\n",
      " {'name': 'X_20'},\n",
      " {'name': 'X_21'},\n",
      " {'name': 'X_22'},\n",
      " {'name': 'X_23'},\n",
      " {'name': 'X_24'},\n",
      " {'name': 'X_25'},\n",
      " {'name': 'X_26'},\n",
      " {'name': 'X_27'},\n",
      " {'name': 'X_28'},\n",
      " {'name': 'X_29'},\n",
      " {'name': 'X_30'},\n",
      " {'name': 'X_31'}]\n"
     ]
    }
   ],
   "source": [
    "# Set example parameters\n",
    "dims = 32\n",
    "acoeff = 0\n",
    "\n",
    "# Get example function and axes definitions from 'ttrecipes.models'\n",
    "f_sobolg, axes_sobolg = tr.models.get_sobol_g(dims, a=acoeff, name_tmpl='X_{:0>2}')\n",
    "pprint.pprint(axes_sobolg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Once the function and axes have been defined for our specific case, we just need to pass them as parameters to the __tr.sensitivity_analysis.var_metrics()__  function to get all the sensitivity metrics:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+ Computing tensor approximations of variance-based sensitivity metrics...\n",
      "\n",
      "-> Building surrogate model\n",
      "Cross-approximating a 32D function with target error 1e-10...\n",
      "=multifuncrs= sweep 1{2}, max_dy: 1.456e+58, erank: 2.93684\n",
      "=multifuncrs= sweep 2{1}, max_dy: 5.295e-16, erank: 2.93684\n",
      "Function evaluations: 97800 in 3.089887857437134 seconds (time/evaluation: 3.159394537256783e-05)\n",
      "The resulting tensor has ranks [1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1] and 27600 elements\n",
      "\n",
      "-> Computing sensitivity metrics\n",
      "=multifuncrs= sweep 1{2}, max_dy: 1.365e-01, erank: 2.93684\n",
      "=multifuncrs= sweep 2{1}, max_dy: 5.478e-16, erank: 2.93684\n",
      "\n",
      "-> Exporting results\n",
      "\n",
      "\t\t ** SENSITIVITY INDICES **\n",
      " Variable   |    Sobol |    Total |   Shapley |   Banzhaf-Coleman\n",
      "------------+----------+----------+-----------+-------------------\n",
      " X_00       | 0.000034 | 0.249950 |  0.031250 |          0.003987\n",
      " X_01       | 0.000034 | 0.249950 |  0.031250 |          0.003987\n",
      " X_02       | 0.000034 | 0.249950 |  0.031250 |          0.003987\n",
      " X_03       | 0.000034 | 0.249950 |  0.031250 |          0.003987\n",
      " X_04       | 0.000034 | 0.249950 |  0.031250 |          0.003987\n",
      " X_05       | 0.000034 | 0.249950 |  0.031250 |          0.003987\n",
      " X_06       | 0.000034 | 0.249950 |  0.031250 |          0.003987\n",
      " X_07       | 0.000034 | 0.249950 |  0.031250 |          0.003987\n",
      " X_08       | 0.000034 | 0.249950 |  0.031250 |          0.003987\n",
      " X_09       | 0.000034 | 0.249950 |  0.031250 |          0.003987\n",
      " X_10       | 0.000034 | 0.249950 |  0.031250 |          0.003987\n",
      " X_11       | 0.000034 | 0.249950 |  0.031250 |          0.003987\n",
      " X_12       | 0.000034 | 0.249950 |  0.031250 |          0.003987\n",
      " X_13       | 0.000034 | 0.249950 |  0.031250 |          0.003987\n",
      " X_14       | 0.000034 | 0.249950 |  0.031250 |          0.003987\n",
      " X_15       | 0.000034 | 0.249950 |  0.031250 |          0.003987\n",
      " X_16       | 0.000034 | 0.249950 |  0.031250 |          0.003987\n",
      " X_17       | 0.000034 | 0.249950 |  0.031250 |          0.003987\n",
      " X_18       | 0.000034 | 0.249950 |  0.031250 |          0.003987\n",
      " X_19       | 0.000034 | 0.249950 |  0.031250 |          0.003987\n",
      " X_20       | 0.000034 | 0.249950 |  0.031250 |          0.003987\n",
      " X_21       | 0.000034 | 0.249950 |  0.031250 |          0.003987\n",
      " X_22       | 0.000034 | 0.249950 |  0.031250 |          0.003987\n",
      " X_23       | 0.000034 | 0.249950 |  0.031250 |          0.003987\n",
      " X_24       | 0.000034 | 0.249950 |  0.031250 |          0.003987\n",
      " X_25       | 0.000034 | 0.249950 |  0.031250 |          0.003987\n",
      " X_26       | 0.000034 | 0.249950 |  0.031250 |          0.003987\n",
      " X_27       | 0.000034 | 0.249950 |  0.031250 |          0.003987\n",
      " X_28       | 0.000034 | 0.249950 |  0.031250 |          0.003987\n",
      " X_29       | 0.000034 | 0.249950 |  0.031250 |          0.003987\n",
      " X_30       | 0.000034 | 0.249950 |  0.031250 |          0.003987\n",
      " X_31       | 0.000034 | 0.249950 |  0.031250 |          0.003987\n",
      "\n",
      "\t\t ** SENSITIVITY INDICES (ORDER 2) **\n",
      " Variable 1   | Variable 2   |    Sobol |    Total |   Closed |   Superset\n",
      "--------------+--------------+----------+----------+----------+------------\n",
      " X_00         | X_01         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_00         | X_02         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_00         | X_03         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_00         | X_04         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_00         | X_05         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_00         | X_06         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_00         | X_07         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_00         | X_08         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_00         | X_09         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_00         | X_10         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_00         | X_11         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_00         | X_12         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_00         | X_13         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_00         | X_14         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_00         | X_15         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_00         | X_16         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_00         | X_17         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_00         | X_18         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_00         | X_19         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_00         | X_20         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_00         | X_21         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_00         | X_22         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_00         | X_23         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_00         | X_24         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_00         | X_25         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_00         | X_26         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_00         | X_27         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_00         | X_28         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_00         | X_29         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_00         | X_30         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_00         | X_31         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_01         | X_02         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_01         | X_03         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_01         | X_04         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_01         | X_05         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_01         | X_06         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_01         | X_07         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_01         | X_08         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_01         | X_09         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_01         | X_10         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_01         | X_11         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_01         | X_12         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_01         | X_13         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_01         | X_14         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_01         | X_15         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_01         | X_16         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_01         | X_17         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_01         | X_18         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_01         | X_19         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_01         | X_20         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_01         | X_21         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_01         | X_22         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_01         | X_23         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_01         | X_24         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_01         | X_25         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_01         | X_26         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_01         | X_27         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_01         | X_28         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_01         | X_29         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_01         | X_30         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_01         | X_31         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_02         | X_03         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_02         | X_04         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_02         | X_05         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_02         | X_06         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_02         | X_07         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_02         | X_08         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_02         | X_09         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_02         | X_10         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_02         | X_11         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_02         | X_12         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_02         | X_13         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_02         | X_14         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_02         | X_15         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_02         | X_16         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_02         | X_17         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_02         | X_18         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_02         | X_19         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_02         | X_20         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_02         | X_21         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_02         | X_22         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_02         | X_23         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_02         | X_24         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_02         | X_25         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_02         | X_26         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_02         | X_27         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_02         | X_28         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_02         | X_29         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_02         | X_30         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_02         | X_31         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_03         | X_04         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_03         | X_05         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_03         | X_06         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_03         | X_07         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_03         | X_08         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_03         | X_09         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_03         | X_10         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_03         | X_11         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_03         | X_12         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_03         | X_13         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_03         | X_14         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_03         | X_15         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_03         | X_16         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_03         | X_17         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_03         | X_18         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_03         | X_19         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_03         | X_20         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_03         | X_21         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_03         | X_22         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_03         | X_23         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_03         | X_24         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_03         | X_25         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_03         | X_26         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_03         | X_27         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_03         | X_28         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_03         | X_29         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_03         | X_30         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_03         | X_31         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_04         | X_05         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_04         | X_06         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_04         | X_07         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_04         | X_08         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_04         | X_09         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_04         | X_10         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_04         | X_11         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_04         | X_12         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_04         | X_13         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_04         | X_14         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_04         | X_15         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_04         | X_16         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_04         | X_17         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_04         | X_18         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_04         | X_19         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_04         | X_20         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_04         | X_21         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_04         | X_22         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_04         | X_23         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_04         | X_24         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_04         | X_25         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_04         | X_26         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_04         | X_27         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_04         | X_28         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_04         | X_29         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_04         | X_30         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_04         | X_31         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_05         | X_06         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_05         | X_07         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_05         | X_08         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_05         | X_09         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_05         | X_10         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_05         | X_11         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_05         | X_12         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_05         | X_13         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_05         | X_14         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_05         | X_15         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_05         | X_16         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_05         | X_17         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_05         | X_18         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_05         | X_19         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_05         | X_20         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_05         | X_21         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_05         | X_22         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_05         | X_23         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_05         | X_24         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_05         | X_25         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_05         | X_26         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_05         | X_27         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_05         | X_28         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_05         | X_29         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_05         | X_30         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_05         | X_31         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_06         | X_07         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_06         | X_08         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_06         | X_09         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_06         | X_10         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_06         | X_11         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_06         | X_12         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_06         | X_13         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_06         | X_14         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_06         | X_15         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_06         | X_16         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_06         | X_17         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_06         | X_18         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_06         | X_19         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_06         | X_20         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_06         | X_21         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_06         | X_22         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_06         | X_23         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_06         | X_24         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_06         | X_25         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_06         | X_26         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_06         | X_27         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_06         | X_28         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_06         | X_29         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_06         | X_30         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_06         | X_31         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_07         | X_08         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_07         | X_09         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_07         | X_10         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_07         | X_11         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_07         | X_12         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_07         | X_13         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_07         | X_14         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_07         | X_15         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_07         | X_16         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_07         | X_17         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_07         | X_18         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_07         | X_19         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_07         | X_20         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_07         | X_21         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_07         | X_22         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_07         | X_23         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_07         | X_24         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_07         | X_25         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_07         | X_26         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_07         | X_27         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_07         | X_28         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_07         | X_29         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_07         | X_30         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_07         | X_31         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_08         | X_09         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_08         | X_10         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_08         | X_11         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_08         | X_12         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_08         | X_13         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_08         | X_14         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_08         | X_15         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_08         | X_16         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_08         | X_17         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_08         | X_18         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_08         | X_19         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_08         | X_20         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_08         | X_21         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_08         | X_22         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_08         | X_23         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_08         | X_24         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_08         | X_25         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_08         | X_26         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_08         | X_27         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_08         | X_28         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_08         | X_29         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_08         | X_30         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_08         | X_31         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_09         | X_10         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_09         | X_11         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_09         | X_12         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_09         | X_13         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_09         | X_14         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_09         | X_15         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_09         | X_16         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_09         | X_17         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_09         | X_18         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_09         | X_19         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_09         | X_20         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_09         | X_21         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_09         | X_22         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_09         | X_23         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_09         | X_24         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_09         | X_25         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_09         | X_26         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_09         | X_27         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_09         | X_28         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_09         | X_29         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_09         | X_30         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_09         | X_31         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_10         | X_11         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_10         | X_12         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_10         | X_13         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_10         | X_14         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_10         | X_15         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_10         | X_16         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_10         | X_17         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_10         | X_18         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_10         | X_19         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_10         | X_20         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_10         | X_21         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_10         | X_22         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_10         | X_23         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_10         | X_24         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_10         | X_25         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_10         | X_26         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_10         | X_27         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_10         | X_28         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_10         | X_29         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_10         | X_30         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_10         | X_31         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_11         | X_12         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_11         | X_13         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_11         | X_14         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_11         | X_15         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_11         | X_16         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_11         | X_17         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_11         | X_18         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_11         | X_19         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_11         | X_20         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_11         | X_21         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_11         | X_22         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_11         | X_23         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_11         | X_24         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_11         | X_25         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_11         | X_26         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_11         | X_27         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_11         | X_28         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_11         | X_29         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_11         | X_30         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_11         | X_31         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_12         | X_13         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_12         | X_14         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_12         | X_15         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_12         | X_16         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_12         | X_17         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_12         | X_18         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_12         | X_19         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_12         | X_20         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_12         | X_21         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_12         | X_22         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_12         | X_23         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_12         | X_24         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_12         | X_25         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_12         | X_26         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_12         | X_27         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_12         | X_28         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_12         | X_29         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_12         | X_30         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_12         | X_31         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_13         | X_14         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_13         | X_15         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_13         | X_16         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_13         | X_17         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_13         | X_18         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_13         | X_19         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_13         | X_20         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_13         | X_21         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_13         | X_22         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_13         | X_23         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_13         | X_24         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_13         | X_25         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_13         | X_26         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_13         | X_27         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_13         | X_28         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_13         | X_29         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_13         | X_30         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_13         | X_31         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_14         | X_15         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_14         | X_16         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_14         | X_17         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_14         | X_18         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_14         | X_19         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_14         | X_20         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_14         | X_21         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_14         | X_22         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_14         | X_23         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_14         | X_24         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_14         | X_25         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_14         | X_26         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_14         | X_27         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_14         | X_28         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_14         | X_29         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_14         | X_30         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_14         | X_31         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_15         | X_16         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_15         | X_17         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_15         | X_18         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_15         | X_19         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_15         | X_20         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_15         | X_21         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_15         | X_22         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_15         | X_23         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_15         | X_24         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_15         | X_25         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_15         | X_26         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_15         | X_27         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_15         | X_28         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_15         | X_29         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_15         | X_30         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_15         | X_31         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_16         | X_17         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_16         | X_18         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_16         | X_19         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_16         | X_20         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_16         | X_21         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_16         | X_22         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_16         | X_23         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_16         | X_24         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_16         | X_25         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_16         | X_26         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_16         | X_27         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_16         | X_28         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_16         | X_29         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_16         | X_30         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_16         | X_31         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_17         | X_18         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_17         | X_19         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_17         | X_20         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_17         | X_21         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_17         | X_22         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_17         | X_23         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_17         | X_24         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_17         | X_25         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_17         | X_26         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_17         | X_27         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_17         | X_28         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_17         | X_29         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_17         | X_30         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_17         | X_31         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_18         | X_19         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_18         | X_20         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_18         | X_21         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_18         | X_22         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_18         | X_23         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_18         | X_24         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_18         | X_25         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_18         | X_26         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_18         | X_27         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_18         | X_28         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_18         | X_29         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_18         | X_30         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_18         | X_31         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_19         | X_20         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_19         | X_21         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_19         | X_22         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_19         | X_23         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_19         | X_24         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_19         | X_25         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_19         | X_26         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_19         | X_27         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_19         | X_28         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_19         | X_29         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_19         | X_30         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_19         | X_31         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_20         | X_21         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_20         | X_22         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_20         | X_23         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_20         | X_24         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_20         | X_25         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_20         | X_26         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_20         | X_27         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_20         | X_28         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_20         | X_29         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_20         | X_30         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_20         | X_31         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_21         | X_22         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_21         | X_23         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_21         | X_24         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_21         | X_25         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_21         | X_26         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_21         | X_27         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_21         | X_28         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_21         | X_29         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_21         | X_30         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_21         | X_31         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_22         | X_23         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_22         | X_24         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_22         | X_25         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_22         | X_26         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_22         | X_27         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_22         | X_28         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_22         | X_29         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_22         | X_30         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_22         | X_31         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_23         | X_24         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_23         | X_25         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_23         | X_26         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_23         | X_27         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_23         | X_28         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_23         | X_29         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_23         | X_30         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_23         | X_31         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_24         | X_25         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_24         | X_26         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_24         | X_27         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_24         | X_28         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_24         | X_29         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_24         | X_30         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_24         | X_31         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_25         | X_26         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_25         | X_27         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_25         | X_28         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_25         | X_29         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_25         | X_30         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_25         | X_31         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_26         | X_27         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_26         | X_28         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_26         | X_29         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_26         | X_30         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_26         | X_31         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_27         | X_28         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_27         | X_29         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_27         | X_30         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_27         | X_31         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_28         | X_29         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_28         | X_30         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_28         | X_31         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_29         | X_30         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_29         | X_31         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      " X_30         | X_31         | 0.000011 | 0.437432 | 0.000078 |   0.062469\n",
      "\n",
      "\t\t ** DIMENSION METRICS **\n",
      " Dimension Metric          |     Value |   Rel. Variance | Variables\n",
      "---------------------------+-----------+-----------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------\n",
      " Mean dimension            |  7.998406 |                 |\n",
      " Effective (superposition) | 12.000000 |        0.962330 |\n",
      " Effective (successive)    | 32.000000 |        1.000000 |\n",
      " Effective (truncation)    | 32.000000 |        1.000000 | X_00, X_01, X_02, X_03, X_04, X_05, X_06, X_07, X_08, X_09, X_10, X_11, X_12, X_13, X_14, X_15, X_16, X_17, X_18, X_19, X_20, X_21, X_22, X_23, X_24, X_25, X_26, X_27, X_28, X_29, X_30, X_31\n",
      "\n",
      "\t ** DIMENSION DISTRIBUTION **\n",
      "   Order |   Rel. Variance |   Cumul. Variance\n",
      "---------+-----------------+-------------------\n",
      "       1 |        0.001075 |          0.001075\n",
      "       2 |        0.005550 |          0.006625\n",
      "       3 |        0.018492 |          0.025117\n",
      "       4 |        0.044672 |          0.069789\n",
      "       5 |        0.083354 |          0.153143\n",
      "       6 |        0.124981 |          0.278124\n",
      "       7 |        0.154677 |          0.432800\n",
      "       8 |        0.161057 |          0.593857\n",
      "       9 |        0.143104 |          0.736962\n",
      "      10 |        0.109670 |          0.846631\n",
      "      11 |        0.073084 |          0.919715\n",
      "      12 |        0.042615 |          0.962330\n",
      "      13 |        0.021845 |          0.984175\n",
      "      14 |        0.009878 |          0.994054\n",
      "      15 |        0.003950 |          0.998004\n",
      "      16 |        0.001398 |          0.999402\n",
      "      17 |        0.000439 |          0.999840\n",
      "      18 |        0.000122 |          0.999962\n",
      "      19 |        0.000030 |          0.999992\n",
      "      20 |        0.000006 |          0.999999\n",
      "      21 |        0.000001 |          1.000000\n",
      "      22 |        0.000000 |          1.000000\n",
      "      23 |        0.000000 |          1.000000\n",
      "      24 |        0.000000 |          1.000000\n",
      "      25 |        0.000000 |          1.000000\n",
      "      26 |        0.000000 |          1.000000\n",
      "      27 |        0.000000 |          1.000000\n",
      "      28 |        0.000000 |          1.000000\n",
      "      29 |        0.000000 |          1.000000\n",
      "      30 |        0.000000 |          1.000000\n",
      "      31 |        0.000000 |          1.000000\n",
      "      32 |        0.000000 |          1.000000\n",
      "\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead>\n",
       "<tr><th>Variable  </th><th style=\"text-align: right;\">   Sobol</th><th style=\"text-align: right;\">   Total</th><th style=\"text-align: right;\">  Shapley</th><th style=\"text-align: right;\">  Banzhaf-Coleman</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "<tr><td>X_00      </td><td style=\"text-align: right;\">0.000034</td><td style=\"text-align: right;\">0.249950</td><td style=\"text-align: right;\"> 0.031250</td><td style=\"text-align: right;\">         0.003987</td></tr>\n",
       "<tr><td>X_01      </td><td style=\"text-align: right;\">0.000034</td><td style=\"text-align: right;\">0.249950</td><td style=\"text-align: right;\"> 0.031250</td><td style=\"text-align: right;\">         0.003987</td></tr>\n",
       "<tr><td>X_02      </td><td style=\"text-align: right;\">0.000034</td><td style=\"text-align: right;\">0.249950</td><td style=\"text-align: right;\"> 0.031250</td><td style=\"text-align: right;\">         0.003987</td></tr>\n",
       "<tr><td>X_03      </td><td style=\"text-align: right;\">0.000034</td><td style=\"text-align: right;\">0.249950</td><td style=\"text-align: right;\"> 0.031250</td><td style=\"text-align: right;\">         0.003987</td></tr>\n",
       "<tr><td>X_04      </td><td style=\"text-align: right;\">0.000034</td><td style=\"text-align: right;\">0.249950</td><td style=\"text-align: right;\"> 0.031250</td><td style=\"text-align: right;\">         0.003987</td></tr>\n",
       "<tr><td>X_05      </td><td style=\"text-align: right;\">0.000034</td><td style=\"text-align: right;\">0.249950</td><td style=\"text-align: right;\"> 0.031250</td><td style=\"text-align: right;\">         0.003987</td></tr>\n",
       "<tr><td>X_06      </td><td style=\"text-align: right;\">0.000034</td><td style=\"text-align: right;\">0.249950</td><td style=\"text-align: right;\"> 0.031250</td><td style=\"text-align: right;\">         0.003987</td></tr>\n",
       "<tr><td>X_07      </td><td style=\"text-align: right;\">0.000034</td><td style=\"text-align: right;\">0.249950</td><td style=\"text-align: right;\"> 0.031250</td><td style=\"text-align: right;\">         0.003987</td></tr>\n",
       "<tr><td>X_08      </td><td style=\"text-align: right;\">0.000034</td><td style=\"text-align: right;\">0.249950</td><td style=\"text-align: right;\"> 0.031250</td><td style=\"text-align: right;\">         0.003987</td></tr>\n",
       "<tr><td>X_09      </td><td style=\"text-align: right;\">0.000034</td><td style=\"text-align: right;\">0.249950</td><td style=\"text-align: right;\"> 0.031250</td><td style=\"text-align: right;\">         0.003987</td></tr>\n",
       "<tr><td>X_10      </td><td style=\"text-align: right;\">0.000034</td><td style=\"text-align: right;\">0.249950</td><td style=\"text-align: right;\"> 0.031250</td><td style=\"text-align: right;\">         0.003987</td></tr>\n",
       "<tr><td>X_11      </td><td style=\"text-align: right;\">0.000034</td><td style=\"text-align: right;\">0.249950</td><td style=\"text-align: right;\"> 0.031250</td><td style=\"text-align: right;\">         0.003987</td></tr>\n",
       "<tr><td>X_12      </td><td style=\"text-align: right;\">0.000034</td><td style=\"text-align: right;\">0.249950</td><td style=\"text-align: right;\"> 0.031250</td><td style=\"text-align: right;\">         0.003987</td></tr>\n",
       "<tr><td>X_13      </td><td style=\"text-align: right;\">0.000034</td><td style=\"text-align: right;\">0.249950</td><td style=\"text-align: right;\"> 0.031250</td><td style=\"text-align: right;\">         0.003987</td></tr>\n",
       "<tr><td>X_14      </td><td style=\"text-align: right;\">0.000034</td><td style=\"text-align: right;\">0.249950</td><td style=\"text-align: right;\"> 0.031250</td><td style=\"text-align: right;\">         0.003987</td></tr>\n",
       "<tr><td>X_15      </td><td style=\"text-align: right;\">0.000034</td><td style=\"text-align: right;\">0.249950</td><td style=\"text-align: right;\"> 0.031250</td><td style=\"text-align: right;\">         0.003987</td></tr>\n",
       "<tr><td>X_16      </td><td style=\"text-align: right;\">0.000034</td><td style=\"text-align: right;\">0.249950</td><td style=\"text-align: right;\"> 0.031250</td><td style=\"text-align: right;\">         0.003987</td></tr>\n",
       "<tr><td>X_17      </td><td style=\"text-align: right;\">0.000034</td><td style=\"text-align: right;\">0.249950</td><td style=\"text-align: right;\"> 0.031250</td><td style=\"text-align: right;\">         0.003987</td></tr>\n",
       "<tr><td>X_18      </td><td style=\"text-align: right;\">0.000034</td><td style=\"text-align: right;\">0.249950</td><td style=\"text-align: right;\"> 0.031250</td><td style=\"text-align: right;\">         0.003987</td></tr>\n",
       "<tr><td>X_19      </td><td style=\"text-align: right;\">0.000034</td><td style=\"text-align: right;\">0.249950</td><td style=\"text-align: right;\"> 0.031250</td><td style=\"text-align: right;\">         0.003987</td></tr>\n",
       "<tr><td>X_20      </td><td style=\"text-align: right;\">0.000034</td><td style=\"text-align: right;\">0.249950</td><td style=\"text-align: right;\"> 0.031250</td><td style=\"text-align: right;\">         0.003987</td></tr>\n",
       "<tr><td>X_21      </td><td style=\"text-align: right;\">0.000034</td><td style=\"text-align: right;\">0.249950</td><td style=\"text-align: right;\"> 0.031250</td><td style=\"text-align: right;\">         0.003987</td></tr>\n",
       "<tr><td>X_22      </td><td style=\"text-align: right;\">0.000034</td><td style=\"text-align: right;\">0.249950</td><td style=\"text-align: right;\"> 0.031250</td><td style=\"text-align: right;\">         0.003987</td></tr>\n",
       "<tr><td>X_23      </td><td style=\"text-align: right;\">0.000034</td><td style=\"text-align: right;\">0.249950</td><td style=\"text-align: right;\"> 0.031250</td><td style=\"text-align: right;\">         0.003987</td></tr>\n",
       "<tr><td>X_24      </td><td style=\"text-align: right;\">0.000034</td><td style=\"text-align: right;\">0.249950</td><td style=\"text-align: right;\"> 0.031250</td><td style=\"text-align: right;\">         0.003987</td></tr>\n",
       "<tr><td>X_25      </td><td style=\"text-align: right;\">0.000034</td><td style=\"text-align: right;\">0.249950</td><td style=\"text-align: right;\"> 0.031250</td><td style=\"text-align: right;\">         0.003987</td></tr>\n",
       "<tr><td>X_26      </td><td style=\"text-align: right;\">0.000034</td><td style=\"text-align: right;\">0.249950</td><td style=\"text-align: right;\"> 0.031250</td><td style=\"text-align: right;\">         0.003987</td></tr>\n",
       "<tr><td>X_27      </td><td style=\"text-align: right;\">0.000034</td><td style=\"text-align: right;\">0.249950</td><td style=\"text-align: right;\"> 0.031250</td><td style=\"text-align: right;\">         0.003987</td></tr>\n",
       "<tr><td>X_28      </td><td style=\"text-align: right;\">0.000034</td><td style=\"text-align: right;\">0.249950</td><td style=\"text-align: right;\"> 0.031250</td><td style=\"text-align: right;\">         0.003987</td></tr>\n",
       "<tr><td>X_29      </td><td style=\"text-align: right;\">0.000034</td><td style=\"text-align: right;\">0.249950</td><td style=\"text-align: right;\"> 0.031250</td><td style=\"text-align: right;\">         0.003987</td></tr>\n",
       "<tr><td>X_30      </td><td style=\"text-align: right;\">0.000034</td><td style=\"text-align: right;\">0.249950</td><td style=\"text-align: right;\"> 0.031250</td><td style=\"text-align: right;\">         0.003987</td></tr>\n",
       "<tr><td>X_31      </td><td style=\"text-align: right;\">0.000034</td><td style=\"text-align: right;\">0.249950</td><td style=\"text-align: right;\"> 0.031250</td><td style=\"text-align: right;\">         0.003987</td></tr>\n",
       "</tbody>\n",
       "</table>\n",
       "\n",
       "<table>\n",
       "<thead>\n",
       "<tr><th>Variable 1  </th><th>Variable 2  </th><th style=\"text-align: right;\">   Sobol</th><th style=\"text-align: right;\">   Total</th><th style=\"text-align: right;\">  Closed</th><th style=\"text-align: right;\">  Superset</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "<tr><td>X_00        </td><td>X_01        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_00        </td><td>X_02        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_00        </td><td>X_03        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_00        </td><td>X_04        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_00        </td><td>X_05        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_00        </td><td>X_06        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_00        </td><td>X_07        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_00        </td><td>X_08        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_00        </td><td>X_09        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_00        </td><td>X_10        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_00        </td><td>X_11        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_00        </td><td>X_12        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_00        </td><td>X_13        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_00        </td><td>X_14        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_00        </td><td>X_15        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_00        </td><td>X_16        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_00        </td><td>X_17        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_00        </td><td>X_18        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_00        </td><td>X_19        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_00        </td><td>X_20        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_00        </td><td>X_21        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_00        </td><td>X_22        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_00        </td><td>X_23        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_00        </td><td>X_24        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_00        </td><td>X_25        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_00        </td><td>X_26        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_00        </td><td>X_27        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_00        </td><td>X_28        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_00        </td><td>X_29        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_00        </td><td>X_30        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_00        </td><td>X_31        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_01        </td><td>X_02        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_01        </td><td>X_03        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_01        </td><td>X_04        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_01        </td><td>X_05        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_01        </td><td>X_06        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_01        </td><td>X_07        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_01        </td><td>X_08        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_01        </td><td>X_09        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_01        </td><td>X_10        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_01        </td><td>X_11        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_01        </td><td>X_12        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_01        </td><td>X_13        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_01        </td><td>X_14        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_01        </td><td>X_15        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_01        </td><td>X_16        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_01        </td><td>X_17        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_01        </td><td>X_18        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_01        </td><td>X_19        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_01        </td><td>X_20        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_01        </td><td>X_21        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_01        </td><td>X_22        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_01        </td><td>X_23        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_01        </td><td>X_24        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_01        </td><td>X_25        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_01        </td><td>X_26        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_01        </td><td>X_27        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_01        </td><td>X_28        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_01        </td><td>X_29        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_01        </td><td>X_30        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_01        </td><td>X_31        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_02        </td><td>X_03        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_02        </td><td>X_04        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_02        </td><td>X_05        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_02        </td><td>X_06        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_02        </td><td>X_07        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_02        </td><td>X_08        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_02        </td><td>X_09        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_02        </td><td>X_10        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_02        </td><td>X_11        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_02        </td><td>X_12        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_02        </td><td>X_13        