predictive-map-simulations.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import itertools as it\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Maze Construction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def square_maze(size):\n",
    "    return np.ones((size, size))\n",
    "\n",
    "def circular_maze(size):\n",
    "    r = size // 2 - 1\n",
    "    a, b = r, r\n",
    "\n",
    "    y,x = np.ogrid[-a:size-a, -b:size-b]\n",
    "    mask = x*x + y*y <= r*r\n",
    "\n",
    "    maze = np.zeros((size, size))\n",
    "    maze[mask] = 1\n",
    "    return maze\n",
    "\n",
    "def trapezoidal_maze(size, repeats=5):\n",
    "    tri_idx = np.triu_indices(size)\n",
    "    base_maze = np.ones((size, size))\n",
    "    base_maze[tri_idx] = 0\n",
    "    maze_upper = np.repeat(base_maze, repeats, axis=1)\n",
    "    maze_lower = np.flip(maze_upper, axis=0)\n",
    "    maze_mid = np.ones((size, size*repeats))\n",
    "    maze = np.vstack([maze_upper, maze_mid, maze_lower])\n",
    "    return maze\n",
    "\n",
    "def hexagonal_maze(size):\n",
    "    tri_idx = np.triu_indices(size)\n",
    "    tri_maze = np.ones((size, size))\n",
    "    tri_maze[tri_idx] = 0\n",
    "    \n",
    "    upper = np.hstack([np.flip(tri_maze, axis=1), np.ones((size, int(size*1.7))), tri_maze])\n",
    "    upper = np.repeat(upper, 2, axis=0)\n",
    "    lower = np.flip(upper, axis=0)\n",
    "    mid = np.ones((size, 3*size))\n",
    "    return np.vstack([upper, lower])\n",
    "    \n",
    "def hairpin_maze():\n",
    "    return np.array([\n",
    "        [1,1,1,1,1],\n",
    "        [1,0,1,0,1],\n",
    "        [1,0,1,0,1],\n",
    "        [1,0,1,0,1],\n",
    "        [1,1,1,1,1]\n",
    "    ])\n",
    "\n",
    "\n",
    "def multicomp_maze():\n",
    "    maze = np.ones((20, 20))\n",
    "    maze[:, 10] = 0\n",
    "    maze[13, range(10)] = 0\n",
    "    maze[7, range(10, 20)] = 0\n",
    "    maze[10,10] = 1\n",
    "    maze[13,5] = 1\n",
    "    maze[7,15] = 1\n",
    "    return maze\n",
    "\n",
    "\n",
    "def multicomp_maze_circ():\n",
    "    maze = np.ones((20, 20))\n",
    "    maze[:, 10] = 0\n",
    "    maze[13, range(10)] = 0\n",
    "    maze[7, range(10, 20)] = 0\n",
    "    maze[3,10] = 1\n",
    "    maze[16,10] = 1\n",
    "    maze[13,5] = 1\n",
    "    maze[7,15] = 1\n",
    "    return maze"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f7297147250>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.matshow(hairpin_maze())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f72970b35b0>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.matshow(circular_maze(50))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f729701b5e0>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZYAAAECCAYAAADdD/HDAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8rg+JYAAAACXBIWXMAAAsTAAALEwEAmpwYAAANn0lEQVR4nO3ccaxe9V3H8ffHFuwAySjS5kKZzITMkSUF0zAUY3AdDjey8g+6JZjGYPrPjMzMjG7/7Q8T/jDLTDQmDZvWbE4JY6Ehy1jXjajJgiuCG6xoCTKGVNp1m0P/cMK+/nEP41Ja7+m93/vc57n3/UrIc855nueeX7709tPf73vOSVUhSVKXn1rtAUiS1haDRZLUymCRJLUyWCRJrQwWSVIrg0WS1GqiwZLkpiT/kuSpJHsnee5pl+TyJF9NciTJE0nuGI5vTnIwydHh9aLVHus0SLIhyaNJHhj2rdMpkrwxyb1Jnhz+XP2SdTq9JH8w/N49nuSzSTZZq6WbWLAk2QD8GfAbwFXA+5NcNanzz4CXgA9V1VuB64APDPXZCxyqqiuBQ8O+4A7gyIJ96/R6fwJ8sap+AdjOfL2s0ymSXAb8PrCjqt4GbADeh7VasknOWK4Fnqqqp6vqR8DfALsmeP6pVlXHquqfhu0Xmf9L4DLma7R/+Nh+4JZVGeAUSbINeA9w94LD1mmBJBcCvwp8EqCqflRVP8A6nclG4A1JNgLnAc9jrZZsksFyGfCdBfvPDcd0iiRXANcADwNbq+oYzIcPsGUVhzYtPgF8GPjxgmPW6bV+HjgB/MWwZHh3kvOxTq9TVf8O/DHwLHAM+M+q+hLWaskmGSw5zTGfJ3OKJBcAnwM+WFU/XO3xTJskNwPHq+qR1R7LlNsI/CLw51V1DfDfuJRzWkPvZBfwZuBS4Pwkt63uqGbbJIPlOeDyBfvbmJ9uapDkHOZD5TNVdd9w+IUkc8P7c8Dx1RrflLgeeG+SZ5hfTn1Hkk9jnU71HPBcVT087N/LfNBYp9d7J/BvVXWiqv4XuA/4ZazVkk0yWL4OXJnkzUnOZb45dmCC559qScL8eviRqvr4grcOALuH7d3A/ZMe2zSpqo9U1baquoL5P0NfqarbsE6vUVX/AXwnyVuGQzuBb2GdTudZ4Lok5w2/hzuZ73FaqyXKJJ9unOTdzK+PbwA+VVV/NLGTT7kkvwL8PfBNXu0dfJT5Pss9wJuY/wW4taq+tyqDnDJJbgD+sKpuTnIx1uk1klzN/AUO5wJPA7/D/D8mrdMpknwM+C3mr858FPhd4AKs1ZJMNFgkSWufd95LkloZLJKkVgaLJKmVwSJJamWwSJJarUqwJNmzGuedNdZpPGs1jnUaxzotz7KCZRmPwfd/2jjWaTxrNY51Gsc6LcOSg8XH4EuSTmfjMr77k8fgAyR55TH43zrTF87NT9cmzmcT53FhNntn5iKs03jWahzrNI51WtyLfP+7VXXJ6d5bTrCc7jH4b///vrCJ83l7di7jlJKkafDluvfbZ3pvOcEy6jH4QxNsD8z/K0CStLYtJ1hGPQa/qvYB+wB2bN9UDz742DJO+ap3XXp1y8+RJPVazlVhPgZfkvQ6S56xVNVLSX4PeJBXH4P/RNvIJEkzaTlLYVTVF4AvNI3lrDz4/GMtP8clNUnq5SNdJEmtDBZJUiuDRZLUalk9lrWgq1cD9mskCZyxSJKaGSySpFYGiySp1brvsXTy3hpJcsYiSWpmsEiSWhkskqRW9limkPfWSJplzlgkSa0MFklSK5fC1jiX1SRNmjMWSVIrg0WS1MpgkSS1ssei0XxkjaQxnLFIkloZLJKkVgaLJKmVPRZNnPfWSGubMxZJUiuDRZLUymCRJLWyx6KZ5r010vRxxiJJarVosCT5VJLjSR5fcGxzkoNJjg6vF63sMCVJs2LMUthfAn8K/NWCY3uBQ1V1V5K9w/6d/cOTJsNLoKU+i85YqurvgO+dcngXsH/Y3g/c0jssSdKsWmqPZWtVHQMYXrf0DUmSNMtWvHmfZE+Sw0kOnzj58kqfTpK0ypZ6ufELSeaq6liSOeD4mT5YVfuAfQA7tm+qJZ5Pmhn2a7TeLXXGcgDYPWzvBu7vGY4kadaNudz4s8DXgLckeS7J7cBdwI1JjgI3DvuSJC2+FFZV7z/DWzubxyJJWgN8pIs0xXxkjWaRj3SRJLUyWCRJrQwWSVIreyzSOuC9NZokZyySpFYGiySplUthks6Kl0BrMc5YJEmtDBZJUiuDRZLUyh6LpFXhJdBrlzMWSVIrg0WS1MpgkSS1ssciaebZr5kuzlgkSa0MFklSK5fCJGkBH1mzfM5YJEmtDBZJUiuDRZLUyh6LJK2A9XwJtDMWSVIrg0WS1MpgkSS1ssciSVNu1u6tccYiSWq1aLAkuTzJV5McSfJEkjuG45uTHExydHi9aOWHK0madmNmLC8BH6qqtwLXAR9IchWwFzhUVVcCh4Z9SdI6t2iPpaqOAceG7ReTHAEuA3YBNwwf2w88BNy5IqOUJC1b5701G+bO/N5Z9ViSXAFcAzwMbB1C55Xw2bLkEUqS1ozRwZLkAuBzwAer6odn8b09SQ4nOXzi5MtLGaMkaYaMCpYk5zAfKp+pqvuGwy8kmRvenwOOn+67VbWvqnZU1Y5LLt7QMWZJ0hQbc1VYgE8CR6rq4wveOgDsHrZ3A/f3D0+SNGvG3CB5PfDbwDeTPDYc+yhwF3BPktuBZ4FbV2SEkqSZMuaqsH8Acoa3d/YOR5I067zzXpLUymCRJLUyWCRJrQwWSVIrg0WS1MpgkSS1MlgkSa0MFklSK4NFktTKYJEktTJYJEmtDBZJUiuDRZLUymCRJLUyWCRJrQwWSVIrg0WS1MpgkSS1MlgkSa0MFklSK4NFktTKYJEktTJYJEmtDBZJUiuDRZLUymCRJLUyWCRJrQwWSVIrg0WS1GrRYEmyKck/JvnnJE8k+dhwfHOSg0mODq8XrfxwJUnTbsyM5X+Ad1TVduBq4KYk1wF7gUNVdSVwaNiXJK1ziwZLzfuvYfec4b8CdgH7h+P7gVtWYoCSpNkyqseSZEOSx4DjwMGqehjYWlXHAIbXLSs2SknSzBgVLFX1clVdDWwDrk3ytrEnSLInyeEkh0+cfHmJw5QkzYqzuiqsqn4APATcBLyQZA5geD1+hu/sq6odVbXjkos3LG+0kqSpN+aqsEuSvHHYfgPwTuBJ4ACwe/jYbuD+FRqjJGmGbBzxmTlgf5INzAfRPVX1QJKvAfckuR14Frh1BccpSZoRiwZLVX0DuOY0x08CO1diUJKk2eWd95KkVgaLJKmVwSJJamWwSJJaGSySpFYGiySplcEiSWplsEiSWhkskqRWBoskqZXBIklqZbBIkloZLJKkVgaLJKmVwSJJamWwSJJaGSySpFYGiySplcEiSWplsEiSWhkskqRWBoskqZXBIklqZbBIkloZLJKkVgaLJKmVwSJJamWwSJJajQ6WJBuSPJrkgWF/c5KDSY4Orxet3DAlSbNi41l89g7gCHDhsL8XOFRVdyXZO+zf2Tw+SVKTd116deNPe+qM74yasSTZBrwHuHvB4V3A/mF7P3DL0gYnSVpLxi6FfQL4MPDjBce2VtUxgOF1S+/QJEmzaNFgSXIzcLyqHlnKCZLsSXI4yeETJ19eyo+QJM2QMT2W64H3Jnk3sAm4MMmngReSzFXVsSRzwPHTfbmq9gH7AHZs31RN45akdaO3N7LyFp2xVNVHqmpbVV0BvA/4SlXdBhwAdg8f2w3cv2KjlCTNjOXcx3IXcGOSo8CNw74kaZ07m8uNqaqHgIeG7ZPAzv4hSZJm2VkFiyRpnFnri3TykS6SpFYGiySplcEiSWplj0WSFljPvZEuzlgkSa0MFklSK5fCJM08l6+mizMWSVIrg0WS1MpgkSS1ssciaVXYF1m7nLFIkloZLJKkVgaLJKmVPRZJZ8XeiBbjjEWS1MpgkSS1cilMWgdcvtIkOWORJLUyWCRJrQwWSVIreyzSFLM3olnkjEWS1MpgkSS1MlgkSa3ssUjN7ItovXPGIklqNWrGkuQZ4EXgZeClqtqRZDPwt8AVwDPAb1bV91dmmJKkWXE2M5Zfq6qrq2rHsL8XOFRVVwKHhn1J0jq3nB7LLuCGYXs/8BBw5zLHI60K+yJSn7EzlgK+lOSRJHuGY1ur6hjA8LplJQYoSZotY2cs11fV80m2AAeTPDn2BEMQ7QF402VehCZJa92ov+mr6vnh9XiSzwPXAi8kmauqY0nmgONn+O4+YB/Aju2bqmfY0jyXsKTps+hSWJLzk/zMK9vArwOPAweA3cPHdgP3r9QgJUmzY8yMZSvw+SSvfP6vq+qLSb4O3JPkduBZ4NaVG6YkaVYsGixV9TSw/TTHTwI7V2JQkqTZZTddE2dfRFrbfKSLJKmVwSJJamWwSJJa2WPRaPZGJI3hjEWS1MpgkSS1MlgkSa3ssaxx9kUkTZozFklSK4NFktTKpbAp5PKVpFnmjEWS1MpgkSS1MlgkSa3ssTSyNyJJzlgkSc0MFklSK4NFktRq3fdY7ItIUi9nLJKkVgaLJKmVwSJJajWzPRZ7I5I0nZyxSJJaGSySpFYTXQr712+c5xKWJK1xzlgkSa0MFklSK4NFktQqVTW5kyUngG8DPwt8d2Innl3WaTxrNY51Gsc6Le7nquqS070x0WD5yUmTw1W1Y+InnjHWaTxrNY51Gsc6LY9LYZKkVgaLJKnVagXLvlU676yxTuNZq3Gs0zjWaRlWpcciSVq7XAqTJLUyWCRJrQwWSVIrg0WS1MpgkSS1+j+ld1xD11kf5AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 480x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.matshow(trapezoidal_maze(20, 5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f7296ff4820>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 288x311.351 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.matshow(hexagonal_maze(20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f7296f61d30>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.matshow(multicomp_maze())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f7296f37400>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.matshow(multicomp_maze_circ())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# TD Learning"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def V(s):\n",
    "    return values[s[0],s[1]]\n",
    "\n",
    "def R(s):\n",
    "    return r[s[0],s[1]]\n",
    "\n",
    "def get_visited(s):\n",
    "    return visited[s[0],s[1]]\n",
    "\n",
    "def inc_visited(s):\n",
    "    visited[s[0],s[1]] += 1.0\n",
    "    \n",
    "def set_V(s, value):\n",
    "    values[s[0],s[1]] = value\n",
    "    \n",
    "def in_maze(s):\n",
    "    return s[0] >= 0 and s[0] < maze.shape[0] and s[1] >= 0 and s[1] < maze.shape[1]\n",
    "\n",
    "def is_free(s):\n",
    "    return maze[s[0],s[1]] == 1\n",
    "    \n",
    "def valid_state(s):\n",
    "    return in_maze(s) and is_free(s)\n",
    "\n",
    "def sigmoid(x):\n",
    "    return 1 / (1 + np.exp(-x))\n",
    "\n",
    "def softmax(values, beta=10):\n",
    "    values = np.exp(values) * beta\n",
