smd_handson_unfolding.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Entfaltung: Hands-On\n",
    "\n",
    "In diesem Hands-On sollen die in den letzten Vorlesungen vorgestellten Grundlagen der Entfaltung anhand eines einfachen Beispiels praktisch demonstriert werden."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "from matplotlib.colors import LogNorm\n",
    "from tqdm.auto import tqdm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib widget"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.rcParams['image.cmap'] = 'inferno'\n",
    "plt.rcParams['figure.dpi'] = 100\n",
    "plt.rcParams['figure.constrained_layout.use'] = True"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Daten einlesen und ansehen\n",
    "\n",
    "Zunächst wird der \"Trainings\"-Datensatz eingelesen.\n",
    "\n",
    "Training meint hier die Berechnung der Antwortmatrix und Detektionseffizienz. \n",
    "\n",
    "Diese enthalten sowohl die im echten Experiment verfügbaren Observablen als auch die Wahrheit,\n",
    "die aus Simulation bekannt ist."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "labels_train = pd.read_hdf('training.hdf5', 'labels')\n",
    "observables_train = pd.read_hdf('training.hdf5', 'observables')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Die Labels in unseren Simulationen beinhalten die Energien und eine Parametrisierung des Tracks (mit den Komponenten $\\phi$ und $d$). Zusätzlich existiert noch der Eintrag `noise`, der das Level des Hintergrundrauschens angibt. Dieser ist hier konstant auf 4.5 gesetzt und nicht weiter wichtig."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>E</th>\n",
       "      <th>phi</th>\n",
       "      <th>d</th>\n",
       "      <th>noise</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.110809</td>\n",
       "      <td>2.300641</td>\n",
       "      <td>-0.018607</td>\n",
       "      <td>4.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.768499</td>\n",
       "      <td>0.825967</td>\n",
       "      <td>-0.207421</td>\n",
       "      <td>4.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3.900696</td>\n",
       "      <td>1.399377</td>\n",
       "      <td>-1.148939</td>\n",
       "      <td>4.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2.352842</td>\n",
       "      <td>1.483698</td>\n",
       "      <td>-0.080060</td>\n",
       "      <td>4.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.527332</td>\n",
       "      <td>2.743621</td>\n",
       "      <td>-0.475558</td>\n",
       "      <td>4.5</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      ],
      "text/plain": [
       "          E       phi         d  noise\n",
       "0  1.110809  2.300641 -0.018607    4.5\n",
       "1  1.768499  0.825967 -0.207421    4.5\n",
       "2  3.900696  1.399377 -1.148939    4.5\n",
       "3  2.352842  1.483698 -0.080060    4.5\n",
       "4  1.527332  2.743621 -0.475558    4.5"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "labels_train.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
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       "      <th></th>\n",
       "      <th>px_0_0</th>\n",
       "      <th>px_0_1</th>\n",
       "      <th>px_0_2</th>\n",
       "      <th>px_0_3</th>\n",
       "      <th>px_0_4</th>\n",
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       "      <th>px_0_7</th>\n",
       "      <th>px_1_0</th>\n",
       "      <th>px_1_1</th>\n",
       "      <th>...</th>\n",
       "      <th>px_7_7</th>\n",
       "      <th>q_tot</th>\n",
       "      <th>cog_x</th>\n",
       "      <th>cog_y</th>\n",
       "      <th>conc</th>\n",
       "      <th>cov_xx</th>\n",
       "      <th>cov_yy</th>\n",
       "      <th>cov_xy</th>\n",
       "      <th>cov_phi</th>\n",
       "      <th>cov_a</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>11</td>\n",
       "      <td>5</td>\n",
       "      <td>6</td>\n",
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       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>9</td>\n",
       "      <td>5</td>\n",
       "      <td>6</td>\n",
       "      <td>6</td>\n",
       "      <td>...</td>\n",
       "      <td>7</td>\n",
       "      <td>322.0</td>\n",
       "      <td>-0.013310</td>\n",
       "      <td>-0.011535</td>\n",
       "      <td>0.034161</td>\n",
       "      <td>0.436000</td>\n",
       "      <td>0.453283</td>\n",
       "      <td>0.036226</td>\n",
       "      <td>0.902483</td>\n",
       "      <td>0.407399</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>3</td>\n",
       "      <td>7</td>\n",
       "      <td>3</td>\n",
       "      <td>5</td>\n",
       "      <td>4</td>\n",
       "      <td>...</td>\n",
       "      <td>5</td>\n",
       "      <td>372.0</td>\n",
       "      <td>0.050691</td>\n",
       "      <td>0.079109</td>\n",
       "      <td>0.032258</td>\n",
       "      <td>0.390891</td>\n",
       "      <td>0.388080</td>\n",
       "      <td>-0.026942</td>\n",
       "      <td>0.811457</td>\n",
       "      <td>0.416464</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>5</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>9</td>\n",
       "      <td>10</td>\n",
       "      <td>11</td>\n",
       "      <td>4</td>\n",
       "      <td>8</td>\n",
       "      <td>...</td>\n",
       "      <td>11</td>\n",
       "      <td>402.0</td>\n",
       "      <td>0.285714</td>\n",
       "      <td>0.022743</td>\n",
       "      <td>0.042289</td>\n",
       "      <td>0.426947</td>\n",
       "      <td>0.424399</td>\n",
       "      <td>-0.002335</td>\n",
       "      <td>1.035102</td>\n",
       "      <td>0.428333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2</td>\n",
       "      <td>5</td>\n",
       "      <td>7</td>\n",
       "      <td>4</td>\n",
       "      <td>14</td>\n",
       "      <td>7</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>374.0</td>\n",
       "      <td>-0.015279</td>\n",
       "      <td>-0.011459</td>\n",
       "      <td>0.048128</td>\n",
       "      <td>0.316148</td>\n",
       "      <td>0.431059</td>\n",
       "      <td>-0.023530</td>\n",
       "      <td>-1.376449</td>\n",
       "      <td>0.311516</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>6</td>\n",
       "      <td>6</td>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>2</td>\n",
       "      <td>5</td>\n",
       "      <td>7</td>\n",
       "      <td>6</td>\n",
       "      <td>6</td>\n",
       "      <td>...</td>\n",
       "      <td>4</td>\n",
       "      <td>327.0</td>\n",
       "      <td>-0.010048</td>\n",
       "      <td>-0.053735</td>\n",
       "      <td>0.039755</td>\n",
       "      <td>0.428221</td>\n",
       "      <td>0.386490</td>\n",
       "      <td>0.011131</td>\n",
       "      <td>-1.325768</td>\n",
       "      <td>0.431004</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 73 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   px_0_0  px_0_1  px_0_2  px_0_3  px_0_4  px_0_5  px_0_6  px_0_7  px_1_0  \\\n",
       "0      11       5       6       5       1       4       9       5       6   \n",
       "1       3       3       4       5       5       3       7       3       5   \n",
       "2       5       3       1       2       2       9      10      11       4   \n",
       "3       2       5       7       4      14       7       2       3       4   \n",
       "4       4       6       6       5       5       2       5       7       6   \n",
       "\n",
       "   px_1_1  ...  px_7_7  q_tot     cog_x     cog_y      conc    cov_xx  \\\n",
       "0       6  ...       7  322.0 -0.013310 -0.011535  0.034161  0.436000   \n",
       "1       4  ...       5  372.0  0.050691  0.079109  0.032258  0.390891   \n",
       "2       8  ...      11  402.0  0.285714  0.022743  0.042289  0.426947   \n",
       "3       5  ...       0  374.0 -0.015279 -0.011459  0.048128  0.316148   \n",
       "4       6  ...       4  327.0 -0.010048 -0.053735  0.039755  0.428221   \n",
       "\n",
       "     cov_yy    cov_xy   cov_phi     cov_a  \n",
       "0  0.453283  0.036226  0.902483  0.407399  \n",
       "1  0.388080 -0.026942  0.811457  0.416464  \n",
       "2  0.424399 -0.002335  1.035102  0.428333  \n",
       "3  0.431059 -0.023530 -1.376449  0.311516  \n",
       "4  0.386490  0.011131 -1.325768  0.431004  \n",
       "\n",
       "[5 rows x 73 columns]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "observables_train.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# the first 64 columns have the detector pixels\n",
    "images_train = observables_train.iloc[:, :64].to_numpy().reshape((-1, 8, 8))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "56f892f380dd4520bbb6329a5820f1f9",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "daf532f2405b4e1caf2cc7e033b1ba85",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(IntSlider(value=0, description='event', max=545662), Output()), _dom_classes=('widget-in…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<function __main__.show_event(event=0)>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from ipywidgets import interact\n",
    "\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "plot = ax.imshow(images_train[0])\n",
    "bar = fig.colorbar(plot)\n",
    "\n",
    "\n",
    "def show_event(event=0):\n",
    "    plot.set_data(images_train[event])\n",
    "    plot.autoscale()\n",
    "    bar.update_normal(plot)\n",
    "    \n",
    "interact(show_event, event=(0, len(images_train) - 1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Die Observablen sind einerseits die genauen Ladungswerte für alle Pixel (`px_i_j`), und andererseits eine Anzahl an Features, die im Anschluss an die Simulation anhand der Pixelwerte berechnet wurden. \n",
    "\n",
    "Wichtig ist hier zuächst nur die Gesamtladung $Q_\\mathrm{tot}$. \n",
    "\n",
    "Diese ist besonders stark korreliert mit der ursprünglichen Energie $E$ der Einzelereignisse."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "bcd2965100064341b70d9dc5accd659b",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "\n",
    "# geomspace creates bins that are equidistant in log-space\n",
    "bins_E = np.geomspace(labels_train.E.min(), labels_train.E.max(), 101)\n",
    "bins_q_tot = np.geomspace(observables_train.q_tot.min(), observables_train.q_tot.max(), 101)\n",
    "\n",
    "h = plt.hist2d(\n",
    "    labels_train.E,\n",
    "    observables_train.q_tot,\n",
    "    bins=[bins_E, bins_q_tot], \n",
    "    norm=LogNorm(),\n",
    ")\n",
    "\n",
    "plt.xscale('log')\n",
    "plt.yscale('log')\n",
    "\n",
    "plt.xlabel('$E$')\n",
    "plt.ylabel(r'$Q_\\mathrm{tot}$')\n",
    "plt.colorbar(h[3])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Wir lesen nun auch einen Test-Datensatz ein.\n",
    "\n",
    "Gemessene Daten verfügen nicht wie die Simulationsdaten über Label/Wahrheit, d.h. es gibt nur Observablen.\n",
    "\n",
    "Die Aufgabe der Entfaltung ist es nun die Verteilung einer Variablen nur durch Kenntnis über die Observablen und über den Detektionsprozess zu ermitteln.\n",
    "\n",
    "Damit im Anschluss unsere Entfaltung dennoch mit einer Wahrheit verglichen werden kann, werden hier Simulationsdaten verwendet, die die Wahrheit dennoch enthalten."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "observables_test = pd.read_hdf('test.hdf5', 'observables')\n",
    "labels_test = pd.read_hdf('test.hdf5', 'labels')\n",
    "images_test = observables_test.iloc[:, :64].to_numpy().reshape((-1, 8, 8))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vergleicht man nun die Verteilungen der Observablen miteinander, so wird klar, dass das simulierte Energiespektrum des Trainingsdatensatzes nicht dem im Testdatensatz entspricht:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "2f89d93c1e664203b96f947bd735a2ea",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "\n",
    "# creates bins that are equidistant in log-space\n",
    "bins = np.geomspace(observables_test.q_tot.min(), observables_test.q_tot.max(), 21)\n",
    "\n",
    "plt.hist(observables_train.q_tot, bins=bins, density=True, histtype='step', label='Training')\n",
    "plt.hist(observables_test.q_tot, bins=bins, density=True, histtype='step', label='Test')\n",
    "\n",
    "\n",
    "plt.xlabel(r'$Q_\\mathrm{tot}$')\n",
    "plt.yscale('log')\n",
    "plt.xscale('log')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Trigger\n",
    "\n",
    "Um die Detektion von reinen Rausch-Ereignissen zu verringern, ist es notwendig eine Trigger-Bedingung an den Detektor zu stellen, d.h. das Ereignis muss eine gewisse Bedingung erfüllen um als Ereignis gewertet zu werden. Hier wird die Bedingung gestellt, dass für die Gesamtladung $Q_\\mathrm{tot} > 385$ gilt. Dies sorgt dafür, dass Hintergrundereignisse weggeschnitten werden, aber auch, dass Ereignisse weggeworfen werden, insbesondere im Niederenergie-Bereich:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "all events:       545663\n",
      "Q_tot_min:        321.0\n",
      "triggered events: 177638\n",
      "ratio:            32.6%\n"
     ]
    }
   ],
   "source": [
    "q_tot_cut = 385.0\n",
    "\n",
    "\n",
    "triggered_train = observables_train.q_tot > q_tot_cut\n",
    "triggered_test = observables_test.q_tot > q_tot_cut\n",
    "\n",
    "\n",
    "print(f'all events:       {len(observables_train)}')\n",
    "print(f'Q_tot_min:        {observables_train.q_tot.min()}')\n",
    "print(f'triggered events: {np.count_nonzero(triggered_train)}')\n",
    "print(f'ratio:            {np.count_nonzero(triggered_train) / len(observables_train):.1%}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "all events:       545663\n",
      "Q_tot_min:        321.0\n",
      "triggered events: 109377\n",
      "ratio:            20.0%\n"
     ]
    }
   ],
   "source": [
    "threshold = 10\n",
    "n_over_threshold = 10\n",
    "\n",
    "def trigger(images, threshold, n_over_threshold):\n",
    "    return np.count_nonzero(images > threshold, axis=(-2, -1)) >= n_over_threshold\n",
    "\n",
    "triggered_train = trigger(images_train, threshold, n_over_threshold)\n",
    "triggered_test = trigger(images_test, threshold, n_over_threshold)\n",
    "\n",
    "\n",
    "print(f'all events:       {len(observables_train)}')\n",
    "print(f'Q_tot_min:        {observables_train.q_tot.min()}')\n",
    "print(f'triggered events: {np.count_nonzero(triggered_train)}')\n",
    "print(f'ratio:            {np.count_nonzero(triggered_train) / len(observables_train):.1%}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "ce4785d946844f609ae151fba5c7c088",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "\n",
    "kwargs = dict(bins=bins_q_tot, histtype='step', )\n",
    "plt.hist(observables_train.q_tot, label='All Events', **kwargs)\n",
    "plt.hist(observables_train.q_tot[triggered_train], label='Triggered Events', **kwargs)\n",
    "# plt.axvline(q_tot_cut, color='C1', label='trigger cut')\n",
    "\n",
    "plt.xscale('log')\n",
    "plt.yscale('log')\n",
    "plt.xlabel(r'$Q_\\mathrm{tot}$')\n",
    "\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "8929d4bbd3c94ecd8408952138d792e7",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, '$E$')"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plt.figure()\n",
    "\n",
    "plt.hist(\n",
    "    labels_train.E, bins=bins_E,\n",
    "    histtype='step',\n",
    "    label='Alle simulierten Ereignisse',\n",
    ")\n",
    "\n",
    "plt.hist(\n",
    "    labels_train.E[triggered_train], bins=bins_E,\n",
    "    histtype='step',\n",
    "    label='Vom Trigger akzeptiert'\n",
    ")\n",
    "\n",
    "plt.legend()\n",
    "plt.yscale('log')\n",
    "plt.xscale('log')\n",
    "plt.xlabel('$E$')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Es ist von Interesse diese Effekte des Triggers auszugleichen. Bei echten Experimenten muss darüber hinaus von der entfalteten Zählrate auf den eigentlich gesuchten physikalischen Fluss geschlossen werden. Dieses Vorgehen wird als _Akzeptanzkorrektur_ bezeichnet."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Definition des Binnings für die Entfaltung\n",
    "\n",
    "Um die Entfaltung mit den hier behandelten Methoden durchzuführen ist es notwendig ein Binning, sowohl für die Zielvariable (hier die Energie), als auch die Observable (hier die Gesamtladung $Q_\\mathrm{tot}$)  zu definieren."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_bins_E = 27\n",
    "n_bins_qtot = 60\n",
    "\n",
    "binning_E = np.geomspace(3, 250, n_bins_E + 1)\n",
    "binning_qtot = np.geomspace(450, 225e3, n_bins_qtot + 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Underflow und Overflow Bins\n",
    "\n",
    "Um den Fall einzuschließen, dass Ereignisse in keines der so definierten Bins fallen, sollte man Under- und Overflow-Bins definieren. Ein Ereignis liegt innerhalb eines Underflow-Bins, wenn es unterhalb der kleinsten Bingrenze liegt und innerhalb des Overflow-Bins, wenn es oberhalb der größten Bingrenze liegt."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "def add_overflow(bins, positive=True):\n",
    "    new = np.empty(len(bins) + 2)\n",
    "    new[0] = 0 if positive else -np.inf\n",
    "    new[1:-1] = bins\n",
    "    new[-1] = np.inf\n",
    "    return new\n",
    "\n",
    "binning_E = add_overflow(binning_E)\n",
    "binning_qtot = add_overflow(binning_qtot)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Berechung der Migrationsmatrix\n",
    "\n",
    "Die Einträge der Migrationsmatrix $\\mathrm{A}$ beschreiben wie ein Ereignis aus einem Energie-Bin sich statistisch in Observablenbins wiederfinden wird. D.h, dass der Eintrag $A_{ij}$ die Wahrscheinlichkeit ist, dass ein Ereignis, das im Energiebin $j$ liegt, ebenfalls im Observablenbin $i$ liegt.\n",
    "\n",
    "Diese Matrix ist eine sogenannte stochastische Matrix, d.h. dass\n",
    "\n",
    "$$\\sum_i A_{ij} = 1$$\n",
    "\n",
    "Die Migrationsmatrix berechnet man, indem man ausgehend von Simulationen ein zweidimensionales Histogramm bzgl. der gewählten Observablen und Zielvariablen berechnet und dieses anschließend normiert."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "observable_train = observables_train.q_tot[triggered_train]\n",
    "energy_train = labels_train.E[triggered_train]\n",
    "\n",
    "observable_test = observables_test.q_tot[triggered_test]\n",
    "energy_test = labels_test.E[triggered_test]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "H, *_ = np.histogram2d(\n",
    "    observable_train,\n",
    "    energy_train,\n",
    "    bins=(binning_qtot, binning_E)\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "A = H / np.sum(H, axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "e3c153900eab4363a3ead0a80cbf6f6e",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "im = plt.pcolormesh(A)\n",
    "\n",
    "plt.gca().set_aspect(1)\n",
    "plt.xlabel('Energie Index')\n",
    "plt.ylabel('$Q_\\mathrm{tot}$ Index')\n",
    "plt.colorbar(im)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Berechnung der Vektoren $\\mathbf{g}$ und $\\mathbf{f}$\n",
    "Ähnlich können auch die Vektoren $\\mathbf{g}$ (der Vektor, der die Bininhalte in den Observablenbins enthält) und $\\mathbf{f}$ (der Vektor, der die Bininhalte in den Bins der Zielvariablen enthält) berechnet werden. Im Anschluss kann auch geprüft werden, ob die Entfaltungsgleichung \n",
    "$$A \\cdot \\mathbf{f} = \\mathbf{g}$$\n",
    "gültig ist."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([10317, 16201, 16051, 13657, 11309,  9101,  7161,  5755,  4560,\n",
       "         3495,  2783,  2070,  1594,  1234,   966,   766,   570,   479,\n",
       "          322,   258,   159,   145,   113,    81,    61,    45,    27,\n",
       "           28,    69]),\n",
       " array([233, 389, 387, 374, 309, 250, 266, 440, 662, 238, 103,  98,  87,\n",
       "         64,  55,  36,  30,  21,  15,  12,  13,   8,   9,   9,   6,   6,\n",
       "          0,   2,  22]),\n",
       " array([288, 604, 463, 355, 279, 239, 188, 190, 158, 167, 156, 165, 183,\n",
       "        141, 101,  55,  49,  32,  32,  24,  34,  25,  19,  21,  15,  10,\n",
       "         11,  15,  14,  10,   4,   7,   4,   8,   7,   8,   2,   6,   4,\n",
       "          4,   1,   3,   0,   1,   0,   4,   4,   5,   2,   3,   0,   2,\n",
       "          1,   4,   2,   0,   1,   0,   0,   0,   2,  12]),\n",
       " array([288, 604, 463, 355, 279, 239, 188, 190, 158, 167, 156, 165, 183,\n",
       "        141, 101,  55,  49,  32,  32,  24,  34,  25,  19,  21,  15,  10,\n",
       "         11,  15,  14,  10,   4,   7,   4,   8,   7,   8,   2,   6,   4,\n",
       "          4,   1,   3,   0,   1,   0,   4,   4,   5,   2,   3,   0,   2,\n",
       "          1,   4,   2,   0,   1,   0,   0,   0,   2,  12]))"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g_train, _ = np.histogram(observable_train, binning_qtot)\n",
    "f_train, _ = np.histogram(energy_train, binning_E)\n",
    "\n",
    "g_test, _ = np.histogram(observable_test, binning_qtot)\n",
    "f_test, _ = np.histogram(energy_test, binning_E)\n",
    "\n",
    "f_train, f_test, g_test, g_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "9d83414499ae40559353bcecb11ec667",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "\n",
    "plt.stairs(g_train, lw=5, label='$g$')\n",
    "plt.stairs(A @ f_train, label='$A \\cdot f$')\n",
    "\n",
    "plt.legend()\n",
    "plt.yscale('log')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Berechnung der Akzeptanz\n",
    "\n",
    "Wie zuvor angekündigt ist es interessant die Trigger-bedingten Akzeptanz-Effekte herauszurechnen. Hierzu wird der Vektor $\\mathbf{f}$ mit allen Events ohne Berücksichtigung des Triggers berechnet und einmal mit Trigger. Das Verhältnis der einzelnen Einträge dieser Vektoren ist dann die Akzeptanz in diesem Fall."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "energy_all = labels_train.E.values\n",
    "f_untriggered, _ = np.histogram(energy_all, binning_E)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "acceptance = f_train / f_untriggered"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.02529985, 0.53154631, 0.66419763, 0.71803365, 0.76226746,\n",
       "       0.78019717, 0.80154466, 0.82901181, 0.85425253, 0.86467095,\n",
       "       0.90327816, 0.91877497, 0.92566783, 0.96481626, 0.982706  ,\n",
       "       0.98966408, 0.9947644 , 1.        , 1.        , 1.        ,\n",
       "       1.        , 1.        , 1.        , 1.        , 1.        ,\n",
       "       1.        , 1.        , 1.        , 1.        ])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "acceptance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "5c07b44d4c2f4747940bd3bbb1838b4b",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.lines.Line2D at 0x7f7d61c40e20>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "e_center = 0.5 * (binning_E[:-1] + binning_E[1:])\n",
    "\n",
    "\n",
    "plt.figure()\n",
    "plt.stairs(acceptance[1:-1], binning_E[1:-1])\n",
    "plt.xscale('log')\n",
    "plt.xlabel('$E$')\n",
    "plt.ylabel('Akzeptanz')\n",
    "plt.axhline(1.0, ls=':', color='k')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Lösung der Entfaltungsgleichung\n",
    "\n",
    "## Naiver Ansatz: Pseudo-Inverse\n",
    "\n",
    "Der naivste Ansatz zur Lösung der Entfaltungsgleichung ist die Pseudoinverse:\n",
    "\n",
    "$$\\mathrm A \\cdot \\mathbf f = \\mathbf g \\Longleftrightarrow \\mathbf f = \\mathrm A^+ \\mathbf g$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_unfolding_result(unfolded_hist, legend_title=None):\n",
    "    fig, ax = plt.subplots()\n",
    "    \n",
    "    ax.stairs(unfolded_hist[1:-1], binning_E[1:-1], label='Entfaltung')\n",
    "    ax.stairs((f_test / acceptance)[1:-1], binning_E[1:-1], label='Wahrheit')\n",
    "    \n",
    "    ax.legend(title=legend_title)\n",
    "    \n",
    "    ax.set_xscale('log')\n",
    "    ax.set_yscale('log')\n",
    "    \n",
    "    ax.set_xlabel('E')\n",
    "    ax.set_ylim(0.5, None)\n",
    "    \n",
    "    return fig, ax"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[0;31mSignature:\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlinalg\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpinv\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mrcond\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m1e-15\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mhermitian\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mFalse\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
       "\u001b[0;31mDocstring:\u001b[0m\n",
       "Compute the (Moore-Penrose) pseudo-inverse of a matrix.\n",
       "\n",
       "Calculate the generalized inverse of a matrix using its\n",
       "singular-value decomposition (SVD) and including all\n",
       "*large* singular values.\n",
       "\n",
       ".. versionchanged:: 1.14\n",
       "   Can now operate on stacks of matrices\n",
       "\n",
       "Parameters\n",
       "----------\n",
       "a : (..., M, N) array_like\n",
       "    Matrix or stack of matrices to be pseudo-inverted.\n",
       "rcond : (...) array_like of float\n",
       "    Cutoff for small singular values.\n",
       "    Singular values less than or equal to\n",
       "    ``rcond * largest_singular_value`` are set to zero.\n",
       "    Broadcasts against the stack of matrices.\n",
       "hermitian : bool, optional\n",
       "    If True, `a` is assumed to be Hermitian (symmetric if real-valued),\n",
       "    enabling a more efficient method for finding singular values.\n",
       "    Defaults to False.\n",
       "\n",
       "    .. versionadded:: 1.17.0\n",
       "\n",
       "Returns\n",
       "-------\n",
       "B : (..., N, M) ndarray\n",
       "    The pseudo-inverse of `a`. If `a` is a `matrix` instance, then so\n",
       "    is `B`.\n",
       "\n",
       "Raises\n",
       "------\n",
       "LinAlgError\n",
       "    If the SVD computation does not converge.\n",
       "\n",
       "See Also\n",
       "--------\n",
       "scipy.linalg.pinv : Similar function in SciPy.\n",
       "scipy.linalg.pinv2 : Similar function in SciPy (SVD-based).\n",
       "scipy.linalg.pinvh : Compute the (Moore-Penrose) pseudo-inverse of a\n",
       "                     Hermitian matrix.\n",
       "\n",
       "Notes\n",
       "-----\n",
       "The pseudo-inverse of a matrix A, denoted :math:`A^+`, is\n",
       "defined as: \"the matrix that 'solves' [the least-squares problem]\n",
       ":math:`Ax = b`,\" i.e., if :math:`\\bar{x}` is said solution, then\n",
       ":math:`A^+` is that matrix such that :math:`\\bar{x} = A^+b`.\n",
       "\n",
       "It can be shown that if :math:`Q_1 \\Sigma Q_2^T = A` is the singular\n",
       "value decomposition of A, then\n",
       ":math:`A^+ = Q_2 \\Sigma^+ Q_1^T`, where :math:`Q_{1,2}` are\n",
       "orthogonal matrices, :math:`\\Sigma` is a diagonal matrix consisting\n",
       "of A's so-called singular values, (followed, typically, by\n",
       "zeros), and then :math:`\\Sigma^+` is simply the diagonal matrix\n",
       "consisting of the reciprocals of A's singular values\n",
       "(again, followed by zeros). [1]_\n",
       "\n",
       "References\n",
       "----------\n",
       ".. [1] G. Strang, *Linear Algebra and Its Applications*, 2nd Ed., Orlando,\n",
       "       FL, Academic Press, Inc., 1980, pp. 139-142.\n",
       "\n",
       "Examples\n",
       "--------\n",
       "The following example checks that ``a * a+ * a == a`` and\n",
       "``a+ * a * a+ == a+``:\n",
       "\n",
       ">>> a = np.random.randn(9, 6)\n",
       ">>> B = np.linalg.pinv(a)\n",
       ">>> np.allclose(a, np.dot(a, np.dot(B, a)))\n",
       "True\n",
       ">>> np.allclose(B, np.dot(B, np.dot(a, B)))\n",
       "True\n",
       "\u001b[0;31mFile:\u001b[0m      ~/.local/anaconda3/envs/ml/lib/python3.8/site-packages/numpy/linalg/linalg.py\n",
       "\u001b[0;31mType:\u001b[0m      function\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.linalg.pinv?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "48aeea472238457198c73b627b46ede3",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(<Figure size 640x480 with 1 Axes>, <AxesSubplot:xlabel='E'>)"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f_est_naive = np.linalg.pinv(A) @ g_test / acceptance\n",
    "\n",
    "plot_unfolding_result(f_est_naive)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Deutlich zu sehen sind die starken Oszillationen, die das Ergebnis unbrauchbar machen. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Die Likelihood der Entfaltung\n",
    "\n",
    "Die Bininhalte der Observablenbins sind Zählraten, somit können wir annehmen, dass diese einer Poisson-Statistik folgen:\n",
    "\n",
    "$$f(g_j|\\lambda_j) = \\frac{\\lambda_j^{g_j}}{g_j!} e^{-\\lambda_j}$$\n",
    "\n",
    "Der Erwartungswert $\\lambda_j$ der einzelnen Observablen-Bininhalte lautet gemäß Entfaltungsgleichung\n",
    "\n",
    "$$\\lambda_j = \\sum_i A_{ij} f_i = (\\mathrm A \\cdot \\mathbf f)_j$$\n",
    "\n",
    "Die Likelihood lautet entsprechend\n",
    "\n",
    "$$\\mathcal{L} = \\prod_j f(g_j|\\lambda_j) = \\prod_j \\frac{e^{-(\\mathrm A \\cdot \\mathbf f)_j} (\\mathrm A \\cdot \\mathbf f)_j^{g_j}}{g_j!}$$\n",
    "\n",
    "Aus numerischen Gründen wird im Folgenden stets der negative Logarithmus der Likelihood verwendet:\n",
    "\n",
    "$$-\\log \\mathcal{L} = \\sum_j \\left[(\\mathrm A \\cdot \\mathbf f)_j - g_j\\log(\\mathrm A \\cdot \\mathbf f)_j\\right]$$\n",
    "\n",
    "Ebenfalls müssen wir verhindern, dass der Minimierer ungültige Funktionswerte erhält. Statt `nan` oder `inf` sollten immer sehr große, aber valide Werte zurückgegeben werden.\n",
    "\n",
    "Insbesondere für den Fall das einzelne \"Ausreißer\" eine Wahrscheinlichkeit von \"0\" zugeordnet bekommen, verhindert dies vollständig die Minimierung, falls diese nicht durch eine sehr kleine, aber endliche Wahrscheinlichkeit ersetzt werden:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-31-f3ed73188ef9>:2: RuntimeWarning: divide by zero encountered in log\n",
      "  np.log(0), np.log(eps)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(-inf, -69.07755278982137)"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eps = 1e-30\n",
    "np.log(0), np.log(eps)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "def llh_poisson(f, A, g):\n",
    "    \n",
    "    # force positive f\n",
    "    if np.any(f < 0):\n",