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_02        </td><td>X_14        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_02        </td><td>X_15        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_02        </td><td>X_16        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_02        </td><td>X_17        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_02        </td><td>X_18        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_02        </td><td>X_19        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_02        </td><td>X_20        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_02        </td><td>X_21        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_02        </td><td>X_22        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_02        </td><td>X_23        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_02        </td><td>X_24        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_02        </td><td>X_25        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_02        </td><td>X_26        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_02        </td><td>X_27        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_02        </td><td>X_28        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_02        </td><td>X_29        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_02        </td><td>X_30        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_02        </td><td>X_31        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_03        </td><td>X_04        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_03        </td><td>X_05        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_03        </td><td>X_06        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_03        </td><td>X_07        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_03        </td><td>X_08        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_03        </td><td>X_09        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_03        </td><td>X_10        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_03        </td><td>X_11        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_03        </td><td>X_12        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_03        </td><td>X_13        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_03        </td><td>X_14        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_03        </td><td>X_15        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_03        </td><td>X_16        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_03        </td><td>X_17        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_03        </td><td>X_18        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_03        </td><td>X_19        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_03        </td><td>X_20        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_03        </td><td>X_21        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_03        </td><td>X_22        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_03        </td><td>X_23        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_03        </td><td>X_24        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_03        </td><td>X_25        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_03        </td><td>X_26        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_03        </td><td>X_27        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_03        </td><td>X_28        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_03        </td><td>X_29        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_03        </td><td>X_30        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_03        </td><td>X_31        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_04        </td><td>X_05        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_04        </td><td>X_06        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_04        </td><td>X_07        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_04        </td><td>X_08        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_04        </td><td>X_09        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_04        </td><td>X_10        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_04        </td><td>X_11        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_04        </td><td>X_12        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_04        </td><td>X_13        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_04        </td><td>X_14        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_04        </td><td>X_15        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_04        </td><td>X_16        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_04        </td><td>X_17        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_04        </td><td>X_18        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_04        </td><td>X_19        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_04        </td><td>X_20        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_04        </td><td>X_21        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_04        </td><td>X_22        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_04        </td><td>X_23        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_04        </td><td>X_24        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_04        </td><td>X_25        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_04        </td><td>X_26        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_04        </td><td>X_27        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_04        </td><td>X_28        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_04        </td><td>X_29        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_04        </td><td>X_30        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_04        </td><td>X_31        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_05        </td><td>X_06        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_05        </td><td>X_07        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_05        </td><td>X_08        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_05        </td><td>X_09        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_05        </td><td>X_10        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_05        </td><td>X_11        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_05        </td><td>X_12        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_05        </td><td>X_13        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_05        </td><td>X_14        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_05        </td><td>X_15        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_05        </td><td>X_16        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_05        </td><td>X_17        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_05        </td><td>X_18        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_05        </td><td>X_19        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_05        </td><td>X_20        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_05        </td><td>X_21        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_05        </td><td>X_22        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_05        </td><td>X_23        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_05        </td><td>X_24        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_05        </td><td>X_25        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_05        </td><td>X_26        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_05        </td><td>X_27        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_05        </td><td>X_28        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_05        </td><td>X_29        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_05        </td><td>X_30        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_05        </td><td>X_31        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_06        </td><td>X_07        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_06        </td><td>X_08        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_06        </td><td>X_09        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_06        </td><td>X_10        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_06        </td><td>X_11        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_06        </td><td>X_12        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_06        </td><td>X_13        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_06        </td><td>X_14        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_06        </td><td>X_15        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_06        </td><td>X_16        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_06        </td><td>X_17        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_06        </td><td>X_18        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_06        </td><td>X_19        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_06        </td><td>X_20        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_06        </td><td>X_21        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_06        </td><td>X_22        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_06        </td><td>X_23        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_06        </td><td>X_24        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_06        </td><td>X_25        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_06        </td><td>X_26        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_06        </td><td>X_27        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_06        </td><td>X_28        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_06        </td><td>X_29        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_06        </td><td>X_30        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_06        </td><td>X_31        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_07        </td><td>X_08        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_07        </td><td>X_09        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_07        </td><td>X_10        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_07        </td><td>X_11        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_07        </td><td>X_12        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_07        </td><td>X_13        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_07        </td><td>X_14        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_07        </td><td>X_15        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_07        </td><td>X_16        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_07        </td><td>X_17        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_07        </td><td>X_18        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_07        </td><td>X_19        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_07        </td><td>X_20        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_07        </td><td>X_21        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_07        </td><td>X_22        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_07        </td><td>X_23        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_07        </td><td>X_24        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_07        </td><td>X_25        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_07        </td><td>X_26        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_07        </td><td>X_27        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_07        </td><td>X_28        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_07        </td><td>X_29        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_07        </td><td>X_30        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_07        </td><td>X_31        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_08        </td><td>X_09        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_08        </td><td>X_10        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_08        </td><td>X_11        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_08        </td><td>X_12        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_08        </td><td>X_13        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_08        </td><td>X_14        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_08        </td><td>X_15        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_08        </td><td>X_16        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_08        </td><td>X_17        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_08        </td><td>X_18        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_08        </td><td>X_19        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_08        </td><td>X_20        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_08        </td><td>X_21        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_08        </td><td>X_22        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_08        </td><td>X_23        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_08        </td><td>X_24        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_08        </td><td>X_25        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_08        </td><td>X_26        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_08        </td><td>X_27        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_08        </td><td>X_28        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_08        </td><td>X_29        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_08        </td><td>X_30        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_08        </td><td>X_31        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_09        </td><td>X_10        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_09        </td><td>X_11        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_09        </td><td>X_12        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_09        </td><td>X_13        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_09        </td><td>X_14        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_09        </td><td>X_15        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_09        </td><td>X_16        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_09        </td><td>X_17        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_09        </td><td>X_18        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_09        </td><td>X_19        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_09        </td><td>X_20        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_09        </td><td>X_21        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_09        </td><td>X_22        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_09        </td><td>X_23        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_09        </td><td>X_24        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_09        </td><td>X_25        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_09        </td><td>X_26        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_09        </td><td>X_27        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_09        </td><td>X_28        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_09        </td><td>X_29        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_09        </td><td>X_30        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_09        </td><td>X_31        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_10        </td><td>X_11        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_10        </td><td>X_12        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_10        </td><td>X_13        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_10        </td><td>X_14        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_10        </td><td>X_15        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_10        </td><td>X_16        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_10        </td><td>X_17        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_10        </td><td>X_18        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_10        </td><td>X_19        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_10        </td><td>X_20        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_10        </td><td>X_21        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_10        </td><td>X_22        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_10        </td><td>X_23        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_10        </td><td>X_24        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_10        </td><td>X_25        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_10        </td><td>X_26        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_10        </td><td>X_27        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_10        </td><td>X_28        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_10        </td><td>X_29        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_10        </td><td>X_30        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_10        </td><td>X_31        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_11        </td><td>X_12        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_11        </td><td>X_13        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_11        </td><td>X_14        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_11        </td><td>X_15        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_11        </td><td>X_16        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_11        </td><td>X_17        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_11        </td><td>X_18        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_11        </td><td>X_19        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_11        </td><td>X_20        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_11        </td><td>X_21        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_11        </td><td>X_22        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_11        </td><td>X_23        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_11        </td><td>X_24        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_11        </td><td>X_25        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_11        </td><td>X_26        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_11        </td><td>X_27        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_11        </td><td>X_28        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_11        </td><td>X_29        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_11        </td><td>X_30        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_11        </td><td>X_31        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_12        </td><td>X_13        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_12        </td><td>X_14        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_12        </td><td>X_15        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_12        </td><td>X_16        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_12        </td><td>X_17        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_12        </td><td>X_18        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_12        </td><td>X_19        