06_03_EXP_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([868, 11, 1, 64, 64])\n",
      "torch.Size([918, 12, 1, 64, 64])\n",
      "torch.Size([905, 13, 1, 64, 64])\n",
      "torch.Size([881, 14, 1, 64, 64])\n",
      "torch.Size([902, 15, 1, 64, 64])\n",
      "torch.Size([895, 16, 1, 64, 64])\n",
      "torch.Size([873, 17, 1, 64, 64])\n",
      "torch.Size([881, 18, 1, 64, 64])\n",
      "torch.Size([877, 19, 1, 64, 64])\n",
      "\n",
      "For validation data...\n",
      "torch.Size([123, 11, 1, 64, 64])\n",
      "torch.Size([113, 12, 1, 64, 64])\n",
      "torch.Size([125, 13, 1, 64, 64])\n",
      "torch.Size([108, 14, 1, 64, 64])\n",
      "torch.Size([114, 15, 1, 64, 64])\n",
      "torch.Size([101, 16, 1, 64, 64])\n",
      "torch.Size([100, 17, 1, 64, 64])\n",
      "torch.Size([110, 18, 1, 64, 64])\n",
      "torch.Size([106, 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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3m3OOpRNmnM8kzYxgzEsRli8Yk2E267ZhR+Zrwe3H2JR5X1uzWbDrZztz05r5cfTGVIr5C6vLd2NB+2uFPYsIAKMz5p7l8uYz793qLpDuznSZ98y5KivT02ZlxNDISKm8qb3FqWf/hI9PzTiHOpvMuYverPPwy0dL5S19e0Dqwzr5yhJCVhNqzhNCosgd2ECa8xy4CGkAVPVRAMOLVCtpzqvq4wA6RMQRJxORFhH5pYgcEpHnReR6EfkijOb8w2G9a0TkMRF5WkR+LiKt4f5+EfkbEXlORH4rInvD/R8P2zskIo8u9nkaxscVT5qwh0oR8AAwOzVV8Zjt+Ri1ykUvmUXaCqPoyLiXOGGFX0x4PjTNm+0Zq4+ZtO9Ds/wsnpCgrUzhh0C4ONkyqtRbWXw/lp3c4ujwSeeYWAoZe7ecVyq35V0VhuKLRjywY4crkd6UNL/Nw7NWCIuXqzLdakIe5sZnnWOzBXPnTzzg/k8lu9tK5WZLJUT27EMEqaQ5b4sJzmvOfwgARKRdVcdE5MsINOeHPM35KRG5GYHm/LxS6piqXiwin0agOf9hGM35EyLSgUVY9IlLRJrCkfGQiLwgIl8P9+8RkSdCe/hnIsJAFUI2PutCc74WU3EOwHvD7BuXArhWRK4C8C0A31HVvQBGANxQQ1uEkPVLTZrzAC5HMIB9Q0S+Wqadec35S8PXflW1x4eymvMIntJ2ItCc767W0UVNxVAVcX51ajJ8KYD3AvhUuP9OAH+JpTnz6sqWDmMKnB4xZkLXJi8q2rqk47OuSTk3bRmLlolWzLqmhW1pzM66D6LbLNMilXR/N/JF64fGMvNynmmk1rnFFzG0wjSqRsdXVSNcWezofj8qfWpmolTOzmSdY5vbTZhDbMREtr9wuN+pl86Y0IbUsBf1DnPtYjtNe1PxLqceEtYFybn38/CD95XKZ717sdl6287N5t5GNFJ+Y2nOi0gcwFMA9gL4EYIEj6OqJQdFufxrhJB1QkNqzqtqAcClodPsFwDeXMv7AEBEbkQwtYqd5+1cpDYhZDXYaJrzSwqHUNVRAA8jcKh1iMj8wLfAFrbec6uqHlDVA709PUs5HSGElGXRJy4R6QWQU9VREckA+AACx/zDAD4G4C4Eswb3rGZHl8vItJn8SCfMNPvUlOtXSWaMbyKTdg6hzVIJyGaN/2h8xg1rKGaNHyQ76/pL+gfNubva3Xi9uBUqYN+YBbkTLfzEHHa0QcFyZC3wd61wBES+4Ic5mPJZK8fg0Lg7CZWz1DPO2+IK+LU3mev98tGDpXKx6C7JabfCRca83CeIm/CTMy/3l8o7O10xwuJeE77w3KGHnWPZUdNGzPMpXtxhwpxk31tBqrNSmvO1mIpbAdwZ+rliAO5W1ftE5EUAd4nINwD8DsBtK9EhQghZjFpmFZ8FcFmZ/a8BuGLhOwghZHVpmMh5O4q8aM9oeyZTbtaYjr6FNpG3I68t08gLa2hvN+bm2KQXbjFjTMfhSe99lvpEQcy5Mn44nvVZ/JyONqr1i473Q0cmx42yw+ic0XpPJl37uyNpQhmGx9xQhv7TZiZ+8LnTpXLf/l1OvZfSRhTw4s3u9Zg4WX6VxJHX3Sj91595slTOe2KEnU0mpKira5NzrH2na96S+sC1ioSQyMGBixASORrGVOzImEf8UWt5VWuTO7On1kzcTM6dccxOWmaHpQnvx0gX5swsY7boRlrbi36LntBf0VpULPb7PG36pLVgPJnwfnvqGhFvyjNz7ufMWiKJ6WZjDu7tdVdyjE2besNn3YiagVETVd/aYe6f+Km+8uZDPzfuTit2zprgay2Y6/bkwBGnno6a/nd0tTnHUq3GvN3e5ooYnjhm0prtSFtmcLsX+mPf64S7KN8h50+LOr00xWQVHfwGgE9chJDIwYGLEBI5OHARQiJHw/i4YpZfZNbyXc3OVPYpxDOuLyKWMuN8S8q+dK7PZdbOszjtRpQPTVp+m03u1L1WCG2QuNu+nSwj7/30JGKr91uUy7ufZcCSwSh4dTs2GZ9UzMrGkS24qwxyMGETE7OjzrHzN/eWypvbjN9p6ES/U29iyuRcHDvhRuaftlY7HOx/sVTOxNyvfkfK9Lcr7eZE7G2zQyC8e20pX7zye1uD7w2nXod1Dbp7vEQdFv0D5vvR5N33LVuNvp7svrBiG40An7gIaQCYLIMQEkXuwAZKltEwpqJN3DLJCvnK+vMzk64ZaefUm40bkyftJya0TMoJdTXs7fONTk86xzpT7aVyi5VmPpFwTUhbLz2bc400saxbsX6XVsKCnPC0+sfGzWfb2uktGI+ZPs/mTER8/2k3X4Ntcp864y58nmw11zjVZMy1VMKNXn/17GulcnbOvWfHho0Z2TdnLXDvdYNYdm425mFvU8Y5hlljvnV1uGbe+Jy54FkrWiEu7j0btb47YwOuSby91fRla6t5X9OFnnpUxg3TWAqq+qiI7F6kWilZBoDHRaRDRLbaYoKhKODdCBRh4gD+GkAfTLKMoVCP6xoAXweQRqDf9zlVnRSR/vD9H0SQxuFTodjgxwF8DYHXYUxV312to3ziIoTMUylZhs18soxLVPUiAPer6vcBnESQLONqL1nG5QAOIkiWMc+Yql4M4IcIkmUAJlnGJQA+slhHOXARQpbCukiW0ZCmIiGkLDUlywid9tchSJbxkKr+FVzmk2WUVV1FhWQZInIlgA8hSJbxNlVdnub8RqO31fgzTnvXpiPTWipPZl2fzvSc8dUUrZyIR3/zuFMva4VevD7q+jMwZfwlezwp6/gFe0vl5K7dpXLCU1SwE2J4aQqdr4SKOVhU9+G6aspFi4LfvoXt12rKuEtQUpZY48lh86OcEzccApaPa2efu0zm2deNOsRwwtyn85rdNjZbag7Hdrq+q+3T5hrHWoxvrG+nqzCxvXMbauGkt63TJpzD9i92bWpFJc4Ou77NI1boSF+3+W42LcOndY5srGQZhJBo05DJMggh0WajJctoyIFL1ZgWrUk32/fv3zhq6nmR4nlLSD3TbqbFYwk3JGG6YCLzR2bccIiB4yOl8um8a6+1NJu+jAwZk7LbFyrsMCZabM8FzjGk7al8018tup+laMVH+GajbR5OWUoXmZTrM01ZKwvyRVdJY3DMmMhDgyYn4tbOXqdeztLu7+l2cx3qUWOYnR027cX6XBOqv9v0K5NxQxk6e02ISXOrOXbeVlfloSVtTDv1JDamxy2Ne+87Ic1uaMY8w3PevbXCKFq3u+/ZscmIEaZiXqIDUpaGHLgIIWvDSiXLYDgEISRyNMwTl50GfnLaShnmzZqlrJRYRW9W0b5YuUkzw5i44E1OveLjz5TKHZ5G+QSMCbiryZ0dm82b2aa2lDEZhvOu6TJy1pifLSPPOcf6LjMpsoopY1IWPQF9saYj/dRlxaJtYppyylshYL9v1ls8bQvn2SbaAqz2s2Nu+509xnwbtvrbtsmdwdxT7CuVN7W6ZmRHmzE/t7Tapqi3gNk6lo677WfbjBksVYQaC9ZS85jXfspq04+qJ0uHT1yEkMjBgYsQEjk4cBFCIkfD+LjsHIN5a0p73Jve3tNtUqoPTLhqBX0dZmo9b/mdTo2NO/VGLjf5c1MjA86xdssHk/QE5RLbzBT9biu1e/LMGafeyBnjJxv0/HD5g8+WylssfxdSrnpDtljZWSOW76q5yf6KuGEf43PGVzg66S5Z29xufEYtGRPN/vrwaafehBU6cnbYvY65EXOsqcm0kZ9y71lT0ny21qQbsd7WVCGphKd8eHqwYpA2YIWBtLVUTlIxMWqFvngigJ1WJH1nkytUSJZOzU9cIhIXkd+JyH3h9h4ReSIUHfuZiPjJbgghZFVYiqn4JQCHre1vAfiOqu4FMALghpXsGCGEVKImU1FEdiBYtf3fAHxZgsR27wXwqbDKnQD+EktTTFxVfH3018+a8IXZcWPWtDS7j/5nc5ZAoKc9/uRrJqp+k2VO+VPf+aTZnku4EeXpLkuMEJ6ZZ0WpH58z0do79+x16nWebyLWc795wuu/aTNn9Td24VvhYpuKbv/VCp2fKZr2ZnMzTr2Y1cTohLtw2M792JYxplxG3Ot9fNysJHjj5AhczPlarQj1pla3jaZmEzrSnHBN4jkxNmFLs/mcxVkvDsbajPm/51nTxlhuwjnUZJmOqRZjdPS1uvkjk7EquRTJkqn1ieu7AP4c5vZ2AxhV1flvdTnBMULIOqHhNOdF5MMABlX1qXM5gYjcKCIHReTgmaGhxd9ACFkN7sAG0pyv5YnrnQA+EmpF34XARPwegA4RmTc1FwiOzaOqt6rqAVU90NvTU64KIWSVUdVHAQwvUq2kOa+qjyP4H99qVxCRFhH5pYgcEpHnReR6EfkijOb8w2G9a0TkMRF5WkR+LiKt4f5+EfkbEXlORH4rInvD/R8P2zskIo8u9nkW9XGp6lcAfCVs/D0A/rOq/rGI/BzAxxAMZp8BcM9iba02Ocs3c+qsN7VuCf/FrGQImnZX46etqe+5qWnnWHbGTP+fnDF+j6KXD3HirPl+TE67yRvaOiv7Og4N9pv+qvGNpdJu+30tJmyis8f9kRsdML4m0cohD8mEdevF9XENWGoIqYTl4/JCL7razLk7Wt3QjjOjxl9lCzDOxd3rcWrMXNPeTne5TlzM9m5LZDCddiewOzPlFRoWYHU/F3N9j5oy16ClqbJCw5S9XAxArGB++9tazPcqoj6tSprztpjgvOb8hwBARNpVdUxEvoxAc37I05yfEpGbEWjOzyuljqnqxSLyaQRuqA/DaM6fEBFXsqUMywlAvRmBo/4VBD6v25bRFiEkGkRPc15VHwHwSFh+DcAVS3k/IWRdQ835NcG+HJ5wnli5CTe3GVNjtuBN8cOYCV2e6fKmxL5S+emjJp371tZ2p17KsmRa4+4x5IwJm8q75kTK0ogfPWN+yF7Qo069rj0mKt2P+rXNZTsCPuWJANr5GM+MVs79eGzcCPhtanVNsnibuVYdbe61Gp00bY6PGVNxYNI10ZqsfiTb3Kj3zb3GYmhpNteqtdlVm0hZmvy+CGBu1jqfFS2fjHlXzvq65LxQiVTGtN/a4t6zjrQxkRPRNA9tqDlPCFk/UHOeEBI5qDm/jpmyzI6iuqto29vMR52YNeZhPucK4M3AzHpNJlwTKm2l0rqwz0SzF7024nFTL5VwZ6iSLUZfvNmLWH89Z9wJY4PW7NWc+1leHjBp5fcVvNkxy1SKS+UcZFnbGoq5ZmRzm4kGFyuyHZ5Y4CkrlXxXj2sSd3cYs/LYkGkjUXTPtbndrE5oaXejzfd1W+anYwG6n2tTypiOcc9cK6SN2SuofD2KllCheNctLgmrTEGV9cCGGrgIIesbas4TQhoWDlyEkMixoUzFOUsZYXTSjZxPqYny3mKljo/FXKUBO5xgctKL8j5rotLnLL9WS8aNXm+1hO1m5ly/0NyE8Vd1drjT/3tb9pj3ifFdHZ3xEr9bagWnp931nyk//CLEiw7BSStv4+7N7nvilgiebjc+uWOn3NnpdNz0cWrQDSuxXYy5SePXSvjR/FYewb72Kkk1bLeT18b4pOuLdLASfDSlK3/dZ2csX6Hn42rOmO9Ic6JKH0nd4BMXISRycOAihESODWUqxuxh2LNIstPGlJm0xOZ6u9xwhYKaKG9JueN6zDY7iubSNXsmSIeVmn661bXR4jkTsR3zotnjMdOOHZbR2eYuYIal2Tcx4ppombQJQ7BzSc54i70LWWMaTU67bdjhHC32MgAvFMBuM5V0P8u0FZoSi5lrEEu61ypptT+ddc3q5mZzLJUw5855i72rLWwr5My5p/LmMye9e5ZMW5H5Sdf0j8eYB3G9wScuQkjk4MBFCIkcHLgIIZFjQ/m4Mmnj00m1un4KWwtgcMzkSzx1xvWX2PipBxNWYo3WTjNlvinpjv+FovHvjEy7SSRa48an1tPa5RwbnnQTMVTEymd41vP37LCugW7rK5VjMbePvZbywukhN3Qk02T8PXOWjyjlCSbmLL9Wc7OXI9IKA7GTT8QS7pKctkxlRYXspDl31pJv8IUbM82VM+NNT1nCipbvLp12wxra05FXdqiKiNyOQLBvUFXN3R+aAAAMYklEQVQvqlBHEKgbX4dgkfVnVfXpGtu/CcCtqjq9aOUVgE9chDQGd6DBNOcJIRGn4TTno0TRCg/vbnE/2uCUEeZra7Ei2/1AaEttocULQyjOWZHzE8ZcOx33QhJsq+Oll5xjU91GDWFrl5s8xM6rKJaZ2pHyRPqOPG7eE3M/Z5+lYDGbNhHxmzyTLGNFaYx6IQqT4+Uj0Yue7ZxpM2oOCS/lfCJZPsI8nfE0/q33zc24IRsouqoY88QK7v65KfO+dMZdCdHcaq5dl2VSJhP8zS5DQ2jOE0Iaj+hpzhNCNjTUnF8LYlWeH9Uyw+aSxtR46/bznXpiPYSOZ93ZttezxiTMZo04nh52U0oOW7r1vnRdixoTs//R/+ue27obTW95S6kcU/cHaHjMmEba4d7CFmvB9KR1dj9RmSVHjy1drkl8zFpo3mmZmDGvlZRllvozjhWJuVck02TMN/VnB63TVdFEdNZc+yarTTxWpRECUHOeELKeoOY8ISRybDTNeTrnCSGRY0M9cbUkjK9mLFE5Cr231cy2nh1zQ1tOjBlhvvyMq1ageePjGn7htVJ5KO+mZd9jpXDf0dXrtpEwDpmnTroigGkrz+KO7OFSeXLanbgZzhsfXY/v/Ok10fIpSwFhfMoNNUhaUe8FL8yh18qX6Pq13N+5ZK1+LRvvXL5qhYOlxpFKVv6qZrO2CKDbx1TKXNMMfVxrzkppztc0cIlIPwLnWwFAXlUPiEgXgJ8B2A2gH8AnVHWkUhuEELJSLMVUvFpVL1XVA+H2LQAeUtV9CJxpt6x47wghpAzLMRU/imCWAgDuBPAIgJsrVa4Hdj68TNyN3O62ssfn4sYEPDPsmmH5WXOsvceNWG9Vsz34mjEVU6c8kb5LLzHtb3KXbxWt34peuDkRU2eMyTmTN5/l1QE3LMNOF3/xru3usWbzQWPWSoKiH22eN4uzc54efcw+QcKKNvcWk9sLt32LtVL4QiHnRcP7K9mdytYiazXXKu6ZjfZ2xj9G83BDUusTlwL4ZxF5SkRuDPf1WTEepwH0lX8rIYSsLLU+cb0rXEO0GcCDIvJ7+6CqqoiU/ekMB7obAWDneTvLVSGEkCVR0xOXqp4I/w4C+AWAKwAMzK8cD/8OVnjvrap6QFUP9Pb0lKtCCCFLYtEnrjBcP6aqE2H5GgSrvO9FsHjym+Hfe1azo0sl5vk27KU8mDN+lukZV/dsc5dRPLig+zzn2NjLRlMtYy3raf837rKheJs5d4e4uRPt0IPOPRc7xzreZnxoR3/9sGnPCztItJrbNn3GDdloOtFfKie3mCfcZk+VYcLy5bWmPd+VtVQonqgckhCzHFnVluTYFLw2dMFipPKI3Sf6rRqeWkzFPgC/CB3fCQD/S1XvF5EnAdwtIjcAOAbgE6vXTUIIMSw6cKnqawAuKbP/LID3rUanCCGkGhsqct6mPbXJ2S60GJNkZGTUHMh7igfWJTk+dNI59vLzvyuVXzppwiguz3U79VouM6bjqzlXOSJjSQ1tbXWj6s8cOlgqHxkzC+O7U66Z99YLjChlfNbLdXjULOaP91qhEp4t15qsHPUetxQWEglTL+a1Uc08rBTlIN6b4rXamIRYcK0iIQ2AiNwuIoMi8nyVOiIi3xeRV0Tk2VB3q9b2bxIRas4TQlaUO8BkGYSQKMFkGRHB96V0Z4wixFzRLNEp5t31LsNF47s6c8pdM95s+Zp2bTf+o+m064MafvY3pXI+46qLTjWZZA6TI884x46fNUkqspNmicv+i97i1Ou5/N1mo+D5qmw5UK2wf8FB91oVrKU2BTVhE8Wkm3AjXk1xtlh+vyfeANXKjVRrn6wKTJZBCNmQMFkGIWRdwWQZ65mklYvQFh8EgGTBmJFv5FzVh56LTTjbFeMm+v7Q4IBTr5A192Vu1BU0HM8Z8cBC3j33trhRYuj+gy2mfNmlTj2BZbL5S0RrDi+wEmn4ZqS9aZl8uTk3Sj9nnUq8TCUxK9rfzl+R99UhYLbt0AsAiNMgqDdMlkEIWT8wWQYhJHJstGQZDTlw9TR1lsr5dnf6a2DAErnwZhwzCSNOeLLXhKz0tLuCgz2jp0vltpnNzrGpopmBnI67s9Mzm7aVygUxZtPQmCsk2JI0bbQm251jsZhlbq1AULovQLiEN5aKapmNMX/BeIyLp8nSaciBixCyNqxUsgx6PwkhkYMDFyEkcjSkqShW+PbWFlehYabbCAsWsq5/Z0hNaMNOaz1p5xa3jfZd+0rluBcqPjBtQicmB1z/VNoS7WtpNaESo5MzTr2hKdOPrl5XmcJeMbASLqPCCjRC3xVZafjERQiJHBy4CCGRoyFNxWqk4yYq3RcjhElFiKmYMd+2JV1Tsaim4qnJIefYiB1J760i3txl1pb2tVjZ3jqr6bKvrhlGM4+sR/jERQiJHBy4CCGRgwMXISRy0Mflsa3FqDJku90lP5Mjk2Yja44dOdZf+wlS5rfivL4+51B7qpJ+Gv1MhNjwiYsQEjk4cBFCIgdNRQ87qn5P+w7nWGGTEdIbmzOKDUOTrljg3ORsqby5t9M51tPcUyrHZVGFWkJIGWp64hKRDhH5BxH5vYgcFpF3iEiXiDwoIkfCv52Lt0QIIcunVlPxewDuV9U3A7gEwGEAtwB4SFX3IVAsvGV1ukgIIS6Lmooi0g7g3QA+CwCqmgWQFZGPIpCCBYA7ATwC4OaFLWwc4mKi6ruausuWAQA9IISsIrU8ce0BcAbA/xCR34nIfw/F7/ssIf3TAPoqtkAIIStILQNXAsDlAP5OVS8DMAXPLAy1qssuqBORG0XkoIgcPDM0VK4KIYQsiVoGruMAjoepgwDgHxAMZAPz6bnDv4Pl3qyqt6rqAVU90NtDG4oQsnwWHbhU9TSAN0TkwnDX+wC8iCAH22fCfZ8BcM+q9JAQQjxqjeP6TwB+IiIpAK8hyLcWA3C3iNwA4BiAT6xOFwkhxKWmgUtVnwFwoMyh961sdwghZHG45IcQEjk4cBFCIgcHLkJI5ODARQiJHBy4CCGRgwMXISRycOAihEQOCZYZ1ulkImcQBKv2AFjrhYvroQ8A++HDfrgstR+7VLV38WrRpq4DV+mkIgdVtVxAa0P1gf1gP6LSj/UGTUVCSOTgwEUIiRxrNXDdukbntVkPfQDYDx/2w2W99GNdsSY+LkIIWQ40FQkhkaOuA5eIXCsiL4nIKyJSt6xAInK7iAyKyPPWvrqnVxORnSLysIi8KCIviMiX1qIvItIkIr8VkUNhP74e7t8jIk+E9+dnof7aqiMi8TCfwX1r1Q8R6ReR50TkGRE5GO5bi+8IUwHWQN0GLhGJA/gRgA8C2A/gkyKyv06nvwPAtd6+tUivlgfwZ6q6H8BVAD4fXoN692UOwHtV9RIAlwK4VkSuAvAtAN9R1b0ARgDcsMr9mOdLCFLezbNW/bhaVS+1wg/W4jvCVIC1oKp1eQF4B4AHrO2vAPhKHc+/G8Dz1vZLALaG5a0AXqpXX6w+3APgA2vZFwDNAJ4GcCWCQMdEufu1iuffgeCf8b0A7gMga9SPfgA93r663hcA7QCOIvQ9r1U/ovCqp6m4HcAb1vbxcN9asabp1URkN4DLADyxFn0JzbNnECQ5eRDAqwBGVTUfVqnX/fkugD8HUAy3u9eoHwrgn0XkKRG5MdxX7/vCVIA1Quc8qqdXWw1EpBXAPwK4SVXH16IvqlpQ1UsRPPFcAeDNq31OHxH5MIBBVX2q3ucuw7tU9XIErozPi8i77YN1ui/LSgXYSNRz4DoBYKe1vSPct1bUlF5tpRGRJIJB6yeq+k9r2RcAUNVRAA8jMMk6RGQ+D0E97s87AXxERPoB3IXAXPzeGvQDqnoi/DsI4BcIBvN635dlpQJsJOo5cD0JYF84Y5QC8EcIUpytFXVPryYiAuA2AIdV9W/Xqi8i0isiHWE5g8DPdhjBAPaxevVDVb+iqjtUdTeC78OvVfWP690PEWkRkbb5MoBrADyPOt8XZSrA2qmnQw3AdQBeRuBP+a91PO9PAZwCkEPwq3YDAl/KQwCOAPg/ALrq0I93IXjMfxbAM+Hrunr3BcAfAPhd2I/nAXw13H8+gN8CeAXAzwGk63iP3gPgvrXoR3i+Q+Hrhfnv5hp9Ry4FcDC8N/8bQOda9GO9vxg5TwiJHHTOE0IiBwcuQkjk4MBFCIkcHLgIIZGDAxchJHJw4CKERA4OXISQyMGBixASOf4/a8z/X20XsfkAAAAASUVORK5CYII=\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": [
    "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_x = 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",
    "        self.T1_conv_t = nn.Conv2d(in_channels=1,\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_x = 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",
    "        self.T2_conv_t = nn.Conv2d(in_channels=1,\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 + 1,\n",
    "                                out_channels=self.hidden_dim,\n",
    "                                kernel_size=self.kernel_size,\n",
    "                                padding=self.padding,\n",
    "                                bias=self.bias)\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",
    "        ## 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",
    "        x_h_t_combined = torch.cat([input_tensor, h_cur, time_tensor], 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 for x ##\n",
    "        T1_x_conv_output = self.T1_conv_x(input_tensor)\n",
    "        ## Running the first time convolution for t ##\n",
    "        ## Ensuring that the theoretical constraint of non-positive is met ##\n",
    "        self.T1_conv_t.weight = torch.nn.Parameter(self.T1_conv_t.weight.clamp(max = 0))\n",
    "        ## Passing the convolution ##\n",
    "        T1_t_conv_output = self.T1_conv_t(time_tensor)\n",
    "        ## Performing the internally nested non-linearity ##\n",
    "        T1_t_conv_output = torch.tanh(T1_t_conv_output)\n",
    "        ## Consolidating the output of image and time ##\n",
    "        T1_conv_outputs = T1_t_conv_output + T1_x_conv_output\n",
    "        ## Performing the externally nested non-linearity ##\n",
    "        T1_m = torch.sigmoid(T1_conv_outputs)\n",
    "        \n",
    "        \n",
    "        ## The second time gate ##\n",
    "        ## Running the second time convolution for x ##\n",
    "        T2_x_conv_output = self.T2_conv_x(input_tensor)\n",
    "        ## Running the first time convolution for t ##\n",
    "        ## Passing the convolution ##\n",
    "        T2_t_conv_output = self.T2_conv_t(time_tensor)\n",
    "        ## Performing the internally nested non-linearity ##\n",
    "        T2_t_conv_output = torch.tanh(T2_t_conv_output)\n",
    "        ## Consolidating the output of image and time ##\n",
    "        T2_conv_outputs = T2_t_conv_output + T2_x_conv_output\n",
    "        ## Performing the externally nested non-linearity ##\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_t_combined)\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": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Picking one of the like-sequence tensors within the list to set parameters\n",
    "channels = x.shape[2]\n",
    "height = x.shape[3]\n",
    "width = x.shape[4]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "conv_time_lstm = ConvTime_LSTM(input_size = (height,\n",
    "                                             width),\n",
    "                               input_dim = channels,\n",
    "                               hidden_dim = [128, 64, 64, 1],\n",
    "                               kernel_size = (5, 5),\n",
    "                               num_layers = 4,\n",
    "                               batch_first = True,\n",
    "                               bias = True,\n",
    "                               return_all_layers = False,\n",
    "                               GPU = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "ConvTime_LSTM(\n",
       "  (cell_list): ModuleList(\n",
       "    (0): ConvTime_LSTMCell(\n",
       "      (i_conv): Conv2d(129, 128, kernel_size=(5, 5), stride=(1, 1), padding=(2, 2))\n",
       "      (T1_conv_x): Conv2d(1, 128, kernel_size=(5, 5), stride=(1, 1), padding=(2, 2))\n",
       "      (T1_conv_t): Conv2d(1, 128, kernel_size=(5, 5), stride=(1, 1), padding=(2, 2))\n",
       "      (T2_conv_x): Conv2d(1, 128, kernel_size=(5, 5), stride=(1, 1), padding=(2, 2))\n",
       "      (T2_conv_t): Conv2d(1, 128, kernel_size=(5, 5), stride=(1, 1), padding=(2, 2))\n",
       "      (c_conv): Conv2d(129, 128, kernel_size=(5, 5), stride=(1, 1), padding=(2, 2))\n",
       "      (o_conv): Conv2d(130, 128, kernel_size=(5, 5), stride=(1, 1), padding=(2, 2))\n",
       "    )\n",
       "    (1): ConvTime_LSTMCell(\n",
       "      (i_conv): Conv2d(192, 64, kernel_size=(5, 5), stride=(1, 1), padding=(2, 2))\n",
       "      (T1_conv_x): Conv2d(128, 64, kernel_size=(5, 5), stride=(1, 1), padding=(2, 2))\n",
       "      (T1_conv_t): Conv2d(1, 64, kernel_size=(5, 5), stride=(1, 1), padding=(2, 2))\n",
       "      (T2_conv_x): Conv2d(128, 64, kernel_size=(5, 5), stride=(1, 1), padding=(2, 2))\n",
       "      (T2_conv_t): Conv2d(1, 64, kernel_size=(5, 5), stride=(1, 1), padding=(2, 2))\n",
       "      (c_conv): Conv2d(192, 64, kernel_size=(5, 5), stride=(1, 1), padding=(2, 2))\n",
       "      (o_conv): Conv2d(193, 64, kernel_size=(5, 5), stride=(1, 1), padding=(2, 2))\n",
       "    )\n",
       "    (2): ConvTime_LSTMCell(\n",
       "      (i_conv): Conv2d(128, 64, kernel_size=(5, 5), stride=(1, 1), padding=(2, 2))\n",
       "      (T1_conv_x): Conv2d(64, 64, kernel_size=(5, 5), stride=(1, 1), padding=(2, 2))\n",
       "      (T1_conv_t): Conv2d(1, 64, kernel_size=(5, 5), stride=(1, 1), padding=(2, 2))\n",
       "      (T2_conv_x): Conv2d(64, 64, kernel_size=(5, 5), stride=(1, 1), padding=(2, 2))\n",
       "      (T2_conv_t): Conv2d(1, 64, kernel_size=(5, 5), stride=(1, 1), padding=(2, 2))\n",
       "      (c_conv): Conv2d(128, 64, kernel_size=(5, 5), stride=(1, 1), padding=(2, 2))\n",
       "      (o_conv): Conv2d(129, 64, kernel_size=(5, 5), stride=(1, 1), padding=(2, 2))\n",
       "    )\n",
       "    (3): ConvTime_LSTMCell(\n",
       "      (i_conv): Conv2d(65, 1, kernel_size=(5, 5), stride=(1, 1), padding=(2, 2))\n",
       "      (T1_conv_x): Conv2d(64, 1, kernel_size=(5, 5), stride=(1, 1), padding=(2, 2))\n",
       "      (T1_conv_t): Conv2d(1, 1, kernel_size=(5, 5), stride=(1, 1), padding=(2, 2))\n",
       "      (T2_conv_x): Conv2d(64, 1, kernel_size=(5, 5), stride=(1, 1), padding=(2, 2))\n",
       "      (T2_conv_t): Conv2d(1, 1, kernel_size=(5, 5), stride=(1, 1), padding=(2, 2))\n",
       "      (c_conv): Conv2d(65, 1, kernel_size=(5, 5), stride=(1, 1), padding=(2, 2))\n",
       "      (o_conv): Conv2d(66, 1, kernel_size=(5, 5), stride=(1, 1), padding=(2, 2))\n",
       "    )\n",
       "  )\n",
       ")"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "conv_time_lstm.cuda()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Training"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "loss = torch.nn.MSELoss()\n",
    "optimizer = torch.optim.Adam(conv_time_lstm.parameters())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "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": 19,
   "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": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "device = torch.device(\"cuda\" if torch.cuda.is_available() else \"cpu\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "conv_time_lstm = torch.nn.DataParallel(conv_time_lstm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch:  0 \n",
      "\tBatch loss:  0.026610225439071655 \n",
      "\n",
      "Epoch:  1 \n",
      "\tBatch loss:  0.020982731133699417 \n",
      "\n",
      "Epoch:  2 \n",
      "\tBatch loss:  0.018289979547262192 \n",
      "\n",
      "Epoch:  3 \n",
      "\tBatch loss:  0.03285464271903038 \n",
      "\n",
      "Epoch:  4 \n",
      "\tBatch loss:  0.02568833902478218 \n",
      "\n",
      "Epoch:  5 \n",
      "\tBatch loss:  0.022497549653053284 \n",
      "\n",
      "Epoch:  6 \n",
      "\tBatch loss:  0.02526514232158661 \n",
      "\n",
      "Epoch:  7 \n",
      "\tBatch loss:  0.01275978796184063 \n",
      "\n",
      "Epoch:  8 \n",
      "\tBatch loss:  0.032252080738544464 \n",
      "\n",
      "Epoch:  9 \n",
      "\tBatch loss:  0.01897526904940605 \n",
      "\n",
      "Epoch:  10 \n",
      "\tBatch loss:  0.02761051617562771 \n",
      "\n",
      "Epoch:  11 \n",
      "\tBatch loss:  0.01891762763261795 \n",
      "\n",
      "Epoch:  12 \n",
      "\tBatch loss:  0.01321781799197197 \n",
      "\n",
      "Epoch:  13 \n",
      "\tBatch loss:  0.017052195966243744 \n",
      "\n",
      "Epoch:  14 \n",
      "\tBatch loss:  0.01718285121023655 \n",
      "\n",
      "Epoch:  15 \n",
      "\tBatch loss:  0.019929900765419006 \n",
      "\n",
      "Epoch:  16 \n",
      "\tBatch loss:  0.016184601932764053 \n",
      "\n",
      "Epoch:  17 \n",
      "\tBatch loss:  0.021280063316226006 \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": 23,
   "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": 24,
   "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": 25,
   "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": 26,
   "metadata": {},
   "outputs": [
    {
     "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"
    },
    {
     "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": 27,
   "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": 28,
   "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": 29,
   "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": 30,
   "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"
    },
    {
     "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()\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": 31,
