06_02_TransfLearn_MissingMNIST_ConvTimeLSTM.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import torch\n",
    "from torch.autograd import Variable\n",
    "import torch.nn as nn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Import moving MNIST"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(20, 10000, 64, 64)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Moving_MNIST = np.load('data/mnist_test_seq.npy')\n",
    "Moving_MNIST = Moving_MNIST / 255\n",
    "Moving_MNIST.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Give `torch` the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([10000, 20, 1, 64, 64])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Making into PyTorch tensor\n",
    "Moving_MNIST_tensor = torch.from_numpy(Moving_MNIST)\n",
    "\n",
    "# Putting the existing dimensions into appropriate order\n",
    "Moving_MNIST_tensor = Moving_MNIST_tensor.permute(1, 0, 2, 3)\n",
    "\n",
    "# Added the acknowledge that this is 1 spectral band\n",
    "Moving_MNIST_tensor = Moving_MNIST_tensor.unsqueeze(2)\n",
    "\n",
    "# Checking shape\n",
    "Moving_MNIST_tensor.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Train/validation split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "train_indices = np.random.choice(range(10000), size = 8000, replace = False)\n",
    "\n",
    "OutofSample_indices = [index for index in range(10000) if index not in train_indices.tolist()]\n",
    "validation_indices = np.random.choice(OutofSample_indices, size = 1000, replace = False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Creating 9 data subsets, which the data will be uniformly sampled into and subsetted from 20 frames to [11, 20] frames, keep tracking of the number of frames omitted (i.e. $\\Delta{t}$ where 1 = no omission, 2 = 1 omission, etc...)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Creating empty nested lists to store data...\n",
    "train_data = []\n",
    "for i in range(9):\n",
    "    train_data.append([])\n",
    "# ...and time steps in\n",
    "train_delta_Ts = []\n",
    "for i in range(9):\n",
    "    train_delta_Ts.append([])\n",
    "\n",
    "# For the train (above) and validation (below) data\n",
    "validation_data = []\n",
    "for i in range(9):\n",
    "    validation_data.append([])\n",
    "validation_delta_Ts = []\n",
    "for i in range(9):\n",
    "    validation_delta_Ts.append([])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in range(Moving_MNIST_tensor.shape[0]):\n",
    "    \n",
    "    # Determine how many frames to keep out of the 20 possible\n",
    "    #     leaving 11 so that there is at least 10 for input and 1 for out\n",
    "    num_frames = np.random.choice(range(11, 20))\n",
    "    \n",
    "    # Determining what index that places the data in\n",
    "    data_index = (num_frames - 11)\n",
    "    \n",
    "    # Now that we have a number to keep, picking which specific ones to keep\n",
    "    frame_indices = np.random.choice(range(20),\n",
    "                                     size = num_frames,\n",
    "                                     replace = False)\n",
    "    \n",
    "    # Sorting those frames to proper chronological order\n",
    "    sorted_frame_indices = sorted(frame_indices)\n",
    "    \n",
    "    # Getting the missing-frames-data\n",
    "    frame_data = Moving_MNIST_tensor[i, sorted_frame_indices]\n",
    "    frame_data = frame_data.unsqueeze(dim = 0)\n",
    "    \n",
    "    # Determining \"time steps\" between indices\n",
    "    #     1 = proper sequence\n",
    "    #     2 = missing one index inbetween\n",
    "    #     3 = missing two indices inbetween\n",
    "    #     etc...\n",
    "    delta_Ts = []\n",
    "    for j in range(1, len(sorted_frame_indices)):\n",
    "        delta_Ts.append(sorted_frame_indices[j] - sorted_frame_indices[j-1])\n",
    "        \n",
    "    # Getting delta_Ts as an image band\n",
    "    #     \"num_frames - 1\" because it's not necessary for the first band\n",
    "    #     since it has no prior reference\n",
    "    delta_T_tensors = torch.ones([1, num_frames - 1, 1, 64, 64])\n",
    "    for k in range(delta_T_tensors.shape[1]):\n",
    "        delta_T_tensors[:, k, :, :, :] *= delta_Ts[k]\n",
    "    \n",
    "    # Storing it and its time steps appropriately\n",
    "    if i in train_indices:\n",
    "        # Initiating the tensor within the empty list\n",
    "        if train_data[data_index] == []:\n",
    "            train_data[data_index].append(frame_data)\n",
    "            train_delta_Ts[data_index].append(delta_T_tensors)\n",
    "        # Or expanding upon the tensor\n",
    "        else:\n",
    "            train_data[data_index][0] = torch.cat([train_data[data_index][0],\n",
    "                                                   frame_data])\n",
    "            train_delta_Ts[data_index][0] = torch.cat([train_delta_Ts[data_index][0],\n",
    "                                                       delta_T_tensors])\n",
    "    elif i in validation_indices:\n",
    "        if validation_data[data_index] == []:\n",
    "            validation_data[data_index].append(frame_data)\n",
    "            validation_delta_Ts[data_index].append(delta_T_tensors)\n",
    "        else:\n",
    "            validation_data[data_index][0] = torch.cat([validation_data[data_index][0],\n",
    "                                                        frame_data])\n",
    "            validation_delta_Ts[data_index][0] = torch.cat([validation_delta_Ts[data_index][0],\n",
    "                                                            delta_T_tensors])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For train data...\n",
      "torch.Size([896, 11, 1, 64, 64])\n",
      "torch.Size([884, 12, 1, 64, 64])\n",
      "torch.Size([869, 13, 1, 64, 64])\n",
      "torch.Size([887, 14, 1, 64, 64])\n",
      "torch.Size([930, 15, 1, 64, 64])\n",
      "torch.Size([857, 16, 1, 64, 64])\n",
      "torch.Size([887, 17, 1, 64, 64])\n",
      "torch.Size([882, 18, 1, 64, 64])\n",
      "torch.Size([908, 19, 1, 64, 64])\n",
      "\n",
      "For validation data...\n",
      "torch.Size([128, 11, 1, 64, 64])\n",
      "torch.Size([97, 12, 1, 64, 64])\n",
      "torch.Size([118, 13, 1, 64, 64])\n",
      "torch.Size([135, 14, 1, 64, 64])\n",
      "torch.Size([111, 15, 1, 64, 64])\n",
      "torch.Size([112, 16, 1, 64, 64])\n",
      "torch.Size([91, 17, 1, 64, 64])\n",
      "torch.Size([114, 18, 1, 64, 64])\n",
      "torch.Size([94, 19, 1, 64, 64])\n"
     ]
    }
   ],
   "source": [
    "print('For train data...')\n",
    "for i in range(len(train_data)):\n",
    "    print(train_data[i][0].shape)\n",
    "\n",
    "print('\\nFor validation data...')\n",
    "for i in range(len(validation_data)):\n",
    "    print(validation_data[i][0].shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Separating $x$ and $y$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sep_x_y(tensor_to_separate, time_tensor_to_separate):\n",
    "    x = []\n",
    "    y = []\n",
    "    t = []\n",
    "    for i in range(len(tensor_to_separate)):\n",
    "        current_seq = tensor_to_separate[i, :, :, :, :]\n",
    "        current_time_seq = time_tensor_to_separate[i, :, :, :, :]\n",
    "        for j in range(current_seq.shape[0]):\n",
    "            if j >= 10:\n",
    "                current_x = current_seq[(j-10):j].numpy()\n",
    "                x.append(current_x)\n",
    "                current_y = current_seq[j].unsqueeze(dim = 0).numpy()\n",
    "                y.append(current_y)\n",
    "                current_t = current_time_seq[(j-10):j].numpy()\n",
    "                t.append(current_t)\n",
    "    x = np.asarray(x)\n",
    "    x = torch.from_numpy(x).type(torch.FloatTensor)\n",
    "    y = np.asarray(y)\n",
    "    y = torch.from_numpy(y).type(torch.FloatTensor)\n",
    "    t = np.asarray(t)\n",
    "    t = torch.from_numpy(t).type(torch.FloatTensor)\n",
    "    return(x, y, t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_11, y_11, t_11 = sep_x_y(train_data[0][0], train_delta_Ts[0][0])\n",
    "x_12, y_12, t_12 = sep_x_y(train_data[1][0], train_delta_Ts[1][0])\n",
    "x_13, y_13, t_13 = sep_x_y(train_data[2][0], train_delta_Ts[2][0])\n",
    "x_14, y_14, t_14 = sep_x_y(train_data[3][0], train_delta_Ts[3][0])\n",
    "x_15, y_15, t_15 = sep_x_y(train_data[4][0], train_delta_Ts[4][0])\n",
    "x_16, y_16, t_16 = sep_x_y(train_data[5][0], train_delta_Ts[5][0])\n",