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_12        </td><td>X_20        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_12        </td><td>X_21        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_12        </td><td>X_22        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_12        </td><td>X_23        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_12        </td><td>X_24        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_12        </td><td>X_25        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_12        </td><td>X_26        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_12        </td><td>X_27        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_12        </td><td>X_28        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_12        </td><td>X_29        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_12        </td><td>X_30        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_12        </td><td>X_31        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_13        </td><td>X_14        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_13        </td><td>X_15        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_13        </td><td>X_16        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_13        </td><td>X_17        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_13        </td><td>X_18        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_13        </td><td>X_19        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_13        </td><td>X_20        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_13        </td><td>X_21        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_13        </td><td>X_22        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_13        </td><td>X_23        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_13        </td><td>X_24        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_13        </td><td>X_25        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_13        </td><td>X_26        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_13        </td><td>X_27        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_13        </td><td>X_28        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_13        </td><td>X_29        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_13        </td><td>X_30        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_13        </td><td>X_31        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_14        </td><td>X_15        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_14        </td><td>X_16        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_14        </td><td>X_17        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_14        </td><td>X_18        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_14        </td><td>X_19        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_14        </td><td>X_20        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_14        </td><td>X_21        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_14        </td><td>X_22        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_14        </td><td>X_23        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_14        </td><td>X_24        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_14        </td><td>X_25        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_14        </td><td>X_26        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_14        </td><td>X_27        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_14        </td><td>X_28        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_14        </td><td>X_29        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_14        </td><td>X_30        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_14        </td><td>X_31        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_15        </td><td>X_16        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_15        </td><td>X_17        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_15        </td><td>X_18        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_15        </td><td>X_19        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_15        </td><td>X_20        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_15        </td><td>X_21        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_15        </td><td>X_22        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_15        </td><td>X_23        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_15        </td><td>X_24        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_15        </td><td>X_25        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_15        </td><td>X_26        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_15        </td><td>X_27        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_15        </td><td>X_28        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_15        </td><td>X_29        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_15        </td><td>X_30        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_15        </td><td>X_31        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_16        </td><td>X_17        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_16        </td><td>X_18        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_16        </td><td>X_19        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_16        </td><td>X_20        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_16        </td><td>X_21        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_16        </td><td>X_22        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_16        </td><td>X_23        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_16        </td><td>X_24        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_16        </td><td>X_25        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_16        </td><td>X_26        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_16        </td><td>X_27        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_16        </td><td>X_28        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_16        </td><td>X_29        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_16        </td><td>X_30        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_16        </td><td>X_31        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_17        </td><td>X_18        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_17        </td><td>X_19        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_17        </td><td>X_20        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_17        </td><td>X_21        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_17        </td><td>X_22        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_17        </td><td>X_23        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_17        </td><td>X_24        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_17        </td><td>X_25        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_17        </td><td>X_26        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_17        </td><td>X_27        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_17        </td><td>X_28        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_17        </td><td>X_29        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_17        </td><td>X_30        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_17        </td><td>X_31        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_18        </td><td>X_19        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_18        </td><td>X_20        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_18        </td><td>X_21        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_18        </td><td>X_22        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_18        </td><td>X_23        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_18        </td><td>X_24        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_18        </td><td>X_25        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_18        </td><td>X_26        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_18        </td><td>X_27        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_18        </td><td>X_28        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_18        </td><td>X_29        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_18        </td><td>X_30        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_18        </td><td>X_31        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_19        </td><td>X_20        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_19        </td><td>X_21        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_19        </td><td>X_22        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_19        </td><td>X_23        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_19        </td><td>X_24        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_19        </td><td>X_25        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_19        </td><td>X_26        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_19        </td><td>X_27        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_19        </td><td>X_28        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_19        </td><td>X_29        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_19        </td><td>X_30        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_19        </td><td>X_31        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_20        </td><td>X_21        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_20        </td><td>X_22        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_20        </td><td>X_23        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_20        </td><td>X_24        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_20        </td><td>X_25        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_20        </td><td>X_26        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_20        </td><td>X_27        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_20        </td><td>X_28        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_20        </td><td>X_29        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_20        </td><td>X_30        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_20        </td><td>X_31        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_21        </td><td>X_22        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_21        </td><td>X_23        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_21        </td><td>X_24        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_21        </td><td>X_25        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_21        </td><td>X_26        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_21        </td><td>X_27        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_21        </td><td>X_28        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_21        </td><td>X_29        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_21        </td><td>X_30        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_21        </td><td>X_31        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_22        </td><td>X_23        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_22        </td><td>X_24        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_22        </td><td>X_25        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_22        </td><td>X_26        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_22        </td><td>X_27        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_22        </td><td>X_28        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_22        </td><td>X_29        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_22        </td><td>X_30        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_22        </td><td>X_31        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_23        </td><td>X_24        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_23        </td><td>X_25        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_23        </td><td>X_26        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_23        </td><td>X_27        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_23        </td><td>X_28        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_23        </td><td>X_29        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_23        </td><td>X_30        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_23        </td><td>X_31        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_24        </td><td>X_25        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_24        </td><td>X_26        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_24        </td><td>X_27        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_24        </td><td>X_28        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_24        </td><td>X_29        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_24        </td><td>X_30        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_24        </td><td>X_31        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_25        </td><td>X_26        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_25        </td><td>X_27        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_25        </td><td>X_28        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_25        </td><td>X_29        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_25        </td><td>X_30        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_25        </td><td>X_31        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_26        </td><td>X_27        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_26        </td><td>X_28        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_26        </td><td>X_29        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_26        </td><td>X_30        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_26        </td><td>X_31        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_27        </td><td>X_28        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_27        </td><td>X_29        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_27        </td><td>X_30        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_27        </td><td>X_31        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_28        </td><td>X_29        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_28        </td><td>X_30        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_28        </td><td>X_31        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_29        </td><td>X_30        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_29        </td><td>X_31        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "<tr><td>X_30        </td><td>X_31        </td><td style=\"text-align: right;\">0.000011</td><td style=\"text-align: right;\">0.437432</td><td style=\"text-align: right;\">0.000078</td><td style=\"text-align: right;\">  0.062469</td></tr>\n",
       "</tbody>\n",
       "</table>\n",
       "\n",
       "<table>\n",
       "<thead>\n",
       "<tr><th>Dimension Metric         </th><th style=\"text-align: right;\">    Value</th><th style=\"text-align: right;\">  Rel. Variance</th><th>Variables                                                                                                                                                                                     </th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "<tr><td>Mean dimension           </td><td style=\"text-align: right;\"> 7.998406</td><td style=\"text-align: right;\">               </td><td>                                                                                                                                                                                              </td></tr>\n",
       "<tr><td>Effective (superposition)</td><td style=\"text-align: right;\">12.000000</td><td style=\"text-align: right;\">       0.962330</td><td>                                                                                                                                                                                              </td></tr>\n",
       "<tr><td>Effective (successive)   </td><td style=\"text-align: right;\">32.000000</td><td style=\"text-align: right;\">       1.000000</td><td>                                                                                                                                                                                              </td></tr>\n",
       "<tr><td>Effective (truncation)   </td><td style=\"text-align: right;\">32.000000</td><td style=\"text-align: right;\">       1.000000</td><td>X_00, X_01, X_02, X_03, X_04, X_05, X_06, X_07, X_08, X_09, X_10, X_11, X_12, X_13, X_14, X_15, X_16, X_17, X_18, X_19, X_20, X_21, X_22, X_23, X_24, X_25, X_26, X_27, X_28, X_29, X_30, X_31</td></tr>\n",
       "</tbody>\n",
       "</table>\n",
       "\n",
       "<table>\n",
       "<thead>\n",
       "<tr><th style=\"text-align: right;\">  Order</th><th style=\"text-align: right;\">  Rel. Variance</th><th style=\"text-align: right;\">  Cumul. Variance</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "<tr><td style=\"text-align: right;\">      1</td><td style=\"text-align: right;\">       0.001075</td><td style=\"text-align: right;\">         0.001075</td></tr>\n",
       "<tr><td style=\"text-align: right;\">      2</td><td style=\"text-align: right;\">       0.005550</td><td style=\"text-align: right;\">         0.006625</td></tr>\n",
       "<tr><td style=\"text-align: right;\">      3</td><td style=\"text-align: right;\">       0.018492</td><td style=\"text-align: right;\">         0.025117</td></tr>\n",
       "<tr><td style=\"text-align: right;\">      4</td><td style=\"text-align: right;\">       0.044672</td><td style=\"text-align: right;\">         0.069789</td></tr>\n",
       "<tr><td style=\"text-align: right;\">      5</td><td style=\"text-align: right;\">       0.083354</td><td style=\"text-align: right;\">         0.153143</td></tr>\n",
       "<tr><td style=\"text-align: right;\">      6</td><td style=\"text-align: right;\">       0.124981</td><td style=\"text-align: right;\">         0.278124</td></tr>\n",
       "<tr><td style=\"text-align: right;\">      7</td><td style=\"text-align: right;\">       0.154677</td><td style=\"text-align: right;\">         0.432800</td></tr>\n",
       "<tr><td style=\"text-align: right;\">      8</td><td style=\"text-align: right;\">       0.161057</td><td style=\"text-align: right;\">         0.593857</td></tr>\n",
       "<tr><td style=\"text-align: right;\">      9</td><td style=\"text-align: right;\">       0.143104</td><td style=\"text-align: right;\">         0.736962</td></tr>\n",
       "<tr><td style=\"text-align: right;\">     10</td><td style=\"text-align: right;\">       0.109670</td><td style=\"text-align: right;\">         0.846631</td></tr>\n",
       "<tr><td style=\"text-align: right;\">     11</td><td style=\"text-align: right;\">       0.073084</td><td style=\"text-align: right;\">         0.919715</td></tr>\n",
       "<tr><td style=\"text-align: right;\">     12</td><td style=\"text-align: right;\">       0.042615</td><td style=\"text-align: right;\">         0.962330</td></tr>\n",
       "<tr><td style=\"text-align: right;\">     13</td><td style=\"text-align: right;\">       0.021845</td><td style=\"text-align: right;\">         0.984175</td></tr>\n",
       "<tr><td style=\"text-align: right;\">     14</td><td style=\"text-align: right;\">       0.009878</td><td style=\"text-align: right;\">         0.994054</td></tr>\n",
