{
 "cells": [
  {
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   "execution_count": 2,
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     "start_time": "2022-09-02T11:13:12.165387Z"
    },
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   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-09-02T11:14:10.246402Z",
     "start_time": "2022-09-02T11:14:10.235135Z"
    },
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "class Walker:\n",
    "    \"\"\" The Walker knows how to walk at random on a context map. \"\"\"\n",
    "\n",
    "    def __init__(self, sigma_i, sigma_j, size, map_type='flat'):\n",
    "        self.sigma_i = sigma_i\n",
    "        self.sigma_j = sigma_j\n",
    "        self.size = size\n",
    "\n",
    "        if map_type == 'flat':\n",
    "            context_map = np.ones((size, size))\n",
    "        elif map_type == 'hills':\n",
    "            grid_ii, grid_jj = np.mgrid[0:size, 0:size]\n",
    "            i_waves = np.sin(grid_ii / 130) + np.sin(grid_ii / 10)\n",
    "            i_waves /= i_waves.max()\n",
    "            j_waves = np.sin(grid_jj / 100) + np.sin(grid_jj / 50) + \\\n",
    "                np.sin(grid_jj / 10)\n",
    "            j_waves /= j_waves.max()\n",
    "            context_map = j_waves + i_waves\n",
    "        elif map_type == 'labyrinth':\n",
    "            context_map = np.ones((size, size))\n",
    "            context_map[50:100, 50:60] = 0\n",
    "            context_map[20:89, 80:90] = 0\n",
    "            context_map[90:120, 0:10] = 0\n",
    "            context_map[120:size, 30:40] = 0\n",
    "            context_map[180:190, 50:60] = 0\n",
    "\n",
    "            context_map[50:60, 50:200] = 0\n",
    "            context_map[179:189, 80:130] = 0\n",
    "            context_map[110:120, 0:190] = 0\n",
    "            context_map[120:size, 30:40] = 0\n",
    "            context_map[180:190, 50:60] = 0\n",
    "        context_map /= context_map.sum()\n",
    "        self.context_map = context_map\n",
    "\n",
    "        # Pre-compute a 2D grid of coordinates for efficiency\n",
    "        self._grid_ii, self._grid_jj = np.mgrid[0:size, 0:size]\n",
    "\n",
    "walker = Walker(sigma_i=3, sigma_j=4, size=200, map_type='hills')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
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     "start_time": "2022-09-02T11:15:44.351558Z"
    },
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   },
   "outputs": [],
   "source": [
    "class Walker:\n",
    "    \"\"\" The Walker knows how to walk at random on a context map. \"\"\"\n",
    "\n",
    "    def __init__(self, sigma_i, sigma_j, size, context_map):\n",
    "        self.sigma_i = sigma_i\n",
    "        self.sigma_j = sigma_j\n",
    "        self.size = size\n",
    "        self.context_map = context_map\n",
    "        # Pre-compute a 2D grid of coordinates for efficiency\n",
    "        self._grid_ii, self._grid_jj = np.mgrid[0:size, 0:size]\n",
    "\n",
    "    @classmethod\n",
    "    def from_context_map_type(cls, sigma_i, sigma_j, size, map_type):\n",
    "        \"\"\" Create an instance of Walker with a context map defined by type.\"\"\"\n",
    "        if map_type == 'flat':\n",
    "            context_map = np.ones((size, size))\n",
    "        elif map_type == 'hills':\n",
    "            grid_ii, grid_jj = np.mgrid[0:size, 0:size]\n",
    "            i_waves = np.sin(grid_ii / 130) + np.sin(grid_ii / 10)\n",
    "            i_waves /= i_waves.max()\n",
    "            j_waves = np.sin(grid_jj / 100) + np.sin(grid_jj / 50) +\\\n",
    "                np.sin(grid_jj / 10)\n",
    "            j_waves /= j_waves.max()\n",
    "            context_map = j_waves + i_waves\n",
    "        elif map_type == 'labyrinth':\n",
    "            context_map = np.ones((size, size))\n",
    "            context_map[50:100, 50:60] = 0\n",
    "            context_map[20:89, 80:90] = 0\n",
    "            context_map[90:120, 0:10] = 0\n",