    "x_17, y_17, t_17 = sep_x_y(train_data[6][0], train_delta_Ts[6][0])\n",
    "x_18, y_18, t_18 = sep_x_y(train_data[7][0], train_delta_Ts[7][0])\n",
    "x_19, y_19, t_19 = sep_x_y(train_data[8][0], train_delta_Ts[8][0])\n",
    "\n",
    "x_11_validation, y_11_validation, t_11_validation = sep_x_y(validation_data[0][0],\n",
    "                                                            validation_delta_Ts[0][0])\n",
    "x_12_validation, y_12_validation, t_12_validation = sep_x_y(validation_data[1][0],\n",
    "                                                            validation_delta_Ts[1][0])\n",
    "x_13_validation, y_13_validation, t_13_validation = sep_x_y(validation_data[2][0],\n",
    "                                                            validation_delta_Ts[2][0])\n",
    "x_14_validation, y_14_validation, t_14_validation = sep_x_y(validation_data[3][0],\n",
    "                                                            validation_delta_Ts[3][0])\n",
    "x_15_validation, y_15_validation, t_15_validation = sep_x_y(validation_data[4][0],\n",
    "                                                            validation_delta_Ts[4][0])\n",
    "x_16_validation, y_16_validation, t_16_validation = sep_x_y(validation_data[5][0],\n",
    "                                                            validation_delta_Ts[5][0])\n",
    "x_17_validation, y_17_validation, t_17_validation = sep_x_y(validation_data[6][0],\n",
    "                                                            validation_delta_Ts[6][0])\n",
    "x_18_validation, y_18_validation, t_18_validation = sep_x_y(validation_data[7][0],\n",
    "                                                            validation_delta_Ts[7][0])\n",
    "x_19_validation, y_19_validation, t_19_validation = sep_x_y(validation_data[8][0],\n",
    "                                                            validation_delta_Ts[8][0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Consolidating the 9 subsets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = torch.cat([x_11, x_12, x_13,\n",
    "               x_14, x_15, x_16,\n",
    "               x_17, x_18, x_19])\n",
    "t = torch.cat([t_11, t_12, t_13,\n",
    "               t_14, t_15, t_16,\n",
    "               t_17, t_18, t_19])\n",
    "y = torch.cat([y_11, y_12, y_13,\n",
    "               y_14, y_15, y_16,\n",
    "               y_17, y_18, y_19])\n",
    "\n",
    "x_validation = torch.cat([x_11_validation, x_12_validation, x_13_validation,\n",
    "                          x_14_validation, x_15_validation, x_16_validation,\n",
    "                          x_17_validation, x_18_validation, x_19_validation])\n",
    "t_validation = torch.cat([t_11_validation, t_12_validation, t_13_validation,\n",
    "                          t_14_validation, t_15_validation, t_16_validation,\n",
    "                          t_17_validation, t_18_validation, t_19_validation])\n",
    "y_validation = torch.cat([y_11_validation, y_12_validation, y_13_validation,\n",
    "                          y_14_validation, y_15_validation, y_16_validation,\n",
    "                          y_17_validation, y_18_validation, y_19_validation])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Viewing the overlaid $(x, y)$ sequences where blue = early $x$ frame, green = late $x$ frame, and red = $y$ frame"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_ex():\n",
    "    random_index = np.random.choice(len(x_validation))\n",
    "    for i in range(10):\n",
    "        if i > 5:\n",
    "            plt.imshow(x_validation[random_index, i, 0], alpha = 0.25, cmap = 'Greens')\n",
    "            plt.text(65, 60/10*i, str(t_validation[random_index, i, 0][0, 0].item()) + ' steps')\n",
    "        else:\n",
    "            plt.imshow(x_validation[random_index, i, 0], alpha = 0.5, cmap = 'Blues')\n",
    "            plt.text(65, 60/10*i, str(t_validation[random_index, i, 0][0, 0].item()) + ' steps')\n",
    "    plt.imshow(y_validation[random_index, 0, 0], cmap = 'Reds', alpha = 0.25)\n",
    "    plt.pause(0.01);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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3LYi1zZiRjrHMCkI8O4N5N8rEbba/kxSfmDcz/TUIZ++0Bq9zzsx0EGpnUAt5395MosCcJMhltapsFJP3oK0l/VqWzl+UjClIJ2pqzUxDCmo/ljPThlqDGNeOLX/MHcbMIFZ10Oz5qWOv73or97zOWa4CMRTMbNbgrQZn0DsuSUskrYmTw56RdHG8f56k+yS9GP+dOxoDchzHGYx6XMV+4KtmtgI4AbhI0gqihLH7zWw50VOEy8ZumI7jOAmDuopxCe7N8fouSc8RZdieRfSEAaJg3W8JgnONSkshcFeaMn5HmIZQTB7Bt7SlM757e5P0gte7027Gso7DK+uziunfjd2B0F1pU5JV37s8nUhc6k0y1ltmpa9dDGdo1Khn2B+K6mW/BoVwXOF62lW0nFb7Yck4Fs7NCismx3r706kSs4Ns+XLgDs5qb021e7s7Sfvo3ZtWwZgRZP4vnJ243Nu2ptND2hcnDkOxdgpReowt7ipOBEMKzsezxd8HrAUWxkYN4E1gYc5pjuM4o0rdhkvSLOAXwCVm9k54LE5SqxqBlXSBpHWS1m3dtq1aE8dxnCFRl+GK5yX9ArjZzAbmFr0laVF8fBHJXKQUZrbazFaZ2aoFnfn6647jOPUyqDMfy1pcBzxnZt8LDg1MD/hO/PfOMRnhONNSSOInTc3pt6c/iMHs7kke/ze1pNuFE3669qXVCsLZKoVMDKo/qNG3M6gPuGN7OqUijGplo1hNQYyu0JT/u7QvlCidlY4ZzZ4xg2o0Z2JyFMPXnZ7m1FuqXouwqHxF1ZZiJlaYapq8cUWlx1ssZhQhQoKYX6HG73TzwkW5x3Zn4mapaw8hHuaMHvW86ycBfwU8JWlgJvjXiQzW7ZLOJ0rl/8zYDNFxHCdNPU8VHyK/ltWpozscx3GcwfH73FooP50g5F3z0kUSntryfGW9O1NWvico595+5BGpY/v+PZE2emdvIALYnS4w0RIU6mhrzlcnCB2j7CsJn6Qo41I2FRKXLXwLmorpXgpN+V+frqAQSOiEZYQdCL3PYsZ1VpCWYcGJ+7uh+Z9TIehj1zv5Lt+cA+blHuvfk3+ealzbGTt8rqLjTHHyZr9UaSdJ18TFMjZIWjmEa1wiaebojbo2brgcZ+qTN/slyxnA8ni5APjREK5xCTBuhstdxRosOiA92fa1PZurtps/84DUdn8wWXrntrSsUPngGkJ6AX/YmjwpO6gz/VSROUm2dvZBX8jslmQ+a7dSqXcpB8cy5ei3dydjLgQXKJfTqXq1RAELQdP+oKZjc6E12zK3jzyyzplquPStQeb8S33Vn3QCzGxpzz1W8+INQI3ZL89mmp4F/DTOy3xUUoekRUGiOZLagduBQ4h0tP6RKPn8YGCNpG1mdoqk04BvEpXE/APwBTPrjlVYbycyknuBc8xso6RPE+nPl4AuM/tgrdfkd1yOM43IzH7JUimWEbMp3hdyOvCGmR1tZkcC95jZNcAbwCmx0eoELgc+YmYrgXVAqMHVZWZHAT8kKuIBcAXw52Z2NHDmYK/DDZfjTBNqzX4ZAk8BH5V0paQPmFlXlTYnACuAh+MUqvOAw4LjtwR/T4zXHybSsP9boju5mrir6DjTgJzZL1kqxTJiDon3VTCzF+Kg/ceAb0u638y+lb0ccJ+ZfS7nOpZdN7MLJR1PVDTjcUnHmtnbVc/GDdew2b0ryZxva05nfO/tTVIBbG86rlIq5xdieGdf0rZ7V5ACkZkFOm92Nk40DGrFaoKQlwWFLiyTytAZKFO8mRUSDNruDtQsOprqH3t7a/L17O6rUcCixmsJBR/39QbCipl2hRoZ/SEzO9KxsIImv9NSY/ZLlruAL8UFWY8nculSgV1JBwPbzewmSTuBv4kP7SKq2bgNeBS4VtKyOH7VDiw2sxfitmcTJbCfTVSYA0nvNrO1wFpJZxAZUDdcjjONqTr7xczulnQhgJn9GLib6E5qI7AH+EKVvo4CrpJUJiqC8cV4/2rgHklvxHGuvwZuiSsBQRTzGjBccyVtAHqAgbuyqyQtJ/pNuR94stYLcsPlOFOcWrNfYoM1sG5E1Xhq9XUvcG+V/T8AfhBsPwC8P6ebq+LiGuH5n6x13SxuuIZLkBoQZsMDWKrcffr70hyKE/alfcA9QbZ56B6qJe2KtjbV59bUQkH/HbMzYnjBEFMjzGjH79ybSdMI6OlJJom3N8/PbTcc+jNuY6k/P82hEKRKlIKJ5Ydm3G0V8/8VWgIh/8UHLKh7nM7Y4YbLcZxxw8yWjkY/kz+y6DiOk8ENl+M4DYe7iqNAgbRCw+z5ScxoV0YE8OXtydPlI+a/K3VsyYwkHvNCEF3avf6JVLvNc5IpRirmx7tK/b25xwiKZfRkpvyE6R1hjCgb3i0okwKRIqU/kezNpFSEm4V6f0YzfZR681MlwpognUFssHnZ4VVaV+eIBfW3dcYHv+NyHKfhcMPlOE7D4a5iDZoLaRewLSgrv/3tJLN99/Z09aI5cxJVhr49aXft9a1bK+uHzElXdOsLStD3BdO13u5NP+4/KHA3rePA3PGHv0rNrenX0rsvGder29MKFkcszO+zXop1+32jTb5k4uzjj62sz5idVmBphAx4J8E/LcdxGg43XI7jNBzuKg6B1uAJXl+QrV0qp125uWGpd9ueOlbam7hou/rSZbUWvz+ZIdG1698q6y0taTfvoAMSl7XU2ZE73q7gWk396aebvYFe/NwZ6a9BqZxkmBcyJcNCmgJ3cMastOvVFLhoW3clk6wXddQvkhk+0SwGE65LPemniHsCV3r2rOwk7qSPprbktSxon1P3OJzJh99xOc4UxzXnHcdpRKac5rwbLseZ4pjZZjNbH6/vAgY057NUNOfN7FGgQ1KqxLekdkn/KulJSU9LOlvSl0k059fE7U6T9Iik9ZJ+FquvIullSd+V9JSk30laFu//dNzfk5IeHOw1eYxrCMxpSWJX5f4krcEy6eBtQSb9uxels+OLobJDX7rUfdmS2M17/tOJlfUZmRiXZiSxmram/N+e7h4F7dI/hnt7knSOpkyxiVJY7j5QhNiv7mFwXlOmakezBUU2AjWHrJLGjOClFTK/o+GwioXkfSuRjnEVA8WN2TNmkceiWQdV1lsmLF1jYhmm5nwoJjigOf/xuL85ZtYl6StEmvPbMprzuyVdSqQ5P6CU2mVmR0n6PJHm/CdINOdfl5QfuI0Z9NOTNCO2jE/G/vE34/2HS1ob+8O3ScqP4jqOM+FMJc35en52eoAPx9U3jgFOl3QCcCVwtZktA3YA59fRl+M4E8Boas4DK4kM2LclXVHtckSa88fEywozC+1DVc15oru0JUSa8zVF3AZ1FWNVxAG/ojleDPgwcE68/0bgHxhaMK+heffByQ9IT39aYM9KSTrBnPnpmovF4LeiN5NGUS4HLmfoJ2XqGe4N6gNmXbS8EoOlctqd7ZzXWVmff0DajbSsyP3A/szu/lLisnW0pd3ZPXtC4fpkvZzpJNwsZV5n6Jq2NQfvW2Zu94EzExc+O9shvEC5HKawpN+orBs8lZi2mvOSisDjwDLgWqICjzvNKkGZavXXHMeZHExPzXkzKwHHxEGzXwHvqec8AEkXED1aZcmhSwZp7TjOaDMVNeeH9GjFzHYCa4gCah2SBgzffr5wcM5qM1tlZqsWdHZWa+I4jjMkBr3jkrQA6DOznZLagI8SBebXAJ8CbiV6anDnWA50MhCGk9qClISW/vTj+bIlD0VaW9NvcRjTaSml4057gmIO/UGflom/tDUn/WdjRsUgyFUOY0aZdjODcWUzAzLDSrrIbuc1BA49KIitBsoL5XL+OfUyJ5jyNBh7e/pyjmRfzdSNcU0mRktzvh5XcRFwYxznKgC3m9mvJT0L3Crp28DviYJ/juM4Y049TxU3ECWsZfe/BBw3FoNyHMephWfOjwbKf7TeVCNDO5teoLxchowbU69TUz2pIaItyDbPjiNPL75WxkCxmBljofp54y0w2JYRUHSmBtNz3oPjOA2NGy7HcRoOdxWHQF/wFK1Uyi/73lRj4vNwsFwXskrbwMvrCcp2Zd3BQiH/yWSmx2A9fxxNmYnghSGM2XGGit9xOY7TcLjhchyn4XDD5ThOw+ExriFQzgkFFTKP+DUKvwepDPum/HhRNpaUUlvo2Zd73nBCUPvFyYLiIe3NM3Cc8cLvuBxnipMnBlqlXWssCroxFgldOoRrfH20xlsPbrgcZ+qTJwaa5XxgRywOejXRnOR6GVfD5a5iDbLzgcs5KRDZicO9wbZqpJtbnu8JWOCX1fp1yfZezsuXH4prmJMBkR3unLa0SKIzOakhBprlLCJBUICfAz+UJAu+jHHxjNuAA4jsxxeBjwNtsdbXM2Z2rqS/BL4MtBDp2/9nMytJ6gb+GTgNeBP4rJltjQtuXEhUkehZM/tsrdfkd1yOMw2QVIwNyxYiWeWaxTJikdAuICuhfA5wr5kdAxwNPGFmlwF7Y5nmcyX9KZG66UlxuxJwbnx+O7DOzN4L/D/gG/H+y4D3mdmfERmwmvgdl+NMA7JioJKONLOnh9HVY8D1sYb9HWb2RJU2pwLHAo/F82/biAwmQJnojg3gJmBA/34DcLOkO4A7BhuE33E5zjQiEAM9vcrhSrGMWCR0DhnddzN7EPhg3PaGuMRYFgE3BsUyjjCzf8gbUvz340Sy8CuJDF7Nmyo3XGOMlS13ydLXX6osVipXlpKRWgoFVZaSWWqJvgcDS0Jr+8zUIqgs6XNqTf9xGhFJCwZqFQZioP9RpeldRKKgEImEPhDGt+LzDwPeMrN/Bn5CZGgA+uK7MIg04z8l6cD4nHnxeRDZnE/F6+cAD0kqAEvMbA1wKZHBzC+QibuKjjMdqCoGCiDpW0Qxp7uIxED/RdJGYDtQLUD+IeDvJPURBfwH7rhWAxskrY/jXJcDv4mNUh+Rlv0rwG7guPj4FqJYWBG4SdIcot/Sa+I7w1xkNSfYji7HHrvS/v2Rh8bteiMl+1Sxpy9PBnh0eGdPb2W91Jtc64A57al2bS21fm+Sz/OVzdsr660z03LHB85OtveTyMqdV12rYZqpXO5rMnPiCSezfv36SfvmS+o2s5p3U/Xgd1w1yP5DtzTnidINz/j3Z9zFclCnMExtb2lKF/YNBQdr/fA0tSbZ7PNmpguN1xzxpP3aO06Ex7gcxxk3RuNuC9xwOY7TgLirOASKuWZ+eL5VtuS8lYLtlIZ7ul1/WBashqt4UMfM3BGGZ+2vfZ/bpeNMCvyOy3GchsMNl+M4DYcbLsdxGg6PcU1Sii1J+oLIigUmMS7LxL/CtuH6/pGwpI+ypX+/ih7jciY5dd9xxbPLfy9pIOP28FhsbGMsPtYyWB+O4zijwVBcxYuB54LtK4GrY9GxHUQiZI7jOGNOXYZL0iFEs7d/Em8L+DCR2BjAjcBfjMUApxPNra2VpWNmshQKhdRSTC3F1BK2S02dLpfSi1FZCkov+fhkbGdyUO8d1/eBvycJjMwHdsZiYwCbiETIHMeZhEi6XtIWSbkaXIq4Jg7/bJC0Mq9tlXMvkTRz8Jajw6CGS9IngC1m9vhwLiDpAknrJK3bum3bcLpwHGfk3EB1Da6QM4Dl8XIB8KMh9H8JMHkMF3AScKakl4FbiVzEfwI6ArGvQ4iExfbDzFab2SozW7Wgs3MUhuw4zlCJBQC3D9LsLOCnFvEo0f/4orCBpHZJ/xpXDHpa0tmxXvzBwBpJa+J2p0l6RNJ6ST+TNCve/7Kk70p6Kq48tCze/+m4vyclPTjY6xnUcJnZ18zsEDNbSqTP84CZnUukojggCHYecOdgfTm1mdXWVFmaCqos+8WggkU1lhT7haeSjZrnOdOJiuZ8TLUQ0OnAG2Z2tJkdCdxjZtcAbwCnmNkpkjqBy4GPmNlKYB3wlaCPLjM7CvghURgK4Argz+NKRGcONtCRJKBeCnwlFh2bTyRC5jjO1OYp4KOSrpT0ATPrqtLmBGAF8HBcoOM84LDg+C3B3xPj9YeJpKD/lkhYsCZDSkA1s98Cv43XXwKOG8r5juNMaiqa8zH7hYDM7IU4aP8x4NuS7jezb2X6EVEloc/lXMey62Z2oaTjibIXHpd0rJlCMnNUAAAJrUlEQVS9XfVsfMrPhBKmJOwv8pD4g1lXrqBC7qJwCXspZBYVK8tg46o+vvpfm9Mw3AV8Pn66eAKRS7c5bCDpYGCPmd0EXEWiOb8LmB2vPwqcFMSv2iX9SdDN2cHfR+I27zaztWZ2BbCVtAHdD5/y4zjTAEm3EOnFd0raBHzDzK6TdCGAmf0YuJvoTmojsAf4QpWujgKuklQm0pL/Yrx/NXCPpDfiONdfA7dIao2PXw68EK/PlbSBqML2wF3ZVZKWE/3O3g88WfP1uOb8xNHTlxa1L5eTStmhTHRWB6zWRxYeKgW6XVFZvYDgTqve/jWEyH0haOsB//GjATTnXwZWmdmIcqP8jmsCCQ1Vllr/7DUNQZ2FLvYrkFFXH/UTaiT6pG1ntHHD5TjOuBGnVY0YD847jtNwuOFyHKfhcFdxihHGv1KxMEsHmpT6zcqIERbygly1Sm6k8Xqwzljid1yO4zQcbrgcx2k43FWcRBSKSW7VaLhatfK9wv7LNVP5hjcQz91yxhK/43Icp+Fww+U4TsPhhstxnIbDDdcEUigUU0soHjgqjEJdi/qKaDiTGUlLJK2R9KykZyRdnNNu6mjOO47T8PQDXzWzFUQifxdJWlGl3ZTSnHccp4Exs81mtj5e30VUH7VaVa6G0Zz3dIgJpLV56vxuDEXyxpk4JC0F3gesrXI4T3M+FBMc0Jz/eNzfHDPrkvQVIs35bRnN+d2SLiXSnB9QSu0ys6MkfZ5Ic/4TJJrzr0vqGOx1TJ3/HMdxahLf9fwCuMTM3hlmN42nOe84TmMiqZnIaN1sZr/Maeaa887kYn/N+bAc2X61y4bef2ZxJg+K/PjrgOfM7Hs1mrrmvOM4k4aTgL8CnopdN4Cvm9ndrjlfB645P7709Sea88rcWzcF2s2lclr7PqQQnLj/nEYL2mVkc/y2a0KYLprz7io6jtNwuKs4hUmJCo7Kb5QXSXRGxmhpztdluOLbu11ACeg3s1WS5gG3AUuBl4HPmNmO0RiU4zhOLYbyM3yKmR1jZqvi7cuA+81sOVEw7bJRH53jOE4VRuI/nAXcGK/fCPzFyIfjjCZNxUJlKRZILbVJEhvSaROOMzmo13AZ8BtJj0u6IN63MMjxeBNYOOqjcxzHqUK9wfmT4zlEBwL3SfqP8KCZmaSqkdvY0F0AsOTQmjlljuM4dVHXHZeZvR7/3QL8CjgOeGtg5nj8d0vOuavNbJWZrVrQ2Tk6o3YcZ1ozeLQjStefPbAOnAY8TTQ94Ly42XnAnWM1SGesSU/YkZLFcSYj9biKC4FfxV/iJuD/mNk9kh4Dbpd0PvAK8JmxG6bjOE7CoIbLzF4Cjq6y/23g1LEYlOM4Ti08c96hOGxB+eQ89yqd8cTnKjrONEDS9ZK2SHq6RhsvluE4zqTiBiLZ5Vp4sQzHcSYPZvYgsH2QZg1TLMMNlzNsvObilCOvWEbIQLGMo83sSOAeM7sGeINoPvMpmWIZK4F1RMUyBugys6OAHxIVy4CkWMbRwJmDDdQNl+M4Q8GLZTiOM6nwYhnO1KNYUGpx5YgphxfLcBxn8iDpFuBDQKekTcA3zOw6L5ZRB14sw3HGFi+W4TiOM0lxV9FxnHFjtIpl+B2X4zgNhxsux3EaDjdcjuM0HG64HMdpONxwOY7TcLjhchyn4XDD5ThOw+GGy3GchsMNl+M4DYcbLsdxGg43XI7jNBxuuBzHaTjccDmO03DUZbgkdUj6uaT/kPScpBMlzZN0n6QX479zx3qwjuM4UP8d1z8RVfN4D3A08BxwGXC/mS0nUiy8bGyG6DiOk2ZQwyVpDvBB4DoAM+s1s51ENdhujJvdCPzFWA3ScRwnpJ47rsOJxOv/t6TfS/qJpHZgYSCk/yawcKwG6TiOE1KP4WoiquTxIzN7H7CbjFtokXB9VfF6SRdIWidp3dZtI5KZdhzHAeozXJuATWa2Nt7+OZEhe2ugPHf8d0u1k81stZmtMrNVCzo7R2PMjuNMcwY1XGb2JvCapCPiXacCzxLVYDsv3ncecOeYjNBxHCdDvcUy/gtws6QW4CWiemsF4HZJ5wOvAJ8ZmyE6juOkqctwmdkTwKoqh04d3eE4juMMjmfOO47TcLjhchyn4XDD5ThOw+GGy3GchsMNl+M4DYcbLsdxGg43XI7jNByKphmO08WkrUTJqp3ARE9cnAxjAB9HFh9HmqGO4zAzWzBWg5ksjKvhqlxUWmdm1RJap9UYfBw+jkYZx2TDXUXHcRoON1yO4zQcE2W4Vk/QdUMmwxjAx5HFx5FmsoxjUjEhMS7HcZyR4K6i4zgNx7gaLkmnS3pe0kZJ41YVSNL1krZIejrYN+7l1SQtkbRG0rOSnpF08USMRdIMSb+T9GQ8jm/G+w+XtDb+fG6L9dfGHEnFuJ7BrydqHJJelvSUpCckrYv3TcR3xEsB1sG4GS5JReBa4AxgBfA5SSvG6fI3AKdn9k1EebV+4KtmtgI4Abgofg/Geyw9wIfN7GjgGOB0SScAVwJXm9kyYAdw/hiPY4CLiUreDTBR4zjFzI4J0g8m4jvipQDrwczGZQFOBO4Ntr8GfG0cr78UeDrYfh5YFK8vAp4fr7EEY7gT+OhEjgWYCawHjidKdGyq9nmN4fUPIfpn/DDwa0ATNI6Xgc7MvnH9XIA5wB+JY88TNY5GWMbTVVwMvBZsb4r3TRQTWl5N0lLgfcDaiRhL7J49QVTk5D7gD8BOM+uPm4zX5/N94O+Bcrw9f4LGYcBvJD0u6YJ433h/Ll4KsE48OE/t8mpjgaRZwC+AS8zsnYkYi5mVzOwYojue44D3jPU1s0j6BLDFzB4f72tX4WQzW0kUyrhI0gfDg+P0uYyoFOB0YjwN1+vAkmD7kHjfRFFXebXRRlIzkdG62cx+OZFjAbCoKvkaIpesQ9JAHYLx+HxOAs6U9DJwK5G7+E8TMA7M7PX47xbgV0TGfLw/lxGVApxOjKfhegxYHj8xagE+S1TibKIY9/JqkgRcBzxnZt+bqLFIWiCpI15vI4qzPUdkwD41XuMws6+Z2SFmtpTo+/CAmZ073uOQ1C5p9sA6cBrwNOP8uZiXAqyf8QyoAR8DXiCKp/z3cbzuLcBmoI/oV+18oljK/cCLwP8F5o3DOE4mus3fADwRLx8b77EAfwb8Ph7H08AV8f53Ab8DNgI/A1rH8TP6EPDriRhHfL0n4+WZge/mBH1HjgHWxZ/NHcDciRjHZF88c95xnIbDg/OO4zQcbrgcx2k43HA5jtNwuOFyHKfhcMPlOE7D4YbLcZyGww2X4zgNhxsux3Eajv8PBjYhhQPoJv0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_ex()\n",
    "plot_ex()\n",
    "plot_ex()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Defining the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "class ConvTime_LSTMCell(nn.Module):\n",
    "\n",
    "    def __init__(self, input_size, input_dim, hidden_dim, kernel_size, bias, GPU):\n",
    "        \"\"\"\n",
    "        Initialize ConvTime_LSTM cell.\n",
    "        \n",
    "        Parameters\n",
    "        ----------\n",
    "        input_size: (int, int)\n",
    "            Height and width of input tensor as (height, width).\n",
    "        input_dim: int\n",
    "            Number of channels of input tensor.\n",
    "        hidden_dim: int\n",
    "            Number of channels of hidden state.\n",
    "        kernel_size: (int, int)\n",
    "            Size of the convolutional kernel.\n",
    "        bias: bool\n",
    "            Whether or not to add the bias.\n",
    "        \"\"\"\n",
    "\n",
    "        super(ConvTime_LSTMCell, self).__init__()\n",
    "\n",
    "        self.height, self.width = input_size\n",
    "        self.input_dim  = input_dim\n",
    "        self.hidden_dim = hidden_dim\n",
    "\n",
    "        self.kernel_size = kernel_size\n",
    "        self.padding     = kernel_size[0] // 2, kernel_size[1] // 2\n",
    "        self.bias        = bias\n",
    "        self.GPU         = GPU\n",
    "        \n",
    "        ## Defining the input convolutional layer ##\n",
    "        self.i_conv = nn.Conv2d(in_channels=self.input_dim + self.hidden_dim,\n",
    "                                out_channels=self.hidden_dim,\n",
    "                                kernel_size=self.kernel_size,\n",
    "                                padding=self.padding,\n",
    "                                bias=self.bias)\n",
    "        \n",
    "        ## Defining the T2 convolutional layer ##\n",
    "        self.T1_conv = nn.Conv2d(in_channels=self.input_dim,\n",
    "                                 out_channels=self.hidden_dim,\n",
    "                                 kernel_size=self.kernel_size,\n",
    "                                 padding=self.padding,\n",
    "                                 bias=self.bias)\n",
    "        \n",
    "        ## Defining the T1 convolutional layer ##\n",
    "        self.T2_conv = nn.Conv2d(in_channels=self.input_dim,\n",
    "                                 out_channels=self.hidden_dim,\n",
    "                                 kernel_size=self.kernel_size,\n",
    "                                 padding=self.padding,\n",
    "                                 bias=self.bias)\n",
    "        \n",
    "        ## Defining the activation convolutional layer ##\n",
    "        self.c_conv = nn.Conv2d(in_channels=self.input_dim + self.hidden_dim,\n",
    "                                out_channels=self.hidden_dim,\n",
    "                                kernel_size=self.kernel_size,\n",
    "                                padding=self.padding,\n",
    "                                bias=self.bias)\n",
    "        \n",
    "        ## Defining the output convolutional layer ##\n",
    "        self.o_conv = nn.Conv2d(in_channels=self.input_dim + self.hidden_dim,\n",
    "                                out_channels=self.hidden_dim,\n",
    "                                kernel_size=self.kernel_size,\n",
    "                                padding=self.padding,\n",
