AnalysingPlottingExperiments.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Analysing experiments\n",
    "\n",
    "This notebook accompanies the AAAI 2021 submission \n",
    "_Practical and Rigorous Uncertainty Bounds for Gaussian Process Regression_.\n",
    "\n",
    "Here we analyse the results of the numerical experiments. The results have to be contained in a\n",
    "directory (in the same directory as this notebook) named by the tag of the experiment.\n",
    "As an alternative, the corresponding directory can be changed for each experiment (argument for\n",
    "function load_failures_and_scalings or output_dir for Experiment 1_4_c)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy.linalg as la\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Auxiliary functions\n",
    "def load_failures_and_scalings(output_dir):\n",
    "    files = [f for f in os.listdir(os.path.join(output_dir)) if f.endswith('.npz')]\n",
    "    \n",
    "    # All runs have the same config\n",
    "    n_rep_funcs = len(files)\n",
    "    with open(os.path.join(output_dir, files[0]), 'rb') as file:\n",
    "        result = np.load(file)\n",
    "        n_rep_training = result['scalings'].shape[0]\n",
    "        n_scalings = result['failures'].shape[1]\n",
    "        \n",
    "    # Load results\n",
    "    failures = np.zeros([n_rep_funcs, n_rep_training, n_scalings])\n",
    "    scalings = np.zeros([n_rep_funcs, n_rep_training, n_scalings])\n",
    "    for i in range(len(files)):\n",
    "        with open(os.path.join(output_dir, files[i]), 'rb') as file:\n",
    "            result = np.load(file)\n",
    "            scalings[i,:] = result['scalings']\n",
    "            failures[i,:] = result['failures']\n",
    "    return (scalings, failures)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Experiment 1\n",
    "### Experiment 1.1: Basic test of nominal aposteriori bound\n",
    "This corresponds to Table 1, upper row."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Experiment 1.1 a)\n",
      "\n",
      "Failures: [0. 0. 0. 0.]\n",
      "0: 6.95 +/- 0.04\n",
      "\n",
      "1: 7.39 +/- 0.04\n",
      "\n",
      "2: 7.80 +/- 0.03\n",
      "\n",
      "3: 8.19 +/- 0.03\n",
      "\n"
     ]
    }
   ],
   "source": [
    "(scalings_a, failures_a) = load_failures_and_scalings('exp_1_1_a')\n",
    "scalings_mean_a = np.mean(scalings_a, axis=(0,1))\n",
    "scalings_var_a = np.var(scalings_a, axis=(0,1))\n",
    "failures_a = np.sum(failures_a, axis=(0,1))\n",
    "\n",
    "print('Experiment 1.1 a)\\n')\n",
    "print(f'Failures: {failures_a}')\n",
    "for i in range(4):\n",
    "    print(f\"{i}: {scalings_mean_a[i]:1.2f} +/- {np.sqrt(scalings_var_a[i]):1.2f}\\n\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following corresponds to Table 1, lower row."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Experiment 1.1 b)\n",
      "\n",
      "Failures: [0. 0. 0. 0.]\n",
      "0: 7.36 +/- 0.04\n",
      "\n",
      "1: 7.78 +/- 0.04\n",
      "\n",
      "2: 8.16 +/- 0.04\n",
      "\n",
      "3: 8.53 +/- 0.04\n",
      "\n"
     ]
    }
   ],
   "source": [
    "(scalings_b, failures_b) = load_failures_and_scalings('exp_1_1_b')\n",
    "scalings_mean_b = np.mean(scalings_b, axis=(0,1))\n",
    "scalings_var_b = np.var(scalings_b, axis=(0,1))\n",
    "failures_b = np.sum(failures_b, axis=(0,1))\n",
    "\n",
    "print('Experiment 1.1 b)\\n')\n",
    "print(f'Failures: {failures_b}')\n",
    "for i in range(4):\n",
    "    print(f\"{i}: {scalings_mean_b[i]:1.2f} +/- {np.sqrt(scalings_var_b[i]):1.2f}\\n\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Experiment 1.2: Exploring conservatism\n",
    "The results of this experiment are reported in the supplementary material.\n",
    "\n",
    "SE kernel, using generic kernel approach to sample the functions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Experiment 1.2 a)\n",
      "\n",
      "0: 2.00 +/- 0.00\n",
      "\n",
      "1: 2.28 +/- 0.00\n",
      "\n",
      "2: 2.57 +/- 0.00\n",
