{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Model"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "raw_mimetype": "text/restructuredtext"
   },
   "source": [
    ".. toctree::                                               \n",
    "   :maxdepth: 2                                       \n",
    "   :caption: Contents: \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch_struct\n",
    "import torch\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "matplotlib.rcParams['figure.figsize'] = (7.0, 7.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Chain"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "raw_mimetype": "text/restructuredtext"
   },
   "source": [
    ".. autoclass:: torch_struct.LinearChainCRF "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "batch, N, C = 3, 7, 2\n",
    "def show_chain(chain):\n",
    "    plt.imshow(chain.detach().sum(-1).transpose(0, 1))\n",
    "\n",
    "# batch, N, z_n, z_n_1\n",
    "log_potentials = torch.rand(batch, N, C, C)\n",
    "dist = torch_struct.LinearChainCRF(log_potentials)\n",
    "show_chain(dist.argmax[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_chain(dist.marginals[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "event = dist.to_event(torch.tensor([[0, 1, 0, 1, 1, 1, 0, 1]]), 2)\n",
    "show_chain(event[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Hidden Markov Model"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "raw_mimetype": "text/restructuredtext"
   },
   "source": [
    ".. autoclass:: torch_struct.HMM"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "batch, V, N, C = 10, 3, 7, 2\n",
    "\n",
    "transition = torch.rand(C, C).log_softmax(0)\n",
    "emission = torch.rand(V, C).log_softmax(0)\n",
    "init = torch.rand(C).log_softmax(0)\n",
    "observations = torch.randint(0, V, size=(batch, N))\n",
    "\n",
    "dist = torch_struct.HMM(transition, emission, init, observations)\n",
    "show_chain(dist.argmax[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Semi-Markov"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "raw_mimetype": "text/restructuredtext"
   },
   "source": [
    ".. autoclass:: torch_struct.SemiMarkovCRF"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "batch, N, C, K = 3, 10, 2, 6\n",
    "def show_sm(chain):\n",
    "    plt.imshow(chain.detach().sum(1).sum(-1).transpose(0, 1))\n",
    "\n",
    "# batch, N, K, z_n, z_n_1\n",
    "log_potentials = torch.rand(batch, N, K, C, C)\n",
    "log_potentials[:, :, :3] = -1e9\n",
    "dist = torch_struct.SemiMarkovCRF(log_potentials)\n",
    "show_sm(dist.argmax[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_sm(dist.marginals[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Use -1 for segments.\n",
    "event = dist.to_event(torch.tensor([[0, 1, -1, 1, -1, -1, 0, 1,  1, -1, -1]]), (2, 6))\n",
    "show_sm(event[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Alignment"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "raw_mimetype": "text/restructuredtext"
   },
   "source": [
    ".. autoclass:: torch_struct.AlignmentCRF"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "batch, N, M = 3, 15, 20\n",
    "def show_deps(tree):\n",
    "    plt.imshow(tree.detach())\n",
    "\n",
    "log_potentials = torch.rand(batch, N, M, 3)\n",
    "dist = torch_struct.AlignmentCRF(log_potentials)\n",
    "show_deps(dist.argmax[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_deps(dist.marginals[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Dependency Tree"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "raw_mimetype": "text/restructuredtext"
   },
   "source": [
    ".. autoclass:: torch_struct.DependencyCRF"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "batch, N, N = 3, 10, 10\n",
    "def show_deps(tree):\n",
    "    plt.imshow(tree.detach())\n",
    "\n",
    "log_potentials = torch.rand(batch, N, N)\n",
    "dist = torch_struct.DependencyCRF(log_potentials)\n",