    "                                bias=self.bias)\n",
    "        \n",
    "        ## Defining the learnable parameter for time scaling ##\n",
    "        self.constrained_scalar = nn.Parameter(torch.rand(1, 1))\n",
    "        self.unconstrained_scalars = nn.Parameter(torch.rand(2, 1))\n",
    "\n",
    "    def forward(self, input_tensor, time_tensor, cur_state):\n",
    "        \n",
    "        \n",
    "        ## Getting the h_{m-1} and c_{m-1} ##\n",
    "        ##     the previous hidden and activations ##\n",
    "        h_cur, c_cur = cur_state\n",
    "        \n",
    "        \n",
    "        ## Getting the (time tensor)*(their learned scalar) ##\n",
    "        ## For T1, with a constrained weight ##\n",
    "        t_T1 = self.constrained_scalar.clamp(max = 0) * time_tensor\n",
    "        ## For T2 and output gate, without constraints ##\n",
    "        t_bands_list = []\n",
    "        for i in range(2):\n",
    "            unconstrained_scalar = self.unconstrained_scalars[i]\n",
    "            scaled_time_tensors = time_tensor * unconstrained_scalar\n",
    "            t_bands_list.append(scaled_time_tensors)\n",
    "        t_T2, t_o = t_bands_list\n",
    "        ## Applying the appropriate non-linearities to t_T1 and t_T2 ##\n",
    "        t_T1 = torch.sigmoid(t_T1)\n",
    "        t_T2 = torch.sigmoid(t_T2)\n",
    "\n",
    "\n",
    "        ## concatenate the prev. hidden state and the current input along the color channel dim ##\n",
    "        x_h_combined = torch.cat([input_tensor, h_cur], dim = 1)\n",
    "        \n",
    "        \n",
    "        ## The input gate ##\n",
    "        ## Running the input convolution ##\n",
    "        i_conv_outputs = self.i_conv(x_h_combined)\n",
    "        ## Running the input LSTM gate equations ##\n",
    "        i_m = torch.sigmoid(i_conv_outputs)\n",
    "        \n",
    "        \n",
    "        ## The first time gate ##\n",
    "        ## Running the first time convolution ##\n",
    "        T1_conv_outputs = self.T1_conv(input_tensor)\n",
    "        T1_conv_outputs = T1_conv_outputs + t_T1\n",
    "        ## Running the T1 LSTM gate equations ##\n",
    "        T1_m = torch.sigmoid(T1_conv_outputs)\n",
    "        \n",
    "        \n",
    "        ## The second time gate ##\n",
    "        ## Running the second time convolution ##\n",
    "        T2_conv_outputs = self.T2_conv(input_tensor)\n",
    "        T2_conv_outputs = T2_conv_outputs + t_T2\n",
    "        ## Running the T2 LSTM gate equations ##\n",
    "        T2_m = torch.sigmoid(T2_conv_outputs)\n",
    "        \n",
    "        \n",
    "        ## The c vectors ##\n",
    "        ## Running the c convolution ##\n",
    "        c_conv_outputs = self.c_conv(x_h_combined)\n",
    "        ## Computing the c tilde and c activation vectors ##\n",
    "        c_m_tilde = (((1 - i_m * T1_m) * c_cur) +\n",
    "                     (i_m * T1_m * torch.tanh(c_conv_outputs)))\n",
    "        c_m = (((1 - i_m) * c_cur) +\n",
    "               (i_m * T2_m * torch.tanh(c_conv_outputs)))\n",
    "        \n",
    "         \n",
    "        ## The output gate ##\n",
    "        ## Running the output gate convolution\n",
    "        o_conv_output = self.o_conv(x_h_combined)\n",
    "        o_conv_output = o_conv_output + t_o\n",
    "        ## Running the output LSTM gate equations\n",
    "        o_m = torch.sigmoid(o_conv_output)\n",
    "        \n",
    "        \n",
    "        ## The hidden vector ##\n",
    "        h_m = o_m * torch.tanh(c_m_tilde)\n",
    "        \n",
    "        \n",
    "        return h_m, c_m\n",
    "\n",
    "    def init_hidden(self, batch_size):\n",
    "        to_return = (Variable(torch.zeros(batch_size, self.hidden_dim, self.height, self.width)),\n",
    "                     Variable(torch.zeros(batch_size, self.hidden_dim, self.height, self.width)))\n",
    "        if self.GPU:\n",
    "            to_return = (to_return[0].cuda(), to_return[1].cuda())\n",
    "        return(to_return)\n",
    "\n",
    "\n",
    "class ConvTime_LSTM(nn.Module):\n",
    "\n",
    "    def __init__(self, input_size, input_dim, hidden_dim, kernel_size, num_layers,\n",
    "                 batch_first, bias, return_all_layers, GPU):\n",
    "        super(ConvTime_LSTM, self).__init__()\n",
    "\n",
    "        self._check_kernel_size_consistency(kernel_size)\n",
    "\n",
    "        # Make sure that both `kernel_size` and `hidden_dim` are lists having len == num_layers\n",
    "        kernel_size = self._extend_for_multilayer(kernel_size, num_layers)\n",
    "        hidden_dim  = self._extend_for_multilayer(hidden_dim, num_layers)\n",
    "        if not len(kernel_size) == len(hidden_dim) == num_layers:\n",
    "            raise ValueError('Inconsistent list length.')\n",
    "\n",
    "        self.height, self.width = input_size\n",
    "\n",
    "        self.input_dim  = input_dim\n",
    "        self.hidden_dim = hidden_dim\n",
    "        self.kernel_size = kernel_size\n",
    "        self.num_layers = num_layers\n",
    "        self.batch_first = batch_first\n",
    "        self.bias = bias\n",
    "        self.return_all_layers = return_all_layers\n",
    "        self.GPU = GPU\n",
    "\n",
    "        cell_list = []\n",
    "        for i in range(0, self.num_layers):\n",
    "            cur_input_dim = self.input_dim if i == 0 else self.hidden_dim[i-1]\n",
    "\n",
    "            cell_list.append(ConvTime_LSTMCell(input_size=(self.height, self.width),\n",
    "                                               input_dim=cur_input_dim,\n",
    "                                               hidden_dim=self.hidden_dim[i],\n",
    "                                               kernel_size=self.kernel_size[i],\n",
    "                                               bias=self.bias,\n",
    "                                               GPU=self.GPU))\n",
    "\n",
    "        self.cell_list = nn.ModuleList(cell_list)\n",
    "\n",
    "    def forward(self, input_tensor, time_tensor, hidden_state=None):\n",
    "        \"\"\"\n",
    "        \n",
    "        Parameters\n",
    "        ----------\n",
    "        input_tensor: todo \n",
    "            5-D Tensor either of shape (t, b, c, h, w) or (b, t, c, h, w)\n",
    "        hidden_state: todo\n",
    "            None. todo implement stateful\n",
    "            \n",
    "        Returns\n",
    "        -------\n",
    "        last_state_list, layer_output\n",
    "        \"\"\"\n",
    "        \n",
    "        if not self.batch_first:\n",
    "            # (t, b, c, h, w) -> (b, t, c, h, w)\n",
    "            input_tensor.permute(1, 0, 2, 3, 4)\n",
    "\n",
    "        # Implement stateful ConvLSTM\n",
    "        if hidden_state is not None:\n",
    "            raise NotImplementedError()\n",
    "        else:\n",
    "            hidden_state = self._init_hidden(batch_size=input_tensor.size(0))\n",
    "\n",
    "        layer_output_list = []\n",
    "        last_state_list   = []\n",
    "\n",
    "        seq_len = input_tensor.size(1)\n",
    "        cur_layer_input = input_tensor\n",
    "        cur_time_input = time_tensor\n",
    "\n",
    "        for layer_idx in range(self.num_layers):\n",
    "            h, c = hidden_state[layer_idx]\n",
    "            output_inner = []\n",
    "            for t in range(seq_len):\n",
    "\n",
    "                h, c = self.cell_list[layer_idx](input_tensor = cur_layer_input[:, t, :, :, :],\n",
    "                                                 time_tensor = cur_time_input[:, t, :, :, :],\n",
    "                                                 cur_state=[h, c])\n",
    "                output_inner.append(h)\n",
    "\n",
    "            layer_output = torch.stack(output_inner, dim=1)\n",
    "            cur_layer_input = layer_output\n",
    "\n",
    "            layer_output_list.append(layer_output)\n",
    "            last_state_list.append([h, c])\n",
    "\n",
    "        if not self.return_all_layers:\n",
    "            layer_output_list = layer_output_list[-1:]\n",
    "            last_state_list   = last_state_list[-1:]\n",
    "\n",
    "        return layer_output_list, last_state_list\n",
    "\n",
    "    def _init_hidden(self, batch_size):\n",
    "        init_states = []\n",
    "        for i in range(self.num_layers):\n",
    "            init_states.append(self.cell_list[i].init_hidden(batch_size))\n",