    "        return np.finfo(np.float32).max\n",
    "    \n",
    "    lambda_ = A @ f\n",
    "    \n",
    "    eps = 1e-30 # to avoid log of 0\n",
    "    return np.sum(lambda_ - g * np.log(lambda_ + eps))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Um eine solche Likelihood zu minimieren, kann man numerische Minimierer verwendet, so z.B. `scipy.optimize.minimize` oder wie zuletzt `iminuit`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "from iminuit import Minuit\n",
    "from functools import partial"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "    <tr>\n",
       "        <th colspan=\"5\" style=\"text-align:center\" title=\"Minimizer\"> Migrad </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td colspan=\"2\" style=\"text-align:left\" title=\"Minimum value of function\"> FCN = -1.79e+04 </td>\n",
       "        <td colspan=\"3\" style=\"text-align:center\" title=\"No. of function evaluations in last call and total number\"> Nfcn = 21436 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td colspan=\"2\" style=\"text-align:left\" title=\"Estimated distance to minimum and goal\"> EDM = 0.000171 (Goal: 0.0001) </td>\n",
       "        <td colspan=\"3\" style=\"text-align:center\" title=\"No. of gradient evaluations in last call and total number\">  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td colspan=\"2\" style=\"text-align:center;background-color:#92CCA6;color:black\"> Valid Minimum </td>\n",
       "        <td colspan=\"3\" style=\"text-align:center;background-color:#FFF79A;color:black\"> SOME Parameters at limit </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td colspan=\"2\" style=\"text-align:center;background-color:#92CCA6;color:black\"> Below EDM threshold (goal x 10) </td>\n",
       "        <td colspan=\"3\" style=\"text-align:center;background-color:#92CCA6;color:black\"> Below call limit </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Covariance </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Hesse ok </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\" title=\"Is covariance matrix accurate?\"> Accurate </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\" title=\"Is covariance matrix positive definite?\"> Pos. def. </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\" title=\"Was positive definiteness enforced by Minuit?\"> Not forced </td>\n",
       "    </tr>\n",
       "</table><table>\n",
       "    <tr>\n",
       "        <td></td>\n",
       "        <th title=\"Variable name\"> Name </th>\n",
       "        <th title=\"Value of parameter\"> Value </th>\n",
       "        <th title=\"Hesse error\"> Hesse Error </th>\n",
       "        <th title=\"Minos lower error\"> Minos Error- </th>\n",
       "        <th title=\"Minos upper error\"> Minos Error+ </th>\n",
       "        <th title=\"Lower limit of the parameter\"> Limit- </th>\n",
       "        <th title=\"Upper limit of the parameter\"> Limit+ </th>\n",
       "        <th title=\"Is the parameter fixed in the fit\"> Fixed </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 0 </th>\n",
       "        <td> f_0 </td>\n",
       "        <td> 200 </td>\n",
       "        <td> 60 </td>\n",
       "        <td> -60 </td>\n",
       "        <td> 60 </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 1 </th>\n",
       "        <td> f_1 </td>\n",
       "        <td> 470 </td>\n",
       "        <td> 100 </td>\n",
       "        <td> -100 </td>\n",
       "        <td> 100 </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 2 </th>\n",
       "        <td> f_2 </td>\n",
       "        <td> 390 </td>\n",
       "        <td> 90 </td>\n",
       "        <td> -90 </td>\n",
       "        <td> 90 </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 3 </th>\n",
       "        <td> f_3 </td>\n",
       "        <td> 360 </td>\n",
       "        <td> 80 </td>\n",
       "        <td> -80 </td>\n",
       "        <td> 80 </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 4 </th>\n",
       "        <td> f_4 </td>\n",
       "        <td> 270 </td>\n",
       "        <td> 70 </td>\n",
       "        <td> -70 </td>\n",
       "        <td> 70 </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 5 </th>\n",
       "        <td> f_5 </td>\n",
       "        <td> 270 </td>\n",
       "        <td> 70 </td>\n",
       "        <td> -70 </td>\n",
       "        <td> 70 </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 6 </th>\n",
       "        <td> f_6 </td>\n",
       "        <td> 240 </td>\n",
       "        <td> 70 </td>\n",
       "        <td> -70 </td>\n",
       "        <td> 70 </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 7 </th>\n",
       "        <td> f_7 </td>\n",
       "        <td> 440 </td>\n",
       "        <td> 70 </td>\n",
       "        <td> -70 </td>\n",
       "        <td> 70 </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 8 </th>\n",
       "        <td> f_8 </td>\n",
       "        <td> 700 </td>\n",
       "        <td> 60 </td>\n",
       "        <td> -60 </td>\n",
       "        <td> 60 </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 9 </th>\n",
       "        <td> f_9 </td>\n",
       "        <td> 220 </td>\n",
       "        <td> 40 </td>\n",
       "        <td> -40 </td>\n",
       "        <td> 50 </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 10 </th>\n",
       "        <td> f_10 </td>\n",
       "        <td> 81 </td>\n",
       "        <td> 33 </td>\n",
       "        <td> -33 </td>\n",
       "        <td> 34 </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 11 </th>\n",
       "        <td> f_11 </td>\n",
       "        <td> 119 </td>\n",
       "        <td> 35 </td>\n",
       "        <td> -34 </td>\n",
       "        <td> 36 </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 12 </th>\n",
       "        <td> f_12 </td>\n",
       "        <td> 103 </td>\n",
       "        <td> 32 </td>\n",
       "        <td> -31 </td>\n",
       "        <td> 32 </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 13 </th>\n",
       "        <td> f_13 </td>\n",
       "        <td> 24 </td>\n",
       "        <td> 25 </td>\n",
       "        <td> -24 </td>\n",
       "        <td> 26 </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 14 </th>\n",
       "        <td> f_14 </td>\n",
       "        <td> 88 </td>\n",
       "        <td> 26 </td>\n",
       "        <td> -25 </td>\n",
       "        <td> 27 </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 15 </th>\n",
       "        <td> f_15 </td>\n",
       "        <td> 25 </td>\n",
       "        <td> 18 </td>\n",
       "        <td> -17 </td>\n",
       "        <td> 19 </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 16 </th>\n",
       "        <td> f_16 </td>\n",
       "        <td> 3.3 </td>\n",
       "        <td> 13.0 </td>\n",
       "        <td> -3.3 </td>\n",
       "        <td> 17.6 </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 17 </th>\n",
       "        <td> f_17 </td>\n",
       "        <td> 34 </td>\n",
       "        <td> 17 </td>\n",
       "        <td> -16 </td>\n",
       "        <td> 17 </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 18 </th>\n",
       "        <td> f_18 </td>\n",
       "        <td> 21 </td>\n",
       "        <td> 14 </td>\n",
       "        <td> -13 </td>\n",
       "        <td> 15 </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 19 </th>\n",
       "        <td> f_19 </td>\n",
       "        <td> 14 </td>\n",
       "        <td> 11 </td>\n",
       "        <td> -10 </td>\n",
       "        <td> 13 </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 20 </th>\n",
       "        <td> f_20 </td>\n",
       "        <td> 1.1e-6 </td>\n",
       "        <td> 1491714.7e-6 </td>\n",
       "        <td> -1.1e-6 </td>\n",
       "        <td> 2493007.1e-6 </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 21 </th>\n",
       "        <td> f_21 </td>\n",
       "        <td> 1.3e-6 </td>\n",
       "        <td> 1921159.5e-6 </td>\n",
       "        <td> -1.3e-6 </td>\n",
       "        <td> 3309223.2e-6 </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 22 </th>\n",
       "        <td> f_22 </td>\n",
       "        <td> 28 </td>\n",
       "        <td> 10 </td>\n",
       "        <td> -10 </td>\n",
       "        <td> 10 </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 23 </th>\n",
       "        <td> f_23 </td>\n",
       "        <td> 7 </td>\n",
       "        <td> 6 </td>\n",
       "        <td> -5 </td>\n",
       "        <td> 7 </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 24 </th>\n",
       "        <td> f_24 </td>\n",
       "        <td> 10 </td>\n",
       "        <td> 7 </td>\n",
       "        <td> -6 </td>\n",
       "        <td> 8 </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 25 </th>\n",
       "        <td> f_25 </td>\n",
       "        <td> 5 </td>\n",
       "        <td> 5 </td>\n",
       "        <td> -5 </td>\n",
       "        <td> 7 </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 26 </th>\n",
       "        <td> f_26 </td>\n",
       "        <td> 1.0e-6 </td>\n",
       "        <td> 1065843.0e-6 </td>\n",
       "        <td> -1.0e-6 </td>\n",
       "        <td> 1584117.8e-6 </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 27 </th>\n",
       "        <td> f_27 </td>\n",
       "        <td> 0.4 </td>\n",
       "        <td> 7.6 </td>\n",
       "        <td> -0.4 </td>\n",
       "        <td> 7.6 </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 28 </th>\n",
       "        <td> f_28 </td>\n",
       "        <td> 19 </td>\n",
       "        <td> 5 </td>\n",
       "        <td> -5 </td>\n",
       "        <td> 5 </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "</table><table>\n",
       "    <tr>\n",
       "        <td></td>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Parameter name\"> f_0 </th>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Parameter name\"> f_1 </th>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Parameter name\"> f_2 </th>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Parameter name\"> f_3 </th>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Parameter name\"> f_4 </th>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Parameter name\"> f_5 </th>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Parameter name\"> f_6 </th>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Parameter name\"> f_7 </th>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Parameter name\"> f_8 </th>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Parameter name\"> f_9 </th>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Parameter name\"> f_10 </th>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Parameter name\"> f_11 </th>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Parameter name\"> f_12 </th>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Parameter name\"> f_13 </th>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Parameter name\"> f_14 </th>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Parameter name\"> f_15 </th>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Parameter name\"> f_16 </th>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Parameter name\"> f_17 </th>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Parameter name\"> f_18 </th>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Parameter name\"> f_19 </th>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Parameter name\"> f_20 </th>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Parameter name\"> f_21 </th>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Parameter name\"> f_22 </th>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Parameter name\"> f_23 </th>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Parameter name\"> f_24 </th>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Parameter name\"> f_25 </th>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Parameter name\"> f_26 </th>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Parameter name\"> f_27 </th>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Parameter name\"> f_28 </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th title=\"Lower and upper minos error of the parameter\"> Error </th>\n",
       "        <td> -60 </td>\n",
       "        <td> 60 </td>\n",
       "        <td> -100 </td>\n",
       "        <td> 100 </td>\n",
       "        <td> -90 </td>\n",
       "        <td> 90 </td>\n",
       "        <td> -80 </td>\n",
       "        <td> 80 </td>\n",
       "        <td> -70 </td>\n",
       "        <td> 70 </td>\n",
       "        <td> -70 </td>\n",
       "        <td> 70 </td>\n",
       "        <td> -70 </td>\n",
       "        <td> 70 </td>\n",
       "        <td> -70 </td>\n",
       "        <td> 70 </td>\n",
       "        <td> -60 </td>\n",
       "        <td> 60 </td>\n",
       "        <td> -40 </td>\n",
       "        <td> 50 </td>\n",
       "        <td> -33 </td>\n",
       "        <td> 34 </td>\n",
       "        <td> -34 </td>\n",
       "        <td> 36 </td>\n",
       "        <td> -31 </td>\n",
       "        <td> 32 </td>\n",
       "        <td> -24 </td>\n",
       "        <td> 26 </td>\n",
       "        <td> -25 </td>\n",
       "        <td> 27 </td>\n",
       "        <td> -17 </td>\n",
       "        <td> 19 </td>\n",
       "        <td> -3.3 </td>\n",
       "        <td> 17.6 </td>\n",
       "        <td> -16 </td>\n",
       "        <td> 17 </td>\n",
       "        <td> -13 </td>\n",
       "        <td> 15 </td>\n",
       "        <td> -10 </td>\n",
       "        <td> 13 </td>\n",
       "        <td> -1.1e-6 </td>\n",
       "        <td> 2493007.1e-6 </td>\n",
       "        <td> -1.3e-6 </td>\n",
       "        <td> 3309223.2e-6 </td>\n",
       "        <td> -10 </td>\n",
       "        <td> 10 </td>\n",
       "        <td> -5 </td>\n",
       "        <td> 7 </td>\n",
       "        <td> -6 </td>\n",
       "        <td> 8 </td>\n",
       "        <td> -5 </td>\n",
       "        <td> 7 </td>\n",
       "        <td> -1.0e-6 </td>\n",
       "        <td> 1584117.8e-6 </td>\n",
       "        <td> -0.4 </td>\n",
       "        <td> 7.6 </td>\n",
       "        <td> -5 </td>\n",
       "        <td> 5 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th title=\"Validity of lower/upper minos error\"> Valid </th>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th title=\"Did scan hit limit of any parameter?\"> At Limit </th>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#c15ef7;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#c15ef7;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#c15ef7;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#c15ef7;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#c15ef7;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#c15ef7;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#c15ef7;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th title=\"Did scan hit function call limit?\"> Max FCN </th>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th title=\"New minimum found when doing scan?\"> New Min </th>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "    </tr>\n",
       "</table><table>\n",
       "    <tr>\n",
       "        <td></td>\n",
       "        <th> f_0 </th>\n",
       "        <th> f_1 </th>\n",
       "        <th> f_2 </th>\n",
       "        <th> f_3 </th>\n",
       "        <th> f_4 </th>\n",
       "        <th> f_5 </th>\n",
       "        <th> f_6 </th>\n",
       "        <th> f_7 </th>\n",
       "        <th> f_8 </th>\n",
       "        <th> f_9 </th>\n",
       "        <th> f_10 </th>\n",
       "        <th> f_11 </th>\n",
       "        <th> f_12 </th>\n",
       "        <th> f_13 </th>\n",
       "        <th> f_14 </th>\n",
       "        <th> f_15 </th>\n",
       "        <th> f_16 </th>\n",
       "        <th> f_17 </th>\n",
       "        <th> f_18 </th>\n",
       "        <th> f_19 </th>\n",
       "        <th> f_20 </th>\n",
       "        <th> f_21 </th>\n",
       "        <th> f_22 </th>\n",
       "        <th> f_23 </th>\n",
       "        <th> f_24 </th>\n",
       "        <th> f_25 </th>\n",
       "        <th> f_26 </th>\n",
       "        <th> f_27 </th>\n",
       "        <th> f_28 </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> f_0 </th>\n",
       "        <td> 3.6e+03 </td>\n",
       "        <td style=\"background-color:rgb(145,145,250);color:black\"> -4.74e+03 <strong>(-0.807)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,190,190);color:black\"> 2.14e+03 <strong>(0.399)</strong> </td>\n",
       "        <td style=\"background-color:rgb(221,221,250);color:black\"> -1.05e+03 <strong>(-0.225)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,240,240);color:black\"> 258 <strong>(0.064)</strong> </td>\n",
       "        <td style=\"background-color:rgb(247,247,250);color:black\"> -81.9 <strong>(-0.020)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.22 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 19 <strong>(0.005)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 48.3 <strong>(0.013)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0212 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 14.8 <strong>(0.007)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -13 <strong>(-0.006)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 10 <strong>(0.005)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.27 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.883 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0769 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.3 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.274 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.287 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.381 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -3.62e-07 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 4.09e-07 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0914 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0563 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0258 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.032 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.76e-07 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.00471 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0189 <strong>(0.000)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> f_1 </th>\n",
       "        <td style=\"background-color:rgb(145,145,250);color:black\"> -4.74e+03 <strong>(-0.807)</strong> </td>\n",
       "        <td> 9.59e+03 </td>\n",
       "        <td style=\"background-color:rgb(159,159,250);color:black\"> -6.13e+03 <strong>(-0.698)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,201,201);color:black\"> 2.5e+03 <strong>(0.328)</strong> </td>\n",
       "        <td style=\"background-color:rgb(234,234,250);color:black\"> -796 <strong>(-0.121)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,246,246);color:black\"> 172 <strong>(0.026)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -88.9 <strong>(-0.013)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 46.2 <strong>(0.007)</strong> </td>\n",
       "        <td style=\"background-color:rgb(247,247,250);color:black\"> -126 <strong>(-0.020)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 56.8 <strong>(0.013)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -35.7 <strong>(-0.011)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 23.1 <strong>(0.007)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -5.19 <strong>(-0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -2.87 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.654 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 2.16 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 4.01 <strong>(0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.11 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.55 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.403 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -9.02e-07 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.35e-07 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.384 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.077 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0798 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.000585 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -5.92e-08 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0233 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.00722 <strong>(-0.000)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> f_2 </th>\n",
       "        <td style=\"background-color:rgb(250,190,190);color:black\"> 2.14e+03 <strong>(0.399)</strong> </td>\n",
       "        <td style=\"background-color:rgb(159,159,250);color:black\"> -6.13e+03 <strong>(-0.698)</strong> </td>\n",
       "        <td> 8.03e+03 </td>\n",
       "        <td style=\"background-color:rgb(165,165,250);color:black\"> -4.59e+03 <strong>(-0.657)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,218,218);color:black\"> 1.29e+03 <strong>(0.214)</strong> </td>\n",
       "        <td style=\"background-color:rgb(241,241,250);color:black\"> -401 <strong>(-0.067)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 140 <strong>(0.023)</strong> </td>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -207 <strong>(-0.034)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,246,246);color:black\"> 145 <strong>(0.025)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -47.2 <strong>(-0.012)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 6.14 <strong>(0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 8.79 <strong>(0.003)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -7.82 <strong>(-0.003)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 4.49 <strong>(0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 5.84 <strong>(0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -2.66 <strong>(-0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -2.45 <strong>(-0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.97 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.175 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.217 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 2.42e-07 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.58e-06 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.125 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0786 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.106 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.188 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.94e-07 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.14 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.00427 <strong>(-0.000)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> f_3 </th>\n",
       "        <td style=\"background-color:rgb(221,221,250);color:black\"> -1.05e+03 <strong>(-0.225)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,201,201);color:black\"> 2.5e+03 <strong>(0.328)</strong> </td>\n",
       "        <td style=\"background-color:rgb(165,165,250);color:black\"> -4.59e+03 <strong>(-0.657)</strong> </td>\n",
       "        <td> 6.07e+03 </td>\n",
       "        <td style=\"background-color:rgb(178,178,250);color:black\"> -2.91e+03 <strong>(-0.555)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,231,231);color:black\"> 674 <strong>(0.129)</strong> </td>\n",
       "        <td style=\"background-color:rgb(243,243,250);color:black\"> -272 <strong>(-0.052)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 65.6 <strong>(0.012)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -89 <strong>(-0.018)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -32.6 <strong>(-0.009)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 18 <strong>(0.007)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -24 <strong>(-0.009)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.26 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 2.96 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -22.1 <strong>(-0.011)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 11.1 <strong>(0.008)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 9.05 <strong>(0.007)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.872 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.01 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0576 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 6.43e-07 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -2.82e-06 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.64 <strong>(-0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.102 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.333 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.122 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -5.45e-07 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.00609 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.00198 <strong>(-0.000)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> f_4 </th>\n",
       "        <td style=\"background-color:rgb(250,240,240);color:black\"> 258 <strong>(0.064)</strong> </td>\n",
       "        <td style=\"background-color:rgb(234,234,250);color:black\"> -796 <strong>(-0.121)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,218,218);color:black\"> 1.29e+03 <strong>(0.214)</strong> </td>\n",
       "        <td style=\"background-color:rgb(178,178,250);color:black\"> -2.91e+03 <strong>(-0.555)</strong> </td>\n",
       "        <td> 4.54e+03 </td>\n",
       "        <td style=\"background-color:rgb(182,182,250);color:black\"> -2.35e+03 <strong>(-0.519)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,232,232);color:black\"> 562 <strong>(0.123)</strong> </td>\n",
       "        <td style=\"background-color:rgb(242,242,250);color:black\"> -282 <strong>(-0.061)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 9.03 <strong>(0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -41.6 <strong>(-0.014)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -2.89 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.55 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -11 <strong>(-0.005)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.213 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 13.3 <strong>(0.008)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -11.4 <strong>(-0.009)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -5.73 <strong>(-0.005)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 6.59 <strong>(0.006)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.41 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.44 <strong>(0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 5.22e-07 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.52e-06 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.253 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.466 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.398 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.439 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -4.05e-07 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.348 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.127 <strong>(-0.000)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> f_5 </th>\n",
       "        <td style=\"background-color:rgb(247,247,250);color:black\"> -81.9 <strong>(-0.020)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,246,246);color:black\"> 172 <strong>(0.026)</strong> </td>\n",
       "        <td style=\"background-color:rgb(241,241,250);color:black\"> -401 <strong>(-0.067)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,231,231);color:black\"> 674 <strong>(0.129)</strong> </td>\n",
       "        <td style=\"background-color:rgb(182,182,250);color:black\"> -2.35e+03 <strong>(-0.519)</strong> </td>\n",
       "        <td> 4.5e+03 </td>\n",
       "        <td style=\"background-color:rgb(178,178,250);color:black\"> -2.5e+03 <strong>(-0.551)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,233,233);color:black\"> 528 <strong>(0.115)</strong> </td>\n",
       "        <td style=\"background-color:rgb(242,242,250);color:black\"> -264 <strong>(-0.061)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 23.9 <strong>(0.008)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.879 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -27.7 <strong>(-0.012)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 26 <strong>(0.012)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -15.6 <strong>(-0.009)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -13.5 <strong>(-0.008)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 10 <strong>(0.008)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -14.4 <strong>(-0.013)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 3.16 <strong>(0.003)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 5.33 <strong>(0.006)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.366 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.37e-06 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -5.93e-06 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.273 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.245 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.134 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.381 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.57e-07 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.388 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0396 <strong>(-0.000)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> f_6 </th>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.22 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -88.9 <strong>(-0.013)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 140 <strong>(0.023)</strong> </td>\n",
       "        <td style=\"background-color:rgb(243,243,250);color:black\"> -272 <strong>(-0.052)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,232,232);color:black\"> 562 <strong>(0.123)</strong> </td>\n",
       "        <td style=\"background-color:rgb(178,178,250);color:black\"> -2.5e+03 <strong>(-0.551)</strong> </td>\n",
       "        <td> 4.58e+03 </td>\n",