      "\n",
      "3: 2.85 +/- 0.01\n",
      "\n"
     ]
    }
   ],
   "source": [
    "(scalings_a, failures_a) = load_failures_and_scalings('exp_1_2_a/')\n",
    "scalings_mean_a = np.mean(scalings_a, axis=(0,1))\n",
    "scalings_var_a = np.var(scalings_a, axis=(0,1))\n",
    "\n",
    "print('Experiment 1.2 a)\\n')\n",
    "for i in range(4):\n",
    "    print(f\"{i}: {scalings_mean_a[i]:1.2f} +/- {np.sqrt(scalings_var_a[i]):1.2f}\\n\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This figure is shown as Figure 4 (left) in the supplementary material."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "failures_mean_a = np.mean(failures_a, axis=(0,1))\n",
    "plt.plot(np.arange(20), failures_mean_a, 'o')\n",
    "worst_a = np.max(np.mean(failures_a, axis=1), axis=0)\n",
    "plt.plot(np.arange(20), worst_a, 'o')\n",
    "\n",
    "plt.xticks(ticks=np.arange(20), labels=['2'] + [None]*18 + [r'$\\beta_{50}$'])\n",
    "plt.ylabel(\"Failure frequency\")\n",
    "plt.title('SE kernel (length scale 0.2)')\n",
    "_ = plt.legend(['Mean', 'Worst function'])\n",
    "plt.savefig('figures/figure4_left.pdf')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Matern kernel. The corresponding figures is not included in the supplementary material."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Experiment 1.2 b)\n",
      "\n",
      "0: 2.00 +/- 0.00\n",
      "\n",
      "1: 2.30 +/- 0.00\n",
      "\n",
      "2: 2.61 +/- 0.00\n",
      "\n",
      "3: 2.91 +/- 0.01\n",
      "\n"
     ]
    }
   ],
   "source": [
    "(scalings_b, failures_b) = load_failures_and_scalings('exp_1_2_b/')\n",
    "scalings_mean_b = np.mean(scalings_b, axis=(0,1))\n",
    "scalings_var_b = np.var(scalings_b, axis=(0,1))\n",
    "\n",
    "print('Experiment 1.2 b)\\n')\n",
    "for i in range(4):\n",
    "    print(f\"{i}: {scalings_mean_b[i]:1.2f} +/- {np.sqrt(scalings_var_b[i]):1.2f}\\n\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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fP66qVauqfv366ty5s1u2Kzg4WOvWrVOXLl2UmJior7/+Wi1atLihfTr75xIZGamEhAR99tlnGjRo0A1dt3TlAojLly/X2LFj1bNnT4WFhWnIkCE6cuSIPvjgA5u5pb1froefn59atWqlDz74QPv379fly5cVFRWlF154weak3jvuuEPfffedxo0bp9GjRys3N1dhYWFq3769dU+Qve/7klzvz3bFihV66aWXNHbsWJ0+fVqxsbFasmRJsfPsDMNQQUGB9bY2n3/+uaQrh5qTk5OL1S06BCVd2eMnmZ93VyQyMlIXL15Uq1attGDBgmJ73Fzlqaee0oEDB6zPly1bpmXLlkmyPXx39c9BuvKFgKVLl2rOnDk6e/asqlevrjZt2uiDDz5Qy5Yti60rNTVV2dnZevTRR127UbBhMf74rgSAG6To8M2BAwdK/bbSjXT58mU1adJEtWrV0po1a9zdDv7P6tWr1bVrV23fvt26l+/PLCkpSb/++qv1cC1uDMISALcwDEOtW7dW8+bNNXPmzBu+/v79++u+++5TeHi4srKyNGfOHKWlpWnNmjW69957b3g/KNlzzz2nw4cPX/N+c38G+/btU8OGDbVu3Tq1adPG3e38qXAYDoBbWCwWzZ07V6tWrVJhYeENv5lubm6unn32WZ04cUI+Pj5q1qyZVq9eTVAqZ9544w13t1BuHDx4UDNnziQouQF7lgAAAExwBW8AAAAThCUAAAAThCUAAAATnODtBIWFhTpy5IgCAgJcevsLAADgPIZhKDc3VxEREaZfMiEsOcGRI0esd7wGAACe5dChQ6ZXvScsOUFAQICkKz/swMBAN3cDAADskZOTo8jISOvneGkIS05QdOgtMDCQsAQAgIe51ik0nOANAABggrAEAABggrAEAABggnOWAADlhmEYys/PV0FBgbtbwU3Ay8tL3t7e131ZH8ISAKBcyMvL09GjR3X+/Hl3t4KbiL+/v8LDw1WxYsUy1yAsAQDcrrCwUJmZmfLy8lJERIQqVqzIRX5xXQzDUF5enk6cOKHMzEzVr1/f9MKTZghLAAC3y8vLU2FhoSIjI+Xv7+/udnCTqFSpknx8fHTgwAHl5eXJz8+vTHU4wRsAUG6U9V/+QGmc8Z7iXQkAAGCCsAQAAGCCc5YAADeVgkJD32We1vHciwoJ8NOd0dXlVYGTxVF27FkCANw0knceVZvX16nX3E36+8cZ6jV3k9q8vk7JO4+6bJ19+/aVxWLR4MGDi702ZMgQWSwW9e3b12Xrh+sRlgAAN4XknUf11Ic/6Gj2RZvxrOyLeurDH1wamCIjI/Xxxx/rwoUL1rGLFy9qyZIlioqKctl6cWMQlgAAHq+g0NCEz3+SUcJrRWMTPv9JBYUlzbh+zZo1U1RUlFasWGEdW7FihSIjI9W0adP/vxfD0JQpUxQTE6NKlSrpjjvu0L///e//fzsKCtS/f39FR0erUqVKatCggWbMmGGzrr59+6p79+6aOnWqwsPDVaNGDT399NO6fPmyS7YNhCUAwE3gu8zTxfYo/ZEh6Wj2RX2XedplPTzxxBN67733rM8XLFigfv362cwZM2aM3nvvPc2ePVu7du3SiBEj9NhjjyktLU3SlYtz3nLLLfrkk0/0008/aezYsXrxxRf1ySef2NRJSUnRvn37lJKSokWLFmnhwoVauHChy7btz44TvAEAHu94bulBqSzzyiIpKUmjR4/W/v37ZbFY9O233+rjjz9WamqqJOncuXN68803tW7dOsXHx0uSYmJitGHDBv3rX/9SYmKifHx8NGHCBGvN6Ohobdy4UZ988okeeeQR63i1atU0c+ZMeXl5KTY2Vl26dNE333yjgQMHumz7/swISwAAjxcSYN+Vme2dVxbBwcHq0qWLFi1aJMMw1KVLFwUHB1tf/+mnn3Tx4kXdd999Nsvl5eXZHKqbM2eO5s2bpwMHDujChQvKy8tTkyZNbJa57bbb5OXlZX0eHh6uHTt2uGbDQFgCAHi+O6OrKzzIT1nZF0s8b8kiKSzoymUEXKlfv34aOnSoJGnWrFk2rxUWFkqSvvzyS9WqVcvmNV9fX0nSJ598ohEjRmjatGmKj49XQECA3njjDW3evNlmvo+Pj81zi8VirQ/nIywBADyeVwWLxnWL01Mf/iCLZBOYiq6wNK5bnMuvt9SpUyfl5eVJkjp27GjzWlxcnHx9fXXw4EElJiaWuPz69evVunVrDRkyxDq2b98+1zUMuxCWAAA3hU6NwjX7sWaa8PlPNid7hwX5aVy3OHVqFO7yHry8vLR7927r//9RQECAnn32WY0YMUKFhYVq06aNcnJytHHjRlWpUkV9+vRRvXr19P777+vrr79WdHS0PvjgA23ZskXR0dEu7x2lIywBAG4anRqF6764MLdewTswMLDU1yZOnKiQkBBNnjxZv/76q6pWrapmzZrpxRdflCQNHjxYGRkZ6tmzpywWi3r16qUhQ4boq6++ulHtowQWwzBcc9GJP5GcnBwFBQUpOzvb9A8JAKBkFy9eVGZmpqKjo+Xn57qTsPHnY/besvfzm+ssAQAAmCAsAQAAmCAsAQAAmCAsAQAAmCAsAQAAmCAsAQAAmCAsAQAAmCAsAQAAmCAsAQAAmCAsAQBuLoUFUuZ6ace/r/y3sMDdHZU748ePV2hoqCwWiz799FO39lIeergWwhIA4Obx0yppeiNpUVdpef8r/53e6Mq4C8yZM0cBAQHKz8+3jp09e1Y+Pj5KSEiwmbt+/XpZLBb9/PPPLull/PjxatKkyTXn7d69WxMmTNC//vUvHT16VPfff79L+rlaaf3dyB7KirAEALg5/LRK+uRxKeeI7XjO0SvjLghM7dq109mzZ7V161br2Pr16xUWFqYtW7bo/Pnz1vHU1FRFRETo1ltvdXg9BQUFKiwsdErP+/btkyQ9+OCDCgsLk6+vr1PqllV56OFaCEsAAM9XWCAlvyCppHvD/99Y8iinH5Jr0KCBIiIilJqaah1LTU3Vgw8+qLp162rjxo024+3atZMknTlzRo8//riqVasmf39/3X///frll1+scxcuXKiqVavqiy++UFxcnHx9fXXgwAGlpqbqzjvvVOXKlVW1alXdfffdOnDggBYuXKgJEyZo+/btslgsslgsWrhwYbF+x48fr27dukmSKlSoIIvFIklq27athg8fbjO3e/fu6tu3r/V5nTp1NGnSJPXr108BAQGKiorSu+++a7PMb7/9pr/97W+qXr26KleurBYtWmjz5s2m/V19GG7Hjh1q3769KlWqpBo1amjQoEE6e/as9fW+ffuqe/fumjp1qsLDw1WjRg09/fTTunz58jV/X2VFWAIAeL4DG4vvUbJhSDmHr8xzsrZt2yolJcX6PCUlRW3btlViYqJ1PC8vT+np6daw1LdvX23dulWrVq1Senq6DMNQ586dbT7wz58/r8mTJ2vevHnatWuXqlevru7duysxMVE//vij0tPTNWjQIFksFvXs2VP/7//9P9122206evSojh49qp49exbr9dlnn9V7770nSdZ5jpg2bZpatGihbdu2aciQIXrqqae0Z88eSVcOPyYmJurIkSNatWqVtm/frueff16FhYV293f+/Hl16tRJ1apV05YtW7Rs2TL95z//0dChQ23mpaSkaN++fUpJSdGiRYu0cOHCEsOhs3i7rDIAADfK2WPOneeAtm3basSIEcrPz9eFCxe0bds23XPPPSooKNDbb78tSdq0aZMuXLigdu3a6ZdfftGqVav07bffqnXr1pKkxYsXKzIyUp9++qn+53/+R5J0+fJlvfPOO7rjjjskSadPn1Z2dra6du2qunXrSpIaNmxo7aNKlSry9vZWWFhYqb1WqVJFVatWlSTTeaXp3LmzhgwZIkl64YUX9NZbbyk1NVWxsbH66KOPdOLECW3ZskXVq1eXJNWrV8+h/hYvXqwLFy7o/fffV+XKlSVJM2fOVLdu3fT6668rNDRUklStWjXNnDlTXl5eio2NVZcuXfTNN99o4MCBDm+TPdizBADwfFVCnTvPAe3atdO5c+e0ZcsWrV+/XrfeeqtCQkKUmJioLVu26Ny5c0pNTVVUVJRiYmK0e/dueXt7q1WrVtYaNWrUUIMGDbR7927rWMWKFdW4cWPr8+rVq6tv377q2LGjunXrphkzZji8Z+h6/bEfi8WisLAwHT9+XJKUkZGhpk2bWoNSWezevVt33HGHNShJ0t13363CwkLt3bvXOnbbbbfJy8vL+jw8PNzahysQlgAAnq92aykwQpKllAkWKbDWlXlOVq9ePd1yyy1KSUlRSkqKEhMTJV3ZcxMdHa1vv/1WKSkpat++vSTJMEo6r+rKeNE5RJJUqVIlm+eS9N577yk9PV2tW7fW0qVLdeutt2rTpk3XvQ0VKlQo1ldJ5wD5+PjYPLdYLNYTzytVqnTdfVz9M7h6Xfb04QqEJQCA56vgJXV6/f+eXP1h+3/PO712ZZ4LtGvXTqmpqUpNTVXbtm2t44mJifr666+1adMm6/lKcXFxys/P1+bNm63zTp06pZ9//tnmsFppmjZtqtGjR2vjxo1q1KiRPvroI0lX9kQVFJTtBPaaNWva7KUqKCjQzp07HarRuHFjZWRk6PTp0yW+bk9/cXFxysjI0Llz56xj3377rSpUqFCmbxE6C2EJAHBziHtAeuR9KTDcdjww4sp43AMuW3W7du20YcMGZWRkWPcsSVfC0ty5c3Xx4kVrWKpfv74efPBBDRw4UBs2bND27dv12GOPqVatWnrwwQdLXUdmZqZGjx6t9PR0HThwQGvWrLEJWHXq1FFmZqYyMjJ08uRJXbp0ye7+27dvry+//FJffvml9uzZoyFDhuj333936GfQq1cvhYWFqXv37vr222/166+/avny5UpPT7e7v0cffVR+fn7q06ePdu7cqZSUFD3zzDNKSkqynq/kDoQlAMDNI+4BafhOqc8XUo/5V/47fIdLg5J0JSxduHBB9erVs/lQT0xMVG5ururWravIyEjr+HvvvafmzZura9euio+Pl2EYWr16dbHDS3/k7++vPXv2qEePHrr11ls1aNAgDR06VE8++aQkqUePHurUqZPatWunmjVrasmSJXb3369fP/Xp00ePP/64EhMTFR0dbQ139qpYsaLWrFmjkJAQde7cWbfffrtee+0167lF9vTn7++vr7/+WqdPn1bLli3117/+VX/5y180c+ZMh3pxNotR2sFT2C0nJ0dBQUHKzs5WYGCgu9sBAI9z8eJFZWZmKjo6Wn5+fu5uBzcRs/eWvZ/fHrdn6Z133rFucPPmzbV+/XrT+WlpaWrevLn8/PwUExOjOXPmlDr3448/lsViUffu3Z3cNQAA8FQeFZaWLl2q4cOH66WXXtK2bduUkJCg+++/XwcPHixxfmZmpjp37qyEhARt27ZNL774ooYNG6bly5cXm3vgwAE9++yzxe7lAwAA/tw8Kiy9+eab6t+/vwYMGKCGDRtq+vTpioyM1OzZs0ucP2fOHEVFRWn69Olq2LChBgwYoH79+mnq1Kk28woKCvToo49qwoQJiomJuRGbAgAAPITHhKW8vDx9//336tChg814hw4dbO6980fp6enF5nfs2FFbt261uX7Eyy+/rJo1a6p///529XLp0iXl5OTYPAAAwM3JY8LSyZMnVVBQUOyrg6GhocrKyipxmaysrBLn5+fn6+TJk5KuXL9h/vz5mjt3rt29TJ48WUFBQdbHH7/hAAAoO75zBGdzxnvKY8JSkauv7Gl2tc/S5heN5+bm6rHHHtPcuXMVHBxsdw+jR49Wdna29XHo0CEHtgAAcLWir8yfP3/ezZ3gZlP0njK7LMO1eMyNdIODg+Xl5VVsL9Lx48dLvVBVWFhYifO9vb1Vo0YN7dq1S/v371e3bt2srxddLt3b21t79+613qzwj3x9feXr63u9mwQA+D9eXl6qWrWq9f5e/v7+pv8QBq7FMAydP39ex48fV9WqVW3uJecojwlLFStWVPPmzbV27Vo99NBD1vG1a9eWesXT+Ph4ff755zZja9asUYsWLeTj46PY2Fjt2LHD5vUxY8YoNzdXM2bM4PAaANxARXejd+UNUfHnU7VqVet7q6w8JixJ0siRI5WUlKQWLVooPj5e7777rg4ePKjBgwdLunJ47PDhw3r//fclSYMHD9bMmTM1cuRIDRw4UOnp6Zo/f771qqF+fn5q1KiRzTqqVq0qScXGAQCuZbFYFB4erpCQkBJv4go4ysfH57r2KBXxqLDUs2dPnTp1Si+//LKOHj2qRo0aafXq1apdu7Yk6ejRozbXXIqOjtbq1as1YsQIzZo1SxEREXr77bfVo0cPd20CAOAavLy8nPIBBzgLtztxAm53AgCA57lpb3cCAABwIxGWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATHhcWHrnnXcUHR0tPz8/NW/eXOvXrzedn5aWpubNm8vPz08xMTGaM2eOzetz585VQkKCqlWrpmrVqunee+/Vd99958pNAAAAHsSjwtLSpUs1fPhwvfTSS9q2bZsSEhJ0//336+DBgyXOz8zMVOfOnZWQkKBt27bpxRdf1LBhw7R8+XLrnNTUVPXq1UspKSlKT09XVFSUOnTooMOHD9+ozQIAAOWYxTAMw91N2KtVq1Zq1qyZZs+ebR1r2LChunfvrsmTJxeb/8ILL2jVqlXavXu3dWzw4MHavn270tPTS1xHQUGBqlWrppkzZ+rxxx+3q6+cnBwFBQUpOztbgYGBDm4VAABwB3s/vz1mz1JeXp6+//57dejQwWa8Q4cO2rhxY4nLpKenF5vfsWNHbd26VZcvXy5xmfPnz+vy5cuqXr16qb1cunRJOTk5Ng8AAHBz8piwdPLkSRUUFCg0NNRmPDQ0VFlZWSUuk5WVVeL8/Px8nTx5ssRlRo0apVq1aunee+8ttZfJkycrKCjI+oiMjHRwawAAgKfwmLBUxGKx2Dw3DKPY2LXmlzQuSVOmTNGSJUu0YsUK+fn5lVpz9OjRys7Otj4OHTrkyCYAAAAP4u3uBuwVHBwsLy+vYnuRjh8/XmzvUZGwsLAS53t7e6tGjRo241OnTtWkSZP0n//8R40bNzbtxdfXV76+vmXYCgAA4Gk8Zs9SxYoV1bx5c61du9ZmfO3atWrdunWJy8THxxebv2bNGrVo0UI+Pj7WsTfeeEMTJ05UcnKyWrRo4fzmAQCAx/KYsCRJI0eO1Lx587RgwQLt3r1bI0aM0MGDBzV48GBJVw6P/fEbbIMHD9aBAwc0cuRI7d69WwsWLND8+fP17LPPWudMmTJFY8aM0YIFC1SnTh1lZWUpKytLZ8+eveHbBwAAyh+POQwnST179tSpU6f08ssv6+jRo2rUqJFWr16t2rVrS5KOHj1qc82l6OhorV69WiNGjNCsWbMUERGht99+Wz169LDOeeedd5SXl6e//vWvNusaN26cxo8ff0O2CwAAlF8edZ2l8orrLAEA4HluuussAQAAuANhCQAAwITDYWnhwoU6f/68K3oBAAAodxwOS6NHj1ZYWJj69+9f6m1GAAAAbhYOh6XffvtNH374oc6cOaN27dopNjZWr7/+eqm3HAEAAPBkDoclLy8vPfDAA1qxYoUOHTqkQYMGafHixYqKitIDDzygzz77TIWFha7oFQAA4Ia7rhO8Q0JCdPfddys+Pl4VKlTQjh071LdvX9WtW1epqalOahEAAMB9yhSWjh07pqlTp+q2225T27ZtlZOToy+++EKZmZk6cuSIHn74YfXp08fZvQIAANxwDl+Uslu3bvr666916623asCAAXr88cdVvXp1mzlHjhzRLbfc8qc5HMdFKQEA8Dz2fn47fLuTkJAQpaWlKT4+vtQ54eHhyszMdLQ0AABAucPtTpyAPUsAAHgel93uZNiwYXr77beLjc+cOVPDhw93tBwAAEC55nBYWr58ue6+++5i461bt9a///1vpzQFAABQXjgclk6dOqWgoKBi44GBgTp58qRTmgIAACgvHA5L9erVU3JycrHxr776SjExMU5pCgAAoLxw+NtwI0eO1NChQ3XixAm1b99ekvTNN99o2rRpmj59urP7AwAAcCuHw1K/fv106dIlvfrqq5o4caIkqU6dOpo9e7Yef/xxpzcIAADgTtd16YATJ06oUqVKqlKlijN78jhcOgAAAM/jsotS/lHNmjWvZ3EAAIByz+ETvI8dO6akpCRFRETI29tbXl5eNg8AAICbicN7lvr27auDBw/qH//4h8LDw2WxWFzRFwAAQLngcFjasGGD1q9fryZNmrigHQAAgPLF4cNwkZGR4nZyAADgz8LhsDR9+nSNGjVK+/fvd0E7AAAA5YvDh+F69uyp8+fPq27duvL395ePj4/N66dPn3ZacwAAAO7mcFjiKt0AAODPxOGw1KdPH1f0AQAAUC45fM6SJO3bt09jxoxRr169dPz4cUlScnKydu3a5dTmAAAA3M3hsJSWlqbbb79dmzdv1ooVK3T27FlJ0o8//qhx48Y5vUEAAAB3cjgsjRo1Sq+88orWrl2rihUrWsfbtWun9PR0pzYHAADgbg6HpR07duihhx4qNl6zZk2dOnXKKU0BAACUFw6HpapVq+ro0aPFxrdt26ZatWo5pSkAAIDywuGw1Lt3b73wwgvKysqSxWJRYWGhvv32Wz377LN6/PHHXdEjAACA2zgcll599VVFRUWpVq1aOnv2rOLi4nTPPfeodevWGjNmjCt6BAAAcBuLUcYbve3bt0/btm1TYWGhmjZtqvr16zu7N4+Rk5OjoKAgZWdnKzAw0N3tAAAAO9j7+e3wRSmL1K1bV3Xr1i3r4gAAAB7B4bDUr18/09cXLFhQ5mYAAADKG4fD0pkzZ2yeX758WTt37tTvv/+u9u3bO60xAACA8sDhsLRy5cpiY4WFhRoyZIhiYmKc0hQAAEB5UaZ7wxUrUqGCRowYobfeessZ5QAAAMoNp4Ql6cq34/Lz851VDgAAoFxw+DDcyJEjbZ4bhqGjR4/qyy+/VJ8+fZzWGAAAQHngcFjatm2bzfMKFSqoZs2amjZt2jW/KQcAAOBpHA5LKSkprugDAACgXHLaOUsAAAA3I4f3LDVt2lQWi8WuuT/88IPDDQEAAJQnDoelTp066Z133lFcXJzi4+MlSZs2bdKuXbv01FNPqVKlSk5vEgAAwF0cDksnTpzQsGHDNHHiRJvxcePG6dChQ9zuBAAA3FQshmEYjiwQFBSkrVu3qn79+jbjv/zyi1q0aKHs7GynNugJ7L1rMQAAKD/s/fx2+ATvSpUqacOGDcXGN2zYID8/P0fLAQAAlGsOH4YbPny4nnrqKX3//fe66667JF05Z2nBggUaO3as0xsEAABwJ4fD0qhRoxQTE6MZM2boo48+kiQ1bNhQCxcu1COPPOL0BgEAANzJ4XOWUBznLAEA4Hlcds6SJP3++++aN2+eXnzxRZ0+fVrSlWsqHT58uGzdAgAAlFMOH4b78ccfde+99yooKEj79+/XgAEDVL16da1cuVIHDhzQ+++/74o+AQAA3MLhsDRy5Ej17dtXU6ZMUUBAgHX8/vvvV+/evZ3a3J9ZQX6+9mz+WhfOHFalarUU26qjvLwd/nVRv5zVpr77alPffbU9vb4n9+7p9V3du73KdJ2lH374QXXr1lVAQIC2b9+umJgYHThwQA0aNNDFixdd1Wu55exzlrZ9vUgR6RMUqlPWsWOqoSPx49S0Yx/qu7C+J/fu6fU9uXdPr+/Jvbu6vif37un1Xd275MJzlvz8/JSTk1NsfO/evapZs6aj5Rz2zjvvKDo6Wn5+fmrevLnWr19vOj8tLU3NmzeXn5+fYmJiNGfOnGJzli9frri4OPn6+iouLk4rV650VfvXtO3rRbpj4zDVNE7ZjNc0TumOjcO07etF1HdRfU/u3dPre3Lvnl7fk3t3dX1P7t3T67u6d0c5HJYefPBBvfzyy7p8+bIkyWKx6ODBgxo1apR69Ojh9Ab/aOnSpRo+fLheeuklbdu2TQkJCbr//vt18ODBEudnZmaqc+fOSkhI0LZt2/Tiiy9q2LBhWr58uXVOenq6evbsqaSkJG3fvl1JSUl