    "show_deps(dist.argmax[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_deps(dist.marginals[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZgAAAGbCAYAAAD5r4b7AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjEsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy8QZhcZAAANn0lEQVR4nO3b34ulB33H8c+3u2tioiJtU0myofHCCiJ1U4b0IlJoim7UoL1U0CthbypEWhC99B8Qb3qzaGiL1iDEgFjrGjQiAU3cxDU1PwxBUkwU1h+IptL88tuLHdsYN50jzPc8c868XjDszJ6Hk8/DbvY9zznPVHcHAPbbHyw9AIDtJDAAjBAYAEYIDAAjBAaAEUcnnvRldUlfmssnnhoOrD/7818tPWFRjz5w2dITWMB/57/yTD9dF3tsJDCX5vL8Zf3NxFPDgXXmzLmlJyzq5FUnlp7AAu7pr7zkY14iA2CEwAAwQmAAGCEwAIwQGABGCAwAIwQGgBECA8AIgQFghMAAMEJgABghMACMEBgARggMACMEBoARAgPACIEBYITAADBCYAAYITAAjBAYAEYIDAAjBAaAEQIDwAiBAWCEwAAwQmAAGLFSYKrqpqr6XlU9VlUfnh4FwObbMzBVdSTJPyZ5W5I3JHlPVb1hehgAm22VK5jrkzzW3d/v7meS3JbkXbOzANh0qwTm6iQ/eMHXT+z+3m+pqlNVdbaqzj6bp/drHwAbat/e5O/u09290907x3LJfj0tABtqlcA8meSaF3x9fPf3AOAlrRKYbyV5XVW9tqpeluTdST4/OwuATXd0rwO6+7mq+kCSM0mOJLm1ux8cXwbARtszMEnS3V9M8sXhLQBsET/JD8AIgQFghMAAMEJgABghMACMEBgARggMACMEBoARAgPACIEBYITAADBCYAAYITAAjBAYAEYIDAAjBAaAEQIDwAiBAWCEwAAwQmAAGCEwAIwQGABGCAwAIwQGgBECA8CI6u59f9KdN13a9565Zt+fdxOcvOrE0hMA1uae/kp+0T+riz3mCgaAEQIDwAiBAWCEwAAwQmAAGCEwAIwQGABGCAwAIwQGgBECA8AIgQFghMAAMEJgABghMACMEBgARggMACMEBoARAgPACIEBYITAADBCYAAYITAAjBAYAEYIDAAjBAaAEQIDwAiBAWCEwAAwYs/AVNWtVXW+qr67jkEAbIdVrmD+KclNwzsA2DJ7Bqa7v57kZ2vYAsAW2bf3YKrqVFWdraqzP/7p8/v1tABsqH0LTHef7u6d7t654o+O7NfTArCh3EUGwAiBAWDEKrcpfybJN5K8vqqeqKr3z88CYNMd3euA7n7POoYAsF28RAbACIEBYITAADBCYAAYITAAjBAYAEYIDAAjBAaAEQIDwAiBAWCEwAAwQmAAGCEwAIwQGABGCAwAIwQGgBECA8AIgQFghMAAMEJgABghMACMEBgARggMACMEBoARAgPACIEBYMTRiSd99IHLcvKqExNPfeCd+eG5pScs6rD+uQO/yxUMACMEBoARAgPACIEBYITAADBCYAAYITAAjBAYAEYIDAAjBAaAEQIDwAiBAWCEwAAwQmAAGCEwAIwQGABGCAwAIwQGgBECA8AIgQFghMAAMEJgABghMACMEBgARggMACMEBoARAgPACIEBYMSegamqa6rqrqp6qKoerKpb1jEMgM12dIVjnkvyD919f1W9Msl9VXVndz80vA2ADbbnFUx3/6i779/9/JdJHk5y9fQwADbbKlcw/6uqrk1yXZJ7LvLYqSSnkuTSXLYP0wDYZCu/yV9Vr0hye5IPdvcvXvx4d5/u7p3u3jmWS/ZzIwAbaKXAVNWxXIjLp7v7c7OTANgGq9xFVkk+meTh7v7Y/CQAtsEqVzA3JHlfkhur6tzux9uHdwGw4fZ8k7+7705Sa9gCwBbxk/wAjBAYAEYIDAAjBAaAEQIDwAiBAWCEwAAwQmAAGCEwAIwQGABGCAwAIwQGgBECA8AIgQFghMAAMEJgABghMACMEBgARggMACMEBoARAgPACIEBYITAADBCYAAYITAAjDi69IBtc/KqE0tPWNSZH55besJiDvuf/WF2mP/eX3/yVy/5mCsYAEYIDAAjBAaAEQIDwAiBAWCEwAAwQmAAGCEwAIwQGABGCAwAIwQGgBECA8AIgQFghMAAMEJgABghMACMEBgARggMACMEBoARAgPACIEBYITAADBCYAAYITAAjBAYAEYIDAAjBAaAEQIDwIg9A1NVl1bVvVX1nap6sKo+uo5hAGy2oysc83SSG7v7qao6luTuqvr37v7m8DYANtiegenuTvLU7pfHdj96chQAm2+l92Cq6khVnUtyPsmd3X3PRY45VVVnq+rss3l6v3cCsGFWCkx3P9/dJ5IcT3J9Vb3xIsec7u6d7t45lkv2eycAG+b3uousu3+e5K4kN83MAWBbrHIX2RVV9erdz1+e5C1JHpkeBsBmW+UusiuT/HNVHcmFIH22u78wOwuATbfKXWQPJLluDVsA2CJ+kh+AEQIDwAiBAWCEwAAwQmAAGCEwAIwQGABGCAwAIwQGgBECA8AIgQFghMAAMEJgABghMACMEBgARggMACMEBoARAgPACIEBYITAADBCYAAYITAAjBAYAEYIDAAjBAaAEQIDwIijSw9gu5y86sTSE1jImR+eW3rCYg7z3/tH+6cv+ZgrGABGCAwAIwQGgBECA8AIgQFghMAAMEJgABghMACMEBgARggMACMEBoARAgPACIEBYITAADBCYAAYITAAjBAYAEYIDAAjBAaAEQIDwAiBAWCEwAAwQmAAGCEwAIwQGABGCAwAIwQGgBECA8CIlQNTVUeq6ttV9YXJQQBsh9/nCuaWJA9PDQFgu6wUmKo6nuQdST4xOweAbbHqFczHk3woya9f6oCqOlVVZ6vq7LN5el/GAbC59gxMVd2c5Hx33/f/Hdfdp7t7p7t3juWSfRsIwGZa5QrmhiTvrKrHk9yW5Maq+tToKgA23p6B6e6PdPfx7r42ybuTfLW73zu+DICN5udgABhx9Pc5uLu/luRrI0sA2CquYAAYITAAjBAYAEYIDAAjBAaAEQIDwAiBAWCEwAAwQmAAGCEwAIwQGABGCAwAIwQGgBECA8AIgQFghMAAMEJgABghMACMEBgARggMACMEBoARAgPACIEBYITAADBCYAAYcXTpAcB2OHnViaUncMC4ggFghMAAMEJgABghMACMEBgARggMACMEBoARAgPACIEBYITAADBCYAAYITAAjBAYAEYIDAAjBAaAEQIDwAiBAWCEwAAwQmAAGCEwAIwQGABGCAwAIwQGgBECA8AIgQFghMAAMEJgABghMACMOLrKQVX1eJJfJnk+yXPdvTM5CoDNt1Jgdv11d/9kbAkAW8VLZACMWDUwneTLVXVfVZ262AFVdaqqzlbV2Wfz9P4tBGAjrfoS2Zu7+8mq+pMkd1bVI9399Rce0N2nk5xOklfVH/Y+7wRgw6x0BdPdT+7+ej7JHUmunxwFwObbMzBVdXlVvfI3nyd5a5LvTg8DYLOt8hLZa5LcUVW/Of5fu/tLo6sA2Hh7Bqa7v5/kTWvYAsAWcZsyACMEBoARAgPACIEBYITAADBCYAAYITAAjBAYAEYIDAAjBAaAEQIDwAiBAWCEwAAwQmAAGCEwAIwQGABGCAwAIwQGgBECA8AIgQFghMAAMEJgABghMACMEBgARggMACMEBoAR1d37/6RVP07yn/v+xKv54yQ/Wei/fRAc5vM/zOeeHO7zd+7L+dPuvuJiD4wEZklVdba7d5besZTDfP6H+dyTw33+zv1gnruXyAAYITAAjNjGwJxeesDCDvP5H+ZzTw73+Tv3A2jr3oMB4GDYxisYAA4AgQFgxFYFpqpuqqrvVdVjVfXhpfesU1XdWlXnq+q7S29Zt6q6pqruqqqHqurBqrpl6U3rUlWXVtW9VfWd3XP/6NKb1q2qjlTVt6vqC0tvWbeqeryq/qOqzlXV2aX3vNjWvAdTVUeSPJrkLUmeSPKtJO/p7ocWHbYmVfVXSZ5K8i/d/cal96xTVV2Z5Mruvr+qXpnkviR/exj+7Kuqklze3U9V1bEkdye5pbu/ufC0tamqv0+yk+RV3X3z0nvWqaoeT7LT3Qfyh0y36Qrm+iSPdff3u/uZJLcledfCm9amu7+e5GdL71hCd/+ou+/f/fyXSR5OcvWyq9ajL3hq98tjux/b8V3jCqrqeJJ3JPnE0lv4XdsUmKuT/OAFXz+RQ/KPDP+nqq5Ncl2Se5Zdsj67LxGdS3I+yZ3dfWjOPcnHk3woya+XHrKQTvLlqrqvqk4tPebFtikwHHJV9Yoktyf5YHf/Yuk969Ldz3f3iSTHk1xfVYfiJdKqujnJ+e6+b+ktC3pzd/9Fkrcl+bvdl8oPjG0KzJNJrnnB18d3f49DYPf9h9uTfLq7P7f0niV098+T3JXkpqW3rMkNSd65+z7EbUlurKpPLTtpvbr7yd1fzye5IxfeKjgwtikw30ryuqp6bVW9LMm7k3x+4U2swe4b3Z9M8nB3f2zpPetUVVdU1at3P395Ltzk8siyq9ajuz/S3ce7+9pc+P/9q9393oVnrU1VXb57U0uq6vIkb01yoO4i3ZrAdPdzST6Q5EwuvMn72e5+cNlV61NVn0nyjSSvr6onqur9S29aoxuSvC8XvoM9t/vx9qVHrcmVSe6qqgdy4ZusO7v70N2ue0i9JsndVfWdJPcm+bfu/tLCm37L1tymDMDBsjVXMAAcLAIDwAiBAWCEwAAwQmAAGCEwAIwQGABG/A9gCmL7XTdKRwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Convert from 1-index standard format. (Head is 0)\n",
    "event = dist.to_event(torch.tensor([[2, 3, 4, 1, 0, 4]]), None)\n",
    "show_deps(event[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Non-Projective Dependency Tree"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "raw_mimetype": "text/restructuredtext"
   },
   "source": [
    ".. autoclass:: torch_struct.NonProjectiveDependencyCRF"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "batch, N, N = 3, 10, 10\n",
    "def show_deps(tree):\n",
    "    plt.imshow(tree.detach())\n",
    "\n",
    "log_potentials = torch.rand(batch, N, N)\n",
    "dist = torch_struct.NonProjectiveDependencyCRF(log_potentials)\n",
    "show_deps(dist.marginals[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Binary Labeled Tree"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "raw_mimetype": "text/restructuredtext"
   },
   "source": [
    "    .. autoclass:: torch_struct.TreeCRF"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "batch, N, NT = 3, 20, 3\n",
    "def show_tree(tree):\n",
    "    t = tree.detach()\n",
    "    plt.imshow(t[ :, : , 0] + \n",
    "               2 * t[ :,:, 1] +\n",
    "               3 * t[ :,:, 2])\n",
    "\n",
    "log_potentials = torch.rand(batch, N, N, NT)\n",
    "dist = torch_struct.TreeCRF(log_potentials)\n",
    "show_tree(dist.argmax[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_tree(dist.marginals[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Probabilistic Context-Free Grammar"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "raw_mimetype": "text/restructuredtext"
   },
   "source": [
    "    .. autoclass:: torch_struct.SentCFG"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "batch, N, NT, T = 3, 20, 3, 3\n",
    "def show_prob_tree(tree):\n",
    "    t = tree.detach().sum(-1).sum(-1)\n",
    "    plt.imshow(t[ :, : , 0] + \n",
    "               2 * t[ :,:, 1] +\n",
    "               3 * t[ :,:, 2])\n",
    "\n",
    "terminals = torch.rand(batch, N, T)\n",
    "rules = torch.rand(batch, NT, NT+T,  NT+T)\n",
    "init = torch.rand(batch, NT).log_softmax(-1)\n",
    "\n",
    "dist = torch_struct.SentCFG((terminals, rules, init))\n",
    "term, rules, init = dist.argmax"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Rules\n",
    "show_prob_tree(rules[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f1877a1fb70>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Terminals\n",
    "plt.imshow(term[:1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Autoregressive / Beam Search"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "raw_mimetype": "text/restructuredtext"
   },
   "source": [
    "    .. autoclass:: torch_struct.Autoregressive\n",
    "         :members: sample,sample_without_replacement,greedy_max,beam_topk,greedy_tempmax\n",
    "    .. autoclass:: torch_struct.AutoregressiveModel\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "batch, N, C, H, layer = 3, 10, 4, 5, 1\n",
    "init = (torch.rand(batch, layer, H), \n",
    "        torch.rand(batch, layer, H))\n",
    "def t(a):                                                                                                                                                                    \n",
    "    return [t.transpose(0, 1) for t in a]\n",
    "\n",
    "def show_ar(chain):\n",
    "     plt.imshow(chain.detach().transpose(0, 1))\n",
    "\n",