       "        <td style=\"background-color:rgb(185,185,250);color:black\"> -2.3e+03 <strong>(-0.497)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,242,242);color:black\"> 237 <strong>(0.055)</strong> </td>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -94.5 <strong>(-0.032)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.655 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -32.2 <strong>(-0.014)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0163 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -25.2 <strong>(-0.015)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,245,245);color:black\"> 59.1 <strong>(0.033)</strong> </td>\n",
       "        <td style=\"background-color:rgb(247,247,250);color:black\"> -31 <strong>(-0.025)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 6.89 <strong>(0.006)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -17.7 <strong>(-0.015)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 13.3 <strong>(0.014)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.94 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 5.58e-06 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 6.85e-06 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 2.18 <strong>(0.003)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.589 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.354 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0715 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 4.13e-07 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0528 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.394 <strong>(-0.001)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> f_7 </th>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 19 <strong>(0.005)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 46.2 <strong>(0.007)</strong> </td>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -207 <strong>(-0.034)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 65.6 <strong>(0.012)</strong> </td>\n",
       "        <td style=\"background-color:rgb(242,242,250);color:black\"> -282 <strong>(-0.061)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,233,233);color:black\"> 528 <strong>(0.115)</strong> </td>\n",
       "        <td style=\"background-color:rgb(185,185,250);color:black\"> -2.3e+03 <strong>(-0.497)</strong> </td>\n",
       "        <td> 4.68e+03 </td>\n",
       "        <td style=\"background-color:rgb(183,183,250);color:black\"> -2.25e+03 <strong>(-0.513)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,239,239);color:black\"> 228 <strong>(0.076)</strong> </td>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -63.5 <strong>(-0.028)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.714 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 3.04 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -10.8 <strong>(-0.006)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -21.8 <strong>(-0.012)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 8.57 <strong>(0.007)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.531 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 5.13 <strong>(0.004)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -13 <strong>(-0.013)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 6.22 <strong>(0.008)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.03e-06 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.65e-05 </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 3.34 <strong>(0.005)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.32 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.715 <strong>(-0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.293 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.35e-06 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.758 <strong>(-0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.533 <strong>(0.001)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> f_8 </th>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 48.3 <strong>(0.013)</strong> </td>\n",
       "        <td style=\"background-color:rgb(247,247,250);color:black\"> -126 <strong>(-0.020)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,246,246);color:black\"> 145 <strong>(0.025)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -89 <strong>(-0.018)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 9.03 <strong>(0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(242,242,250);color:black\"> -264 <strong>(-0.061)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,242,242);color:black\"> 237 <strong>(0.055)</strong> </td>\n",
       "        <td style=\"background-color:rgb(183,183,250);color:black\"> -2.25e+03 <strong>(-0.513)</strong> </td>\n",
       "        <td> 4.11e+03 </td>\n",
       "        <td style=\"background-color:rgb(194,194,250);color:black\"> -1.22e+03 <strong>(-0.431)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,239,239);color:black\"> 154 <strong>(0.072)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -7.66 <strong>(-0.003)</strong> </td>\n",
       "        <td style=\"background-color:rgb(245,245,250);color:black\"> -70.6 <strong>(-0.035)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,246,246);color:black\"> 42.1 <strong>(0.026)</strong> </td>\n",
       "        <td style=\"background-color:rgb(247,247,250);color:black\"> -35.8 <strong>(-0.021)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 15.1 <strong>(0.013)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 6.2 <strong>(0.006)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -4.07 <strong>(-0.004)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -3.4 <strong>(-0.004)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -5.06 <strong>(-0.007)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.07e-05 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 7.05e-06 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.04 <strong>(-0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 1.47 <strong>(0.004)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.236 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.304 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 8.28e-07 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.324 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.25 <strong>(0.001)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> f_9 </th>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0212 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 56.8 <strong>(0.013)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -47.2 <strong>(-0.012)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -32.6 <strong>(-0.009)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -41.6 <strong>(-0.014)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 23.9 <strong>(0.008)</strong> </td>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -94.5 <strong>(-0.032)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,239,239);color:black\"> 228 <strong>(0.076)</strong> </td>\n",
       "        <td style=\"background-color:rgb(194,194,250);color:black\"> -1.22e+03 <strong>(-0.431)</strong> </td>\n",
       "        <td> 1.94e+03 </td>\n",
       "        <td style=\"background-color:rgb(197,197,250);color:black\"> -603 <strong>(-0.411)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 20.9 <strong>(0.014)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.4 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -15.3 <strong>(-0.014)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 11.3 <strong>(0.010)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -11.9 <strong>(-0.015)</strong> </td>\n",
       "        <td style=\"background-color:rgb(247,247,250);color:black\"> -15.5 <strong>(-0.021)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 8.96 <strong>(0.012)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -3.26 <strong>(-0.005)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 2.6 <strong>(0.005)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.5e-05 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 2.87e-06 </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 2.16 <strong>(0.005)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0186 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.47 <strong>(0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0929 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -7.24e-07 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.149 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.126 <strong>(0.001)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> f_10 </th>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 14.8 <strong>(0.007)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -35.7 <strong>(-0.011)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 6.14 <strong>(0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 18 <strong>(0.007)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -2.89 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.879 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.655 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -63.5 <strong>(-0.028)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,239,239);color:black\"> 154 <strong>(0.072)</strong> </td>\n",
       "        <td style=\"background-color:rgb(197,197,250);color:black\"> -603 <strong>(-0.411)</strong> </td>\n",
       "        <td> 1.11e+03 </td>\n",
       "        <td style=\"background-color:rgb(189,189,250);color:black\"> -540 <strong>(-0.466)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,240,240);color:black\"> 71.2 <strong>(0.068)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -2.46 <strong>(-0.003)</strong> </td>\n",
       "        <td style=\"background-color:rgb(242,242,250);color:black\"> -51.6 <strong>(-0.059)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,245,245);color:black\"> 19.2 <strong>(0.032)</strong> </td>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -15.2 <strong>(-0.027)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 7.78 <strong>(0.014)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 4.54 <strong>(0.010)</strong> </td>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -10.9 <strong>(-0.029)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 6.54e-06 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -3.71e-06 </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -1.78 <strong>(-0.005)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 3.46 <strong>(0.017)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0836 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 1.19 <strong>(0.005)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -5.59e-07 </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -1.01 <strong>(-0.005)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.254 <strong>(0.001)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> f_11 </th>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -13 <strong>(-0.006)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 23.1 <strong>(0.007)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 8.79 <strong>(0.003)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -24 <strong>(-0.009)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.55 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -27.7 <strong>(-0.012)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -32.2 <strong>(-0.014)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.714 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -7.66 <strong>(-0.003)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 20.9 <strong>(0.014)</strong> </td>\n",
       "        <td style=\"background-color:rgb(189,189,250);color:black\"> -540 <strong>(-0.466)</strong> </td>\n",
       "        <td> 1.21e+03 </td>\n",
       "        <td style=\"background-color:rgb(184,184,250);color:black\"> -555 <strong>(-0.505)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,235,235);color:black\"> 87.7 <strong>(0.099)</strong> </td>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -25.2 <strong>(-0.028)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.54 <strong>(-0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 6.2 <strong>(0.011)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.65 <strong>(0.003)</strong> </td>\n",
       "        <td style=\"background-color:rgb(244,244,250);color:black\"> -22.8 <strong>(-0.046)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 5.22 <strong>(0.013)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -6.35e-06 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.12e-05 </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 1.58 <strong>(0.004)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.209 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 2.32 <strong>(0.010)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -1.36 <strong>(-0.006)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.22e-06 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.36 <strong>(0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.485 <strong>(0.003)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> f_12 </th>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 10 <strong>(0.005)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -5.19 <strong>(-0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -7.82 <strong>(-0.003)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.26 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -11 <strong>(-0.005)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 26 <strong>(0.012)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0163 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 3.04 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(245,245,250);color:black\"> -70.6 <strong>(-0.035)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.4 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,240,240);color:black\"> 71.2 <strong>(0.068)</strong> </td>\n",
       "        <td style=\"background-color:rgb(184,184,250);color:black\"> -555 <strong>(-0.505)</strong> </td>\n",
       "        <td> 995 </td>\n",
       "        <td style=\"background-color:rgb(188,188,250);color:black\"> -383 <strong>(-0.478)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,242,242);color:black\"> 44.1 <strong>(0.053)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -10.8 <strong>(-0.019)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -8.17 <strong>(-0.015)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -8.38 <strong>(-0.016)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,246,246);color:black\"> 12.2 <strong>(0.027)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 1.3 <strong>(0.004)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -2.03e-05 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -2.94e-05 </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -5.58 <strong>(-0.018)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.529 <strong>(-0.003)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.197 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 4.56 <strong>(0.022)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -6.86e-06 </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -0.899 <strong>(-0.004)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -1 <strong>(-0.006)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> f_13 </th>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.27 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -2.87 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 4.49 <strong>(0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 2.96 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.213 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -15.6 <strong>(-0.009)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -25.2 <strong>(-0.015)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -10.8 <strong>(-0.006)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,246,246);color:black\"> 42.1 <strong>(0.026)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -15.3 <strong>(-0.014)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -2.46 <strong>(-0.003)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,235,235);color:black\"> 87.7 <strong>(0.099)</strong> </td>\n",
       "        <td style=\"background-color:rgb(188,188,250);color:black\"> -383 <strong>(-0.478)</strong> </td>\n",
       "        <td> 645 </td>\n",
       "        <td style=\"background-color:rgb(184,184,250);color:black\"> -336 <strong>(-0.506)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,229,229);color:black\"> 65.5 <strong>(0.142)</strong> </td>\n",
       "        <td style=\"background-color:rgb(247,247,250);color:black\"> -9.66 <strong>(-0.023)</strong> </td>\n",
       "        <td style=\"background-color:rgb(247,247,250);color:black\"> -8.67 <strong>(-0.020)</strong> </td>\n",
       "        <td style=\"background-color:rgb(247,247,250);color:black\"> -8.14 <strong>(-0.023)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.117 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 5.37e-06 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 4.49e-06 </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -4.51 <strong>(-0.018)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.48 <strong>(-0.003)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -2.44 <strong>(-0.014)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -0.879 <strong>(-0.005)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 8.01e-06 </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 1.65 <strong>(0.010)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.177 <strong>(0.001)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> f_14 </th>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.883 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.654 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 5.84 <strong>(0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -22.1 <strong>(-0.011)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 13.3 <strong>(0.008)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -13.5 <strong>(-0.008)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,245,245);color:black\"> 59.1 <strong>(0.033)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -21.8 <strong>(-0.012)</strong> </td>\n",
       "        <td style=\"background-color:rgb(247,247,250);color:black\"> -35.8 <strong>(-0.021)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 11.3 <strong>(0.010)</strong> </td>\n",
       "        <td style=\"background-color:rgb(242,242,250);color:black\"> -51.6 <strong>(-0.059)</strong> </td>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -25.2 <strong>(-0.028)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,242,242);color:black\"> 44.1 <strong>(0.053)</strong> </td>\n",
       "        <td style=\"background-color:rgb(184,184,250);color:black\"> -336 <strong>(-0.506)</strong> </td>\n",
       "        <td> 685 </td>\n",
       "        <td style=\"background-color:rgb(182,182,250);color:black\"> -248 <strong>(-0.521)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,242,242);color:black\"> 22.4 <strong>(0.051)</strong> </td>\n",
       "        <td style=\"background-color:rgb(241,241,250);color:black\"> -29.7 <strong>(-0.066)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,235,235);color:black\"> 37.9 <strong>(0.102)</strong> </td>\n",
       "        <td style=\"background-color:rgb(242,242,250);color:black\"> -18.4 <strong>(-0.062)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -6.56e-06 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 7.37e-05 </td>\n",
       "        <td style=\"background-color:rgb(250,240,240);color:black\"> 17.3 <strong>(0.066)</strong> </td>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -5.46 <strong>(-0.034)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 3.29 <strong>(0.018)</strong> </td>\n",
       "        <td style=\"background-color:rgb(245,245,250);color:black\"> -6.36 <strong>(-0.037)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 5.29e-06 </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 3.35 <strong>(0.020)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -1.18 <strong>(-0.008)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> f_15 </th>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0769 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 2.16 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -2.66 <strong>(-0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 11.1 <strong>(0.008)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -11.4 <strong>(-0.009)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 10 <strong>(0.008)</strong> </td>\n",
       "        <td style=\"background-color:rgb(247,247,250);color:black\"> -31 <strong>(-0.025)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 8.57 <strong>(0.007)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 15.1 <strong>(0.013)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -11.9 <strong>(-0.015)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,245,245);color:black\"> 19.2 <strong>(0.032)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.54 <strong>(-0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -10.8 <strong>(-0.019)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,229,229);color:black\"> 65.5 <strong>(0.142)</strong> </td>\n",
       "        <td style=\"background-color:rgb(182,182,250);color:black\"> -248 <strong>(-0.521)</strong> </td>\n",
       "        <td> 330 </td>\n",
       "        <td style=\"background-color:rgb(206,206,250);color:black\"> -103 <strong>(-0.335)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,242,242);color:black\"> 16.9 <strong>(0.054)</strong> </td>\n",
       "        <td style=\"background-color:rgb(231,231,250);color:black\"> -37.6 <strong>(-0.146)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,245,245);color:black\"> 6.98 <strong>(0.034)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 4.38e-07 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -3.63e-05 </td>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -5.4 <strong>(-0.029)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,242,242);color:black\"> 5.66 <strong>(0.051)</strong> </td>\n",
       "        <td style=\"background-color:rgb(244,244,250);color:black\"> -6.14 <strong>(-0.049)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,246,246);color:black\"> 3.43 <strong>(0.028)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.34e-05 </td>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -3.94 <strong>(-0.034)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,245,245);color:black\"> 3.01 <strong>(0.031)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> f_16 </th>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.3 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 4.01 <strong>(0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -2.45 <strong>(-0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 9.05 <strong>(0.007)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -5.73 <strong>(-0.005)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -14.4 <strong>(-0.013)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 6.89 <strong>(0.006)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.531 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 6.2 <strong>(0.006)</strong> </td>\n",
       "        <td style=\"background-color:rgb(247,247,250);color:black\"> -15.5 <strong>(-0.021)</strong> </td>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -15.2 <strong>(-0.027)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 6.2 <strong>(0.011)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -8.17 <strong>(-0.015)</strong> </td>\n",
       "        <td style=\"background-color:rgb(247,247,250);color:black\"> -9.66 <strong>(-0.023)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,242,242);color:black\"> 22.4 <strong>(0.051)</strong> </td>\n",
       "        <td style=\"background-color:rgb(206,206,250);color:black\"> -103 <strong>(-0.335)</strong> </td>\n",
       "        <td> 285 </td>\n",
       "        <td style=\"background-color:rgb(187,187,250);color:black\"> -140 <strong>(-0.484)</strong> </td>\n",
       "        <td style=\"background-color:rgb(244,244,250);color:black\"> -11 <strong>(-0.046)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,246,246);color:black\"> 5.37 <strong>(0.028)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.2e-05 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 2.66e-05 </td>\n",
       "        <td style=\"background-color:rgb(242,242,250);color:black\"> -10.9 <strong>(-0.064)</strong> </td>\n",
       "        <td style=\"background-color:rgb(247,247,250);color:black\"> -2.65 <strong>(-0.026)</strong> </td>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -3.34 <strong>(-0.029)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 2.01 <strong>(0.018)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -7.04e-06 </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 0.831 <strong>(0.008)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -1.47 <strong>(-0.016)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> f_17 </th>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.274 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.11 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.97 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.872 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 6.59 <strong>(0.006)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 3.16 <strong>(0.003)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -17.7 <strong>(-0.015)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 5.13 <strong>(0.004)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -4.07 <strong>(-0.004)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 8.96 <strong>(0.012)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 7.78 <strong>(0.014)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.65 <strong>(0.003)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -8.38 <strong>(-0.016)</strong> </td>\n",
       "        <td style=\"background-color:rgb(247,247,250);color:black\"> -8.67 <strong>(-0.020)</strong> </td>\n",
       "        <td style=\"background-color:rgb(241,241,250);color:black\"> -29.7 <strong>(-0.066)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,242,242);color:black\"> 16.9 <strong>(0.054)</strong> </td>\n",
       "        <td style=\"background-color:rgb(187,187,250);color:black\"> -140 <strong>(-0.484)</strong> </td>\n",
       "        <td> 292 </td>\n",
       "        <td style=\"background-color:rgb(206,206,250);color:black\"> -82.9 <strong>(-0.341)</strong> </td>\n",
       "        <td style=\"background-color:rgb(241,241,250);color:black\"> -14.1 <strong>(-0.073)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.18e-06 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.92e-05 </td>\n",
       "        <td style=\"background-color:rgb(245,245,250);color:black\"> -6.58 <strong>(-0.038)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -0.45 <strong>(-0.004)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,245,245);color:black\"> 3.93 <strong>(0.034)</strong> </td>\n",
       "        <td style=\"background-color:rgb(239,239,250);color:black\"> -9.37 <strong>(-0.083)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.03e-05 </td>\n",
       "        <td style=\"background-color:rgb(250,241,241);color:black\"> 6.32 <strong>(0.057)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,246,246);color:black\"> 2.17 <strong>(0.024)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> f_18 </th>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.287 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.55 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.175 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.01 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.41 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 5.33 <strong>(0.006)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 13.3 <strong>(0.014)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -13 <strong>(-0.013)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -3.4 <strong>(-0.004)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -3.26 <strong>(-0.005)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 4.54 <strong>(0.010)</strong> </td>\n",
       "        <td style=\"background-color:rgb(244,244,250);color:black\"> -22.8 <strong>(-0.046)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,246,246);color:black\"> 12.2 <strong>(0.027)</strong> </td>\n",
       "        <td style=\"background-color:rgb(247,247,250);color:black\"> -8.14 <strong>(-0.023)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,235,235);color:black\"> 37.9 <strong>(0.102)</strong> </td>\n",
       "        <td style=\"background-color:rgb(231,231,250);color:black\"> -37.6 <strong>(-0.146)</strong> </td>\n",
       "        <td style=\"background-color:rgb(244,244,250);color:black\"> -11 <strong>(-0.046)</strong> </td>\n",
       "        <td style=\"background-color:rgb(206,206,250);color:black\"> -82.9 <strong>(-0.341)</strong> </td>\n",
       "        <td> 202 </td>\n",
       "        <td style=\"background-color:rgb(198,198,250);color:black\"> -64.3 <strong>(-0.400)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 2.29e-05 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 9.68e-06 </td>\n",
       "        <td style=\"background-color:rgb(242,242,250);color:black\"> -9.13 <strong>(-0.064)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 1.52 <strong>(0.018)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,243,243);color:black\"> 4.32 <strong>(0.044)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 1.34 <strong>(0.014)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 4.04e-06 </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -0.492 <strong>(-0.005)</strong> </td>\n",
       "        <td style=\"background-color:rgb(241,241,250);color:black\"> -5.02 <strong>(-0.066)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> f_19 </th>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.381 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.403 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.217 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0576 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.44 <strong>(0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.366 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.94 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 6.22 <strong>(0.008)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -5.06 <strong>(-0.007)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 2.6 <strong>(0.005)</strong> </td>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -10.9 <strong>(-0.029)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 5.22 <strong>(0.013)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 1.3 <strong>(0.004)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.117 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(242,242,250);color:black\"> -18.4 <strong>(-0.062)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,245,245);color:black\"> 6.98 <strong>(0.034)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,246,246);color:black\"> 5.37 <strong>(0.028)</strong> </td>\n",