   "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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HACva26O2sxZbs+Kbltha7WG4oA+BzNbHbc2uP9FB6cwrI4HJxTtNFzZZU8vbu1dGfT5V70XdNiDApwWG0IwUmp/iXvt+NKEvJuPv4f2fCWMKEZ4irXUHadFOURGZA9wF/L0x5kjYZ6y7O9GsJSIbRWSbiGgIh1KVTGVuh/N6ssngFKVcFKWhi0g9dsLfbozxJ3peF5EuY8xuEekC9iZ91hizCdjk7lO0L6PS+IyKocP0sssuyxu3fv36nPdhAenvf//7ZZJOKRVTndvhvF537rqi5rXX/ox3BAaf8ppwJtAQs1EOl/qcVyu3He9LtzUEYYXe6dhUF/95+7Jx/hBRqF37w0n1QS6XyAnqi0YE5e98NsSRoOCGf+bCJpsj5sJlb476zl5si78sd0Uzch2sLjSzYNhiTknonM8B+G8SH7wqTk8tVhefTHhjTn6eCmj7E35zsb/0T4CnjTFhSaDfABvc9QZgc+nFU5TyoXNbSRvFaOhvBa4G/iYij7m264GbgJ+LyDXAy8D4BmlFqU50biupYsIF3RjzR8bfnVxcWnGqh8svvxzIzcPS32+T+NcFW9n3vOc9QJzL5aabbor6Bgbi/Boen55XZll8bDVSqbntt+Jh7DVi509YW7MJ6zyMzCuBIzMSOsEk4u/RlI3H7zlurUYr5trTo6FpIE7TG8sT9Zt8E0eSfcnfw8fHtzXEJ0U7nBkmk5Aq18eyZ4vI6QKxSSopj4yXMZPj5Jzc2cmkeqRj+6rZcaonRRVFUVJCzeVymSnuu+8+AJ544om8vs9+9rPRtS+O8fvf/x6Ae+65p+B9L7roIgBOP906ig4cOBD1rV1rM+Bt374diE+aKrOHUKOMtfV8rdRruT6fyuDoQNBl2xa1xKc12wONGeIycgBzXem5bOCs9LsC/8QcDT3ShMOwS3vt88LklNJzp059qOVooAV77VpMcFJUxuqZodYsY15jknLfJMdhjPlsWBCjxnfOqqEriqKkBNXQx+BzxNxyyy15ffPn21wUn/vc5/L6br/99nHvGeZ3CbV7gAULYi3q1ltvBeDjH/84AM8991yxYis1SK7G7e3ksZZsCmUddB8dHbWhgz70EKClzmrCaztOjdpOajvZ9dm52BgcUqrzhZolwVZdICd5uJsYjXLR2Nfw8FBzndsN+ANJxCGTkTadUCMuCvNMCgVMsKH7POuZIIQz2e7tZU14ZlJ2xhoqPq0auqIoSkrQBV1RFCUlzDqTiw8vhLhYxpo1a6K2m2++GYDHHnuMsXhzTJKz8h/+4R8AuP766/P6wvwxvkyeZ//+/dH1O97xDgCOHTs2wbdQapGxIXG5zrukAgyj7tWPj/EOQH9qs38kTift79U9Z3nUtqDROu+jVLlBeKR3bian87WvPpVveI/wtGlmjCMzfN/ncsX0j/Q72ePPtbsCGvVBvpboCK37HiOj8YnUsd8R4Piw/XvpHfJl85YF43Kdu+F3SjKgeDOMmPHDF6sZ1dAVRVFSwqzT0IeH43/tfehgsfiDRVdddVXU5otVn3baaUAcxghxcYwcZ1PGaUNOAwiLWKtmriQ5SqFAKTo3j4YDLXZOvQ0T7GiKy9LlF2Me/14Q52nxzs7DQ4eivoERGyIZOnB9LhffF4Y5HhiId6HhWPfUvPHDDIddDAUhmf57hruDff320NSRQZtXzeerAWgW6wQeDXcQPuTT+1cDaeLcj5LXVs0HijyqoSuKoqQEXdAVRVFSwqwzuZSCZ599Nro+6yxbPd3ndAnZsmULAEuWLInann/+eQDuv/9+ALZu3Vo2OZXqIimuerwx7o0lIUZ77D3qg9S6DWJNGmEaWj/amyrC3C9kXHx46Hz0ph9nnugfjp2uwz5tbpBuN+pzseBhqt8h1zbXnVZtCU6pRjHw4XczPj2vlTWMsfeO1fBk7L4+Wzv14IA1C82tfzHqO7X9DABi41DwnFF7/zCdb2yGCWPfa0fvrR1JFUVRlIKohj5NvJP1t7/97bhjPvGJT+S1vfLKKzmfV2YPxWjq4bgkB6bXKn2Ww/bG+VFfHNIYZDX0IZA+30lYLMPpdWEOFX/tww87mhZHfV5DD3cTfpzXxo8MHo76/Pf0u4g59XFeGR8+GYYyeods38jxcZ8zp35u1NYQafl23CvHdkZ9p8w7zX2feKmLQzIto0HIpEQq+tR03Uo7TlVDVxRFSQkTaugi0gT8O9Doxv/SGHODiKwE7gQWAo8AVxtjBse/0+zl61//el6bZlKsPDUztxMOHWV8SKPTcBszcf4Sr3GGh3u85ug14voE+3e4HGSiAzmSN95nRgzDCfuGrW37lWN25/la72tR38ltJzkZrW2/LhPmdbf3Ghztj9oODR4EYH+/rdUahl96uXwGx/A7efqH43sNGbtjaJTmYITPVOl2MuEBqYTdSi1RjNQDwDuNMWcBZwOXisibge8AtxhjVgEHgWvKJ6ailAWd20qqmHBBNxZ/4qXe/WeAdwK/dO23AVeURUJFKRM6t5W0UZRTVESy2K3nKuAfgReBQ8ZEZb93AUvH+fisxYcyhrlcfLjiDTfcUBGZlFxqYW4nOtpckze9hCaRpNwv3onqTRb5J0dhREbz2nwa3frgdOfosDVR9AWhjAMunNCfNp0XFNRY0tIFQFtDu3t2/PfgQxP39++L2va7k6X+5OfS1jg3i0/LG37f3qFjTh4rw8H+I1FfjztF2ja3Pe+7ZaNwzdia5h3JmTCXS6b6T4h6ijIUGWNGjDFnA8uA84E1E3wkQkQ2isg2Edk2RRkVpWxMdW6H87qnp6esMipKsUwqbNEYc0hEHgQuANpFpM5pMsuAV8f5zCZgE4Ak14NKLevXrwdyc2T88Ic/BODw4cOJn1Eqw2Tndjiv1527bubntcnNGBgejokInKlZcp2cSU6/ugT9zmv0OblWXPihz5QI0DdsMx36sMVsJg5zbG+w4yLNPJBr0Gn2249sj9pa6m3+lc6WTvu+Li4Q44tJj5g43PfJ/faw3s4j9h/WPz3/UtR3aMBq799443V538kvf8JQ3veuhWIWSUyooYvIIhFpd9fNwCXA08CDwIfdsA3A5nIJqSjlQOe2kjaK0dC7gNucrTED/NwYc7eIPAXcKSI3Ao8CPymjnDXDpZdeGl1v3LgRyNXG/dF/pSqo3bktuSXiQs0ssVyc00rHauq5Y4rTSr39PbyHt2n7EMNwB+DDCv2BpN7B2Mbt29oCm/sp7dbqFReeDkIm3TN9igGA3cdsofUH/2rrGzz7p/hv7MWXbPjk1877StTmNXT/7DANQuJOp4aYcEE3xjwOnJPQvh1rc1SUmkTntpI2ajN6XlEURclDc7mUmIaGeHvoi1kcOHAgavNl7xQlZLI5QMaOH1sCDibOFZM3ziS0OXJzrdjr4SDcz5/u9HlVfKELiMvXPb7/rwAcD8IdL+i8AICT2k6O2lr8KVAfTBAWiHE6aCYbn/y84IQ3AHDHA3+yDfvjk6JHh62j9MmDf43aVs5dBcCePuvrbqufF/X50Mrcohe14yBVDV1RFCUlqIZeYvbs2RNd+3wtLS1x/mefGz0cpyhTJXJkmvy2MNRwbIbHJO09p0i0yT1kFN7LhwwOBhr60SHr6GxvsFkfnz74dNR300P20O2uXfbw0AXr4lD/cxedC0BHU2fU5p2uRnxoZlgOzjmBgx3Jqnar3ddnExyag3Y38d/u+l/xM1ed6L6Tvf+GMy6P+k5fYLX9usRcN9WPauiKoigpQRd0RVGUlKAmlxLz8MMPR9ff/e53AfjiF78YtXV0dABqclFKy0Qx5MU6SPM/l//5sQUoQg64PCx3Pv1Q1LbtgcetjAttit+hkdjB2lJnzZE5ZpUodW8hwWJ5DvTboIO+AWcCSsi98rc/Pxdf/8XGqS9dYc08f7f8DVHfKe2n5t2/hnyiqqEriqKkBdXQy8i3vvWtnFdFmUmSwu2K1tSjk6juc4HG6sMQw9DE3qHenHFzg/Bd2uz1yctt1sUPnBqf2fIhitmcohe5cifJ3D8Shz7+85P3AnB4jy0STVPgHK1z9zoa1CcZtffr7ex3ssc7jaggdFpzuSiKoii1gWroipIyvJZcrDZezMGZcIwx+eGEPnf5khYblnvd+Z+J+tqbrO38LUttloW3Lnlb1JdJ0ClHx4RMmqCIs98dbNu3NWrb/IDzWwUHiuKbudeR4J4tNutjV+dCAJbO6Yq6/MGoTC0ZzgNUQ1cURUkJuqAriqKkBDW5KEoVkWQmKWQSCZ2VpXzm2LbhoKCE72uui/OpeFOLLzc3r35+1Pffz/wkAFmXmrYpG5+czjhnaK7pxd7fn0Q9Pnw06tl93KbD/Z8P/UvUdvwllytp0JlVwp8rm//bZRfb57/h5G4Als/pjvsyvjyemlwURVGUClK0hu6KAGwDXjXGrBeRlcCdwEJskd2rjTGDhe6hKNVGrc5rryUXmwmwmFDApPFJ47zT8uBAnEXUhy36wtELG+PcLD6/y2AQ5hjJ4e5lAvH8/Q+5Q0ovHnkx6vvP3Y8A8Kf/fCL+wHG3exh2GnpSUec5cWHq1SfZmt9vWXaKlbWpI+rzu4ja1M8np6F/AVuey/Md4BZjzCrgIHBNKQVTlBlC57WSGopa0EVkGXA58GP3XoB3Ar90Q24DriiHgIpSLnReK2mjWJPL94GvAHPd+4XAIVcVHWAXsLTEsilKuampeT3VfCzTe6h9ZljgYm//6wD8refJqO3ooDW51Dmn4uLmJVGfN6H4uqNh6ltv2glNQr5/Tr2tM9rVEt/LP4cDgfnGjPMKsVO0M3bEnnPKCgBOW7AaCApqhLKl9aSoiKwH9hpjHpnKA0Rko4hsE5FtU/m8opSDUs7rnp6eEkunKFOjGA39rcD7ROQyoAloA34AtItIndNmlgGvJn3YGLMJ2AQgIhVQMRQlkZLN63XnrivrvC6kmU+6zNwkn5nkfPUFKOY1tkVtDVmrmbc32nJuQ0HxC6/1NrqycbkaususGGjE4nYFTW58W0NcIi4K02wIdFF/PWK8gHGfOxXq88gAnN9lC2Kc0HICEO8cIA6frKWycyETaujGmOuMMcuMMSuAjwIPGGM+DjwIfNgN2wBsLpuUilJidF4raWQ6B4u+CtwpIjcCjwI/KY1IilJRdF7nkK+pttZbm/PqeauitoZsIwDzG21+lDqJwwTH7g7Cd4kaZaSt29f+kThHy19ft/b7liXx7uB4