    "class RNN_AR(torch.nn.Module):                                                                                                                                                                                       \n",
    "    def __init__(self, sparse=True):                                                                                                                                                                             \n",
    "        super().__init__()                                                                                                                                                                                       \n",
    "        self.sparse = sparse                                                                                                                                                                                     \n",
    "        self.rnn = torch.nn.RNN(H, H, batch_first=True)                                                                                                                                                          \n",
    "        self.proj = torch.nn.Linear(H, C)                                                                                                                                                                        \n",
    "        if sparse:                                                                                                                                                                                               \n",
    "            self.embed = torch.nn.Embedding(C, H)                                                                                                                                                                \n",
    "        else:                                                                                                                                                                                                    \n",
    "            self.embed = torch.nn.Linear(C, H)                                                                                                                                                                   \n",
    "\n",
    "    def forward(self, inputs, state):                                                                                                                                                                            \n",
    "        if not self.sparse and inputs.dim() == 2:                                                                                                                                                                \n",
    "            inputs = torch.nn.functional.one_hot(inputs, C).float()                                                                                                                                              \n",
    "        inputs = self.embed(inputs)                                                                                                                                                                              \n",
    "        out, state = self.rnn(inputs, t(state)[0])                                                                                                                                                               \n",
    "        out = self.proj(out)                                                                                                                                                                                     \n",
    "        return out, t((state,)) \n",
    "\n",
    "    \n",
    "dist = torch_struct.Autoregressive(RNN_AR(), init, C, N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor(-11.7909, grad_fn=<SelectBackward>)\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "path, scores, _ = dist.greedy_max()\n",
    "show_ar(path[0])\n",