65JFHtHnzZpduS0kK8vMVkT5BklThqnsVFz0PT5+ggvx86ju5vif37un1Pbl3T6/vyb27ur4n9+7p9V3de1k4HJamTp2qEydOKCQkRBcuXFBiYqLq1aungIAAvfrqq67o0erNN99U//79NWDAADVs2FDTp09XZGSkZs+eXeL8OXPmKCoqStOnT1fDhg01YMAA9evXT1OnTrXOmT59uu677z6NHj1asbGxGj16tP7yl79o+vTppfZx6dIl5eTk2DycYc/mrxWqU8XeHEUqWKQwndKezV9T38n1Pbl3T6/vyb17en1P7t3V9T25d0+v7+rey8LhsBQYGKgNGzZo+fLleu211zR06FCtXr1aaWlpqly5sit6lCTl5eXp+++/V4cOHWzGO3TooI0bN5a4THp6erH5HTt21NatW617xkqbU1pNSZo8ebKCgoKsj8jIyLJsUjEXzth36QV751G/fNSmvvtqU999tT29vif37un1Xd17WTh0Snl+fr78/PyUkZGh9u3bq3379q7qq5iTJ0+qoKBAoaGhNuOhoaHKysoqcZmsrKwS5+fn5+vkyZMKDw8vdU5pNSVp9OjRGjlypPV5Tk6OUwJTpWq1nDqP+uWjNvXdV5v67qvt6fU9uXdPr+/q3svCoT1L3t7eql27tgoKClzVzzVZLLb75QzDKDZ2rflXjzta09fXV4GBgTYPZ4ht1VHHVEOFpXw/sdCQslRDsa06Ut/J9T25d0+v78m9e3p9T+7d1fU9uXdPr+/q3svC4cNwY8aM0ejRo61X7r5RgoOD5eXlVWyPz/Hjx4vtGSoSFhZW4nxvb2/VqFHDdE5pNV3Jy9tbR+LHSVKxN0nR86Px48p8jQnqu6c29d1Xm/ruq+3p9T25d0+v7+rey8LhsPT2229r/fr1ioiIUIMGDdSsWTObh6tUrFhRzZs319q1a23G165dq9atW5e4THx8fLH5a9asUYsWLeTj42M6p7Sarta0Yx9tb/22Tlhq2Iwft9TQ9tZvX/e1JajvntrUd19t6ruvtqfX9+TePb2+q3t3lMMXpZwwYYLp6+PGjbuuhswsXbpUSUlJmjNnjuLj4/Xuu+9q7ty52rVrl2rXrq3Ro0fr8OHD1luuZGZmqlGjRnryySc1cOBApaena/DgwVqyZIn1MgcbN27UPffco1dffVUPPvigPvvsM40ZM0YbNmxQq1at7OrLFTfS9eQrrnp6fU/u3dPre3Lvnl7fk3t3dX1P7t3T67u6d7s/vw07zJgxw7hw4YJhGIZx4MABo6CgwJ7FXGLWrFlG7dq1jYoVKxrNmjUz0tLSrK/16dPHSExMtJmfmppqNG3a1KhYsaJRp04dY/bs2cVqLlu2zGjQoIHh4+NjxMbGGsuXL3eop+zsbEOSkZ2dXaZtAgAAN569n9927Vny9vbWkSNHFBISIi8vLx09elQhISFOS3aezhV7lgAAgGvZ+/lt176siIgILV++XJ07d5ZhGPrtt99KvQdcVFRU2ToGAAAoh+zas/Tuu+/qmWeeUb7JpcWN//u6vTsvK+Au7FkCAMDz2Pv5bfcJ3rm5uTpw4IAaN26s//znP9av3l/tjjvuKFvHHoywBACA53HqYThJCggIUKNGjfTee+/p7rvvlq+vr1MaBQAAKM8c/v5dnz439toGAAAA7uTwRSkBAAD+TAhLAAAAJghLAAAAJsoclvLy8rR3717TywkAAAB4OofD0vnz59W/f3/5+/vrtttu08GDByVJw4YN02uvveb0BgEAANzJ4bA0evRobd++XampqfLz87OO33vvvVq6dKlTmwMAAHA3hy8d8Omnn2rp0qW66667ZLFYrONxcXHat2+fU5sDAABwN4f3LJ04caLEm+ieO3fOJjwBAADcDBwOSy1bttSXX35pfV4UkObOnav4+HjndQYAAFAOOHwYbvLkyerUqZN++ukn5efna8aMGdq1a5fS09OVlpbmih4BAADcxuE9S61bt9bGjRt1/vx51a1bV2vWrFFoaKjS09PVvHlzV/QIAADgNg7tWbp8+bIGDRqkf/zjH1q0aJGregIAACg3HNqz5OPjo5UrV7qqFwAAgHLH4cNwDz30kD799FMXtAIAAFD+OHyCd7169TRx4kRt3LhRzZs3V+XKlW1eHzZsmNOaAwAAcDeLYRiGIwtER0eXXsxi0a+//nrdTXmanJwcBQUFKTs7W4GBge5uBwAA2MHez2+H9yxlZmZeV2MAAACexOFzlgAAAP5MHN6z1K9fP9PXFyxYUOZmAAAAyhuHw9KZM2dsnl++fFk7d+7U77//rvbt2zutMQAAgPLA4bBU0nWWCgsLNWTIEMXExDilKQAAgPLCKecsVahQQSNGjNBbb73ljHIAAADlhtNO8N63b5/y8/OdVQ4AAKBccPgw3MiRI22eG4aho0eP6ssvv1SfPn2c1hgAAEB54HBY2rZtm83zChUqqGbNmpo2bdo1vykHAADgaRwOSykpKa7oAwAAoFziopQAAAAm7Nqz1LRpU1ksFrsK/vDDD9fVEAAAQHliV1jq3r27i9sAAAAonyyGYRjubsLT2XvXYgAAUH7Y+/nNOUsAAAAm7DoMV716df38888KDg5WtWrVTM9fOn36tNOaAwAAcDe7wtJbb72lgIAASdL06dNd2Q8AAEC5wjlLTsA5SwAAeB57P78dvijlH124cEGXL1+2GSMsAACAm4nDJ3ifO3dOQ4cOVUhIiKpUqaJq1arZPAAAAG4mDoel559/XuvWrdM777wjX19fzZs3TxMmTFBERITef/99V/QIAADgNg4fhvv888/1/vvvq23bturXr58SEhJUr1491a5dW4sXL9ajjz7qij4BAADcwuE9S6dPn1Z0dLSkK+cnFV0qoE2bNvrf//1f53YHAADgZg6HpZiYGO3fv1+SFBcXp08++UTSlT1OVatWdWZvAAAAbudwWHriiSe0fft2SdLo0aOt5y6NGDFCzz33nNMbBAAAcCe7r7P066+/Kjo6utjVuw8ePKitW7eqbt26uuOOO1zSZHnHdZYAAPA8Tr83XP369XXixAnr8549e+rYsWOKiorSww8//KcNSgAA4OZmd1i6egfU6tWrde7cOac3BAAAUJ44fM4SAADAn4ndYclisRQ7X+nq5wAAADcbuy9KaRiG+vbtK19fX0nSxYsXNXjwYFWuXNlm3ooVK5zbIQAAgBvZHZb69Olj8/yxxx5zejMAAADljd1h6b333nNlHwAAAOUSJ3gDAACYICwBAACY8JiwdObMGSUlJSkoKEhBQUFKSkrS77//brqMYRgaP368IiIiVKlSJbVt21a7du2yvn769Gk988wzatCggfz9/RUVFaVhw4YpOzvbxVsDAAA8hceEpd69eysjI0PJyclKTk5WRkaGkpKSTJeZMmWK3nzzTc2cOVNbtmxRWFiY7rvvPuXm5kqSjhw5oiNHjmjq1KnasWOHFi5cqOTkZPXv3/9GbBIAAPAAdt8bzp12796tuLg4bdq0Sa1atZIkbdq0SfHx8dqzZ48aNGhQbBnDMBQREaHhw4frhRdekCRdunRJoaGhev311/Xkk0+WuK5ly5bpscce07lz5+Ttbd/579wbDgAAz+P0e8O5U3p6uoKCgqxBSZLuuusuBQUFaePGjSUuk5mZqaysLHXo0ME65uvrq8TExFKXkWT9gZkFpUuXLiknJ8fmAQAAbk4eEZaysrIUEhJSbDwkJERZWVmlLiNJoaGhNuOhoaGlLnPq1ClNnDix1L1ORSZPnmw9dyooKEiRkZH2bAYAAPBAbg1L48ePt95GpbTH1q1bJZV8axXDMK55y5WrXy9tmZycHHXp0kVxcXEaN26cac3Ro0crOzvb+jh06NC1NhUAAHgouy9K6QpDhw7V3/72N9M5derU0Y8//qhjx44Ve+3EiRPF9hwVCQsLk3RlD1N4eLh1/Pjx48WWyc3NVadOnVSlShWtXLlSPj4+pj35+vpab/sCAABubm4NS8HBwQoODr7mvPj4eGVnZ+u7777TnXfeKUnavHmzsrOz1bp16xKXiY6OVlhYmNauXaumTZtKkvLy8pSWlqbXX3/dOi8nJ0cdO3aUr6+vVq1aJT8/PydsGQAAuFl4xDlLDRs2VKdOnTRw4EBt2rRJmzZt0sCBA9W1a1ebb8LFxsZq5cqVkq4cfhs+fLgmTZqklStXaufOnerbt6/8/f3Vu3dvSVf2KHXo0EHnzp3T/PnzlZOTo6ysLGVlZamgoMAt2woAAMoXt+5ZcsTixYs1bNgw67fbHnjgAc2cOdNmzt69e20uKPn888/rwoULGjJkiM6cOaNWrVppzZo1CggIkCR9//332rx5sySpXr16NrUyMzNVp04dF24RAADwBB5xnaXyjussAQDgeW6q6ywBAAC4C2EJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADAhMeEpTNnzigpKUlBQUEKCgpSUlKSfv/9d9NlDMPQ+PHjFRERoUqVKqlt27batWtXqXPvv/9+WSwWffrpp87fAAAA4JE8Jiz17t1bGRkZSk5OVnJysjIyMpSUlGS6zJQpU/Tmm29q5syZ2rJli8LCwnTfffcpNze32Nzp06fLYrG4qn0AAOChvN3dgD12796t5ORkbdq0Sa1atZIkzZ07V/Hx8dq7d68aNGhQbBnDMDR9+nS99NJLevjhhyVJixYtUmhoqD766CM9+eST1rnbt2/Xm2++qS1btig8PPzGbBQAAPAIHrFnKT09XUFBQdagJEl33XWXgoKCtHHjxhKXyczMVFZWljp06GAd8/X1VWJios0y58+fV69evTRz5kyFhYXZ1c+lS5eUk5Nj8wAAADcnjwhLWVlZCgkJKTYeEhKirKysUpeRpNDQUJvx0NBQm2VGjBih1q1b68EHH7S7n8mTJ1vPnQoKClJkZKTdywIAAM/i1rA0fvx4WSwW08fWrVslqcTziQzDuOZ5Rle//sdlVq1apXXr1mn69OkO9T169GhlZ2dbH4cOHXJoeQAA4Dnces7S0KFD9be//c10Tp06dfTjjz/q2LFjxV47ceJEsT1HRYoOqWVlZdmch3T8+HHrMuvWrdO+fftUtWpVm2V79OihhIQEpaamlljb19dXvr6+pn0DAICbg1vDUnBwsIKDg685Lz4+XtnZ2fruu+905513SpI2b96s7OxstW7dusRloqOjFRYWprVr16pp06aSpLy8PKWlpen111+XJI0aNUoDBgywWe7222/XW2+9pW7dul3PpgEAgJuER3wbrmHDhurUqZMGDhyof/3rX5KkQYMGqWvXrjbfhIuNjdXkyZP10EMPyWKxaPjw4Zo0aZLq16+v+vXra9KkSfL391fv3r0lXdn7VNJJ3VFRUYqOjr4xGwcAAMo1jwhLkrR48WINGzbM+u22Bx54QDNnzrSZs3fvXmVnZ1ufP//887pw4YKGDBmiM2fOqFWrVlqzZo0CAgJuaO8AAMBzWQzDMNzdhKfLyclRUFCQsrOzFRgY6O52AACAHez9/PaISwcAAAC4C2EJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADABGEJAADAhLe7G7gZGIYhScrJyXFzJwAAwF5Fn9tFn+OlISw5QW5uriQpMjLSzZ0AAABH5ebmKigoqNTXLca14hSuqbCwUEeOHFFAQIAsFovT6ubk5CgyMlKHDh1SYGCg0+pS3721qe++2tR3X21Pr+/JvXt6fVfWNgxDubm5ioiIUIUKpZ+ZxJ4lJ6hQoYJuueUWl9UPDAx0yZub+u6tTX331aa++2p7en1P7t3T67uqttkepSKc4A0AAGCCsAQAAGCCsFSO+fr6aty4cfL19aX+Da7vyb17en1P7t3T63ty766u78m9e3p9V/duD07wBgAAMMGeJQAAABOEJQAAABOEJQAAABOEJQAAABOEJQAAABOEpXJo8uTJatmypQICAhQSEqLu3btr79697m4LAIA/JcJSOZSWlqann35amzZt0tq1a5Wfn68OHTro3Llz7m4NAACXWLRokeLi4uTv76/Y2Fh98cUX7m7JiusseYATJ04oJCREaWlpuueee9zdDgAATrVy5UolJSXp3Xff1V133aV//vOfWrZsmX777Td3tyaJPUseITs7W5JUvXp1N3cCAIDzTZs2TSNHjlTv3r0VExOjzp076+zZs+5uy4qwVM4ZhqGRI0eqTZs2atSokbvbAQDAqXJzc5Wenq4uXbpYx5KTk9WkSRP3NXUVb3c3AHNDhw7Vjz/+qA0bNri7FQAAnG779u2yWCxq3Lixzp8/r8WLF+uf//ynli9f7u7WrNizVI4988wzWrVqlVJSUnTLLbe4ux0AAJwuIyNDsbGxysjIUOXKlTVo0CB17drVuqfJ29tbTZo0UZMmTTRgwACbZb/44gs1aNBA9evX17x581zWIyd4l0OGYeiZZ57RypUrlZqaqvr167u7JQAAXGLAgAG6dOmS3nnnHe3evVvp6el66aWXNGLECE2cOFHBwcE6efJkseXy8/MVFxenlJQUBQYGqlmzZtq8ebNLzu/lMFw59PTTT+ujjz7SZ599poCAAGVlZUmSgoKCVKlSJTd3BwCA82RkZKh3794KCAjQnXfeqTvvvFN79uzRpk2bTJf77rvvdNttt6lWrVqSpM6dO+vrr79Wr169nN4jh+HKodmzZys7O1tt27ZVeHi49bF06VJ3twYAgNPk5+dr165dio2NtRnfvn27EhISJEk5OTlq3ry52rRpo7S0NOucI0eOWIOSJN1yyy06fPiwS/pkz1I5xJFRAMCfwZ49e3Tx4kW98sorCg8Pl7+/v2bPnq3MzEwNHDhQkrR//35FRERo586d6tKli3bs2KHAwMASPystFotL+mTPEgAAcIuMjAyFh4ercuXKSkhI0D333KNDhw4pJSVF4eHhkqSIiAhJUqNGjRQXF6eff/5ZklSrVi2bPUm//fabdRlnY88SAABwi4yMDLVq1UorV64s8fUzZ87I399fvr6++u233/TTTz8pJiZGknTnnXdq586dOnz4sAIDA7V69WqNHTvWJX0SlgAAgFtkZGTo7rvvLvX13bt368knn1SFChVksVg0Y8YM67fdvL29NW3aNLVr106FhYV6/vnnVaNGDZf0yaUDAACAW9SsWVNz5sxRjx493N2KKcISAACACU7wBgAAMEFYAgAAMEFYAgAAMEFYAgAAMEFYAgAAMEFYAgAAMEFYAgAAMEFYAgAAMEFYAgAAMEFYAgAAMPH/AQQib1fxmMEUAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "failures_mean_b = np.mean(failures_b, axis=(0,1))\n",
    "plt.plot(np.arange(20), failures_mean_b, 'o')\n",
    "worst_b = np.max(np.mean(failures_b, axis=1), axis=0)\n",
    "plt.plot(np.arange(20), worst_b, 'o')\n",
    "\n",
    "plt.xticks(ticks=np.arange(20), labels=['2'] + [None]*18 + [r'$\\beta_{50}$'])\n",
    "plt.ylabel(\"Failure frequency\")\n",
    "plt.title(r'Matern kernel (length scale 0.2, $\\nu=1.5$)')\n",
    "_ = plt.legend(['Mean', 'Worst function'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "SE kernel, functions sampled using the ONB approach."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Experiment 1.2 c)\n",
      "\n",
      "0: 2.00 +/- 0.00\n",
      "\n",
      "1: 2.28 +/- 0.00\n",