    "    return values / np.sum(values)\n",
    "    \n",
    "def policy(s):\n",
    "    possible_next_states = [s + d for d in np.array([[1,0],[-1,0],[0,1],[0,-1]])]\n",
    "    filtered = list(filter(valid_state, possible_next_states))\n",
    "    vs = np.array([V(s) for s in filtered])\n",
    "    p = softmax(vs)\n",
    "    return filtered[np.random.choice(range(len(filtered)), 1, p=p)[0]]\n",
    "\n",
    "def alpha(s):\n",
    "    return 1 / (get_visited(s) + 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "s_0 = np.array([2,0])\n",
    "\n",
    "maze = np.array([\n",
    "    [1,1,1,1],\n",
    "    [1,0,1,1],\n",
    "    [1,0,1,1],\n",
    "    [1,1,1,1]\n",
    "])\n",
    "r = np.array([\n",
    "    [0,0,0,0],\n",
    "    [0,0,0,1],\n",
    "    [0,0,0,-1],\n",
    "    [0,0,0,0]    \n",
    "])\n",
    "\n",
    "values = np.zeros(maze.shape)\n",
    "visited = np.zeros(maze.shape)\n",
    "\n",
    "s_new = s_0\n",
    "s = None\n",
    "\n",
    "alpha = 0.1\n",
    "gamma = 0.9\n",
    "\n",
    "for i in range(1500):\n",
    "    s = s_new\n",
    "    s_new = policy(s)\n",
    "    if get_visited(s_new) == 0:\n",
    "        set_V(s_new, R(s_new))\n",
    "    inc_visited(s_new)\n",
    "    \n",
    "    new_V = V(s) + alpha * (R(s_new) + gamma * V(s_new) - V(s))\n",
    "    set_V(s, new_V)\n",
    "    if R(s_new) != 0:\n",
    "        s_new = s_0\n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.371,  0.677,  0.825,  1.229],\n",
       "       [ 0.2  ,  0.   ,  1.119,  1.   ],\n",
       "       [ 0.097,  0.   ,  0.876, -1.   ],\n",
       "       [ 0.097,  0.19 ,  0.353, -0.537]])"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.round(values, 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.heatmap(values, annot=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Successor Representation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def state2idx(state):\n",
    "    for i in range(len(all_states)):\n",
    "        if np.all(all_states[i] == state):\n",
    "            return i\n",
    "        \n",
    "def M(s, s_new):\n",
    "    idx_s = state2idx(s)\n",
    "    idx_s_new = state2idx(s_new)\n",
    "    return sr_matrix[idx_s, idx_s_new]\n",
    "\n",
    "def set_M(s, s_new, value, sr_matrix):\n",
    "    idx_s = state2idx(s)\n",
    "    idx_s_new = state2idx(s_new)\n",
    "    sr_matrix[idx_s, idx_s_new] = value\n",
    "    \n",
    "def random_policy(s, beta=5):\n",
    "    possible_next_states = [s + d for d in np.array([[1,0],[-1,0],[0,1],[0,-1]])]\n",
    "    filtered = list(filter(valid_state, possible_next_states))\n",
    "    vs = np.array([1 for s in filtered])\n",
    "    p = softmax(vs, beta)\n",
    "    return filtered[np.random.choice(range(len(filtered)), 1, p=p)[0]]\n",
    "\n",
    "def same_state(s1, s2):\n",
    "    return np.all(s1 == s2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Learn the successor representation by traversing the maze by a random walk."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_16670/256625750.py:10: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  values = np.zeros(maze.shape, dtype=np.float)\n",
      "/tmp/ipykernel_16670/256625750.py:14: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  sr_matrix = np.eye(len(all_states), dtype=np.float)\n"
     ]
    }
   ],
   "source": [
    "s_0 = np.array([2,0])\n",
    "\n",
    "maze = np.array([\n",
    "    [1,1,1,1],\n",
    "    [1,0,1,1],\n",
    "    [1,0,1,1],\n",
    "    [1,1,1,1]\n",
    "])\n",
    "\n",
    "values = np.zeros(maze.shape, dtype=np.float)\n",
    "visited = np.zeros(maze.shape)\n",
    "all_states = [np.array(s) for s in it.product(range(maze.shape[0]), range(maze.shape[1]))]\n",
    "n_states = maze.shape[0] * maze.shape[1]\n",
    "sr_matrix = np.eye(len(all_states), dtype=np.float)\n",
    "\n",
    "s_new = s_0\n",
    "s = None\n",
    "\n",
    "alpha = 0.1\n",
    "gamma = 0.9\n",
    "\n",
    "for i in range(500):\n",
    "    s = s_new\n",
    "    s_new = random_policy(s)\n",
    "    \n",
    "    inc_visited(s_new)\n",
    "    next_sr_matrix = sr_matrix.copy()\n",
    "    \n",
    "    # s' include all possible future states\n",
    "    for s_prime in all_states:\n",
    "        I = 1 if same_state(s, s_prime) else 0\n",
    "        new_M = M(s, s_prime) + alpha * (I + gamma * M(s_new, s_prime) - M(s, s_prime))\n",
    "        set_M(s, s_prime, new_M, next_sr_matrix)\n",
    "    sr_matrix = next_sr_matrix\n",
    "    \n",
