{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "canadian-hampton",
   "metadata": {},
   "source": [
    "# Results for a 5D multinomial (incl. VD)\n",
    "\n",
    "This notebook produces the results of EiV and non-EiV models for data following a modulated, 5 dimensional random multinomial as presented in the preprint \"Errors-in-Variables for deep learning: rethinking aleatoric uncertainty\" submitted to NeurIPS 2021.\n",
    "\n",
    "\n",
    "This notebook produces Figures 4 and part of Table 1 of the preprint. \n",
    "\n",
    "How to use this notebook: \n",
    "\n",
    "+ This notebook assumes that the corresponding trained networks exist in `saved_networks`. To achieve this either run the training scripts described in the `README` or load the pre-trained networks from the link in the `README` into the `saved_networks` folder. \n",
    "\n",
    "+ To run this notebook click, \"Run\" in the menu above. \n",
    "\n",
    "+ To consider different levels of input noise, change `std_x` in cell [3]\n",
    "\n",
    "+ To run this notebook with a GPU, set `use_gpu` to `True` in cell [3] (default is `False`)\n",
    "\n",
    "+ Plots will be displayed inline and, in addition, saved to `saved_images`\n",
    "\n",
    "+ The content of Table 1 is produced under \"Coverage\" below . To get the different columns, change `std_x` as explained above.\n",
    "\n",
    "**Note**: Running the \"Coverage\" section below will take around 1h 45 min."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "higher-johnston",
   "metadata": {},
   "outputs": [],
   "source": [
    "import random\n",
    "import os\n",
    "\n",
    "import numpy as np\n",
    "import torch\n",
    "import torch.nn as nn\n",
    "from torch.utils.data import DataLoader, TensorDataset\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "from tqdm.notebook import tqdm\n",
    "\n",
    "from train_noneiv_multinomial_ensemble_seed import seed_list as ensemble_seed_list\n",
    "\n",
    "from EIVArchitectures import Networks\n",
    "import generate_multinomial_data\n",
    "from EIVTrainingRoutines import train_and_store\n",
    "from EIVGeneral.ensemble_handling import create_strings, Ensemble\n",
    "\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "89700d89",
   "metadata": {},
   "source": [
    "## Fix relevant hyperparameters"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "70eabc92",
   "metadata": {},
   "source": [
    "### Values that can be changed"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "4346c8f2",
   "metadata": {},
   "outputs": [],
   "source": [
    "# The std_x used for data generation and model loading. \n",
    "# Pick either 0.05, 0.07 or 0.10\n",
    "# For figure 4 in the preprint 0.07 was used\n",
    "std_x = 0.07\n",
    "\n",
    "# Switch to True if GPU should be used\n",
    "use_gpu = False\n",
    "\n",
    "# Uncertainty coverage factor (1.96 taken from the standard normal)\n",
    "k=1.96"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "lesser-brave",
   "metadata": {},
   "outputs": [],
   "source": [
    "# graphics\n",
    "fontsize=15\n",
    "matplotlib.rcParams.update({'font.size': fontsize})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "45e3d119",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Set device\n",
    "if not use_gpu:\n",
    "    device = torch.device('cpu')\n",
    "else:\n",
    "    device = torch.device('cuda:0' if torch.cuda.is_available() else 'cpu')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e5ffa66f",
   "metadata": {},
   "source": [
    "### Values to keep fixed\n",
    "The following values assume the settings from the training scripts. To change the following values, these scripts must be adapted and rerun."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "d99d560d",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Set further hyperparameters\n",
    "from train_eiv_multinomial import std_y, init_std_y_list, \\\n",
    "    precision_prior_zeta, deming_scale_list, dim\n",
    "init_std_y = init_std_y_list[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "micro-chest",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Choosing deming  0.2\n"
     ]
    }
   ],
   "source": [
    "# Fix the maximal Deming factor below std_x/std_y\n",
    "def find_nearest(a, x):\n",
    "    idx = (np.abs(a - x)).argmin()\n",
    "    return a[idx]\n",
    "\n",
    "\n",
    "def find_min_max(a, x):\n",
    "    idx = np.argwhere(a<x).max()\n",
    "    return a[idx]\n",
    "\n",
    "deming = find_min_max(np.array(deming_scale_list), std_x/std_y)\n",
    "print('Choosing deming ', deming)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "24199de2",
   "metadata": {},
   "outputs": [],
   "source": [
    "# function to fix seeds (for reproducability)\n",
    "def set_seeds(seed):\n",
    "    torch.backends.cudnn.benchmark = False \n",
    "    random.seed(seed)\n",
    "    np.random.seed(seed)\n",
    "    torch.manual_seed(seed)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "specific-divide",
   "metadata": {},
   "source": [
    "## Prediction (for a single seed)\n",
    "Produces Figure 4 from the preprint"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "10b4adf8",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Change this to take a different network\n",
    "# Choose an integer between 0 and 19\n",
    "single_seed = 0"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ec7a913c",
   "metadata": {},
   "source": [
    "### Load networks and data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "88ba4449",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load EiV model\n",
    "net = Networks.FNNEIV(p=0.5, init_std_y=init_std_y,\n",
    "        precision_prior_zeta=precision_prior_zeta, deming=deming,\n",
    "                        h=[dim, 500, 300, 100, 1])\n",
    "saved_file = os.path.join('saved_networks', \n",
    "        'eiv_multinomial_std_x_%.3f_std_y_%.3f_init_std_y_%.3f_deming_scale_%.3f_seed_%i.pkl'\n",
    "        % (std_x, std_y, init_std_y, deming, single_seed))\n",
    "net.to(device)\n",
    "train_loss, test_loss, stored_std_x, stored_std_y, state_dict, extra_list\\\n",
    "            = train_and_store.open_stored_training(saved_file, net=net, extra_keys=['rmse'], device=device)\n",
    "rmse = extra_list[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "21ea183b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load non-EiV model\n",
    "ber_net = Networks.FNNBer(p=0.5, init_std_y=init_std_y, h=[dim,500,300,100,1])\n",
    "ber_saved_file = os.path.join('saved_networks', \n",
    "        'noneiv_multinomial_std_x_%.3f_std_y_%.3f_init_std_y_%.3f_seed_%i.pkl'\n",
    "        % (std_x, std_y, init_std_y,single_seed))\n",
    "ber_net.to(device)\n",
    "ber_train_loss, ber_test_loss, ber_stored_std_x, ber_stored_std_y, ber_state_dict\\\n",
    "        = train_and_store.open_stored_training(ber_saved_file, net=ber_net, device=device)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "438a5389",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Generate data\n",
    "train_data_pure, train_data, test_data_pure, test_data, val_data_pure, val_data, func = generate_multinomial_data.get_data(std_x=std_x, std_y=std_y, dim=dim, n_train=10000)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "protective-warning",
   "metadata": {},
   "source": [
    "Cycle through different dimensions and plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "progressive-wheat",
   "metadata": {},
   "outputs": [],
   "source": [
    "set_seeds(0)\n",
    "\n",
    "# will be taken for all coordinates\n",
    "# except for the plot dimension\n",
    "cut_offset = 0.0\n",
    "\n",
    "# Plot EiV along plot_dim\n",
    "def plot_eiv_uncertainty(net, plot_dim, ax):\n",
    "    offset = cut_offset\n",
    "    steps = 50\n",
    "    x_slice = torch.linspace(-1, 1, steps=steps)\n",
    "    plot_x = torch.zeros((steps,dim)) + offset\n",
    "    plot_x[:,plot_dim] = x_slice\n",
    "    plot_y = func(plot_x)\n",
    "    net_train_state = net.training\n",
    "    net_noise_state = net.noise_is_on\n",
    "    net.train()\n",
    "    net.noise_on()\n",
    "    val_x = plot_x + std_x * torch.randn_like(plot_x)\n",
    "    pred, _ = [t.cpu().detach().numpy()\n",
    "                   for t in net.predict(val_x.to(device), number_of_draws=5000,\n",
    "                                       take_average_of_prediction=False)]\n",
    "    pred_mean = np.mean(pred, axis=1).flatten()\n",
    "    pred_std = np.std(pred, axis=1).flatten()\n",
    "    print('RMSE: ', np.sqrt(np.mean( ((plot_y-pred_mean)**2).detach().cpu().numpy() )))\n",
    "#     ax.plot(x_slice, plot_y, color='b', label='ground truth', linewidth=2)\n",
    "    ax.plot(x_slice, pred_mean, color='r', label='EiV', linewidth=2)\n",
    "    ax.fill_between(x_slice, pred_mean-k*pred_std, pred_mean+k*pred_std, color='r', alpha=0.2)\n",
    "    ax.set_ylim([-2.5,2.5])\n",
    "#     ax.legend()\n",
    "    if net_train_state:\n",
    "        net.train()\n",
    "    else:\n",
    "        net.eval()\n",
    "    if net_noise_state:\n",
    "        net.noise_on()\n",
    "    else:\n",
    "        net.noise_off()\n",
    "        \n",
    "# Plot non-EiV along plot_dim        \n",
    "def plot_ber_uncertainty(ber_net, plot_dim, ax):\n",
    "    offset = cut_offset\n",
    "    steps = 50\n",
    "    x_slice = torch.linspace(-1, 1, steps=steps)\n",
    "    plot_x = torch.zeros((steps,dim)) + offset\n",
    "    plot_x[:,plot_dim] = x_slice\n",
    "    plot_y = func(plot_x)\n",
    "    ber_net_train_state = ber_net.training\n",
    "    ber_net.train()\n",
    "    val_x = plot_x + std_x * torch.randn_like(plot_x)\n",
    "    ber_pred, _ = [t.cpu().detach().numpy()\n",
    "                   for t in ber_net.predict(val_x.to(device), number_of_draws=5000,\n",
    "                                       take_average_of_prediction=False)]\n",
    "    ber_pred_mean = np.mean(ber_pred, axis=1).flatten()\n",
    "    ber_pred_std = np.std(ber_pred, axis=1).flatten()\n",
    "    print('RMSE: ', np.sqrt(np.mean( ((plot_y-ber_pred_mean)**2).detach().cpu().numpy() )))\n",