       "        <td style=\"background-color:rgb(241,241,250);color:black\"> -14.1 <strong>(-0.073)</strong> </td>\n",
       "        <td style=\"background-color:rgb(198,198,250);color:black\"> -64.3 <strong>(-0.400)</strong> </td>\n",
       "        <td> 128 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -8.34e-05 <strong>(-0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 3.43e-05 </td>\n",
       "        <td style=\"background-color:rgb(226,226,250);color:black\"> -20.7 <strong>(-0.181)</strong> </td>\n",
       "        <td style=\"background-color:rgb(229,229,250);color:black\"> -11 <strong>(-0.160)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0161 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.211 <strong>(0.003)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -2.63e-06 </td>\n",
       "        <td style=\"background-color:rgb(250,239,239);color:black\"> 5.16 <strong>(0.071)</strong> </td>\n",
       "        <td style=\"background-color:rgb(245,245,250);color:black\"> -2.19 <strong>(-0.036)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> f_20 </th>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -3.62e-07 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -9.02e-07 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 2.42e-07 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 6.43e-07 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 5.22e-07 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.37e-06 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 5.58e-06 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.03e-06 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.07e-05 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.5e-05 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 6.54e-06 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -6.35e-06 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -2.03e-05 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 5.37e-06 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -6.56e-06 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 4.38e-07 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.2e-05 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.18e-06 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 2.29e-05 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -8.34e-05 <strong>(-0.002)</strong> </td>\n",
       "        <td> 1.13e-05 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 3.44e-11 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -5.32e-05 <strong>(-0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.17e-05 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.01e-05 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 4.58e-06 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.96e-11 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -3.21e-06 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 3.76e-07 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> f_21 </th>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 4.09e-07 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.35e-07 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.58e-06 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -2.82e-06 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.52e-06 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -5.93e-06 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 6.85e-06 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.65e-05 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 7.05e-06 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 2.87e-06 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -3.71e-06 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.12e-05 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -2.94e-05 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 4.49e-06 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 7.37e-05 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -3.63e-05 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 2.66e-05 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.92e-05 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 9.68e-06 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 3.43e-05 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 3.44e-11 </td>\n",
       "        <td> 2.02e-05 </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 0.000187 <strong>(0.004)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -6.36e-06 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.21e-05 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -4.65e-06 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 6.08e-11 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.09e-07 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 9.95e-07 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> f_22 </th>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0914 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.384 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.125 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.64 <strong>(-0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.253 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.273 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 2.18 <strong>(0.003)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 3.34 <strong>(0.005)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.04 <strong>(-0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 2.16 <strong>(0.005)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -1.78 <strong>(-0.005)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 1.58 <strong>(0.004)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -5.58 <strong>(-0.018)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -4.51 <strong>(-0.018)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,240,240);color:black\"> 17.3 <strong>(0.066)</strong> </td>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -5.4 <strong>(-0.029)</strong> </td>\n",
       "        <td style=\"background-color:rgb(242,242,250);color:black\"> -10.9 <strong>(-0.064)</strong> </td>\n",
       "        <td style=\"background-color:rgb(245,245,250);color:black\"> -6.58 <strong>(-0.038)</strong> </td>\n",
       "        <td style=\"background-color:rgb(242,242,250);color:black\"> -9.13 <strong>(-0.064)</strong> </td>\n",
       "        <td style=\"background-color:rgb(226,226,250);color:black\"> -20.7 <strong>(-0.181)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -5.32e-05 <strong>(-0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 0.000187 <strong>(0.004)</strong> </td>\n",
       "        <td> 102 </td>\n",
       "        <td style=\"background-color:rgb(228,228,250);color:black\"> -10.6 <strong>(-0.172)</strong> </td>\n",
       "        <td style=\"background-color:rgb(223,223,250);color:black\"> -14.5 <strong>(-0.211)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -0.835 <strong>(-0.012)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -8.32e-06 </td>\n",
       "        <td style=\"background-color:rgb(218,218,250);color:black\"> -16 <strong>(-0.245)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,229,229);color:black\"> 7.67 <strong>(0.143)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> f_23 </th>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0563 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.077 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0786 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.102 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.466 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.245 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.589 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.32 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 1.47 <strong>(0.004)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0186 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 3.46 <strong>(0.017)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.209 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.529 <strong>(-0.003)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.48 <strong>(-0.003)</strong> </td>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -5.46 <strong>(-0.034)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,242,242);color:black\"> 5.66 <strong>(0.051)</strong> </td>\n",
       "        <td style=\"background-color:rgb(247,247,250);color:black\"> -2.65 <strong>(-0.026)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -0.45 <strong>(-0.004)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 1.52 <strong>(0.018)</strong> </td>\n",
       "        <td style=\"background-color:rgb(229,229,250);color:black\"> -11 <strong>(-0.160)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.17e-05 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -6.36e-06 </td>\n",
       "        <td style=\"background-color:rgb(228,228,250);color:black\"> -10.6 <strong>(-0.172)</strong> </td>\n",
       "        <td> 37.3 </td>\n",
       "        <td style=\"background-color:rgb(215,215,250);color:black\"> -11.3 <strong>(-0.271)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,221,221);color:black\"> 7.95 <strong>(0.196)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -5.32e-06 </td>\n",
       "        <td style=\"background-color:rgb(215,215,250);color:black\"> -10.6 <strong>(-0.269)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,234,234);color:black\"> 3.38 <strong>(0.104)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> f_24 </th>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0258 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0798 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.106 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.333 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.398 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.134 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.354 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.715 <strong>(-0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.236 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.47 <strong>(0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0836 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 2.32 <strong>(0.010)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.197 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -2.44 <strong>(-0.014)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 3.29 <strong>(0.018)</strong> </td>\n",
       "        <td style=\"background-color:rgb(244,244,250);color:black\"> -6.14 <strong>(-0.049)</strong> </td>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -3.34 <strong>(-0.029)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,245,245);color:black\"> 3.93 <strong>(0.034)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,243,243);color:black\"> 4.32 <strong>(0.044)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0161 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.01e-05 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.21e-05 </td>\n",
       "        <td style=\"background-color:rgb(223,223,250);color:black\"> -14.5 <strong>(-0.211)</strong> </td>\n",
       "        <td style=\"background-color:rgb(215,215,250);color:black\"> -11.3 <strong>(-0.271)</strong> </td>\n",
       "        <td> 46.6 </td>\n",
       "        <td style=\"background-color:rgb(191,191,250);color:black\"> -20.7 <strong>(-0.456)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.83e-05 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,209,209);color:black\"> 12.1 <strong>(0.273)</strong> </td>\n",
       "        <td style=\"background-color:rgb(235,235,250);color:black\"> -4.16 <strong>(-0.114)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> f_25 </th>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.032 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.000585 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.188 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.122 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.439 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.381 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0715 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.293 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.304 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0929 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 1.19 <strong>(0.005)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -1.36 <strong>(-0.006)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 4.56 <strong>(0.022)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -0.879 <strong>(-0.005)</strong> </td>\n",
       "        <td style=\"background-color:rgb(245,245,250);color:black\"> -6.36 <strong>(-0.037)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,246,246);color:black\"> 3.43 <strong>(0.028)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 2.01 <strong>(0.018)</strong> </td>\n",
       "        <td style=\"background-color:rgb(239,239,250);color:black\"> -9.37 <strong>(-0.083)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 1.34 <strong>(0.014)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.211 <strong>(0.003)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 4.58e-06 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -4.65e-06 </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -0.835 <strong>(-0.012)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,221,221);color:black\"> 7.95 <strong>(0.196)</strong> </td>\n",
       "        <td style=\"background-color:rgb(191,191,250);color:black\"> -20.7 <strong>(-0.456)</strong> </td>\n",
       "        <td> 44.1 </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -7.54e-05 <strong>(-0.004)</strong> </td>\n",
       "        <td style=\"background-color:rgb(183,183,250);color:black\"> -22.1 <strong>(-0.516)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 0.151 <strong>(0.004)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> f_26 </th>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.76e-07 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -5.92e-08 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.94e-07 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -5.45e-07 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -4.05e-07 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.57e-07 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 4.13e-07 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.35e-06 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 8.28e-07 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -7.24e-07 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -5.59e-07 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.22e-06 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -6.86e-06 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 8.01e-06 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 5.29e-06 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.34e-05 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -7.04e-06 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.03e-05 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 4.04e-06 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -2.63e-06 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.96e-11 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 6.08e-11 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -8.32e-06 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -5.32e-06 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.83e-05 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -7.54e-05 <strong>(-0.004)</strong> </td>\n",
       "        <td> 6.59e-06 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 8.35e-06 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.38e-06 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> f_27 </th>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.00471 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0233 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.14 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.00609 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.348 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.388 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0528 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.758 <strong>(-0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.324 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.149 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -1.01 <strong>(-0.005)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.36 <strong>(0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -0.899 <strong>(-0.004)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 1.65 <strong>(0.010)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 3.35 <strong>(0.020)</strong> </td>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -3.94 <strong>(-0.034)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 0.831 <strong>(0.008)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,241,241);color:black\"> 6.32 <strong>(0.057)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -0.492 <strong>(-0.005)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,239,239);color:black\"> 5.16 <strong>(0.071)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -3.21e-06 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.09e-07 </td>\n",
       "        <td style=\"background-color:rgb(218,218,250);color:black\"> -16 <strong>(-0.245)</strong> </td>\n",
       "        <td style=\"background-color:rgb(215,215,250);color:black\"> -10.6 <strong>(-0.269)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,209,209);color:black\"> 12.1 <strong>(0.273)</strong> </td>\n",
       "        <td style=\"background-color:rgb(183,183,250);color:black\"> -22.1 <strong>(-0.516)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 8.35e-06 </td>\n",
       "        <td> 41.8 </td>\n",
       "        <td style=\"background-color:rgb(201,201,250);color:black\"> -13.1 <strong>(-0.379)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> f_28 </th>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0189 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.00722 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.00427 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.00198 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.127 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0396 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.394 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.533 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.25 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.126 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.254 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.485 <strong>(0.003)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -1 <strong>(-0.006)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.177 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -1.18 <strong>(-0.008)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,245,245);color:black\"> 3.01 <strong>(0.031)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -1.47 <strong>(-0.016)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,246,246);color:black\"> 2.17 <strong>(0.024)</strong> </td>\n",
       "        <td style=\"background-color:rgb(241,241,250);color:black\"> -5.02 <strong>(-0.066)</strong> </td>\n",
       "        <td style=\"background-color:rgb(245,245,250);color:black\"> -2.19 <strong>(-0.036)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 3.76e-07 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 9.95e-07 </td>\n",
       "        <td style=\"background-color:rgb(250,229,229);color:black\"> 7.67 <strong>(0.143)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,234,234);color:black\"> 3.38 <strong>(0.104)</strong> </td>\n",
       "        <td style=\"background-color:rgb(235,235,250);color:black\"> -4.16 <strong>(-0.114)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 0.151 <strong>(0.004)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.38e-06 </td>\n",
       "        <td style=\"background-color:rgb(201,201,250);color:black\"> -13.1 <strong>(-0.379)</strong> </td>\n",
       "        <td> 28.5 </td>\n",
       "    </tr>\n",
       "</table>"
      ],
      "text/plain": [
       "┌─────────────────────────────────────────────────────────────────────────┐\n",
       "│                                Migrad                                   │\n",
       "├──────────────────────────────────┬──────────────────────────────────────┤\n",
       "│ FCN = -1.79e+04                  │             Nfcn = 21436             │\n",
       "│ EDM = 0.000171 (Goal: 0.0001)    │                                      │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│          Valid Minimum           │       SOME Parameters at limit       │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│ Below EDM threshold (goal x 10)  │           Below call limit           │\n",
       "├───────────────┬──────────────────┼───────────┬─────────────┬────────────┤\n",
       "│  Covariance   │     Hesse ok     │ Accurate  │  Pos. def.  │ Not forced │\n",
       "└───────────────┴──────────────────┴───────────┴─────────────┴────────────┘\n",
       "┌───┬──────┬───────────┬───────────┬────────────┬────────────┬─────────┬─────────┬───────┐\n",
       "│   │ Name │   Value   │ Hesse Err │ Minos Err- │ Minos Err+ │ Limit-  │ Limit+  │ Fixed │\n",
       "├───┼──────┼───────────┼───────────┼────────────┼────────────┼─────────┼─────────┼───────┤\n",
       "│ 0 │ f_0  │    200    │    60     │    -60     │     60     │    0    │         │       │\n",
       "│ 1 │ f_1  │    470    │    100    │    -100    │    100     │    0    │         │       │\n",
       "│ 2 │ f_2  │    390    │    90     │    -90     │     90     │    0    │         │       │\n",
       "│ 3 │ f_3  │    360    │    80     │    -80     │     80     │    0    │         │       │\n",
       "│ 4 │ f_4  │    270    │    70     │    -70     │     70     │    0    │         │       │\n",
       "│ 5 │ f_5  │    270    │    70     │    -70     │     70     │    0    │         │       │\n",
       "│ 6 │ f_6  │    240    │    70     │    -70     │     70     │    0    │         │       │\n",
       "│ 7 │ f_7  │    440    │    70     │    -70     │     70     │    0    │         │       │\n",
       "│ 8 │ f_8  │    700    │    60     │    -60     │     60     │    0    │         │       │\n",
       "│ 9 │ f_9  │    220    │    40     │    -40     │     50     │    0    │         │       │\n",
       "│ 10│ f_10 │    81     │    33     │    -33     │     34     │    0    │         │       │\n",
       "│ 11│ f_11 │    119    │    35     │    -34     │     36     │    0    │         │       │\n",
       "│ 12│ f_12 │    103    │    32     │    -31     │     32     │    0    │         │       │\n",
       "│ 13│ f_13 │    24     │    25     │    -24     │     26     │    0    │         │       │\n",
       "│ 14│ f_14 │    88     │    26     │    -25     │     27     │    0    │         │       │\n",
       "│ 15│ f_15 │    25     │    18     │    -17     │     19     │    0    │         │       │\n",
       "│ 16│ f_16 │    3.3    │   13.0    │    -3.3    │    17.6    │    0    │         │       │\n",
       "│ 17│ f_17 │    34     │    17     │    -16     │     17     │    0    │         │       │\n",
       "│ 18│ f_18 │    21     │    14     │    -13     │     15     │    0    │         │       │\n",
       "│ 19│ f_19 │    14     │    11     │    -10     │     13     │    0    │         │       │\n",
       "│ 20│ f_20 │  1.1e-6   │1491714.7e-6│  -1.1e-6   │2493007.1e-6│    0    │         │       │\n",
       "│ 21│ f_21 │  1.3e-6   │1921159.5e-6│  -1.3e-6   │3309223.2e-6│    0    │         │       │\n",
       "│ 22│ f_22 │    28     │    10     │    -10     │     10     │    0    │         │       │\n",
       "│ 23│ f_23 │     7     │     6     │     -5     │     7      │    0    │         │       │\n",
       "│ 24│ f_24 │    10     │     7     │     -6     │     8      │    0    │         │       │\n",
       "│ 25│ f_25 │     5     │     5     │     -5     │     7      │    0    │         │       │\n",
       "│ 26│ f_26 │  1.0e-6   │1065843.0e-6│  -1.0e-6   │1584117.8e-6│    0    │         │       │\n",
       "│ 27│ f_27 │    0.4    │    7.6    │    -0.4    │    7.6     │    0    │         │       │\n",
       "│ 28│ f_28 │    19     │     5     │     -5     │     5      │    0    │         │       │\n",
       "└───┴──────┴───────────┴───────────┴────────────┴────────────┴─────────┴─────────┴───────┘\n",
       "┌──────────┬───────────────────────┬───────────────────────┬───────────────────────┬───────────────────────┬───────────────────────┬───────────────────────┬───────────────────────┬───────────────────────┬───────────────────────┬───────────────────────┬───────────────────────┬───────────────────────┬───────────────────────┬───────────────────────┬───────────────────────┬───────────────────────┬───────────────────────┬───────────────────────┬───────────────────────┬───────────────────────┬───────────────────────┬───────────────────────┬───────────────────────┬───────────────────────┬───────────────────────┬───────────────────────┬───────────────────────┬───────────────────────┬───────────────────────┐\n",
       "│          │          f_0          │          f_1          │          f_2          │          f_3          │          f_4          │          f_5          │          f_6          │          f_7          │          f_8          │          f_9          │         f_10          │         f_11          │         f_12          │         f_13          │         f_14          │         f_15          │         f_16          │         f_17          │         f_18          │         f_19          │         f_20          │         f_21          │         f_22          │         f_23          │         f_24          │         f_25          │         f_26          │         f_27          │         f_28          │\n",
       "├──────────┼───────────┬───────────┼───────────┬───────────┼───────────┬───────────┼───────────┬───────────┼───────────┬───────────┼───────────┬───────────┼───────────┬───────────┼───────────┬───────────┼───────────┬───────────┼───────────┬───────────┼───────────┬───────────┼───────────┬───────────┼───────────┬───────────┼───────────┬───────────┼───────────┬───────────┼───────────┬───────────┼───────────┬───────────┼───────────┬───────────┼───────────┬───────────┼───────────┬───────────┼───────────┬───────────┼───────────┬───────────┼───────────┬───────────┼───────────┬───────────┼───────────┬───────────┼───────────┬───────────┼───────────┬───────────┼───────────┬───────────┼───────────┬───────────┤\n",
       "│  Error   │    -60    │    60     │   -100    │    100    │    -90    │    90     │    -80    │    80     │    -70    │    70     │    -70    │    70     │    -70    │    70     │    -70    │    70     │    -60    │    60     │    -40    │    50     │    -33    │    34     │    -34    │    36     │    -31    │    32     │    -24    │    26     │    -25    │    27     │    -17    │    19     │   -3.3    │   17.6    │    -16    │    17     │    -13    │    15     │    -10    │    13     │  -1.1e-6  │2493007.1e-6│  -1.3e-6  │3309223.2e-6│    -10    │    10     │    -5     │     7     │    -6     │     8     │    -5     │     7     │  -1.0e-6  │1584117.8e-6│   -0.4    │    7.6    │    -5     │     5     │\n",
       "│  Valid   │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │\n",
       "│ At Limit │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   True    │   False   │   False   │   False   │   False   │   False   │   True    │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   True    │   False   │   True    │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   True    │   False   │   True    │   False   │   True    │   False   │   False   │   False   │\n",
       "│ Max FCN  │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │\n",
       "│ New Min  │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │\n",
       "└──────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┘\n",
       "┌──────┬───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────┐\n",
       "│      │       f_0       f_1       f_2       f_3       f_4       f_5       f_6       f_7       f_8       f_9      f_10      f_11      f_12      f_13      f_14      f_15      f_16      f_17      f_18      f_19      f_20      f_21      f_22      f_23      f_24      f_25      f_26      f_27      f_28 │\n",
       "├──────┼───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────┤\n",
       "│  f_0 │   3.6e+03 -4.74e+03  2.14e+03 -1.05e+03       258     -81.9     -1.22        19      48.3    0.0212      14.8       -13        10      1.27     0.883    0.0769      -1.3    -0.274    -0.287    -0.381 -3.62e-07  4.09e-07    0.0914    0.0563   -0.0258     0.032  1.76e-07  -0.00471    0.0189 │\n",
       "│  f_1 │ -4.74e+03  9.59e+03 -6.13e+03   2.5e+03      -796       172     -88.9      46.2      -126      56.8     -35.7      23.1     -5.19     -2.87    -0.654      2.16      4.01     -1.11     -0.55     0.403 -9.02e-07 -1.35e-07    -0.384    -0.077   -0.0798 -0.000585 -5.92e-08    0.0233  -0.00722 │\n",
       "│  f_2 │  2.14e+03 -6.13e+03  8.03e+03 -4.59e+03  1.29e+03      -401       140      -207       145     -47.2      6.14      8.79     -7.82      4.49      5.84     -2.66     -2.45      1.97    -0.175    -0.217  2.42e-07  1.58e-06     0.125   -0.0786     0.106    -0.188  1.94e-07      0.14  -0.00427 │\n",
       "│  f_3 │ -1.05e+03   2.5e+03 -4.59e+03  6.07e+03 -2.91e+03       674      -272      65.6       -89     -32.6        18       -24      1.26      2.96     -22.1      11.1      9.05     0.872     -1.01    0.0576  6.43e-07 -2.82e-06     -1.64     0.102    -0.333     0.122 -5.45e-07  -0.00609  -0.00198 │\n",
       "│  f_4 │       258      -796  1.29e+03 -2.91e+03  4.54e+03 -2.35e+03       562      -282      9.03     -41.6     -2.89     -1.55       -11     0.213      13.3     -11.4     -5.73      6.59      1.41      1.44  5.22e-07  1.52e-06     0.253    -0.466     0.398    -0.439 -4.05e-07     0.348    -0.127 │\n",