    "    if R(s_new) != 0:\n",
    "        s_new = s_0\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.heatmap(visited)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Heatmap of tbe successor representation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.heatmap(sr_matrix)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Reward and Successor Representation are decoupled"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is now possible to compute different \"value maps\" for different reward structures without recomputing the successor representation. Thus, only a dot product between reward vector and successor representation is required."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "r = np.array([\n",
    "    [0,0,0,0],\n",
    "    [0,0,0,1],\n",
    "    [0,0,0,-1],\n",
    "    [0,0,0,0]    \n",
    "])\n",
    "reward_vec = np.array(r.flatten())\n",
    "v_sr = (sr_matrix @ reward_vec).reshape(maze.shape)\n",
    "sns.heatmap(v_sr, annot=True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "r = np.array([\n",
    "    [0,0,0,-1],\n",
    "    [0,0,0,1],\n",
    "    [0,0,0,-1],\n",
    "    [0,0,0,1]    \n",
    "])\n",
    "reward_vec = np.array(r.flatten())\n",
    "v_sr = (sr_matrix @ reward_vec).reshape(maze.shape)\n",
    "sns.heatmap(v_sr, annot=True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "r = np.array([\n",
    "    [0,0,0,0],\n",
    "    [0,0,0,0],\n",
    "    [0,0,0,-1],\n",
    "    [0,0,0,1]    \n",
    "])\n",
    "reward_vec = np.array(r.flatten())\n",
    "v_sr = (sr_matrix @ reward_vec).reshape(maze.shape)\n",
    "sns.heatmap(v_sr, annot=True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Try the same principle using a epsilon-greedy policy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_16670/129993482.py:28: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  values = np.zeros(maze.shape, dtype=np.float)\n",
      "/tmp/ipykernel_16670/129993482.py:32: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  sr_matrix = np.eye(len(all_states), dtype=np.float)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def epsilon_greedy_policy(s, epsilon=0.05):\n",
    "    possible_next_states = [s + d for d in np.array([[1,0],[-1,0],[0,1],[0,-1]])]\n",
    "    filtered = list(filter(valid_state, possible_next_states))\n",
    "    # Get reward vector\n",
    "    reward_vec = np.array(r.flatten())\n",
    "    # Determine new values for all states\n",
    "    v_sr = (sr_matrix @ reward_vec).reshape(maze.shape)\n",
    "    # Get values of valid next states\n",
    "    vs = np.array([v_sr[s[0], s[1]] for t in filtered])\n",
    "    # Get probabilities according to epsilon-greedy policy\n",
    "    p = [1-epsilon if i == np.argmax(vs) else epsilon / (len(filtered)-1) for i in range(len(filtered))]\n",
    "    return filtered[np.random.choice(range(len(filtered)), 1, p=p)[0]]\n",
    "\n",
    "s_0 = np.array([2,0])\n",
    "r = np.array([\n",
    "    [0,0,0,-1],\n",
    "    [0,0,0,1],\n",
    "    [0,0,0,-1],\n",
    "    [0,0,0,1]    \n",
    "])\n",
    "\n",
    "s_new = s_0\n",
    "s = None\n",
    "\n",
    "alpha = 0.1\n",
    "gamma = 0.9\n",
    "\n",
    "values = np.zeros(maze.shape, dtype=np.float)\n",
    "visited = np.zeros(maze.shape)\n",
    "all_states = [np.array(s) for s in it.product(range(maze.shape[0]), range(maze.shape[1]))]\n",
    "n_states = maze.shape[0] * maze.shape[1]\n",
    "sr_matrix = np.eye(len(all_states), dtype=np.float)\n",
    "\n",
    "for i in range(500):\n",
    "    s = s_new\n",
    "    s_new = epsilon_greedy_policy(s)\n",
    "    s_new = random_policy(s)\n",
    "    \n",
    "    inc_visited(s_new)\n",
    "    next_sr_matrix = sr_matrix.copy()\n",
    "    \n",
    "    # s' include all possible future states\n",
    "    for s_prime in all_states:\n",
    "        I = 1 if same_state(s, s_prime) else 0\n",
    "        new_M = M(s, s_prime) + alpha * (I + gamma * M(s_new, s_prime) - M(s, s_prime))\n",
    "        set_M(s, s_prime, new_M, next_sr_matrix)\n",
    "    sr_matrix = next_sr_matrix\n",
    "    \n",
    "    if R(s_new) != 0:\n",
    "        s_new = s_0\n",
    "    \n",
    "    if i % 50 == 0:\n",
    "        v_sr = (sr_matrix @ reward_vec).reshape(maze.shape)\n",
    "        sns.heatmap(v_sr, annot=True)\n",
    "        # sns.heatmap(visited, annot=True)\n",
    "        plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Skew of place fields in opposite direction of travel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_16670/637973618.py:11: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  values = np.zeros(maze.shape, dtype=np.float)\n",