    "    ax.plot(x_slice, plot_y, color='b', label='ground truth', linewidth=2)\n",
    "    ax.plot(x_slice, ber_pred_mean, color='k', label='No EiV', linewidth=2)\n",
    "    ax.fill_between(x_slice, ber_pred_mean-k*ber_pred_std, ber_pred_mean+k*ber_pred_std, color='k', alpha=0.2)\n",
    "    ax.set_ylim([-2.7,2.7])\n",
    "#     ax.legend()\n",
    "    if ber_net_train_state:\n",
    "        ber_net.train()\n",
    "    else:\n",
    "        ber_net.eval()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b08b228a",
   "metadata": {},
   "source": [
    "The plot in Figure 4 is for `dim = 3`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "neither-dryer",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dim=0\n",
      "RMSE:  0.23739706\n",
      "RMSE:  0.28432894\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dim=1\n",
      "RMSE:  0.26377413\n",
      "RMSE:  0.3419102\n"
     ]
    },
    {
     "data": {
      "image/png": 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XUrJ27Vrk/v0UtbfTBSxdtsxojx4OGx2avF4j4BcWjj7g+3ykXn2dx3bN5Md/KuOVtw7le5kxpZdT5rWxam47K+Z0UOCJTci+DUVKaOtxsqfZy550yW3X/gL2NOejy4G/2EJPlOWzO1g1r41V89qYVtmnAv9Jqi9kYd2uMtZuL+ONHWXsOeAd8v97fl03s6b2Zu/4plX2TcydnpSYe3sJLF+OtNmIRqP09fVht7vZv7+Y9es9rF/vYeNGN5GIcaHIz09y2WWdXHllBzabj3A4jMvlwuPx4HQ68Xg82KxW7G1tOKxWTLNnH/vtniQq0B+l7u5u1q5dy7S2NpCS7lCI+fPnD2yWGAoZk8sFs2YZnZ6GqyfUdUKtffzuTh8/eaCcfQeNh61uR4zLz97DR9+9m8riE+9ZdShqZmt9EZv2FmdLeYPrX4vzI+mg386p81uZUhKapK1VRhKNm1i/q5S128tYu72cbQ2FAwK72aQzt6aHRdO7WDyjiyUzOplSEjquF3JTTw/R6dNJlJcP+x29u49X/xzh/15cxpb9xvcsFp0LL+zh6qvbqasLZNMypCIRnI2N2Lq7cbndzPz4x7EUFR2v3ZlQKtAfBSkla9asgXCYkh07SBUW0uv3U1NdTWVl5eEzRKNGD1ebDWbOJFFUxMHOTqqnTEGk28q/9GSYj3xvAS3dRpCsmxLjk++tZ2Xdi1RVHp7F8USVqbN9Y0c5a7eX8fr2crr9A1sITav0c/rCg5yx+CArZrdjs6qOMJNFSmhq87B6cyWrN1fy5o6yAc9+zCadRdO7shfqRdO7Jv2ZjIjHIZUitHTpsL3FXZs3G3l5zBY2bXDw29dO5d/rq5DS+P7VV7fzmc+0YI8HcO7aBYkEen4+gbY2PEVFzPrYxzCNJoVFIGAkGTxBqUB/FDo6Oli3bh1VUmKvrydVUEAkEsHhdDJ3zpzhZ4zHwe/HHwyyobGR+RUVFOYX8e2/zeI7f65D1wXL5oT4ynVtvP8sH1u2bgLAfhI3D5MS9h3M54100H99W/mAun67Nckpc9s5Y3ELZy1uoapUlfYnWjRuYu32cl5+q5JXtlRyoGNgoJpb08NpC1pZNa+NpbM6cdmTk7SlwzP19BBetIjUEEHWun8/tuZmUv36g2h9fezv9vLbjWfy0D+nkEoJ5kz389MPPUpNTQy9X3PlUH09rtNPZ8455xz5wW1nJ2zYAKtWGdW0JyAV6MdJ13VeeeUVTCYTRbt2GZkBbTaSqRTRSISVK1eOuIz9DQ20NTTQHCzgx49czprNXoSQfPX6Nr7xqYOYzRAIBNi0aRNFOXILmZFICjbtLcmWIHc2FQ74fPqUXs5e0sJZS5tZXt6Ao7ONVDqjo5zkgS1EIoGlowNLVxep/Hxi5eXIoVI1H2PJVIpQNEooEiEaClFZWIjd4RiYQngEbT1OXnprCi9tnMK2bU6mJXZTQidbWYDPVcE7F7ZxxuIWTlvQSon3xG9GawoESBQWEp0xY8D7WjCI6623jCA/6GmviEbRQiHeTCzlf360jOZ2Nw5bgq9//A3ef3rDoS/G4/S1tlLw/vcza8GCoTcgFDJyUElpNLpYMWQsnXRHCvRqbLIj6OjoIBQKUZaXhxYMkio0ApXZZMqOnDTSABg9fj+vNi3hm787k76wjcriOH/6TgPnrAhmv9Pa2nrSdPQw+f3Ym5qwNzZib2zEduAA2uBMmumc8BGnE1dJCbNKSnjvykJ2nV7KmwdL2NNcTWj/cpa3bGN5y2qWPrGaeWwbsJ6Uy0XC6yXp9ZIsKDBeCwtJFhSQKCgw3svPH/Y5iEgksHR2Yu3owNLebrx2dGAKh9EdDlIuFymnE93pJOV0Is1mrB0dWNvasLa1YensPJSyNy1RUEC8vDw7IQSmQABTIGA0k/X7MfX1YY7HMUmJSUoj9XE6HbBMp2oOeL0ctFrZnUqxKRxma28v+ZEIVbEYNakU04GZQBWHd12XQoCmkXK5iHm9BFwuumx2dkUcbPTb6PHbqYnYWYmf69hLDfsHzJ/ERSxQS/RADb36FBqcToKxGLFQiFg4TDwcJhmJkIxEyBOCEpOJQiHIlxJPKoUzkcAspZHpUwjjVdOQmka8spLuiy8eeybPEaRcLiwdHcRqarJjAaDrOPbtQzqdQ/ZnkXY7KauVlf5NPPr57Xz94Qt44vU6vvzrd7JmawVfv/YNXA4jDbg3L4+WV17B5vFQU1MzcEHJJLz1lpGeweMxOjb29R1VqpLJoEr0w0ilUrz88svYbDbcPl+22ibD5/OxYMGCIzbdisaSfOzLdh56eTEA71zQyB2ffoPTTqnLjrQUjUZZv349BQUFx7TNr67r/PnZZ6kuK+OsJUtGNY/lvvuofeEFdLPZ+AE5neh2u5EHXtOwNTdj8fmOartagARQO+j9KDZ2MocCfFTQipVhusj3I/vli5cwYLL0yx8/HjpGj75GoAyYARzvS3EK41iZ0tN4uufFhKAjL4+ky0VxVxeefiNoTYTA0qW03HTTMb8jM/l8RGbOJJnukW45eBBHYyPJUabwkBIeXj2N239/CpG4meqyPu6++WVmTe01UmF3d9NYVcWSM86gPPPgV0oj505rq9FfBoycVAUFRpbNE4wq0Y9Da2sr0WiUvLw8rB0dA+r1wBhYIvP5UKSEm75fxUMvT8FsSvGFD23kYxfspKenm5aDNqZWVQHQ2dmJlhksY7wyqYv7+elDD3HvY48B8N0bbuADZ5xxxEW0bNzIWc8/b5wQmXz3vb2HfS9usdBZUkJHSQltRUUcyMvj9eZm3ti+nd5wODvIhsNiYWVREQtSKeYmk8yKxZgejTIlnZXQD7wKvAysBnbaTbjyTLT7kiQSCYqACqASI39GZb9/Z6ZSKdGGyZmSBPYD+9JTPdBitdItBOZYjALAC9lXB9AA7E5P9YDZbqcwL49YIkEwGKQ0kWAWMAujxK0DnUAX0Gc2E3e5SLrdBIWgIxCgMxAgouskMQK2HaNL+EK7nVX5+cy32aiVksJkklRREYnycvTKSpLl5cTLykgUFRFOJNje1MRbe/bxyqb97GzcRzTaRhEwFQtVFDEVD3UmM7PtCZy2GLtMMV7u8/NGLMY+KUn5/UaASh+3ZcByYIUQLNA0hKaRNJnQTSZS6QFLdLOZkKbRA3SlUrQnk7TFYjRHo4R1PXvxyUx5QnA7ULBxI4FbbuGHCxbgzM8n3+2mpqyM81euxHwUvVV1pxNbczPJ4mK0aNQI8mMoVQsBl55Zz5IZXfz3z85g14ECPvH983jgG08ZLYmcTqb09bFxwwaWLV+OyWQisXcviU2bCDochBob0YRg8aJFmNvaTvgHs4OpEv0Qent7ef3118nPz8em67jXr89W22SEQiHyvV5mDqo3zPj+fWX8z8+qsJqT3PvFf7NybgdglLR7fD4WzJ+Px+Nh3bp1uNzucf8IXFu2MOVnP6PvlFNou+460DT++cor/M+vf50d01QTgh/ceCMXn3rqkMvY09wMX/sa70smedjt5s6SEtqbm7EkEngAD0aQ2gXsZdCISf1MLS3lzMWLOWvJElbOmYNtcKlO17F0dKAlEnQVFLB2505e27qVV7duZX97e/ZrVrOFEm81mjaXnr7lhKJzMUJqPVCPzbKHlN6ATEWwYnS/dtts5Dmd5Dud5DkchDWN3kiEvnCYQDhMMBLJLt9iNlNeWEhZQQFl/V5LvF6KvV5KvF5K8vNxDqqTjycS+EMh+kIhAuEwVouFAo+HAo8H+xAlWF3X8YdCdPX20un3k0gmmV1dTdko7t6khP0dbl7bWsGarRWs3V5OIJxZRwcmLcXy2ZKzl7Zy1pIWassH9l+QUtLc2cm2hga2NTTQ1tNDZXEx1aWlVJeVUV1WRonXO+axgaWUHOzqYteBA+zav9+YDhxgf3s786XkOYw7oBeB9wKZCsoPn38+t15zTXbnXFu24HnzTXouvJD4lCmjWre5p4fg4sXYm5rQwmH0cQ5SEotr3HjnOby+rYK6Cj9//vrTeN1xzN3d+Orq6LZYsASDeHfuRBYWYrbZMFss9Pn9LFq0CE8qZZTwFy8e1/qPKBzOpkMZK/Uwdgz8fj+vv/46brcbu92Opb0d+969hwX6ZDJJPB5n+fLlhy3jL08V8JFbpyGE5Pv/8TyXvLNtwOfxeJxIJEJVVRVNTU0UDlr2aJl7eqj76lcxB42fU++ZZ/KvM8/k43fcQSKZ5GvXXktvMMj//v3vmDSNuz7zGd416EHSvpYWfvatb/FUOExUCPb98IdoZWUkUykaWlvZ0djI9sZG6g8eBIwMhCZNw5x+NZlMzK2p4awlS6irqBj3ncmBjg4aWlupLi2lqrQ0e+GTEnbuL2DN1grWbKlg/e5S4gkTxuWmE7MJFk5Lsnx2D8tnd7B0Zid5rsNL+SldJxSJkNJ1vG73Cdc1PqUL9hzIZ/3uUtbvKmXD7lI6fAN/8DXlfbxzQSunLmhl1bx23I6Rq7eOl3A0ysHubmRjI+f+8Y+4QyGaior44bJl3PPCCySSSe74j//gw243xQ8/jKO+HoDQvHns//KXR7UOU18fKacTs99P8igbLgTCFj72nXez+0ABy2Z18NsvPYddxBDRKOF583Bu324MW9nv2Vmv309tTQ0V5eVGK5wzzji2I2J1dcG+fUbLnnFQgX6UMkHe5XJlM0a6Nm+GVGrIFhc9PT2sWrXKGNs07YV1bi64aSaJpMbNl67mhg80DhlUgqEQkXCYvLy88T2ITSap+d73cO7eTWTaNGzNzWjxOL+3WLgukeDqd72LW6+9FiklP33oIe755z8xm0z87y23ZOvsG1pbufY73+Hhvj5OB9re8x58H/rQ2LflOMp08lmztYI1W8vZfaAg214aQAjJrKpeFs/sZG6NjznVPcya2ovDduLk6JESWjpd7NxfyI6mArbWF/HW3pJ+JXaD1x1l1bx2TlvQymkLTp7OZ5b2dqrvuANrVxfRmhruPu00Xr3/fr4hBMvS8Sbp8RgDoCcS7PvBD4hXVIy8YF3H0tlJoqjomDzwbetx8uHbLqCtx8W7VzZx502rsfh92ec+g+8YotEoNpuNefPmGdWapaWwcOFRbwdgDLG5erVRBXv22eNahAr0o+D3+1m7di1OpzMb5EU0OmS1TYbP52PRokW40yfElr12Tv/EHPpCJv7rimauPv0fRyytj6bVznBKHniA4ieeIFFQQMN3voPct4+au+7CLiX/KChg5p13Zi9AUkp+cP/9/P7JJ7FaLPzi85+nsriYa2+/nXf29vIwkPB4qP/xjw97FnGi84esvLWnhPW7Sli/q5Qt9UUkUwOrwTShU1fZx9waH7Om+phaGmRqaZCqksCQpf9jJZEUtHa7aO5wc6DTQ8PBPHbuL2BnUwF94cMv7pXFQZbP7mD5rA6Wz+44qdNJmLu6qLnjDqzt7egWS/ZZSoemEb70UqIXXED5n/6E96WX6L7wQjo+8pFJ2c49B/L56HcuIBC2cu2FO/jS1W+iRSLoLtdh39V1nb5AgFWnnIImhFGqP/NMozf8UPqNWTyiXbuM0rzTOSGBPrcfxkppDLS9f7/RLMpiMXqsWq3Gq80GTid9Dgdr168fEOQBzH7/iP9J0XRSpuZ2CxffPJO+kIkr3tXDrdduoaHhyPWfQwX53z7+OI+tWcO1F17I+08/fcg6VPfGjRQ/8QRS02j5r/8i7nbzmX//G4uUPAZc6vPRc//9tH/0o8ZA3ELwxauvJh6Pc//zz3PTXXfhcTrx9fbyE6sV4nG6P/jBky7IA+S74py1pIWzlrQARol/a30RWxuK2NlUwI6mAuoP5rOvxcu+Fi/G49BD8lwxqkqCTCkO4XXHyHfHyHPFyXfFyUtPZu3w3rwSQThqpi9kxR+y4g/Z8Aet9IWtdPgcNHd4aO12HpYrJqMoL2LccdT0MLfGx5KZnVQUnXhpL8YrWVxM0623Un3HHdhaWogXFPBDIfhOTw8rd+/ml+99L75zz8X70kt4V6+m84orkFYrTe3tPPDcc8yrreWS006b8Cq2mVP93H3zS3zqB+fy+6fmUl4Y4tqLdg75XU3TkLpOJBLB5XIZ8aSpycid3J+U0N0N27cbwyMuXHjklOZ9fVBfb7TmiU1MTqvcDPTRqDEsX3298W+73TiIum6kF45EjMGIUylCvb3s3reP/NmzMQ8qfVvb2wcEv2Qqxd7mZuak29qazWYCwSBWeykX3zyD5nYrpy8J8IfbGmls6BlzaT2eSPDKI49wUSzGL+69l/ufe46vfOxjLJk5M/sdc1cXFffcA0DnFVcQnjWLOx94gBffeos8l4stV13Fsj/8gcJnnkGaTHRcfXU22H/1mmuIJRL84+WXicbjfLe0lJqODmLl5fjOOWe8R/uEYremWDGngxVzOrLvReMm9jbns6OpkH0t+TR3umnudHOgw01fyMb2kI3tjce+s5oQkooi4+5hSkmQ6rIAc6p9zKv1UZwfOWlL66OV9Hpp/PrXcezZQ3jePFb5/di/9jVWb97Mzx9+mM9cdhmRujocDQ0knnuOb7S08M9XXiGVbpn13Lp13Hb99XiP0Lolnkzy4AsvUN/SwvXveQ9TxjEg0Kp57Xz3htf44i9P5wf3L6e8KMwFp+wf8rtCiGyiNPLzjUBfVweZOBEIGKXzjg6jrX1Li3FBmDt36EKjrsPWrUZJ/liNbzHUdudU1U00ahzkgweNg5aXZ5Teh5FMJtm4cSMWKXHF4yTz84nW1aG73UNW23zrvvt44Pnn+fnnPsc5y5YRi8UQQvCrf72XX/29hDm1EV797S4K8pKsXbt22PSrw3lp40bOuvNO5mI0D3wQ+AlQ9s538vkrr6QsL4+a22/HuXcvTXV1fLmujhc3baK1uxuzycS9X/wiq+bNw71hA1V3341IpfCdfTadl11GKt1tO6Xr/PTBBwl0dfHHbduwBAI0f/azBEbRyzfXSAk9fTaaOz0c7HLhD1rxh6309SudB0JWUvrQEdlhS5LvjpPnipHf7y6gKD/C1NIglUUhrBaV26e/NVu2cMMPf4guJb/4/Oc5q7mZeX/7G68DpwImTeO85ct5dcsWQtEoJV4vt3/qU5y+aNGA5ei6ztNvvMFPHnyQAx3GRd1msXD9e97DJy+5BMc4nnv99vF5/Pivy3A74jzxg8co8UYO+044HMbj8TBr1izjjZ4emDoVamuNgmVTk1GwzDT9lNII+jNmGMkOB9u/H7ZtM+r7k0mjEKrq6EfQ3g5vvgnpXosj8fX2sn3btmw9uhYOo0UixCsr0e12bI2N2U5SHT4f7/rc50imUnzk/PP56jXXIKXk1bfs/Mddl2PSYNP925k3LUokEmHDhg1jbk1z7513cufGjcQ1DQsg0iWb14BfmEx8tKqKC5qaOAAsAXrS8xXl5fGlj3yES047Lbssz7p1TPnZzxCpFLrFgu+88+h+z3uyAb/473+n5JFHCM+YQdPXv350g6coyhjc889/8pMHH8Rhs2FJJGjSdbzA55Ys4YKPfpSasjJaOjv50q9+xYbduwH46Lvfzeevugq71cobO3bwo/vvZ2uDkcpgWmUlM6ZM4Zk33wSgvLCQL3zoQ1z0jneMqepHSrjprrN5YWMVF7+jkR/91yuHfSeZShEJh1m5cqWxbF036uozD4eHSMeArhvBfv5844KQEYnAyy8buXPM5gkN9LlXdZN+Yj4aXZ2dWPtd+XWnE93hwNzZiSkWI9nvlvGPTz9NMmW03Nje2AhAStf4wV/PRkrBFz7WyrxpRt6QcDg85rrFRDJJ7datABxctYrEVVdR8Nxz5D//PKdGIpyaSkFTEwngSqCyro4PLVnCWUuWML+29rC6/MCKFTTcdhsl//gHng0bKHrqKQqefx7fuefiP/10iv71LwA6PvQhFeSV4+pT730vW+rreX79emJCsLqigve2tvL1wkLa0iOtTSkp4fdf/Sq/ffxxfvaPf/CnZ57htW3bmFJczMubjASAJV4vN116KR8880zMJhMbdu/mu3/8I9sbG/nCL37B/c8/z5c/+lHm9Q+uRyAEfOVjb/LatnL+9Xotl565l9MWDmwabTaZSCaTRGMxYzwKTTOqcMzm4VsCaZqRtnzbNuM7xjiIsGPHkec7hnKvRL9xo3FQR5BMJnlz3TryPJ4RO40EIxHOvfnmbKcbu9XKG/fcw1+enc8df15BdXmEHQ/twGk3juW+ffvo6enJtsYZjVc3b+aCH/6QqUDj175GJH2bJ6JR8l99Fcdjj+Ht7uaZU0/F/uEPUzKGDHq2xkZKHnkEz/r1A94PLF9O8y23jHo5inKshKNRHl+zhhVz5jBHSqb/z/+QstvZe/fdhzUK2NbQwJd+9atsXw6X3c4n3vMerrnwwsM6taV0nX+89BI/efBBfIEAYNzx1pSXU1dRQW1FBbXl5UyvrKR2mCadv3l8Hnf+dRnVZX08+t3HD0ut7fP5mDNnztj7vySTRlv5FSuMq8q6ddkhRLOfqxL9sRUIBtFTqVH1DPzbv/9NMBJhxezZtPX00NzZyRs7erj770bPuG9e/xZO+6FnAT0+H/YxZjo88OyzTAW6nU4i/R6+Srud3vPOo/ecc+gIBJianz+m5QLEamtpvuUWbE1NFD/yCHnr1hkPaq+8cszLUpRjwWm3c+W55wIQB0KzZ+PatYu8NWvoPe+8Ad+dX1fHg9/6Fr/+5z9JJpNcd/HFFA3zOzBpGleccw4XnHIKv3j4YR588UW6+/ro7uvLVgNlXHHOOXzzuusOu/u+5sKdPPrKNPa1eLn38QXcdOnmAZ9bLBb8fv/YA73ZbGS/3LDBeEB7HNMdv20DfUd7+6g6KsWTSf749NMAfOKSS3hk9WqaOzu5669JwlEL5yxtZOWs3YCR4jQWixGPxXAP17Z2CMlUitptRvbG7pUrh65K0TRS4wjy/cVqami5+WY6W1tB14kPNXCKokyC3vPOw7VrFwXPP0/vuece9htw2GzccsUVo15ensvF/3z0o3zxwx+m3eejobWVxtZWGtvaaGxt5c2dO3nwhReoLi3lE5dcMmBeq1nnGx9/g2tufzf3PjafS05toLYikP3cbrfT3d1NXV3d4NWOzGIxqnpiMaN593Eyce15TmDJZJKenp4BbeaH86/XXqPd52P6lCmcsWgRC9L/udsaG3HYEnzlY+sIBoNkqsDCkcOf1I9k4/btvC/docR0/vljnn+s4hUVo84voijHQ2DFCpIeD/YDB3Ds3XvMlqtpGhVFRZy2YAEfPv98vvKxj3HPF7/ID