       "│  f_5 │     -81.9       172      -401       674 -2.35e+03   4.5e+03  -2.5e+03       528      -264      23.9    -0.879     -27.7        26     -15.6     -13.5        10     -14.4      3.16      5.33     0.366  1.37e-06 -5.93e-06     0.273     0.245     0.134     0.381 -1.57e-07    -0.388   -0.0396 │\n",
       "│  f_6 │     -1.22     -88.9       140      -272       562  -2.5e+03  4.58e+03  -2.3e+03       237     -94.5     0.655     -32.2   -0.0163     -25.2      59.1       -31      6.89     -17.7      13.3     -0.94  5.58e-06  6.85e-06      2.18    -0.589     0.354   -0.0715  4.13e-07   -0.0528    -0.394 │\n",
       "│  f_7 │        19      46.2      -207      65.6      -282       528  -2.3e+03  4.68e+03 -2.25e+03       228     -63.5     0.714      3.04     -10.8     -21.8      8.57    -0.531      5.13       -13      6.22  1.03e-06 -1.65e-05      3.34     -0.32    -0.715     0.293 -1.35e-06    -0.758     0.533 │\n",
       "│  f_8 │      48.3      -126       145       -89      9.03      -264       237 -2.25e+03  4.11e+03 -1.22e+03       154     -7.66     -70.6      42.1     -35.8      15.1       6.2     -4.07      -3.4     -5.06  1.07e-05  7.05e-06     -1.04      1.47    -0.236     0.304  8.28e-07    -0.324      0.25 │\n",
       "│  f_9 │    0.0212      56.8     -47.2     -32.6     -41.6      23.9     -94.5       228 -1.22e+03  1.94e+03      -603      20.9       1.4     -15.3      11.3     -11.9     -15.5      8.96     -3.26       2.6  -1.5e-05  2.87e-06      2.16    0.0186      0.47   -0.0929 -7.24e-07    -0.149     0.126 │\n",
       "│ f_10 │      14.8     -35.7      6.14        18     -2.89    -0.879     0.655     -63.5       154      -603  1.11e+03      -540      71.2     -2.46     -51.6      19.2     -15.2      7.78      4.54     -10.9  6.54e-06 -3.71e-06     -1.78      3.46   -0.0836      1.19 -5.59e-07     -1.01     0.254 │\n",
       "│ f_11 │       -13      23.1      8.79       -24     -1.55     -27.7     -32.2     0.714     -7.66      20.9      -540  1.21e+03      -555      87.7     -25.2     -1.54       6.2      1.65     -22.8      5.22 -6.35e-06  1.12e-05      1.58     0.209      2.32     -1.36  1.22e-06      0.36     0.485 │\n",
       "│ f_12 │        10     -5.19     -7.82      1.26       -11        26   -0.0163      3.04     -70.6       1.4      71.2      -555       995      -383      44.1     -10.8     -8.17     -8.38      12.2       1.3 -2.03e-05 -2.94e-05     -5.58    -0.529     0.197      4.56 -6.86e-06    -0.899        -1 │\n",
       "│ f_13 │      1.27     -2.87      4.49      2.96     0.213     -15.6     -25.2     -10.8      42.1     -15.3     -2.46      87.7      -383       645      -336      65.5     -9.66     -8.67     -8.14    -0.117  5.37e-06  4.49e-06     -4.51     -0.48     -2.44    -0.879  8.01e-06      1.65     0.177 │\n",
       "│ f_14 │     0.883    -0.654      5.84     -22.1      13.3     -13.5      59.1     -21.8     -35.8      11.3     -51.6     -25.2      44.1      -336       685      -248      22.4     -29.7      37.9     -18.4 -6.56e-06  7.37e-05      17.3     -5.46      3.29     -6.36  5.29e-06      3.35     -1.18 │\n",
       "│ f_15 │    0.0769      2.16     -2.66      11.1     -11.4        10       -31      8.57      15.1     -11.9      19.2     -1.54     -10.8      65.5      -248       330      -103      16.9     -37.6      6.98  4.38e-07 -3.63e-05      -5.4      5.66     -6.14      3.43  1.34e-05     -3.94      3.01 │\n",
       "│ f_16 │      -1.3      4.01     -2.45      9.05     -5.73     -14.4      6.89    -0.531       6.2     -15.5     -15.2       6.2     -8.17     -9.66      22.4      -103       285      -140       -11      5.37  -1.2e-05  2.66e-05     -10.9     -2.65     -3.34      2.01 -7.04e-06     0.831     -1.47 │\n",
       "│ f_17 │    -0.274     -1.11      1.97     0.872      6.59      3.16     -17.7      5.13     -4.07      8.96      7.78      1.65     -8.38     -8.67     -29.7      16.9      -140       292     -82.9     -14.1 -1.18e-06 -1.92e-05     -6.58     -0.45      3.93     -9.37 -1.03e-05      6.32      2.17 │\n",
       "│ f_18 │    -0.287     -0.55    -0.175     -1.01      1.41      5.33      13.3       -13      -3.4     -3.26      4.54     -22.8      12.2     -8.14      37.9     -37.6       -11     -82.9       202     -64.3  2.29e-05  9.68e-06     -9.13      1.52      4.32      1.34  4.04e-06    -0.492     -5.02 │\n",
       "│ f_19 │    -0.381     0.403    -0.217    0.0576      1.44     0.366     -0.94      6.22     -5.06       2.6     -10.9      5.22       1.3    -0.117     -18.4      6.98      5.37     -14.1     -64.3       128 -8.34e-05  3.43e-05     -20.7       -11    0.0161     0.211 -2.63e-06      5.16     -2.19 │\n",
       "│ f_20 │ -3.62e-07 -9.02e-07  2.42e-07  6.43e-07  5.22e-07  1.37e-06  5.58e-06  1.03e-06  1.07e-05  -1.5e-05  6.54e-06 -6.35e-06 -2.03e-05  5.37e-06 -6.56e-06  4.38e-07  -1.2e-05 -1.18e-06  2.29e-05 -8.34e-05  1.13e-05  3.44e-11 -5.32e-05  1.17e-05 -1.01e-05  4.58e-06 -1.96e-11 -3.21e-06  3.76e-07 │\n",
       "│ f_21 │  4.09e-07 -1.35e-07  1.58e-06 -2.82e-06  1.52e-06 -5.93e-06  6.85e-06 -1.65e-05  7.05e-06  2.87e-06 -3.71e-06  1.12e-05 -2.94e-05  4.49e-06  7.37e-05 -3.63e-05  2.66e-05 -1.92e-05  9.68e-06  3.43e-05  3.44e-11  2.02e-05  0.000187 -6.36e-06  1.21e-05 -4.65e-06  6.08e-11  1.09e-07  9.95e-07 │\n",
       "│ f_22 │    0.0914    -0.384     0.125     -1.64     0.253     0.273      2.18      3.34     -1.04      2.16     -1.78      1.58     -5.58     -4.51      17.3      -5.4     -10.9     -6.58     -9.13     -20.7 -5.32e-05  0.000187       102     -10.6     -14.5    -0.835 -8.32e-06       -16      7.67 │\n",
       "│ f_23 │    0.0563    -0.077   -0.0786     0.102    -0.466     0.245    -0.589     -0.32      1.47    0.0186      3.46     0.209    -0.529     -0.48     -5.46      5.66     -2.65     -0.45      1.52       -11  1.17e-05 -6.36e-06     -10.6      37.3     -11.3      7.95 -5.32e-06     -10.6      3.38 │\n",
       "│ f_24 │   -0.0258   -0.0798     0.106    -0.333     0.398     0.134     0.354    -0.715    -0.236      0.47   -0.0836      2.32     0.197     -2.44      3.29     -6.14     -3.34      3.93      4.32    0.0161 -1.01e-05  1.21e-05     -14.5     -11.3      46.6     -20.7  1.83e-05      12.1     -4.16 │\n",
       "│ f_25 │     0.032 -0.000585    -0.188     0.122    -0.439     0.381   -0.0715     0.293     0.304   -0.0929      1.19     -1.36      4.56    -0.879     -6.36      3.43      2.01     -9.37      1.34     0.211  4.58e-06 -4.65e-06    -0.835      7.95     -20.7      44.1 -7.54e-05     -22.1     0.151 │\n",
       "│ f_26 │  1.76e-07 -5.92e-08  1.94e-07 -5.45e-07 -4.05e-07 -1.57e-07  4.13e-07 -1.35e-06  8.28e-07 -7.24e-07 -5.59e-07  1.22e-06 -6.86e-06  8.01e-06  5.29e-06  1.34e-05 -7.04e-06 -1.03e-05  4.04e-06 -2.63e-06 -1.96e-11  6.08e-11 -8.32e-06 -5.32e-06  1.83e-05 -7.54e-05  6.59e-06  8.35e-06  1.38e-06 │\n",
       "│ f_27 │  -0.00471    0.0233      0.14  -0.00609     0.348    -0.388   -0.0528    -0.758    -0.324    -0.149     -1.01      0.36    -0.899      1.65      3.35     -3.94     0.831      6.32    -0.492      5.16 -3.21e-06  1.09e-07       -16     -10.6      12.1     -22.1  8.35e-06      41.8     -13.1 │\n",
       "│ f_28 │    0.0189  -0.00722  -0.00427  -0.00198    -0.127   -0.0396    -0.394     0.533      0.25     0.126     0.254     0.485        -1     0.177     -1.18      3.01     -1.47      2.17     -5.02     -2.19  3.76e-07  9.95e-07      7.67      3.38     -4.16     0.151  1.38e-06     -13.1      28.5 │\n",
       "└──────┴───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────┘"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# use pinv unfolding as initial guess, replacing very small values\n",
    "x0 = np.clip(np.linalg.pinv(A) @ g_test, 10, np.inf)\n",
    "\n",
    "\n",
    "m = Minuit(\n",
    "    partial(llh_poisson, A=A, g=g_test),\n",
    "    x0,\n",
    "    # generate names for our parameters\n",
    "    name=[f\"f_{i}\" for i in range(n_bins_E + 2)]\n",
    ")\n",
    "\n",
    "m.errordef = m.LIKELIHOOD\n",
    "m.limits = [(0, None) for _ in range(n_bins_E + 2)]\n",
    "\n",
    "m.migrad()\n",
    "m.hesse()\n",
    "m.minos()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "2132a9039b604dc1aa9f8943f07dc261",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(<Figure size 640x480 with 1 Axes>, <AxesSubplot:xlabel='E'>)"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot_unfolding_result(m.values / acceptance)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Regularisierung"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Zuletzt fügen wir die Annahme hinzu, dass unsere Lösung _glatt_ sein soll. Dazu definieren wir eine Matrix, die die numerische zweite Ableitung repräsentiert:\n",
    "\n",
    "$$C = \\begin{bmatrix}\n",
    "1 & -1 & 0 & \\dots \\\\\n",
    "-1 &  2 & -1 & \\dots \\\\\n",
    "0 & -1 & \\ddots & & \\vdots & \\vdots \\\\\n",
    "\\vdots & \\vdots & & \\ddots & -1 & 0 \\\\\n",
    "& & \\dots & -1 & 2 & -1\\\\\n",
    "& & \\dots & 0 & -1 & 1\\\\\n",
    "\\end{bmatrix}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "from functools import lru_cache\n",
    "\n",
    "@lru_cache()\n",
    "def C_matrix(n):\n",
    "    I = np.eye(n)\n",
    "    C = 2.0 * I - np.roll(I, 1) - np.roll(I, -1)\n",
    "    return C"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1., -1.,  0.,  0.,  0.],\n",
       "       [-1.,  2., -1.,  0.,  0.],\n",
       "       [ 0., -1.,  2., -1.,  0.],\n",
       "       [ 0.,  0., -1.,  2., -1.],\n",
       "       [ 0.,  0.,  0., -1.,  1.]])"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C_matrix(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "72.9 ns ± 2.72 ns per loop (mean ± std. dev. of 7 runs, 10000000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%timeit C_matrix(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Eine besonders glatte Kurve, so kann man annehmen, soll nun über eine kleine zweite Ableitung verfügen, d.h. wir addieren den Term\n",
    "\n",
    "$$\\mathcal{L}_\\mathrm{tik} = \\tau \\sum_j |C_{ji} f_i|^2 = \\tau \\ \\mathbf f^\\top \\mathrm C^\\top \\mathrm C \\ \\mathbf f$$\n",
    "zur bestehenden Likelihood hinzu. Den offenen Parameter $\\tau$ bezeichnen wir dabei als Regularisierungsstärke. Je größer er ist, desto stärker wird Nicht-Glattheit bestraft.\n",
    "\n",
    "Da die erwartete Flusskurve hier einem Potenzgesetz folgt, kann die Bedingung, dass die zweite Ableitung möglichst klein werden muss besonders gut in der doppelt-logarithmischen Darstellung gerechtfertigt werden: Das Potenzgesetz wird hier zu einem linearen Zusammenhang:\n",
    "\n",
    "$$\\mathcal{L}_\\mathrm{tik} = \\tau \\sum_j |C_{ji} f_i|^2 = \\tau \\log (\\mathbf f)^\\top \\mathrm C^\\top \\mathrm C \\log (\\mathbf f)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "def tikhonov_reg(f, tau, acceptance): \n",
    "    eps = 1e-30\n",
    "    \n",
    "    # we ignore under and overflow for the regularization\n",
    "    C = C_matrix(len(f) - 2)\n",
    "    \n",
    "    # we regularize on the log of f with acceptance correction,\n",
    "    # since only that is expected to be flat\n",
    "    flat_f = np.log(f[1:-1] / acceptance[1:-1] + eps)\n",
    "    return tau * np.sum((C @ flat_f) ** 2)\n",
    "\n",
    "\n",
    "def llh_poisson_tikhonov(f, A, g, tau, acceptance):  \n",
    "    if np.any(f < 0):\n",
    "        return np.finfo(np.float32).max\n",
    "        \n",
    "    return llh_poisson(f, A, g) + tikhonov_reg(f, tau, acceptance)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "tau_regularization = 0.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "    <tr>\n",
       "        <th colspan=\"5\" style=\"text-align:center\" title=\"Minimizer\"> Migrad </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td colspan=\"2\" style=\"text-align:left\" title=\"Minimum value of function\"> FCN = -1.789e+04 </td>\n",
       "        <td colspan=\"3\" style=\"text-align:center\" title=\"No. of function evaluations in last call and total number\"> Nfcn = 29138 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td colspan=\"2\" style=\"text-align:left\" title=\"Estimated distance to minimum and goal\"> EDM = 0.000175 (Goal: 0.0001) </td>\n",
       "        <td colspan=\"3\" style=\"text-align:center\" title=\"No. of gradient evaluations in last call and total number\">  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td colspan=\"2\" style=\"text-align:center;background-color:#92CCA6;color:black\"> Valid Minimum </td>\n",
       "        <td colspan=\"3\" style=\"text-align:center;background-color:#92CCA6;color:black\"> No Parameters at limit </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td colspan=\"2\" style=\"text-align:center;background-color:#92CCA6;color:black\"> Below EDM threshold (goal x 10) </td>\n",
       "        <td colspan=\"3\" style=\"text-align:center;background-color:#92CCA6;color:black\"> Below call limit </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Covariance </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Hesse ok </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\" title=\"Is covariance matrix accurate?\"> Accurate </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\" title=\"Is covariance matrix positive definite?\"> Pos. def. </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\" title=\"Was positive definiteness enforced by Minuit?\"> Not forced </td>\n",
       "    </tr>\n",
       "</table><table>\n",
       "    <tr>\n",
       "        <td></td>\n",
       "        <th title=\"Variable name\"> Name </th>\n",
       "        <th title=\"Value of parameter\"> Value </th>\n",
       "        <th title=\"Hesse error\"> Hesse Error </th>\n",
       "        <th title=\"Minos lower error\"> Minos Error- </th>\n",
       "        <th title=\"Minos upper error\"> Minos Error+ </th>\n",
       "        <th title=\"Lower limit of the parameter\"> Limit- </th>\n",
       "        <th title=\"Upper limit of the parameter\"> Limit+ </th>\n",
       "        <th title=\"Is the parameter fixed in the fit\"> Fixed </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 0 </th>\n",
       "        <td> f_0 </td>\n",
       "        <td> 200 </td>\n",
       "        <td> 60 </td>\n",
       "        <td> -60 </td>\n",
       "        <td> 60 </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 1 </th>\n",
       "        <td> f_1 </td>\n",
       "        <td> 470 </td>\n",
       "        <td> 90 </td>\n",
       "        <td> -90 </td>\n",
       "        <td> 90 </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 2 </th>\n",
       "        <td> f_2 </td>\n",
       "        <td> 400 </td>\n",
       "        <td> 80 </td>\n",
       "        <td> -80 </td>\n",
       "        <td> 80 </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 3 </th>\n",
       "        <td> f_3 </td>\n",
       "        <td> 360 </td>\n",
       "        <td> 70 </td>\n",
       "        <td> -70 </td>\n",
       "        <td> 70 </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 4 </th>\n",
       "        <td> f_4 </td>\n",
       "        <td> 280 </td>\n",
       "        <td> 60 </td>\n",
       "        <td> -60 </td>\n",
       "        <td> 60 </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 5 </th>\n",
       "        <td> f_5 </td>\n",
       "        <td> 260 </td>\n",
       "        <td> 60 </td>\n",
       "        <td> -60 </td>\n",
       "        <td> 60 </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 6 </th>\n",
       "        <td> f_6 </td>\n",
       "        <td> 240 </td>\n",
       "        <td> 60 </td>\n",
       "        <td> -60 </td>\n",
       "        <td> 60 </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 7 </th>\n",
       "        <td> f_7 </td>\n",
       "        <td> 440 </td>\n",
       "        <td> 60 </td>\n",
       "        <td> -60 </td>\n",
       "        <td> 70 </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 8 </th>\n",
       "        <td> f_8 </td>\n",
       "        <td> 700 </td>\n",
       "        <td> 60 </td>\n",
       "        <td> -60 </td>\n",
       "        <td> 60 </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 9 </th>\n",
       "        <td> f_9 </td>\n",
       "        <td> 210 </td>\n",
       "        <td> 40 </td>\n",
       "        <td> -40 </td>\n",
       "        <td> 40 </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 10 </th>\n",
       "        <td> f_10 </td>\n",
       "        <td> 89 </td>\n",
       "        <td> 28 </td>\n",
       "        <td> -27 </td>\n",
       "        <td> 30 </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 11 </th>\n",
       "        <td> f_11 </td>\n",
       "        <td> 117 </td>\n",
       "        <td> 30 </td>\n",
       "        <td> -29 </td>\n",
       "        <td> 31 </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 12 </th>\n",
       "        <td> f_12 </td>\n",
       "        <td> 91 </td>\n",
       "        <td> 26 </td>\n",
       "        <td> -25 </td>\n",
       "        <td> 28 </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 13 </th>\n",
       "        <td> f_13 </td>\n",
       "        <td> 44 </td>\n",
       "        <td> 19 </td>\n",
       "        <td> -17 </td>\n",
       "        <td> 20 </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 14 </th>\n",
       "        <td> f_14 </td>\n",
       "        <td> 71 </td>\n",
       "        <td> 20 </td>\n",
       "        <td> -20 </td>\n",
       "        <td> 21 </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 15 </th>\n",
       "        <td> f_15 </td>\n",
       "        <td> 28 </td>\n",
       "        <td> 14 </td>\n",
       "        <td> -12 </td>\n",
       "        <td> 15 </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 16 </th>\n",
       "        <td> f_16 </td>\n",
       "        <td> 15 </td>\n",
       "        <td> 9 </td>\n",
       "        <td> -8 </td>\n",
       "        <td> 11 </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 17 </th>\n",
       "        <td> f_17 </td>\n",
       "        <td> 27 </td>\n",
       "        <td> 12 </td>\n",
       "        <td> -11 </td>\n",
       "        <td> 13 </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 18 </th>\n",
       "        <td> f_18 </td>\n",
       "        <td> 23 </td>\n",
       "        <td> 11 </td>\n",
       "        <td> -9 </td>\n",
       "        <td> 12 </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 19 </th>\n",
       "        <td> f_19 </td>\n",
       "        <td> 9 </td>\n",
       "        <td> 7 </td>\n",
       "        <td> -6 </td>\n",
       "        <td> 9 </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 20 </th>\n",
       "        <td> f_20 </td>\n",
       "        <td> 2.7 </td>\n",
       "        <td> 2.3 </td>\n",
       "        <td> -1.7 </td>\n",
       "        <td> 3.3 </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 21 </th>\n",
       "        <td> f_21 </td>\n",
       "        <td> 3.9 </td>\n",
       "        <td> 3.0 </td>\n",
       "        <td> -2.3 </td>\n",
       "        <td> 4.0 </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 22 </th>\n",
       "        <td> f_22 </td>\n",
       "        <td> 20 </td>\n",
       "        <td> 9 </td>\n",
       "        <td> -8 </td>\n",
       "        <td> 9 </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 23 </th>\n",
       "        <td> f_23 </td>\n",
       "        <td> 12 </td>\n",
       "        <td> 6 </td>\n",
       "        <td> -5 </td>\n",
       "        <td> 7 </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 24 </th>\n",
       "        <td> f_24 </td>\n",
       "        <td> 9 </td>\n",
       "        <td> 5 </td>\n",
       "        <td> -4 </td>\n",
       "        <td> 6 </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 25 </th>\n",
       "        <td> f_25 </td>\n",
       "        <td> 3.4 </td>\n",
       "        <td> 3.2 </td>\n",
       "        <td> -2.4 </td>\n",
       "        <td> 4.3 </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 26 </th>\n",
       "        <td> f_26 </td>\n",
       "        <td> 0.9 </td>\n",
       "        <td> 1.1 </td>\n",
       "        <td> -1.1 </td>\n",
       "        <td> 1.8 </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 27 </th>\n",
       "        <td> f_27 </td>\n",
       "        <td> 0.4 </td>\n",
       "        <td> 0.8 </td>\n",
       "        <td> -0.8 </td>\n",
       "        <td> 3.1 </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 28 </th>\n",
       "        <td> f_28 </td>\n",
       "        <td> 19 </td>\n",
       "        <td> 5 </td>\n",
       "        <td> -5 </td>\n",
       "        <td> 5 </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "</table><table>\n",
       "    <tr>\n",
       "        <td></td>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Parameter name\"> f_0 </th>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Parameter name\"> f_1 </th>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Parameter name\"> f_2 </th>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Parameter name\"> f_3 </th>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Parameter name\"> f_4 </th>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Parameter name\"> f_5 </th>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Parameter name\"> f_6 </th>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Parameter name\"> f_7 </th>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Parameter name\"> f_8 </th>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Parameter name\"> f_9 </th>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Parameter name\"> f_10 </th>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Parameter name\"> f_11 </th>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Parameter name\"> f_12 </th>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Parameter name\"> f_13 </th>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Parameter name\"> f_14 </th>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Parameter name\"> f_15 </th>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Parameter name\"> f_16 </th>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Parameter name\"> f_17 </th>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Parameter name\"> f_18 </th>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Parameter name\"> f_19 </th>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Parameter name\"> f_20 </th>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Parameter name\"> f_21 </th>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Parameter name\"> f_22 </th>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Parameter name\"> f_23 </th>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Parameter name\"> f_24 </th>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Parameter name\"> f_25 </th>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Parameter name\"> f_26 </th>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Parameter name\"> f_27 </th>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Parameter name\"> f_28 </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th title=\"Lower and upper minos error of the parameter\"> Error </th>\n",
       "        <td> -60 </td>\n",
       "        <td> 60 </td>\n",
       "        <td> -90 </td>\n",
       "        <td> 90 </td>\n",
       "        <td> -80 </td>\n",
       "        <td> 80 </td>\n",
       "        <td> -70 </td>\n",
       "        <td> 70 </td>\n",
       "        <td> -60 </td>\n",
       "        <td> 60 </td>\n",
       "        <td> -60 </td>\n",
       "        <td> 60 </td>\n",
       "        <td> -60 </td>\n",
       "        <td> 60 </td>\n",
       "        <td> -60 </td>\n",
       "        <td> 70 </td>\n",
       "        <td> -60 </td>\n",
       "        <td> 60 </td>\n",
       "        <td> -40 </td>\n",
       "        <td> 40 </td>\n",
       "        <td> -27 </td>\n",
       "        <td> 30 </td>\n",
       "        <td> -29 </td>\n",
       "        <td> 31 </td>\n",
       "        <td> -25 </td>\n",
       "        <td> 28 </td>\n",
       "        <td> -17 </td>\n",
       "        <td> 20 </td>\n",
       "        <td> -20 </td>\n",
       "        <td> 21 </td>\n",
       "        <td> -12 </td>\n",
       "        <td> 15 </td>\n",
       "        <td> -8 </td>\n",
       "        <td> 11 </td>\n",
       "        <td> -11 </td>\n",
       "        <td> 13 </td>\n",
       "        <td> -9 </td>\n",
       "        <td> 12 </td>\n",
       "        <td> -6 </td>\n",
       "        <td> 9 </td>\n",
       "        <td> -1.7 </td>\n",
       "        <td> 3.3 </td>\n",
       "        <td> -2.3 </td>\n",
       "        <td> 4.0 </td>\n",
       "        <td> -8 </td>\n",
       "        <td> 9 </td>\n",
       "        <td> -5 </td>\n",
       "        <td> 7 </td>\n",
       "        <td> -4 </td>\n",
       "        <td> 6 </td>\n",
       "        <td> -2.4 </td>\n",
       "        <td> 4.3 </td>\n",
       "        <td> -1.1 </td>\n",
       "        <td> 1.8 </td>\n",
       "        <td> -0.8 </td>\n",
       "        <td> 3.1 </td>\n",
       "        <td> -5 </td>\n",
       "        <td> 5 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th title=\"Validity of lower/upper minos error\"> Valid </th>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#c15ef7;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#c15ef7;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th title=\"Did scan hit limit of any parameter?\"> At Limit </th>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th title=\"Did scan hit function call limit?\"> Max FCN </th>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th title=\"New minimum found when doing scan?\"> New Min </th>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "    </tr>\n",
       "</table><table>\n",
       "    <tr>\n",
       "        <td></td>\n",
       "        <th> f_0 </th>\n",
       "        <th> f_1 </th>\n",
       "        <th> f_2 </th>\n",
       "        <th> f_3 </th>\n",
       "        <th> f_4 </th>\n",
       "        <th> f_5 </th>\n",
       "        <th> f_6 </th>\n",
       "        <th> f_7 </th>\n",
       "        <th> f_8 </th>\n",
       "        <th> f_9 </th>\n",
       "        <th> f_10 </th>\n",
       "        <th> f_11 </th>\n",
       "        <th> f_12 </th>\n",
       "        <th> f_13 </th>\n",
       "        <th> f_14 </th>\n",
       "        <th> f_15 </th>\n",
       "        <th> f_16 </th>\n",
       "        <th> f_17 </th>\n",
       "        <th> f_18 </th>\n",
       "        <th> f_19 </th>\n",
       "        <th> f_20 </th>\n",
       "        <th> f_21 </th>\n",
       "        <th> f_22 </th>\n",
       "        <th> f_23 </th>\n",
       "        <th> f_24 </th>\n",
       "        <th> f_25 </th>\n",
       "        <th> f_26 </th>\n",
       "        <th> f_27 </th>\n",
       "        <th> f_28 </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> f_0 </th>\n",
       "        <td> 3.45e+03 </td>\n",
       "        <td style=\"background-color:rgb(146,146,250);color:black\"> -4.37e+03 <strong>(-0.799)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,197,197);color:black\"> 1.69e+03 <strong>(0.354)</strong> </td>\n",
       "        <td style=\"background-color:rgb(228,228,250);color:black\"> -706 <strong>(-0.171)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,246,246);color:black\"> 89 <strong>(0.025)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -17.5 <strong>(-0.005)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -22.7 <strong>(-0.006)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 30.4 <strong>(0.008)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 38.7 <strong>(0.011)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 4.64 <strong>(0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 10.1 <strong>(0.006)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -8.84 <strong>(-0.005)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 7.42 <strong>(0.005)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 2.02 <strong>(0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.559 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0119 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.443 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.613 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.42 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.226 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0444 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0245 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0628 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0405 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0114 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.00958 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.00579 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.00405 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0157 <strong>(0.000)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> f_1 </th>\n",
       "        <td style=\"background-color:rgb(146,146,250);color:black\"> -4.37e+03 <strong>(-0.799)</strong> </td>\n",
       "        <td> 8.66e+03 </td>\n",
       "        <td style=\"background-color:rgb(164,164,250);color:black\"> -5e+03 <strong>(-0.660)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,213,213);color:black\"> 1.62e+03 <strong>(0.249)</strong> </td>\n",
       "        <td style=\"background-color:rgb(242,242,250);color:black\"> -358 <strong>(-0.063)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -7.37 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -17.1 <strong>(-0.003)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 4.19 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -95.2 <strong>(-0.016)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 40.9 <strong>(0.011)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -22.6 <strong>(-0.009)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 15.1 <strong>(0.005)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -2.73 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -2.52 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.205 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.83 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.4 <strong>(0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.384 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.23 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0287 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0072 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0161 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.146 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0563 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0362 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0157 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.00218 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.000338 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0116 <strong>(0.000)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> f_2 </th>\n",