      "/tmp/ipykernel_16670/637973618.py:15: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  sr_matrix = np.eye(len(all_states), dtype=np.float)\n"
     ]
    }
   ],
   "source": [
    "s_0 = np.array([0,0])\n",
    "\n",
    "maze = np.array([\n",
    "    [1,1,1,1,1]\n",
    "])\n",
    "\n",
    "r = np.array([\n",
    "    [0,0,0,0,1]\n",
    "])\n",
    "\n",
    "values = np.zeros(maze.shape, dtype=np.float)\n",
    "visited = np.zeros(maze.shape)\n",
    "all_states = [np.array(s) for s in it.product(range(maze.shape[0]), range(maze.shape[1]))]\n",
    "n_states = maze.shape[0] * maze.shape[1]\n",
    "sr_matrix = np.eye(len(all_states), dtype=np.float)\n",
    "\n",
    "s_new = s_0\n",
    "s = None\n",
    "\n",
    "alpha = 0.1\n",
    "gamma = 0.9\n",
    "\n",
    "def preferred_direction_policy(s):\n",
    "    possible_next_states = [s + d for d in np.array([[0,1],[0,-1]])]\n",
    "    filtered = list(filter(valid_state, possible_next_states))\n",
    "    if len(filtered) == 2:\n",
    "        p = np.array([0.8, 0.2])\n",
    "    else:\n",
    "        p = np.array([1])\n",
    "    return filtered[np.random.choice(range(len(filtered)), 1, p=p)[0]]\n",
    "\n",
    "for i in range(4000):\n",
    "    s = s_new\n",
    "    s_new = preferred_direction_policy(s)\n",
    "    \n",
    "    inc_visited(s_new)\n",
    "    next_sr_matrix = sr_matrix.copy()\n",
    "    for s_prime in all_states:\n",
    "        I = 1 if same_state(s, s_prime) else 0\n",
    "        new_M = M(s, s_prime) + alpha * (I + gamma * M(s_new, s_prime) - M(s, s_prime))\n",
    "        set_M(s, s_prime, new_M, next_sr_matrix)\n",
    "    sr_matrix = next_sr_matrix\n",
    "    \n",
    "    if R(s_new) != 0:\n",
    "        s_new = s_0\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.heatmap(sr_matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array([0, 0]), array([0, 1]), array([0, 2]), array([0, 3]), array([0, 4])]"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "all_states"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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YywMZc2lob+R01VlOVBShOou53nCT10u2k2VJZ0bKdApTppFqvvdaKS3qBVqL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\nECLC/X/IQh2x3EBYWQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11bde2208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sr_vals = [M(s, all_states[4]) for s in all_states]\n",
    "plt.plot(sr_vals, label='M(:, $s^5$)')\n",
    "\n",
    "\n",
    "sr_vals = [M(all_states[0], s) for s in all_states]\n",
    "plt.plot(sr_vals, label='M($s^1$, :)')\n",
    "\n",
    "sr_vals = [M(all_states[4], s) for s in all_states]\n",
    "plt.plot(sr_vals, label='M($s^5$, :)')\n",
    "plt.legend()\n",
    "plt.xticks(np.arange(5))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Compute SR with transition matrix T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "def transition_matrix(maze):\n",
    "    m = make_matrix_from(maze)\n",
    "    return m / m.sum(axis=1)\n",
    "\n",
    "def make_matrix_from(maze):\n",
    "    \n",
    "    def in_maze(s):\n",
    "        return s[0] >= 0 and s[0] < maze.shape[0] and s[1] >= 0 and s[1] < maze.shape[1]\n",
    "\n",
    "    def is_free(s):\n",
    "        return maze[s[0],s[1]] == 1\n",
    "\n",
    "    def valid_state(s):\n",
    "        return in_maze(s) and is_free(s)\n",
    "    \n",
    "    states = [np.array(s) for s in it.product(range(maze.shape[0]), range(maze.shape[1])) if maze[s[0], s[1]] == 1]\n",
    "    adja = np.eye(len(states))\n",
    "    idx = np.zeros(maze.shape, dtype=np.int)\n",
    "    c = 0\n",
    "    for i in range(maze.shape[0]):\n",
    "        for j in range(maze.shape[1]):\n",
    "            if maze[i, j] == 0:\n",
    "                continue\n",
    "            idx[i, j] = c\n",
    "            c += 1\n",
    "    \n",
    "    for i, state in enumerate(states):\n",
    "        possible_next_states = [state + d for d in np.array([[1,0],[-1,0],[0,1],[0,-1]])]\n",
    "        filtered = list(filter(valid_state, possible_next_states))\n",
    "        for f in filtered:\n",
    "            adja[i, idx[f[0], f[1]]] = 1\n",
    "            adja[idx[f[0], f[1]], i] = 1\n",
    "    return adja\n",
    "        \n",
    "\n",
    "def sr_matrix_from(maze, gamma):\n",
    "    T = transition_matrix(maze)\n",
    "    n = T.shape[0]\n",