268EYA7//Y3nhuiqnjFnA4+cMY+EkkT3/79KQOycJvNZuLxOPHxZgK12Y57muO3ZaAPBALouj5itY2Ukv974gkArr/4YjRNY+bUTBKz9dx06WamlETRdZ1YuqNDn9+PJZ0zW083ZXx+UN34YG1PP00R0OLxEK+uPqp9U5STkbRY6D3rLAC8//73hK/v/JUrueWKK5BS8qVf/jLbwKK/L3xoA/nuGK9tq+Bfr9ce9nk4fPJ0cHtbVt10dHSMqtrm5U2b2NvSQmlBAe9JN118fdtFwO0I3uKqc7cCJqSUxGIx7HY7Pp8vu+zXtm3j1//8J1aLhUduv33Ihz+6rlO3fTsAvlWrMJ1MLWBSKbR4HJFMIs1mpKYhTSZjMJDR7kdmGfG40QytH8GhTJlCCGQ6ha40mQ6t50ikNHKNpwf/yPybzLI0DTLL0jTj82QSkUigJRJIKQ9tgxDG8oQw5knvb3Y9me3M/FvK7CT6/XvwYB3ZV8gOUJLdZl0/lCk0PeCIzHSp1zR0q3XkY4Ax7qoWixnph+32E7aVVe8551D0xBPkrV1Lx4c/POTQgcfSp977XhpaW3n0lVe46a67+Otttw1o5FCYF+O/r9rI13/7Dr7/5+WcsaglmzLDZDLR19eH9wQdVnCwt12gz1TbHGnAkIzfpZsgfuyCC7CazdQfzONPz7wDmIFkL03tzcytqUHTNMKRCE6Xi3A4TEG67f2adHPJeCLBN/7v//jdl7982F3E5m3beG+62sZ24YWcUCN2ZoJO5jUdBDNhQrdYSHk86Ha7EaxjMSNIBoPZ4JcJlEO9ZpeRl0eyvBzd6TQCl64fmj/9b5FKGUmwolG0SAQtEkFkctELMWA0KJkOykIIdIsFabGQcjjQrVZ0mw0tmTRGxUok0GIxTJGI0WNaCHSnk0RBAbrLhW63I202pBDGvqfny2yHiMUOBXsYMNyf7BfIMZnQ0/8WqZRxjJJJY/3pYwpGqVZ3ONAtFiOIWyxIk8m4OGVGqkr/W4vHMQUCiGQyu27dZkNardnAnrlw6g4H8ZIStHAYS2+vMQKYw3Hsgr6U2e2TR1HvnCgtJbRwIe7Nm8l/5RV6Lrro6LftCIQQ3Hb99Rzo6GDD7t3cdNdd/P6rXx2QcvrSM/fy8MvT2LinlLsfWsKt1xpt9W02Gz09PVSfJHfgb7tAP9pqmy319byxYwcuu50r0+kBfvzXpSRTJqaWzuZAx162NTQwt6YGq9WKv7cX16A80plAbzaZeHPnTv7x8stcPqjpVM9TT+EG9nm9JPs3tZokJr/fCOqZYGU2GyVBqxU9L49UXh7SbjeCYGZYt6EkkwNLqINepdU68jJGkll+mhwctMZyZzFCAqrMZeTEyYGJcTGLx40LXzCI2e/HHAySdLuJl5Whu93G6GD9jnE0HsfU14elsxNzerQwIQQys/8ZmYslw48/cOirgpTNBlKiBYPjzhMP4DvvPNybN1P49NP43vWuozs/RsFqsXD3zTdz1Te+wZb6er5yzz386D//E03TSOk6PX19fOTdf2HT3mn85blpfOTdedRV9GGz2fD5fCSSSSzHoR380Trxt/AYG221TaZu/qpzz8XjdLKjqYAXNkzFbk3yvncW8vOHYWtDA5effTZWm41AIEAgEECkLyBdfj+79u/HZrHwtY9/nFvvvZcf3X8/Zy1Zkr091HWd6Tt2AOA/9VQmPaVYuqojuGKF8QM7mtJe+gIxob00MtUux8IE5hkZSiqVIpVKoev6Ya+6rhvVRpmBYzQNi8WSnbJpsYVA2mwkLBZ0t5tUSQlSSsxm84DU2f1Jq5VkcTHJ4mLjYtzbi4zFkCYTuhDGnUf6DkQKcWgUKSnRMKqXkNL4v03fLWXOFS0YxL1pE3qmimscgkuWEK2qwt7cjPeFF/C9+93jWs5YFObl8Yv//m8+fNttPLV2Lbv27ycYidDt9xv7kuXkZ39/mR/f1Jd9JxIOYzkJxo99WwX6xCirbfa3t/Psm29iNpn42AUXAPDrRxdwEf/ip85bibY7eAXYnh48ITNYeGdnZ7b9/Ovp5pIr5szhg2ecwdNr17J682Zu/8Mf+MlnPwvArm3buCSRIAW4Lr6YY50VJRaLEQgE8BYUjG4Eq3CYTikJ+P0IIbBardhsNqxW65A9faWUpFIpkskkyaQxBGAyOfrKp0wwM5lMWK3WbHBKJpPZ5erpEnsm6AkhMJvNmEwmzGYzQojs+pPJJEN1ABw8b+a9wa9SyuyUCbaZaajlDeVIn/X/TiZoW61WnE5ndv8z75lMJkwm4/lPNBolGAwSCoUIhULE4/EB6zCZTNnlmUwmwuFwtnFAhtlszl5E+m+j2WzGVlCQHc5S0zQ0TcOsaUgpSSQSRNMtTPR+d08kEohkEruU2NL7o7vdxEtKMPv9A0r1mWM/KppG5+WXM/UnP6H40UfpPfPMIceCONZmVlXx45tu4j9//GMaWluz7xd6PJR4vbT7+ugN+nnqjd3c3O6muiyIEIJgMDhkPJFS0tDQgBCC2traSR/o5m0V6IOjqLaRUvLLRx5Bl5L3nXYaZYWF7DmQz4tvlrOHM6juPQBr4C1gV2Mj3r/+ldBpp4HbTSQSIT/d1j1TbXPq/PkIIfj6ddfxvv/5H555802eX7+e85Yvx//kk1iBrUVFmI7ioY4WDqNFoyT7deBIJpMEg0Fqa2tpamoi3+s9YrDXdZ1QRwdlZ57JvEWLCIfD9Pb20tvbS3d395DBDsheDLxeLx6PB6fTmb04ZLJ3DnWSJxIJYrEYsViMUChEIBAgFAohhCAvLw+Hw5ENgBaLBSEEiUSCRCJBJBIhGo0Si8VIJpO43W5cLlf2+5mgqev6gItAPB4nFouRSqey6B/I+190MlPmgpI5XwbvRyYwZr6Tee0/BnD/efp//2h++Jn9OtKyUqlU9vjGYjGCwSBms3nAMep/cR3tejMX4EgkQigUoqenB5/PR296fGGTzYa3o4NEPI5IXyxEukrMO8p+IMFly4hMn45j3z4Kn3mG7ve9b9TbOBq2xkaKH38c3znnEJ4/P/v+mYsX88877iAQDlNaUEBRfj7W9PH57RNP8OMHHkDKp7n3sVv59idfzza+qByiP0praysHDx5EYtTnD/Wd4+ltFehHqraJJxJ87be/5bFXX8WkaVx38cUA/PqfC/kkv6GaA8QqKwnPmUPqxReZrevw+OPw+OOUl5fTsXIl8QsuIJmXx2vpQH/aAqMj1ZTiYm654gq+96c/8e3f/55T5s5l1k4j73XgtNPwHsV+adEoevohnLRaSaVS9Pr9zJ0zh+LiYux2O7t27SI/P3/IH7au6/h8PuoqK6lctgzh8VBQUMCUdFt7PZ2DW9f1AQFwLJk5BzObzaPqx6AcTtO0EVNgm0wmnE4nznGOPzrcejPVSA6Hg8LCQqZOnQqQvQALITBPmYLW04NWWIhJ09B1nR07dhAIBPCMpiWNEHRccQU1d9xB0RNP4Dv33KOq98+SEu8LL1D2pz+hJRI4t22j/o47BnREnDZMQD5z0SJ+/MADwFM8svo3fPoDW6goNAYiGVx47OnpYV99PQXpwtu++npsNhtFRzn84dF427SjT4zQScoXCHD9HXfw2Kuv4rDZ+OnNNzOzqor6g3m88HopX+V2wMgB33bddXxi1SreBayfNYuk242zrY3axx5j5s03U/j977PM56PE42FW+ocAxgDJi6ZPp8Pn41s//CGnJhJEAW/6gjIeIpFAt9mI1taihUJIKent7aWutpbi4mIASkpKmDt3Ln6/n0Ri4IhKqVQKn89HTVUVlbW1iCF+UJqm4XK5siX2TNWComRYLBby8vLweDw45s/HBljSdzhms5lZs2YhNI1Ivw6FWiSCNkxb9PD8+YTmz8cUDlOUfl52NEQ0SuWvf03F736HlkiQzM/HHAxS/sc/jmr+GVVVlBUUAO2k9C389vF52YFI+renDwaDRqEqLy9bGMrPy2Pnzp0EgsHhVzDBJizQCyHmCSGeF0KEhRAHhRDfEkJMWnQ4UrVN/cGDfOib32TD7t2UFRTwx1tv5dxlywC4558LuIF7qKSVaE0NgfRg4POmTeN54I7KSvb87/9y4POfNz6TkvJt2/gXsC0Wo/Thh3Fu347twAGsfX18++Mfx2wyMXPvXjRgc0nJYQMM9/r9o+6MoYVCxCorSRYWGp1OOjuprKzMlsYzioqKmDdvHoFAIBvsk+kgX1dXx1SvF1FZecK2sVZOIm63kaHR78++ZbPZmDtnDrFYjEQiYTSPTTfJHU5HOuVB4TPPYE5XDR1G1yl++GGqv/tdih95BHt9/WH9MawtLdR985vkv/oqutVKy6c/TePXv45utZK3di3uUSRRFEJwxuLF6b/+xd9fmkF7jyM7EAkYz8R27NyJzWbLdpoE4yLodLnYvm0bkWh0xHVNhAmpuhFCFADPAduB9wPTgR9jXFhunYh1jmS4apvXt23jlrvvpi8cZm5NDb/4/OcpS9d1729388KaEu7hewB0XnZZNhDOz6RCaGgAs5ng0qUEly7F3NvLi9/9Lue0tjIjHodHHjGmtFlAr8VitNsGwqefTv+bWZnpZCMEvX7/kes1pUToulE3bzLR5vFQEYtRU1MzZL1tYWEh8+bNY9u2bbhcLoKhEDNmzKCiosLIqT2O0XkUZUjTpkFz86FOZoDb7Wb27Nns2LgRq8NBeNEiXFu2DPhOIpEgEAggpcRZWUnRihXkrVtH0SOP0P7xjw9YhYhGmfLLX+LZsAEA144dlPz97yTz8gguWkRo0SJEIkH5H/6AFosRq6yk+bOfzab/6LjySsr/9Ccq7ruPfXPnDjlObH9nLFrEQy++SIHnEXyBr/LbJ+Zzy2Xd+Hw+CgsL2b17N1LXcQyxHLvNRjKZZOeOHSxYsGDAheB4mKgS/acBB3CplPJZKeWvgNuAzwshjntbpFgsNmS1zcMvv8wNP/whfeEw5y5bxh9vvTUb5AHufWwBn5a/pIwOItOmEVyyJPvZnJoaNCHY09xMrF/Oi4jbzed8PmYBG2+6id4zzyQ0e7ZR6vZ4kELgSiRwAR0mEyWDqm2i0Sh5eXksXLgQb34+3d3dA1s79KNFIiQKCpB2O319fZimTKFu1ixMw3wfoKCggAULFhCNxZg1c6YR5DMPWk+CZmLKScLlgupqGFQSL3Q6mV5WRlNZGSmXi2ReHiIWy95dxmIxZs2ezeIlS4yWKxdcgBSCghdfxNJxaHhIc1cXtd/6Fp4NG0g6ney77DLa3vlO4oWFmPv68L7yClN+8Qsq770XLRbDf+qpNNx224AcT77zzyc8cyZmv5+yv/xlxF16x/z5mE0m/KENQC8PvjCDQCSf3t5eGhoaCAaDR3wG4Xa5iMVi7NmzJ9sg4HiZqIexFwFPSyn7+r33APB94CzgsQla7wDJZJLOzk6ampowm80Dqm0aWlv52m9+gy4l1118MZ+/6ipM/T5v6XTx/OoSfsUPgEOl+Xg8jslkwmW3U1dZyb6WFnYdOMCi6dMB2LxvH6FolGmVldhXraJ11aqBG6XrmEIhNL+fVEEB2qCmY7FYjMrKSiwWC7Nnz6a5uZn9+/cP+SBVRKOEqqrwdXdjMplYduqpWDo7jQENjlA693q9rFix4lBHj2jUyKg3xjFuFeWIamuNofJ03einEI+D30/ZJZcwpbWV5uZmygsKSG7dSiIvj5qaGsrKyrLn+aJFi9jnctGxYgVlb75J8T/+QeunP41j926qfvpTzH19REpLabz5Zirf8Q56fD7ebG4mv6eHkt27cW/ahKW7m+6LLx4yIyaaRusnP0ndrbfiffll+latIjRoyEIAkkny16zBG4+zfPp01u7ezYJp97O1/kZ+//RCrr/gWTo6OrI94o8kPz8fn8/Hxo0bjTp+KY22+lLi2rULt8tF9Tjz0R/JRAX6OcCAzERSyv1CiHD6swkN9Lqu093dTWNDA9b6emobGsDpJFpTQ6y6Gt3h4FePPoouJZeeeSb/7+qrD1vGbx6fz3/qP6OYbsIzZxJauBCAvkAAs8mE1+tlQV0d+1pa2NbQkA30/ZtVDknTSHk8w+bx0HU9O2CJpmlUV1fjcrnYtWsXdrsdu91OLBYjGgoZ9fMOBzNqaigvLzdaWFRWGuPmJpNHHLlmQG++UAjmzBnxuCrKmGRK9a2t4PEYpfsVKxBFRcz1egmHw3Q0NjK7sJDyhQsPq1rNFHY6PvUp9A0byF+zhkRpKUWPPYaWTOKfM4fEt7/N7HQakvz8fEpLSqhvaGBvURGed797xCqSeGUlXR/8IKV/+xsV//d/1H/ve4cGPtF1PG+8QelDD2FtbwfgIa+XS4Ai78PAjfz1+Vlce8FbFHqTA6tLdR1LVxeJkpLDLjAFBQWH+pukP/OuXs2U++4j6XbDZz4zcECSY2CiAn0B0DvE+770ZwMIIW4AbgCOKneElBJ/dzedzzyDa906Fm/dijXdzbu/UFER13R3s0gI3rdkyYA6QoC2HifPvVTML/kRcKg0H41Gcdjt2fSk8+vqePSVV7JjVwKHNasci1QqhZZuFtdfUVERixcvZseOHfh8PvLy85lRUoLrnHNwDi6BWCzGQMR79kC61c2IpDTGulSUY62uzijVd3XBsmXGINgYzT+XLFlCYvZsXK+/PuzdpBCCsmXLiF9yCdZHH6Xk4YcB6LvoIpxf/SqWQXfELpeLBfPn09XdTUN9PaFwGLfbfcQ+JN0XX4znjTdwNDZS8re/0X7ttbi2bKHkb3/Dkc5qGSsvRySTVHV18Sbws+2r0Rbu4bktM/nL84v43JVvAUZ1av7q1RQ8+yy2tjaCCxfSev31Rk/kfrJ357pO6QMPUPTkkwD0LlpE6QQ0w5zIdvRDdQ8cMnWGlPIe4B4whhIc19pefJHYnXfifvZZvP2ebCcKCgguXWr04mtqwtbcjKu7m8uBy6WEu+8mUldHzwUX0LdqFZjN/PbxedyUupsCegnNmUN43jwAQumHl/XpHrGZ3PTb04E+EA6zpb4es8nEKXPnjnkXYrEYheleioO5XC4Wpy9KFovFGGx42rShFzRlCuzdazzwHakZZCpllPyPRTtlRRnM6TQKHg4HDMremu1UlxmI4wg9YK033oh89lmIRkl87nPkDXEXniGEoKS4GG9+Pi0tLXR2dg5oVmw2m7PrFulspK2f/CR13/gGhc89h72pCeeePYARP7o+8AF6zzwTkUxS8re/UfDss3wuGuWaA2dwCQ/z52dXcOOKf1Oz5l/kv/QSpn7xx71lC9O+/GU6rr6a3nPOGVCg1MJhpvz857g3b0aaTLR8+MN0LltG6QTkzpmoQO+DIfsA5TN0Sf/orVmD/TGjRihWWUlg+XICK1YQra0dkMek8cABvvKVr7BUCG477TQqNm3C0dDAlF/9itIHHqDlnRfy1gvL+Dl3AYdK88lUCrPZTHFxMa2trSQSCWZXV2PSNPa2tBCJxVi7fTspXWfZrFm4xtEZKBaLUV1TM+zn2eqWSMT4cQwXnG02oyRVXz9yqT4UMm4Tj3OuF+VtpN/QmEMqLTUKJkdKdVBcjPjLX0BKrP36phyJxWKhtraW2tpaI5VDLEYsGiUQDBLo66O7u5vCwkI0TSNWU0P3JZdQ/OijOPfsIeV00v3e99Jz/vnZjJzSbKbjmmv4cUcH12zaxJzedl7lnayNrmLxN9aipcuwodmz8V1wAZHp0yn/wx/wrF9Pxe9+R97atbR+4hMkSkuxtLcz9c47sR08SNLtpuWzn6Vv2jQIBI60S+M2UYF+J0ZdfJYQYirgSn927F15JcGuLhpSKcwrVw77tV8+8QRvATPPOovgJz7B3nic/DVrKHjqKewtLdQ+8QBbeQCA4Pz5RNJ116FgkMrKSsxmM16vl66uLtxuN9OnTGH3gQPs2r//qKptMkY1BGEgAP1aAA1p6lTYt+/Qg7DhxGLHvD5QUcakoOCwtu9Dqqoa9yoyuYA8bne2I2FDYyMtzc3ZHqtd738/WiiE7nLRfdFFwza3LDnjDJZs2sQvi4q4tsfHqfJ1otjoO+1Ughe/i1i/wlrzzTfjWbuW8j/8Adf27Uz78pfpefe78b74IuZgkOiUKTR//vMkSkuN3+IEmahi3JPABUKI/k8crwIiwEsTssYZM4hcfz3RI5RgG1tbeWLNGswmEzek82dIq5Xes8+m4XvfY8tNX+MJ8R7jfWEkV8pIpVKUpFuy5OXlZW8FM+3ptzY0sCadyGw8gT6ZSmGxWIykaInE8Cd+JnCPVFK3241WD8N1NOlPNatUJtMkVRvWVFdTUFBAIF2KlhYL7ddeS+fllx+xTf2pCxaQEIIbenvZfutX+X75HVTRzLfLfzIgyAMgBIF3vIP6O+7Av2oVWjxO8eOPYw4GCSxdStM3vmEE+Qk2UYH+V0AM+IcQ4l3ph63fBO4c1OTyuMq0tPngGWcwZXDzQyH4Sf1VXCIf56PzX6bh298iOsMYNjAcDuP1erPt8Pu3x8/U0z+3bh1NbW24HQ4WDFd3fgTRSISioiKjzrC723h41a9nYVZfn1GyGU2Hi+pq48IwXEkhGjV+ZMchO6CiDMtiMVrlHOdeo5qmMXPmTES6ocVo5btcLJk5k2QqxQt9fVRcv5RuivnDU3MIRob+Xaby8jh4000033wz0ZoaOj/wAZpvueVQC58JNiGBXkrpA87DSGX9GEZnqbuAb0zE+kajsbWVxweV5vvr6bNx/3OzAfjAVYEBV+ZoNEplv44WdrsdkU7WlCnRv5HOK3/K3LmjSwk8SDweN9rhJhJGs7TTTwevF9rbjXr0Q180HraOhtMJK1YYpfqhBjIOhYzmmIoy2crKjGdPx5nVamXO3LmEQiGSY+jEdHq6tdvqTZtYObeDFbPb6Qvb+POzs444X2DFChq+8x26LrvsuD4Xm7A1SSm3SynPlVI6pJQVUsqvSSknbYCeI5bmgfuenEskbuasJc3Mr+vJvp9MJrFYLOT3q97QNA2P2008kWD21KkDAvvgaptUKpW9NTwSIYTRrDIUgvJyo4SzbBmceqrRKqa93aibdzqNB7GjVVQEK1cOHexTKejXE1hRJk2mkDMJPG43s2bNore3d8SxBDLOTOe9Wb15M1JK/vODmwG478l5hCInXlLgt0VTi5FK870BK39Jl+Y//f4tAz4LhkJUVlYe1uTR6/USi0axWa3M7PeQaHCgD4fDpFIpokd40BKPx7Hb7UaHkURiYP17QYER7NMJ05g2beyJx0pKjPl9vkM/Jl03ml5O8ADMijIqbvekJtQrLS1lSmVlNq/+SOZUV1OUl0dbTw97W1pYNa+dZbM68Adt3P/8LOoPHuSPTz/N2u3bSYxhMJ6JcuJdeiZApjR/2TCl+T88PZdw1MLpCw+yeEZ39n0pJXoqlX1K35/b7c7mq5hfV8eOpiYqioqoKS8f8L1EIkF1dTX79+/HPkwu/Gg0auScMVZ6+MNRIYxb2yF62Y1aaakR7NevN0rxsZhxQVHphpUTgc1mVFnG45OWiqOmpoZQKESv34/VYskO7dh/cBqv15vNy3/6okU8+sorrN60iZlVVdz4gS186gel/O/fv8ddf/t79u7A7XBw2oIFnLVkCWcsXkzxWO7Ij5GcDvS9gQC/e/LJI5bm/SErf3rGKM3f+IHNAz4LhcMUFRVlhwfsr/8D2RVz5vDQiy9yztKlA7pBp1IpTCYTlZWV2dTDQw0EkUwmjeHIolEjyA93oh9tnV5ZmVEdtGGDUaKfdeT6REU5rkpKoKVl0gK9yWRi5syZ7N+/H5HOo2+zWrFYrZg0jfb2doKhULYJ9BmZQL95M6vmzeP+5+4CNpBIgqaZOX/FUvYdPMi+lhaeefNNnnnzTYQQzK+tpSg/n0QySTKVIplKkUgPxemx23njlluO+b7lZKD3h0L84amn+MNTTxFKP02/4ZJLhizN//HpOQQjVt4xv5Wls7oGfBaPxagYprNHZri8ZCrFJaeeSr7LxYpB+WIi0SjFxcWYTCZqa2vZ9NZbOByOAReDzFXf5XYbrWzSLX0mTHm50QZ/27ax1fUrykQrKoJ0yoHJYrfbmTVMAUhoGtu3bTPuPDCqaTUheGPHDq74+tcBsJitJJL/QZ7zM3zvP9bhsKVo7ujg5U2beOmtt1i7Y8eAlCmDFUxQU9OcCvR9gQC/eeEF7l+7lkB6MIDTFy7kvy69lMVDBNBA2MIfnzaCc+ZhSkY8Hsdmsx1xIHGv14vf78flcnHWEB2YEvE4RelqH4/bTWlpKb29vQNSmcbjcTwej9Hr9Xg9HK2sNIL8MRxmTlGO2gn+vCjP48FkMhm95E0mvB4PS2bOZMPu3ThsNj503nlce+FF3HTX1WxtKOLBF/xcc+FOqkpL+fD55/Ph888nEouxcc8e4okEFrMZs8mUnTQpMQ3VOu4YyJlAf8899/Cl//f/6O0zmum/Y/58brr0UpYdoXriz8/MJhC2csrcNlbM7hzwWSgUYtq0aUccxDk/P5+urq4hP8vWz/W7Qk+dOpWOjo4BI11FolFqMu3dNe34neyj6YGrKMeT3W7U1ScSo+sncpyZTCbKysro7OzMFtZuv+EG1m7bxvkrV1KQfu/GD2zmv+46h988Pp8rz92D3XqosaHDZhu2Q2UyFiN5kqVAOO5MJhO9fX0sranhlo98hJUjJBVr7nBx35PGd278wKGWNlJK/H4/DodjxMF8HU7nsM2xIpEIBYWFA9IBOxwOplRV0dbWlh05Sk+ljJMmElEPRxWlrAza2k7YasXi4mIOHjyY/bumrIyaQSlEzl7awpyaHnY2FXLvY/P5zGWbBy/muMuZQH/NNddQrGlUHDiAZ4SeqcGIhf+88xz6wjbOWtLMKXONXNOxWIxAMEjVlClMnTr1sIE+BnPY7QghkOmh//qLpYf0G2xKZSVtbW0kUyk0IdA0zXhA6/NBOqe9orxtFRcbaY1PUG63G2t6WMDh4oMQ8IUPbeBTPziPXz6yiJlVvVy4anL3KWfa0VssFk5bufKIVS0AKV3whZ+fzt4WL9Mqe/nBja8CRik+kUiwcMEC6urqRgzyYKQ7dTgc2fz0/Ukph6zft1qt1FRXE+jrIxaL4fV6MZlMQzerVJS3G7f70NCWJyAhBBXl5QT791YfwmkL2vjCh4yxbL9yz2lsrZ/cjok5E+hH60cPLOXlTVPId8f4xedfxGGN0N3TQ2FhIUuWLMHr9Y5peQUFBYcF+mgsRl5enpFrewilpaVYLBaCwaBRPZQZDUrlhFfe7hwOo57+BOhkNJzCwkL0UaRL+PhFO7j0zL1E42Zu+snZtPccn7w2Q8mZQB8Ow+76oTskZfz9xen8/sl5mE06d3/2JUrzuwgGg8ydM4eZM2eOa2T2vLy8Q8OCpUUjEUqPkJHObDZTW1uLEAKXy2VsfGnppPYMVJQTghBGe/pJyHszWk6nE1d6oO8jEQK+ft0brJjdTofPyU0/OZtIbPhncOGYmYb2iRnpLWcC/UMPwenvn8n191zH3/49g0B4YNB+c0cpt913CgDf+PhaFk47QDQWY+HChRQXF49Y5TMc+xDZ53RdJ2+Eh0lFRUXU1dUZ9fMqJ7yiHFJSctwzWY5VeXk5kVFcjKxmnZ/e/DJVJQG2NRTx5V+fNiADuZSwYXcJX/vNOzjvv6/my3+4eEK2N2cexvb0gNuVYmtzFVt/V8Udf17Bu1Yc4INn7qOyOMjNd59JMmXi2ou2855TtxONRlmwYMGA5o/jYbfZ0DQt2ws2Ho/jdDpxjJD6V9M0qjI5clT9vKIckvktjDDA/WQqKChg3759QzbEOOy7nhi/+O8X+fBtF/DMmzX8/GE/V527h0dfmcbDL0+nse3Qb99hTeD3H/tGR2K02dqOlxUrVsh169aNa96mN7dx3x17eHLHO1i741DOGZOmk9I1zlzcwp3/9TTxWJgFCxfiOUZ14jt27iQSDuNwOOj1+6mprqZytOl/43GjRH/22cdkWxQlJzQ1Gb23J6pKMxQyOigeRQFr27ZtxGKxAelQjmT15gpu/NE56FJDEzq6NCpUSrxh3n96Pe9dtZOp7maWjjMFghBivZRyxVCfnZiXy3FyOiQXL9nClR8M0tzh4pFXpvPwy9No7XYzY0ovt3/yeSPIL1gwviCfTBqDgmRyzkgJFgsFViu93d04HA70VIr8sVyOw+GjGiJNUXJSdbUxyM7BgyOPpjYWUhq3/5kEg5GI8QB4HMrLy9m5c+eoA/0Zi1r50kfW870/rUTTJO9a1sQHz9zHOxe2YjbJdIepcW3KiHIq0PdXVRripks3858f2Mz2xkIqvB2YCBpBfjy9TxMJ4wRZsMDIFxONGlNfHw6TCdO+fQhdxxmLMabEAvH4sT2RFSUXCAFz5xpjMPT1HZuqzWTSGLlt6lRj2cEgvPaakURtHB0V8/Lz0dIDEA1OYz6cj12wixVzOigvDFPgmbgxYgfLzUCv62ixGCIWw6TrzLS1kAymmD1zJp5kcuxdrNMBneXLDz00tVqNk6+0FEd1Nd3RKEFdp9rjQdhs0NFhnKxOpzENd/spxAmf40NRJoXZDEuXwiuvGL/BoxnyMhQyAvvixcYIbUIYYz3Mng27dxtVRGNkMZspLi6m1+/PZrQcIJlESIkcFGumlbcRDofx+ch2uMx83z1BPeNzLtCLVApTIEDC48HndBKxWCiqqWH27Nl4ADo7obnZGHFJiJHHTA2HjWnVqmETjlmtVpxOJ36/n6KFC40TKBo1ers2NxvrNJuNJyz9/yNHSkusKG93DodRwHr9deM3NNaHs/2rak4//fA7g7q6Q+Mzj+MJaElJCR0dHUbuKCkRsRhaJIIAdKsVqWmYAwGkECQBfyyGNS+PmTNnomkaQghjAkQigWWCnpnmVKDXCwroXriQXo+HRCpFVVUVi2trB1bVeL1GKuBQyDgBWlqMQCylEfBdrkPBOBAwHticeuqIt47FxcXEYrFD9fN2O1RUGFMkYjxcamw06vfz840TNhhUOeEVZSSFhTB//sgPZ3XdaNgQixnVNFIaU2UlzJs39F28psHChcZdwzgGPfF4PNgSCfT2dixWK6m8PKIVFaTy89HtdhACGY0SaG3FEgwyY8oUSux2TEIY25vZFyGMmDGOO4vRyKlAj9lM0m5nalUVtbW1Qw7yARwqybvdxkOfWMy4ore1GVMqZZwgbjeccsqo0vlm2uIPWVfncMCcOVBba5Tw6+uN5adSRulfUZQjq642Cl4HDhzKcDm49GsyGYWo4mLj1eEwgudIVT5OJyxaZIy+VlY2+lY+UmLq6aF62jQaLBZ609U0QgjsqRT2VIpwOEwkEqF23jymT59+aLjQeNzY3sw0wQOF51TzymQySTKZHHJEqFHT9UMPgEpLDz2dH3E2HV3XR5Ujh3jcaE3Q1mYM3K0yVirKyJJJoz5d04zgbLMZJXCL5dDr0TTF3LrV+F2OkLUWMH7DPT3GGM6zZoHJRDKZJBQKEQgE6OrqoqenB4/Hw5w5c8bXAGSMjtS8MqcCvaIoyrglErBmjXGxONJ4DYGAEegXLz6herS/bdrRK4qijJvFYgyz+eabRgOMzHsOx6G6+64u43ndypUn1eA9KtAriqJk5OfDOeccam3X02NMXV3GM4Ha2mxVzclEBXpFUZT+TCajb4vHc6hqJpUyGm2cpOMs50z2SkVRlAljMp20QR5UoFcURcl5KtAriqLkOBXoFUVRcpwK9IqiKDluQgK9EOIqIcQ/hBCtQggphPj4RKxHURRFGdlElegvB2qBxydo+YqiKMooTVQ7+quklLoQwg18coLWoSiKoozChJTopZT6yN9SFEVRjgf1MFZRFCXHqUCvKIqS40ZVRy+EyAcqRvqelHLneDZCCHEDcANAdXX1eBahKIqiDGO0D2OvAO4dxffGlfVfSnkPcA8Y+ejHswxFURRlaKOqupFS/kZKKUaaJnpjFUVRlLFTdfSKoig5bkLa0Qsh5gHzgMzgrSuEEEGgU0r50kSsU1EURRnaRHWYuhL4Rr+//ys9vQScPUHrVBRFUYYwUR2mvjlMPf7ZE7E+RVEUZXiqjl5RFCXHqUCvKIqS41SgVxRFyXEq0CuKouQ4FegVRVFynAr0iqIoOU4FekVRlBynAr2iKEqOU4FeURQlx6lAryiKkuNUoFcURclxKtAriqLkOBXoFUVRcpwK9IqiKDlOBXpFUZQcpwK9oihKjlOBXlEUJcepQK8oipLjVKBXFEXJcSrQK4qi5DgV6BVFUXKcCvSKoig5TgV6RVGUHKcCvaIoSo5TgV5RFCXHqUCvKIqS41SgVxRFyXEq0CuKouQ4FegVRVFynAr0iqIoOU4FekVRlBx3zAO9ECJPCHGbEOINIYRfCNEmhHhYCDHrWK9LURRFGdlElOirgU8BTwOXA/8BVABrhRBTJ2B9iqIoyhGYJ2CZDcB0KWUk84YQYjWwH7geuG0C1qkoiqIM45gHeillaIj3eoQQTUDpsV6foiiKcmTH5WGsEKIEmAFsPx7rUxRFUQ45Xq1ufgwEgQeG+lAIcYMQYp0QYl1nZ+dx2iRFUZS3h1FV3Qgh8jEeqB6RlHLnEPPeCHwUuExK2T3MfPcA9wCsWLFCjmabFEVRlNEZbR39FcC9o/ieGPCHEO8D/hf4kpTy4TFum6IoinIMjKrqRkr5GymlGGnqP48Q4jSMqppfSSl/OBEbryiKooxsQurohRDzgceBp4DPTsQ6FEVRlNE55s0rhRClGAE+CNwNnCJEtrDfJ6VULW8URVGOo4noMDUPqEr/+4VBn70EnD0B61QURVGGMREdpl5k0ENZRVEUZfKo7JWKoig5TgV6RVGUHKcCvaIoSo5TgV5RFCXHqUCvKIqS41SgVxRFyXEq0CuKouQ4FegVRVFynAr0iqIoOU4FekVRlBynAr2iKEqOU4FeURQlx6lAryiKkuNUoFcURclxQsoTayxuIUQn0HQUiygGuo7R5rwdqOM1Nup4jY06XmNzNMerRkpZMtQHJ1ygP1pCiHVSyhWTvR0nC3W8xkYdr7FRx2tsJup4qaobRVGUHKcCvaIoSo7LxUB/z2RvwElGHa+xUcdrbNTxGpsJOV45V0evKIqiDJSLJXpFURSlHxXoFUVRctxJHeiFEFcJIf4hhGgVQkghxMfHMO87hRBrhRARIUSDEOKzE7ipJwwhxKeEEHuEEFEhxHohxHmjmOeb6eM7eLrweGzz8SCEmCeEeF4IERZCHBRCfEsIYRrFfPlCiN8JIXxCCL8Q4s9CiKLjsc2TaTzHSwhRO8x59MDx2u7JIoSYIYT4tRBikxAiJYR4cZTzHZPzyzzmLT6xXA7UAo8DnxztTEKIGcDT6fm+DJwC3CmECEspfzMB23lCEEJ8CPgV8E3gFeA64HEhxEop5dYRZvcDgwP7jmO+kZNACFEAPAdsB94PTAd+jFEQunWE2f8KzMY4/3Tg+8AjwBkTtLmT7iiPF8AXgFf7/f126FA1H7gYeB2wjmG+Y3N+SSlP2gnQ0q9uQAIfH+V8vwZ2A+Z+7/0COED6AXUuTsAu4P/6Hz9gC/CnEeb7JtA12ds/gcfly4APyOv33heBcP/3hpjv1PR5d2a/905Jv/euyd6vE/B41aaPzSWTvQ+TcMy0fv9+CHhxFPMcs/PrpK66kVLq45z1IuAfUspkv/ceAKqABUe9YScgIcQ0YBbwt8x76eP3IMbxeDu7CHhaStnX770HAAdw1gjztUspX868IaV8A2ggt4/peI/X29Y4Y9UxO79O6kA/HkIIFzAV2Dnoo0w1xJzju0XHTWa/htrvQiHEkDky+vEKIbqEEAkhxEYhxKXHfhMnzRwGHRcp5X6MEuqRzofD5kvbMcJ8J7vxHq+M36XrqVuFEHcKIRwTsZE54JidX2+7QA9406+9g973pV8LjtuWHF+Z/eod9P5o9nsvxq35lcBlwEHg7zkU7As4/LiAcWyOdFzGO9/Jbrz7HQN+DnwCOA+jCvVGjLsB5XDH7Pw6oR7GCiHygYqRvielHOoqN1bD9RQ7aXqQjfN4Dd4/Mcz7/ef/06D1PgasAb4O/GNUG3viG2r/xTDvH4v5TnZj3m8pZStwU7+3XhRCtAO/EEIskVK+dWw3MScck/PrhAr0wBXAvaP4nhj5K8PqTb96B70/XIn3RDaW45UpuXsxWtDQ728Yw35LKaUQ4h/A94UQJillarTznqB8HH4+AORz5OPiA4aq8vKOMN/JbrzHaygPYTSEWAa8dTQblYOO2fl1QlXdSCl/I6UUI01HuY4QRuuawXVcw9Vhn7DGeLwy+zXUfvdIKTvHswnj3vgTy04GHRchxFTAxZHPh8PmSxuubjVXjPd4DUUOelUOOWbn1wkV6I+jJ4EPDurgcRXGBWCk9uQnJSllPUaT0isy7wkhtPTfT45lWUIIAXwQ2JQDpXkw9v8CIYSn33tXARHgpRHmKxdCnJ55QwixApjGGI/pSWa8x2sol6df1x+LDcsxx+78muz2pUfZNnUexonyUYwSwc/Sf5/V7ztnAclB780AgsBfgHMwHjQmgE9O9j5N8PG6GkhhdGo5B7gP48e5YITj9RLwWeDdGAH+XxidN9432ft0jI5LAdAKPAu8C7ghfX58Z9D39gK/HfTeU0A9cCnwAYy+Cqsne59OxOOF0R/jx+lj9S7gW+nz7++TvU/H4Zg507HpcuA1YFu/v50TfX5N+gE4yoP3zXSAHzy92O87Z6ffO3vQvKcDbwBRoBH47GTvz3E6Zp9Kn1AxYANw3qDPDztewG/TJ1sECAGrgYsme1+O8XGZB/w7vY+twLcB06DvNAL3DXrPC/wOo860D6PwUDzZ+3MiHi/gQ8A6jGdE8fR5+C3ANtn7cxyOV+0wsUoCtRN9fqk0xYqiKDnu7VpHryiK8rahAr2iKEqOU4FeURQlx6lAryiKkuNUoFcURclxKtAriqLkOBXoFUVRcpwK9IqiKDlOBXpFGYEQ4r5hBrVePdnbpiijoQK9oozsBxjjd56KMbi6BNqB/53MjVKU0VIpEBRlFIQQBcAfMRK7/Qi4XRoprxXlhHeiDTyiKCccIUQxRqZGL3CalHLd5G6RooyNKtEryhGkc/a/ipGa9ywpZfskb5KijJkq0SvKkd0CLACWqCCvnKzUw1hFObKbgTullPsme0MUZbxUoFeUYQghlgPVwAOTvS2KcjRUoFeU4c1Ov7ZM6lYoylFSgV5RhhdOv86d1K1QlKOkWt0oyjCEEPkY45qGgdsxBnTeIqXsm9QNU5QxUoFeUY5ACLEQ+C7wTox29L3ACill/SRulqKMiaq6UZQjkFJukVK+V0pZCBQCbuCMSd4sRRkTFegVZRSEEGbgAow8N69O8uYoypioQK8oo3Mq8G3gainl3sneGEUZC1VHryiKkuNUiV5RFCXHqUCvKIqS41SgVxRFyXEq0CuKouQ4FegVRVFynAr0iqIoOU4FekVRlBz3/wFSKqyVV5kj/AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dim=2\n",
      "RMSE:  0.20732372\n",
      "RMSE:  0.28300324\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dim=3\n",
      "RMSE:  0.4968499\n",
      "RMSE:  0.53823453\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dim=4\n",
      "RMSE:  0.251314\n",
      "RMSE:  0.31473282\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Cycle through plot dimensions\n",
    "for plot_dim in range(0,dim):\n",
    "    f = plt.figure()\n",
    "    ax = plt.gca()\n",
    "    print('dim=%i' % (plot_dim,)) \n",
    "    plot_ber_uncertainty(ber_net, plot_dim, ax)\n",
    "    plot_eiv_uncertainty(net, plot_dim, ax)\n",
    "    plt.xlabel(r'$\\zeta$')\n",
    "    plt.savefig(os.path.join('saved_images','multinomial_noisy_prediction_std_x_%.3f_dim_%i.pdf' % (std_x, plot_dim)))\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "velvet-patrick",
   "metadata": {},
   "source": [
    "## Coverage\n",
    "Produces part of Table 1. Running this section takes around 1h 45 min"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "treated-respondent",
   "metadata": {},
   "outputs": [],
   "source": [
    "def inside_uncertainties(predictions, truth, k=1.96):\n",
    "    mean = np.mean(predictions, axis=1).flatten()\n",
    "    std = np.std(predictions, axis=1).flatten()\n",
    "    inside = np.logical_and(truth.flatten() > mean-k*std, truth < mean+k*std).flatten()\n",
    "    return inside\n",
    "\n",
    "# Use quantiles instead of uncertainties (not used in preprint - for concistency reasons)\n",
    "def inside_intervals(predictions, truth):\n",
    "    up_quantile = np.quantile(predictions, 0.975, axis=1).flatten()\n",
    "    low_quantile = np.quantile(predictions, 0.025, axis=1).flatten()\n",
    "    inside = np.logical_and(truth > low_quantile, truth < up_quantile).flatten()\n",
    "    return inside\n",
    "\n",
    "def inside_explicit_uncertainties(mean, std, truth, k=1.96):\n",
    "    mean = mean.flatten()\n",
    "    std = std.flatten()\n",
    "    truth = truth.flatten()\n",
    "    inside = np.logical_and(truth > mean-k*std, truth < mean+k*std).flatten()\n",
    "    return inside\n",
    "\n",
    "def compute_mse(predictions, noisy_truth):\n",
    "    pred = np.mean(predictions, axis=1).flatten()\n",
    "    y = noisy_truth.flatten()\n",
    "    assert pred.shape == y.shape\n",
    "    mse = np.mean((pred-y)**2)\n",
    "    return mse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "welcome-bread",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
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       "version_major": 2,
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    {
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      },
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     "metadata": {},
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    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "72e5879f097a4c17a935ff9c4675d64a",
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     "metadata": {},