       "        <td style=\"background-color:rgb(250,197,197);color:black\"> 1.69e+03 <strong>(0.354)</strong> </td>\n",
       "        <td style=\"background-color:rgb(164,164,250);color:black\"> -5e+03 <strong>(-0.660)</strong> </td>\n",
       "        <td> 6.64e+03 </td>\n",
       "        <td style=\"background-color:rgb(172,172,250);color:black\"> -3.42e+03 <strong>(-0.598)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,231,231);color:black\"> 637 <strong>(0.128)</strong> </td>\n",
       "        <td style=\"background-color:rgb(247,247,250);color:black\"> -97 <strong>(-0.020)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 8.07 <strong>(0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(247,247,250);color:black\"> -138 <strong>(-0.026)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 105 <strong>(0.021)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -34.6 <strong>(-0.010)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 2.96 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 6.16 <strong>(0.003)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -4.11 <strong>(-0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 2.53 <strong>(0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 3.04 <strong>(0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.821 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.471 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.634 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0878 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.156 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0301 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0399 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0334 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0159 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0106 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0148 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -5.63e-05 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.00186 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0133 <strong>(0.000)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> f_3 </th>\n",
       "        <td style=\"background-color:rgb(228,228,250);color:black\"> -706 <strong>(-0.171)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,213,213);color:black\"> 1.62e+03 <strong>(0.249)</strong> </td>\n",
       "        <td style=\"background-color:rgb(172,172,250);color:black\"> -3.42e+03 <strong>(-0.598)</strong> </td>\n",
       "        <td> 4.94e+03 </td>\n",
       "        <td style=\"background-color:rgb(186,186,250);color:black\"> -2.1e+03 <strong>(-0.491)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,243,243);color:black\"> 200 <strong>(0.047)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -52.2 <strong>(-0.012)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -23.3 <strong>(-0.005)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -58 <strong>(-0.013)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -34.1 <strong>(-0.012)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 9.88 <strong>(0.005)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -15.8 <strong>(-0.007)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.53 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.638 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -12.7 <strong>(-0.009)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 6.84 <strong>(0.007)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 5.41 <strong>(0.008)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 3.69 <strong>(0.004)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.365 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.263 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.00379 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0175 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.791 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0806 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0806 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.052 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0148 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.00646 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0284 <strong>(0.000)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> f_4 </th>\n",
       "        <td style=\"background-color:rgb(250,246,246);color:black\"> 89 <strong>(0.025)</strong> </td>\n",
       "        <td style=\"background-color:rgb(242,242,250);color:black\"> -358 <strong>(-0.063)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,231,231);color:black\"> 637 <strong>(0.128)</strong> </td>\n",
       "        <td style=\"background-color:rgb(186,186,250);color:black\"> -2.1e+03 <strong>(-0.491)</strong> </td>\n",
       "        <td> 3.7e+03 </td>\n",
       "        <td style=\"background-color:rgb(192,192,250);color:black\"> -1.64e+03 <strong>(-0.449)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,245,245);color:black\"> 132 <strong>(0.036)</strong> </td>\n",
       "        <td style=\"background-color:rgb(247,247,250);color:black\"> -102 <strong>(-0.026)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -40.6 <strong>(-0.011)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -29.6 <strong>(-0.012)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -3.57 <strong>(-0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -3.91 <strong>(-0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -7.05 <strong>(-0.004)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.08 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 5.13 <strong>(0.004)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -6.5 <strong>(-0.008)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -2.58 <strong>(-0.005)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 2.78 <strong>(0.004)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.99 <strong>(0.003)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.939 <strong>(0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.119 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0183 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.163 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.252 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0495 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.00117 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.00503 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.00215 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0716 <strong>(-0.000)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> f_5 </th>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -17.5 <strong>(-0.005)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -7.37 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(247,247,250);color:black\"> -97 <strong>(-0.020)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,243,243);color:black\"> 200 <strong>(0.047)</strong> </td>\n",
       "        <td style=\"background-color:rgb(192,192,250);color:black\"> -1.64e+03 <strong>(-0.449)</strong> </td>\n",
       "        <td> 3.62e+03 </td>\n",
       "        <td style=\"background-color:rgb(188,188,250);color:black\"> -1.74e+03 <strong>(-0.476)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,245,245);color:black\"> 131 <strong>(0.034)</strong> </td>\n",
       "        <td style=\"background-color:rgb(245,245,250);color:black\"> -153 <strong>(-0.041)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.229 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -2.76 <strong>(-0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -19.8 <strong>(-0.011)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 12.9 <strong>(0.008)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -9.64 <strong>(-0.009)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -5.81 <strong>(-0.005)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.415 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -4.44 <strong>(-0.008)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -2.52 <strong>(-0.003)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 4.71 <strong>(0.007)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.44 <strong>(0.003)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.179 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.106 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.163 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.156 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.168 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.125 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.016 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.00205 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.202 <strong>(-0.001)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> f_6 </th>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -22.7 <strong>(-0.006)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -17.1 <strong>(-0.003)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 8.07 <strong>(0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -52.2 <strong>(-0.012)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,245,245);color:black\"> 132 <strong>(0.036)</strong> </td>\n",
       "        <td style=\"background-color:rgb(188,188,250);color:black\"> -1.74e+03 <strong>(-0.476)</strong> </td>\n",
       "        <td> 3.7e+03 </td>\n",
       "        <td style=\"background-color:rgb(193,193,250);color:black\"> -1.73e+03 <strong>(-0.439)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 51.5 <strong>(0.014)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -47.8 <strong>(-0.019)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -9.36 <strong>(-0.005)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -23.4 <strong>(-0.013)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -7.12 <strong>(-0.004)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -6.27 <strong>(-0.006)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 28.4 <strong>(0.023)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -12.1 <strong>(-0.015)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -4.62 <strong>(-0.008)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -7.91 <strong>(-0.011)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 5.75 <strong>(0.009)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 1.91 <strong>(0.004)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.295 <strong>(0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.13 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.952 <strong>(0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.373 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.079 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0335 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0151 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.00712 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.195 <strong>(-0.001)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> f_7 </th>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 30.4 <strong>(0.008)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 4.19 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(247,247,250);color:black\"> -138 <strong>(-0.026)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -23.3 <strong>(-0.005)</strong> </td>\n",
       "        <td style=\"background-color:rgb(247,247,250);color:black\"> -102 <strong>(-0.026)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,245,245);color:black\"> 131 <strong>(0.034)</strong> </td>\n",
       "        <td style=\"background-color:rgb(193,193,250);color:black\"> -1.73e+03 <strong>(-0.439)</strong> </td>\n",
       "        <td> 4.21e+03 </td>\n",
       "        <td style=\"background-color:rgb(185,185,250);color:black\"> -2.01e+03 <strong>(-0.497)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,243,243);color:black\"> 131 <strong>(0.049)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -25 <strong>(-0.014)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -11.3 <strong>(-0.006)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.865 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -10.3 <strong>(-0.009)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -14.8 <strong>(-0.011)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 3.53 <strong>(0.004)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.98 <strong>(0.003)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.759 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -6.03 <strong>(-0.009)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.16 <strong>(0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 0.588 <strong>(0.004)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 0.961 <strong>(0.005)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 2.66 <strong>(0.005)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.133 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.52 <strong>(-0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.235 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0716 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0526 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.242 <strong>(0.001)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> f_8 </th>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 38.7 <strong>(0.011)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -95.2 <strong>(-0.016)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 105 <strong>(0.021)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -58 <strong>(-0.013)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -40.6 <strong>(-0.011)</strong> </td>\n",
       "        <td style=\"background-color:rgb(245,245,250);color:black\"> -153 <strong>(-0.041)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 51.5 <strong>(0.014)</strong> </td>\n",
       "        <td style=\"background-color:rgb(185,185,250);color:black\"> -2.01e+03 <strong>(-0.497)</strong> </td>\n",
       "        <td> 3.88e+03 </td>\n",
       "        <td style=\"background-color:rgb(197,197,250);color:black\"> -1.04e+03 <strong>(-0.405)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 40.5 <strong>(0.023)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 25.6 <strong>(0.014)</strong> </td>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -53.4 <strong>(-0.032)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 13.8 <strong>(0.012)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -13.5 <strong>(-0.011)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 7.21 <strong>(0.009)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 3.89 <strong>(0.007)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.445 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -4.6 <strong>(-0.007)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -2.6 <strong>(-0.006)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.162 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.241 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.264 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.07 <strong>(0.003)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.288 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0274 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0138 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0104 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.147 <strong>(0.000)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> f_9 </th>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 4.64 <strong>(0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 40.9 <strong>(0.011)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -34.6 <strong>(-0.010)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -34.1 <strong>(-0.012)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -29.6 <strong>(-0.012)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.229 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -47.8 <strong>(-0.019)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,243,243);color:black\"> 131 <strong>(0.049)</strong> </td>\n",
       "        <td style=\"background-color:rgb(197,197,250);color:black\"> -1.04e+03 <strong>(-0.405)</strong> </td>\n",
       "        <td> 1.71e+03 </td>\n",
       "        <td style=\"background-color:rgb(208,208,250);color:black\"> -384 <strong>(-0.327)</strong> </td>\n",
       "        <td style=\"background-color:rgb(240,240,250);color:black\"> -96.7 <strong>(-0.078)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 22.7 <strong>(0.021)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -6.99 <strong>(-0.009)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.7 <strong>(-0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -9.49 <strong>(-0.017)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -6.91 <strong>(-0.018)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.747 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.206 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.282 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -0.403 <strong>(-0.004)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.217 <strong>(-0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.04 <strong>(0.003)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.73 <strong>(0.003)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.325 <strong>(0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0552 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.011 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0165 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0369 <strong>(-0.000)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> f_10 </th>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 10.1 <strong>(0.006)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -22.6 <strong>(-0.009)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 2.96 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 9.88 <strong>(0.005)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -3.57 <strong>(-0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -2.76 <strong>(-0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -9.36 <strong>(-0.005)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -25 <strong>(-0.014)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 40.5 <strong>(0.023)</strong> </td>\n",
       "        <td style=\"background-color:rgb(208,208,250);color:black\"> -384 <strong>(-0.327)</strong> </td>\n",
       "        <td> 810 </td>\n",
       "        <td style=\"background-color:rgb(205,205,250);color:black\"> -296 <strong>(-0.344)</strong> </td>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -20.7 <strong>(-0.027)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 6.23 <strong>(0.012)</strong> </td>\n",
       "        <td style=\"background-color:rgb(244,244,250);color:black\"> -27 <strong>(-0.046)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 3.19 <strong>(0.008)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -1.43 <strong>(-0.005)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 2 <strong>(0.006)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.1 <strong>(-0.004)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -3.98 <strong>(-0.019)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -0.575 <strong>(-0.008)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -0.387 <strong>(-0.004)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.823 <strong>(-0.003)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 2.17 <strong>(0.014)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 0.822 <strong>(0.006)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0864 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0179 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0226 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.00112 <strong>(-0.000)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> f_11 </th>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -8.84 <strong>(-0.005)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 15.1 <strong>(0.005)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 6.16 <strong>(0.003)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -15.8 <strong>(-0.007)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -3.91 <strong>(-0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -19.8 <strong>(-0.011)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -23.4 <strong>(-0.013)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -11.3 <strong>(-0.006)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 25.6 <strong>(0.014)</strong> </td>\n",
       "        <td style=\"background-color:rgb(240,240,250);color:black\"> -96.7 <strong>(-0.078)</strong> </td>\n",
       "        <td style=\"background-color:rgb(205,205,250);color:black\"> -296 <strong>(-0.344)</strong> </td>\n",
       "        <td> 911 </td>\n",
       "        <td style=\"background-color:rgb(196,196,250);color:black\"> -335 <strong>(-0.418)</strong> </td>\n",
       "        <td style=\"background-color:rgb(245,245,250);color:black\"> -23.5 <strong>(-0.042)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 2.95 <strong>(0.005)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -2.87 <strong>(-0.007)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.758 <strong>(0.003)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.191 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(245,245,250);color:black\"> -11.3 <strong>(-0.035)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -1.56 <strong>(-0.007)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.188 <strong>(-0.003)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.111 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 0.921 <strong>(0.004)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 1.79 <strong>(0.011)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 1.75 <strong>(0.011)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0972 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0725 <strong>(-0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0721 <strong>(-0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.141 <strong>(0.001)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> f_12 </th>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 7.42 <strong>(0.005)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -2.73 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -4.11 <strong>(-0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.53 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -7.05 <strong>(-0.004)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 12.9 <strong>(0.008)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -7.12 <strong>(-0.004)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.865 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -53.4 <strong>(-0.032)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 22.7 <strong>(0.021)</strong> </td>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -20.7 <strong>(-0.027)</strong> </td>\n",
       "        <td style=\"background-color:rgb(196,196,250);color:black\"> -335 <strong>(-0.418)</strong> </td>\n",
       "        <td> 702 </td>\n",
       "        <td style=\"background-color:rgb(210,210,250);color:black\"> -150 <strong>(-0.306)</strong> </td>\n",
       "        <td style=\"background-color:rgb(233,233,250);color:black\"> -72.6 <strong>(-0.134)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,246,246);color:black\"> 9.52 <strong>(0.027)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -2.29 <strong>(-0.009)</strong> </td>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -8.92 <strong>(-0.028)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 3.02 <strong>(0.011)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 2.41 <strong>(0.012)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0877 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.00953 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(247,247,250);color:black\"> -5.15 <strong>(-0.022)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -1.66 <strong>(-0.011)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 0.847 <strong>(0.006)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 1.6 <strong>(0.018)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 0.335 <strong>(0.010)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 0.17 <strong>(0.006)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -0.662 <strong>(-0.005)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> f_13 </th>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 2.02 <strong>(0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -2.52 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 2.53 <strong>(0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.638 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.08 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -9.64 <strong>(-0.009)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -6.27 <strong>(-0.006)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -10.3 <strong>(-0.009)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 13.8 <strong>(0.012)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -6.99 <strong>(-0.009)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 6.23 <strong>(0.012)</strong> </td>\n",
       "        <td style=\"background-color:rgb(245,245,250);color:black\"> -23.5 <strong>(-0.042)</strong> </td>\n",
       "        <td style=\"background-color:rgb(210,210,250);color:black\"> -150 <strong>(-0.306)</strong> </td>\n",
       "        <td> 344 </td>\n",
       "        <td style=\"background-color:rgb(217,217,250);color:black\"> -94.8 <strong>(-0.250)</strong> </td>\n",
       "        <td style=\"background-color:rgb(244,244,250);color:black\"> -11.2 <strong>(-0.044)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -1.26 <strong>(-0.007)</strong> </td>\n",
       "        <td style=\"background-color:rgb(247,247,250);color:black\"> -5.12 <strong>(-0.023)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.395 <strong>(0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -0.756 <strong>(-0.005)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -0.171 <strong>(-0.004)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -0.298 <strong>(-0.005)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.412 <strong>(-0.003)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -1.31 <strong>(-0.013)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -0.994 <strong>(-0.011)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.112 <strong>(-0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 0.0908 <strong>(0.004)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 0.0968 <strong>(0.005)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.143 <strong>(0.002)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> f_14 </th>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.559 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.205 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 3.04 <strong>(0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -12.7 <strong>(-0.009)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 5.13 <strong>(0.004)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -5.81 <strong>(-0.005)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 28.4 <strong>(0.023)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -14.8 <strong>(-0.011)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -13.5 <strong>(-0.011)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.7 <strong>(-0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(244,244,250);color:black\"> -27 <strong>(-0.046)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 2.95 <strong>(0.005)</strong> </td>\n",
       "        <td style=\"background-color:rgb(233,233,250);color:black\"> -72.6 <strong>(-0.134)</strong> </td>\n",
       "        <td style=\"background-color:rgb(217,217,250);color:black\"> -94.8 <strong>(-0.250)</strong> </td>\n",
       "        <td> 417 </td>\n",
       "        <td style=\"background-color:rgb(201,201,250);color:black\"> -105 <strong>(-0.378)</strong> </td>\n",
       "        <td style=\"background-color:rgb(226,226,250);color:black\"> -35.2 <strong>(-0.186)</strong> </td>\n",
       "        <td style=\"background-color:rgb(242,242,250);color:black\"> -14.4 <strong>(-0.058)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,242,242);color:black\"> 12.1 <strong>(0.056)</strong> </td>\n",
       "        <td style=\"background-color:rgb(247,247,250);color:black\"> -3.61 <strong>(-0.024)</strong> </td>\n",
       "        <td style=\"background-color:rgb(247,247,250);color:black\"> -1.2 <strong>(-0.025)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -0.976 <strong>(-0.016)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,242,242);color:black\"> 9.63 <strong>(0.054)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -1.78 <strong>(-0.015)</strong> </td>\n",
       "        <td style=\"background-color:rgb(247,247,250);color:black\"> -2.21 <strong>(-0.021)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -1.24 <strong>(-0.018)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0634 <strong>(-0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0411 <strong>(0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 0.377 <strong>(0.004)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> f_15 </th>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0119 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.83 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.821 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 6.84 <strong>(0.007)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -6.5 <strong>(-0.008)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.415 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -12.1 <strong>(-0.015)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 3.53 <strong>(0.004)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 7.21 <strong>(0.009)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -9.49 <strong>(-0.017)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 3.19 <strong>(0.008)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -2.87 <strong>(-0.007)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,246,246);color:black\"> 9.52 <strong>(0.027)</strong> </td>\n",