    "        return init_states\n",
    "\n",
    "    @staticmethod\n",
    "    def _check_kernel_size_consistency(kernel_size):\n",
    "        if not (isinstance(kernel_size, tuple) or\n",
    "                    (isinstance(kernel_size, list) and all([isinstance(elem, tuple) for elem in kernel_size]))):\n",
    "            raise ValueError('`kernel_size` must be tuple or list of tuples')\n",
    "\n",
    "    @staticmethod\n",
    "    def _extend_for_multilayer(param, num_layers):\n",
    "        if not isinstance(param, list):\n",
    "            param = [param] * num_layers\n",
    "        return param"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The model already trained on standard MovingMNIST was saved as a parallel GPU PyTorch model, so it automatically loads back as such"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "conv_time_lstm = torch.load('ConvTimeLSTMSavedModel.pt')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Training"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "loss = torch.nn.MSELoss()\n",
    "optimizer = torch.optim.Adam(conv_time_lstm.parameters())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "from torch.utils import data\n",
    "\n",
    "class train_Dataset(data.Dataset):\n",
    "    'Characterizes a dataset for PyTorch'\n",
    "    def __init__(self, data_indices):\n",
    "        'Initialization'\n",
    "        self.data_indices = data_indices\n",
    "    \n",
    "    def __len__(self):\n",
    "        'Denotes the total number of samples'\n",
    "        return len(self.data_indices)\n",
    "    \n",
    "    def __getitem__(self, index):\n",
    "        'Generates one sample of data'\n",
    "        # Select sample\n",
    "        IDs = self.data_indices[index]\n",
    "\n",
    "        # Load data and get label\n",
    "        curr_x = x[IDs, :, :, :, :]\n",
    "        curr_t = t[IDs, :, :, :, :] * 1/10\n",
    "        curr_y = y[IDs, :, :, :, :]\n",
    "\n",
    "        #return X, y\n",
    "        return(curr_x, curr_y, curr_t)\n",
    "    \n",
    "class validation_Dataset(data.Dataset):\n",
    "    'Characterizes a dataset for PyTorch'\n",
    "    def __init__(self, data_indices):\n",
    "        'Initialization'\n",
    "        self.data_indices = data_indices\n",
    "    \n",
    "    def __len__(self):\n",
    "        'Denotes the total number of samples'\n",
    "        return len(self.data_indices)\n",
    "    \n",
    "    def __getitem__(self, index):\n",
    "        'Generates one sample of data'\n",
    "        # Select sample\n",
    "        IDs = self.data_indices[index]\n",
    "\n",
    "        # Load data and get label\n",
    "        curr_x = x_validation[IDs, :, :, :, :]\n",
    "        curr_t = t_validation[IDs, :, :, :, :] * 1/10\n",
    "        curr_y = y_validation[IDs, :, :, :, :]\n",
    "\n",
    "        #return X, y\n",
    "        return(curr_x, curr_y, curr_t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "training_set = train_Dataset(data_indices = range(y.shape[0]))\n",
    "validation_set = validation_Dataset(data_indices = range(y_validation.shape[0]))\n",
    "\n",
    "batch_size = 64\n",
    "\n",
    "train_loader = torch.utils.data.DataLoader(dataset = training_set,\n",
    "                                           batch_size = batch_size,\n",
    "                                           shuffle = True)\n",
    "validation_loader = torch.utils.data.DataLoader(dataset = validation_set,\n",
    "                                                batch_size = batch_size,\n",
    "                                                shuffle = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "device = torch.device(\"cuda\" if torch.cuda.is_available() else \"cpu\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch:  0 \n",
      "\tBatch loss:  0.019405774772167206 \n",
      "\n",
      "Epoch:  1 \n",
      "\tBatch loss:  0.02295311912894249 \n",
      "\n",
      "Epoch:  2 \n",
      "\tBatch loss:  0.01983240433037281 \n",
      "\n",
      "Epoch:  3 \n",
      "\tBatch loss:  0.01857680454850197 \n",
      "\n",
      "Epoch:  4 \n",
      "\tBatch loss:  0.019397582858800888 \n",
      "\n",
      "Epoch:  5 \n",
      "\tBatch loss:  0.017405904829502106 \n",
      "\n",
      "Epoch:  6 \n",
      "\tBatch loss:  0.019709371030330658 \n",
      "\n",
      "Epoch:  7 \n",
      "\tBatch loss:  0.018002094700932503 \n",
      "\n",
      "Epoch:  8 \n",
      "\tBatch loss:  0.015344567596912384 \n",
      "\n",
      "Epoch:  9 \n",
      "\tBatch loss:  0.01571454480290413 \n",
      "\n",
      "Epoch:  10 \n",
      "\tBatch loss:  0.01947551593184471 \n",
      "\n",
      "Epoch:  11 \n",
      "\tBatch loss:  0.016999736428260803 \n",
      "\n",
      "Epoch:  12 \n",
      "\tBatch loss:  0.013804811052978039 \n",
      "\n",
      "Epoch:  13 \n",
      "\tBatch loss:  0.01667061075568199 \n",
      "\n",
      "Epoch:  14 \n",
      "\tBatch loss:  0.012634426355361938 \n",
      "\n",
      "Epoch:  15 \n",
      "\tBatch loss:  0.01328028179705143 \n",
      "\n",
      "Epoch:  16 \n",
      "\tBatch loss:  0.01632414013147354 \n",
      "\n",
      "Epoch:  17 \n",
      "\tBatch loss:  0.015761692076921463 \n",
      "\n"
     ]
    }
   ],
   "source": [
    "loss_list = []\n",
    "epochs = int(np.ceil((7*10**5) / x.shape[0]))\n",
    "for i in range(epochs):\n",
    "    for data in train_loader:\n",
    "\n",
    "        # data loader\n",
    "        batch_x, batch_y, batch_t = data\n",
    "\n",
    "        # move to GPU\n",
    "        batch_x = batch_x.to(device)\n",
    "        batch_t = batch_t.to(device)\n",
    "        batch_y = batch_y.to(device)\n",
    "\n",
    "        # run model and get the prediction\n",
    "        batch_y_hat = conv_time_lstm(batch_x,\n",
    "                                     batch_t)\n",
    "        batch_y_hat = batch_y_hat[0][0][:, -2:-1, :, :, :]\n",
    "\n",
    "        # calculate and store the loss\n",
    "        batch_loss = loss(batch_y, batch_y_hat)\n",
    "        loss_list.append(batch_loss.item())\n",
    "\n",
    "        # update parameters\n",
    "        optimizer.zero_grad()\n",
    "        batch_loss.backward()\n",
    "        optimizer.step()\n",
    "\n",
    "    print('Epoch: ', i, '\\n\\tBatch loss: ', batch_loss.item(), '\\n')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(loss_list,\n",
    "         color = 'cyan',\n",
    "         label = 'Batch')\n",
    "plt.plot(np.convolve(loss_list, 1/10*np.ones(10))[10:-10],\n",
    "         color = 'navy',\n",
    "         label = 'Running average')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Getting random predictions for the validation set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "rand_x, rand_y, rand_t = next(iter(validation_loader))\n",
    "\n",
    "rand_y_hat = conv_time_lstm(rand_x.to(device),\n",
    "                            rand_t.to(device))[0][0][:, -2:-1, :, :, :]\n",
    "rand_y_hat = rand_y_hat.cpu().data.numpy()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# View prediction on sequence ($\\hat{y}$ on $x$)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_random_validation_pred():\n",
    "    f, axarr = plt.subplots(1, 2)\n",
    "    f.set_figheight(4)\n",
    "    f.set_figwidth(8)\n",
    "    random_index = np.random.choice(len(rand_x))\n",
    "    for i in range(10):\n",
    "        axarr[0].imshow(rand_x[random_index, i, 0], alpha = 0.25, cmap = 'gist_gray')\n",
    "        axarr[1].imshow(rand_x[random_index, i, 0], alpha = 0.25, cmap = 'gist_gray')\n",
    "        axarr[1].text(65,\n",
    "                      60/10*i,\n",
    "                      str(int(rand_t[random_index, i, 0, 0, 0].item()*10)) + ' steps')\n",
    "    axarr[0].imshow(rand_y[random_index, 0, 0], cmap = 'Reds', alpha = 0.5)\n",
    "    axarr[0].set_title('Red = True', fontsize = 15)\n",
    "    axarr[1].imshow(rand_y_hat[random_index, 0, 0], cmap = 'Blues', alpha = 0.5)\n",