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    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "02478cdaac93417c8cea0287a7114da5",
       "version_major": 2,
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     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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       "model_id": "b58bbb6add9c4fa2986ef46621e6fdd7",
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   ],
   "source": [
    "# Collect coverage and RMSE given a seed\n",
    "def coverage_computation(net, ber_net, seed):\n",
    "    set_seeds(seed)\n",
    "    coverage_x = torch.tensor(np.random.uniform(low=-1.0,high=1.0, size=(1000,5)), dtype=torch.float32)\n",
    "    coverage_y = func(coverage_x)\n",
    "    net_train_state = net.training\n",
    "    net_noise_state = net.noise_is_on\n",
    "    ber_net_state = ber_net.training\n",
    "    number_of_repeated_draws = 100\n",
    "    net.train()\n",
    "    net.noise_on()\n",
    "    ber_net.train()\n",
    "    inside_map = inside_uncertainties\n",
    "    net_inside_list, ber_net_inside_list = [], []\n",
    "    mse_list, ber_mse_list = [], []\n",
    "    for _ in tqdm(range(number_of_repeated_draws)):\n",
    "        noisy_coverage_x = coverage_x + std_x * torch.randn_like(coverage_x)\n",
    "        noisy_coverage_y = coverage_y + std_y * torch.randn_like(coverage_y)\n",
    "        pred, _ = [t.cpu().detach().numpy()\n",
    "                       for t in net.predict(noisy_coverage_x.to(device), number_of_draws=100,\n",
    "                                           take_average_of_prediction=False)]\n",
    "        ber_pred, _ = [t.cpu().detach().numpy()\n",
    "                       for t in ber_net.predict(noisy_coverage_x.to(device), number_of_draws=100,\n",
    "                                           take_average_of_prediction=False)]\n",
    "        net_inside_list.append(inside_map(pred, coverage_y.numpy()))\n",
    "        ber_net_inside_list.append(inside_map(ber_pred, coverage_y.numpy()))\n",
    "        mse_list.append(compute_mse(pred, noisy_coverage_y.numpy()))\n",
    "        ber_mse_list.append(compute_mse(ber_pred, noisy_coverage_y.numpy()))\n",
    "    net_inside = np.mean(np.stack(net_inside_list), axis=0)\n",
    "    ber_net_inside = np.mean(np.stack(ber_net_inside_list), axis=0)\n",
    "    mse = np.mean(np.array(mse_list))\n",
    "    ber_mse = np.mean(np.array(ber_mse_list))\n",
    "    if net_train_state:\n",
    "        net.train()\n",
    "    else:\n",
    "        net.eval()\n",
    "    if net_noise_state:\n",
    "        net.noise_on()\n",
    "    else:\n",
    "        net.noise_off()\n",
    "    if ber_net_state:\n",
    "        ber_net.train()\n",
    "    else:\n",
    "        ber_net.eval()\n",
    "    return coverage_x.numpy(), coverage_y.numpy(), net_inside, ber_net_inside, np.sqrt(mse), np.sqrt(ber_mse)\n",
    "\n",
    "# Loop over seeds\n",
    "net_inside_collection, ber_net_inside_collection, rmse_collection, ber_rmse_collection = [], [], [], []\n",
    "for seed in tqdm(range(0,20)):\n",
    "    seed_net = Networks.FNNEIV(p=0.5, init_std_y=init_std_y,\n",
    "        precision_prior_zeta=precision_prior_zeta, deming=deming,\n",
    "                        h=[dim, 500, 300, 100, 1]).to(device)\n",
    "    seed_ber_net = Networks.FNNBer(p=0.5, init_std_y=init_std_y, h=[dim,500,300,100,1]).to(device)\n",
    "    ber_saved_file = os.path.join('saved_networks', \n",
    "        'noneiv_multinomial_std_x_%.3f_std_y_%.3f_init_std_y_%.3f_seed_%i.pkl'\n",
    "        % (std_x, std_y, init_std_y, seed))\n",
    "    ber_train_loss, ber_test_loss, ber_stored_std_x, ber_stored_std_y, ber_state_dict\\\n",
    "            = train_and_store.open_stored_training(ber_saved_file, net=seed_ber_net, device=device)\n",
    "    saved_file = os.path.join('saved_networks', 'eiv_multinomial_std_x_%.3f_std_y_%.3f_init_std_y_%.3f_deming_scale_%.3f_seed_%i.pkl'% (std_x, std_y, init_std_y, deming, seed))\n",
    "    train_loss, test_loss, stored_std_x, stored_std_y, state_dict\\\n",
    "          = train_and_store.open_stored_training(saved_file, net=seed_net, device=device)\n",
    "    coverage_x, coverage_y, net_inside, ber_net_inside, rmse, ber_rmse = coverage_computation(seed=seed, net=seed_net, ber_net=seed_ber_net)\n",
    "    net_inside_collection.append(net_inside)\n",
    "    ber_net_inside_collection.append(ber_net_inside)\n",
    "    rmse_collection.append(rmse)\n",
    "    ber_rmse_collection.append(ber_rmse)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "initial-schedule",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Reshape and process results\n",
    "net_inside_collection = np.stack(net_inside_collection)\n",
    "rmse_collection = np.stack(rmse_collection)\n",
    "ber_net_inside_collection= np.stack(ber_net_inside_collection)\n",
    "number_of_draws = net_inside_collection.shape[0]\n",
    "net_inside_mean = np.mean(net_inside_collection, axis=0)\n",
    "net_inside_std = np.std(net_inside_collection, axis=0)/np.sqrt(number_of_draws)\n",
    "ber_net_inside_mean = np.mean(ber_net_inside_collection, axis=0)\n",
    "ber_net_inside_std = np.std(ber_net_inside_collection, axis=0)/np.sqrt(number_of_draws)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "3f7de695",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RMSE\n",
      "===========\n",
      "EiV:        Average 0.759893, Error 0.004582\n",
      "non-EiV:    Average 0.712723, Error 0.004070\n",
      "\n",
      "\n",
      "Coverage\n",
      "===========\n",
      "EiV:        Average 0.916003, Error 0.000054\n",
      "non-EiV:    Average 0.639944, Error 0.000110\n"
     ]
    }
   ],
   "source": [
    "# Results for Table 1 in preprint\n",
    "print('RMSE\\n===========')\n",
    "print('EiV:        Average %.6f, Error %.6f' %( np.mean(rmse_collection),\n",
    "            np.std(rmse_collection)/np.sqrt(len(rmse_collection))))\n",
    "print('non-EiV:    Average %.6f, Error %.6f' % (np.mean(ber_rmse_collection), \n",
    "            np.std(ber_rmse_collection)/np.sqrt(len(ber_rmse_collection))))\n",
    "print('\\n')\n",
    "\n",
    "print('Coverage\\n===========')\n",
    "print('EiV:        Average %.6f, Error %.6f' %(net_inside_collection.mean(), \n",
    "                                   net_inside_collection.mean(axis=1).std()/np.sqrt(net_inside_collection.size)))\n",
    "print('non-EiV:    Average %.6f, Error %.6f' % (ber_net_inside_collection.mean(),\n",
    "                                               ber_net_inside_collection.mean(axis=1).std()\n",
    "                                               /np.sqrt(net_inside_collection.size)))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fe4575c0",
   "metadata": {},
   "source": [
    "# Results for Variational Dropout"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "5c518121",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "FNN_VD_EIV(\n",
       "  (main): Sequential(\n",
       "    (0): EIVInput()\n",
       "    (1): Linear(in_features=5, out_features=500, bias=True)\n",
       "    (2): LeakyReLU(negative_slope=0.01)\n",
       "    (3): EIVVariationalDropout()\n",
       "    (4): Linear(in_features=500, out_features=300, bias=True)\n",
       "    (5): LeakyReLU(negative_slope=0.01)\n",
       "    (6): EIVVariationalDropout()\n",
       "    (7): Linear(in_features=300, out_features=100, bias=True)\n",
       "    (8): LeakyReLU(negative_slope=0.01)\n",
       "    (9): EIVVariationalDropout()\n",
       "    (10): Linear(in_features=100, out_features=1, bias=True)\n",
       "  )\n",
       ")"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Load EiV VD model\n",
    "vd_net = Networks.FNN_VD_EIV(initial_alpha=0.5, deming=deming,\n",
    "                             h=[dim, 500, 300, 100, 1])\n",
    "saved_file = os.path.join('saved_networks', \n",
    "        'eiv_vd_multinomial_std_x_%.3f_std_y_%.3f_init_std_y_%.3f_deming_scale_%.3f_seed_%i.pkl'\n",
    "        % (std_x, std_y, init_std_y, deming, single_seed))\n",
    "train_loss, test_loss, stored_std_x, stored_std_y, state_dict\\\n",
    "        = train_and_store.open_stored_training(saved_file, net=vd_net, device=device)\n",
    "vd_net.to(device)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "b278a0b8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(2.0671e-06, dtype=torch.float64, grad_fn=<SoftplusBackward>)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vd_net.main[9].alpha()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "f8cce563",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "FNN_VD_Ber(\n",
       "  (main): Sequential(\n",
       "    (0): Linear(in_features=5, out_features=500, bias=True)\n",
       "    (1): LeakyReLU(negative_slope=0.01)\n",
       "    (2): EIVVariationalDropout()\n",
       "    (3): Linear(in_features=500, out_features=300, bias=True)\n",
       "    (4): LeakyReLU(negative_slope=0.01)\n",
       "    (5): EIVVariationalDropout()\n",
       "    (6): Linear(in_features=300, out_features=100, bias=True)\n",
       "    (7): LeakyReLU(negative_slope=0.01)\n",
       "    (8): EIVVariationalDropout()\n",
       "    (9): Linear(in_features=100, out_features=1, bias=True)\n",
       "  )\n",
       ")"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Load non-EiV VD model\n",
    "vd_ber_net = Networks.FNN_VD_Ber(initial_alpha=0.5, init_std_y=init_std_y, h=[dim, 500, 300, 100, 1])\n",
    "vd_ber_saved_file = os.path.join('saved_networks', \n",
    "        'noneiv_vd_multinomial_std_x_%.3f_std_y_%.3f_init_std_y_%.3f_seed_%i.pkl'\n",
    "        % (std_x, std_y, init_std_y, single_seed))\n",
    "vd_ber_train_loss, ber_test_loss, ber_stored_std_x, ber_stored_std_y, ber_state_dict\\\n",
    "        = train_and_store.open_stored_training(vd_ber_saved_file, net=vd_ber_net, device=device)\n",
    "vd_ber_net.to(device)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "d35a165e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dim=0\n",
      "RMSE:  0.23865137\n",
      "RMSE:  0.24064223\n"
     ]
    },
    {
     "data": {