q8uW2OPGBWGLDUute+TMNSuitjULVuXI6kMVc59dm0xqQTfGPAQ85K63A+cXGq8otYDOayUt6ElRRVGUlKC5XBRFmZDQbOJTzLY0xqGAPlzROxULnTANHY4j3vmakJPGO1bDE6nrljjn5pvica/ttidKt7+828qSjfXUtWecBMC7VqyN2pa22kjUxqxN65sURlmrqIauKIqSElRDVxQlj1hTtZpz6DhsqWuNRo0d71uSQhO91j4SHFLybeHBJa+Z7+uzDtDXendHfd1tVkPvH4mzP85tdA7ZBdYBOr813jm8fbk9PLRm/uqobV5DOxCHX0qK9Nr0fBNFUZRZji7oiqIoKUFNLoqi5DH2pGguBRyHLo47dHIaya0RStA3ZIYA6B2Ki1gcGTxsX4dsndLh0aGorz5jTT8dzfHp0c5Wm553uNOabRY0xX2r21cCcEJrnJKn2RXY8MU1pMZjz0NUQ1cURUkJqqErilIAGfMaEzoyo9GuUoVk4pOimbHFNXLyttjr0OnqdwUH+g8C8Frv3qhvYMQ6TOc2xI7PtkZ7crXOae+dzYujPh+i6B2hEGR9rPG8LUmohq4oipISVENXFCWPsWGLmYR85SNB4WivrXvbeWh7Fzfel5sbHI1zmfs8LX3Dx6O2w86Gvq/PpiXe33co6mtrsNr4srlx9sSOJpuTpdHlkwm18fZGa19vyDTG8qfQdu5RDV1RFCUl6IKuKIqSEtTkoijK+DizhDdTANQnOTKdqcWHIQ6NxGaVY8PHADjQb3OuHByITSjeVDM0GptvBtxnm+qsmeS8zjdEfV2t1tQytz4oruGcnPXOERsWrPDXdTlO2vGdob5tsgVBqsWxqhq6oihKSihKQxeRHcBRYAQYNsacJyILgJ8BK4AYv7XjAAAHUklEQVQdwJXGmIPlEVNRyoPO7eLICT10mnkm0AeNry7ptPfw8JDPmdJcZ0vKNdU15fWFGrHPyljndgVx7pj4OtwdjC1jlwn6/Lic3DIFnKFTLcSdVKqvEkxGQ3+HMeZsY8x57v21wBZjzGpgi3uvKLWIzm0lFUzH5PJ+4DZ3fRtwxfTFUZSqQOe2UpMU6xQ1wH0iYoD/4yqedxpjfF7LPUBnOQRUlDKjc7sogjh092okv7/OLSlhmc55YmPBvSMzNGuMRE7Rwaht2DlIvcmlKdsc9WUlP4Y8St3rzCrZJJML6SliUYhiF/S3GWNeFZHFwP0i8kzYaYwx7g8iDxHZCGycppyKUi6mNLfDed29vHtmJFWUCShqQTfGvOpe94rIv2KL6L4uIl3GmN0i0gXsHeezm4BNAOMt+opSKaY6t8N5ve7cdVOa17WkKYaSmjHFLHxrODLUiL2mPWryT5h6bb0+CCuMQg2dNh46Ob1mLgknV7PR+PjZkRwpPBWaxIQ2dBFpFZG5/hp4N/AE8Btggxu2AdhcLiEVpRzo3FbSRjEaeifwr+5fxjrgX4wx94jIn4Gfi8g1wMvAleUTU1HKQtXN7VDznGoIXSmJDtqEUYtRvpbQjk3OuLCsWybS6H14YaC9JxSHzhci316epIX7tpydT4JGn2YmXNCNMduBsxLa9wMXl0MoRZkJdG4raUNPiiqKoqQEzeWiKFVKMXlFppp7pFii+4Yl5RKv/ElJL1gQJuhNNOJT8eafMC1kEhHJN9+QYO6ZbeaVJFRDVxRFSQmqoStKlVJNTtHcsL/cEMXcq8SblJzZrIUXQjV0RVGUlKAauqJUAdPN8jeTqHZcvaiGriiKkhJ0QVcURUkJanJRlCpgumaManCgVjOlMBNVSxGLQqiGriiKkhJUQ1cUJfUk7WAmq2lXs2buUQ1dURQlJeiCriiKkhLU5KIoKaAWzAHlohaclTOFauiKoigpoagFXUTaReSXIvKMiDwtIheIyAIRuV9Ennev88strKKUGp3bM4+Z5P9N576zjWI19B8A9xhj1mALAjwNXAtsMcasBra494pSa+jcVlJDMTVF5wEXAj8BMMYMGmMOAe8HbnPDbgOuKJeQilIOdG5XBpnk/03nfrONYjT0lcA+4FYReVREfuwK6nYaY3a7MXuw9RnzEJGNIrJNRLaVRmRFKRlTntvhvO7p6ZlBkRVlfIpZ0OuAdcD/NsacA/QyZgtqjDGQbLAyxmwyxpxnjDlvusIqSomZ8twO53VHR8eMCKsoE1HMgr4L2GWM2ere/xL7R/C6iHQBuNe95RFRUcpGSea2CIjMvu29Un1MuKAbY/YAO0XkVNd0MfAU8Btgg2vbAGwui4SKUiZ0bitpo9iDRf8DuF1EGoDtwH/F/mPwcxG5BngZuLI8IipKWZn23DYGjJl9IXJK9VHUgm6MeQxIsoFfXFpxFGVm0bmtpAk9KaooipISNJeLoihKlTJZZ7tq6IqiKClBZtKZIyL7sLG+tXwSo4Palb+WZYeJ5T/RGLNopoTxuHn9MrX9+9ay7FDb8hcje1Fze0YXdAAR2VbLh4xqWf5alh2qX/5ql68QtSw71Lb8pZRdTS6KoigpQRd0RVGUlFCJBX1TBZ5ZSmpZ/lqWHapf/mqXrxC1LDvUtvwlk33GbeiKoihKeVCTi6IoSkqY0QVdRC4VkWdF5AURqeoqMCLSLSIPishTIvKkiHzBtddMeTIRybo833e79ytFZKv7/X/m8pdUJbVUGq6W5jXo3K405ZzbM7agi0gW+EfgPcDpwFUicvpMPX8KDANfNMacDrwZ+JyTt5bKk30BW1LN8x3gFmPMKuAgcE1FpCqOmigNV4PzGnRuV5ryzW1jzIz8B1wA3Bu8vw64bqaeXwL5NwOXAM8CXa6tC3i20rKNI+8yNzHeCdwNCPbwQl3S/z+q6T9gHvASzscTtFfdb1/r89rJrHN75mQv69yeSZPLUmBn8H6Xa6t6RGQFcA6wlSJL71UB3we+Aoy69wuBQ8aYYfe+mn//aZU9nGFqdl6Dzu0KUNa5rU7RCRCROcBdwN8bY46Efcb+c1p1YUIish7Ya4x5pNKyTJFplT1UikPndkUo69yeyQX9VaA7eL/MtVUtIlKPnfC3G2N+5ZprofTeW4H3icgO4E7s1vQHQLuI+Ayb1fz711LZw5qb16Bzu4KUdW7P5IL+Z2C180Y3AB/FlvqqSsTmrfwJ8LQx5ntBV9WXJzPGXGeMWWaMWYH9nR8wxnwceBD4sBtWlbJDzZWGq6l5DTq3K0nZ5/YMOwQuA54DXgS+VmkHxQSyvg277XkceMz9dxnWXrcFeB74f8CCSss6wfe4CLjbXZ8EPAy8APwCaKy0fAXkPhvY5n7/XwPzq/W3r6V57eTVuV1Zucs2t/WkqKIoSkpQp6iiKEpK0AVdURQlJeiCriiKkhJ0QVcURUkJuqAriqKkBF3QFUVRUoIu6IqiKClBF3RFUZSU8P8BUIjJLFEOhpkAAAAASUVORK5CYII=\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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XKTH+6+2L8heuF4AvfOELC16jc4DGuESlr33tayVzLkHKhVE+/fTTC16DMDvz3dvxvr78isvnta91FLZ4YsL4XI+NH4/XBsC5XReUvLfYYdicCsp+24rLAfjIO474sV3HzEf4lbPeXvA+81lcHZngjHeNqX1DaMpL5HGNNO58JLR1JGc/Z7vZ351bVvipv73p981UFEbpkqvKbeI8a4XEWcKQy1HvS405Fboy38hXgRe01vFd7gfAbfb1bcD9xe8VhHpG9rbQaJSj0K8Bfgt4Rim10459Bvg88C2l1B3AXuDW6ixREKqG7G2hoZjzhq61fhRmfKZ5Z2WXMz927TJxrpdccgkQarrEPPyw6TQeN5R46aWXgOTHshUrzGPhmdpH4/6kH/3oR0vmXWz65s2bAfjt3w59HF3W6He/+11AMkWrTa32tst2jOu2uNoqw5Ohts+rQ6YmS7tt6hA7TF0zilab5RlnUHZlTUOM928KJXKbzjcmk2yCM9TFw8fZnaM2Lr7TXmcuR6Aztfxk/48AePRHT4ZJmw267BIThPDBt7/RT63v2GDWP4uxYK5rl8xHvyb923amljM13ywFJFNUEAShQWiIWi4Ol2H5wx/+cMZjfvM3f7Osc/3oR0ZpPP74437MVUFcvXq1H7vpppsK3uecsBDUeIx7QojP67jzTpO/4ppfCI2JU6OxQnfquzkdnI+vDhlH/t5TBwGYmA5VCrcsMw73bcu32XMFbTaeMw5Np9ShqEkEhQ0xRnMmsGf/aGixmLV1ZHxzjVj7WdU7nQ+K/meHfgrAJ75tnaHDUUXFlebav3btVQDceO6v+Kkm+8SQqKTLDA/0DUO8kzOqeaMTFLe9lq9YGany2RT9bJxptcVy6uHMB1HogiAIDUJDKfRy+KM/+qOSMRfuCPC+970PCElHt9xyi5+LX8+Xo0dN+NiTTxobY1x9cXjY2C0r0epOqF+cmo5rqGRs0+d4bM+Q2Ss79xuFvvuloKBbm42CPv+C9QBcGPlueluMXf0d667xY2s71gHQlLY29EhInpo0Cn3fcDj/RcsuBmBo8iQAuUxIghqfNiHDrw2/6sf+51Pm6fXQURt22Rfs/VddcxEAv3a+SbA7vyeEYTrfwZkq1cKm2C4Jatr+DE8OymrWuLJleEKyja2j2vBpEuralFEjpl6SjUShC4IgNAhyQxcEQWgQfmlMLi6UMa7l4krY3nHHHX7M1VhJqr8yG1ddZRw+55xzTsmcC5kEuP3224GQuSr8MmI73UflcTubOgFozQRTxbBtm3jwgAmdPb4nCqFNmXOcGDJlnl/q6fRTXV3G5DJ4etiPvX29aet25Yqr7NuDlnMmimzkkJ2wZpVnjpk2iGd3nu3njo2bujM7Dj/jx1wLvHPONgEDG9aF8je/f6WpH7O19yL7GUMJa+cYni2EsGAuIeTQmVryPuM1NlnmE85vG4zY9xU0DrFO2lRBJu3MYY7Vcm7OF1HogiAIDcIvjUK/8UaTZBE7Nv7qr/4KgKGhIT/29a9/veDnXDiHiQs1TFLoTvWDKHMhZDLFDtDeZtOcfFVbULZdzUYtjo/b1m1jUeOTjNFip0eLKhkCo2Nm7KnuoITP7jaJcus7jRM1GzVZHp4yKn90KlQt/cWASZzdP2zqwfS3hBZxaatez+1d58e29p8LwLI3ms+xpTe0dezImDotziGbTtKRuiAbyAz5cMS4VV+hA9S8ztm3pUqOT6oLU/xUEIdwugSp2FE6W7XFpAqPtUQUuiAIQoMgN3RBEIQGoeFNLtdffz0A27dvBwrNK66Wy0JwTtZbb525ftNTTz3lX69caR6p160zj6s7dkiZ+F867ON5HPPcnjFOzZVtodbQ+i4TW57N2sf/TKS/mu170+ZcuahRSqt17MXmxYlpE0d++PRhc0ymNbq2Mc3kovjtwbETdg1mPX0tfX6uLWMyPy/o3ezHuppMVqrLSE2lwq1F+Z+q4PPHJDk+HYXmFfPamUbMa2OSarJmpPhzu2YiqcRs0KSsUOdYDdd0ceshDzUfHV+4VnWGvVcrjSh0QRCEBqHhFXo2a/5qu2YWx4+HBgILaS93JsQVFZ3T9D3vec+iXFuoPxSlCtGpy77m4Hw8v8/slf5+o34Prjzm59Ipo9Cbs+afcCYT1P7yZeb4c1aEukKrO8xrFx4ZK+7lLeapsb0pOFGXtZjs1O5sl/09nKvTqvFY9TqHZ8aHYsbqtDDsTyVkXMYq3L/LquVYjbuMTxdWCTBmm3G0Z0oVsavlEj8BNNnXzikdhyjO9vTg1hi3DnTrcVUs46cupUqzTquNKHRBEIQGYU6FrpRqAX4GNNvjv6O1/lOl1EbgPmAZ8CTwW1rryZnPVBsOHzY2Q9dIuq0tVJ1zlQ/dMdXihhtu8K+vu+46oLCFnlAbar63E+ytTVE44cbODQBccY4JNczng8ocPhXqpgO0tIY651ecb9537fqL/dgFvecBsKLVqPGebFDorqJiNh3O4WqwO3XaGbWIc2uMFbpT5knJQIWJPqBVqY07VuHuHE4RT1obOQQ1naTo3Vx8PXfekdyIH3PK3FW4bIsSnTL2syXZv925Ttn6NgATdm3uyao5HXwTTa6a4yIq9XIU+gTwDq31JcClwPVKqauBvwC+qLXeBJwA7pjlHIJQj8jeFhqKOW/o2uD+vDXZ/zTwDuA7dvwe4OaqrFAQqoTsbaHRKMspqswzw5PAJuBvgFeAk1r7OKf9wJqqrHCBuEYSf/mXfwnAJz7xCT/nmlFU2+Ty0EMP+dfPPvtsVa8lnBm12NveHBE5B90jfuygc9mj79xg6rCsbA9mj3/btwcIZpiNfb1+7j9vNE0vzrZZoQDLW02mqDO1NEft7MK1g2nAmVhcGF5zKjrerlHFzsQiE0VSqGGSGcOFSsYml7AO89maoqxN36ouwYqR1ODidM6YWvcNv+7HTkwYk8nyVhMWusGatgA6rNOYqFWfC2E8NmFq6RwZC/eLkSlj+pruNMc4BzNAJpOxqyn9/1wtynKKaq2ntdaXAmuBq4DNc7zFo5TarpTaoZSSgGuh7pjv3o739Zn2nRWEanFGYYta65NKqUeANwE9SqmMVTJrgQMzvOdu4G4ApVRpvNIi8Wd/9mcFPxeDsTETTvXFL35x0a4pzI8z3dvxvr78issrsK+tSo40llPRF/ScD0Bfc1DhzZlC593mvo1+bkvvFgBaMyEAwIUaunMmVROMtaN3fLrQvihRyDlDk9Sm+yJix2Tx00ecfJPPzxyumLbXbFJNJcdEuT1MYhyTxyYGgNCAA+DAiAm/HBgLf3QPDJvGIQez5mfcEGOVTeyKw0ddE+1XTr0CwP7hsB3GbVtA9x22Rk7R2Nm6WMyp0JVSy5VSPfZ1K3Ad8ALwCPABe9htwP3VWqQgVAPZ20KjUY5CXw3cY22NKeBbWusHlFLPA/cppT4LPAV8tYrrrFtcuziXpLR5c3hiv+uuuwDYuXPn4i9MKIea7G0f2leQe+Oq9gWN5UIBnVpsb+rwc86u7KoCroyqNHZnjZKP1b4LSQwVHiOVjK1WGB2fThXayZOaRMcKvbhyYcETAIWfreB9urTdorOnu+NT6UzJ8fETw2jO2LG//4ppg3d45ISf23fKtNe7ZOVZfsw14t4zZGzhrswBQFez+Y7fvHqbH+u2zbZdq76TE6HO/PCksdE32fWsbg+lG/qtPT0d/X+udqu6OW/oWuungcsSxl/F2BwFYUkie1toNCRTVBAEoUFo+Fou1SaXM4+rW7duneNI4ZedxJZqfs7+jEwVzqzgnJutBCdnW3dbwfEtkTMulZCZWNzoIenBPzaTFJtmCkMUE7Amo6npCXt81FDC6UY7lE+4euyYdE7IOGvWX4ZSB+64reXywuAhAJ7fe9DPjQwbk8iqjmCuOqujB4Ajo8ZU8/ThI35ucjLUaXG8abUJG83Y76SvtTusx37usZz53C4kEoJjOClssVrhi6LQBUEQGgRR6IJQIwqcg/ZlKvKUOpWsfO2UoL+aisZUQRiidTQW1Iqxc/5naVhhYi3vMlurORU6pY3CbVEhEan4HAUt5ShtKecqSbqwxfjdeV/fJSQiHR83Ts1BW6/p8OFQlfLUqFHvh0dCLZeUXc+AVehxXZypKfOksO9UCHPcttJ8pg7rlO7MhobcLdbZfHrKXGd0KlwnZ7+LjA632bgxeDUQhS4IgtAgyA1dEAShQRCTiyDUAUlNL4odmbHTMuV/mrkkR2NBd3r/Kl/0ezC1FDjqksZmwTkyfX0aFceaF9ZYiU0uIUu1tNmHaxoRm5qco3Egqqfyi6NPm7FB45AcGjkdjre1bprTwVHcZGPsm+xYOh1l5zYbZ3NLJtwas3Y9LVljRpqcDo7TbNrEph8bM9c+Nh5i2l0TjjjTNZUu/H9aaUShC4IgNAii0AWhnojD/Vz7NJ9hGfRXiZ5PyLhMqqeii34353dqfGaSQu/i8+eKsjvzBQ0oCsM1neM0pjBkMlMwFj9NjNms0F8MhMbr//iseb3/oHFkToyGWi5tnUZxr2gPdVXO7TVZo53NJtRzb3tQ1c5R2paJqy0WfrdxiOXolHkaGDhtznE6F659csK0u8xEjlDXQKNaRRdFoQuCIDQIotAFYZGZPcFIFfw2F8E6HdvLC+uqxOf1Z4wThawdOx+rZDvmoih1QWNn1zQ5VzQSxvLT4drOF+B0ebwup8anpoPd27Vxc9fMRd3/Xht+DYB/P/i8H9u129Q6P3k81FhxdHUYhd7fFkIN+1pMYtC6TqPUN3YHhb7zyMsAtDWFsMvTuTH7Ocz3Mx6pcLfGCVt1MTcevpOB8YGS9bTbeuua0ro2lUAUuiAIQoMgN3RBEIQGQUwuglCvOAept3aUWXpVl4YH5rFt4JyDtcBhSsFc4SXtuaLM0rw3MwTTw4Stp+IyOOMWd5N5W9/FXimey9hs0LgWTcaG+ekE047L8jw9FRyrJwdM6CCjNjNzeXCAnnWWaTPZlQ21XJzjsitr2uz1NofaLM40E2fNupBMlZA122Kdp64k79BEMB0dHD1U8H6A9Z3nlpyjkohCFwRBaBDKVui2CcAO4IDW+kal1EbgPmAZpsnub2kdeS8EYQlQL/s6yVEaHGZWqRbMxTMznDOhyQQJdV6critQ9P4CzjEZVHLOKs4Tk6Fmyrh1HIa2d2FlE7YCY5udy+XDuVwYX1xZ0Slht+b4SWDSOh8HTgcl7JS5+0wb1q7wU2/atAGAzmyoVHl41IQ3Dp42yUBdzUHRj0yazxE7K93nLXQMu/WbW6hzop4YD3VhToybJ4eOpqgVnU+8KjlVRTgThf67mPZcjr8Avqi13gScAO6o5MIEYZGQfS00DGXd0JVSa4EbgK/Y3xXwDuA79pB7gJursUBBqBayr4VGo1yTy5eAPwRcMOcy4KTtig6wH1hT4bUJQrWp6b4uOwbZZXIm2FecmSSfUJI2Nt/4Zgv2Z0EjDe8oLe316c41MhVivE9NDgFwZCw0hnCx2hf0XFCyRnd+VyL3wOheP3du1/lA3FAjNnGYa5+YCKad4anSWHN6jGNyywVnA3DbNW/xU1v6Ntn3hbK2B22suTPbLGsNDtmXj5vszk19fX6sM2saZrRZ08nQxJCfG5kyJpZMKqmpiLJzoZZLtXuKzqnQlVI3Ake11k/O5wJKqe1KqR1KqR3zeb8gVINK7uvBwcG53yAIi0A5Cv0a4Cal1HuAFqAL+DLQo5TKWDWzFjiQ9Gat9d3A3QBKJWkMQagJFdvXl19xecX2dUGNlTLUXFJWqHsdN41woYMuhC4bOSFdJmdh5qcLfTQ/Y4U+5kIUp4OveHjSzLfYkMSWdHBCujDEoSnjhHTVEQG6siZksC063q37tK3bcnLyZDRnVPs5PT1+7E1XXwTAJ68x1rHze873c822YuOLJ4ObxIVdjtv2kacmJvzcxMSU/Wzhu3POTfcZXzm5z8+5EMg1HcYR29UcQjJXtJmQyd7msNZqM6dC11p/Wmu9Vmu9Afgg8C9a698AHgE+YA+7Dbi/aqsUhAoj+1poRBaSWPQp4D6l1GeBp4CvVmZJglBT6m5fJ9natS5U0LFCn7Bq3ClcgLGcsRe78MM4kadxUvt2AAARaklEQVTZtlErsMMX2ebj5Bh3zabINryyzShUF7YY243dOV4fNjVXHju4O1w7Y45b0drvx5zyd63ezu3a5Oc2dp4DwPqOdX7sw1vM8StbVxV8nnjdzw2Ga/7H6+ahy6nxtvagqsdOG8W979QpPzadN+vP5Z+35zpKMes6VwLQ1RwSmFa0mu+kOxsUerXqoDvO6Iautf4p8FP7+lXgqsovSRAWF9nXQqMgmaKCIAgNgtRyEYQliHda+izSYC6ZsvVUYpOLy9Z05FQwobiwwlxkVnE1WRz56PxNaWMmSUehes7MMW2zQGPzjVvPgdED9nrB7HBoxEQItWeCU3R1uzGdOPNKTzaEEKZsZmZrJmRf+jBH10AjWvuB0f0AfOOJx/zYiy+9bs9lPndfdzCT9PQYM48zxwAczxgzzPFx8/PwQCi329yStZ/XXDuuGdNlTUadTaF0b1I9mEoiCl0QBKFBEIUuCHVOUOPJs+ZHmHWKO07WiR2FUKgUfdJRQiKSO0fc6DhW647TthVbUsNpd47lrcsB2LY6VBxc32nytjZ2bfRjfc3LAGjLGGWbiUIsi88JkFfGITxuwymPRglPD+75KQCvvBaiTydPmuPImO9pOBPO5RT65ERQ+UfHzdPN5KR5+hgZDnVklq/oBUI1yrZM7GxuKfgJhW0Eq4EodEEQhAZBbuiCIAgNgphcBKHO8eaLyKxSkkWa4GyLHZMu+9LHrxeU4rX9MKNMUXfNDuvQa4ucltN5c67Y0Tpia6W4HqFxQwxnhnGx4yus6QVCLHtHpjMaa7bncqaQsFb3OQqba5jXQzaj9ODoQT/36OumB+lULsTpOzJtxpTT0RbMJG1tzSXHnRoyzuXTYxMlc61thWt1DS/isZQqrfNSLUShC4IgNAii0AWhzikOUYS4eqIZi/W5U9ex49Opave+uMlEUnONVuvcyzjFHT0dTOkpe46gen3YolXQceigC590oZDxdZKaRrh598SQVJNmcDxka56aNFmd7inh9eHgAB0fN9dsaw3K2V2ys6O1ZM6FIQ6fCo7P4RHjRB2zjtL26PjWJvOEcWrCXHt5awix9P8fqpwdGiMKXRAEoUEQhS4IdU5iLRdXZTEhhNAd7+zZ5rWx48Z2dT9nE4Ti67gqhSlVqvncuTqbQhKNO4dL8nG1YwCOTZjkIVdHvCN6X0vWhPTFdWHcOvL2KcI9EQDsHTY28acHn/VjrqXc5LQ5/vGDoRriwBGTBDQ1FZ5InCJ3tvNMU1SL3draxyN7ed7Wcsna8MZ0Ohw/alX766cGALigL4RkuieLuPZ8tbW6KHRBEIQGQW7ogiAIDYKYXARhiVDQNk6b1y48MM5ATNt6J3F2qCuv600ukZRzjs/YvOLK37qu9rH5JoOZU9nSbNPphOYarbZUb7bVhglGtU06m7oKrmc+lDEnjU0bs83+0WBCefaYKWH7/LE9fuyALXV7ZNg4Jo8cCi3rRkaNQzOTCet3tVuamszY1GQwx7gs0Nih3N1l6saM2/ouuSgEcnDAhEqOLQvO0GJS8ZedkElbSUShC4IgNAhlKXSl1B5gGJgGclrrbUqpPuCbwAZgD3Cr1vrETOcQhHpkKe3tVNyeTjmFbn9Gzk6n/jKRqk75JJfChs3xWNyWzqn75pRxWjrVX3D+SFU7Z6j7Oa3C+Z0Dd9wmAMVPAs7BGl/bHeecqYNjoWfrxHRhFciYSaugM01hrU5d5/MhPNKHJlo1Ph21m0ulVMExZt6MTZwy4ZejYyGpKZNxDmX3ecJnc99hkmO5WpzJld6utb5Ua73N/n4n8LDW+jzgYfu7ICxFZG8LDcFC/nS8F7jHvr4HuHnhyxGEukD2trAkKdcpqoGHlFIa+F+24/lKrfUhO38YWFmNBQpClVkyezt2pKW8ycU88msVlc/F9fwMZoNsyppCbPZl7KhrsVmhLVGZV9dz1JlVYqeoM6EU3Dzs6VyG6PBU6Ml5YMRkbp6cNHHo7VFzir6WXru+sFaXURrqyYS49TUdq+26wtWXtRprWE+LWf/wZDDLjE6Z10ePh/WcsqaTcVsWN5sNpiOXRRo7Pl226YjtN5qLTDSZtPng7VmzftcHFcJ3WBiHXh89Rd+itT6glFoB/Fgp9WI8qbXW9h9ECUqp7cD2Ba5TEKrFvPZ2vK/XrV9XPC0INaGsG7rW+oD9eVQp9Y+YJrpHlFKrtdaHlFKrgdJW2OY9dwN3A8x00xeEWjHfvR3v68uvuHxx9nUUSqds2GJK+YGS42JnnHvtlG1cQ8Up9KTMUudMjXVl3rW9ixyruSJlvnf4dT/34vFXABgaHwagt6XLz63uMKGGsQp3qr2nuQeAbCqEXy5rMc0vVrau8GOj3UZxn9tjnKevnAxhjs8NmMqLk5Mh29Q5Q4et4u6Kv1f7OlbhTqGnnRqParmsOqsfgDesMBmiq9pW+znX2CK1iMGEc15JKdWulOp0r4F3Ac8CPwBus4fdBtxfrUUKQjWQvS00GuUo9JXAP9q/XBng/2qtH1RKPQF8Syl1B7AXuLV6yxSEqlDXe7u4CmKB/dW+dAlGRDZlrHKOlaFKFar2+JEirUpruQS7r2tCHd6RS2hCfXLC2LH3DO8F4InDz/i5nYeNSj45YpRxb2ewoV++yiT+XLz8fD/WkzXKvLe5NFlnLGfWFTexdtUW954y13lh8JCf23fcJP64muYAwzbZyNVomYrUuJpydWTCd+ds7F2dpib8ytXL/Nz15201n2P5pQD0Nff7OefDSNWTDV1r/SpwScL4MeCd1ViUICwGsreFRkMyRQVBEBoEqeUiCEsQ/+hebHoh+E4L2sw5R6k9Lp+QWVrQxk678ry65HhXGvfI2GE/tuvEbgD+46j5+cJgyO48MWzMHfnp0tK9nVljxljXsdaPLWsxZgvnkB2fHvNz7vXx8eN+7JljJjDpmaP7AXjtaKjlcvCgWceRwZDoOzluHKRpWzZ3YiI4TN331NEe2tL1rzAmoG3rzRqvXL3Fz13YZ0wua9rXA9CaDq36FrP1nL/mol9REARBqAqi0AWhzklqEVc8V+Brsyo8jhIuboeWiua0V+NBQbvqjK4NXOwAdTVWdp98yY89cegFAJ63yvz0aKh34tbWZeuqnNcXnJ0buo3qjcMWXfNp1/x5JDfi506MG6X9/PFw7ccPvArAa4fNtQdsBUSAE0MmVHIyanBB2izIVVuMwxCXLesGYNPZIfzw2rM3A3Bxv/m5IgqZXNG6CgjKPB2pcmlBJwiCIMwbUeiCUEckqfByKFSBrql0FIZof/qwxSixKK9sTfWES7vkodFIJQ/Y6ofHxoISnrChf502Bb4pFbRim22kvLbLJBRd2L/Rz7kEoemo4fTQtDnv8JRR13G1xVdOmoSlp46ExCWnzEdtM+dUKnxu32YuE5SzayHX3VEahvjWjRsA2LbqIj+2scustytr1Htcz73FK3NzK1WLWFkxCVHogiAIDYLc0AVBEBoEMbkIQh1RrgNtNtOMf+yPQg21d9D5C3l8yGM05swwzskXV27saza1Vjb3bvJjazuMc3AqHzkfLa22Voyr0dJr3w+h3kkuet/QpDG5HDltSui8OhRqs7x03IRKHh8LoYzZZmPSabHOzdi80mRfZ9NhbE2nMZls7TdF1bb2hSzVNTZ8siMTnLRuja7yZPxdJLXvcyymM9QhCl0QBKFBEIUuCFUkbjY8G7GTsvi9iXNF6i9RsRdUZyx0lBa8OyE5ySlPZSsM9jUHx2FXk3EOntUeEnKcwnYJSPHnbnINp5X5GatZVz/9RC4kCg1NmLrpo1MmgSn+/Mtajdrvag6hhil7rZ5mExbZ19rt5/pbTYhkf0uosbKsxYw5J2ecDOSqUcZJQc7h6WvDJzR99r/WQJXHiEIXBEFoEOSGLgiC0CCIyUUQqshsppT5vHcm5nzUV4WmloI6L+GK/pUzi6Rdu7m4BV26tL6Lyyx1Y3HWKd7c4xpjBAfomK3NMj4dMkun7Tma0uaaXc2h3G5LxphamtPBMenqwTina2xe6bEO2NjJ6ZyaxU084tfpgjGbeZtQ86bWJpZiRKELgiA0CGUpdKVUD/AV4CLMn/HbgV3AN4ENwB7gVq31iRlOIQh1SSX2tlKlqrscdX2m6v1MFDskq8fEZhnh4gVHQnCmFmZAWoUep5ZqcytxyrwgE9WOORWv8uE6rjF1Z1NoS+cUcUeTUeaTbaGZhbIatDUTGlq7ptOd2S77e6kaTyXVWPFPLaXNt1XcHMS/KD1+qSr0LwMPaq03YxoCvADcCTystT4PeNj+LghLDdnbQsOg5vqrr5TqBnYC5+joYKXULuDaqJHuT7XWF8xxLmkSLVQVrXXZkqlSe/uKbZfrf3vs0eJ1nPHa64nZEpcS57ydPBw10/vi78aPxe8ssrkXtsaz1SJjBe2Vs1PXEWX6K/zhZSjuWqjytqaOJ7XW2+Y6rhyFvhEYAL6mlHpKKfUV21B3pdbaNe87jOnPWIJSartSaodSake5ixeERWLeezve1wMDg8XTglATyrmhZ4DLgb/VWl8GjFL0CGrVTeKfdK313VrrbeX8dRGERWbeezve18uX9xdPC0JNKMcpuh/Yr7V+zP7+HcymP6KUWh09lh6t1iIFoUrUzd6eLSu0FsxmVkhsuFEUFjnHyT3llAuuhYmj3pyd5TKnQtdaHwb2KaWcDfGdwPPAD4Db7NhtwP1VWaEgVAnZ20KjUW5i0X8D7lVKZYFXgf+C+WPwLaXUHcBe4NbqLFEQqsqC97bWRlmXmzCUfI76UOZngijn+qOsG7rWeieQZAN/Z2WXIwiLi+xtoZGQTFFBEIQGQWq5CEKFWIpmk1ojJpRAkmP8TM14otAFQRAahDkzRSt6MaUGMLG+SzkTo5+lu/6lvHaYe/1na62XL9ZiHHZf72Vpf79Lee2wtNdfztrL2tuLekMHUErtWMpJRkt5/Ut57VD/66/39c3GUl47LO31V3LtYnIRBEFoEOSGLgiC0CDU4oZ+dw2uWUmW8vqX8tqh/tdf7+ubjaW8dlja66/Y2hfdhi4IgiBUBzG5CIIgNAiLekNXSl2vlNqllHpZKVXXXWCUUuuUUo8opZ5XSj2nlPpdO96nlPqxUuol+7O31mudCaVU2tb5fsD+vlEp9Zj9/r9p65fUJUqpHqXUd5RSLyqlXlBKvalev/ultK9B9natqebeXrQbulIqDfwN8G5gK/AhpdTWxbr+PMgBn9BabwWuBj5m17uU2pP9LqalmuMvgC9qrTcBJ4A7arKq8lgSreGW4L4G2du1pnp7W2u9KP8BbwJ+FP3+aeDTi3X9Cqz/fuA6TAPh1XZsNbCr1mubYb1r7cZ4B/AApgr1IJBJ+v9RT/8B3cBrWB9PNF533/1S39d2zbK3F2/tVd3bi2lyWQPsi37fb8fqHqXUBuAy4DHKbL1XB3wJ+EOwLddhGXBSa52zv9fz97+gtoeLzJLd1yB7uwZUdW+LU3QOlFIdwHeB39Nan4rntPlzWndhQkqpG4GjWusna72WebKgtodCecjerglV3duLeUM/AKyLfl9rx+oWpVQTZsPfq7X+nh0+YtuSUcet964BblJK7QHuwzyafhnoUUq5Cpv1/P0ntYa7nPr87pfcvgbZ2zWkqnt7MW/oTwDnWW90FvggptVXXaJM3cqvAi9orb8QTdV9ezKt9ae11mu11hsw3/O/aK1/A3gE+IA9rC7XDkuuNdyS2tcge7uWVH1vL7JD4D3AbuAV4H/U2kExx1rfgnnseRrYaf97D8Ze9zDwEvAToK/Wa53jc1wLPGBfnwM8DrwMfBtorvX6Zln3pcAO+/1/H+it1+9+Ke1ru17Z27Vdd9X2tmSKCoIgNAjiFBUEQWgQ5IYuCILQIMgNXRAEoUGQG7ogCEKDIDd0QRCEBkFu6IIgCA2C3NAFQRAaBLmhC4IgNAj/H308V141TTwnAAAAAElFTkSuQmCC\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 = 'Greens')\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
}