       "<tr><td style=\"text-align: right;\">     15</td><td style=\"text-align: right;\">       0.003950</td><td style=\"text-align: right;\">         0.998004</td></tr>\n",
       "<tr><td style=\"text-align: right;\">     16</td><td style=\"text-align: right;\">       0.001398</td><td style=\"text-align: right;\">         0.999402</td></tr>\n",
       "<tr><td style=\"text-align: right;\">     17</td><td style=\"text-align: right;\">       0.000439</td><td style=\"text-align: right;\">         0.999840</td></tr>\n",
       "<tr><td style=\"text-align: right;\">     18</td><td style=\"text-align: right;\">       0.000122</td><td style=\"text-align: right;\">         0.999962</td></tr>\n",
       "<tr><td style=\"text-align: right;\">     19</td><td style=\"text-align: right;\">       0.000030</td><td style=\"text-align: right;\">         0.999992</td></tr>\n",
       "<tr><td style=\"text-align: right;\">     20</td><td style=\"text-align: right;\">       0.000006</td><td style=\"text-align: right;\">         0.999999</td></tr>\n",
       "<tr><td style=\"text-align: right;\">     21</td><td style=\"text-align: right;\">       0.000001</td><td style=\"text-align: right;\">         1.000000</td></tr>\n",
       "<tr><td style=\"text-align: right;\">     22</td><td style=\"text-align: right;\">       0.000000</td><td style=\"text-align: right;\">         1.000000</td></tr>\n",
       "<tr><td style=\"text-align: right;\">     23</td><td style=\"text-align: right;\">       0.000000</td><td style=\"text-align: right;\">         1.000000</td></tr>\n",
       "<tr><td style=\"text-align: right;\">     24</td><td style=\"text-align: right;\">       0.000000</td><td style=\"text-align: right;\">         1.000000</td></tr>\n",
       "<tr><td style=\"text-align: right;\">     25</td><td style=\"text-align: right;\">       0.000000</td><td style=\"text-align: right;\">         1.000000</td></tr>\n",
       "<tr><td style=\"text-align: right;\">     26</td><td style=\"text-align: right;\">       0.000000</td><td style=\"text-align: right;\">         1.000000</td></tr>\n",
       "<tr><td style=\"text-align: right;\">     27</td><td style=\"text-align: right;\">       0.000000</td><td style=\"text-align: right;\">         1.000000</td></tr>\n",
       "<tr><td style=\"text-align: right;\">     28</td><td style=\"text-align: right;\">       0.000000</td><td style=\"text-align: right;\">         1.000000</td></tr>\n",
       "<tr><td style=\"text-align: right;\">     29</td><td style=\"text-align: right;\">       0.000000</td><td style=\"text-align: right;\">         1.000000</td></tr>\n",
       "<tr><td style=\"text-align: right;\">     30</td><td style=\"text-align: right;\">       0.000000</td><td style=\"text-align: right;\">         1.000000</td></tr>\n",
       "<tr><td style=\"text-align: right;\">     31</td><td style=\"text-align: right;\">       0.000000</td><td style=\"text-align: right;\">         1.000000</td></tr>\n",
       "<tr><td style=\"text-align: right;\">     32</td><td style=\"text-align: right;\">       0.000000</td><td style=\"text-align: right;\">         1.000000</td></tr>\n",
       "</tbody>\n",
       "</table>\n",
       "\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Compute sensitivity indices and print result tables\n",
    "print(\"+ Computing tensor approximations of variance-based sensitivity metrics...\")\n",
    "metrics = tr.sensitivity_analysis.var_metrics(\n",
    "    f_sobolg, axes_sobolg, default_bins=bins, verbose=verbose, eps=1e-10,\n",
    "    random_seed=random_seed, cross_kwargs=dict(kickrank=2), max_order=max_order)\n",
    "\n",
    "display(HTML(tr.sensitivity_analysis.tabulate_metrics(\n",
    "    metrics, show_titles=False, output_mode='string', tablefmt='html')))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simulated decay chain\n",
    "\n",
    "The third example simulates a radioactive decay chain that concatenates Poisson processes (it is a linear Jackson network) for 11 chemical species. Each species (except the last one) can decay into the next species in the chain.\n",
    "\n",
    "This model has 10 parameters, namely the decay rates $\\lambda_n$ of the 10 first species. The result of simulation $f_T(\\lambda_1, \\dots, \\lambda_{10})$ is the amount of stable material (last node in the chain) measured after a certain time span $T$. The function $f_T$ simulates the decay chain by discretizing the span $T$ into timesteps of one day. The $\\lambda_n$ (decay rates) represent the fraction of each material that decays every day. They are independent and uniformly distributed in the interval $[0.00063281, 0.00756736]$, which corresponds to half-lives from 3 years down to 3 months. The simulated time span for this example is set to 2 years ($T = 2$) as in [2]:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[{'domain': (0.00063281081452581933, 0.0075673557761656296),\n",
      "  'name': 'lambda_00'},\n",
      " {'domain': (0.00063281081452581933, 0.0075673557761656296),\n",
      "  'name': 'lambda_01'},\n",
      " {'domain': (0.00063281081452581933, 0.0075673557761656296),\n",
      "  'name': 'lambda_02'},\n",
      " {'domain': (0.00063281081452581933, 0.0075673557761656296),\n",
      "  'name': 'lambda_03'},\n",
      " {'domain': (0.00063281081452581933, 0.0075673557761656296),\n",
      "  'name': 'lambda_04'},\n",
      " {'domain': (0.00063281081452581933, 0.0075673557761656296),\n",
      "  'name': 'lambda_05'},\n",
      " {'domain': (0.00063281081452581933, 0.0075673557761656296),\n",
      "  'name': 'lambda_06'},\n",
      " {'domain': (0.00063281081452581933, 0.0075673557761656296),\n",
      "  'name': 'lambda_07'},\n",
      " {'domain': (0.00063281081452581933, 0.0075673557761656296),\n",
      "  'name': 'lambda_08'},\n",
      " {'domain': (0.00063281081452581933, 0.0075673557761656296),\n",
      "  'name': 'lambda_09'}]\n",
      "+ Computing tensor approximations of variance-based sensitivity metrics...\n",
      "\n",
      "-> Building surrogate model\n",
      "Cross-approximating a 10D function with target error 0.0001...\n",
      "=multifuncrs= sweep 1{2}, max_dy: 1.490e+22, erank: 5.47723\n",
      "=multifuncrs= sweep 2{1}, max_dy: 1.387e-05, erank: 6.37181\n",
      "Function evaluations: 134400 in 14.932926893234253 seconds (time/evaluation: 0.00011110808700323104)\n",
      "The resulting tensor has ranks [1, 7, 7, 7, 7, 7, 7, 7, 7, 7, 1] and 40600 elements\n",
      "\n",
      "-> Computing sensitivity metrics\n",
      "=multifuncrs= sweep 1{2}, max_dy: 1.530e+03, erank: 6.37181\n",
      "=multifuncrs= sweep 2{1}, max_dy: 1.454e-07, erank: 6.37181\n",
      "\n",
      "-> Exporting results\n",
      "\n",
      "\t\t ** SENSITIVITY INDICES **\n",
      " Variable   |    Sobol |    Total |   Shapley |   Banzhaf-Coleman\n",
      "------------+----------+----------+-----------+-------------------\n",
      " lambda_00  | 0.049342 | 0.172755 |  0.100000 |          0.094528\n",
      " lambda_01  | 0.049342 | 0.172755 |  0.100000 |          0.094528\n",
      " lambda_02  | 0.049342 | 0.172755 |  0.100000 |          0.094528\n",
      " lambda_03  | 0.049342 | 0.172755 |  0.100000 |          0.094528\n",
      " lambda_04  | 0.049342 | 0.172755 |  0.100000 |          0.094528\n",
      " lambda_05  | 0.049342 | 0.172755 |  0.100000 |          0.094528\n",
      " lambda_06  | 0.049342 | 0.172755 |  0.100000 |          0.094528\n",
      " lambda_07  | 0.049342 | 0.172755 |  0.100000 |          0.094528\n",
      " lambda_08  | 0.049342 | 0.172755 |  0.100000 |          0.094528\n",
      " lambda_09  | 0.049342 | 0.172755 |  0.100000 |          0.094528\n",
      "\n",
      "\t\t ** SENSITIVITY INDICES (ORDER 2) **\n",
      " Variable 1   | Variable 2   |    Sobol |    Total |   Closed |   Superset\n",
      "--------------+--------------+----------+----------+----------+------------\n",
      " lambda_00    | lambda_01    | 0.007416 | 0.323177 | 0.106099 |   0.022333\n",
      " lambda_00    | lambda_02    | 0.007416 | 0.323177 | 0.106099 |   0.022333\n",
      " lambda_00    | lambda_03    | 0.007416 | 0.323177 | 0.106099 |   0.022333\n",
      " lambda_00    | lambda_04    | 0.007416 | 0.323177 | 0.106099 |   0.022333\n",
      " lambda_00    | lambda_05    | 0.007416 | 0.323177 | 0.106099 |   0.022333\n",
      " lambda_00    | lambda_06    | 0.007416 | 0.323177 | 0.106099 |   0.022333\n",
      " lambda_00    | lambda_07    | 0.007416 | 0.323177 | 0.106099 |   0.022333\n",
      " lambda_00    | lambda_08    | 0.007416 | 0.323177 | 0.106099 |   0.022333\n",
      " lambda_00    | lambda_09    | 0.007416 | 0.323177 | 0.106099 |   0.022333\n",
      " lambda_01    | lambda_02    | 0.007416 | 0.323177 | 0.106099 |   0.022333\n",
      " lambda_01    | lambda_03    | 0.007416 | 0.323177 | 0.106099 |   0.022333\n",
      " lambda_01    | lambda_04    | 0.007416 | 0.323177 | 0.106099 |   0.022333\n",
      " lambda_01    | lambda_05    | 0.007416 | 0.323177 | 0.106099 |   0.022333\n",
      " lambda_01    | lambda_06    | 0.007416 | 0.323177 | 0.106099 |   0.022333\n",
      " lambda_01    | lambda_07    | 0.007416 | 0.323177 | 0.106099 |   0.022333\n",
      " lambda_01    | lambda_08    | 0.007416 | 0.323177 | 0.106099 |   0.022333\n",
      " lambda_01    | lambda_09    | 0.007416 | 0.323177 | 0.106099 |   0.022333\n",
      " lambda_02    | lambda_03    | 0.007416 | 0.323177 | 0.106099 |   0.022333\n",
      " lambda_02    | lambda_04    | 0.007416 | 0.323177 | 0.106099 |   0.022333\n",
      " lambda_02    | lambda_05    | 0.007416 | 0.323177 | 0.106099 |   0.022333\n",
      " lambda_02    | lambda_06    | 0.007416 | 0.323177 | 0.106099 |   0.022333\n",
      " lambda_02    | lambda_07    | 0.007416 | 0.323177 | 0.106099 |   0.022333\n",
      " lambda_02    | lambda_08    | 0.007416 | 0.323177 | 0.106099 |   0.022333\n",
      " lambda_02    | lambda_09    | 0.007416 | 0.323177 | 0.106099 |   0.022333\n",
      " lambda_03    | lambda_04    | 0.007416 | 0.323177 | 0.106099 |   0.022333\n",
      " lambda_03    | lambda_05    | 0.007416 | 0.323177 | 0.106099 |   0.022333\n",
      " lambda_03    | lambda_06    | 0.007416 | 0.323177 | 0.106099 |   0.022333\n",
      " lambda_03    | lambda_07    | 0.007416 | 0.323177 | 0.106099 |   0.022333\n",
      " lambda_03    | lambda_08    | 0.007416 | 0.323177 | 0.106099 |   0.022333\n",
      " lambda_03    | lambda_09    | 0.007416 | 0.323177 | 0.106099 |   0.022333\n",
      " lambda_04    | lambda_05    | 0.007416 | 0.323177 | 0.106099 |   0.022333\n",
      " lambda_04    | lambda_06    | 0.007416 | 0.323177 | 0.106099 |   0.022333\n",
      " lambda_04    | lambda_07    | 0.007416 | 0.323177 | 0.106099 |   0.022333\n",
      " lambda_04    | lambda_08    | 0.007416 | 0.323177 | 0.106099 |   0.022333\n",
      " lambda_04    | lambda_09    | 0.007416 | 0.323177 | 0.106099 |   0.022333\n",
      " lambda_05    | lambda_06    | 0.007416 | 0.323177 | 0.106099 |   0.022333\n",
      " lambda_05    | lambda_07    | 0.007416 | 0.323177 | 0.106099 |   0.022333\n",
      " lambda_05    | lambda_08    | 0.007416 | 0.323177 | 0.106099 |   0.022333\n",
      " lambda_05    | lambda_09    | 0.007416 | 0.323177 | 0.106099 |   0.022333\n",
      " lambda_06    | lambda_07    | 0.007416 | 0.323177 | 0.106099 |   0.022333\n",
      " lambda_06    | lambda_08    | 0.007416 | 0.323177 | 0.106099 |   0.022333\n",
      " lambda_06    | lambda_09    | 0.007416 | 0.323177 | 0.106099 |   0.022333\n",
      " lambda_07    | lambda_08    | 0.007416 | 0.323177 | 0.106099 |   0.022333\n",
      " lambda_07    | lambda_09    | 0.007416 | 0.323177 | 0.106099 |   0.022333\n",
      " lambda_08    | lambda_09    | 0.007416 | 0.323177 | 0.106099 |   0.022333\n",
      "\n",
      "\t\t ** DIMENSION METRICS **\n",
      " Dimension Metric          |     Value |   Rel. Variance | Variables\n",
      "---------------------------+-----------+-----------------+--------------------------------------------------------------------------------------------------------------\n",
      " Mean dimension            |  1.727548 |                 |\n",
      " Effective (superposition) |  3.000000 |        0.959378 |\n",
      " Effective (successive)    |  9.000000 |        0.977667 |\n",
      " Effective (truncation)    | 10.000000 |        1.000000 | lambda_00, lambda_01, lambda_02, lambda_03, lambda_04, lambda_05, lambda_06, lambda_07, lambda_08, lambda_09\n",
      "\n",
      "\t ** DIMENSION DISTRIBUTION **\n",
      "   Order |   Rel. Variance |   Cumul. Variance\n",
      "---------+-----------------+-------------------\n",
      "       1 |        0.493417 |          0.493417\n",
      "       2 |        0.333721 |          0.827138\n",
      "       3 |        0.132241 |          0.959378\n",
      "       4 |        0.033962 |          0.993341\n",
      "       5 |        0.005899 |          0.999240\n",
      "       6 |        0.000701 |          0.999941\n",
      "       7 |        0.000056 |          0.999997\n",
      "       8 |        0.000003 |          1.000000\n",
      "       9 |        0.000000 |          1.000000\n",
      "      10 |        0.000000 |          1.000000\n",
      "\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead>\n",
       "<tr><th>Variable  </th><th style=\"text-align: right;\">   Sobol</th><th style=\"text-align: right;\">   Total</th><th style=\"text-align: right;\">  Shapley</th><th style=\"text-align: right;\">  Banzhaf-Coleman</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "<tr><td>lambda_00 </td><td style=\"text-align: right;\">0.049342</td><td style=\"text-align: right;\">0.172755</td><td style=\"text-align: right;\"> 0.100000</td><td style=\"text-align: right;\">         0.094528</td></tr>\n",
       "<tr><td>lambda_01 </td><td style=\"text-align: right;\">0.049342</td><td style=\"text-align: right;\">0.172755</td><td style=\"text-align: right;\"> 0.100000</td><td style=\"text-align: right;\">         0.094528</td></tr>\n",
       "<tr><td>lambda_02 </td><td style=\"text-align: right;\">0.049342</td><td style=\"text-align: right;\">0.172755</td><td style=\"text-align: right;\"> 0.100000</td><td style=\"text-align: right;\">         0.094528</td></tr>\n",
       "<tr><td>lambda_03 </td><td style=\"text-align: right;\">0.049342</td><td style=\"text-align: right;\">0.172755</td><td style=\"text-align: right;\"> 0.100000</td><td style=\"text-align: right;\">         0.094528</td></tr>\n",
       "<tr><td>lambda_04 </td><td style=\"text-align: right;\">0.049342</td><td style=\"text-align: right;\">0.172755</td><td style=\"text-align: right;\"> 0.100000</td><td style=\"text-align: right;\">         0.094528</td></tr>\n",
       "<tr><td>lambda_05 </td><td style=\"text-align: right;\">0.049342</td><td style=\"text-align: right;\">0.172755</td><td style=\"text-align: right;\"> 0.100000</td><td style=\"text-align: right;\">         0.094528</td></tr>\n",
       "<tr><td>lambda_06 </td><td style=\"text-align: right;\">0.049342</td><td style=\"text-align: right;\">0.172755</td><td style=\"text-align: right;\"> 0.100000</td><td style=\"text-align: right;\">         0.094528</td></tr>\n",
       "<tr><td>lambda_07 </td><td style=\"text-align: right;\">0.049342</td><td style=\"text-align: right;\">0.172755</td><td style=\"text-align: right;\"> 0.100000</td><td style=\"text-align: right;\">         0.094528</td></tr>\n",
       "<tr><td>lambda_08 </td><td style=\"text-align: right;\">0.049342</td><td style=\"text-align: right;\">0.172755</td><td style=\"text-align: right;\"> 0.100000</td><td style=\"text-align: right;\">         0.094528</td></tr>\n",
       "<tr><td>lambda_09 </td><td style=\"text-align: right;\">0.049342</td><td style=\"text-align: right;\">0.172755</td><td style=\"text-align: right;\"> 0.100000</td><td style=\"text-align: right;\">         0.094528</td></tr>\n",
       "</tbody>\n",
       "</table>\n",
       "\n",
       "<table>\n",
       "<thead>\n",
       "<tr><th>Variable 1  </th><th>Variable 2  </th><th style=\"text-align: right;\">   Sobol</th><th style=\"text-align: right;\">   Total</th><th style=\"text-align: right;\">  Closed</th><th style=\"text-align: right;\">  Superset</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "<tr><td>lambda_00   </td><td>lambda_01   </td><td style=\"text-align: right;\">0.007416</td><td style=\"text-align: right;\">0.323177</td><td style=\"text-align: right;\">0.106099</td><td style=\"text-align: right;\">  0.022333</td></tr>\n",
       "<tr><td>lambda_00   </td><td>lambda_02   </td><td style=\"text-align: right;\">0.007416</td><td style=\"text-align: right;\">0.323177</td><td style=\"text-align: right;\">0.106099</td><td style=\"text-align: right;\">  0.022333</td></tr>\n",
       "<tr><td>lambda_00   </td><td>lambda_03   </td><td style=\"text-align: right;\">0.007416</td><td style=\"text-align: right;\">0.323177</td><td style=\"text-align: right;\">0.106099</td><td style=\"text-align: right;\">  0.022333</td></tr>\n",
       "<tr><td>lambda_00   </td><td>lambda_04   </td><td style=\"text-align: right;\">0.007416</td><td style=\"text-align: right;\">0.323177</td><td style=\"text-align: right;\">0.106099</td><td style=\"text-align: right;\">  0.022333</td></tr>\n",
       "<tr><td>lambda_00   </td><td>lambda_05   </td><td style=\"text-align: right;\">0.007416</td><td style=\"text-align: right;\">0.323177</td><td style=\"text-align: right;\">0.106099</td><td style=\"text-align: right;\">  0.022333</td></tr>\n",
       "<tr><td>lambda_00   </td><td>lambda_06   </td><td style=\"text-align: right;\">0.007416</td><td style=\"text-align: right;\">0.323177</td><td style=\"text-align: right;\">0.106099</td><td style=\"text-align: right;\">  0.022333</td></tr>\n",
       "<tr><td>lambda_00   </td><td>lambda_07   </td><td style=\"text-align: right;\">0.007416</td><td style=\"text-align: right;\">0.323177</td><td style=\"text-align: right;\">0.106099</td><td style=\"text-align: right;\">  0.022333</td></tr>\n",
       "<tr><td>lambda_00   </td><td>lambda_08   </td><td style=\"text-align: right;\">0.007416</td><td style=\"text-align: right;\">0.323177</td><td style=\"text-align: right;\">0.106099</td><td style=\"text-align: right;\">  0.022333</td></tr>\n",
       "<tr><td>lambda_00   </td><td>lambda_09   </td><td style=\"text-align: right;\">0.007416</td><td style=\"text-align: right;\">0.323177</td><td style=\"text-align: right;\">0.106099</td><td style=\"text-align: right;\">  0.022333</td></tr>\n",
       "<tr><td>lambda_01   </td><td>lambda_02   </td><td style=\"text-align: right;\">0.007416</td><td style=\"text-align: right;\">0.323177</td><td style=\"text-align: right;\">0.106099</td><td style=\"text-align: right;\">  0.022333</td></tr>\n",
       "<tr><td>lambda_01   </td><td>lambda_03   </td><td style=\"text-align: right;\">0.007416</td><td style=\"text-align: right;\">0.323177</td><td style=\"text-align: right;\">0.106099</td><td style=\"text-align: right;\">  0.022333</td></tr>\n",
       "<tr><td>lambda_01   </td><td>lambda_04   </td><td style=\"text-align: right;\">0.007416</td><td style=\"text-align: right;\">0.323177</td><td style=\"text-align: right;\">0.106099</td><td style=\"text-align: right;\">  0.022333</td></tr>\n",
       "<tr><td>lambda_01   </td><td>lambda_05   </td><td style=\"text-align: right;\">0.007416</td><td style=\"text-align: right;\">0.323177</td><td style=\"text-align: right;\">0.106099</td><td style=\"text-align: right;\">  0.022333</td></tr>\n",
       "<tr><td>lambda_01   </td><td>lambda_06   </td><td style=\"text-align: right;\">0.007416</td><td style=\"text-align: right;\">0.323177</td><td style=\"text-align: right;\">0.106099</td><td style=\"text-align: right;\">  0.022333</td></tr>\n",
       "<tr><td>lambda_01   </td><td>lambda_07   </td><td style=\"text-align: right;\">0.007416</td><td style=\"text-align: right;\">0.323177</td><td style=\"text-align: right;\">0.106099</td><td style=\"text-align: right;\">  0.022333</td></tr>\n",
       "<tr><td>lambda_01   </td><td>lambda_08   </td><td style=\"text-align: right;\">0.007416</td><td style=\"text-align: right;\">0.323177</td><td style=\"text-align: right;\">0.106099</td><td style=\"text-align: right;\">  0.022333</td></tr>\n",
       "<tr><td>lambda_01   </td><td>lambda_09   </td><td style=\"text-align: right;\">0.007416</td><td style=\"text-align: right;\">0.323177</td><td style=\"text-align: right;\">0.106099</td><td style=\"text-align: right;\">  0.022333</td></tr>\n",