      "image/png": 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evXnuf/8jMS6ORTNm0L9Pn/p90N274c034aOPKnt/gUl9DBxogv6gQdChg0mF1LMfvcfjYfSkSXz3009cMGoUH/7tbxSV2JnxfgbPzmzL7gNRnMmXPBD5FOWXXctZd/Wt+va5uaZ23qtX3RsrL4cFC0zvtPx86N27WXvvSKBval6vqbmkpTW4llJWrvh0URJvzk5j76KNfOoZRwZF9XqPPJuNlIwM7E6nucT0+2J5YuPZPOYmvu07ia35KezcH8XO/ZFs3hXNjn3RgGYyD/NXHiMKDz8Rzy+2VDpFQocIFxmUEVfuQFmpBKVMHj4uznxBra6b0dGV6QPrZ5utMnfs395gDXN3Os2XyLr5BwRAK0WZ00mRw4Hbbie6TRsS09KIbtOmcvpna5uxsXhiYthZXMzPe/dSWlTE0JgYstxu7Dt3mhSbVcOMioKTT4ZRo8yAsZgY87lqqqV5PJU9m3JzzaX/oUPmcWuovbU/rH1hs5naopXisH5OSSFn+3Ze++orPlyyhF927z68mVEjRjD51lv51a9+hc3KxfvvQ797r9vNNwsX8vqbbzJ7/nz25uYGKHgEMISoiJPp3+N4zhjRnkvPTGfI8XGV7wVoj4eFP/zAv955h8+WLqXU7//w+NVX88DEiWb/WPu7PgPs8vNh9mxYuRJWrTK/B2KzVe6/2Fjo1w/uvrvWrsZbd++m/xVXUFJWxqtTp3LdeecBUFFUztb7X6D3D28A8APZPHbqHF6asp22qW7zYq/X/C9PPrnusSsbN5q0VFpa5ajy005rtgZdCfRNraQEvvkG/PLCwVq5Ppbn3mnLe/NTKCqxM5oFfMz5JOLgS+A94JxTR3Ph6WNRkZEmSCgF+/ejd+1i9ddfE7l/P90w9fMjWF9KKw+elgY33QQXX3z4crVwrwP3Q4+StnIeAO9l3MxtZU9zwFF1BGFUhIdRPfcyYlA5I4d7GDmklPjYGnK+WlcOaY+MNAEwKsp8KaweRNblstUoaDUcejzmBlVzytaxGxFhXm+3V/4cEWHe1wqo/nOiWHOhHDoE+/aZS+/8fOjb13Q/TUkx/7vkZPN7bZfxbnflCamszIxXKCkx24mMrFqWyEhTZqvh0/9zxsSYmmFCAsTEsHbdOj766CP69u3LBRdcUNlWUget4eef4eOP4cMPNT/+uBxz1KwHhpCVdRIXXTSUyy5LZdiw4GNScXExr732Gv/973/p3Lkzb770EtFer/ms+fmm80F5eWUhlKo6dYF14qup0Dt2mKD/00/mVlBgjhW3+8jnp6TAlCkwenSN5X3lww+56bHHaBMXx7pZs+iUmwsPPQQ7dqAjIvBqG3ZPBZnswJnSjpenbOeC0b7vhPX/GzGi5h3kdMLCheYYsZ5z4IC5GmnfvpY9GToS6L1ec9AkJDTu+9YkL88MlqpHj5tCh40Hn+/I9FkZeL3mKuDuzFk8uecaIjxOZgIPtm3L5txctNZcPX48rzz0UJWRgM/NnMnkp54iKjKSNx98kAlDhphAUr1GCaZ8zz0Ha30zSHfqBLfdZi6Z//hHU9NNSDBfjrFj8RYWs2Gzne9zkvk+J5nFOcms25GA1pVXLJERXkb0K2LsUAenD3cwrF8pUcplTioej9kfWVkmoLWUkYhamy9taan5wlqziB5D3G5YtAg+/NBkRKyUMZjYetZZcP75cM45IZ7axTppWT18rHuXy3RMsNvr31fd7a6criA/H5591kz6B6ZycvfdAU8gWmvOv/tuvly0iPd69OCCLVtMebp3h0cegZdfhq+/5tnOT3HXjt8BcOOFeTxzz07axPtq9T171twLZ8sWU6P372xRXm4+76hRjT9tQxAk0OfnmxrDwIFH/14VFZW1w5ps2wYbNgQ1klVrmDU3hbue7sTevCjsds3tlx3g/ox/0376g+Dx8Dxwb2Qkc6dP50BxMVf88Y+UOZ2cMnAgHz39NGnJyXy1ZAlnT56M1+vlyVtv5d4bb6z7s2ht+vpPn1454ZOlb194/HFzAgBTWxk61HypfJ+/sNjG90ttfD1fM3+ulxWrbFUCf0Ksm7GD8hk/Hs66JIFu/WQ2zsZSVgZffWWC+yefmJ6sluOOM4H9wgtNW2eLmAS1tNRULlyuo5vOw+uFt982x2xFhWnEfeQR6N+/8jlFRbBlC3uXLmXPSy9xIibdpyZOhFtuMRWeTz+FqVPRw4bx91Pe5YHpHXFW2Oja0cmbj25lRL8is1MDDaSqqDC5+aSkI6/2DhwwU5Y0dBT7UZBAv2ePCbxjxhzd+7jdpm98p061N7qsXGkOtjquIDbviuK30zrz5femZ86IAQ5eeGAHA1b8B556CoDn4uOZXFLCvVdeyZO/MzWPlevXc/Ydd7A/P5+uHTrwj3vvZeKDD1LocDDpggt4fsqUoC/1D3+uTz6BGTNMTebKK+GOO0y6ASpruyefXOvb5Oebq9n58zTz5mrWra9ahp49Te1y/HjzrwiTuaSaTF4efPaZqbV/+WXVZQt69jQV3IsugpNOajkXTFU4nWb9ZIej4fM/WTZtMumbTZvMsXnmmSbds3mzCbZ+tgGzx43j1ieeqHywoMAcjABz5rA2ty0TH+zKqg1xxER7+fCpzZzVf49Jtw0fXnWHbttmetsE6jrtcJgz67BhR/f5GkAC/fr1ptHkrLOO7huwfr05sOLjTX6wpvf6+mtT860ht6s1nHTdX1mRU4xXv0hKYjum3bGbGy/Mw/bm6+byFPhw0CAuXrWKfllZfP/qq7SJiTEHktvN7txcxk+Zwhq/mvjpAwfyyXPPEdvQuXWcThPoq08ze+CAaZys50CXXbtMQPriCzMbREFB5d+io+HUU+Hss03g79OnWa52W7yNG02+/aOP4LvvqjZRZGdXBvfjjz9G9p/LZXLweXlHP5iwogKefx7eeKNqe0B0tOk50707m+PjGfzOO9gTEtj9xRfE+feCu+UWc5Xx6KNw9tlUuBS/nZbJyx9mEBXp5d1pWzi/9wbTAGwNbHO5TG0+MbHmtpsDB0zX0VDOOhuABPolS8zOP/PMhnd3PHjQrOuakWEO0pouz1wumDevxoNYa7j9SS//mmXO+FGRKbw29TGuOOskcyVw882gNVuuv54er76KTSk+mjaNc087zXyGrKzDi4s7nE4mXH89X86bR89u3Zg/fTqdtDY18aSkxvnmezwmQo8de1Qjbt1uM2bmiy/Mbfnyqt/NLl1M0D/jDLOpxpys81jidMK335oOKZ9/buoWlshI06njwgtNaiYzs/nKeVQ8HlizxnS1bNv26I/Tn382PXc6dzY59Q4dDqdWtdYMv/56lq1dy1N33snvrrmm8nUzZ5or53HjwFfb1xrufCqT595pS4RdM/PRjVwyeIvJu8fHmxTn+vW1D4QsKDCfyz+d1ARad6DX2lQn3e6Gn2WdTtPaZU0x4HCYtMyJJx753KIi04c+QKDXGh56oQOPvTIbuBG7LRKP1/TDfviqq3hw3jzU/v14rrmGQYsXs2bzZm4891xemjrVdGMsLjZR0O9KwuPxMHv2bPr160fXrl1N2bZtM20SVsA/mquY/HxTw69vf+k65OaaHPMXX5hav38vQJvNNAeMG2cC/4gRlVmkcLRli9kPs2ebQZb+KZnkZNOIeuGF5sqniSuJoeP1mvTHli2mwhTCtQ/emzePCfffT2bbtmz5+GMirArL3r3mjBkXZ7pD+7rRag33/6Mjf329HXa75r/3r+Oqi0pNj5qFC+ueGFBrc0CPGdOkDSS1Bfrwn5LQ6TQ1CKVMbbu+tIZ166oOfoqPN7Xr0tIjW/xrWVXq4RnteeyV9ig1F63hvqsuJyYujodnzKD3W2+hgIpevXg6NpY1mzeT2bYtj0+ebOZdKSoyNZZqQdtut3Oer58wYA7CE04wl67WMHqv13x+/z7mwXK5oGPH4J8fpIwMM+3J1Veb4v34Y2WKZ/Fic/G0dCn8+c9md48YYSpVo0aZHPTRzPzcnLQ2sW3hwspb9XbwgQNNUB8/3tRNwnL9F5vN5JuSk02NPCoqZGexi8aMoXunTmzetYuZX37JxHPPNX9o394McvrlF9OTZ+RIwHxVpk3eTUy0l0df7sDEv/TFWbqaX0euNd+Huv4hSpkril27TONJCxD+gd7q26uUyenV1+7dpjHXPz+tlDlQ9+49svtVfn7AA+HhGe15+KUOKOWhTdyXFJXAOSNHMjI7m0vLyjj+9dcpBk7fu5efX33VvOaGG2hrpYfc7vrlyOPiTM+ZXr0q5zbJzzcpqLw8c/JLS6s9HVNWZr58IZ6+1WYz+ebsbNO+5nCYYQhz5pjb2rXmBDB3rnl+RIS5mBo1ymTQBg8257WW2ABZUmJS0itWmAziwoXmkPKXnGyuXKzgHoJ521qu9u3NMfbzz6bylJ7e6P9Iu93O7yZO5LYnnmDaq69y9TnnVM4gOmaMCfQLFx4O9GC+4o/cspfoSM2U5ztyw98H4CxbyS3XJQe30aQk0y6YldUiztThn7rZt8/k7yIjTSK4PhMpORwmZZOScmRArGkk3JIlJoj6tQU8+nI7HnqhIzab5vHbZvOHf57LcSkp7Pz8cyJ374aJE6G8nMcyM3lw504ALh41inefftr0nrFGi44e3Th5d7fbnLzWrKm9Y3VurqleNtMAEMu+febf8O235vbTT0fOxZWYaIo6eLC5nXCCOQenpDRNGT0ec/G0aZPZrStWmKuU9euPLGtammmIHj3a3Pr3P+a67jc+j8f0mNm40Zz5GmHqEH9l5eV0Pu888goKmDN9OuN69TLfg4IC08ssNdXkzgL8I55+oy2//7tpEHl32mYuOb0guI3m5Zkr7MzMyoXJQ9hi3rpTNwUFlaMTS0qCf53HYyJKbGzgWm9EhLmMO3SoMh+vtUmx+EWXx/9dGeT/+/A29h+cA8CIfv2IBFOFLS+H8eN5YOpUvP/5D0tWreKpu+6q7CJZVGQuMRvrIImIMAefVbsP1NXN4zE1q2aYfbO6du1gwgRzA7M7vv/eBP8VK0wb9r59lScCf8nJprZv3Tp3Nh83JcXcrJ8TE83Hteo91r3Xaw6hQ4fM7eDByvvt201s2rTJZMkCZQYjIkwgHzLEXLGceqq50GqJVx/Nym43V59paaZi5nCYq1Jr5s2jFBsTwx2XX86fXnyRx2bMYNyTT5p/co8eJjW5e7c5QwcYa/O7iQdwuxV/+GcnJj7UlczjfmHYCQGX06gqPd18t3NyzIEUE2Pau9LTG2dBonoI/xr9smWmRmwdLHX0BT9s40bzLa6tC1hJifnnWX1my8rMJaDvNZ8vSuTcu3qilOa1qdu45txDnDN5MrMXL2baLbdwX0mJmdGvQwd4662a+90fOGAiRGN3PHc6TZ89a14Yf/n55gvQzFOvBsu6cFu50tysdr5qsw+HVIcO5iqiTx+TWhoyxAT5Rq6chj+n0wTeQ4fMcWhNf2GzVc4d1AB5BQV0PvdcypxOfpo7lwFam4D77LPm+3fNNXDnnQFfqzVM+nNnXv4wg+PSXCx7LYfO7VzsP3iQNZs3M3bo0LoXlHG5zAHpclXOoZSUZL73bdqY362TWwO03hq91mb4vTVVcFE9JgXbtavu636rUdbqhePXEOsotXHrE50BmHbHbq459xAVLhcLf/wRgCtSU+GFF8xZ/bHHag7yZWWm/KEYXRQdbXoSLFliGsP8a04haoQNlXbtKnPcFq3NBcuWLZW3XbtM7LBiiPWz/6FhfV+tRbqSkkzNPy2t6n2nTiaw9+gBXbseuw3ELY7VD75bN/NP9F8ac/t2c9+AdqP05GRuGD+e6R99xMPTp/Oe1SA0ZowJ9AsWwOTJAa+clYJ//WEHW3ZHM/+HRM67qwffzMjhvLvvZvm6dTxyyy08eNNNtRcgMrJqTHG7K+cKcrnMZ01MNC3wjSy8A721GpN1iWRNJFVXf3CPx9QqgukFEBFhah+9e1fOZw1Meb4DO/ZFc+LxJdx9lZnqdcnq1ZSWl3N7aiqZzz1nXv+b38CAATW/v8NR+9+PVmqq6RmwaVPlJGzl5eazH+N9+ZQyF1cZGaanjjgGWcthxsaaM2xGRmVX5/o2crrd3HPhhTz/ySd8/Mkn7L7vPjqWlZnvV3KyaWTZutWcYAKIjIB3p23h5Bt6s3pTHKfd8jPHb1jHvcDNL7xA7y5duOyMM4IvjzVzqVVDsOb1CYHwzhRaPW78BdPzptq0uLVKTDS1DKthJzqaZWvi+MfMttjtmpf+b/vh88q3ixbxKvDcoUOo4mJTk/j1r2t+b63NLdTzZnTrZg50q1pbVFTjwS5Es4qPN3n0gwerjrgLxqFDdBs9mgkTJuB2u7nlT3/CbVX8Ro0yz1mwoNa3SEn08OnfN5GWVELChim8BlwGPAxc96c/8YM1SWALE96BPtDZMdhAH+xBFBFRuQzZoUO4ImL5zZ+7oLXinqv2M9haq3LVKq6fOZPrAHdEBNx/P/z1r7U3yJSUmFp2qFetsdtNraaiwpwcW0gjrBABtWtncmWHDgX/Gmv22i5dmDJlCrGxsXz61Vf86tFHKXc6K+fBqiPQA3TvVMHtp0/hf+zBuqa4TSkyKyo498472blvX30/UciFd6AvKjry8i6YQVNOZ/1a+tu0MamPsjKefqcjP2+Mo1tHJ1Nv3mNq+s8/j540iY4VFawADv3zn3DppXX3oiktbbpx7vHxJtjv32+22QL6/gpRo169zDEbTGu71iavf8IJYLfTv39/5s2bR5s2bfhk6VLOvv12HAMGmHTQunXmO1ALR1ER4z/+J+2BBfTjVa4nQmteSUoit6CA8XfcgaM0iF45TSi8A70vlXKYUoHTOdUVFdVvXpfYWCguZtOeOB5+yYx2eeGB7cRFuMzESa+8AlrzF+C2nj1pmx2wYbwqr9fUtI92lr/6aN/edBPp3LnptilEQ0REmBROWVngxUn8HTpkBi75NYSOGDGCRYsWkZ6czIKVKzlt8mQqrO/lN9/U+nZrJk9muNvNfrudZVe9xh/4Cw7iGVVYyBXp6azbupXL/vAHPLUs5B7Ie/Pn8+GiRfV6TbDCO9AXFVWdJCUyMri+9A5HvWu0Oiqam5/rR7nTxrXnHuSM4cWVky2lpPDcmDH8Ecg+4YTg3rC42PTXO4qJxBqkZ8+mW6BFiKORkGAqJnl5NadanU5TYQowUHLAgAEs/vBDOqWlsTwnh4esGeTeftvMuhdA4XvvMXzNGiqAVddey713wyWX2pjG/QA8H51Ecnw8sxcv5vd//3tQH6O0vJxbHn+cCX/8I79+4gn27t0b1OvqI3wDfUWFOdP758AjI6vOGFWT4uJ6z6L12rfdmL8qjfRkF0/fbUa3smuXuR8+nBd8y/6cFkxtHswB2qrGwgvRAB06mBHv1lq9JSWmodZax7e01JwMavg+9+zfn++feYYenTrxQl4eu+x2MyHgLbfApElmRJ5l0yZinnwSgOkdOzLulltQCv7x+51sG/trdtGR5N2b+XT8FUTY7fz97be5esoUNvlGuweyetMmhl57LS++/z6RERHcfv75tKvndODBCN9AH6ghNpjRsV6vSe/Uo0Z/4FAEv/u7mcP9mXt2kZ7su2Tz/YOLUlLI2bqV2OhozgxmwJbbbQ7M1jpXrxDBUsp0bY6LM1fw8fEmfz90qJlf4vTTa1+7OT6eThkZLP7Pf8jq2ZO+Hg8PR0RQFhVl5rC4+WYT9BcvpuKee4j2ePgv0O93v8Puq0Ta7fDyYwd4q+sUALp9+AXP/vYBIux23vriC/pccgk3PvIIW/0mOdJa869Zsxh67bWs27KFru3b88Gjj/LozTfXPfCqAcI30AfKxVs1+tp61NSnx43P028cx6HCCM4cXsjVZ/v1BPDV6H/2XUUM7dOHxGAGehQVmdE4Mk5eiLpFRpoR76efboYkZ2WZLsmxsXV3eIiOhqgoMtq04ZuXXmL0yJFMdbtpV1HBk7GxOKOjTRpn8mSi9uxhFfDJ8OGcYXXHtN4mSnPrv4eyPmYg7T278b5pZ/kbH3KFr1/9vz/+mF6/+hW3PP44P23YwMW//z2/nTYNZ0UFl4wezXcvv2zWnAiR8I0khYVH1sqtlelr63lTnz70mBGwMz4wXREfvWVP1ePKdwaf72vFH9GvX3BvWt+ZKoVo7Wy2hs8FlZIC5eUkJiTwyd//zrznn6dL9+7cX1bGcU4n05OScEZFkQtcYbdz36RJAWvdbdpAu0dvB+D6g08x9fE+vPzQNHLefZdLTjsNr9fLi++/z6CrruKjhQtJiI3l6d/+lneefJL2IV21PZwDffWGWH+19aUPpleOn/9+lkZBcQQnD3AcOdGRr0b/7i+/AHBWMGkbj8ekmEI8NbAQwseafMxn7NChrHr7bV5/+GES0tO5vbCQlIoKugPDzzyTobWMVE8+bTClw0aTQAlnr36SHhedwLxlQ3j7L39l9TvvcMGoUSilGNSjB3OefZZ7fv1r7HY7O/ZFMuWFTtz/YmgGKobvFAiFhTUHy9pq9A5H0D1dvF549m2T/7vrqmp9bwsLoagIb3Q0qw8dIi0xkVMCrUhVXVmZGeYtaRshmkZCwhHpWpvNxsRzz+XSM87gmTfe4C+vvUZMVBRTbryxzreLu+8O9GWLuNH7CvEHS6h4Ior3nrNx4gkVfNi1E+WXXkpUx46o0jK++SifZxYM4uPv0vB6FTFRHh4oaPzmufAM9BUVJpjXNOq0thp9cXHQDbFfLE5kw44YOrdzcvGYgqp/9NXmDyYmQm4uw/v1IyqY9y0rM41JQoimERdXY7tcdFQUf7jhBu6eOJGS0lJSg4nAWVmoSydgf+cdruYt81gJsNTc/OfePBUYQQTb6IojvQsZ/dqS1OZ1GjvZEp6Bvry85gZVu732iYOKi4OecuCZt0xe7Y7Lc4+8CPAF+o2+VSdGBNt/Ho75ycSEOKZY03TXMuFhdFQU0fXpcn3nnabnT2kpngo336+I5otv4yhxaGIopwvb6clG+tg20NG7i55shLyNsCYN7I1/NR+egb6srOaGmdoGTXm9gdeBDWDNphjmLkskPtbDjRfmHfkEX6Bf5pso7LxTT6273Fa3SpnvVoimlZpqRtI31mDBqKjD8+fYgZEXwYnlin/+ry0vf5hO905Obrs0l3YnF4Kr3MSLbdvqN5V6PYQs0Cul+gLPASOAAuBl4GGtdf3GBTdEcXHNefba+tJbPW6CaL1/dqbJzV9/3kFSEgN8JF+gz3G56NKuHf17967zPSkpMUv7hXC5MSFEAKmpZvWaEI4Kj43R3Hvtfu69tlp7nj3GjNzNygrZNMUhCfRKqRRgLrAOuBDoDjyNSTxNCcU2q6g+x42/2mr0QXatzM2P4PXPzdTBk684EPhJvkC/GTixV6/KZQFrU1FR+4pWQojQaNOm/tMeH0NCVaO/BdPm8CutdREwRymVCExVSj3peyx0rBFygUREmIDu9R7ZsyXIQP/ie+k4K2ycN6qAXl1qeI1foL+hZ8/gym2tMCOEaFphni4NVR++s4EvqwX0mZjgPzpE2zRcLhOw6+oiGajnTUlJra9zud2s3rSd6bN8XSqvrKE2X14OublUADuBMUOH1l3uigpzcpIFRoVoelFRJgsQzDTmx6BQBfo+wHr/B7TWO4BS399Cp7aGWH+B/qGB5q/38/CMGQy44hL2HfyS/j1KGTu0OPATfSNitwHxcXEMC2YpwNJSk58XQjSPagOnwkmoAn0KpgG2unzf36pQSk1SSi1XSi3Pzc09ui0H+48KVKOvY9bK97/+2vfTu9x15YGazye+ycw2AwN69AiuW1ZFhazqJERzSk2t9xQolJebhUpa2EIj1YVy+GWglg0V6HGt9QytdbbWOjvjaBsjg1k0RKkjA73W5p9VQ43+wKFD5Gzd6nv5HK4862DN7++Xnx8UYB7sGssk0x4I0XwSEkzbXTDKy+HAAfP8E04wI+rrWgClGYWqMTYfSA7weBKBa/qNp7Y5biyBulhas1bWUE1f+OOPh3/Weg9bdm+mX/fugd/fl7rZBIzo37/uMpeXmyBfzznwhRCNKC6u7rRvWZm58k9IMDNlpqebTh1aw9q1LTb9Gqoa/Xqq5eKVUplAPNVy942utq6VltoCfQ3mLbMCvdllH9eyiLBn+3YAtgBjhg2rvSxgytK+fd3PE0KETmSkmdo4UPudVYPX2gT4U04x89xbPfc6dzZBPj+/acscpFAF+tnAWUop/1zE5UAZsDBE2zT/oIqKulM3NQX6Ws7mn3+3EoDUxMsBmLdsWY3PrfCtJuVp144OwZzhvd4q