    "    return np.linalg.inv(np.eye(n) - gamma * T)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Eigendecomposition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "def eigdecomp(M):\n",
    "    E, V = np.linalg.eig(M)\n",
    "    idx = np.argsort(E)[::-1]\n",
    "    return V[:, idx[:]].astype(float), E\n",
    "\n",
    "def vec2maze(vec, maze):\n",
    "    vec_iter = iter(vec)\n",
    "    res = []\n",
    "    walls = []\n",
    "    for i in range(maze.shape[0]):\n",
    "        for j in range(maze.shape[1]):\n",
    "            if maze[i, j] == 1:\n",
    "                res.append(next(vec_iter))\n",
    "            else:\n",
    "                res.append(0)\n",
    "    return np.array(res).reshape(maze.shape)\n",
    "\n",
    "def plot_eigvecs(eig_vecs, maze, grid_size=10, filename=None, figsize=(15,15)):\n",
    "    plt.figure(figsize=figsize)\n",
    "    for i in range(eig_vecs.shape[0]-1):\n",
    "        if i >= grid_size**2:\n",
    "            break\n",
    "        ax = plt.subplot(grid_size, grid_size, i+1)\n",
    "        ax.matshow(vec2maze(eig_vecs[:, i+1], maze), cmap='RdBu_r')\n",
    "        ax.axes.get_xaxis().set_ticks([])\n",
    "        ax.axes.get_yaxis().set_ticks([])\n",
    "        plt.grid(False)\n",
    "    plt.tight_layout()\n",
    "    if filename is not None:\n",
    "        plt.savefig(filename, bbox_inches='tight')\n",
    "    plt.show()\n",
    "    \n",
    "def plot_from_maze(maze, filename=None, figsize=(15,15), grid_size=5, gamma=0.9):\n",
    "    M = sr_matrix_from(maze, gamma)\n",
    "    V, E = eigdecomp(M)\n",
    "    V[V < 0] = 0\n",
    "    plot_eigvecs(V, maze, grid_size=grid_size, filename=filename, figsize=figsize)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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oe0NwVPcFdb3D41SC4p4FxpiAOBKs73Z5bwBAbDhd04czXvXqnC36UZT06Vv7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\nGEEQHOMvqJKXeRIYDtkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11bc4bd30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_from_maze(square_maze(20), figsize=(4,4), filename='square.pdf', gamma=0.9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAARgAAADhCAYAAAATZKrpAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nBAyQRsAAaf4NQ8cuU0omyeMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11ba01e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_from_maze(hairpin_maze(), figsize=(4,4), filename='hairpin.pdf', gamma=0.9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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JmUA3kXR0dLJGxtuWvJVQtROr0fCGintqQSyDcYQGYzSCQY7T6X+u6DYduezsKkAKdI/0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\nFxgdHR2PoS8wOjo6HkNfYHR0dDzG/wWZH9igiYQvWQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b5cbda0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_from_maze(circular_maze(30), figsize=(4,4), filename='circle.pdf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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toAuNIFJ4ocTrBvRaPu3lRULvuZfLf/gP/5FYJRXnmtAwMgZWzsKpOGTHi+Qm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\nRqZi/A8Nu8vvrjiz/AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11bc4bc88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_from_maze(trapezoidal_maze(20, 5), figsize=(4,4), filename='trapezoidal.pdf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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13oVIW5/FYS/B/WOT1Morn6EthWF48v/VoUOHDk9Bx9naoUOHJdMRkg4dOiyZ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URGoqjlMvQKKeOnlsuIjEQZfqcNwfkMlQ0bKXcWgTw7jyg0SHz3Pob3HCCw4z8xbfrKvF7X1/7l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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11bc4b390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_from_maze(hexagonal_maze(10), figsize=(4,4), filename='hexagon.pdf', gamma=0.9)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Subgoal discovery"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "def compute_cut(orig_maze, mask, d):\n",
    "    maze = np.zeros(orig_maze.shape)\n",
    "    maze[np.logical_and(orig_maze, mask)] = 1\n",
    "    M = sr_matrix_from(maze, 0.9)\n",
    "    V, E = eigdecomp(M)\n",
    "    cut = V.copy()\n",
    "    cut[V < 0] = 0\n",
    "    cut[V > 0] = 1\n",
    "    cut = cut[:,1]\n",
    "    cut1 = vec2maze(cut, np.logical_and(maze, mask))\n",
    "    cut2 = vec2maze(np.invert(cut.astype(int))+2, np.logical_and(maze, mask))\n",
    "    \n",
    "    res = np.zeros(orig_maze.shape)\n",