       "        <td style=\"background-color:rgb(244,244,250);color:black\"> -11.2 <strong>(-0.044)</strong> </td>\n",
       "        <td style=\"background-color:rgb(201,201,250);color:black\"> -105 <strong>(-0.378)</strong> </td>\n",
       "        <td> 184 </td>\n",
       "        <td style=\"background-color:rgb(250,240,240);color:black\"> 7.99 <strong>(0.063)</strong> </td>\n",
       "        <td style=\"background-color:rgb(230,230,250);color:black\"> -25.8 <strong>(-0.156)</strong> </td>\n",
       "        <td style=\"background-color:rgb(232,232,250);color:black\"> -20 <strong>(-0.139)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.136 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 0.246 <strong>(0.008)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.137 <strong>(0.003)</strong> </td>\n",
       "        <td style=\"background-color:rgb(247,247,250);color:black\"> -2.35 <strong>(-0.020)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 1.04 <strong>(0.014)</strong> </td>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -2.13 <strong>(-0.031)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -0.327 <strong>(-0.007)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 0.0965 <strong>(0.006)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 0.0748 <strong>(0.005)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 0.927 <strong>(0.014)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> f_16 </th>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.443 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.4 <strong>(0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.471 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 5.41 <strong>(0.008)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -2.58 <strong>(-0.005)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -4.44 <strong>(-0.008)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -4.62 <strong>(-0.008)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.98 <strong>(0.003)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 3.89 <strong>(0.007)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -6.91 <strong>(-0.018)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -1.43 <strong>(-0.005)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.758 <strong>(0.003)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -2.29 <strong>(-0.009)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -1.26 <strong>(-0.007)</strong> </td>\n",
       "        <td style=\"background-color:rgb(226,226,250);color:black\"> -35.2 <strong>(-0.186)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,240,240);color:black\"> 7.99 <strong>(0.063)</strong> </td>\n",
       "        <td> 86.3 </td>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -3.51 <strong>(-0.031)</strong> </td>\n",
       "        <td style=\"background-color:rgb(221,221,250);color:black\"> -22.1 <strong>(-0.224)</strong> </td>\n",
       "        <td style=\"background-color:rgb(244,244,250);color:black\"> -3.12 <strong>(-0.045)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -0.191 <strong>(-0.009)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -0.258 <strong>(-0.009)</strong> </td>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -2.64 <strong>(-0.033)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.183 <strong>(-0.003)</strong> </td>\n",
       "        <td style=\"background-color:rgb(247,247,250);color:black\"> -1.12 <strong>(-0.024)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -0.398 <strong>(-0.013)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -0.0767 <strong>(-0.007)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0221 <strong>(-0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 0.675 <strong>(0.015)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> f_17 </th>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.613 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.384 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.634 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 3.69 <strong>(0.004)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 2.78 <strong>(0.004)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -2.52 <strong>(-0.003)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -7.91 <strong>(-0.011)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.759 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.445 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.747 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 2 <strong>(0.006)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.191 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -8.92 <strong>(-0.028)</strong> </td>\n",
       "        <td style=\"background-color:rgb(247,247,250);color:black\"> -5.12 <strong>(-0.023)</strong> </td>\n",
       "        <td style=\"background-color:rgb(242,242,250);color:black\"> -14.4 <strong>(-0.058)</strong> </td>\n",
       "        <td style=\"background-color:rgb(230,230,250);color:black\"> -25.8 <strong>(-0.156)</strong> </td>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -3.51 <strong>(-0.031)</strong> </td>\n",
       "        <td> 148 </td>\n",
       "        <td style=\"background-color:rgb(218,218,250);color:black\"> -31.4 <strong>(-0.243)</strong> </td>\n",
       "        <td style=\"background-color:rgb(217,217,250);color:black\"> -23.4 <strong>(-0.256)</strong> </td>\n",
       "        <td style=\"background-color:rgb(238,238,250);color:black\"> -2.78 <strong>(-0.096)</strong> </td>\n",
       "        <td style=\"background-color:rgb(247,247,250);color:black\"> -1 <strong>(-0.027)</strong> </td>\n",
       "        <td style=\"background-color:rgb(244,244,250);color:black\"> -4.74 <strong>(-0.045)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 1.17 <strong>(0.017)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 0.218 <strong>(0.004)</strong> </td>\n",
       "        <td style=\"background-color:rgb(245,245,250);color:black\"> -1.71 <strong>(-0.042)</strong> </td>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -0.489 <strong>(-0.032)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -0.219 <strong>(-0.016)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,245,245);color:black\"> 1.84 <strong>(0.030)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> f_18 </th>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.42 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.23 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0878 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.365 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.99 <strong>(0.003)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 4.71 <strong>(0.007)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 5.75 <strong>(0.009)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -6.03 <strong>(-0.009)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -4.6 <strong>(-0.007)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.206 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.1 <strong>(-0.004)</strong> </td>\n",
       "        <td style=\"background-color:rgb(245,245,250);color:black\"> -11.3 <strong>(-0.035)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 3.02 <strong>(0.011)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.395 <strong>(0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,242,242);color:black\"> 12.1 <strong>(0.056)</strong> </td>\n",
       "        <td style=\"background-color:rgb(232,232,250);color:black\"> -20 <strong>(-0.139)</strong> </td>\n",
       "        <td style=\"background-color:rgb(221,221,250);color:black\"> -22.1 <strong>(-0.224)</strong> </td>\n",
       "        <td style=\"background-color:rgb(218,218,250);color:black\"> -31.4 <strong>(-0.243)</strong> </td>\n",
       "        <td> 113 </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -0.48 <strong>(-0.006)</strong> </td>\n",
       "        <td style=\"background-color:rgb(236,236,250);color:black\"> -2.66 <strong>(-0.105)</strong> </td>\n",
       "        <td style=\"background-color:rgb(238,238,250);color:black\"> -3.05 <strong>(-0.093)</strong> </td>\n",
       "        <td style=\"background-color:rgb(233,233,250);color:black\"> -12.3 <strong>(-0.133)</strong> </td>\n",
       "        <td style=\"background-color:rgb(243,243,250);color:black\"> -3.22 <strong>(-0.054)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,242,242);color:black\"> 2.87 <strong>(0.053)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,243,243);color:black\"> 1.64 <strong>(0.046)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,246,246);color:black\"> 0.333 <strong>(0.025)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 0.182 <strong>(0.015)</strong> </td>\n",
       "        <td style=\"background-color:rgb(241,241,250);color:black\"> -3.81 <strong>(-0.072)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> f_19 </th>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.226 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0287 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.156 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.263 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.939 <strong>(0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.44 <strong>(0.003)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 1.91 <strong>(0.004)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.16 <strong>(0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -2.6 <strong>(-0.006)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.282 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -3.98 <strong>(-0.019)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -1.56 <strong>(-0.007)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 2.41 <strong>(0.012)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -0.756 <strong>(-0.005)</strong> </td>\n",
       "        <td style=\"background-color:rgb(247,247,250);color:black\"> -3.61 <strong>(-0.024)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.136 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(244,244,250);color:black\"> -3.12 <strong>(-0.045)</strong> </td>\n",
       "        <td style=\"background-color:rgb(217,217,250);color:black\"> -23.4 <strong>(-0.256)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -0.48 <strong>(-0.006)</strong> </td>\n",
       "        <td> 56.3 </td>\n",
       "        <td style=\"background-color:rgb(250,196,196);color:black\"> 6.46 <strong>(0.360)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -0.22 <strong>(-0.010)</strong> </td>\n",
       "        <td style=\"background-color:rgb(222,222,250);color:black\"> -13.9 <strong>(-0.214)</strong> </td>\n",
       "        <td style=\"background-color:rgb(227,227,250);color:black\"> -7.62 <strong>(-0.180)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.111 <strong>(-0.003)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,240,240);color:black\"> 1.68 <strong>(0.067)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,243,243);color:black\"> 0.466 <strong>(0.050)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,245,245);color:black\"> 0.302 <strong>(0.035)</strong> </td>\n",
       "        <td style=\"background-color:rgb(245,245,250);color:black\"> -1.39 <strong>(-0.037)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> f_20 </th>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0444 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0072 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0301 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.00379 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.119 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.179 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.295 <strong>(0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 0.588 <strong>(0.004)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.162 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -0.403 <strong>(-0.004)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -0.575 <strong>(-0.008)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.188 <strong>(-0.003)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0877 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -0.171 <strong>(-0.004)</strong> </td>\n",
       "        <td style=\"background-color:rgb(247,247,250);color:black\"> -1.2 <strong>(-0.025)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 0.246 <strong>(0.008)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -0.191 <strong>(-0.009)</strong> </td>\n",
       "        <td style=\"background-color:rgb(238,238,250);color:black\"> -2.78 <strong>(-0.096)</strong> </td>\n",
       "        <td style=\"background-color:rgb(236,236,250);color:black\"> -2.66 <strong>(-0.105)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,196,196);color:black\"> 6.46 <strong>(0.360)</strong> </td>\n",
       "        <td> 5.72 </td>\n",
       "        <td style=\"background-color:rgb(250,194,194);color:black\"> 2.75 <strong>(0.373)</strong> </td>\n",
       "        <td style=\"background-color:rgb(229,229,250);color:black\"> -3.34 <strong>(-0.161)</strong> </td>\n",
       "        <td style=\"background-color:rgb(234,234,250);color:black\"> -1.61 <strong>(-0.120)</strong> </td>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -0.389 <strong>(-0.032)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 0.168 <strong>(0.021)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 0.0467 <strong>(0.016)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 0.0318 <strong>(0.012)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -0.093 <strong>(-0.008)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> f_21 </th>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0245 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0161 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0399 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0175 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0183 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.106 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.13 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 0.961 <strong>(0.005)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.241 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.217 <strong>(-0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -0.387 <strong>(-0.004)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.111 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.00953 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -0.298 <strong>(-0.005)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -0.976 <strong>(-0.016)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.137 <strong>(0.003)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -0.258 <strong>(-0.009)</strong> </td>\n",
       "        <td style=\"background-color:rgb(247,247,250);color:black\"> -1 <strong>(-0.027)</strong> </td>\n",
       "        <td style=\"background-color:rgb(238,238,250);color:black\"> -3.05 <strong>(-0.093)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -0.22 <strong>(-0.010)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,194,194);color:black\"> 2.75 <strong>(0.373)</strong> </td>\n",
       "        <td> 9.46 </td>\n",
       "        <td style=\"background-color:rgb(250,241,241);color:black\"> 1.62 <strong>(0.061)</strong> </td>\n",
       "        <td style=\"background-color:rgb(231,231,250);color:black\"> -2.55 <strong>(-0.147)</strong> </td>\n",
       "        <td style=\"background-color:rgb(237,237,250);color:black\"> -1.51 <strong>(-0.097)</strong> </td>\n",
       "        <td style=\"background-color:rgb(245,245,250);color:black\"> -0.422 <strong>(-0.041)</strong> </td>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -0.105 <strong>(-0.027)</strong> </td>\n",
       "        <td style=\"background-color:rgb(247,247,250);color:black\"> -0.0684 <strong>(-0.019)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 0.269 <strong>(0.018)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> f_22 </th>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0628 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.146 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0334 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.791 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.163 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.163 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.952 <strong>(0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 2.66 <strong>(0.005)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.264 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.04 <strong>(0.003)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.823 <strong>(-0.003)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 0.921 <strong>(0.004)</strong> </td>\n",
       "        <td style=\"background-color:rgb(247,247,250);color:black\"> -5.15 <strong>(-0.022)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.412 <strong>(-0.003)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,242,242);color:black\"> 9.63 <strong>(0.054)</strong> </td>\n",
       "        <td style=\"background-color:rgb(247,247,250);color:black\"> -2.35 <strong>(-0.020)</strong> </td>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -2.64 <strong>(-0.033)</strong> </td>\n",
       "        <td style=\"background-color:rgb(244,244,250);color:black\"> -4.74 <strong>(-0.045)</strong> </td>\n",
       "        <td style=\"background-color:rgb(233,233,250);color:black\"> -12.3 <strong>(-0.133)</strong> </td>\n",
       "        <td style=\"background-color:rgb(222,222,250);color:black\"> -13.9 <strong>(-0.214)</strong> </td>\n",
       "        <td style=\"background-color:rgb(229,229,250);color:black\"> -3.34 <strong>(-0.161)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,241,241);color:black\"> 1.62 <strong>(0.061)</strong> </td>\n",
       "        <td> 75.3 </td>\n",
       "        <td style=\"background-color:rgb(236,236,250);color:black\"> -5.41 <strong>(-0.111)</strong> </td>\n",
       "        <td style=\"background-color:rgb(208,208,250);color:black\"> -14.2 <strong>(-0.324)</strong> </td>\n",
       "        <td style=\"background-color:rgb(219,219,250);color:black\"> -6.92 <strong>(-0.238)</strong> </td>\n",
       "        <td style=\"background-color:rgb(231,231,250);color:black\"> -1.59 <strong>(-0.147)</strong> </td>\n",
       "        <td style=\"background-color:rgb(236,236,250);color:black\"> -1.04 <strong>(-0.105)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,237,237);color:black\"> 3.73 <strong>(0.086)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> f_23 </th>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0405 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0563 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0159 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0806 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.252 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.156 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.373 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.133 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.07 <strong>(0.003)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.73 <strong>(0.003)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 2.17 <strong>(0.014)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 1.79 <strong>(0.011)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -1.66 <strong>(-0.011)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -1.31 <strong>(-0.013)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -1.78 <strong>(-0.015)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 1.04 <strong>(0.014)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.183 <strong>(-0.003)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 1.17 <strong>(0.017)</strong> </td>\n",
       "        <td style=\"background-color:rgb(243,243,250);color:black\"> -3.22 <strong>(-0.054)</strong> </td>\n",
       "        <td style=\"background-color:rgb(227,227,250);color:black\"> -7.62 <strong>(-0.180)</strong> </td>\n",
       "        <td style=\"background-color:rgb(234,234,250);color:black\"> -1.61 <strong>(-0.120)</strong> </td>\n",
       "        <td style=\"background-color:rgb(231,231,250);color:black\"> -2.55 <strong>(-0.147)</strong> </td>\n",
       "        <td style=\"background-color:rgb(236,236,250);color:black\"> -5.41 <strong>(-0.111)</strong> </td>\n",
       "        <td> 31.7 </td>\n",
       "        <td style=\"background-color:rgb(250,244,244);color:black\"> 1.22 <strong>(0.043)</strong> </td>\n",
       "        <td style=\"background-color:rgb(233,233,250);color:black\"> -2.54 <strong>(-0.135)</strong> </td>\n",
       "        <td style=\"background-color:rgb(237,237,250);color:black\"> -0.683 <strong>(-0.097)</strong> </td>\n",
       "        <td style=\"background-color:rgb(241,241,250);color:black\"> -0.431 <strong>(-0.067)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,246,246);color:black\"> 0.753 <strong>(0.027)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> f_24 </th>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0114 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0362 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0106 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0806 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0495 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.168 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.079 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.52 <strong>(-0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.288 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.325 <strong>(0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 0.822 <strong>(0.006)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 1.75 <strong>(0.011)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 0.847 <strong>(0.006)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -0.994 <strong>(-0.011)</strong> </td>\n",
       "        <td style=\"background-color:rgb(247,247,250);color:black\"> -2.21 <strong>(-0.021)</strong> </td>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -2.13 <strong>(-0.031)</strong> </td>\n",
       "        <td style=\"background-color:rgb(247,247,250);color:black\"> -1.12 <strong>(-0.024)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 0.218 <strong>(0.004)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,242,242);color:black\"> 2.87 <strong>(0.053)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.111 <strong>(-0.003)</strong> </td>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -0.389 <strong>(-0.032)</strong> </td>\n",
       "        <td style=\"background-color:rgb(237,237,250);color:black\"> -1.51 <strong>(-0.097)</strong> </td>\n",
       "        <td style=\"background-color:rgb(208,208,250);color:black\"> -14.2 <strong>(-0.324)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,244,244);color:black\"> 1.22 <strong>(0.043)</strong> </td>\n",
       "        <td> 25.8 </td>\n",
       "        <td style=\"background-color:rgb(250,230,230);color:black\"> 2.3 <strong>(0.136)</strong> </td>\n",
       "        <td style=\"background-color:rgb(238,238,250);color:black\"> -0.581 <strong>(-0.092)</strong> </td>\n",
       "        <td style=\"background-color:rgb(236,236,250);color:black\"> -0.602 <strong>(-0.104)</strong> </td>\n",
       "        <td style=\"background-color:rgb(234,234,250);color:black\"> -3.08 <strong>(-0.122)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> f_25 </th>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.00958 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0157 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0148 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.052 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.00117 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.125 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0335 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.235 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0274 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0552 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0864 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0972 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 1.6 <strong>(0.018)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.112 <strong>(-0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -1.24 <strong>(-0.018)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -0.327 <strong>(-0.007)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -0.398 <strong>(-0.013)</strong> </td>\n",
       "        <td style=\"background-color:rgb(245,245,250);color:black\"> -1.71 <strong>(-0.042)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,243,243);color:black\"> 1.64 <strong>(0.046)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,240,240);color:black\"> 1.68 <strong>(0.067)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 0.168 <strong>(0.021)</strong> </td>\n",
       "        <td style=\"background-color:rgb(245,245,250);color:black\"> -0.422 <strong>(-0.041)</strong> </td>\n",
       "        <td style=\"background-color:rgb(219,219,250);color:black\"> -6.92 <strong>(-0.238)</strong> </td>\n",
       "        <td style=\"background-color:rgb(233,233,250);color:black\"> -2.54 <strong>(-0.135)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,230,230);color:black\"> 2.3 <strong>(0.136)</strong> </td>\n",
       "        <td> 11.2 </td>\n",
       "        <td style=\"background-color:rgb(250,188,188);color:black\"> 1.73 <strong>(0.414)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,229,229);color:black\"> 0.529 <strong>(0.139)</strong> </td>\n",
       "        <td style=\"background-color:rgb(220,220,250);color:black\"> -3.8 <strong>(-0.228)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> f_26 </th>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.00579 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.00218 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -5.63e-05 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0148 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.00503 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.016 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0151 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0716 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0138 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.011 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0179 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0725 <strong>(-0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 0.335 <strong>(0.010)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 0.0908 <strong>(0.004)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0634 <strong>(-0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 0.0965 <strong>(0.006)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -0.0767 <strong>(-0.007)</strong> </td>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -0.489 <strong>(-0.032)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,246,246);color:black\"> 0.333 <strong>(0.025)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,243,243);color:black\"> 0.466 <strong>(0.050)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 0.0467 <strong>(0.016)</strong> </td>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -0.105 <strong>(-0.027)</strong> </td>\n",
       "        <td style=\"background-color:rgb(231,231,250);color:black\"> -1.59 <strong>(-0.147)</strong> </td>\n",
       "        <td style=\"background-color:rgb(237,237,250);color:black\"> -0.683 <strong>(-0.097)</strong> </td>\n",
       "        <td style=\"background-color:rgb(238,238,250);color:black\"> -0.581 <strong>(-0.092)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,188,188);color:black\"> 1.73 <strong>(0.414)</strong> </td>\n",
       "        <td> 1.56 </td>\n",
       "        <td style=\"background-color:rgb(250,135,135);color:black\"> 1.09 <strong>(0.764)</strong> </td>\n",
       "        <td style=\"background-color:rgb(226,226,250);color:black\"> -1.13 <strong>(-0.182)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> f_27 </th>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.00405 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.000338 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.00186 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.00646 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.00215 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.00205 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.00712 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0526 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0104 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0165 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0226 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0721 <strong>(-0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 0.17 <strong>(0.006)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 0.0968 <strong>(0.005)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0411 <strong>(0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 0.0748 <strong>(0.005)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0221 <strong>(-0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -0.219 <strong>(-0.016)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 0.182 <strong>(0.015)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,245,245);color:black\"> 0.302 <strong>(0.035)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 0.0318 <strong>(0.012)</strong> </td>\n",
       "        <td style=\"background-color:rgb(247,247,250);color:black\"> -0.0684 <strong>(-0.019)</strong> </td>\n",
       "        <td style=\"background-color:rgb(236,236,250);color:black\"> -1.04 <strong>(-0.105)</strong> </td>\n",
       "        <td style=\"background-color:rgb(241,241,250);color:black\"> -0.431 <strong>(-0.067)</strong> </td>\n",
       "        <td style=\"background-color:rgb(236,236,250);color:black\"> -0.602 <strong>(-0.104)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,229,229);color:black\"> 0.529 <strong>(0.139)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,135,135);color:black\"> 1.09 <strong>(0.764)</strong> </td>\n",