61kKIZpJWlrVQUsVFSbAu90wZMiRAd6ilEnh2GwtskE3VIH+BcAJvK+UGqeUmgRMBf4W0j70we7gQEsKOhw1ToKWm5/Pzv0bgRhuvNDMXrcsJwd3oJyc201UnpkSISWY0bBWukjy80I0v9TUymVIc3NN0B8wAEaNMjX22gY+RkfD4MFm5tp6LgweaiEJ9FrrfOB0zDQPnwAPA88AfwrF9g6rbTIzf3a7+Uf6B+paetx8sXiV76cR3HllBj0yMykuLWXJ6tVHPnnfPuxeLzuB/scfX3dZyspMbb6pFwEXQhwpPt4E+qIiOP54OPVU6Ngx+GnDU1LM0oZ5Aea/akYhiy5a63XA2FC9f0Beb/3miXG5KgOsw1Fjj5vXP18DQIf0bDq2dTFu2DA27dzJxwsWMHLw4CrP1bt2oTA9boIaKFVaahY3FkI0v4QEk6LJyGh454iuXc0C5QUFlRPLWxMmlpUd2elDKRN7appWvRG07mpkRYVpfNHaBPq0tIBPW7L6BwDOGWFSMeOGDeOF996r0hPHkrdmDRnArshILu/bt+4yeL2yCLgQLYXdbmrwR8Nmg/79YdEiU7P3es37ZmRAz56QlGTSPE6nyUKUl5sriMJCE49CQAK9dV9D18qN24spLl0HRHPvdaZP/GnZ2SilWLlxI6Xl5cT5TVuQ+/PPZADl6elE1rXQiHUAhHDGPCFEM4iNhexskxJOTjbf8erpn4iIyjm5jvbkUofWu16dUpWj4GppxH3mLbPea1L8EHplmYCcmpTEkD59cLndzF2ypMrzrR43kcGkY0pLK/vhCiHCS0qK6XaZmNjs3/HWG2EiIky6Bmod9vzJop8AOLF31YbVcb7+8Z99+22Vx+N8jTAdquXuAyorg3btgi2xEEI0SOsN9P5dLEtLA55x9+ZFsGv/YgCuHl91KgMr0H+7atXhxxwlJXT0pYMGjxsXXDlkWmIhRIi17kBvDZqqoWvla58o4GeUiuKisVVHuJ4ycCDRUVHkbN9Orm803KrvvyceKLDZSK8rdVNYaBplapo3XwghGknrDvSlpaYRtqZA/+k6QNO1/fFm9fcNG2DaNCgsJDYmhpGDBgHw6UIz2HezL19/sK7GVauL1aBBsmygECLkWm+gV8oEW5fLBPpqPWS2741i/XYzzcHYId1ND5kHH4RZs+DVV4HK9M2X338PwMG1awFw1TbtgbW97OyQdaUSQgh/rTfQWxwOE/Cr5ej/NycFWADA2KEDYd482LzZ/PHjj6G8nNN9A6IWr16N1+vFs2MHAMk1jYj1es1AikGDTNpGCCGagAT64sCrRL0xWwGrsNsjOWPYMJgxw/whOtrk1+fOZUifPiS3acPOAweYvXgxHXy9dzJqWlEqLw969ZKZKoUQTap1B3qlAgb6jTui+Xnjj4BmQLdupK9YAVu3mgB9zz3mSbNmYbfbGZudDcDUF1/E6pdjD9QQe/Cg6UpZ0xz2QggRIhLoHY4j0jbvfJWCNZvyiD69KmvzN94I555rukSuXQvr1jHupJMAWJ6Tw+EQnplZdTtFRaZ3jTWNqRBCNKHWEXV27jxy/nmo7GJZrcfNzK9SsfLzV9tssGMHdOoE550HMTFw/vnmie++e7hBNhFIB9yRkVXnzHG5zCyZgwfXuvC4EEKESvgH+l9+gQkT4JFHjvyb1cXSLwCv3RzD2i0VwEpibDZOshYYuemmypkuL7nE3H/5JT2Skujcrt3h2rzq1Klql0mn0yxUEBfX6B9NCCGCEf6Bfs4cswjAd98duUSYFej9avT/m5sCLAK8PJCRgX3vXjNfxfjxla/r3BmGDwenE/XZZ5w+dGhlfr5z56rbcLulG6UQolmFf6D/5htzX15u8ur+IiKqrBqjtdWtciGRwG1FvsWwJk06cmGQCRPM/bvvctWZZx4O9Efk591uGf0qhGhW4R3od++GLVsqf1++/Mjn+C3ht3pTLOu3xRJhX8ANQHpZGXTrBmecceTrRo40J4kdOxhns/HQ2Webxzt1qvo8reterFwIIUIovAO9NbOkNXFYgIVC/JnafAWR3lX8n/XgpEmBV36JiICLLzY/v/suMQcOmJ+rB3po+Eo1QgjRCFpHoL/hBnP/00+Vi41UozW8MycFWMsN2kUmmNVgxtayGuJFF5mTwMKFptEXAgd66W0jhGhG4RvoHQ5YscLk3887D3r0MD1gqufpfVb9EsumnTG0iV3K3daDkybV3u89Pd2cCLxesz27PfD88lKjF0I0o/AN9EuXmobQ/v3NUl4nnmgeD5Snx+ptA+NTP6M7UBQTY1aAr8ull1b+3L591UZbj8cE+RAu+iuEEHUJ30BvpW1GjTL3vqkKAgV6k7ZJBeAMx1IA9g8cGFyAHjzYNNjCkWkbl8sMsBJCiGYUnoHe4zErsENloB882AxkWr36iKUDV+TEsXV3NMellDC2MBeA5AsvDG5bSsFVV5mf+/at+jfpWimEaAEi6n7KMWjNGigoMCurW7Xt5GTTuLphgwn2Vg0fq7cNXN/7LbovgVybjfTaGmGru/BC0wbQo+pygxLohRAtQVjW6J3z5wOwMiODax56iOxrruGlDz6ozNOvWHH4uVpX5ufPKn0TgGXp6ajqA6Rqo5SZsKx6mkYCvRCiBQibQP/ZZ59x1a230vumm9jwpgnY965axRuzZ7MiJ4eHnn8eHSDQL1sbx/a90XTMcNJ3i3l8Z79+jVMoraVrpRCi2YVNoM/JyeHtDz7AuXs3/QGHUqSPGsVD119PelIS+w4dYl1SUmWevrwcgHe+Mo2wk7O/5ziHg1wgJZjeNsGSrpVCiGYWNjn68847jwSvl7HffAOffUbC2LHMnDYNgM379/Pm7Nl88MMP9OvVywxuWr0a74lDmTXPpG2usM8E4APgbL/8/VGTQC+EaGZhU6Pv06cPt1x3Hb327DEPWL1tgDN8i4PMXbasSp5+yep4du2PonM7J21XfgrAwuRkOgUa9NRQkroRQjSzsAn0gBmdunq1Gc06cuThh61AvywnB9egQebB5ct9Ux7A7dlLiNm9m4NAYc+eKP/55BvK7ZbBUkKIFiEkgV4pdblS6n2l1F6llFZKXR+K7RxhwYKqo2F9OmRk0K9bN8qcTr7VGmw29Jo1fDrHzCp5ZcQswKRtelvdMY+W2y2LjQghWoRQ1egnAFnApyF6/8C++src+6VtLGcOHw7A+8uWQe/eKLebrgeX0yerjI6rvwDgXeDE449vnLLIgiNCiBYiVIH+cq31EKicHyzkPB6YO9f8HCDQW+mbb1aupGKAaWwdwwKeveRb1ObNHALmAacMHtw45XG5pA+9EKJFCEmg11p7Q/G+tVq6FA4dMrNHBki/nDpkCFGRkazZupW380zt/vzYeZxR8gEAHwHtMjLo3KFD45RHBksJIVqI8GmM/dSXJTrppKqLc/vEx8YyctAgtNbc9000Hmz0dy5HzZ4NmLRN36ysxmmItUjXSiFECxA+gf766+H//g9OO63Gp1jpmwOuJWxKGITN64bt2ymNjGQu0K9r18Ytk3StFEK0AEEFeqVUklKqT123hhZCKTVJKbVcKbU8Nze3YW/SqxfccQf07l3jU07obnW5/Irk0QMPP74wPp4K4MQ+Df4IgUmNXgjRAgQ7MvZS4KUgntegvIfWegYwAyA7O1s35D2C8c5XY4F0YAfOge3hM/P4KyUlAJwyZEjjblACvRCiBQiqRq+1fllrreq6hbqwR+PnjbG8+UU6Sp0OwKz9+yE+HndiIp+6XHRMT6dLx46NszFrsFRtyxAKIUQTCZtItHo1XD85ka9WpOF2H/n3B/7ZEa0VY4eaPP1nP/4Ir77KJ9ddhxOTn2+0hlgZLCWEaEFCNTK2r1JqAnCR76FspdQEpdToUGwP4I034LX/xXLWlKF0PGcAt0/LZPFP8WgNC1ck8Pl3SbSJ9/DUnWYVqKU5ObgyM1ngaxPom5XVeIWRrpVCiBYkVLNXXgb8ye/33/puC4ExodjgTTdBrMfB2zMVG3bHM31WW6bPakuX9k7svtPZvdfsY1DvdPpkZbF+2zYWrljBipwcoBFHxIIZLCWjYoUQLUSoBkxNrSGPPyYU2wOzSuDUe0tY/9K3rHhjHb+/Zh+djqtg+95otuyO5rg0F3dfdQConA7ho/nzWfnLL0AjjogFqdELIVqUsJmP3qIUDOlTxpA+u5l2x24WrTJpm/NGFZAQZwbsnjl8OP+YOZO358yhtLyc9mlpZHXq1LgFkR43QogWIuwCvT+bDU4d4uDUIY4qj48eMoTIiAgOFhUBjdwQa5FAL4RoIcKm1019JMTFcfKAAYd/b9SGWIuMihVCtBCtMtBD5XQIAEMae0QsSI1eCNFitNpAbzXIAoxs7IbY6GgZLCWEaDHCOkdfmyF9+nDGSSdhB7p17tx4bywLjgghWphWG+jtdjtfTZ/e+G/sckFiYuO/rxBCNJDkFxqb9KEXQrQwEugbm8xzI4RoYSTQh4J0rRRCtCAS6OvrwAEoKKj9OdK1UgjRgkigrw+3GyIioKKi9udJoBdCtCAS6OujqAiysiAjAxyOmp8nqRshRAsigb4+3G7o0MEE+9LSwH+XwVJCiBam1fajr7eSEkhNNV0nY2MhJsakcPzTNNK1UgjRAknVM1glJdC1q/nZZoNu3Uwqx58sOCKEaIEk0AfDaoRNTa18rF070Bq83srHXC6p0QshWhwJ9MEoLobOnU2wt0RHQ2Zm1Vq9xyODpYQQLY4E+mC4XKYRtrrMzCO7WkrXSiFEC9O6A315Oezfb1IzNSktheRkaNPmyL8lJkJSEpSVVT4mXSuFEC1M6w30BQUmQPfsCXl5NQd7h6OyETaQbt1MasciNXohRAvT+rpXejxw8KAZ9HTCCaabZFQUrF4NbduC3V71uXY7pKfX/H4ZGaYWb50oJNALIVqY1hXoy8pM42mfPmbQkzWwqUsX04Nm7VoTuK1gX1R0ZCNsdXa7qfGvX28aYht7kXEhhDhKrSd1c+iQaVQdMcKkW6qPXs3KMieA3NzKLpM1NcJW1769eY10rRRCtEDhX6MvL4fCQhOM+/Y13SJr0r27CdgbNpiGVutWl7g46NRJ0jZCiBYpfAO9x2Nq8dHRMHSoybMHk1bp0aMyjeO3gHiduncHp7Ph5RVCiBAJz0BfWGiCbq9eJv9eW469OqVMT5yEBJOvD5asEyuEaKHCL9CXlpra+/HHNzxnrlRwuXkhhDgGhFegb9MGTj0V0tKk94sQQviEV6CPi5O5ZoQQoprW071SCCFaqUYP9EqpRKXUw0qpZUqpQqXUPqXUB0qpXo29LSGEEHULRY2+M/Ab4EtgAnAz0B5YqpTKDMH2hBBC1CIUOfqtQHet9eEpHZVS3wI7gBuAh0OwTSGEEDVo9ECvtS4J8NghpdR2oG1jb08IIUTtmqQxVimVAfQA1jXF9oQQQlRqql43TwMOYGagPyqlJimlliullufm5jZRkYQQonUIKnWjlErCNKjWSmu9PsBrbwUmApdorQ/W8LoZwAyA7OxsHUyZhBBCBCfYHP2lwEtBPK/KcFSl1AXAc8D9WusP6lk2IYQQjSCo1I3W+mWttarr5v8apdTJmFTNC1rrv4ai8EIIIeoWkhy9Uqof8CnwBTA5FNsQQggRnEbvXqmUaosJ8A7gH8AwVTnBWJHWWnreCCFEEwrFgKm+QCffz19X+9tCYEwItimEEKIGoRgwtYBqjbJCCCGaj8xeKYQQYU4CvRBChDkJ9EIIEeYk0AshRJiTQC+EEGFOAr0QQoQ5CfRCCBHmJNALIUSYk0AvhBBhTgK9EEKEOQn0QggR5iTQCyFEmJNAL4QQYU4CvRBChDmldctai1splQtsP4q3SAfyGqk4rYHsr/qR/VU/sr/q52j2VxetdUagP7S4QH+0lFLLtdbZzV2OY4Xsr/qR/VU/sr/qJ1T7S1I3QggR5iTQCyFEmAvHQD+juQtwjJH9VT+yv+pH9lf9hGR/hV2OXgghRFXhWKMXQgjhRwK9EEKEuWM60CulLldKva+U2quU0kqp6+vx2lOUUkuVUmVKqa1KqckhLGqLoZT6jVJqo1KqXCm1Qil1ehCvmerbv9Vv45uizE1BKdVXKTVPKVWqlNqjlHpEKWUP4nVJSqn/KKXylVKFSqk3lVJpTVHm5tSQ/aWUyqrhOJrZVOVuLkqpHkqpF5VSPymlPEqpBUG+rlGOr4h6l7hlmQBkAZ8CNwX7IqVUD+BL3+seAIYBf1NKlWqtXw5BOVsEpdQVwAvAVGAR8GvgU6XUUK31mjpeXghUD+w5jV7IZqCUSgHmAuuAC4HuwNOYitCUOl7+DtAbc/x5gWnAh8CoEBW32R3l/gL4PfCd3++tYUBVP+AcYAkQVY/XNc7xpbU+Zm+AzXefAGjg+iBf9yKwAYjwe+xfwE58DdTheAN+Af7tv/+A1cAbdbxuKpDX3OUP4X55AMgHEv0euw8o9X8swOtG+I67U/0eG+Z7bFxzf64WuL+yfPvmvOb+DM2wz2x+P78LLAjiNY12fB3TqRuttbeBLz0beF9r7fZ7bCbQCTjhqAvWAimlugG9gP9Zj/n23yzM/mjNzga+1FoX+T02E4gFRtfxuv1a62+sB7TWy4CthPc+bej+arUaGKsa7fg6pgN9Qyil4oFMYH21P1lpiD5NW6ImY32uQJ87VSkVcI4MP8lKqTyllEsptVIp9avGL2Kz6UO1/aK13oGpodZ2PBzxOp+cOl53rGvo/rL8x5en3quU+ptSKjYUhQwDjXZ8tbpADyT77guqPZ7vu09pspI0LetzFVR7PJjPvQlzaX4ZcAmwB3gvjIJ9CkfuFzD7prb90tDXHesa+rmdwHTgRuB0TAr1VszVgDhSox1fLaoxVimVBLSv63la60BnufqqaaTYMTOCrIH7q/rnUzU87v/6N6pt9xNgMfAQ8H5QhW35An1+VcPjjfG6Y129P7fWei9wu99DC5RS+4F/KaUGaa1XNW4Rw0KjHF8tKtADlwIvBfE8VfdTalTgu0+u9nhNNd6WrD77y6q5J2N60OD3O9Tjc2uttVLqfWCaUsqutfYE+9oWKp8jjweAJGrfL/lAoJRXch2vO9Y1dH8F8i6mI8QQYNXRFCoMNdrx1aJSN1rrl7XWqq7bUW6jBNO7pnqOq6YcdotVz/1lfa5An/uQ1jq3IUVocOFblvVU2y9KqUwgntqPhyNe51NTbjVcNHR/BaKr3YtKjXZ8tahA34RmAxdXG+BxOeYEUFd/8mOS1noLpkvppdZjSimb7/fZ9XkvpZQCLgZ+CoPaPJjPf5ZSqo3fY5cDZcDCOl7XTik10npAKZUNdKOe+/QY09D9FcgE3/2KxihYmGm846u5+5ceZd/UvpgDZSKmRvBP3++j/Z4zGnBXe6wH4ADeAk7DNDS6gJua+zOFeH9dCXgwg1pOA17FfDlPqGN/LQQmA2diAvznmMEbFzT3Z2qk/ZIC7AXmAOOASb7j47Fqz9sEvFLtsS+ALcCvgIswYxW+be7P1BL3F2Y8xtO+fTUOeMR3/L3X3J+pCfZZnC82TQC+B9b6/R4X6uOr2XfAUe68qb4AX/22wO85Y3yPjan22pHAMqAc2AZMbu7P00T77De+A8oJ/AicXu3vR+wv4BXfwVYGlADfAmc392dp5P3SF5jv+4x7gUcBe7XnbANerfZYMvAfTM60CFN5SG/uz9MS9xdwBbAc00ZU4TsOHwGim/vzNMH+yqohVmkgK9THl0xTLIQQYa615uiFEKLVkEAvhBBhTgK9EEKEOQn0QggR5iTQCyFEmJNAL4QQYU4CvRBChDkJ9EIIEeYk0AtRB6XUqzUsav1tc5dNiGBIoBeibk9i1u8cgVlcXQP7geeas1BCBEumQBAiCEqpFOB1zMRuTwF/1mbKayFavJa28IgQLY5SKh0zU2MycLLWennzlkiI+pEavRC18M3Z/x1mat7RWuv9zVwkIepNavRC1O4u4ARgkAR5caySxlghancn8Det9ebmLogQDSWBXogaKKVOBDoDM5u7LEIcDQn0QtSst+9+d7OWQoijJIFeiJqV+u6Pb9ZSCHGUpNeNEDVQSiVh1jUtBf6MWdB5tda6qFkLJkQ9SaAXohZKqf7A48ApmH70BUC21npLMxZLiHqR1I0QtdBar9Zan6+1TgVSgQRgVDMXS4h6kUAvRBCUUhHAWZh5br5r5uIIUS8S6IUIzgjgUeBKrfWm5i6MEPUhOXohhAhzUqMXQogwJ4FeCCHCnAR6IYQIcxLohRAizEmgF0KIMCeBXgghwpwEeiGECHP/D8PTh7MGdttWAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dim=1\n",
      "RMSE:  0.23949231\n",
      "RMSE:  0.27066055\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dim=2\n",
      "RMSE:  0.2618301\n",
      "RMSE:  0.25091672\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dim=3\n",
      "RMSE:  0.5101809\n",
      "RMSE:  0.57865644\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dim=4\n",
      "RMSE:  0.25385875\n",
      "RMSE:  0.31200337\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Cycle through plot dimensions\n",
    "for plot_dim in range(0,dim):\n",
    "    f = plt.figure()\n",
    "    ax = plt.gca()\n",
    "    print('dim=%i' % (plot_dim,)) \n",
    "    plot_ber_uncertainty(vd_ber_net, plot_dim, ax)\n",
    "    plot_eiv_uncertainty(vd_net, plot_dim, ax)\n",
    "    plt.xlabel(r'$\\zeta$')\n",
    "    plt.show()"
   ]
  },
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   ],
   "source": [
    "net_inside_collection, ber_net_inside_collection, rmse_collection, ber_rmse_collection = [], [], [], []\n",
    "\n",
    "for seed in tqdm(range(0,20)):\n",
    "    seed_net = Networks.FNN_VD_EIV(initial_alpha=0.5, init_std_y=init_std_y,\n",
    "        precision_prior_zeta=precision_prior_zeta, deming=deming,\n",
    "                        h=[dim, 500, 300, 100, 1]).to(device)\n",
    "    seed_ber_net = Networks.FNN_VD_Ber(initial_alpha=0.5, init_std_y=init_std_y, h=[dim,500,300,100,1]).to(device)\n",
    "    ber_saved_file = os.path.join('saved_networks', \n",
    "        'noneiv_vd_multinomial_std_x_%.3f_std_y_%.3f_init_std_y_%.3f_seed_%i.pkl'\n",
    "        % (std_x, std_y, init_std_y, seed))\n",
    "    ber_train_loss, ber_test_loss, ber_stored_std_x, ber_stored_std_y, ber_state_dict\\\n",
    "            = train_and_store.open_stored_training(ber_saved_file, net=seed_ber_net, device=device)\n",