    "    res[orig_maze == 0] = -1\n",
    "    res[cut1 == 1] = 2\n",
    "    res[cut2 == 1] = 3\n",
    "    yield res    \n",
    "    if d < 3:\n",
    "        yield from compute_cut(orig_maze, np.logical_and(mask, cut1), d+1)\n",
    "        yield from compute_cut(orig_maze, np.logical_and(mask, cut2), d+1)\n",
    "\n",
    "def cut_approx(maze):\n",
    "    yield from compute_cut(maze, np.ones(maze.shape), 1)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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R/o3zTlEaI3ucFMcZfrum0VO9xosd5n7+i0qvTEuJy3zW+BOwFkDObBvwJo740lW2jtPl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\nfAkhRAMcfAkhRAMcfAkhRAP/H3l29G100U07AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b9ffb70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_from_maze(multicomp_maze(), figsize=(5,5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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XEEIcgJ0vIYQ4gGXbId/p2v6yn96pVfLaa17Sf4w5Imf7VR1qTcxZdKX+oc6g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\nEOIA7HwJIcQB2PkSQogD/H9I3vDn2W7LywAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b9bcdd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_from_maze(multicomp_maze_circ(), figsize=(5,5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAO0AAADtCAYAAABTTfKPAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n0UKMaCFGtBDzBaWqIr3trEQKAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11d5a6da0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAO0AAADtCAYAAABTTfKPAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAA2lJREFUeJzt3DFKI2EYgOGJWAn2S05hp7BYb714Au/jXazFC2hnb7dF\nLiBY7ngBiTOKGd/hecrJX3wJvHxFfmYzjuMAdBwtPQAwj2ghRrQQI1qIES3EiBZijvd9+Pvqxv9B\nYSe3j5PP3u2evnESPuPo1/Pm3eeHHgT4GtFCjGghRrQQI1qIES3EiBZiRAsxooUY0UKMaCFGtBAj\nWogRLcSIFmJECzGihRjRQoxoIUa0ECNaiBEtxIgWYkQLMaKFGNFCjGghRrQQI1qIES3EiBZiRAsx\nooUY0UKMaCFGtBAjWogRLcSIFmJECzGihRjRQoxoIUa0ECNaiBEtxIgWYkQLMaKFGNFCjGghRrQQ\nI1qIES3EiBZiRAsxooUY0UKMaCFGtBAjWogRLcSIFmJECzGihRjRQoxoIUa0ECNaiBEtxIgWYkQL\nMaKFGNFCjGghRrQQc7z0APwMf7ZnS48w293uafLZ4ve7///+c5sWYkQLMaKFGNFCjGghRrQQI1qI\nES3EiBZiRAsxooUYd48ZhmEYtg+nS48w2/W/y8lntw/fOMiB2bQQI1qIES3EiBZiRAsxooUY0UKM\naCFGtBAjWogRLcSIFmJECzGihRjRQoxoIUa0ECNaiBEtxIgWYkQLMd7GuGLFNyzyMZsWYkQLMaKF\nGNFCjGghRrQQI1qIES3EiBZiRAsxrjGu2O7iZfJZVx47bFqIES3EiBZiRAsxooUY0UKMaCFGtBAj\nWogRLcSIFmJECzGihRjRQoxoIUa0ECNaiBEtxIgWYkQLMaKFGNFCzN5XqJ7cPh5qjkW8/j2ffHbt\nvwUdNi3EiBZiRAsxooUY0UKMaCFGtBAjWogRLcSIFmL2XmOcc81v7Yq/hauX62TTQoxoIUa0ECNa\niBEtxIgWYkQLMaKFGNFCjGghRrQQI1qIES3EiBZiRAsxooUY0UKMaCFGtBAjWogRLcSIFmJECzGi\nhRjRQoxoIUa0ECNaiBEtxIgWYkQLMaKFGNFCjGghRrQQI1qIES3EiBZiRAsxooUY0UKMaCFGtBAj\nWogRLcSIFmJECzGihRjRQoxoIUa0ECNaiBEtxIgWYkQLMaKFGNFCjGghRrQQI1qIES3EiBZiRAsx\nooUY0UKMaCFmM47j0jMAM9i0ECNaiBEtxIgWYkQLMaKFmDfxZiRr03GLKgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11ee50198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAO0AAADtCAYAAABTTfKPAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAA25JREFUeJzt3LFNI1EUQNHxisgVoK2CzAEi3tiiAnqgDFIKoADkmAII\nnFHDBpTgdGgAjMeSGa51Tjj+wbOlqxf4axbjOA5Ax5+5BwCmES3EiBZiRAsxooUY0ULMxb4Pr28f\n/B8UttxsDz67W69OOAnHeH2+X3z23KaFGNFCjGghRrQQI1qIES3EiBZiRAsxooUY0UKMaCFGtBAj\nWogRLcSIFmJECzGihRjRQoxoIUa0ECNaiBEtxIgWYkQLMaKFGNFCjGghRrQQI1qIES3EiBZiRAsx\nooUY0UKMaCFGtBAjWogRLcSIFmJECzGihRjRQoxoIUa0ECNaiBEtxIgWYkQLMaKFGNFCjGghRrQQ\nI1qIES3EiBZiRAsxooUY0UKMaCFGtBAjWogRLcSIFmJECzGihRjRQoxoIUa0ECNaiBEtxIgWYkQL\nMaKFGNFCjGghRrQQczH3APwOy8127hEm261XB58tfr+v2LQQI1qIES3EiBZiRAsxooUY0UKMaCFG\ntBAjWogRLcS4e8wwDMPw8v429whHmDDz4+mm+Gk2LcSIFmJECzGihRjRQoxoIUa0ECNaiBEtxIgW\nYkQLMaKFGNFCjGghRrQQI1qIES3EiBZiRAsxooUY0UKMtzGeseYbFvmOTQsxooUY0UKMaCFGtBAj\nWogRLcSIFmJECzGihRjXGM/Yv79XB5915bHDpoUY0UKMaCFGtBAjWogRLcSIFmJECzGihRjRQoxo\nIUa0ECNaiBEtxIgWYkQLMaKFGNFCjGghRrQQI1qIES3E7H2F6nKz/ak5ZrFbrw4+e+6/BR02LcSI\nFmJECzGihRjRQoxoIUa0ECNaiBEtxIgWYvZeY5xyze/cFX+LKVcv7/7fnHASjvF0+flzmxZiRAsx\nooUY0UKMaCFGtBAjWogRLcSIFmJECzGihRjRQoxoIUa0ECNaiBEtxIgWYkQLMaKFGNFCjGghRrQQ\nI1qIES3EiBZiRAsxooUY0UKMaCFGtBAjWogRLcSIFmJECzGihRjRQoxoIUa0ECNaiBEtxIgWYkQL\nMaKFGNFCjGghRrQQI1qIES3EiBZiRAsxooUY0UKMaCFGtBAjWogRLcSIFmJECzGihRjRQoxoIUa0\nECNaiBEtxIgWYkQLMYtxHOeeAZjApoUY0UKMaCFGtBAjWogRLcR8AJ4nJ9+ks3TNAAAAAElFTkSu\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11f14d668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAO0AAADtCAYAAABTTfKPAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11ef4cc50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAO0AAADtCAYAAABTTfKPAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAA1NJREFUeJzt3DFKA1EUQNFErAJuIL29XdxB6uzFbUlWIehGxF5I6Vja\naJgR4niHc8rkF38Cl1fkMethGFZAx9XcFwCmES3EiBZiRAsxooUY0ULM9bkvP95u/R8Utt/ejT57\nOuwueBN+4+nxYf3d5yYtxIgWYkQLMaKFGNFCjGghRrQQI1qIES3EiBZiRAsxooUY0UKMaCFGtBAj\nWogRLcSIFmJECzGihRjRQoxoIUa0ECNaiBEtxIgWYkQLMaKFGNFCjGghRrQQI1qIES3EiBZiRAsx\nooUY0UKMaCFGtBAjWogRLcSIFmJECzGihRjRQoxoIUa0ECNaiBEtxIgWYkQLMaKFGNFCjGghRrQQ\nI1qIES3EiBZiRAsxooUY0UKMaCFGtBAjWogRLcSIFmJECzGihRjRQoxoIUa0ECNaiBEtxIgWYkQL\nMaKFmOu5L8D/sDm+zH2FyU6H3eizxef7iUkLMaKFGNFCjGghRrQQI1qIES3EiBZiRAsxooUY0UKM\n3WNWq9W0Pd6iJT2fSQsxooUY0UKMaCFGtBAjWogRLcSIFmJECzGihRjRQoxoIUa0ECNaiBEtxIgW\nYkQLMaKFGNFCjGghRrQQ422MC7akNxDyxaSFGNFCjGghRrQQI1qIES3EiBZiRAsxooUY0UKMNcYF\n2xxfRp+18thh0kKMaCFGtBAjWogRLcSIFmJECzGihRjRQoxoIUa0ECNaiBEtxIgWYkQLMaKFGNFC\njGghRrQQI1qIES3EiBZizr5Cdb+9+6t7zGL7fDP67Ov9+wVvAuOZtBAjWogRLcSIFmJECzGihRjR\nQoxoIUa0ECNaiDm7xjhlzW/pir+F1ctlMmkhRrQQI1qIES3EiBZiRAsxooUY0UKMaCFGtBAjWogR\nLcSIFmJECzGihRjRQoxoIUa0ECNaiBEtxIgWYkQLMaKFGNFCjGghRrQQI1qIES3EiBZiRAsxooUY\n0UKMaCFGtBAjWogRLcSIFmJECzGihRjRQoxoIUa0ECNaiBEtxIgWYkQLMaKFGNFCjGghRrQQI1qI\nES3EiBZiRAsxooUY0UKMaCFGtBAjWogRLcSIFmJECzGihRjRQoxoIUa0ELMehmHuOwATmLQQI1qI\nES3EiBZiRAsxooWYT7k3Il2LSyuZAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11ed0aa58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAO0AAADtCAYAAABTTfKPAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11ecbfb70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAO0AAADtCAYAAABTTfKPAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11ec439b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i, c in enumerate(cut_approx(multicomp_maze())):\n",
    "    plt.matshow(c, cmap='viridis')\n",
    "    plt.grid(False)\n",
    "    plt.gca().axes.get_xaxis().set_ticks([])\n",
    "    plt.gca().axes.get_yaxis().set_ticks([])\n",
    "    plt.savefig('cut_{}.pdf'.format(i))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAO0AAADtCAYAAABTTfKPAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11ee42278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f802080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAO0AAADtCAYAAABTTfKPAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAA65JREFUeJzt3TGK1GAYgOGMWA14AWsrL7CCeIjFQ1jYCp5B8CoytQcQ\nnM7KynousLBtvICGiWw2eePzlDNh+cPw8hX7wX8Yx3EAOp6sfQBgHtFCjGghRrQQI1qIES3EPJ36\n8vXbz/4fFHY8na9+9v72ZsGT8C++fflw+NPnJi3EiBZiRAsxooUY0UKMaCFGtBAjWogRLcSIFmJE\nCzGihRjRQoxoIUa0ECNaiBEtxIgWYkQLMaKFGNFCjGghRrQQI1qIES3EiBZiRAsxooUY0UKMaCFG\ntBAjWoiZvFSaNhdF75NJCzGihRjRQoxoIUa0ECNaiBEtxIgWYkQLMaKFGGuMO3Y8na9+1spjh0kL\nMaKFGNFCjGghRrQQI1qIES3EiBZiRAsxooUY0UKMaCFGtBAjWogRLcSIFmJECzGihRjRQoxoIUa0\nECNaiBEtxIgWYkQLMaKFGNFCjGghRrQQI1qIES3EiBZiXCrNMAzzLqDeijkXYRff729MWogRLcSI\nFmJECzGihRjRQoxoIUa0ECNaiBEtxIgWYuweMwzDvD3eoj29n0kLMaKFGNFCjGghRrQQI1qIES3E\niBZiRAsxooUY0UKMaCFGtBAjWogRLcSIFmJECzGihRjRQoxoIUa0ECNaiBEtxIgWYkQLMaKFGNFC\njGghRrQQI1qIES3EiBZidnep9IuPP9c+wmy/Pr1c+wiEmLQQI1qIES3EiBZiRAsxooUY0UKMaCFG\ntBAjWohJrDEWVxPnmPN+Vh4xaSFGtBAjWogRLcSIFmJECzGihRjRQoxoIUa0ECNaiJncPT6ezo91\njkmX0zJ/9/n3Z9ef4dXdMoeY6Ths4zdhPSYtxIgWYkQLMaKFGNFCjGghRrQQI1qIES3EiBZiJtcY\nv15+PNY5tu9y/aNv3r9b7hwzbGUNlYdl0kKMaCFGtBAjWogRLcSIFmJECzGihRjRQoxoISZxE/wW\nbGU1EUxaiBEtxIgWYkQLMaKFGNFCjGghRrQQI1qIES3E/NdrjHtfTby/vVn7CCzApIUY0UKMaCFG\ntBAjWogRLcSIFmJECzGihRjRQsyDrTHufSWwaM6l0lYeO0xaiBEtxIgWYkQLMaKFGNFCjGghRrQQ\nI1qIES3EiBZiJneP7RPD9pi0ECNaiBEtxIgWYkQLMaKFGNFCjGghRrQQI1qIES3EiBZiRAsxooUY\n0UKMaCFGtBAjWogRLcSIFmJECzGHcRzXPgMwg0kLMaKFGNFCjGghRrQQI1qI+Q0/NDfkbAX0WAAA\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1116f8cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAO0AAADtCAYAAABTTfKPAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nGYAJbFqIES3EiBZiRAsxooUY0ULMb5wkQGJ2AcwfAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11f314668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAO0AAADtCAYAAABTTfKPAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b9bcba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAO0AAADtCAYAAABTTfKPAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b7f6eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAO0AAADtCAYAAABTTfKPAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11c927390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i, c in enumerate(cut_approx(multicomp_maze_circ())):\n",
    "    plt.matshow(c, cmap='viridis')\n",
    "    plt.grid(False)\n",
    "    plt.gca().axes.get_xaxis().set_ticks([])\n",
    "    plt.gca().axes.get_yaxis().set_ticks([])\n",
    "    plt.savefig('circ_cut_{}.pdf'.format(i), bbox_inches='tight')\n",
    "    plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}