       "        <td> 1.3 </td>\n",
       "        <td style=\"background-color:rgb(231,231,250);color:black\"> -0.824 <strong>(-0.145)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> f_28 </th>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0157 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0116 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0133 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0284 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0716 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.202 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.195 <strong>(-0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.242 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.147 <strong>(0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0369 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.00112 <strong>(-0.000)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.141 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -0.662 <strong>(-0.005)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.143 <strong>(0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 0.377 <strong>(0.004)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 0.927 <strong>(0.014)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 0.675 <strong>(0.015)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,245,245);color:black\"> 1.84 <strong>(0.030)</strong> </td>\n",
       "        <td style=\"background-color:rgb(241,241,250);color:black\"> -3.81 <strong>(-0.072)</strong> </td>\n",
       "        <td style=\"background-color:rgb(245,245,250);color:black\"> -1.39 <strong>(-0.037)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -0.093 <strong>(-0.008)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 0.269 <strong>(0.018)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,237,237);color:black\"> 3.73 <strong>(0.086)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,246,246);color:black\"> 0.753 <strong>(0.027)</strong> </td>\n",
       "        <td style=\"background-color:rgb(234,234,250);color:black\"> -3.08 <strong>(-0.122)</strong> </td>\n",
       "        <td style=\"background-color:rgb(220,220,250);color:black\"> -3.8 <strong>(-0.228)</strong> </td>\n",
       "        <td style=\"background-color:rgb(226,226,250);color:black\"> -1.13 <strong>(-0.182)</strong> </td>\n",
       "        <td style=\"background-color:rgb(231,231,250);color:black\"> -0.824 <strong>(-0.145)</strong> </td>\n",
       "        <td> 24.8 </td>\n",
       "    </tr>\n",
       "</table>"
      ],
      "text/plain": [
       "┌─────────────────────────────────────────────────────────────────────────┐\n",
       "│                                Migrad                                   │\n",
       "├──────────────────────────────────┬──────────────────────────────────────┤\n",
       "│ FCN = -1.789e+04                 │             Nfcn = 29138             │\n",
       "│ EDM = 0.000175 (Goal: 0.0001)    │                                      │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│          Valid Minimum           │        No Parameters at limit        │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│ Below EDM threshold (goal x 10)  │           Below call limit           │\n",
       "├───────────────┬──────────────────┼───────────┬─────────────┬────────────┤\n",
       "│  Covariance   │     Hesse ok     │ Accurate  │  Pos. def.  │ Not forced │\n",
       "└───────────────┴──────────────────┴───────────┴─────────────┴────────────┘\n",
       "┌───┬──────┬───────────┬───────────┬────────────┬────────────┬─────────┬─────────┬───────┐\n",
       "│   │ Name │   Value   │ Hesse Err │ Minos Err- │ Minos Err+ │ Limit-  │ Limit+  │ Fixed │\n",
       "├───┼──────┼───────────┼───────────┼────────────┼────────────┼─────────┼─────────┼───────┤\n",
       "│ 0 │ f_0  │    200    │    60     │    -60     │     60     │    0    │         │       │\n",
       "│ 1 │ f_1  │    470    │    90     │    -90     │     90     │    0    │         │       │\n",
       "│ 2 │ f_2  │    400    │    80     │    -80     │     80     │    0    │         │       │\n",
       "│ 3 │ f_3  │    360    │    70     │    -70     │     70     │    0    │         │       │\n",
       "│ 4 │ f_4  │    280    │    60     │    -60     │     60     │    0    │         │       │\n",
       "│ 5 │ f_5  │    260    │    60     │    -60     │     60     │    0    │         │       │\n",
       "│ 6 │ f_6  │    240    │    60     │    -60     │     60     │    0    │         │       │\n",
       "│ 7 │ f_7  │    440    │    60     │    -60     │     70     │    0    │         │       │\n",
       "│ 8 │ f_8  │    700    │    60     │    -60     │     60     │    0    │         │       │\n",
       "│ 9 │ f_9  │    210    │    40     │    -40     │     40     │    0    │         │       │\n",
       "│ 10│ f_10 │    89     │    28     │    -27     │     30     │    0    │         │       │\n",
       "│ 11│ f_11 │    117    │    30     │    -29     │     31     │    0    │         │       │\n",
       "│ 12│ f_12 │    91     │    26     │    -25     │     28     │    0    │         │       │\n",
       "│ 13│ f_13 │    44     │    19     │    -17     │     20     │    0    │         │       │\n",
       "│ 14│ f_14 │    71     │    20     │    -20     │     21     │    0    │         │       │\n",
       "│ 15│ f_15 │    28     │    14     │    -12     │     15     │    0    │         │       │\n",
       "│ 16│ f_16 │    15     │     9     │     -8     │     11     │    0    │         │       │\n",
       "│ 17│ f_17 │    27     │    12     │    -11     │     13     │    0    │         │       │\n",
       "│ 18│ f_18 │    23     │    11     │     -9     │     12     │    0    │         │       │\n",
       "│ 19│ f_19 │     9     │     7     │     -6     │     9      │    0    │         │       │\n",
       "│ 20│ f_20 │    2.7    │    2.3    │    -1.7    │    3.3     │    0    │         │       │\n",
       "│ 21│ f_21 │    3.9    │    3.0    │    -2.3    │    4.0     │    0    │         │       │\n",
       "│ 22│ f_22 │    20     │     9     │     -8     │     9      │    0    │         │       │\n",
       "│ 23│ f_23 │    12     │     6     │     -5     │     7      │    0    │         │       │\n",
       "│ 24│ f_24 │     9     │     5     │     -4     │     6      │    0    │         │       │\n",
       "│ 25│ f_25 │    3.4    │    3.2    │    -2.4    │    4.3     │    0    │         │       │\n",
       "│ 26│ f_26 │    0.9    │    1.1    │    -1.1    │    1.8     │    0    │         │       │\n",
       "│ 27│ f_27 │    0.4    │    0.8    │    -0.8    │    3.1     │    0    │         │       │\n",
       "│ 28│ f_28 │    19     │     5     │     -5     │     5      │    0    │         │       │\n",
       "└───┴──────┴───────────┴───────────┴────────────┴────────────┴─────────┴─────────┴───────┘\n",
       "┌──────────┬───────────────────────┬───────────────────────┬───────────────────────┬───────────────────────┬───────────────────────┬───────────────────────┬───────────────────────┬───────────────────────┬───────────────────────┬───────────────────────┬───────────────────────┬───────────────────────┬───────────────────────┬───────────────────────┬───────────────────────┬───────────────────────┬───────────────────────┬───────────────────────┬───────────────────────┬───────────────────────┬───────────────────────┬───────────────────────┬───────────────────────┬───────────────────────┬───────────────────────┬───────────────────────┬───────────────────────┬───────────────────────┬───────────────────────┐\n",
       "│          │          f_0          │          f_1          │          f_2          │          f_3          │          f_4          │          f_5          │          f_6          │          f_7          │          f_8          │          f_9          │         f_10          │         f_11          │         f_12          │         f_13          │         f_14          │         f_15          │         f_16          │         f_17          │         f_18          │         f_19          │         f_20          │         f_21          │         f_22          │         f_23          │         f_24          │         f_25          │         f_26          │         f_27          │         f_28          │\n",
       "├──────────┼───────────┬───────────┼───────────┬───────────┼───────────┬───────────┼───────────┬───────────┼───────────┬───────────┼───────────┬───────────┼───────────┬───────────┼───────────┬───────────┼───────────┬───────────┼───────────┬───────────┼───────────┬───────────┼───────────┬───────────┼───────────┬───────────┼───────────┬───────────┼───────────┬───────────┼───────────┬───────────┼───────────┬───────────┼───────────┬───────────┼───────────┬───────────┼───────────┬───────────┼───────────┬───────────┼───────────┬───────────┼───────────┬───────────┼───────────┬───────────┼───────────┬───────────┼───────────┬───────────┼───────────┬───────────┼───────────┬───────────┼───────────┬───────────┤\n",
       "│  Error   │    -60    │    60     │    -90    │    90     │    -80    │    80     │    -70    │    70     │    -60    │    60     │    -60    │    60     │    -60    │    60     │    -60    │    70     │    -60    │    60     │    -40    │    40     │    -27    │    30     │    -29    │    31     │    -25    │    28     │    -17    │    20     │    -20    │    21     │    -12    │    15     │    -8     │    11     │    -11    │    13     │    -9     │    12     │    -6     │     9     │   -1.7    │    3.3    │   -2.3    │    4.0    │    -8     │     9     │    -5     │     7     │    -4     │     6     │   -2.4    │    4.3    │   -1.1    │    1.8    │   -0.8    │    3.1    │    -5     │     5     │\n",
       "│  Valid   │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   True    │   False   │   True    │   False   │   True    │   True    │   True    │\n",
       "│ At Limit │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │\n",
       "│ Max FCN  │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │\n",
       "│ New Min  │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │   False   │\n",
       "└──────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┴───────────┘\n",
       "┌──────┬───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────┐\n",
       "│      │       f_0       f_1       f_2       f_3       f_4       f_5       f_6       f_7       f_8       f_9      f_10      f_11      f_12      f_13      f_14      f_15      f_16      f_17      f_18      f_19      f_20      f_21      f_22      f_23      f_24      f_25      f_26      f_27      f_28 │\n",
       "├──────┼───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────┤\n",
       "│  f_0 │  3.45e+03 -4.37e+03  1.69e+03      -706        89     -17.5     -22.7      30.4      38.7      4.64      10.1     -8.84      7.42      2.02     0.559   -0.0119    -0.443    -0.613     -0.42    -0.226   -0.0444   -0.0245    0.0628    0.0405   -0.0114   0.00958   0.00579   0.00405    0.0157 │\n",
       "│  f_1 │ -4.37e+03  8.66e+03    -5e+03  1.62e+03      -358     -7.37     -17.1      4.19     -95.2      40.9     -22.6      15.1     -2.73     -2.52     0.205      1.83       1.4     0.384     -0.23    0.0287   -0.0072   -0.0161    -0.146   -0.0563   -0.0362   -0.0157  -0.00218 -0.000338    0.0116 │\n",
       "│  f_2 │  1.69e+03    -5e+03  6.64e+03 -3.42e+03       637       -97      8.07      -138       105     -34.6      2.96      6.16     -4.11      2.53      3.04    -0.821    -0.471     0.634   -0.0878    -0.156   -0.0301   -0.0399   -0.0334   -0.0159   -0.0106   -0.0148 -5.63e-05   0.00186    0.0133 │\n",
       "│  f_3 │      -706  1.62e+03 -3.42e+03  4.94e+03  -2.1e+03       200     -52.2     -23.3       -58     -34.1      9.88     -15.8     -1.53    -0.638     -12.7      6.84      5.41      3.69    -0.365    -0.263  -0.00379   -0.0175    -0.791   -0.0806   -0.0806    -0.052   -0.0148  -0.00646    0.0284 │\n",
       "│  f_4 │        89      -358       637  -2.1e+03   3.7e+03 -1.64e+03       132      -102     -40.6     -29.6     -3.57     -3.91     -7.05      1.08      5.13      -6.5     -2.58      2.78      1.99     0.939     0.119    0.0183    -0.163    -0.252    0.0495   0.00117  -0.00503  -0.00215   -0.0716 │\n",
       "│  f_5 │     -17.5     -7.37       -97       200 -1.64e+03  3.62e+03 -1.74e+03       131      -153    -0.229     -2.76     -19.8      12.9     -9.64     -5.81     0.415     -4.44     -2.52      4.71      1.44     0.179     0.106    -0.163    -0.156     0.168     0.125     0.016   0.00205    -0.202 │\n",
       "│  f_6 │     -22.7     -17.1      8.07     -52.2       132 -1.74e+03   3.7e+03 -1.73e+03      51.5     -47.8     -9.36     -23.4     -7.12     -6.27      28.4     -12.1     -4.62     -7.91      5.75      1.91     0.295      0.13     0.952    -0.373    -0.079    0.0335    0.0151   0.00712    -0.195 │\n",
       "│  f_7 │      30.4      4.19      -138     -23.3      -102       131 -1.73e+03  4.21e+03 -2.01e+03       131       -25     -11.3     0.865     -10.3     -14.8      3.53      1.98     0.759     -6.03      1.16     0.588     0.961      2.66    -0.133     -0.52    -0.235   -0.0716   -0.0526     0.242 │\n",
       "│  f_8 │      38.7     -95.2       105       -58     -40.6      -153      51.5 -2.01e+03  3.88e+03 -1.04e+03      40.5      25.6     -53.4      13.8     -13.5      7.21      3.89    -0.445      -4.6      -2.6    -0.162    -0.241    -0.264      1.07     0.288   -0.0274   -0.0138   -0.0104     0.147 │\n",
       "│  f_9 │      4.64      40.9     -34.6     -34.1     -29.6    -0.229     -47.8       131 -1.04e+03  1.71e+03      -384     -96.7      22.7     -6.99      -1.7     -9.49     -6.91     0.747     0.206    -0.282    -0.403    -0.217      1.04      0.73     0.325    0.0552    -0.011   -0.0165   -0.0369 │\n",
       "│ f_10 │      10.1     -22.6      2.96      9.88     -3.57     -2.76     -9.36       -25      40.5      -384       810      -296     -20.7      6.23       -27      3.19     -1.43         2      -1.1     -3.98    -0.575    -0.387    -0.823      2.17     0.822    0.0864   -0.0179   -0.0226  -0.00112 │\n",
       "│ f_11 │     -8.84      15.1      6.16     -15.8     -3.91     -19.8     -23.4     -11.3      25.6     -96.7      -296       911      -335     -23.5      2.95     -2.87     0.758     0.191     -11.3     -1.56    -0.188    -0.111     0.921      1.79      1.75    0.0972   -0.0725   -0.0721     0.141 │\n",
       "│ f_12 │      7.42     -2.73     -4.11     -1.53     -7.05      12.9     -7.12     0.865     -53.4      22.7     -20.7      -335       702      -150     -72.6      9.52     -2.29     -8.92      3.02      2.41   -0.0877   0.00953     -5.15     -1.66     0.847       1.6     0.335      0.17    -0.662 │\n",
       "│ f_13 │      2.02     -2.52      2.53    -0.638      1.08     -9.64     -6.27     -10.3      13.8     -6.99      6.23     -23.5      -150       344     -94.8     -11.2     -1.26     -5.12     0.395    -0.756    -0.171    -0.298    -0.412     -1.31    -0.994    -0.112    0.0908    0.0968     0.143 │\n",
       "│ f_14 │     0.559     0.205      3.04     -12.7      5.13     -5.81      28.4     -14.8     -13.5      -1.7       -27      2.95     -72.6     -94.8       417      -105     -35.2     -14.4      12.1     -3.61      -1.2    -0.976      9.63     -1.78     -2.21     -1.24   -0.0634    0.0411     0.377 │\n",
       "│ f_15 │   -0.0119      1.83    -0.821      6.84      -6.5     0.415     -12.1      3.53      7.21     -9.49      3.19     -2.87      9.52     -11.2      -105       184      7.99     -25.8       -20    -0.136     0.246     0.137     -2.35      1.04     -2.13    -0.327    0.0965    0.0748     0.927 │\n",
       "│ f_16 │    -0.443       1.4    -0.471      5.41     -2.58     -4.44     -4.62      1.98      3.89     -6.91     -1.43     0.758     -2.29     -1.26     -35.2      7.99      86.3     -3.51     -22.1     -3.12    -0.191    -0.258     -2.64    -0.183     -1.12    -0.398   -0.0767   -0.0221     0.675 │\n",
       "│ f_17 │    -0.613     0.384     0.634      3.69      2.78     -2.52     -7.91     0.759    -0.445     0.747         2     0.191     -8.92     -5.12     -14.4     -25.8     -3.51       148     -31.4     -23.4     -2.78        -1     -4.74      1.17     0.218     -1.71    -0.489    -0.219      1.84 │\n",
       "│ f_18 │     -0.42     -0.23   -0.0878    -0.365      1.99      4.71      5.75     -6.03      -4.6     0.206      -1.1     -11.3      3.02     0.395      12.1       -20     -22.1     -31.4       113     -0.48     -2.66     -3.05     -12.3     -3.22      2.87      1.64     0.333     0.182     -3.81 │\n",
       "│ f_19 │    -0.226    0.0287    -0.156    -0.263     0.939      1.44      1.91      1.16      -2.6    -0.282     -3.98     -1.56      2.41    -0.756     -3.61    -0.136     -3.12     -23.4     -0.48      56.3      6.46     -0.22     -13.9     -7.62    -0.111      1.68     0.466     0.302     -1.39 │\n",
       "│ f_20 │   -0.0444   -0.0072   -0.0301  -0.00379     0.119     0.179     0.295     0.588    -0.162    -0.403    -0.575    -0.188   -0.0877    -0.171      -1.2     0.246    -0.191     -2.78     -2.66      6.46      5.72      2.75     -3.34     -1.61    -0.389     0.168    0.0467    0.0318    -0.093 │\n",
       "│ f_21 │   -0.0245   -0.0161   -0.0399   -0.0175    0.0183     0.106      0.13     0.961    -0.241    -0.217    -0.387    -0.111   0.00953    -0.298    -0.976     0.137    -0.258        -1     -3.05     -0.22      2.75      9.46      1.62     -2.55     -1.51    -0.422    -0.105   -0.0684     0.269 │\n",
       "│ f_22 │    0.0628    -0.146   -0.0334    -0.791    -0.163    -0.163     0.952      2.66    -0.264      1.04    -0.823     0.921     -5.15    -0.412      9.63     -2.35     -2.64     -4.74     -12.3     -13.9     -3.34      1.62      75.3     -5.41     -14.2     -6.92     -1.59     -1.04      3.73 │\n",
       "│ f_23 │    0.0405   -0.0563   -0.0159   -0.0806    -0.252    -0.156    -0.373    -0.133      1.07      0.73      2.17      1.79     -1.66     -1.31     -1.78      1.04    -0.183      1.17     -3.22     -7.62     -1.61     -2.55     -5.41      31.7      1.22     -2.54    -0.683    -0.431     0.753 │\n",
       "│ f_24 │   -0.0114   -0.0362   -0.0106   -0.0806    0.0495     0.168    -0.079     -0.52     0.288     0.325     0.822      1.75     0.847    -0.994     -2.21     -2.13     -1.12     0.218      2.87    -0.111    -0.389     -1.51     -14.2      1.22      25.8       2.3    -0.581    -0.602     -3.08 │\n",
       "│ f_25 │   0.00958   -0.0157   -0.0148    -0.052   0.00117     0.125    0.0335    -0.235   -0.0274    0.0552    0.0864    0.0972       1.6    -0.112     -1.24    -0.327    -0.398     -1.71      1.64      1.68     0.168    -0.422     -6.92     -2.54       2.3      11.2      1.73     0.529      -3.8 │\n",
       "│ f_26 │   0.00579  -0.00218 -5.63e-05   -0.0148  -0.00503     0.016    0.0151   -0.0716   -0.0138    -0.011   -0.0179   -0.0725     0.335    0.0908   -0.0634    0.0965   -0.0767    -0.489     0.333     0.466    0.0467    -0.105     -1.59    -0.683    -0.581      1.73      1.56      1.09     -1.13 │\n",
       "│ f_27 │   0.00405 -0.000338   0.00186  -0.00646  -0.00215   0.00205   0.00712   -0.0526   -0.0104   -0.0165   -0.0226   -0.0721      0.17    0.0968    0.0411    0.0748   -0.0221    -0.219     0.182     0.302    0.0318   -0.0684     -1.04    -0.431    -0.602     0.529      1.09       1.3    -0.824 │\n",
       "│ f_28 │    0.0157    0.0116    0.0133    0.0284   -0.0716    -0.202    -0.195     0.242     0.147   -0.0369  -0.00112     0.141    -0.662     0.143     0.377     0.927     0.675      1.84     -3.81     -1.39    -0.093     0.269      3.73     0.753     -3.08      -3.8     -1.13    -0.824      24.8 │\n",
       "└──────┴───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────┘"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# use pinv unfolding as initial guess\n",
    "x0 = np.clip(np.linalg.pinv(A) @ g_test, 10, np.inf)\n",
    "\n",
    "m = Minuit(\n",
    "    partial(llh_poisson_tikhonov, A=A, g=g_test, tau=tau_regularization, acceptance=acceptance),\n",
    "    x0,\n",
    "    name=[f\"f_{i}\" for i in range(n_bins_E + 2)]\n",
    ")\n",
    "\n",
    "m.errordef = m.LIKELIHOOD\n",
    "m.limits = [(0, None) for _ in range(n_bins_E + 2)]\n",
    "\n",
    "m.migrad()\n",
    "m.hesse()\n",
    "m.minos()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "42d47b8711c14983b96af5f14870acbf",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(<Figure size 640x480 with 1 Axes>, <AxesSubplot:xlabel='E'>)"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot_unfolding_result(m.values / acceptance)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Natürlich kann diese Regularisierung auch auf die SVD Entfaltung angewendet werden. Dabei ergibt sich der Lösungsvector\n",
    "\n",
    "$f = (A^TA + \\tau\\, C^TC)^{-1} A^T \\mathbf g$\n",
    "\n",
    "und im Vergleich zu der naiv invertierten Lösung oszilliert das Ergebnis schon deutlich weniger."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "217bc304e257467bb07bfa905c1954a5",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(<Figure size 640x480 with 1 Axes>, <AxesSubplot:xlabel='E'>)"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A_inv = np.linalg.pinv(A.T @ A + tau_regularization * C_matrix(A.shape[1]).T @ C_matrix(A.shape[1])) @ A.T\n",
    "\n",
    "plot_unfolding_result(A_inv @ g_test / acceptance)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Variation des Regularisierungsparameters\n",
    "\n",
    "Die Entfaltung enthält den Parameter $\\tau$, über den zunächst nichts weiter bekannt ist. Man \n",
    "kann feststellen, dass der Parameter die Glattheit der Lösung der Entfaltung bestimmt. Der kleine Resonanz-Peak in den Test-Daten bspw. löst sich abhängig von $\\tau$ verschieden gut auf:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "def unfold(tau):\n",
    "    m = Minuit(\n",
    "        partial(llh_poisson_tikhonov, A=A, g=g_test, tau=tau, acceptance=acceptance),\n",
    "        x0,\n",
    "        name=[f\"f_{i}\" for i in range(n_bins_E + 2)]\n",
    "    )\n",
    "\n",
    "    m.errordef = m.LIKELIHOOD\n",
    "    m.limits = [(0, None) for _ in range(n_bins_E + 2)]\n",
    "\n",
    "    m.migrad()\n",
    "    m.hesse()\n",
    "    \n",
    "    return m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "98b5e3d738c64218b703af4eeaaa4e84",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(<Figure size 640x480 with 1 Axes>, <AxesSubplot:xlabel='E'>)"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot_unfolding_result(unfold(0.5).values / acceptance)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Minimum der globalen Korrelation\n",
    "\n",
    "Eine Möglichkeit, einen \"optimalen\" Regularisierungsparameter zu bestimmen, ist die globale Korrelation des Ergebnisses zu minimieren.\n",
    "\n",
    "`iminuit` liefert mithilfe der Hesse-Matrix die Covarianz-Matrix $\\mathrm{Cov}(f)$ des Entfaltungsergebnisses.\n",
    "\n",
    "Hieraus lässt sich die Globale Korrelation jedes Eintrags berechnen:\n",
    "\n",
    "$$\n",
    "\\rho_j = \\sqrt{1 - \\mathrm{Cov}(f)_{jj} \\cdot (\\mathrm{Cov}(f)^{-1})_{jj}}\n",
    "$$\n",
    "\n",
    "Und der Mittelwert über alle Einträge wird minimiert durch einen \"groben\" Scan über verschiedene $\\tau$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "2790b0327624460a8049906d975aecea",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/100 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "taus = np.geomspace(0.01, 10, 100)\n",
    "\n",
    "def mean_global_correlation(cov):\n",
    "    cov_inv = np.linalg.inv(cov)\n",
    "    return np.mean(\n",
    "        np.sqrt(1 - 1 / (np.diag(cov) * np.diag(cov_inv)))\n",
    "    )\n",
    "\n",
    "\n",
    "results = []\n",
    "x0 = np.clip(np.linalg.pinv(A) @ g_test, 10, np.inf)\n",
    "\n",
    "for tau in tqdm(taus):\n",
    "    results.append(unfold(tau))\n",
    "    \n",
    "global_correlations = [mean_global_correlation(m.covariance) for m in results]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "85713a126a494d4abe8e461e43e9c3e3",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(constrained_layout=True)\n",
    "plt.plot(taus, global_correlations, 'o')\n",
    "\n",
    "plt.xlabel(r'$\\tau$')\n",
    "plt.ylabel('Mean Correlation')\n",
    "plt.xscale('log')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "19cf7b4ff5a34155b92a06523d5fbe23",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Unfolding with $\\\\tau=0.43$')"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "best_idx = np.argmin(global_correlations)\n",
    "best_tau = taus[best_idx]\n",
    "best_fit = results[best_idx]\n",
    "\n",
    "fig, ax =plot_unfolding_result(best_fit.values / acceptance)\n",
    "ax.set_title(rf'Unfolding with $\\tau={best_tau:.2f}$')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Abschätzung der Unsicherheiten\n",
    "\n",
    "Wie immer in der Physik sind auch hier Messungen ohne Kenntnis über die Unsicherheiten von geringem Nutzen.\n",
    "\n",
    "Oben haben wir bereits die Kovarianzmatrix der Fit-Parameter über die Hesse-Matrix aus imiuit bekommen.\n",
    "Ebenso können wieder Likelihood-Scans mit der `minos` Methode durchgeführt werden.\n",
    "\n",
    "Alternativ implementieren wir hier (hauptsächlich zur Wiederholung) einen MCMC-Ansatz.\n",
    "\n",
    "\n",
    "Für das MCMC kann man eine simple Implementierung des Metropolis-Algorithmus verwenden. Als Resultat erhalten wir so eine Anzahl von Stichproben aus der Likelihood (die a-posteriori-Verteilung). Diese kann man nutzen um mittels eines Bayesianischen Ansatzes Aussagen über die Unsicherheit der Schätzung zu treffen."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "def mcmc(x0, fun, step_size=1.5, n_steps=10000, print_acceptance=False):\n",
    "    x = [x0]\n",
    "    f = [fun(x0)]\n",
    "    acc = 0\n",
    "   \n",
    "    for _ in tqdm(range(n_steps)):\n",
    "        x_new = x[-1] + step_size * np.random.randn(len(x0))\n",
    "        f_new = fun(x_new)\n",
    "    \n",
    "        prop_eval = -np.log(np.random.rand()) > (f_new - f[-1])\n",
    "        \n",
    "        if prop_eval:\n",
    "            x.append(x_new)\n",
    "            f.append(f_new)\n",
    "            acc += 1\n",
    "        else:\n",
    "            x.append(x[-1])\n",
    "            f.append(f[-1])\n",
    "            \n",
    "    if print_acceptance:\n",
    "        print(f'{acc / n_steps:.2%} of proposed steps accepted.')\n",
    "        \n",
    "    return np.array(x), np.array(f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "5a85f551cf6e4d1e95f991f01b576751",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/100000 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "40.26% of proposed steps accepted.\n"
     ]
    }
   ],
   "source": [
    "from functools import partial\n",
    "\n",
    "function = partial(llh_poisson_tikhonov, A=A, g=g_test, tau=0.43, acceptance=acceptance)\n",
    "\n",
    "m = Minuit(\n",
    "    function,\n",
    "    x0,\n",
    "    name=[f\"f_{i}\" for i in range(n_bins_E + 2)]\n",
    ")\n",
    "\n",
    "m.errordef = m.LIKELIHOOD\n",
    "m.limits = [(0, None) for _ in range(n_bins_E + 2)]\n",
    "\n",
    "m.migrad()\n",
    "m.hesse()\n",
    "\n",
    "    \n",
    "x_sample, f_sample = mcmc(np.array(m.values), function, step_size=0.05 * f_test, n_steps=100000, print_acceptance=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Die Unsicherheit des Entfaltungsergebnisses kann nun bspw. durch die Angabe von Quantilen visualisiert werden.\n",
    "\n",
    "(Dies ist nicht die einzige Möglichkeit, siehe Vorlesung)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8413447460685429"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.stats import norm\n",
    "\n",
    "norm(0, 1).cdf(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "e6a8b2b1bb8a4033863448c931113c9e",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "\n",
    "plt.fill_between(\n",
    "    np.arange(n_bins_E + 1),\n",
    "    (np.quantile(x_sample, norm.cdf(-1), axis=0) / acceptance)[1:],\n",
    "    (np.quantile(x_sample, norm.cdf(1), axis=0) / acceptance)[1:],\n",
    "    alpha=0.2,\n",
    "    step='post'\n",
    ")\n",
    "\n",
    "\n",
    "plt.stairs(\n",
    "    (np.median(x_sample, axis=0) / acceptance)[1:-1],\n",
    "    label='Median'\n",
    ")\n",
    "\n",
    "\n",
    "plt.stairs((f_test / acceptance)[1:-1], label='Wahrheit')\n",
    "plt.stairs((m.values / acceptance)[1:-1], label='Entfaltung')\n",
    "plt.legend()\n",
    "plt.yscale('log')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "2455915e1b6b434583cbcac8e52f392b",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "\n",
    "bins_samples = np.geomspace(x_sample.min(), x_sample.max(), 101)\n",
    "\n",
    "h = plt.hist2d(\n",
    "    np.tile(np.arange(n_bins_E + 2), (len(x_sample), 1)).flatten(),\n",
    "    x_sample.flatten(),\n",
    "    bins=(np.arange(n_bins_E + 2), bins_samples),\n",
    "    norm=LogNorm()\n",
    ")\n",
    "\n",
    "plt.stairs(f_test, label='Wahrheit')\n",
    "plt.stairs(m.values, label='Entfaltung')\n",
    "\n",
    "plt.yscale('log')\n",
    "plt.colorbar(h[3])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "a8cb63c2665a47c898d0b3862f250dad",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bin_idx = 8\n",
    "\n",
    "plt.figure()\n",
    "plt.hist(x_sample[:, bin_idx], bins=np.geomspace(x_sample[:, bin_idx].min(), x_sample[:, bin_idx].max(), 100))\n",
    "plt.axvline(f_test[bin_idx], color='C1')\n",
    "plt.xscale('log')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "9a2cefe4d8c447f3a136d7394c815010",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "d42fb19a3c204a918040e35402e1f343",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f7d21708910>"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bin1_idx = 9\n",
    "\n",
    "plt.figure()\n",
    "plt.scatter(\n",
    "    x_sample[:, bin_idx],\n",
    "    x_sample[:, bin_idx + 1],\n",
    "    s=5, alpha=0.1, linewidth=0,\n",
    ")\n",
    "plt.xscale('log')\n",
    "plt.yscale('log')\n",
    "\n",
    "\n",
    "plt.matshow(np.corrcoef(x_sample.T), cmap='RdBu_r', vmin=-1, vmax=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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