      "\n",
      "2: 2.57 +/- 0.00\n",
      "\n",
      "3: 2.85 +/- 0.01\n",
      "\n"
     ]
    }
   ],
   "source": [
    "(scalings_c, failures_c) = load_failures_and_scalings('exp_1_2_c')\n",
    "scalings_mean_c = np.mean(scalings_c, axis=(0,1))\n",
    "scalings_var_c = np.var(scalings_c, axis=(0,1))\n",
    "\n",
    "print('Experiment 1.2 c)\\n')\n",
    "for i in range(4):\n",
    "    print(f\"{i}: {scalings_mean_c[i]:1.2f} +/- {np.sqrt(scalings_var_c[i]):1.2f}\\n\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This figure is shown as Figure 4 (right) in the supplementary material."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "failures_mean_c = np.mean(failures_c, axis=(0,1))\n",
    "plt.plot(np.arange(20), failures_mean_c, 'o')\n",
    "worst_c = np.max(np.mean(failures_c, axis=1), axis=0)\n",
    "plt.plot(np.arange(20), worst_c, 'o')\n",
    "\n",
    "plt.xticks(ticks=np.arange(20), labels=['2'] + [None]*18 + [r'$\\beta_{50}$'])\n",
    "plt.ylabel(\"Failure frequency\")\n",
    "plt.title('SE (length scale 0.2, ONB approach)')\n",
    "_ = plt.legend(['Mean', 'Worst function'])\n",
    "plt.savefig('figures/figure4_right.pdf')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Experiment 1.3: Model misspecification, benign setting\n",
    "The results of this experiment are reported in Table 2, upper row."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Experiment 1.3 a)\n",
      "\n",
      "Failures: [0. 0. 0. 0.]\n",
      "0: 6.53 +/- 0.038\n",
      "\n",
      "1: 6.97 +/- 0.035\n",
      "\n",
      "2: 7.39 +/- 0.033\n",
      "\n",
      "3: 7.77 +/- 0.031\n",
      "\n"
     ]
    }
   ],
   "source": [
    "(scalings_a, failures_a) = load_failures_and_scalings('exp_1_3_a')\n",
    "scalings_mean_a = np.mean(scalings_a, axis=(0,1))\n",
    "scalings_var_a = np.var(scalings_a, axis=(0,1))\n",
    "failures_a = np.sum(failures_a, axis=(0,1))\n",
    "\n",
    "print('Experiment 1.3 a)\\n')\n",
    "print(f'Failures: {failures_a}')\n",
    "for i in range(4):\n",
    "    print(f\"{i}: {scalings_mean_a[i]:1.2f} +/- {np.sqrt(scalings_var_a[i]):1.3f}\\n\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Experiment 1.4: Model misspecification, problematic setting\n",
    "#### 1.4a) Sampling with standard kernel approach"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Experiment 1.4 a)\n",
      "\n",
      "Number of functions with increased failure frequency\n",
      "[0 0 0 0]\n",
      "Scalings\n",
      "0: 6.11 +/- 0.03\n",
      "\n",
      "1: 6.64 +/- 0.03\n",
      "\n",
      "2: 7.11 +/- 0.02\n",
      "\n",
      "3: 7.54 +/- 0.02\n",
      "\n"
     ]
    }
   ],
   "source": [
    "(scalings_a, failures_a) = load_failures_and_scalings('exp_1_4_a')\n",
    "scalings_mean_a = np.mean(scalings_a, axis=(0,1))\n",
    "scalings_var_a = np.var(scalings_a, axis=(0,1))\n",
    "failures_a = np.sum(failures_a, axis=(1))\n",
    "\n",
    "print('Experiment 1.4 a)\\n')\n",
    "print('Number of functions with increased failure frequency')\n",
    "print(np.sum(failures_a/10000 > np.tile(np.array([0.1, 0.01, 0.001, 0.0001]), (50,1)), axis=0))\n",
    "\n",
    "print('Scalings')\n",
    "for i in range(4):\n",
    "    print(f\"{i}: {scalings_mean_a[i]:1.2f} +/- {np.sqrt(scalings_var_a[i]):1.2f}\\n\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.4b) Sampling with ONB"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Experiment 1.4 b)\n",
      "\n",
      "Number of functions with increased failure frequency\n",
      "[0 0 1 1]\n",
      "Scalings\n",
      "0: 6.96 +/- 0.04\n",
      "\n",
      "1: 7.41 +/- 0.04\n",
      "\n",
      "2: 7.82 +/- 0.03\n",
      "\n",
      "3: 8.20 +/- 0.03\n",
      "\n"
     ]
    }
   ],
   "source": [
    "(scalings, failures) = load_failures_and_scalings('exp_1_4_b')\n",
    "scalings_mean_b = np.mean(scalings, axis=(0,1))\n",
    "scalings_var_b = np.var(scalings, axis=(0,1))\n",
    "failures_b = np.sum(failures, axis=1)\n",
    "\n",
    "print('Experiment 1.4 b)\\n')\n",