    "    axarr[1].set_title('Blue = Predicted', fontsize = 15);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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aa2S55oaNH6EstzLepYCkM81sI7BR0mVkk4V+YIWrdj9wg6QbzMwknWtmT+bHLpG0BhgErgKul7QW2G1md0naC3yi2RhCkxAEQRAEc4ykrwE/AN4qaZukj1dU+5Kkp3I3ye8Dm4GHgLMnFy4CtwKdwBZJT+fbkzwK3A1sAe42s8eBd5CtW9gE3Azc1mycoUkIgiAIgjnGzD7aQp2rK3bvBi4o7ft0TRfbzOyqUp/3k2kfWiImCUcJr0Lr6VnWKHd3d7XSurC1d+9etzU7ClM/3qL670hVgal9W1tRsTUxsRAUwcFCYDafnqIs9zTK3d3dU7ctbXtZnvB2hRYuoJkHgj/SViPLh0hyK6JdU6e9JMsF74yacYaEz09ikhAEQRAEiwwz20AWsOmIiDUJQRAEQRBUEpqEwybp2drbk/tqV1dno9zZmUwHZVW6r+dVfl4VNzw80ih3dLS7cmrbrH0rNPdOmEmzQisUz9HW5q9rwpVDMbmYmIvASk3P7wbgZdnLb1dnkrmyLHd2pXp1sjgyPJzO0ZFeux0dpVdwTXt/X8adGU5tdWbA4nUVPSKqZfmQe38EX8YhuRDcOHGODxMhy/Oe0CQEQRAEQVBJTBKCIAiCIKgkJglBEARBEFQy5ZoESXcCVwA7zOycfN8a4OvAGcALwK+Y2Z7ZG+Zckmxnft0AFN2bOp2N0q8RKNrLfTTBou3NRxccHR1rlMfHx1wtVdYv20SnazwsujO2Nk/06wOKfZVdnfzagcKRRsnfi1ajqR3JuosgsZTk2T9Zft0A1Mtyp1sjULcmwErRBIuyPNooj4+PV47FRyMsP/9FV0F3Drcx5uSnw0dCPGRNQvVqj9qIi2W3xRaiJlrdtTQR68L7p06Wl3CUxflGK/8hNnBozusbgQfN7CzgwXw7CIL5zwZCnoMgaJEpJwk1Oa+vBL6Sl79CFhM6CIJ5TshzEATT4XBdIE80s1fz8mvAiTM0njmjy6kfly9f3ih7VVjZ1bCIVwsmldvIyIirU++e5NWKY2PJxOBdsHx5YmLc1U/lcl911EdMrK9XNDHUuGZZUSVZPxR/firLYUU4ahxVeT7Sr701WW7tVefV+l6WC5JwxLKcZGZsvF6WC6dxYjY27up0OXktjcvLb5v7Pej3++ttZl6ofWPUCfNhfKtLTfyrTH8ttlsPrDWzb83a4BxHvHDRsqe6/l+D9ClJj0t6/ODAwJGeLgiCWaSZPHtZHjh4cI5HFgSLjg0cavprhfXAh2d2KPUc7iThdUknA+R/d9RVNLM7zOx8Mzu/r7f3ME8XBMEs0pI8e1nu7eub0wEGwWKjxvRXQNI1krZK2izpEUldwC3AtZNZICX1SbpT0qOSnpR0Zd72Okn3SnpY0nOSbs7390m6L+9za55JspbDNTd8E/gY8Dv533sPs585JqnD+txLrqsrJWLxK52Hh4cKrb0XgqfO3OBVj2UTgTcfeHrdRMp7MfhkMYODxXHVUTQdtFXuP9T0UKdYrPbaOBwTQVshSlwaV9l0UfYICWaNoyrPh6Ok9m2KspxMD16Wh4aKMuNl02M15gZff7zUdrxGTe9lub1Wlgcr22aDSUUvCiPO3DDuTt3RWfzN56Mc2oSXWZ84qv6Ot5TfyV1XWxMPpAmb2lPCUzS71Jt3WvWOWsDcBHzQzLZLWm1mI5JuAs43s88BSPoi8F0zu17SarI00N/J218InAMMAI9Jug84HXjFzC7P269qNoApNQk1Oa9/B7hE0nPAB/LtIAjmOSHPQbCg+B6wQdIngfaaOpcCN0raBDwM9ADr8mMPmNkuMxsE7gEuAp4ik/fbJV1sZvuaDWBKTUKTnNe/NFXbIAjmFyHPQbBwMLPPSHo3cDnwhKR3VVQT8BEz+0lhZ9aurCoyM3tW0nlk6xpuk/Sgmd1SN4ZFn+DJeygsW7asUR53erphl3zFq/+KgY2KKseRkRQ0xavJ/fl8Uia/urkZdaYAr5Yvj6u+vV/R3Nr56/Dt60wlGT5okg+0Um3u8By6P8wNQcIHOlrWm2R5wnkIjNTKcvGZ9bI87MwKfoV/MWBaOndZluu8iwq7a+S6zuwBxad/cDSN66B7d630RoFmmveaJFZeRsvJlvx1FWTZmxhqxntIMKTpWRtqx9Hs2JGaHgpf1xH1NHNIOtPMNgIbJV0GnAb0AytctfuBGyTdYGYm6VwzezI/dkkeLG2QzLX5eklrgd1mdpekvcAnmo0hwjIHQRAEwRxTY/or8yVJT0naCnwf2Aw8BJw9uXARuBXoBLZIejrfnuRR4G5gC3C3mT0OvINs3cIm4GbgtmbjXPSahCAIgiCYbzQx/fk6V1fs3g1cUNr36ZoutplZITiamd1Ppn1oiUU4SSgqinyM9rpY5gcPHmiUvRdCWa3ot/0KZb+/LjhQ2UTg1fft7dVmAa/i9B4BPs89wPHHL3f1Ul/FcaX2O3fudK3LqrzqFcrexNDco6HO3FEdmKlVIl/D0qP8lBRk2T+nrs4BF7/BeyG0lWTZy1mXkye5em0174uJkumikPNA1eX29iTLXhabybLX0C8fdV4X+5KnxvhYij1jpTvW7k2UziRaNr24Dko4Wa7xYmhVlgu+UTU5MQ6HmTQxBNUswklCEARBECxtzGwDWcCmIyLWJARBEARBUMki1CQUFUgHDiRTgle/d3Z2uHJaxdzdnVSa5b7qYrQPDSVPB6+WnygEWSmqxXyM+ZUrVzbKPgCLD/Lk01bv2l0K0uWGOTaWxuKvxQeZ2bMnZQE+VPVYnZeh9YyuaYc3o/h77z1LJlpIR5udPxSDS43yN14nyx0+1XNBlpP8lFfu+2dwaDjJzNBBp8of9yY2n565+NB3dCeZHXHnP2l1ilFz3LFpMXpPd5LF3YfIcjqPH1efe1/1jadyx4HkzVHO3VBIL+2ut7O9RkWv8qaTZW9u8N4R4/4dMX1Znm7emWDuCU1CEARBEASVxCQhCIIgCIJKYpIQBEEQBEEli2JNgncv6u4uuhTVJTnyyYP8OoLR0WQHLCdl8ja3Yq54Zy/sS/bJ3t6UeKa7J9lHAXqcvXTZstTG2+hGR1MkuJdf3tYo792b1hRkbVLZr1045phjGmXvTukpuiZCW1uqV1yvUG1HLK8pKOSwb6uegxby2TcxY7Zq4wwWNt4qXedmDPWy7KMk+mRLPkHTSCk529BI2v6Zcync8lJ/6tfSWNaevKZRvuAtxxf66lue5PevrVndKPd2edt9eq9s3+ZleW+hLy9b7S56a++KtG6py8nPqFsT0NNZlHG/JmjcRWzsbqt22S6vTyq6Zrcgy655RSzgyvaqSQoV6xDmD6FJCIIgCIKgkpgkBEEQBEFQyQI2NyR1lHfv81H+oKjCGhysdm+qi3jYWVLf+bz1q50qXzVuf171OV4yXfT3J7Xmnj1J5ehV7H4svr43lQC0W1KdTjz2P1Ob7fsb5WFnhtj/2uuN8thYUaW/+uPXpQ1VzyGLkRTrj01XZVi+rnB7XBr4x6TbyXIzl7665E1eLV6U5fT8A/Q59f3a01L5PW9P5+hy8t/T4aIPlrIVjbpkbwf2vJHKTunuXQgPFGS52Jc3C/rL92aYNtL1drRXR24t911w23TFormxHJWyOilVLT7a7HjxugqmBD/GVlwgS9uL5a0g6U7gCmCHmZ0zjXbrgbVm9q1ZG5wjNAlBEARBMPdsAD50GO3Wk6V5nhNikhAEQRAEc4yZPUKWrKkWSddI2ipps6RHJHUBtwDXTmaBlNQn6U5Jj0p6UtKVedvrJN0r6WFJz0m6Od/fJ+m+vM+teSbJWhawuaFa9VhehdvRUZ0wyXsBFHp16q/xksrMRzD0eeu9F8T+/fsa5VG3otqbRKBoyuhy4xrfl9SVE3/1o0b5wA83NcpDA0XTxfMH0iruYafuP+v00xrlM9vTWHb0p7H/+EAywQBc5jwq1OWjT3rVY9rrVbpQ9PQoJ7WqptrLJFg6eI3zgJNllWW5vVqWvSnB9+VV2eWkTN5zQpbMBR1ORb9/165GeY+LsNpV8qDq7PDeVanfgteFqz/q+yqZQfw1+3LPsmTq3LdzR6Oc4jge+r4qeEp4ryNVmxE6SuYKb+IYq0sKVUPZjFKTKyuYmpuAD5rZdkmrzWxE0k3A+Wb2OQBJXwS+a2bXS1pNlgb6O3n7C4FzgAHgMUn3AacDr5jZ5Xn7VeWTekKTEARBEATzk+8BGyR9kvKikcSlwI2SNgEPAz3AuvzYA2a2y8wGgXuAi4CngEsk3S7pYjPbV9XpJDFJCIIgCIJ5iJl9Bvg8cBrwhKRjK6oJ+IiZrc8/68zsmckuDu3SngXOI5ss3JZrJmpZUOaGQg74grnAB1kproWtC/wzMlKdX71ZAJ9XX31lWuPtdOo6vfzjwrHRJzY3yi/tSDnhf+o09KMDKaHNstFkInjXW08u9HXi297SKHeflRbJnvSWsxtlH4DpTf/1jkZ54Pmdhb46XFIpa6sOpuLv46FBVswdc8FkakwJ3qMhnBmWDm1Otd3RUS3L5RX1dbJc50U03iRS12uvvlp5no62arOaNxe2t9Wr5f0Yu5zpwXs0eHV/R2e12ROKwZTGxlO/B4eSSXCFe4NbyRupGGgpndObRya8N1XZM8yVvZzXJb5qlqxtJq0NS8lyIelMM9sIbJR0GdlkoZ+ipel+4AZJN5iZSTrXzJ7Mj10iaQ0wCFwFXC9pLbDbzO6StBf4RLMxhCYhCIIgCOYYSV8DfgC8VdI2SR+vqPYlSU9J2gp8H9gMPAScPblwEbgV6AS2SHo6357kUeBuYAtwt5k9DryDbN3CJuBm4LZm41xQmoQgCIIgWAyY2UdbqHN1xe7dwAWlfZ+u6WKbmV1V6vN+Mu1DSyyASYJTkxWCG1UrnYZdDnZodYX9kTHxQvJC2PbNv2iUO5w3xMvjRcXYGS7e+5uOS8FczjrrpEZ54C3vaJTHelMd70EARXXpspWpnl8BPjSUzBUT7h6d0FVaC+P6Ltxhr0Z1qtdmAZCkamWgV0sWVZSLXXm4xHEPVMHE4PX67vkZGS3JsvMKaCW4j7c8lh7ToirdD9HHHHIb3qRQPrc3PxQ8LWrU7+1OLg8NGOZMEc70t2ckqfhfeD2tM1txgvNAKt2SURcorbdgnq2T5ZJ3hL9pNfe7IMvOvNEsENqRSnm8JeaWKc0Nkk6T9JCkH0l6WtKv5fvXSHog9798QNIxU/UVBMHRI2Q5CJYOZrZh0k3ySGhlTcIY8Otmdjbw88BnJZ0N3Ag8aGZnAQ/m20EQzF9CloMgmBZTmhvM7FXg1bzcL+kZ4BTgSuB9ebWvkPln/ubMD9GbEoab1JtbzK3W3/3tv2yUR5wurNepKD949cWF9l1vf3dlv21O3W9+RbR5r4Hi3M57dPT0JPXjmFPPjg4lD4qtL6YgX29fV/7RWL26u5iTwa9ML8XXd/elbhV0OSVtMDccdVl2suGDkbWqPvZq/roV7oXV9la9H+qDCxXO5717CjkS2mvreZnz9cZrPILKAaN8PCS1JxPBiMsPsbLb5a1xY+/tLPalbhd8qr36nMX028V/B2NWLctjbpBjY9Wy3Gqq6GD+My3vBklnAOcCG4ET85cOwGvAiTM6siAIZo2Q5SAIWqHlSYKk5WSuFP/EzPb7Y5ZNEyunipI+JelxSY8fHBioqhIEwRwyE7I8cPDgHIw0CIKjTUuTBEmdZC+Vr5rZPfnu1yWdnB8/GdhR1dbM7jCz883s/L7e3qoqQRDMETMly70ubXoQBIuXKdckKDNa/QHwjJn9njv0TeBjwO/kf++dlRHOIwouUZ3JPenkGz7bKK9zLlDLli1rlP1aASi6DnV2JjekoaGUcKnodlgdlS6vWXkeH2VxfGeKFvnSwWQPftsJqws9jYykaG7eptrT05q3rG/j3SP99frrahbhMphZFros+4RN7S24QHrKkVjbatwb/XoB70Lc46InlmXZP8/eBdLL8kRNnbKpvt9FU+xalc6/Z29K/LaqJ42xXT7aZNFltKPDRUl1Yf8LSaWaLBWoS/A0VuPqWOfyWT7N9L65cHk82rTy5n8v8PeBp/IITQD/J9kL5U/yKFEvAr8yO0MMgmCGCFkOgmBatOLd8Jc849pIAAAgAElEQVTUT/5+aWaHEwTBbBGyHATBdFkAERdnh6LrT3U0tXJktaLKstoJy7sHthfcpoq3uq2tWok26qLMeXWnP593s4JiDns/ZO8yOvzEDxrlQlKXdxSje9aZAqTq5SvNtL5Fd0ivoqxvEwR1jDvzlX8cC3LqZdk9Z94FEEpuiN7V19XxroJelotyWe/e590WO9qrX7WDwyOF7WXdyRRw0spk1ugYTjLe35bMmN6Md0gUyhoXULVVC23ZhFNwLS2YC6vNDYUAjZVnaOXgof22El1zoSHpNOAPyTyJDLjDzL7cYtv1wFoz+9YsDrFBJHgKgiAIgrmlLrBZK6wHPjxrIysRk4QgCIIgmEPM7FUz+195uR+YDGxWQNI1krZK2izpEUldwC3AtZNZICX1SbpT0qOSnpR0Zd72Okn3Sno4D7l+c76/T9J9eZ9b80yStSw6c8Oh0Qj9ymVvSqibH/nIgMXVuqOjPoJgTfKWJolgin0lVaRPslKn7h8bq1b3AfT0JFWk7/fAgeTLPvL63kb5jJ6k0mxziaPyQVeO30dcK0ec83jNa9ksEgRV1EVPLMtyp5PlzpoIggXVvyuOTxQjA3o5GXVy3u4G01tjhixr64edWaHTybIfgJfZoeFU3nuwaG7Y5zo/fiCZC198LUVJ9REX22qiJ2Znd+d3+0dGq6NCTpQSsvl7OeraFN9RtEbNq/BIvB7KYymcbgGZKEqBzcrcBHzQzLZLWm1mI5JuAs6fzMsg6YvAd83sekmrydJAfydvfyFwDjAAPCbpPuB04BUzuzxvv6rZ+EKTEARBEARHgWaBzXK+B2yQ9Emg7tfZpcCNucfSw0APsC4/9oCZ7TKzQeAe4CLgKeASSbdLutjM9lV1OklMEoIgCIJgjqkJbFbAzD4DfB44DXhC0rFVXQEfMbP1+WedmT0z2cWhXdqzwHlkk4Xbcs1ELQvK3NBWWG2cht7MI8HfI78SeHx8zO2vTkTUKn4s3d1pRXJvb31UOj/OunHVUVbDLl++olH2wZC6J1J54xtJdfkLv/DWRnms06tHiwGQmpkVJimbbcZcQBdvrinnqg+WNgVZ7nBqfepleXis+hkad2Ytbxbz3hBluR4dT9uDI6mNT+REVzr/irZk0psoK8ZrZNmb2/zph53ZcrQ0rt7e5albl2Bpzcr0Lul0Q/Qj8bJfPmnBDFqj2G8vvVeGXX/eXGPuvvomPm/bbGr7F0OyqCaBzcr1zjSzjcBGSZeRTRb6gRWu2v3ADZJuMDOTdK6ZPZkfu0TSGmAQuAq4XtJaYLeZ3SVpL/CJZmMNTUIQBEEQzC2Tgc3eny9A3CSpymPhS5KekrQV+D6wGXgIOHty4SJwK9AJbJH0dL49yaNk2ootwN1m9jjwDrJ1C5uAm4Hbmg10QWkSgiAIgmChM0VgM1/v6ordu4ELSvs+XdPFNjO7qtTn/WTah5ZYUJMEr9b3ngpeRV5eUT8xUZ3vvI6i6aKtybG033sndHZWm0F8YKNym7ZCoBcfU96v2k41li9fjscHUzrosvPZjpca5X7Xvv2EE9JGh88JUaRu5XRRlVhU/Y2MpOssemHUq36DpYc3MbQ5OfOBvsZGS7Ls8wfU6LP9s+XfEVZSmna5zTFL9XwelVEni3uHkhltYKj4TlnV54IeuevywYWcRYOhsXRg2XKvNYaz1x2Xzj+Y1rEt6/TRo3yLtFEO8lS8RdXt/RgnSnLp31neo8O/Fgv3e5ZMDPG+OLosqElCEARBEARTY2YbgA1H2k+sSQiCIAiCoJIFpUkYHR2ZulITvPmgXpXeTGdWrTL3ffnVzYODg43ywEAyA0DRI6GrLak4vemg6PWQ9JUdnfWx4/15Jn7yTKO8ykWJaXvruY1ye1fRu6HOjFPnnXCoeac6R0N4NwSe0ZHRyv3NFMsF2SzkXvGpk6tluaxKL5gonUfR8/uT/AyOp1TPY9bfKHe3FZ/5s9Ymr7Q3rUnByQbG3Bhd/VOOSbkXepcXg5kt70nmiu07BxplHxhJzjzi8zB0HSLL6axjY847oeYul2W5GDTJBVYaqzbhNgs4VejXt6mvFswTQpMQBEEQBEElMUkIgiAIgqCSmCQEQRAEQVDJglqTUIdfa9AsSmBxvUG1vc1HCSwnUvL1vLuRL9ete+jqSmsNoBiZ0Ltp+jadnZ2V+09ZW0wW1t/vQn6PpXUbT299tVG+4M3Jbqru+kiQnrp7WZf4BYq2zyBohYKNWt4FuPj8TRTc7fzvGye/hXU06VkcGik+p0Mu6uGze9Lag/G25M7Y1Z3kemw49btvoPhe2PjjHY3ygTOSXC9zb9eTV/Q2yu3uXXDaaacW+jrYn9Y+eIN9wU3Ure8p/MorB4J0Zf+OqoswO1peX+TWQfkoje3etdR9ea1GWYx1CAuL0CQEQRAEQVBJTBKCIAiCIKhkUZgbfGTCssrLq8OKSZ2m75JXpwptK+SdT/X9OcrR0Dx1Zgnv6tjlIsGVk0ANDCRXS7amlOSvTaTBvPPk42gFby6pcwf1JhkfYRHKblPh9hgkWombV0hEVHr+/C8arzL37sETNScpu0C6R5hhbyFzp+x1bsODQ+k5HxkpPtcTrrNlXUlmj+lNsry8L5kblq9ILpBepQ8wMJjcHv31+3fB+HhrJr3i/fPRJxPjE16Wyy7mU7tAz1d3Rv8eau7WfvSQdCdwBbDDzM6ZRrv1wFoz+9asDc4RmoQgCIIgmHs2AB86jHbrgapkULNCTBKCIAiCYI4xs0fIkjXVIukaSVslbZb0iKQu4Bbg2skskJL6JN0p6VFJT0q6Mm97naR7JT0s6TlJN+f7+yTdl/e5Nc8kWcuiMDeUI4VNl7qkToeoOwtmgWJ0s0l8JLfR0WQGKCeL6u1NKkefVMbjr6vNjaXsQeCTOk288UZq41cnr39Po9zdnc43PFxUMbaipvPmjnLulekm1AqCordM8g4oP391SuOCGbCgYU8bPSX56+5Kx97Vl7x9tg+4d4lr4016w4PFaJE+Smq3ey/0dSXvpA6la2zHR1Itvru8LHtd/niNXHU78+RwyfQ3USPL/haNj3kTbDkqpff0iiRLR4mbgA+a2XZJq81sRNJNwPlm9jkASV8Evmtm10taTZYG+jt5+wuBc4AB4DFJ9wGnA6+Y2eV5+1XNBjClJkFSTz5D2SzpaUm/ne9/k6SNkp6X9PV8hhMEwTwm5DkIFhTfAzZI+iRQ599/KXCjpE3Aw0APsC4/9oCZ7TKzQeAe4CLgKeASSbdLutjM9jUbQCvmhmHg/Wb2c2S2kA9J+nngduBfm9lbgD3Ax1voKwiCo0vIcxAsEMzsM8DngdOAJyQdW1FNwEfMbH3+WWdmk4l7yiogM7NngfPIJgu35ZqJWqY0N1imZzqQb3bmHwPeD/zdfP9XgC8Avz9Vf3NNIelIW/VErG7xa1nDVkgY41RxvuzNCOPjPshSSXXqVJl+tXKb89To6U6BXTrd6mavkgUY3J2CuTz2w+ca5fOOTUmkOlYn7wZ/XT5gUzauVK67xpGa5DzB/Ge+yLNXX3std7PEQAVZdnLSiia8rfRzqN29C9qdF9Cpy5MCpb0nyfL2PUmVv3vsAJ5RF6hpy4t7GuVlPUm2zj5tTaO8amXaP1Qy9w16s8ZwOmenM114E4NP1lSWZW9YKHiAOFkuvEtavPeeNqpNGvPJPLEQPB3qkHSmmW0ENkq6jGyy0A+scNXuB26QdIOZmaRzzezJ/NglktYAg8BVwPWS1gK7zewuSXuBTzQbQ0sLFyW156qMHcADwF8Be81sUjq2AafUtQ+CYP4Q8hwERx9JXwN+ALxV0jZJVdq7L0l6StJW4PvAZuAh4OzJhYvArWST/S2Sns63J3kUuBvYAtxtZo8D7yBbt7AJuBm4rdk4W1q4aGbjwPp8UcQ3gLe10g5A0qeATwGsWtV0fUQQBHPA4cpzyHIQzBxm9tEW6lxdsXs3cEFp36druthmZleV+ryfTPvQEtPybjCzvZIeAt4DrJbUkf/6OBXYXtPmDuAOgFPWrp1zHVRdoKNikKX6fA2eOnWaD5Tkz+frdPck0wFAR7uLC18T5Gn//pST4dhjk7qyraST1VMugNJ4Ovaed76pUW5vr/6q20p6WH/93otibKx6jIcTlCqYH0xXnr0srz3llFmX5bJi2JsYCsGBvOnCP5vNZLnDqeKduaGzM6nyh1xz71zQVrryTu9S4cyIJ6xKMr/Sklmht8uZOkr5KdrcdoczH3jTY0FmC6aaoixPFHLSVMuyD6bkg0KVacV8UJ0ZJ1jotOLdcHz+iwNJy4BLgGfIVB5/O6/2MeDe2RpkEAQzQ8hzECwNzGzDpJvkkdCKJuFk4CuS2skmFX9iZn8u6UfAH0u6DXgS+IMjHUwQBLNOyHMQBC3TinfDFuDciv0/JQvUMK8pByuZDuWVsD5HhDcrePus90LwlNX6Q27l8ogrF/MiJBVls4BRPpjLSc4scfwHrmiUBzuSunJoKKXGLVNMm+2DJtUHgAkWDgtZnsed+curs8tBgBr13bPc2V5SmjrZPjjqVvt3JO+GvYNpf2dnkp/eFcX3gpfNk49J7c90XgzLneOBT8lcHrmX5RXLlzfKfS7g08GBlN9huGVZrvZuGG8yllb8AAom2BbqN6Ou/cLyR1h8RFjmIAiCIAgqiUlCEARBEASVxCQhCIIgCIJKFkWCp8OhLqlTXR0oJmJavXp1o7xyZQp+Vec2WI722OX6WrliZaM8OJgiro2MpjUJPsFMOeJih8t1f9GpKWqnVqYoi11jqc3wcLJjdnQUx3XwYOrLez2NjsY6hGDmKERPbNGaPebWHgyPJjnr6kzPsF/70+66tZIsTyi1OeaYtKZopDutA+jtTc/8azvTOoBD3IbdOqKDY2ntwvMuMONF69I7YsAlcSqvNerybo8lt+lGnS6foC3Ja3tH8XU+5M7j1yfUrW8K239QRWgSgiAIgiCoJCYJQRAEQRBUsoTNDVPPjyZKOdy9e5J3SaqLvujVhWXXSJ83fsTlgfdaUZ+EpmtZl6tTVAzufjFFZhxw11WVLqyMd7OEornDmyK8C1UQzCTe2OBNXOVcPP1DSU3e4aKOdvnn1JkkvAskY8VogqMusuGJztVweV9vo9zjzBgD46n80iv9hb5279zdKJ/kXCB39Sez3uBoGsvyZem9oLai/Pl3TKczK9TJn79FzWU5vX8OR5b9d1RnlvDvwcNxp1xqSLoTuALYYWbnTKPdemCtmX1r1gbnCE1CEARBEMw9G4APHUa79cCHZ3Yo9cQkIQiCIAjmGDN7hCxZUy2SrpG0VdJmSY9I6gJuAa6dzAIpqU/SnZIelfSkpCvzttdJulfSw5Kek3Rzvr9P0n15n1vzTJK1LFlzQ9mUUEV5dfGq1WkVtDc39PR0u1reayKVy1EOvWrQR4zzK48LK8DdiurlTj0KsOpNJzfK/f0+1331qnF/Pq+ShKLK0Hs0tHK/guBwqMsdVE4qdHAkPY/tTjb6upMpYHTcyZJ7zsuyfPIJyRh3/LHJU2l5rzMFuHO8r2dZo/z08uJr82crU731JybZHD4mvReW96Q23c70qG4XihFYUfB0Sh4VOBOBV9376IkHD7r6FOV8xHlEHY65oRUTQ/FAcdMbe3x+ukK1VmwaS4+bgA+a2XZJq81sRNJNwPmTeRkkfRH4rpldn+dleVTSd/L2FwLnAAPAY5LuA04HXjGzy/P2TVO6hiYhCIIgCOYn3wM2SPok0F5T51LgRkmbgIeBHmBdfuwBM9tlZoPAPcBFwFPAJZJul3Sxme1rNoCYJARBEATBPMTMPgN8HjgNeEJS1Xp0AR8xs/X5Z52ZPTPZxaFd2rPAeWSThdtyzUQtS9bcUEd7e7ola9YUv4+TTjypUfYBTUZd0CPvteB1ZgMDRVXgnj3JFOVVdj44ysqVSfXY2ZnK/twA3f/g+lR2qsQDB4qrsKvOUQ7MFATzlWXOi8G/+Uac58KIMzd0ObX+yScch+fNp5/aKHd3e1lO8uBluc2p7k8pxThqd0GXBg/sbZS9ibHLaXR9wKTuLm+qLL4L/LFCsjc3lgF3jrIs15kC/G5fo62Jin+6loCyZ4o3fZQDW01Fs1Bbi90qIelMM9sIbJR0GdlkoR9Y4ardD9wg6QYzM0nnmtmT+bFLJK0BBoGrgOslrQV2m9ldkvYCn2g2htAkBEEQBMEcI+lrwA+At0raJunjFdW+JOkpSVuB7wObgYeAsycXLgK3Ap3AFklP59uTPArcDWwB7jazx4F3kK1b2ATcDNzWbJyhSQiCIAiCOcbMPtpCnasrdu8GLijt+3RNF9vM7KpSn/eTaR9aIiYJJVY7DwafkwHALKk1/ariffvSug/vnTA8nFSE/f0p4BEUPQeKseCTAu3AgaTuPO44l4ehq7gi2mvv2go6Q+9dkUwM3qPhkDwQLuhKeDQEc4F/Ypupltvdsz3sgyM5AejuSOXjjz2mUe5bXpTl8YnpynJS6/fvK8pym/l8Len83iywZ18y/a05Npkxu0umw4L81gR8G3DyOzSYxjVcCqY0bi6PRVt1oKNRl3eiq714Pv9esTp7Q5PgV3W0+n0H84OYJARBEATBIsPMNpAFbDoiYk1CEARBEASVxCQhCIIgCIJKwtwA9PampC7HHXd8o1xOAjXo7H++XHBPGkv2yYGBtKbAux0CtLnkTd4O6d0bfSRHHyVtYKAYJdFHf/R4W2udO6RfZwFFd84gmAvqbNnlRGY+smJvVyp72/8xK1PEw5NOPMH1VZTloSG3Lme4WpbH3ZoEH82wLMsFK7tfH+ETwrmkToUoiSXXaC/LY27dxfBokn+/vsFTdnkcG0vrjdo6pv492GxNgXdhbG/3UWWn7DYbW005mP+EJiEIgiAIgkpikhAEQRAEQSVL1tzgXf2OOSa5ShVdCIuKMa/yP3AwJVIadu6FXpU47tyLOjuLrk7FJCvV5/RmkKK6r9BVYcxSco/0ro4jI6OuXFaXBsHcUidl4+45L3sA+ud8cMS5HU6k/cesSbLszRUTh6jiU/t+ZxYccqaEEZdQ6o39SZbGxot9tTmTXY9L2ORPuWxZr9vvTXzlcPzOzdNd1849ycSwe18yUXSYk+WS7t/fyzH3LvKjHxhO96Gzvf43ozfpeFdU85aW2taLPzLiYqZlTYKk9jwN5Z/n22+StFHS85K+nqewDIJgnhOyHARBq0zH3PBrwDNu+3bgX5vZW4A9QFVIySAI5h8hy0EQtERL5gZJpwKXA/838M+U6fHeD/zdvMpXgC8Avz8LY5wVfN52r3r0UdY6OoqRDX00Nh+BzasSO13ylhUr0krr8upqH2XRe0H4KIvd3X5FtFMLdtZ/bT6R1IEDySRS9mIIliZHU5brVM7eLNA0yZDTk3tzQ3tfkrO9B5JcdnQm+TEV1fovb9/ZKO9yMvfi3tTvzl3JxNDtzIVd3UVFS5fzQrr81BRNcXQ4te90yZq8F0L5HeOx0WRKGBp0Y9yfyut603VJJZOKMzG0ufePsxzQP5zMkCuWFd8r/qsoRGb0nhKH46rQSrao6WaUWoBIuhO4AthhZudMo916YK2ZfWvWBudoVZPwb4DfACaflGOBvWY2+R91G3BKVUNJn5L0uKTHy+4+QRDMOTMiywOFbKdBEBwGG4APHUa79cCHZ3Yo9Uw5SZA0OdN54nBOYGZ3mNn5ZnZ+n1uIFwTB3DKTstxbE5sjCILWMLNHyJI11SLpGklbJW2W9Ei+XugW4NrJLJCS+iTdKenRfK3RlXnb6yTdK+lhSc9Jujnf3yfpvrzPrXkmyVpaMTe8F/hbkj4M9AArgS8DqyV15L9ATgW2t9DXUcWr771ZwDNQ0HYU9VxeZb9mTVIr+gAofoGx9yhYtqyYN76jI6kJ2527Qk9PGuPuPXvS/u5ie483l+zZu6e2XrDkmfey7M0NZU32/sEkTy8dTGbBtx2T1P97XJ2XD+xolH/yajK9Abz8YjI3rHCBmfpWr2mUezqTzI0482KPC4wE0OHk90Bbeq8cvyrVO3AweSes7FvWKJc16RPO68nLv3OaYpe79hO7nGdTqa8R713lTATe3DHmym1NIiPVHTssS8AiNR/MEjcBHzSz7ZJWm9mIpJuA883scwCSvgh818yul7SaLA30d/L2FwLnAAPAY5LuA04HXjGzy/P2q8on9UypSTCzf2Fmp5rZGcDfyQfzq2Q5rf92Xu1jwL3TuvQgCOaUkOUgWHB8D9gg6ZMc6i87yaXAjZI2AQ+T/QBYlx97wMx2mdkgcA9wEfAUcImk2yVdbGb7qjqd5EiCKf0m2cKn58nsmn9wBH0FQXD0CFkOgnmImX0G+DxwGvCEpGMrqgn4iJmtzz/rzGzSe6mskDMzexY4j2yycFuumahlWsGUzOxhspkKZvZTMlXGgsGvovZlny9h2bJlrlxUK3b9aGPa+FlSX37nhz9rlL0qz3stvOeE4nd78id+NW30JHOFj/d+ytq0fsx7XZQ1f97rYsjnmh8q5ngIgknmqyz7N5r3YAB49UB6ngfH0o+qF/YmL4DnXkyyoMFkOlzmPCAATlnt1lS0pddgp1s35T2QxsbrvZ6GXB6XV9xY+k7weSROSmPpqM99sNfJss8Xsc95YJy8Mr2v+rqd18JE8f9Bh8ux0FWTu2HVWLqW8li8N0ln+9QeKE0dEqbrBTGDJolyDpCFhKQzzWwjsFHSZWSThX5ghat2P3CDpBvMzCSda2ZP5scukbQGGASuAq6XtBbYbWZ3SdoLfKLZGCIscxAEQRDMMZK+BvwAeKukbZKq4pN8SdJTkrYC3wc2k5kHz55cuAjcCnQCWyQ9nW9P8ihwN7AFuNvMHgfeQbZuYRNwM3Bbs3Eu2bDMQRAEQXC0MLOPtlDn6ordu4ELSvs+XdPFNjO7qtTn/WTah5ZYUpMEr35fuTIFUzpxTVrcqe3PN8qv3fe9QvtNLlBLm9OHyenfdu5Mq6Z9Stlv7d1b6Ovdv/N7jfI5v/FrjbL1pnF1uAAsPm30/v37C33t3p1WQft8DT6PhDdXBMF8xau4yzkS3jiQnuHtu5MM/PSFVF632pkLljmzQEdJ5dzhAiK5oEvdvc67aNeuRnl4LMny6zteK3Q10p9MAT29y1ybNP6+N6d+j12VzBB79hbXjL2xM51zwMnyss6k9D2xJ5laut11jZfMDe0+D4bb79XvPg9D09wLrk2t5cAdsIWr4Q9KLKlJQhAEQRAsBcxsA1nApiMi1iQEQRAEQVBJTBKCIAiCIKhkSZkb2velCGzLnn+yUd7hAmNu7h+iFfoPpAhq+/Ylm6hfh+DLI6MpEhzAN7Zta5S3/nZan3DN33x3o9z9gV9ulL1N0CduykjGQL8OYWiotWsJgvmCdyHeP1SUmQHnEtm/f6RRPs5FTGzDuS1747lLllSmfyj19fqO1xvl409MawcmJtJY9u4r5qDZ9tMXGuUuF331nDe9o1Fes8y7GiZZHhwo5sDwawR63HqDERdJsse9tQvJsUo/+fwShVaTaHnqPAf9bqs5UG5acD9voX0Lu4M5IjQJQRAEQRBUEpOEIAiCIAgqWfTmhs6B5GL0wv9ILo0/cvOj3hazU/aNJvX9Oz9wfqO8p6O6fdsPH2qU739iW+FYd5fPSe9cKDe/1Cgf/7dSvz7x1GDJjHAw0vYGC5hCwiGnI//pnmLE0BdeSm7Ea9pdNMaxJMuHmuJyuorRU0cm0quvrSOZ6NTu3KSdXG4bTCaJV7clN2eArnEnjwfSGOX0/109yTVy1Jkeh4eLslxIwe307G0FVb5zR3T3ruwCOTKWrqvbRVz0Ltujrk6peeGcE9Y0nuK0mG7wxeDoEpqEIAiCIAgqiUlCEARBEASVLDpzQ8dAMbLhrj9/uFHe6zSUbUpqtv7+5KngoxdedFoxKYy9J0XC3Lvq5Ea5TvmmSz6SNp74cuHYihUpsmJXjenBa/hGRpKKsn9/P55xl4N+tORFEQTzhVbUzD7K4s6DxSihxyxP8tg2nGRgQum3Tv9oat/vIh6+Y51L6ASs6UrHetqTd0Rv53GN8nLnRnDC8mRu+OlfvVHoa+WKNK6u9urIhD5B0ogzXRzoL8qy904aGRmhila8DgA6fDRFb65w5e7O9sr9ZbzporO9+rdlrdcCRbOIWjFXLHKXBkmnAX8InEh2u+4wsy83b9Voux5Ya2bfmsUhNghNQhAEQRDMLWPAr5vZ2cDPA5+VdHaLbdcDH561kZWISUIQBEEQzCFm9qqZ/a+83A88A5xSrifpGklbJW2W9IikLuAW4NrJLJCS+iTdKelRSU9KujJve52keyU9LOk5STfn+/sk3Zf3uTXPJFnLojA3TOzc3ig//61iUqaD7SmIyURNBpI33kirlc9b6fKzX5A8GADa1r55WuMae/knjfLylSsKx3wimHFLqjyvlmtz6sIBF3TFmxeyY8XgLkGwkPCr8odG07O9bNnKQr2JAy7qmZPrtpXHuv3J3Ha2k+Uz+pJaHaDTrfb3Zr2+7na335kuXMClFaVkUb3dyQvJ3Ljeckza39mR+t17MMnr4ciy1dhtyvtH3X2dcPuXuffKsLvf3rwCZRNFTSKoFs0Cbc0iLS1xJJ0BnAtsrDh8E/BBM9suabWZjUi6CTjfzD6Xt/8i8F0zu17SarI00N/J218InAMMAI9Jug84HXjFzC7P268qn9QTmoQgCIIgOApIWg7cDfwTM9tfUeV7wAZJnwTaK44DXArcKGkT8DDQA6zLjz1gZrvMbBC4B7gIeAq4RNLtki42s31VnU4Sk4QgCIIgmGMkdZJNEL5qZvdU1TGzzwCfB04DnpB0bEU1AR8xs/X5Z52ZPTPZxaFd2rPAeWSThdtyzUQtC9bcYLtTTvcX//T+RnlwxepCPR8QxIc8Onv92kb54Mq3N8o6Ofb8jG8AABDDSURBVJkU1N7a7enpSYFaVrrY7UP3fzvtX1E0N3R1JLXkquXpmFfr+dXN27e/0tJYgmCh4QMoDbYlmVuxovjD6eC+JMETbUl+hoeTin61MzHIeT28cqAYtGjEeVH0DyeV+3GrkvxOdKbz/eTZ5DW1ors4rg7nnXT2u89tlE9Y2d0o23jy1Hjl1enLsg90NDqejAdt7n0xUbI3vLI/3Zflnel+daxI4xoan6COOu+MVnIsHGIRmWMTg5q5aswDlA3wD4BnzOz3mtQ708w2AhslXUY2WegH/D+U+4EbJN1gZibpXDObTE50iaQ1wCBwFXC9pLXAbjO7S9Je4BPNxhqahCAIgiCYW94L/H3g/fkCxE