    "print(scores[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[-11.7909, -11.8150, -11.7972]], grad_fn=<ViewBackward>)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dist.log_prob(path.unsqueeze(0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAaIAAAC7CAYAAAAnpZqIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjEsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy8QZhcZAAAI+klEQVR4nO3dXYjl913H8c/X3U22m6r1IRfuAyYXtbIUu5EhVgNeJMqmKva2AXshwt7YNpWCVO+8l6IXRVjaqGBokTQXpUTXUgNS0G236Rq72baEaJtNUhINNX3APNSvFzNKlF3n7HTOfufMeb1gYWfO8OfDj+y+95z550x1dwBgyg9MDwBgvQkRAKOECIBRQgTAKCECYJQQATDq4DIuelPd3IdzyzIuva/91M98d3rCNX318SPTE67Jue2cs9sZ53b9/iPfySv9cl3tsVrG/0f0Q/Wj/XN1z65fd7879+zF6QnXdProqekJ1+Tcds7Z7Yxzu37n+zN5qV+8aoi8NAfAKCECYJQQATBKiAAYJUQAjBIiAEYJEQCjhAiAUUIEwCghAmCUEAEwSogAGCVEAIwSIgBGLRSiqrq3qr5SVU9W1QeXPQqA9bFtiKrqQJIPJ3lHkpNJ7quqk8seBsB6WOQZ0Z1Jnuzup7r7lSQfT/LO5c4CYF0sEqJjSZ5+3cdXtj73v1TVmaq6UFUXXs3Lu7UPgH1u125W6O6z3b3R3RuHcvNuXRaAfW6RED2T5MTrPj6+9TkA+L4tEqLPJ3lzVd1eVTcleVeSTy53FgDr4uB2X9Ddr1XVe5KcS3IgyQPdfWnpywBYC9uGKEm6+5Ekjyx5CwBryDsrADBKiAAYJUQAjBIiAEYJEQCjhAiAUUIEwCghAmCUEAEwSogAGCVEAIwSIgBGCREAo6q7d/2iG2873J87d2L7Lxxw+uip6QkAa+d8fyYv9Yt1tcc8IwJglBABMEqIABglRACMEiIARgkRAKOECIBRQgTAKCECYJQQATBKiAAYJUQAjBIiAEYJEQCjhAiAUUIEwKhtQ1RVD1TV81X1pRsxCID1ssgzoj9Lcu+SdwCwprYNUXf/XZIXb8AWANbQrn2PqKrOVNWFqrrwwr99b7cuC8A+t2sh6u6z3b3R3Ru3/tiB3bosAPucu+YAGCVEAIxa5PbtjyX5+yRvqaorVfVby58FwLo4uN0XdPd9N2IIAOvJS3MAjBIiAEYJEQCjhAiAUUIEwCghAmCUEAEwSogAGCVEAIwSIgBGCREAo4QIgFFCBMCobd99eye++viRnD56ahmXBmCf8YwIgFFCBMAoIQJglBABMEqIABglRACMEiIARgkRAKOECIBRQgTAKCECYJQQATBKiAAYJUQAjBIiAEYJEQCjtg1RVZ2oqker6omqulRV99+IYQCsh0V+QutrST7Q3Y9V1Q8m+UJVfbq7n1jyNgDWwLbPiLr7ue5+bOv330pyOcmxZQ8DYD0s8ozof1TVbUnuSHL+Ko+dSXImSQ7nyC5MA2AdLHyzQlW9Mcknkry/u1/6v49399nu3ujujUO5eTc3ArCPLRSiqjqUzQg92N0PL3cSAOtkkbvmKslHk1zu7g8tfxIA62SRZ0R3JXl3krur6uLWr19Z8i4A1sS2Nyt092eT1A3YAsAa8s4KAIwSIgBGCREAo4QIgFFCBMAoIQJglBABMEqIABglRACMEiIARgkRAKOECIBRQgTAKCECYNS2PwZivzn37MXpCdd0+uip6QnX5Nx2Zi+fW+Lsdsq5Xb87T3/3mo95RgTAKCECYJQQATBKiAAYJUQAjBIiAEYJEQCjhAiAUUIEwCghAmCUEAEwSogAGCVEAIwSIgBGCREAo7YNUVUdrqrPVdU/VtWlqvqDGzEMgPWwyA/GeznJ3d397ao6lOSzVfVX3f0PS94GwBrYNkTd3Um+vfXhoa1fvcxRAKyPhb5HVFUHqupikueTfLq7z1/la85U1YWquvBqXt7tnQDsUwuFqLu/192nkhxPcmdVvfUqX3O2uze6e+NQbt7tnQDsU9d111x3fzPJo0nuXc4cANbNInfN3VpVb9r6/RuS/HKSLy97GADrYZG75n4iyZ9X1YFshusvu/tTy50FwLpY5K65x5PccQO2ALCGvLMCAKOECIBRQgTAKCECYJQQATBKiAAYJUQAjBIiAEYJEQCjhAiAUUIEwCghAmCUEAEwSogAGFXdvfsXrXohydd26XI/nuRfd+la68S57Yxz2xnntnPrcnY/2d23Xu2BpYRoN1XVhe7emN6xapzbzji3nXFuO+fsvDQHwDAhAmDUKoTo7PSAFeXcdsa57Yxz27m1P7s9/z0iAPa3VXhGBMA+tqdDVFX3VtVXqurJqvrg9J5VUFUnqurRqnqiqi5V1f3Tm1ZJVR2oqi9W1aemt6yKqnpTVT1UVV+uqstV9fPTm1ZBVf3O1p/RL1XVx6rq8PSmKXs2RFV1IMmHk7wjyckk91XVydlVK+G1JB/o7pNJ3p7kt53bdbk/yeXpESvmj5P8dXf/dJK3xfltq6qOJXlfko3ufmuSA0neNbtqzp4NUZI7kzzZ3U919ytJPp7kncOb9rzufq67H9v6/bey+ZfCsdlVq6Gqjif51SQfmd6yKqrqh5P8YpKPJkl3v9Ld35xdtTIOJnlDVR1MciTJs8N7xuzlEB1L8vTrPr4Sf6Fel6q6LckdSc7PLlkZf5Tkd5P85/SQFXJ7kheS/OnWS5ofqapbpkftdd39TJI/TPL1JM8l+ffu/pvZVXP2coj4PlTVG5N8Isn7u/ul6T17XVX9WpLnu/sL01tWzMEkP5vkT7r7jiTfSeL7uduoqh/J5is8tyc5muSWqvqN2VVz9nKInkly4nUfH9/6HNuoqkPZjNCD3f3w9J4VcVeSX6+qf8nmy8B3V9VfzE5aCVeSXOnu/37W/VA2w8T/75eS/HN3v9DdryZ5OMkvDG8as5dD9Pkkb66q26vqpmx+I++Tw5v2vKqqbL5ef7m7PzS9Z1V09+919/Huvi2b/639bXev7b9QF9Xd30jydFW9ZetT9yR5YnDSqvh6krdX1ZGtP7P3ZI1v8jg4PeBauvu1qnpPknPZvKPkge6+NDxrFdyV5N1J/qmqLm597ve7+5HBTexv703y4NY/GJ9K8pvDe/a87j5fVQ8leSybd7p+MWv8DgveWQGAUXv5pTkA1oAQATBKiAAYJUQAjBIiAEYJEQCjhAiAUUIEwKj/Apf59Twg6QqbAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAaIAAAC7CAYAAAAnpZqIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjEsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy8QZhcZAAAJC0lEQVR4nO3dX6jf913H8dfbJG2WzjmnvbBJsb3YJmHMVkI3LXjRKu1U3O0K7kKE3GzayUCmd97L0IshhK0qWDak68UY1Ti0IAOty7psLs02Sp1r2krrxuz+sHadby/OUaokO7+e/n55/37n93hA4JzzO3x58SHJM7/f+eac6u4AwJQfmR4AwHYTIgBGCREAo4QIgFFCBMAoIQJg1OFVXPSauraP5rpVXPpVe9Nbvzs94Yq+8oVj0xOuyLntzzqfW+Ls9mudz21dfS/fyYv9Ql3usVrF/yN6Xb2h31Z3Lv26y3D26fPTE67orhtumZ5wRc5tf9b53BJnt1/rfG7r6pH+uzzf37hsiLw0B8AoIQJglBABMEqIABglRACMEiIARgkRAKOECIBRQgTAKCECYJQQATBKiAAYJUQAjBIiAEYtFKKquruqvlxVj1fVB1Y9CoDtsWeIqupQkg8leUeSk0nuqaqTqx4GwHZY5BnRbUke7+4nuvvFJB9L8s7VzgJgWywSouNJnnzZ+5d2P/Z/VNXpqjpXVee+nxeWtQ+AA25pNyt095nuPtXdp47k2mVdFoADbpEQPZXkxpe9f2L3YwDwqi0Sos8keWNV3VxV1yR5V5JPrHYWANvi8F6f0N0vVdV7k5xNcijJfd19YeXLANgKe4YoSbr7oSQPrXgLAFvId1YAYJQQATBKiAAYJUQAjBIiAEYJEQCjhAiAUUIEwCghAmCUEAEwSogAGCVEAIwSIgBGVXcv/aKvqzf02+rOpV8XgB/u7NPnpydc1m13PZlzn/9eXe4xz4gAGCVEAIwSIgBGCREAo4QIgFFCBMAoIQJglBABMEqIABglRACMEiIARgkRAKOECIBRQgTAKCECYJQQATBqzxBV1X1V9WxVffFqDAJguyzyjOjPk9y94h0AbKk9Q9