    "            context_map[120:size, 30:40] = 0\n",
    "            context_map[180:190, 50:60] = 0\n",
    "\n",
    "            context_map[50:60, 50:200] = 0\n",
    "            context_map[179:189, 80:130] = 0\n",
    "            context_map[110:120, 0:190] = 0\n",
    "            context_map[120:size, 30:40] = 0\n",
    "            context_map[180:190, 50:60] = 0\n",
    "\n",
    "            context_map /= context_map.sum()\n",
    "        return cls(sigma_i, sigma_j, size, context_map)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-09-02T11:15:49.092194Z",
     "start_time": "2022-09-02T11:15:49.086575Z"
    },
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "walker = Walker.from_context_map_type(sigma_i=3, sigma_j=4, size=200, map_type='hills')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-09-02T11:19:37.723607Z",
     "start_time": "2022-09-02T11:19:37.717518Z"
    },
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   },
   "outputs": [],
   "source": [
    "def flat_context_map_builder(size):\n",
    "    \"\"\" A context map where all positions are equally likely. \"\"\"\n",
    "    return np.ones((size, size))\n",
    "\n",
    "\n",
    "def hills_context_map_builder(size):\n",
    "    \"\"\" A context map with bumps and valleys. \"\"\"\n",
    "    grid_ii, grid_jj = np.mgrid[0:size, 0:size]\n",
    "    i_waves = np.sin(grid_ii / 130) + np.sin(grid_ii / 10)\n",
    "    i_waves /= i_waves.max()\n",
    "    j_waves = np.sin(grid_jj / 100) + np.sin(grid_jj / 50) + \\\n",
    "        np.sin(grid_jj / 10)\n",
    "    j_waves /= j_waves.max()\n",
    "    context_map = j_waves + i_waves\n",
    "    return context_map\n",
    "\n",
    "\n",
    "def labyrinth_context_map_builder(size):\n",
    "    \"\"\" A context map that looks like a labyrinth. \"\"\"\n",
    "    context_map = np.ones((size, size))\n",
    "    context_map[50:100, 50:60] = 0\n",
    "    context_map[20:89, 80:90] = 0\n",
    "    context_map[90:120, 0:10] = 0\n",
    "    context_map[120:size, 30:40] = 0\n",
    "    context_map[180:190, 50:60] = 0\n",
    "\n",
    "    context_map[50:60, 50:200] = 0\n",
    "    context_map[179:189, 80:130] = 0\n",
    "    context_map[110:120, 0:190] = 0\n",
    "    context_map[120:size, 30:40] = 0\n",
    "    context_map[180:190, 50:60] = 0\n",
    "\n",
    "    return context_map"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-09-02T11:20:25.815725Z",
     "start_time": "2022-09-02T11:20:25.811489Z"
    },
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class Walker:\n",
    "\n",
    "    def __init__(self, sigma_i, sigma_j, size, context_map):\n",
    "        self.sigma_i = sigma_i\n",
    "        self.sigma_j = sigma_j\n",
    "        self.size = size\n",
    "        self.context_map = context_map\n",
    "        # Pre-compute a 2D grid of coordinates for efficiency\n",
    "        self._grid_ii, self._grid_jj = np.mgrid[0:size, 0:size]\n",
    "\n",
    "    @classmethod\n",
    "    def from_context_map_builder(cls, sigma_i, sigma_j, size, context_map_builder):\n",
    "        \"\"\"Initialize the context map from an external builder.\n",
    "\n",
    "        `builder` is a callable that takes a `size` as input parameter\n",
    "        and outputs a `size` x `size` numpy array of positive values.\n",
    "        \"\"\"\n",
    "        context_map = context_map_builder(size)\n",
    "        context_map /= context_map.sum()\n",
    "        return cls(sigma_i, sigma_j, size, context_map)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-09-02T11:20:26.367914Z",
     "start_time": "2022-09-02T11:20:26.362287Z"
    },
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "walker = Walker.from_context_map_builder(\n",
    "    sigma_i=3, \n",
    "    sigma_j=4, \n",
    "    size=200, \n",
    "    context_map_builder=hills_context_map_builder,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a"
   ]
  }
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