2SqjwWviTpKUlbge8Dm4GHgLMnFy4CtwKdwBZJT+fbkzxKpq3YAtxtZo8D7yBbt7AJuBm4rdlAF6wmIQiCIAgWImb2l7SgXzGzqyt27wYuKO37dE0X28zsqlKf95NpH1piwU4SXr3rG43ydiVV2rFN1EzvvfKiRnl4XXJJbS1zQz3LXTCV0Xv+qFHeuCvFgT80gIi5Uioff+7pjfJrryWTio/x7lNQB8FCwXsLeHX0kEsBvdula7CJolrf5xwwJ+fjI0llfnAwvQvGLb3exkpq9aGBZMrzqmnrTKaDoaE0mHafh7kreSYB2LJkojj3tOSR4a+3IMsu90pdwCQ41HyQ+nVldyfbSu++43uTGbS9JrDSyp5O6vDn8YGZ6qJi2VF2YJgtE8PMZa1YmLQ0SZD0ApkdZBwYM7PzczvH14EzgBeAXzGzPXV9BEEwPwh5DoLFj5ltADYcaT/TWZPwN/KVk5PBA24EHjSzs4AH8+0gCBYGIc9BEEzJkSxcvBL4Sl7+CtnKySAIFiYhz0EQHEKraxIM+P8kGfAfzewO4EQzezU//hpZoopZZeJHjzbKPxlMdvnhiVQ+ZVUxStsvXpXWIejtFzbK9Za4euylHzfKu+77i0b5RWff/Fl/iozY4XPYq2jI84lcTul0UR7f+Z5GeefOFAly//6qOBtBcFjMC3mexNvLey3Z64c6i1La0eleV2NJ5jp8BESX4GzU2f5pK65v6J5I6yDaV6SAcz3L0jnd8gSGDriVSxPFKIl9xx7TKJ+6Msn86Fhye6yT5Vbt6P4e+bKnvHflsnS//Hl88xUuymJNt5MdNIp1ibqWor1+KdDqJOGiPCzkCcADkn7sD+a+mZXPjqRPAZ8CWLWqafTHIAjmhsOS55DlIFh6tGRuMLPt+d8dwDfI4kG/LulkgPzvjpq2d5jZ+WZ2fl/vkfoRBEFwpByuPHtZ7u3rKx8OgmARMqUmQVIf0GZm/Xn5UrIsVN8EPgb8Tv733tkcKADOJWm4JlDYUH9RLT+8JSVZYrP7wVSTsMS7LY2Vkq9898UUdW3g4IF0DueSOOrUnR0uquKxx6c89QAdTv35185Omt39I2OuVijwgpnlaMqzV3lPuBCCXn1+7LIUDXAZRflrPzWp9Q8MJLfjEScz7e3pd8+B/c4FuaRL98nTVi6Xa7OrUd7+agppP7grOXocf9LJhb6OW5N+/HQ4Bczufeld1FZwQaxJlkTR7dG7NHqrREd79X0smy78fbUad8qmJoYgoDVzw4nAN/IHsAP4IzP7tqTHgD+R9HHgReBXZm+YQRDMECHPQRC0zJSTBDP7KfBzFft3Ab80G4MKgmB2CHkOgmA6LKiIi23n/WKj/M6//FGjvOlAUve/2F/Mx37Plhca5VYiZ3mvg/79/cVjrof1fWkV85bB6giI7c7cUFb2re1MI3jjnckDY8SpKPv7w6MhWJx4VXh3Z3vl/h4rSumavmRK6HflcUty1uXMDbtWJan78UvFJRYjo+lYh0vQNjKcvCb27U7y1zXoZHGgGHHRezG8vuP1RnnI9dXvPBrqIk+2ir8rBTPGYfR1ODRN5HQk/Wpq80i53kJG0p3AFcAOMztnGu3WA2vN7FuzNjhHJHgKgiAIgrlnA/Chw2i3HqhKBjUrxCQhCIIgCOYYM3uELFlTLZKukbRV0mZJj0jqIltofO1kFkhJfZLulPSopCclXZm3vU7SvZIelvScpJvz/X2S7sv73JpnkqxlQZkbPCddcXGj3Pb176QDVnR76N+XVij7nOxdbnp0cmcx0Mok733Pm4s73vK2RlHHn9Ior925vVF+8o+/3SiPODVmRymYy9kXpwRTAwPJRLJr106CYDFSpyT2JoY2ucBiJY3z2FiSk16XsGlkPFUcGkweEfv7UzClsvLan7PPvQz2d6SyOdNjT3eKrFT+ZdXTlV6jBw5Uy3LBo6FFtXqBmmr+njZTwx/WOVugzvQwnwwCh2MemUkzyhFyE/DBPK7JajMbkXQTcL6ZfQ5A0heB75rZ9ZJWk6WBnvyneCFwDjAAPCbpPuB04BUzuzxv3zToSWgSgiAIgmB+8j1gg6RPAtW/ZjM35hslbQIeBnqAdfmxB8xsl5kNAvcAFwFPAZdIul3SxWa2r6rTSWKSEARBEATzEDP7DPB54DTgCUnHVlQT8JE8Ydt6M1tnZs9MdnFol/YscB7ZZOG2XDNRy4I1N+jUtzTKl57/7PQ7cNEf2957OGtHEub0osM+uImr87ZeFwge0NvPTxs1gaGCYKnh1eIdJZ11uzPZddeYCD1rVyVz39uOGyscG3Ny2u1MDD0dKQDTcz0psBNDyVOBjmJOifVrU76YCSueZ5Ja9XvJRFBnCiio8ufp6v4jHVXdtc/k9ZZ7mkdmhUoknWlmG4GNki4jmyz0AytctfuBGyTdkIdUP9fMnsyPXZKngR8kS9p2vaS1wG4zu0vSXuATzcYQmoQgCIIgmGMkfQ34AfBWSdvyQGZlviTpKUlbge8Dm4GHgLMnFy4Ct5LlLNwi6el8e5JHgbuBLcDdZvY48A6ydQubgJuB25qNc8FqEoIgCIJgoWJmH22hztUVu3cDF5T2fbqmi21mVkj7bmb3k2kfWmLBThLk0jDrkqr7OIf85OlGcUBJDXrK6tWpfHwxuZX60oLSXS+8MHtjC4J5TqvK5CMJ4jM4WrTpufQHBdPD3qFkLuhbkWR25Uonv+1Fc4P3lNi1a1flfk+zsdep1r0qfr6aG46UxXpdC50FO0kIgiAIgqAaM9tAFrDpiIg1CUEQBEEQVBKThCAIgiAIKglzw6zSJJHLfPe9CYJ5xnRFxtu4B0aLronLOtLaIY1X9+yTJ1l7cmHu6lteqDc2PrUP88QMRjlslZmMrDgXzIUL5MK6I/OD0CQEQRAEQVBJTBKCIAiCIKgkzA2HiR1M4a6//dhLjXJHR7qlPkFNz6/+wzkZVxAsNOoSA82karivs/iqGxpLiaB6aqI3jo0lM0LH8uQCeeabjyvUW9mdXCJ3eldFdwET7mXgzRjNFOkzGmlwlhI8zSRHwwVytp63xURoEoIgCIIgqCQmCUEQBEEQVBLmhhnAB1aTU1pNjFcnewmCIFGnZG6mfK5TDde1WbGs+Krr3zfaKHe48ItvXp3MCn1vS21OOvnkRvnYvhTtFYqeC6POU8KbG/24vBmimYa9lSiLrarL59rEcLSjJx7OMxXxHqsJTUIQBEEQBJXEJCEIgiAIgkrC3DDDjI+nVdNvvPFGozw8PFSo199/YM7GFASLgVYU5nV1ujuKv4dOOyaZFdqcatyXfYKmjsH+1FdvCqwEsHfP7ka5YFZwZd9XTd6nQ2hFZX84yaKWAnUeMzPdZinQkiZB0mpJfyrpx5KekfQeSWskPSDpufzvMbM92CAIjoyQ5SAIpkOr5oYvA982s7cBPwc8A9wIPGhmZwEP5ttBEMxvQpaDIGiZKc0NklYB/xtwHYCZjQAjkq4E3pdX+wrwMPCbszHIeUl7unWndaVgLC+PJHPDyMhIo/zaa6/NzbiCoIaFLstHEvimrHrvbK9WKPd0tlWWPcP9uwrbvlZ3TZvg6NHUJDNno1i4tPJEvwl4A/gvkp6U9J8l9QEnmtmreZ3XgBNna5BBEMwIIctBEEyLViYJHcB5wO+b2bnAQUrqSMuccCsnbJI+JelxSY8fHBg40vEGQXD4zJgsDxw8OOuDDYLg6NOKd8M2YJuZbcy3/5TsxfK6pJPN7FVJJwM7qhqb2R3AHQCnrF27aMJjq6evUf7rH7u6UV711W82ymt/8Zw5HVMQTMGMyfLaU045qrI8W2ripewRsNSJb76aKTUJZvYa8LKkt+a7fgn4EfBN4GP5vo8B987KCIMgmBFCloMgmC6txkm4AfiqpC7gp8A/JJtg/ImkjwMvAr8yO0MMgmAGCVkOgqBlWpokmNkm4PyKQ780s8MJgmA2CVkOgmA6RMTFGaDtuFMa5VN/7R8dxZEEQRAEwcwRTr1BEARBEFQSk4QgCIIgCCqJSUIQBEEQBJXEJCEIgiAIgkpikhAEQRAEQSXKorDO0cmkN8hCwe6cs5POP45j6V7/Ur52mN71n25mx8/mYI6EXJZfZGl/p0v52mFpX/+ikeWpmNNJAoCkx82syk97SbCUr38pXzsszutfjNfUKkv52mFpX/9SuvYwNwRBEARBUElMEoIgCIIgqORoTBLuOArnnE8s5etfytcOi/P6F+M1tcpSvnZY2te/ZK59ztckBEEQBEGwMAhzQxAEQRAElczpJEHShyT9RNLzkm6cy3PPNZJOk/SQpB9JelrSr+X710h6QNJz+d9jjvZYZwtJ7ZKelPTn+fabJG3Mv/+v5+mKFyWSVkv6U0k/lvSMpPcspu9+KckyhDxDyPNiludmzNkkQVI78O+By4CzgY9KOnuuzn8UGAN+3czOBn4e+Gx+vTcCD5rZWcCD+fb/3979u0YRRVEc/16MaRQULUIwShRFO42FjSISOw1qISIoBPEP0EIE7S1s/FHZJEoKQSQKprLSwiqIWgimkSAkkhhBg1YG8Vi8J64wrNXOwpvzqfbNDMybvXuWuzOzu6W6AMy0jK8DNyVtB74C57syq3rcBp5K2gXsJj0PRdS+gVkG5xmc5yLz/D91nknYB7yXNCtpBXgAHK9x/7WStCDpdX78nfSi2kQ65om82QRwojsz7KyIGACOAmN5HMAwMJk3KfnY1wEHgXEASSuSlimn9o3KMjjPznPReW6rziZhEzDXMp7Py4oXEYPAEDAN9ElayKsWgb4uTavTbgGXgV95vBFYlvQzj0uu/1bgM3Avn54di4g1lFP7xmYZnOc8dp4bUnvfuNhhEbEWeARclPStdZ3SV0uK+3pJRIwAS5JedXsuXdID7AXuSBoi/RT5P6ciS6196ZznRmp0nutsEj4Cm1vGA3lZsSJiNekN5b6kx3nxp4joz+v7gaVuza+D9gPHIuID6VT0MOma3vqI6MnblFz/eWBe0nQeT5LeZEqpfeOyDM6z81xsntuqs0l4CezId8T2AqeBqRr3X6t8zW4cmJF0o2XVFDCaH48CT+qeW6dJuiJpQNIgqc7PJJ0BngMn82ZFHjuApEVgLiJ25kWHgXeUU/tGZRmcZ+e56Dy3Vfe/QB4hXdtaBdyVdK22ndcsIg4AL4C3/L2Od5V0HfMhsIX0L3qnJH3pyiRrEBGHgEuSRiJiG+mTyAbgDXBW0o9uzq9TImIP6SavXmAWOEdqyouofZOyDM7zH85zmXlux7+4aGZmZpV846KZmZlVcpNgZmZmldwkmJmZWSU3CWZmZlbJTYKZmZlVcpNgZmZmldwkmJmZWSU3CWZmZlbpN2nKe63/H3c9AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 576x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_random_validation_pred()\n",
    "plot_random_validation_pred()\n",
    "plot_random_validation_pred()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# View prediction on true ($\\hat{y}$ on $y$)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "def overlay_pred_true():\n",
    "    random_index = np.random.choice(len(rand_x))\n",
    "    plt.imshow(rand_y[random_index, 0, 0], cmap = 'Reds', alpha = 0.5)\n",
    "    plt.imshow(rand_y_hat[random_index, 0, 0], cmap = 'Blues', alpha = 0.5)\n",
    "    plt.pause(0.01)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "overlay_pred_true()\n",
    "overlay_pred_true()\n",
    "overlay_pred_true()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Viewing effect of different final $\\Delta t$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "def viz_diff_t():\n",
    "    random_index = np.random.choice(len(rand_x))\n",
    "    colors = ['Reds', 'Blues', 'Greens']\n",
    "    alphas = [0.5, 0.3, 0.3]\n",
    "    for i in range(1, 4):\n",
    "        rand_t[:, -2:-1, :, :, :] = torch.ones_like(rand_t[:, -2:-1, :, :, :])*i/10\n",
    "        rand_y_hat_alt = conv_time_lstm(rand_x.to(device),\n",
    "                                        rand_t.to(device))[0][0][:, -2:-1, :, :, :]\n",
    "        rand_y_hat_alt = rand_y_hat_alt.cpu().data.numpy()\n",
    "        plt.imshow(rand_y_hat_alt[random_index, 0, 0], cmap = colors[i-1], alpha = alphas[i-1])\n",
    "    plt.pause(0.01)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "viz_diff_t()\n",
    "viz_diff_t()\n",
    "viz_diff_t()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Mimicking sequence-to-sequence by shuffling in predictions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x216 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x216 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x216 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x216 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x216 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x216 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x216 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x216 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x216 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x216 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "random_index = np.random.choice(len(rand_x) - 1)\n",
    "rand_x = rand_x[random_index:(random_index+1)]\n",
    "\n",
    "for i in range(10):\n",
    "    f, axarr = plt.subplots(1, 2)\n",
    "    f.set_figheight(3)\n",
    "    f.set_figwidth(6)\n",
    "    axarr[0].imshow(rand_x[0, 0, 0], cmap = 'gist_gray')\n",
    "    rand_y_hat = conv_time_lstm(rand_x.to(device),\n",
    "                                torch.ones_like(rand_x.to(device)) / 10)[0][0][:, -2:-1, :, :, :]\n",
    "    axarr[1].imshow(rand_y_hat[0, 0, 0].data.cpu().numpy(), cmap = 'Blues')\n",
    "    rand_x = torch.cat([rand_x, rand_y_hat.data.cpu()], dim = 1)\n",
    "    rand_x = rand_x[:, 1:]\n",
    "    plt.pause(0.01)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}