Td/5DkG1dhCwBb6PCyLlRVp5OcTpKjObasywJwwC3tZoXuPtPdp7r71JFcu6zLAnDAuWsOgFFCBMCoRW7f/miSf0zy5qq6VFW/tfpZAGyLPW9W6O57rsYQALaTl+YAGCVEAIwSIgBGCREAo4QIgFFCBMAoIQJglBABMEqIABglRACMEiIARgkRAKOECIBRS/tR4QDMu+uGW6YnXNZX+utXfMwzIgBGCREAo4QIgFFCBMAoIQJglBABMEqIABglRACMEiIARgkRAKOECIBRQgTAKCECYJQQATBKiAAYJUQAjNozRFV1Y1U9XFWPVdWFqrr3agwDYDss8hNaX0ry/u5+tKp+NMlnq+pT3f3YircBsAX2fEbU3c9096O7b38rycUkx1c9DIDtsMgzov9VVTcluTXJI5d57HSS00lyNMeWMA2AbbDwzQpV9dokH0/yvu5+/v8/3t1nuvtUd586kmuXuRGAA2yhEFXVkexE6P7ufnC1kwDYJovcNVdJPpLkYnd/cPWTANgmizwjuj3Ju5PcUVXnd3/9yop3AbAl9rxZobs/naSuwhYAtpDvrADAKCECYJQQATBKiAAYJUQAjBIiAEYJEQCjhAiAUUIEwCghAmCUEAEwSogAGCVEAIwSIgBG7fljIPbjTW/9bs6ePb+KS79qd91wy/SEKzr79HqeWeLc9mudzy1xdvvl3JbLMyIARgkRAKOECIBRQgTAKCECYJQQATBKiAAYJUQAjBIiAEYJEQCjhAiAUUIEwCghAmCUEAEwSogAGLVniKrqaFX9c1V9vqouVNUfXo1hAGyHRX4w3gtJ7ujub1fVkSSfrqq/7u5/WvE2ALbAniHq7k7y7d13j+z+6lWOAmB7LPQ1oqo6VFXnkzyb5FPd/chlPud0VZ2rqnPPff0Hy94JwAG1UIi6+wfdfUuSE0luq6q3XOZzznT3qe4+df1PHFr2TgAOqFd011x3fzPJw0nuXs0cALbNInfNXV9Vr999+zVJfjnJl1Y9DIDtsMhdcz+V5C+q6lB2wvVX3f3J1c4CYFssctfcF5LcehW2ALCFfGcFAEYJEQCjhAiAUUIEwCghAmCUEAEwSogAGCVEAIwSIgBGCREAo4QIgFFCBMAoIQJglBABMKq6e/kXrXouyb8t6XI/meQ/lnStbeLc9se57Y9z279tObuf7u7rL/fASkK0TFV1rrtPTe/YNM5tf5zb/ji3/XN2XpoDYJgQATBqE0J0ZnrAhnJu++Pc9se57d/Wn93af40IgINtE54RAXCArXWIquruqvpyVT1eVR+Y3rMJqurGqnq4qh6rqgtVde/0pk1SVYeq6nNV9cnpLZuiql5fVQ9U1Zeq6mJV/fz0pk1QVb+7+2f0i1X10ao6Or1pytqGqKoOJflQknckOZnknqo6ObtqI7yU5P3dfTLJ25O8x7m9IvcmuTg9YsP8SZK/6e6fSfKzcX57qqrjSX4nyanufkuSQ0neNbtqztqGKMltSR7v7ie6+8UkH0vyzuFNa6+7n+nuR3ff/lZ2/lI4PrtqM1TViSS/muTD01s2RVX9WJJfTPKRJOnuF7v7m7OrNsbhJK+pqsNJjiV5enjPmHUO0fEkT77s/UvxF+orUlU3Jbk1ySOzSzbGHyf5vST/NT1kg9yc5Lkkf7b7kuaHq+q66VHrrrufSvJHSb6W5Jkk/9ndfzu7as46h4hXoapem+TjSd7X3c9P71l3VfVrSZ7t7s9Ob9kwh5P8XJI/7e5bk3wnia/n7qGqfjw7r/DcnOSGJNdV1W/MrpqzziF6KsmNL3v/xO7H2ENVHclOhO7v7gen92yI25P8elV9NTsvA99RVX85O2kjXEpyqbv/51n3A9kJEz/cLyX51+5+rru/n+TBJL8wvGnMOofoM0neWFU3V9U12flC3ieGN629qqrsvF5/sbs/OL1nU3T373f3ie6+KTu/1/6+u7f2X6iL6u5/T/JkVb1590N3JnlscNKm+FqSt1fVsd0/s3dmi2/yODw94Eq6+6Wqem+Ss9m5o+S+7r4wPGsT3J7k3Un+parO737sD7r7ocFNHGy/neT+3X8wPpHkN4f3rL3ufqSqHkjyaHbudP1ctvg7LPjOCgCMWueX5gDYAkIEwCghAmCUEAEwSogAGCVEAIwSIgBGCREAo/4bafHyb+MtyE8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "out = dist.beam_topk(5)[:, 0]\n",
    "for i in range(3):\n",
    "    show_ar(out[i])\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([5, 10, 4])\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "out = dist.sample((5,))[:, 0 ]\n",
    "print(out.shape)\n",
    "for i in range(3):\n",
    "    show_ar(out[i])\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "out = dist.sample_without_replacement((5,))[:, 0]\n",
    "for i in range(3):\n",
    "    show_ar(out[i])\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "dist = torch_struct.Autoregressive(RNN_AR(sparse=False), init, C, N)\n",
    "_, _, logits = dist.greedy_tempmax(1.0)\n",
    "show_ar(logits[0])\n",
    "loss = logits[0:1, torch.arange(10), torch.zeros(10).long()]\n",
    "loss.sum().backward()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Base Class"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "raw_mimetype": "text/restructuredtext"
   },
   "source": [
    ".. autoclass:: torch_struct.StructDistribution\n",
    "   :members:  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "batch, N, C = 3, 7, 2\n",
    "\n",
    "# batch, N, z_n, z_n_1\n",
    "log_potentials = torch.rand(batch, N, C, C)\n",
    "dist = torch_struct.LinearChainCRF(log_potentials, lengths=torch.tensor([N-1, N, N+1]))\n",
    "show_chain(dist.argmax[0])\n",
    "plt.show()\n",