    "print('Number of functions with increased failure frequency')\n",
    "n_func_reps = 100\n",
    "print(np.sum(failures_b/10000 > np.tile(np.array([0.1, 0.01, 0.001, 0.0001]), (n_func_reps,1)), axis=0))\n",
    "\n",
    "print('Scalings')\n",
    "for i in range(4):\n",
    "    print(f\"{i}: {scalings_mean_b[i]:1.2f} +/- {np.sqrt(scalings_var_b[i]):1.2f}\\n\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100, 10000, 4)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "failures.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.4c) Robust bound with sampling from ONB"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Experiment 1.4 c)\n",
      "\n",
      "Number of functions with increased failure frequency\n",
      "[0 0 0 0]\n"
     ]
    }
   ],
   "source": [
    "output_dir = 'exp_1_4_c'\n",
    "files = [f for f in os.listdir(os.path.join(output_dir)) if f.endswith('.npz')]\n",
    "\n",
    "# All runs have the same config\n",
    "n_rep_funcs = len(files)\n",
    "with open(os.path.join(output_dir, files[0]), 'rb') as file:\n",
    "    result = np.load(file)\n",
    "    n_rep_training = result['failures'].shape[0]\n",
    "    n_scalings = result['failures'].shape[1]\n",
    "    n_eval = result['scalings'].shape[1]\n",
    "\n",
    "# Load results\n",
    "failures_c = np.zeros([n_rep_funcs, n_rep_training, n_scalings])\n",
    "scalings = np.zeros([n_rep_funcs, n_rep_training*4, n_eval])\n",
    "\n",
    "for i in range(len(files)):\n",
    "    # with open(os.path.join(output_dir, files[i]), 'rb') as file:\n",
    "    # with np.load(os.path.join(output_dir, files[i])) as result:\n",
    "    result = np.load(os.path.join(output_dir, files[i]))\n",
    "    scalings[i,:] = result['scalings']\n",
    "    failures_c[i,:] = result['failures']\n",
    "    del result.f\n",
    "    result.close()\n",
    "            \n",
    "failures_c = np.sum(failures_c, axis=(1))\n",
    "\n",
    "print('Experiment 1.4 c)\\n')\n",
    "print('Number of functions with increased failure frequency')\n",
    "print(np.sum(failures_c/10000 > np.tile(np.array([0.1, 0.01, 0.001, 0.0001]), (n_rep_funcs,1)), axis=0))\n",
    "\n",
    "widths = [scalings[:,i,:] for i in range(4)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Means of uncertainty tube width over input space\n",
      "(Averaged over all 50 function\n",
      "$71.68 \\pm 5.36$  & $73.79 \\pm 5.36$  & $75.64 \\pm 5.37$  & $77.33 \\pm 5.37$ \n"
     ]
    }
   ],
   "source": [
    "print('Means of uncertainty tube width over input space')\n",
    "print('(Averaged over all 50 function')\n",
    "mean_over_inputs = np.array([np.mean(widths_delta, axis=1) for widths_delta in widths])\n",
    "output = \"\"\n",
    "for i in range(4):\n",
    "    # print(f\"{i}: {np.mean(mean_over_inputs[i,:]):1.2f} +/- {np.sqrt(np.var(mean_over_inputs[i,:])):1.3f}\\n\")\n",
    "    output += f\"${np.mean(mean_over_inputs[i,:]):1.2f}\" + \" \\pm \" + f\"{np.sqrt(np.var(mean_over_inputs[i,:])):1.2f}$ \"\n",
    "    if i < 3:\n",
    "        output +=\" & \"\n",
    "print(output)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SD of uncertainty tube width over input space\n",
      "(Averaged over all 50 function\n",
      "$6.54 \\pm 1.73$  & $6.73 \\pm 1.78$  & $6.91 \\pm 1.82$  & $7.06 \\pm 1.86$ \n"
     ]
    }
   ],
   "source": [
    "print('SD of uncertainty tube width over input space')\n",
    "print('(Averaged over all 50 function')\n",
    "sd_over_inputs = np.array([np.sqrt(np.var(widths_delta, axis=1)) for widths_delta in widths])\n",
    "output = \"\"\n",
    "for i in range(4):\n",
    "    #print(f\"{i}: {np.mean(sd_over_inputs[i,:]):1.2f} +/- {np.sqrt(np.var(sd_over_inputs[i,:])):1.3f}\\n\")\n",
    "    output += f\"${np.mean(sd_over_inputs[i,:]):1.2f}\" + \" \\pm \" + f\"{np.sqrt(np.var(sd_over_inputs[i,:])):1.2f}$ \"\n",
    "    if i < 3:\n",
    "        output +=\" & \"\n",
    "print(output)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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