       "<tr><td>lambda_02   </td><td>lambda_03   </td><td style=\"text-align: right;\">0.007416</td><td style=\"text-align: right;\">0.323177</td><td style=\"text-align: right;\">0.106099</td><td style=\"text-align: right;\">  0.022333</td></tr>\n",
       "<tr><td>lambda_02   </td><td>lambda_04   </td><td style=\"text-align: right;\">0.007416</td><td style=\"text-align: right;\">0.323177</td><td style=\"text-align: right;\">0.106099</td><td style=\"text-align: right;\">  0.022333</td></tr>\n",
       "<tr><td>lambda_02   </td><td>lambda_05   </td><td style=\"text-align: right;\">0.007416</td><td style=\"text-align: right;\">0.323177</td><td style=\"text-align: right;\">0.106099</td><td style=\"text-align: right;\">  0.022333</td></tr>\n",
       "<tr><td>lambda_02   </td><td>lambda_06   </td><td style=\"text-align: right;\">0.007416</td><td style=\"text-align: right;\">0.323177</td><td style=\"text-align: right;\">0.106099</td><td style=\"text-align: right;\">  0.022333</td></tr>\n",
       "<tr><td>lambda_02   </td><td>lambda_07   </td><td style=\"text-align: right;\">0.007416</td><td style=\"text-align: right;\">0.323177</td><td style=\"text-align: right;\">0.106099</td><td style=\"text-align: right;\">  0.022333</td></tr>\n",
       "<tr><td>lambda_02   </td><td>lambda_08   </td><td style=\"text-align: right;\">0.007416</td><td style=\"text-align: right;\">0.323177</td><td style=\"text-align: right;\">0.106099</td><td style=\"text-align: right;\">  0.022333</td></tr>\n",
       "<tr><td>lambda_02   </td><td>lambda_09   </td><td style=\"text-align: right;\">0.007416</td><td style=\"text-align: right;\">0.323177</td><td style=\"text-align: right;\">0.106099</td><td style=\"text-align: right;\">  0.022333</td></tr>\n",
       "<tr><td>lambda_03   </td><td>lambda_04   </td><td style=\"text-align: right;\">0.007416</td><td style=\"text-align: right;\">0.323177</td><td style=\"text-align: right;\">0.106099</td><td style=\"text-align: right;\">  0.022333</td></tr>\n",
       "<tr><td>lambda_03   </td><td>lambda_05   </td><td style=\"text-align: right;\">0.007416</td><td style=\"text-align: right;\">0.323177</td><td style=\"text-align: right;\">0.106099</td><td style=\"text-align: right;\">  0.022333</td></tr>\n",
       "<tr><td>lambda_03   </td><td>lambda_06   </td><td style=\"text-align: right;\">0.007416</td><td style=\"text-align: right;\">0.323177</td><td style=\"text-align: right;\">0.106099</td><td style=\"text-align: right;\">  0.022333</td></tr>\n",
       "<tr><td>lambda_03   </td><td>lambda_07   </td><td style=\"text-align: right;\">0.007416</td><td style=\"text-align: right;\">0.323177</td><td style=\"text-align: right;\">0.106099</td><td style=\"text-align: right;\">  0.022333</td></tr>\n",
       "<tr><td>lambda_03   </td><td>lambda_08   </td><td style=\"text-align: right;\">0.007416</td><td style=\"text-align: right;\">0.323177</td><td style=\"text-align: right;\">0.106099</td><td style=\"text-align: right;\">  0.022333</td></tr>\n",
       "<tr><td>lambda_03   </td><td>lambda_09   </td><td style=\"text-align: right;\">0.007416</td><td style=\"text-align: right;\">0.323177</td><td style=\"text-align: right;\">0.106099</td><td style=\"text-align: right;\">  0.022333</td></tr>\n",
       "<tr><td>lambda_04   </td><td>lambda_05   </td><td style=\"text-align: right;\">0.007416</td><td style=\"text-align: right;\">0.323177</td><td style=\"text-align: right;\">0.106099</td><td style=\"text-align: right;\">  0.022333</td></tr>\n",
       "<tr><td>lambda_04   </td><td>lambda_06   </td><td style=\"text-align: right;\">0.007416</td><td style=\"text-align: right;\">0.323177</td><td style=\"text-align: right;\">0.106099</td><td style=\"text-align: right;\">  0.022333</td></tr>\n",
       "<tr><td>lambda_04   </td><td>lambda_07   </td><td style=\"text-align: right;\">0.007416</td><td style=\"text-align: right;\">0.323177</td><td style=\"text-align: right;\">0.106099</td><td style=\"text-align: right;\">  0.022333</td></tr>\n",
       "<tr><td>lambda_04   </td><td>lambda_08   </td><td style=\"text-align: right;\">0.007416</td><td style=\"text-align: right;\">0.323177</td><td style=\"text-align: right;\">0.106099</td><td style=\"text-align: right;\">  0.022333</td></tr>\n",
       "<tr><td>lambda_04   </td><td>lambda_09   </td><td style=\"text-align: right;\">0.007416</td><td style=\"text-align: right;\">0.323177</td><td style=\"text-align: right;\">0.106099</td><td style=\"text-align: right;\">  0.022333</td></tr>\n",
       "<tr><td>lambda_05   </td><td>lambda_06   </td><td style=\"text-align: right;\">0.007416</td><td style=\"text-align: right;\">0.323177</td><td style=\"text-align: right;\">0.106099</td><td style=\"text-align: right;\">  0.022333</td></tr>\n",
       "<tr><td>lambda_05   </td><td>lambda_07   </td><td style=\"text-align: right;\">0.007416</td><td style=\"text-align: right;\">0.323177</td><td style=\"text-align: right;\">0.106099</td><td style=\"text-align: right;\">  0.022333</td></tr>\n",
       "<tr><td>lambda_05   </td><td>lambda_08   </td><td style=\"text-align: right;\">0.007416</td><td style=\"text-align: right;\">0.323177</td><td style=\"text-align: right;\">0.106099</td><td style=\"text-align: right;\">  0.022333</td></tr>\n",
       "<tr><td>lambda_05   </td><td>lambda_09   </td><td style=\"text-align: right;\">0.007416</td><td style=\"text-align: right;\">0.323177</td><td style=\"text-align: right;\">0.106099</td><td style=\"text-align: right;\">  0.022333</td></tr>\n",
       "<tr><td>lambda_06   </td><td>lambda_07   </td><td style=\"text-align: right;\">0.007416</td><td style=\"text-align: right;\">0.323177</td><td style=\"text-align: right;\">0.106099</td><td style=\"text-align: right;\">  0.022333</td></tr>\n",
       "<tr><td>lambda_06   </td><td>lambda_08   </td><td style=\"text-align: right;\">0.007416</td><td style=\"text-align: right;\">0.323177</td><td style=\"text-align: right;\">0.106099</td><td style=\"text-align: right;\">  0.022333</td></tr>\n",
       "<tr><td>lambda_06   </td><td>lambda_09   </td><td style=\"text-align: right;\">0.007416</td><td style=\"text-align: right;\">0.323177</td><td style=\"text-align: right;\">0.106099</td><td style=\"text-align: right;\">  0.022333</td></tr>\n",
       "<tr><td>lambda_07   </td><td>lambda_08   </td><td style=\"text-align: right;\">0.007416</td><td style=\"text-align: right;\">0.323177</td><td style=\"text-align: right;\">0.106099</td><td style=\"text-align: right;\">  0.022333</td></tr>\n",
       "<tr><td>lambda_07   </td><td>lambda_09   </td><td style=\"text-align: right;\">0.007416</td><td style=\"text-align: right;\">0.323177</td><td style=\"text-align: right;\">0.106099</td><td style=\"text-align: right;\">  0.022333</td></tr>\n",
       "<tr><td>lambda_08   </td><td>lambda_09   </td><td style=\"text-align: right;\">0.007416</td><td style=\"text-align: right;\">0.323177</td><td style=\"text-align: right;\">0.106099</td><td style=\"text-align: right;\">  0.022333</td></tr>\n",
       "</tbody>\n",
       "</table>\n",
       "\n",
       "<table>\n",
       "<thead>\n",
       "<tr><th>Dimension Metric         </th><th style=\"text-align: right;\">    Value</th><th style=\"text-align: right;\">  Rel. Variance</th><th>Variables                                                                                                   </th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "<tr><td>Mean dimension           </td><td style=\"text-align: right;\"> 1.727548</td><td style=\"text-align: right;\">               </td><td>                                                                                                            </td></tr>\n",
       "<tr><td>Effective (superposition)</td><td style=\"text-align: right;\"> 3.000000</td><td style=\"text-align: right;\">       0.959378</td><td>                                                                                                            </td></tr>\n",
       "<tr><td>Effective (successive)   </td><td style=\"text-align: right;\"> 9.000000</td><td style=\"text-align: right;\">       0.977667</td><td>                                                                                                            </td></tr>\n",
       "<tr><td>Effective (truncation)   </td><td style=\"text-align: right;\">10.000000</td><td style=\"text-align: right;\">       1.000000</td><td>lambda_00, lambda_01, lambda_02, lambda_03, lambda_04, lambda_05, lambda_06, lambda_07, lambda_08, lambda_09</td></tr>\n",
       "</tbody>\n",
       "</table>\n",
       "\n",
       "<table>\n",
       "<thead>\n",
       "<tr><th style=\"text-align: right;\">  Order</th><th style=\"text-align: right;\">  Rel. Variance</th><th style=\"text-align: right;\">  Cumul. Variance</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "<tr><td style=\"text-align: right;\">      1</td><td style=\"text-align: right;\">       0.493417</td><td style=\"text-align: right;\">         0.493417</td></tr>\n",
       "<tr><td style=\"text-align: right;\">      2</td><td style=\"text-align: right;\">       0.333721</td><td style=\"text-align: right;\">         0.827138</td></tr>\n",
       "<tr><td style=\"text-align: right;\">      3</td><td style=\"text-align: right;\">       0.132241</td><td style=\"text-align: right;\">         0.959378</td></tr>\n",
       "<tr><td style=\"text-align: right;\">      4</td><td style=\"text-align: right;\">       0.033962</td><td style=\"text-align: right;\">         0.993341</td></tr>\n",
       "<tr><td style=\"text-align: right;\">      5</td><td style=\"text-align: right;\">       0.005899</td><td style=\"text-align: right;\">         0.999240</td></tr>\n",
       "<tr><td style=\"text-align: right;\">      6</td><td style=\"text-align: right;\">       0.000701</td><td style=\"text-align: right;\">         0.999941</td></tr>\n",
       "<tr><td style=\"text-align: right;\">      7</td><td style=\"text-align: right;\">       0.000056</td><td style=\"text-align: right;\">         0.999997</td></tr>\n",
       "<tr><td style=\"text-align: right;\">      8</td><td style=\"text-align: right;\">       0.000003</td><td style=\"text-align: right;\">         1.000000</td></tr>\n",
       "<tr><td style=\"text-align: right;\">      9</td><td style=\"text-align: right;\">       0.000000</td><td style=\"text-align: right;\">         1.000000</td></tr>\n",
       "<tr><td style=\"text-align: right;\">     10</td><td style=\"text-align: right;\">       0.000000</td><td style=\"text-align: right;\">         1.000000</td></tr>\n",
       "</tbody>\n",
       "</table>\n",
       "\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Set example parameters\n",
    "span = 2\n",
    "products = 10\n",
    "\n",
    "f_decay, axes_decay = tr.models.get_decay_poisson(\n",
    "    N=products, span=span, hl_range=(3.0 * (1 / 12.0), 3.0),\n",
    "    time_step=1.0 / 365.0, name_tmpl='lambda_{:0>2}')\n",
    "pprint.pprint(axes_decay)\n",
    "\n",
    "print(\"+ Computing tensor approximations of variance-based sensitivity metrics...\")\n",
    "metrics = tr.sensitivity_analysis.var_metrics(\n",
    "    f_decay, axes_decay, default_bins=bins, verbose=verbose, eps=1e-4,\n",
    "    random_seed=random_seed, max_order=max_order)\n",
    "\n",
    "display(HTML(tr.sensitivity_analysis.tabulate_metrics(\n",
    "    metrics, show_titles=False, output_mode='string', tablefmt='html')))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fire-spread model\n",
    "\n",
    "In the last example we use a function to model the rate of fire spread in the Mediterranean shrublands according to 10 variables that are fed into Rothermel's equations from [3]. We use the updated equations for the model from [4] since the authors kindly provided us the code of their function.\n",
    "\n",
    "[3] _A mathematical model for predicting fire spread in wildland fuels (Tech.\n",
    "Report)._ R. C. Rothermel. U.S. Department of Agriculture, Intermountain Forest and Range Experiment Station, 1972.\n",
    "\n",
    "[4] _Shapley effects for global sensitivity analysis: Theory\n",
    "and computation._ E. Song, B. L. Nelson, and J. Staum. SIAM/ASA Journal on Uncertainty Quantification, 4 (2016)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[{'display_name': '\\\\delta',\n",
      "  'dist': <scipy.stats._distn_infrastructure.rv_frozen object at 0x10cf78518>,\n",
      "  'name': 'delta'},\n",
      " {'display_name': '\\\\sigma',\n",
      "  'dist': <scipy.stats._distn_infrastructure.rv_frozen object at 0x10cf78b38>,\n",
      "  'domain': (5.0, None),\n",
      "  'name': 'sigma'},\n",
      " {'dist': <scipy.stats._distn_infrastructure.rv_frozen object at 0x10cded630>,\n",
      "  'name': 'h'},\n",
      " {'display_name': '\\\\rho_{p}',\n",
      "  'dist': <scipy.stats._distn_infrastructure.rv_frozen object at 0x10cdce3c8>,\n",
      "  'name': 'rho_p'},\n",
      " {'dist': <scipy.stats._distn_infrastructure.rv_frozen object at 0x10cdce940>,\n",
      "  'domain': (0, None),\n",
      "  'name': 'm_l'},\n",
      " {'dist': <scipy.stats._distn_infrastructure.rv_frozen object at 0x10cdce2b0>,\n",
      "  'name': 'm_d'},\n",
      " {'dist': <scipy.stats._distn_infrastructure.rv_frozen object at 0x10cdce128>,\n",
      "  'domain': (0, None),\n",
      "  'name': 'S_T'},\n",
      " {'dist': <scipy.stats._distn_infrastructure.rv_frozen object at 0x10cdcebe0>,\n",
      "  'name': 'U'},\n",
      " {'display_name': 'tan\\\\ \\\\phi',\n",
      "  'dist': <scipy.stats._distn_infrastructure.rv_frozen object at 0x10cdce4e0>,\n",
      "  'domain': (0, None),\n",
      "  'name': 'tan_phi'},\n",
      " {'dist': <scipy.stats._distn_infrastructure.rv_frozen object at 0x10cdce8d0>,\n",
      "  'domain': (None, 1),\n",
      "  'name': 'P'}]\n",
      "+ Computing tensor approximations of variance-based sensitivity metrics...\n",
      "\n",
      "-> Building surrogate model\n",
      "Cross-approximating a 10D function with target error 0.0001...\n",
      "=multifuncrs= sweep 1{2}, max_dy: 2.045e+26, erank: 4.58258\n",
      "=multifuncrs= sweep 2{1}, max_dy: 1.155e-01, erank: 7.47663\n",
      "=multifuncrs= sweep 2{2}, max_dy: 1.155e-01, erank: 9.61769\n",
      "=multifuncrs= sweep 3{1}, max_dy: 3.848e-03, erank: 11.9331\n",
      "=multifuncrs= sweep 3{2}, max_dy: 3.848e-03, erank: 12.7671\n",
      "=multifuncrs= sweep 4{1}, max_dy: 1.458e-03, erank: 13.0461\n",
      "=multifuncrs= sweep 4{2}, max_dy: 1.458e-03, erank: 13.409\n",
      "=multifuncrs= sweep 5{1}, max_dy: 7.420e-04, erank: 13.9392\n",
      "=multifuncrs= sweep 5{2}, max_dy: 7.420e-04, erank: 14.2056\n",
      "=multifuncrs= sweep 6{1}, max_dy: 3.135e-04, erank: 14.1067\n",
      "=multifuncrs= sweep 6{2}, max_dy: 3.135e-04, erank: 14.5534\n",
      "=multifuncrs= sweep 7{1}, max_dy: 2.758e-04, erank: 14.639\n",
      "=multifuncrs= sweep 7{2}, max_dy: 3.951e-04, erank: 14.7241\n",
      "=multifuncrs= sweep 8{1}, max_dy: 4.270e-04, erank: 14.5258\n",
      "=multifuncrs= sweep 8{2}, max_dy: 4.749e-04, erank: 14.6901\n",
      "=multifuncrs= sweep 9{1}, max_dy: 2.246e-04, erank: 14.6901\n",
      "=multifuncrs= sweep 9{2}, max_dy: 2.735e-04, erank: 14.7716\n",
      "=multifuncrs= sweep 10{1}, max_dy: 3.612e-04, erank: 15.0599\n",
      "=multifuncrs= sweep 10{2}, max_dy: 3.612e-04, erank: 15.0599\n",
      "=multifuncrs= sweep 11{1}, max_dy: 1.882e-04, erank: 14.9766\n",
      "Function evaluations: 4704700 in 22.731523036956787 seconds (time/evaluation: 4.831662600581713e-06)\n",
      "The resulting tensor has ranks [1, 11, 17, 17, 9, 43, 16, 16, 11, 8, 1] and 224300 elements\n",
      "\n",
      "-> Computing sensitivity metrics\n",
      "=multifuncrs= sweep 1{2}, max_dy: 2.873e+00, erank: 11.4368\n",
      "=multifuncrs= sweep 2{1}, max_dy: 1.651e-04, erank: 12.0499\n",
      "=multifuncrs= sweep 2{2}, max_dy: 1.651e-04, erank: 12.1943\n",
      "=multifuncrs= sweep 3{1}, max_dy: 7.938e-05, erank: 12.486\n",
      "\n",
      "-> Exporting results\n",
      "\n",
      "\t\t ** SENSITIVITY INDICES **\n",
      " Variable   |    Sobol |    Total |   Shapley |   Banzhaf-Coleman\n",
      "------------+----------+----------+-----------+-------------------\n",
      " delta      | 0.105786 | 0.331219 |  0.202888 |          0.195103\n",
      " sigma      | 0.047641 | 0.234359 |  0.124657 |          0.116509\n",
      " h          | 0.001227 | 0.005177 |  0.002835 |          0.002653\n",
      " rho_p      | 0.004500 | 0.023318 |  0.012103 |          0.011205\n",
      " m_l        | 0.142362 | 0.346874 |  0.231299 |          0.224659\n",
      " m_d        | 0.095107 | 0.259482 |  0.165486 |          0.159604\n",
      " S_T        | 0.001068 | 0.004506 |  0.002467 |          0.002308\n",
      " U          | 0.090116 | 0.352891 |  0.201416 |          0.191398\n",
      " tan_phi    | 0.002076 | 0.006125 |  0.003844 |          0.003717\n",
      " P          | 0.029115 | 0.085650 |  0.053004 |          0.050828\n",
      "\n",
      "\t\t ** SENSITIVITY INDICES (ORDER 2) **\n",
      " Variable 1   | Variable 2   |    Sobol |    Total |   Closed |   Superset\n",
      "--------------+--------------+----------+----------+----------+------------\n",
      " delta        | sigma        | 0.014159 | 0.512007 | 0.167586 |   0.053570\n",
      " delta        | h            | 0.000420 | 0.335086 | 0.107433 |   0.001310\n",
      " delta        | rho_p        | 0.003101 | 0.346036 | 0.113387 |   0.008501\n",
      " delta        | m_l          | 0.048721 | 0.590339 | 0.296869 |   0.087753\n",
      " delta        | m_d          | 0.032543 | 0.525055 | 0.233435 |   0.065646\n",
      " delta        | S_T          | 0.000365 | 0.334584 | 0.107219 |   0.001140\n",
      " delta        | U            | 0.031430 | 0.595848 | 0.227331 |   0.088262\n",
      " delta        | tan_phi      | 0.000680 | 0.335711 | 0.108542 |   0.001633\n",
      " delta        | P            | 0.009962 | 0.395202 | 0.144863 |   0.021667\n",
      " sigma        | h            | 0.000189 | 0.238609 | 0.049058 |   0.000927\n",
      " sigma        | rho_p        | 0.000891 | 0.253727 | 0.053032 |   0.003950\n",
      " sigma        | m_l          | 0.021938 | 0.518256 | 0.211942 |   0.062977\n",
      " sigma        | m_d          | 0.014714 | 0.446808 | 0.157462 |   0.047033\n",
      " sigma        | S_T          | 0.000165 | 0.238058 | 0.048873 |   0.000807\n",
      " sigma        | U            | 0.042457 | 0.476674 | 0.180214 |   0.110576\n",
      " sigma        | tan_phi      | 0.000165 | 0.239878 | 0.049882 |   0.000606\n",
      " sigma        | P            | 0.004391 | 0.304483 | 0.081147 |   0.015525\n",
      " h            | rho_p        | 0.000018 | 0.028402 | 0.005745 |   0.000092\n",
      " h            | m_l          | 0.000565 | 0.350679 | 0.144155 |   0.001372\n",
      " h            | m_d          | 0.000378 | 0.263633 | 0.096712 |   0.001026\n",
      " h            | S_T          | 0.000004 | 0.009665 | 0.002299 |   0.000018\n",
      " h            | U            | 0.000358 | 0.356673 | 0.091701 |   0.001396\n",
      " h            | tan_phi      | 0.000008 | 0.011278 | 0.003312 |   0.000024\n",
      " h            | P            | 0.000116 | 0.090488 | 0.030458 |   0.000339\n",
      " rho_p        | m_l          | 0.002073 | 0.364014 | 0.148935 |   0.006178\n",
      " rho_p        | m_d          | 0.001385 | 0.278177 | 0.100992 |   0.004623\n",
      " rho_p        | S_T          | 0.000016 | 0.027743 | 0.005583 |   0.000080\n",
      " rho_p        | U            | 0.001416 | 0.370131 | 0.096032 |   0.006078\n",
      " rho_p        | tan_phi      | 0.000022 | 0.029320 | 0.006599 |   0.000123\n",
      " rho_p        | P            | 0.000424 | 0.107441 | 0.034039 |   0.001526\n",
      " m_l          | m_d          | 0.014785 | 0.572950 | 0.252254 |   0.033406\n",
      " m_l          | S_T          | 0.000492 | 0.350186 | 0.143921 |   0.001194\n",
      " m_l          | U            | 0.041505 | 0.605539 | 0.273982 |   0.094227\n",
      " m_l          | tan_phi      | 0.000957 | 0.351322 | 0.145396 |   0.001677\n",
      " m_l          | P            | 0.001249 | 0.428570 | 0.172726 |   0.003954\n",
      " m_d          | S_T          | 0.000328 | 0.263094 | 0.096503 |   0.000893\n",
      " m_d          | U            | 0.027747 | 0.542011 | 0.212970 |   0.070362\n",