    "show_chain(dist.argmax[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAbQAAACSCAYAAAAttj/ZAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjEsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy8QZhcZAAAK4UlEQVR4nO3df6xfd13H8eeL23a44X64Tihts3XYLBI1brupmpGlccxsSFajmGxGHURSYjZEjdFNkxH5a+4Pf0UCNl1lQ2CYMfRKGufIRtAQcB0U94vCtcH01mGhHduKStPx9o97utxdv21nv+d7T++nz0fyzfd8zvn0fN4nTe+r33M+389NVSFJ0nL3qqELkCSpDwaaJKkJBpokqQkGmiSpCQaaJKkJBpokqQljBVqSH0jyUJKvde8XHKffi0l2d6+ZccaUJGmUjPM9tCR3AYeq6s4ktwEXVNXvjeh3uKpeM0adkiSd0LiBtgfYXFXPJFkDfKaqLhvRz0CTJE3UuIH27ao6v9sO8Oyx9qJ+R4HdwFHgzqr62+OcbyuwFSBnrbxy1dqLTrm2093Zq44MXcJEXbrqhaFLmKjZ7547dAkT84Mrnx+6hIn6xhNnD12CxvACz36rqkaGw4qT/eEknwZeN+LQHyxsVFUlOV46XlxV+5NcCjyc5PGq+rfFnapqG7AN4NVvWFsX3/Wuk5W3bF3++rmhS5ioj254ZOgSJurnZ68duoSJuWXtw0OXMFF3veFHhy5BY/h03f/vxzt20kCrqjcf71iS/0yyZsEtxwPHOcf+7n1vks8AlwP/J9AkSTpV407bnwFu7rZvBv5ucYckFyQ5q9teDVwFPDXmuJIkvcy4gXYncG2SrwFv7tokmU6yvevzw8CuJF8GHmH+GZqBJknq1UlvOZ5IVR0Erhmxfxfwzm77c4A3rSVJE+VKIZKkJhhokqQmGGiSpCYYaJKkJhhokqQmGGiSpCYYaJKkJhhokqQmGGiSpCYYaJKkJhhokqQmGGiSpCYYaJKkJhhokqQmGGiSpCYYaJKkJhhokqQmGGiSpCYYaJKkJvQSaEmuS7InyWyS20YcPyvJx7vjX0hySR/jSpJ0zNiBlmQKeD9wPfBG4KYkb1zU7deAZ6vqh4A/Af5o3HElSVqoj09om4DZqtpbVUeA+4Ati/psAe7ptu8HrkmSHsaWJAnoJ9DWAvsWtOe6fSP7VNVR4DngwsUnSrI1ya4ku158/js9lCZJOlOcVpNCqmpbVU1X1fTUuecMXY4kaRnpI9D2A+sXtNd1+0b2SbICOA842MPYkiQB/QTao8DGJBuSrAJuBGYW9ZkBbu623wY8XFXVw9iSJAGwYtwTVNXRJLcCDwJTwI6qejLJ+4BdVTUD3A18OMkscIj50JMkqTdjBxpAVe0Edi7ad8eC7f8BfrGPsSRJGuW0mhQiSdKpMtAkSU0w0CRJTTDQJElNMNAkSU0w0CRJTTDQJElNMNAkSU0w0CRJTTDQJElNMNAkSU0w0CRJTTDQJElNMNAkSU0w0CRJTTDQJElNMNAkSU0w0CRJTTDQJElN6CXQklyXZE+S2SS3jTj+9iTfTLK7e72zj3ElSTpmxbgnSDIFvB+4FpgDHk0yU1VPLer68aq6ddzxJEkapY9PaJuA2araW1VHgPuALT2cV5KkV2zsT2jAWmDfgvYc8BMj+v1CkquBrwK/VVX7FndIshXYCvDa16/gL6/8cA/lnZ4eeHZ66BIm6tIH3jV0CRP1S2/63NAlTMy7v3TT0CVM1HqeGLoETchSTQr5e+CSqvox4CHgnlGdqmpbVU1X1fR5F04tUWmSpBb0EWj7gfUL2uu6fS+pqoNV9d2uuR24sodxJUl6SR+B9iiwMcmGJKuAG4GZhR2SrFnQvAF4uodxJUl6ydjP0KrqaJJbgQeBKWBHVT2Z5H3ArqqaAX4jyQ3AUeAQ8PZxx5UkaaE+JoVQVTuBnYv23bFg+3bg9j7GkiRpFFcKkSQ1wUCTJDXBQJMkNcFAkyQ1wUCTJDXBQJMkNcFAkyQ1wUCTJDXBQJMkNcFAkyQ1wUCTJDXBQJMkNcFAkyQ1wUCTJDXBQJMkNcFAkyQ1wUCTJDXBQJMkNcFAkyQ1oZdAS7IjyYEkTxzneJL8eZLZJP+a5Io+xpUk6Zi+PqF9CLjuBMevBzZ2r63AB3oaV5IkoKdAq6rPAodO0GULcG/N+zxwfpI1fYwtSRIs3TO0tcC+Be25bt/LJNmaZFeSXc8dfHGJSpMkteC0mhRSVduqarqqps+7cGrociRJy8hSBdp+YP2C9rpunyRJvViqQJsBfrWb7fiTwHNV9cwSjS1JOgOs6OMkST4GbAZWJ5kD3gusBKiqDwI7gbcAs8B/Ae/oY1xJko7pJdCq6qaTHC/glj7GkiRplNNqUogkSafKQJMkNcFAkyQ1wUCTJDXBQJMkNcFAkyQ1wUCTJDXBQJMkNcFAkyQ1wUCTJDXBQJMkNcFAkyQ1wUCTJDXBQJMkNcFAkyQ1wUCTJDXBQJMkNcFAkyQ1wUCTJDWhl0BLsiPJgSRPHOf45iTPJdndve7oY1xJko5Z0dN5PgT8BXDvCfr8U1W9tafxJEl6mV4+oVXVZ4FDfZxLkqRTkarq50TJJcCnqupHRhzbDHwCmAP+A/idqnpyRL+twNaueRmwp5fiXpnVwLeWcLyl5vUtb17f8tXytcHSX9/FVXXRqANLFWjnAt+rqsNJ3gL8WVVt7GXgniTZVVXTQ9cxKV7f8ub1LV8tXxucXte3JLMcq+r5qjrcbe8EViZZvRRjS5LODEsSaElelyTd9qZu3INLMbYk6czQyyzHJB8DNgOrk8wB7wVWAlTVB4G3Ab+e5Cjw38CN1de9zv5sG7qACfP6ljevb/lq+drgNLq+3p6hSZI0JFcKkSQ1wUCTJDXBQAOSXJdkT5LZJLcNXU+fTrYs2XKXZH2SR5I8leTJJO8Zuqa+JHl1kn9J8uXu2v5w6JomIclUki8l+dTQtfQtydeTPN4t+bdr6Hr6luT8JPcn+UqSp5P81KD1nOnP0JJMAV8FrmX+i9+PAjdV1VODFtaTJFcDh4F7R31HcLlLsgZYU1VfTPL9wGPAz7Xw99fNDD6n+/7mSuCfgfdU1ecHLq1XSX4bmAbObW15vCRfB6arqskvVie5h/llDbcnWQWcXVXfHqoeP6HBJmC2qvZW1RHgPmDLwDX1pvVlyarqmar6Yrf9AvA0sHbYqvpR8w53zZXdq6n/gSZZB/wssH3oWvT/k+Q84GrgboCqOjJkmIGBBvM//PYtaM/RyA/EM023Ws3lwBeGraQ/3e243cAB4KGqaubaOn8K/C7wvaELmZAC/jHJY93Sfi3ZAHwT+KvulvH2JOcMWZCBpiYkeQ3z64X+ZlU9P3Q9famqF6vqx4F1wKYkzdw2TvJW4EBVPTZ0LRP0pqq6ArgeuKV7BNCKFcAVwAeq6nLgO8CgcxAMNNgPrF/QXtft0zLRPV/6BPCRqnpg6HomobuV8whw3dC19Ogq4IbuOdN9wE8n+ethS+pXVe3v3g8An2T+EUcr5oC5BXcN7mc+4AZjoM1PAtmYZEP3UPNGYGbgmvQKdRMn7gaerqo/HrqePiW5KMn53fb3MT9x6SvDVtWfqrq9qtZV1SXM/7t7uKp+eeCyepPknG6iEt2tuJ8BmpltXFXfAPYluazbdQ0w6GSsvn7B57JVVUeT3Ao8CEwBO0b9apvlatSyZFV197BV9eoq4FeAx7tnTQC/3y2CvdytAe7pZuK+CvibqmpuanvDXgt8slvGdgXw0ar6h2FL6t27gY90Hwb2Au8Yspgzftq+JKkN3nKUJDXBQJMkNcFAkyQ1wUCTJDXBQJMkNcFAkyQ1wUCTJDXhfwEszw/FNNBCzQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_chain(dist.marginals[0])\n",
    "plt.show()\n",
    "show_chain(dist.marginals[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "def show_samples(samples):\n",
    "    show_chain(samples[0, 0])\n",
    "    plt.show()\n",
    "    show_chain(samples[1, 0])\n",
    "    plt.show()\n",
    "    show_chain(samples[0, 1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_samples(dist.sample((10,)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAbQAAACSCAYAAAAttj/ZAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjEsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy8QZhcZAAAKqUlEQVR4nO3df6xfd13H8eeL22664dhYF7m01Y1YiUTJNm6KZGZZHJMOyWoiJluiDiK5iWGKGqObJiPy1/QPf0UCWbpKp8gwQ/RCGuvIRtAYcHfYAdvouDYkvd20ox2DijI73v5xT5e7y7ft2Pf0e+793Ocj+eaeH5+e9/vktt9Xv+d87rmpKiRJWuteNnQDkiT1wUCTJDXBQJMkNcFAkyQ1wUCTJDXBQJMkNWGsQEvyyiT3JflK9/WiU4x7Lsn+7jU3Tk1JkkbJOD+HluSPgGNVdUeSW4GLqup3R4w7XlUvH6NPSZJOa9xAOwBcU1VPJpkGPl1Vrx0xzkCTJJ1V4wba16vqwm45wNMn11eMOwHsB04Ad1TV35/ieLPALMAUU284jwtecm+r3Y++/ltDt6AxPP6F84ZuQVqXvsnTX6uqS0btO2OgJfkU8KoRu34f2LM8wJI8XVXfdR8tyeaqOpzkNcD9wLVV9R+nq3tBXllvzLWn7W0t2/fE/qFb0Bje8urLh25BWpc+Vfc+VFUzo/ZtONMfrqo3n2pfkv9KMr3skuORUxzjcPf1YJJPA1cApw00SZK+F+NO258Dbu6Wbwb+YeWAJBclObdb3gRcBTw6Zl1Jkl5g3EC7A7guyVeAN3frJJlJsqsb82PAfJKHgQdYuodmoEmSenXGS46nU1VHge+60VVV88C7uuV/BX5inDqSJJ2JTwqRJDXBQJMkNcFAkyQ1wUCTJDXBQJMkNcFAkyQ1wUCTJDXBQJMkNcFAkyQ1wUCTJDXBQJMkNcFAkyQ1wUCTJDXBQJMkNcFAkyQ1wUCTJDXBQJMkNcFAkyQ1wUCTJDWhl0BLsiPJgSQLSW4dsf/cJB/t9n8uyaV91JUk6aSxAy3JFPB+4HrgdcBNSV63YtivAE9X1Y8AfwL84bh1JUlaro9PaNuBhao6WFXPAvcAO1eM2Qns6ZbvBa5Nkh5qS5IE9BNom4FDy9YXu20jx1TVCeAZ4OKVB0oym2Q+yfz/8e0eWpMkrReralJIVd1ZVTNVNbORc4duR5K0hvQRaIeBrcvWt3TbRo5JsgF4BXC0h9qSJAH9BNqDwLYklyU5B7gRmFsxZg64uVt+O3B/VVUPtSVJAmDDuAeoqhNJbgH2AVPA7qp6JMn7gPmqmgPuAv4qyQJwjKXQkySpN2MHGkBV7QX2rth2+7Ll/wV+oY9akiSNsqomhUiS9FIZaJKkJhhokqQmGGiSpCYYaJKkJhhokqQmGGiSpCYYaJKkJhhokqQmGGiSpCYYaJKkJhhokqQmGGiSpCYYaJKkJhhokqQmGGiSpCYYaJKkJhhokqQmGGiSpCb0EmhJdiQ5kGQhya0j9r8jyVNJ9nevd/VRV5KkkzaMe4AkU8D7geuAReDBJHNV9eiKoR+tqlvGrSdJ0ih9fELbDixU1cGqeha4B9jZw3ElSXrRxv6EBmwGDi1bXwTeOGLczye5Gngc+M2qOrRyQJJZYBbghzZvYN/8/h7aW53e8urLh25BY9j3RLt/N7W2ref3lklNCvkEcGlVvR64D9gzalBV3VlVM1U1c8nFUxNqTZLUgj4C7TCwddn6lm7b86rqaFV9u1vdBbyhh7qSJD2vj0B7ENiW5LIk5wA3AnPLBySZXrZ6A/BYD3UlSXre2PfQqupEkluAfcAUsLuqHknyPmC+quaAX09yA3ACOAa8Y9y6kiQt18ekEKpqL7B3xbbbly3fBtzWRy1JkkbxSSGSpCYYaJKkJhhokqQmGGiSpCYYaJKkJhhokqQmGGiSpCYYaJKkJhhokqQmGGiSpCYYaJKkJhhokqQmGGiSpCYYaJKkJhhokqQmGGiSpCYYaJKkJhhokqQmGGiSpCb0EmhJdic5kuRLp9ifJH+eZCHJF5Jc2UddSZJO6usT2oeAHafZfz2wrXvNAh/oqa4kSUBPgVZVnwGOnWbITuDuWvJZ4MIk033UliQJJncPbTNwaNn6YrftBZLMJplPMv/U0ecm1JokqQWralJIVd1ZVTNVNXPJxVNDtyNJWkMmFWiHga3L1rd02yRJ6sWkAm0O+OVutuNPAs9U1ZMTqi1JWgc29HGQJB8BrgE2JVkE3gtsBKiqDwJ7gbcCC8C3gHf2UVeSpJN6CbSquukM+wt4dx+1JEkaZVVNCpEk6aUy0CRJTTDQJElNMNAkSU0w0CRJTTDQJElNMNAkSU0w0CRJTTDQJElNMNAkSU0w0CRJTTDQJElNMNAkSU0w0CRJTTDQJElNMNAkSU0w0CRJTTDQJElNMNAkSU3oJdCS7E5yJMmXTrH/miTPJNnfvW7vo64kSSdt6Ok4HwL+Arj7NGP+uare1lM9SZJeoJdPaFX1GeBYH8eSJOml6OsT2ovxpiQPA08Av11Vj6wckGQWmO1Wj09NLxyYYH+bgK9NrtzC5EotmfD5TdxEz29qelKVnuf3b+3yvaVfP3yqHamqXiokuRT4ZFX9+Ih9FwDfqarjSd4K/FlVbeulcE+SzFfVzNB9nC2e39rm+a1dLZ8brK7zm8gsx6r6RlUd75b3AhuTbJpEbUnS+jCRQEvyqiTplrd3dY9OorYkaX3o5R5ako8A1wCbkiwC7wU2AlTVB4G3A7+a5ATwP8CN1de1zv7cOXQDZ5nnt7Z5fmtXy+cGq+j8eruHJknSkHxSiCSpCQaaJKkJBhqQZEeSA0kWktw6dD99OtNjyda6JFuTPJDk0SSPJHnP0D31Jcn3Jfm3JA935/YHQ/d0NiSZSvLvST45dC99S/LVJF/sHvk3P3Q/fUtyYZJ7k3w5yWNJ3jRoP+v9HlqSKeBx4DpgEXgQuKmqHh20sZ4kuRo4Dtw96mcE17ok08B0VX0+yQ8ADwE/18L3r5sZfH7385sbgX8B3lNVnx24tV4l+S1gBrigtcfjJfkqMFNVTf7QeJI9LD3WcFeSc4DzqurrQ/XjJzTYDixU1cGqeha4B9g5cE+9af2xZFX1ZFV9vlv+JvAYsHnYrvpRS453qxu7V1P/A02yBfhZYNfQveh7k+QVwNXAXQBV9eyQYQYGGiy9+R1atr5II2+I6033tJorgM8N20l/ustx+4EjwH1V1cy5df4U+B3gO0M3cpYU8E9JHuoe7deSy4CngL/sLhnvSnL+kA0ZaGpCkpcDHwN+o6q+MXQ/famq56rqcmALsD1JM5eNk7wNOFJVDw3dy1n0U1V1JXA98O7uFkArNgBXAh+oqiuA/wYGnYNgoMFhYOuy9S3dNq0R3f2ljwEfrqq/G7qfs6G7lPMAsGPoXnp0FXBDd5/pHuCnk/z1sC31q6oOd1+PAB9n6RZHKxaBxWVXDe5lKeAGY6AtTQLZluSy7qbmjcDcwD3pReomTtwFPFZVfzx0P31KckmSC7vl72dp4tKXh+2qP1V1W1VtqapLWfp3d39V/eLAbfUmyfndRCW6S3E/AzQz27iq/hM4lOS13aZrgUEnY03y18esSlV1IsktwD5gCtg96lfbrFWjHktWVXcN21WvrgJ+Cfhid68J4Pe6h2CvddPAnm4m7suAv62q5qa2N+wHgY93j7HdAPxNVf3jsC317teAD3cfBg4C7xyymXU/bV+S1AYvOUqSmmCgSZKaYKBJkppgoEmSmmCgSZKaYKBJkppgoEmSmvD/jKIBKLd4Le0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_samples(dist.topk(10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([256, 3, 7, 2, 2])\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Enumerate \n",
    "x,_ = dist.enumerate_support()\n",
    "print(x.shape)\n",
    "for i in range(10):\n",
    "    show_chain(x[i][0])\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f1877c52c18>"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(dist.entropy.detach().unsqueeze(0))"
   ]
  }
 ],
 "metadata": {
  "celltoolbar": "Raw Cell Format",
  "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": "3.7.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}