    "    saved_file = os.path.join('saved_networks', 'eiv_vd_multinomial_std_x_%.3f_std_y_%.3f_init_std_y_%.3f_deming_scale_%.3f_seed_%i.pkl'% (std_x, std_y, init_std_y, deming, seed))\n",
    "    train_loss, test_loss, stored_std_x, stored_std_y, state_dict\\\n",
    "          = train_and_store.open_stored_training(saved_file, net=seed_net, device=device)\n",
    "    coverage_x, coverage_y, net_inside, ber_net_inside, rmse, ber_rmse = coverage_computation(seed=seed, net=seed_net, ber_net=seed_ber_net)\n",
    "    net_inside_collection.append(net_inside)\n",
    "    ber_net_inside_collection.append(ber_net_inside)\n",
    "    rmse_collection.append(rmse)\n",
    "    ber_rmse_collection.append(ber_rmse)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "ab62a608",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Reshape and process results\n",
    "net_inside_collection = np.stack(net_inside_collection)\n",
    "rmse_collection = np.stack(rmse_collection)\n",
    "ber_net_inside_collection= np.stack(ber_net_inside_collection)\n",
    "number_of_draws = net_inside_collection.shape[0]\n",
    "net_inside_mean = np.mean(net_inside_collection, axis=0)\n",
    "net_inside_std = np.std(net_inside_collection, axis=0)/np.sqrt(number_of_draws)\n",
    "ber_net_inside_mean = np.mean(ber_net_inside_collection, axis=0)\n",
    "ber_net_inside_std = np.std(ber_net_inside_collection, axis=0)/np.sqrt(number_of_draws)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "e5621322",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RMSE\n",
      "===========\n",
      "EiV:        Average 0.701436, Error 0.003883\n",
      "non-EiV:    Average 0.772000, Error 0.004710\n",
      "\n",
      "\n",
      "Coverage\n",
      "===========\n",
      "EiV:        Average 0.927530, Error 0.000031\n",
      "non-EiV:    Average 0.001110, Error 0.000002\n"
     ]
    }
   ],
   "source": [
    "# Results for Table 1 in preprint\n",
    "print('RMSE\\n===========')\n",
    "print('EiV:        Average %.6f, Error %.6f' %( np.mean(rmse_collection),\n",
    "            np.std(rmse_collection)/np.sqrt(len(rmse_collection))))\n",
    "print('non-EiV:    Average %.6f, Error %.6f' % (np.mean(ber_rmse_collection), \n",
    "            np.std(ber_rmse_collection)/np.sqrt(len(ber_rmse_collection))))\n",
    "print('\\n')\n",
    "\n",
    "print('Coverage\\n===========')\n",
    "print('EiV:        Average %.6f, Error %.6f' %(net_inside_collection.mean(), \n",
    "                                   net_inside_collection.mean(axis=1).std()/np.sqrt(net_inside_collection.size)))\n",
    "print('non-EiV:    Average %.6f, Error %.6f' % (ber_net_inside_collection.mean(),\n",
    "                                               ber_net_inside_collection.mean(axis=1).std()\n",
    "                                               /np.sqrt(net_inside_collection.size)))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5dfe4eb6",
   "metadata": {},
   "source": [
    "## Results for Ensemble"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "dceb666f",
   "metadata": {},
   "outputs": [],
   "source": [
    "ensemble_files = create_strings('noneiv_multinomial_std_x_%.3f'\\\n",
    "'_std_y_%.3f_init_std_y_%.3f_ensemble_seed_%i.pkl', ensemble_seed_list, (std_x, std_y, init_std_y,), ())\n",
    "ensemble_files = [os.path.join('saved_networks',s) for s in ensemble_files]\n",
    "ensemble_size = 5\n",
    "assert len(ensemble_files) % ensemble_size == 0\n",
    "number_of_ensembles = int(len(ensemble_files) / ensemble_size)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "94df1d1a",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Plot non-EiV along plot_dim        \n",
    "def plot_ens_uncertainty(ens_net, plot_dim, ax):\n",
    "    offset = cut_offset\n",
    "    steps = 50\n",
    "    x_slice = torch.linspace(-1, 1, steps=steps)\n",
    "    plot_x = torch.zeros((steps,dim)) + offset\n",
    "    plot_x[:,plot_dim] = x_slice\n",
    "    plot_y = func(plot_x)\n",
    "    val_x = plot_x + std_x * torch.randn_like(plot_x)\n",
    "    ens_pred_mean, ens_pred_std = ens_net.mean_and_std(val_x)\n",
    "    ens_pred_mean = ens_pred_mean.detach().cpu().numpy().flatten()\n",
    "    ens_pred_std = ens_pred_std.detach().cpu().numpy().flatten()\n",
    "    print('RMSE: ', np.sqrt(np.mean( ((plot_y-ens_pred_mean)**2).detach().cpu().numpy() )))\n",
    "    ax.plot(x_slice, plot_y, color='b', label='ground truth', linewidth=2)\n",
    "    ax.plot(x_slice, ens_pred_mean, color='k', label='No EiV', linewidth=2)\n",
    "    ax.fill_between(x_slice, ens_pred_mean-k*ens_pred_std, ens_pred_mean+k*ens_pred_std, color='k', alpha=0.2)\n",
    "    ax.set_ylim([-2.7,2.7])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "e944f274",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dim=0\n",
      "RMSE:  0.2825916\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dim=1\n",
      "RMSE:  0.25714526\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dim=2\n",
      "RMSE:  0.2792112\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dim=3\n",
      "RMSE:  0.4986663\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dim=4\n",
      "RMSE:  0.28111818\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "file_chunk = ensemble_files[0:ensemble_size]\n",
    "ens = Ensemble(saved_files = file_chunk,\n",
    "                  architecture_class=Networks.FNNBer,\n",
    "                  device=device,\n",
    "                  p=0.5, init_std_y=init_std_y,\n",
    "                  h=[dim,500,300,100,1])\n",
    "\n",
    "# Cycle through plot dimensions\n",
    "for plot_dim in range(0,dim):\n",
    "    f = plt.figure()\n",
    "    ax = plt.gca()\n",
    "    print('dim=%i' % (plot_dim,)) \n",
    "    plot_ens_uncertainty(ens, plot_dim, ax)\n",
    "    plt.xlabel(r'$\\zeta$')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "f40d8346",
   "metadata": {},
   "outputs": [],
   "source": [
    "def ens_coverage_computation(ens, seed):\n",
    "    set_seeds(seed)\n",
    "    coverage_x = torch.tensor(np.random.uniform(low=-1.0,high=1.0, size=(1000,5)), dtype=torch.float32)\n",
    "    coverage_y = func(coverage_x)\n",
    "    number_of_repeated_draws = 100#0\n",
    "    ens_inside_list = []\n",
    "    ens_mse_list = []\n",
    "    for _ in tqdm(range(number_of_repeated_draws)):\n",
    "        noisy_coverage_x = coverage_x + std_x * torch.randn_like(coverage_x)\n",
    "        noisy_coverage_y = coverage_y + std_y * torch.randn_like(coverage_y)\n",
    "        mean, std = [t.cpu().detach().numpy()\n",
    "                       for t in ens.mean_and_std(noisy_coverage_x)]\n",
    "        ens_inside_list.append(inside_explicit_uncertainties(mean, std, coverage_y.cpu().detach().numpy()))\n",
    "        ens_mse_list.append(np.mean((mean.flatten()-noisy_coverage_y.cpu().detach().numpy().flatten())**2))\n",
    "    ens_inside = np.mean(np.stack(ens_inside_list), axis=0)\n",
    "    mse = np.mean(np.array(ens_mse_list))\n",
    "    return coverage_x, coverage_y, ens_inside, np.sqrt(mse)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "e5927fa2",
   "metadata": {},
   "outputs": [
    {
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     "output_type": "display_data"
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    {
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     },
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    },
    {
     "data": {
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     "metadata": {},
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    {
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       "model_id": "d533c44e9c724a2d8eea55fe46d3166e",
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     "metadata": {},
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    {
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       "model_id": "03f7f38aeab44ebc8ce19a884fbc4558",
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     },
     "metadata": {},
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    },
    {
     "data": {
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       "model_id": "f4d35621093746ab98c48d3bb92f0444",
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     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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       "version_major": 2,
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     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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   "source": [
    "ens_inside_collection = []\n",
    "rmse_collection = []\n",
    "for i in tqdm(range(number_of_ensembles)):\n",
    "    file_chunk = ensemble_files[i*ensemble_size: (i+1)*ensemble_size]\n",
    "    ens = Ensemble(saved_files = file_chunk,\n",
    "                  architecture_class=Networks.FNNBer,\n",
    "                  device=device,\n",
    "                  p=0.5, init_std_y=init_std_y,h=[dim, 500, 300, 100, 1] )\n",
    "    _,_, ens_inside, rmse = ens_coverage_computation(ens, seed=i*ensemble_size)\n",
    "    ens_inside_collection.append(ens_inside)\n",
    "    rmse_collection.append(rmse)\n",
    "ens_inside_collection = np.stack(ens_inside_collection)\n",
    "rmse_collection = np.stack(rmse_collection)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "b474e3c4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RMSE\n",
      "===========\n",
      "Average 0.700719, Error 0.005241\n",
      "\n",
      "\n",
      "Coverage\n",
      "===========\n",
      "Average 0.045273, Error 0.010158\n"
     ]
    }
   ],
   "source": [
    "# Results for Table 1 in preprint\n",
    "print('RMSE\\n===========')\n",
    "print('Average %.6f, Error %.6f' %( np.mean(rmse_collection),\n",
    "            np.std(rmse_collection)/np.sqrt(len(rmse_collection))))\n",
    "print(\"\\n\")\n",
    "\n",
    "print('Coverage\\n===========')\n",
    "print('Average %.6f, Error %.6f' %(ens_inside_collection.mean(), \n",
    "                                   ens_inside_collection.mean(axis=1).std()/np.sqrt(ens_inside_collection.shape[0])))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1210bba7",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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