      " m_d          | tan_phi      | 0.000640 | 0.264389 | 0.097823 |   0.001218\n",
      " m_d          | P            | 0.008612 | 0.325816 | 0.132834 |   0.019316\n",
      " S_T          | U            | 0.000311 | 0.356182 | 0.091495 |   0.001215\n",
      " S_T          | tan_phi      | 0.000007 | 0.010610 | 0.003151 |   0.000021\n",
      " S_T          | P            | 0.000101 | 0.089861 | 0.030283 |   0.000295\n",
      " U            | tan_phi      | 0.000000 | 0.358983 | 0.092192 |   0.000033\n",
      " U            | P            | 0.008453 | 0.415164 | 0.127684 |   0.023376\n",
      " tan_phi      | P            | 0.000194 | 0.091337 | 0.031386 |   0.000438\n",
      "\n",
      "\t\t ** DIMENSION METRICS **\n",
      " Dimension Metric          |    Value |   Rel. Variance | Variables\n",
      "---------------------------+----------+-----------------+------------------------------\n",
      " Mean dimension            | 1.649599 |                 |\n",
      " Effective (superposition) | 3.000000 |        0.976000 |\n",
      " Effective (successive)    | 8.000000 |        0.964846 |\n",
      " Effective (truncation)    | 6.000000 |        0.961232 | delta, sigma, m_l, m_d, U, P\n",
      "\n",
      "\t ** DIMENSION DISTRIBUTION **\n",
      "   Order |   Rel. Variance |   Cumul. Variance\n",
      "---------+-----------------+-------------------\n",
      "       1 |        0.518999 |          0.518999\n",
      "       2 |        0.338454 |          0.857452\n",
      "       3 |        0.118548 |          0.976000\n",
      "       4 |        0.022031 |          0.998031\n",
      "       5 |        0.001888 |          0.999920\n",
      "       6 |        0.000079 |          0.999999\n",
      "       7 |        0.000001 |          1.000000\n",
      "       8 |        0.000000 |          1.000000\n",
      "       9 |       -0.000000 |          1.000000\n",
      "      10 |       -0.000000 |          1.000000\n",
      "\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead>\n",
       "<tr><th>Variable  </th><th style=\"text-align: right;\">   Sobol</th><th style=\"text-align: right;\">   Total</th><th style=\"text-align: right;\">  Shapley</th><th style=\"text-align: right;\">  Banzhaf-Coleman</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "<tr><td>delta     </td><td style=\"text-align: right;\">0.105786</td><td style=\"text-align: right;\">0.331219</td><td style=\"text-align: right;\"> 0.202888</td><td style=\"text-align: right;\">         0.195103</td></tr>\n",
       "<tr><td>sigma     </td><td style=\"text-align: right;\">0.047641</td><td style=\"text-align: right;\">0.234359</td><td style=\"text-align: right;\"> 0.124657</td><td style=\"text-align: right;\">         0.116509</td></tr>\n",
       "<tr><td>h         </td><td style=\"text-align: right;\">0.001227</td><td style=\"text-align: right;\">0.005177</td><td style=\"text-align: right;\"> 0.002835</td><td style=\"text-align: right;\">         0.002653</td></tr>\n",
       "<tr><td>rho_p     </td><td style=\"text-align: right;\">0.004500</td><td style=\"text-align: right;\">0.023318</td><td style=\"text-align: right;\"> 0.012103</td><td style=\"text-align: right;\">         0.011205</td></tr>\n",
       "<tr><td>m_l       </td><td style=\"text-align: right;\">0.142362</td><td style=\"text-align: right;\">0.346874</td><td style=\"text-align: right;\"> 0.231299</td><td style=\"text-align: right;\">         0.224659</td></tr>\n",
       "<tr><td>m_d       </td><td style=\"text-align: right;\">0.095107</td><td style=\"text-align: right;\">0.259482</td><td style=\"text-align: right;\"> 0.165486</td><td style=\"text-align: right;\">         0.159604</td></tr>\n",
       "<tr><td>S_T       </td><td style=\"text-align: right;\">0.001068</td><td style=\"text-align: right;\">0.004506</td><td style=\"text-align: right;\"> 0.002467</td><td style=\"text-align: right;\">         0.002308</td></tr>\n",
       "<tr><td>U         </td><td style=\"text-align: right;\">0.090116</td><td style=\"text-align: right;\">0.352891</td><td style=\"text-align: right;\"> 0.201416</td><td style=\"text-align: right;\">         0.191398</td></tr>\n",
       "<tr><td>tan_phi   </td><td style=\"text-align: right;\">0.002076</td><td style=\"text-align: right;\">0.006125</td><td style=\"text-align: right;\"> 0.003844</td><td style=\"text-align: right;\">         0.003717</td></tr>\n",
       "<tr><td>P         </td><td style=\"text-align: right;\">0.029115</td><td style=\"text-align: right;\">0.085650</td><td style=\"text-align: right;\"> 0.053004</td><td style=\"text-align: right;\">         0.050828</td></tr>\n",
       "</tbody>\n",
       "</table>\n",
       "\n",
       "<table>\n",
       "<thead>\n",
       "<tr><th>Variable 1  </th><th>Variable 2  </th><th style=\"text-align: right;\">   Sobol</th><th style=\"text-align: right;\">   Total</th><th style=\"text-align: right;\">  Closed</th><th style=\"text-align: right;\">  Superset</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "<tr><td>delta       </td><td>sigma       </td><td style=\"text-align: right;\">0.014159</td><td style=\"text-align: right;\">0.512007</td><td style=\"text-align: right;\">0.167586</td><td style=\"text-align: right;\">  0.053570</td></tr>\n",
       "<tr><td>delta       </td><td>h           </td><td style=\"text-align: right;\">0.000420</td><td style=\"text-align: right;\">0.335086</td><td style=\"text-align: right;\">0.107433</td><td style=\"text-align: right;\">  0.001310</td></tr>\n",
       "<tr><td>delta       </td><td>rho_p       </td><td style=\"text-align: right;\">0.003101</td><td style=\"text-align: right;\">0.346036</td><td style=\"text-align: right;\">0.113387</td><td style=\"text-align: right;\">  0.008501</td></tr>\n",
       "<tr><td>delta       </td><td>m_l         </td><td style=\"text-align: right;\">0.048721</td><td style=\"text-align: right;\">0.590339</td><td style=\"text-align: right;\">0.296869</td><td style=\"text-align: right;\">  0.087753</td></tr>\n",
       "<tr><td>delta       </td><td>m_d         </td><td style=\"text-align: right;\">0.032543</td><td style=\"text-align: right;\">0.525055</td><td style=\"text-align: right;\">0.233435</td><td style=\"text-align: right;\">  0.065646</td></tr>\n",
       "<tr><td>delta       </td><td>S_T         </td><td style=\"text-align: right;\">0.000365</td><td style=\"text-align: right;\">0.334584</td><td style=\"text-align: right;\">0.107219</td><td style=\"text-align: right;\">  0.001140</td></tr>\n",
       "<tr><td>delta       </td><td>U           </td><td style=\"text-align: right;\">0.031430</td><td style=\"text-align: right;\">0.595848</td><td style=\"text-align: right;\">0.227331</td><td style=\"text-align: right;\">  0.088262</td></tr>\n",
       "<tr><td>delta       </td><td>tan_phi     </td><td style=\"text-align: right;\">0.000680</td><td style=\"text-align: right;\">0.335711</td><td style=\"text-align: right;\">0.108542</td><td style=\"text-align: right;\">  0.001633</td></tr>\n",
       "<tr><td>delta       </td><td>P           </td><td style=\"text-align: right;\">0.009962</td><td style=\"text-align: right;\">0.395202</td><td style=\"text-align: right;\">0.144863</td><td style=\"text-align: right;\">  0.021667</td></tr>\n",
       "<tr><td>sigma       </td><td>h           </td><td style=\"text-align: right;\">0.000189</td><td style=\"text-align: right;\">0.238609</td><td style=\"text-align: right;\">0.049058</td><td style=\"text-align: right;\">  0.000927</td></tr>\n",
       "<tr><td>sigma       </td><td>rho_p       </td><td style=\"text-align: right;\">0.000891</td><td style=\"text-align: right;\">0.253727</td><td style=\"text-align: right;\">0.053032</td><td style=\"text-align: right;\">  0.003950</td></tr>\n",
       "<tr><td>sigma       </td><td>m_l         </td><td style=\"text-align: right;\">0.021938</td><td style=\"text-align: right;\">0.518256</td><td style=\"text-align: right;\">0.211942</td><td style=\"text-align: right;\">  0.062977</td></tr>\n",
       "<tr><td>sigma       </td><td>m_d         </td><td style=\"text-align: right;\">0.014714</td><td style=\"text-align: right;\">0.446808</td><td style=\"text-align: right;\">0.157462</td><td style=\"text-align: right;\">  0.047033</td></tr>\n",
       "<tr><td>sigma       </td><td>S_T         </td><td style=\"text-align: right;\">0.000165</td><td style=\"text-align: right;\">0.238058</td><td style=\"text-align: right;\">0.048873</td><td style=\"text-align: right;\">  0.000807</td></tr>\n",
       "<tr><td>sigma       </td><td>U           </td><td style=\"text-align: right;\">0.042457</td><td style=\"text-align: right;\">0.476674</td><td style=\"text-align: right;\">0.180214</td><td style=\"text-align: right;\">  0.110576</td></tr>\n",
       "<tr><td>sigma       </td><td>tan_phi     </td><td style=\"text-align: right;\">0.000165</td><td style=\"text-align: right;\">0.239878</td><td style=\"text-align: right;\">0.049882</td><td style=\"text-align: right;\">  0.000606</td></tr>\n",
       "<tr><td>sigma       </td><td>P           </td><td style=\"text-align: right;\">0.004391</td><td style=\"text-align: right;\">0.304483</td><td style=\"text-align: right;\">0.081147</td><td style=\"text-align: right;\">  0.015525</td></tr>\n",
       "<tr><td>h           </td><td>rho_p       </td><td style=\"text-align: right;\">0.000018</td><td style=\"text-align: right;\">0.028402</td><td style=\"text-align: right;\">0.005745</td><td style=\"text-align: right;\">  0.000092</td></tr>\n",
       "<tr><td>h           </td><td>m_l         </td><td style=\"text-align: right;\">0.000565</td><td style=\"text-align: right;\">0.350679</td><td style=\"text-align: right;\">0.144155</td><td style=\"text-align: right;\">  0.001372</td></tr>\n",
       "<tr><td>h           </td><td>m_d         </td><td style=\"text-align: right;\">0.000378</td><td style=\"text-align: right;\">0.263633</td><td style=\"text-align: right;\">0.096712</td><td style=\"text-align: right;\">  0.001026</td></tr>\n",
       "<tr><td>h           </td><td>S_T         </td><td style=\"text-align: right;\">0.000004</td><td style=\"text-align: right;\">0.009665</td><td style=\"text-align: right;\">0.002299</td><td style=\"text-align: right;\">  0.000018</td></tr>\n",
       "<tr><td>h           </td><td>U           </td><td style=\"text-align: right;\">0.000358</td><td style=\"text-align: right;\">0.356673</td><td style=\"text-align: right;\">0.091701</td><td style=\"text-align: right;\">  0.001396</td></tr>\n",
       "<tr><td>h           </td><td>tan_phi     </td><td style=\"text-align: right;\">0.000008</td><td style=\"text-align: right;\">0.011278</td><td style=\"text-align: right;\">0.003312</td><td style=\"text-align: right;\">  0.000024</td></tr>\n",
       "<tr><td>h           </td><td>P           </td><td style=\"text-align: right;\">0.000116</td><td style=\"text-align: right;\">0.090488</td><td style=\"text-align: right;\">0.030458</td><td style=\"text-align: right;\">  0.000339</td></tr>\n",
       "<tr><td>rho_p       </td><td>m_l         </td><td style=\"text-align: right;\">0.002073</td><td style=\"text-align: right;\">0.364014</td><td style=\"text-align: right;\">0.148935</td><td style=\"text-align: right;\">  0.006178</td></tr>\n",
       "<tr><td>rho_p       </td><td>m_d         </td><td style=\"text-align: right;\">0.001385</td><td style=\"text-align: right;\">0.278177</td><td style=\"text-align: right;\">0.100992</td><td style=\"text-align: right;\">  0.004623</td></tr>\n",
       "<tr><td>rho_p       </td><td>S_T         </td><td style=\"text-align: right;\">0.000016</td><td style=\"text-align: right;\">0.027743</td><td style=\"text-align: right;\">0.005583</td><td style=\"text-align: right;\">  0.000080</td></tr>\n",
       "<tr><td>rho_p       </td><td>U           </td><td style=\"text-align: right;\">0.001416</td><td style=\"text-align: right;\">0.370131</td><td style=\"text-align: right;\">0.096032</td><td style=\"text-align: right;\">  0.006078</td></tr>\n",
       "<tr><td>rho_p       </td><td>tan_phi     </td><td style=\"text-align: right;\">0.000022</td><td style=\"text-align: right;\">0.029320</td><td style=\"text-align: right;\">0.006599</td><td style=\"text-align: right;\">  0.000123</td></tr>\n",
       "<tr><td>rho_p       </td><td>P           </td><td style=\"text-align: right;\">0.000424</td><td style=\"text-align: right;\">0.107441</td><td style=\"text-align: right;\">0.034039</td><td style=\"text-align: right;\">  0.001526</td></tr>\n",
       "<tr><td>m_l         </td><td>m_d         </td><td style=\"text-align: right;\">0.014785</td><td style=\"text-align: right;\">0.572950</td><td style=\"text-align: right;\">0.252254</td><td style=\"text-align: right;\">  0.033406</td></tr>\n",
       "<tr><td>m_l         </td><td>S_T         </td><td style=\"text-align: right;\">0.000492</td><td style=\"text-align: right;\">0.350186</td><td style=\"text-align: right;\">0.143921</td><td style=\"text-align: right;\">  0.001194</td></tr>\n",
       "<tr><td>m_l         </td><td>U           </td><td style=\"text-align: right;\">0.041505</td><td style=\"text-align: right;\">0.605539</td><td style=\"text-align: right;\">0.273982</td><td style=\"text-align: right;\">  0.094227</td></tr>\n",
       "<tr><td>m_l         </td><td>tan_phi     </td><td style=\"text-align: right;\">0.000957</td><td style=\"text-align: right;\">0.351322</td><td style=\"text-align: right;\">0.145396</td><td style=\"text-align: right;\">  0.001677</td></tr>\n",
       "<tr><td>m_l         </td><td>P           </td><td style=\"text-align: right;\">0.001249</td><td style=\"text-align: right;\">0.428570</td><td style=\"text-align: right;\">0.172726</td><td style=\"text-align: right;\">  0.003954</td></tr>\n",
       "<tr><td>m_d         </td><td>S_T         </td><td style=\"text-align: right;\">0.000328</td><td style=\"text-align: right;\">0.263094</td><td style=\"text-align: right;\">0.096503</td><td style=\"text-align: right;\">  0.000893</td></tr>\n",
       "<tr><td>m_d         </td><td>U           </td><td style=\"text-align: right;\">0.027747</td><td style=\"text-align: right;\">0.542011</td><td style=\"text-align: right;\">0.212970</td><td style=\"text-align: right;\">  0.070362</td></tr>\n",
       "<tr><td>m_d         </td><td>tan_phi     </td><td style=\"text-align: right;\">0.000640</td><td style=\"text-align: right;\">0.264389</td><td style=\"text-align: right;\">0.097823</td><td style=\"text-align: right;\">  0.001218</td></tr>\n",
       "<tr><td>m_d         </td><td>P           </td><td style=\"text-align: right;\">0.008612</td><td style=\"text-align: right;\">0.325816</td><td style=\"text-align: right;\">0.132834</td><td style=\"text-align: right;\">  0.019316</td></tr>\n",
       "<tr><td>S_T         </td><td>U           </td><td style=\"text-align: right;\">0.000311</td><td style=\"text-align: right;\">0.356182</td><td style=\"text-align: right;\">0.091495</td><td style=\"text-align: right;\">  0.001215</td></tr>\n",
       "<tr><td>S_T         </td><td>tan_phi     </td><td style=\"text-align: right;\">0.000007</td><td style=\"text-align: right;\">0.010610</td><td style=\"text-align: right;\">0.003151</td><td style=\"text-align: right;\">  0.000021</td></tr>\n",
       "<tr><td>S_T         </td><td>P           </td><td style=\"text-align: right;\">0.000101</td><td style=\"text-align: right;\">0.089861</td><td style=\"text-align: right;\">0.030283</td><td style=\"text-align: right;\">  0.000295</td></tr>\n",
       "<tr><td>U           </td><td>tan_phi     </td><td style=\"text-align: right;\">0.000000</td><td style=\"text-align: right;\">0.358983</td><td style=\"text-align: right;\">0.092192</td><td style=\"text-align: right;\">  0.000033</td></tr>\n",
       "<tr><td>U           </td><td>P           </td><td style=\"text-align: right;\">0.008453</td><td style=\"text-align: right;\">0.415164</td><td style=\"text-align: right;\">0.127684</td><td style=\"text-align: right;\">  0.023376</td></tr>\n",
       "<tr><td>tan_phi     </td><td>P           </td><td style=\"text-align: right;\">0.000194</td><td style=\"text-align: right;\">0.091337</td><td style=\"text-align: right;\">0.031386</td><td style=\"text-align: right;\">  0.000438</td></tr>\n",
       "</tbody>\n",
       "</table>\n",
       "\n",
       "<table>\n",
       "<thead>\n",
       "<tr><th>Dimension Metric         </th><th style=\"text-align: right;\">   Value</th><th style=\"text-align: right;\">  Rel. Variance</th><th>Variables                   </th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "<tr><td>Mean dimension           </td><td style=\"text-align: right;\">1.649599</td><td style=\"text-align: right;\">               </td><td>                            </td></tr>\n",
       "<tr><td>Effective (superposition)</td><td style=\"text-align: right;\">3.000000</td><td style=\"text-align: right;\">       0.976000</td><td>                            </td></tr>\n",
       "<tr><td>Effective (successive)   </td><td style=\"text-align: right;\">8.000000</td><td style=\"text-align: right;\">       0.964846</td><td>                            </td></tr>\n",
       "<tr><td>Effective (truncation)   </td><td style=\"text-align: right;\">6.000000</td><td style=\"text-align: right;\">       0.961232</td><td>delta, sigma, m_l, m_d, U, P</td></tr>\n",
       "</tbody>\n",
       "</table>\n",
       "\n",
       "<table>\n",
       "<thead>\n",
       "<tr><th style=\"text-align: right;\">  Order</th><th style=\"text-align: right;\">  Rel. Variance</th><th style=\"text-align: right;\">  Cumul. Variance</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "<tr><td style=\"text-align: right;\">      1</td><td style=\"text-align: right;\">       0.518999</td><td style=\"text-align: right;\">         0.518999</td></tr>\n",
       "<tr><td style=\"text-align: right;\">      2</td><td style=\"text-align: right;\">       0.338454</td><td style=\"text-align: right;\">         0.857452</td></tr>\n",
       "<tr><td style=\"text-align: right;\">      3</td><td style=\"text-align: right;\">       0.118548</td><td style=\"text-align: right;\">         0.976000</td></tr>\n",
       "<tr><td style=\"text-align: right;\">      4</td><td style=\"text-align: right;\">       0.022031</td><td style=\"text-align: right;\">         0.998031</td></tr>\n",
       "<tr><td style=\"text-align: right;\">      5</td><td style=\"text-align: right;\">       0.001888</td><td style=\"text-align: right;\">         0.999920</td></tr>\n",
       "<tr><td style=\"text-align: right;\">      6</td><td style=\"text-align: right;\">       0.000079</td><td style=\"text-align: right;\">         0.999999</td></tr>\n",
       "<tr><td style=\"text-align: right;\">      7</td><td style=\"text-align: right;\">       0.000001</td><td style=\"text-align: right;\">         1.000000</td></tr>\n",
       "<tr><td style=\"text-align: right;\">      8</td><td style=\"text-align: right;\">       0.000000</td><td style=\"text-align: right;\">         1.000000</td></tr>\n",
       "<tr><td style=\"text-align: right;\">      9</td><td style=\"text-align: right;\">      -0.000000</td><td style=\"text-align: right;\">         1.000000</td></tr>\n",
       "<tr><td style=\"text-align: right;\">     10</td><td style=\"text-align: right;\">      -0.000000</td><td style=\"text-align: right;\">         1.000000</td></tr>\n",
       "</tbody>\n",
       "</table>\n",
       "\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f_fire, axes_fire = tr.models.get_fire_spread(wind_factor=6.9)\n",
    "pprint.pprint(axes_fire)\n",
    "\n",
    "print(\"+ Computing tensor approximations of variance-based sensitivity metrics...\")\n",
    "metrics = tr.sensitivity_analysis.var_metrics(\n",
    "    f_fire, axes_fire, default_bins=bins, verbose=verbose, eps=1e-4,\n",
    "    random_seed=random_seed, cross_kwargs=dict(kickrank=4), max_order=max_order)\n",
    "\n",
    "display(HTML(tr.sensitivity_analysis.tabulate_metrics(\n",
    "    metrics, show_titles=False, output_mode='string', tablefmt='html')))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c17132860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = tr.sensitivity_analysis.plot_indices(metrics)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c17132ba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = tr.sensitivity_analysis.plot_dim_distribution(metrics, max_order=6)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}