Demo of region's AZP (21st of July 2017)

tryout_region_azp.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from region.azp import azp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "import pandas as pd\n",
    "import geopandas as gpd\n",
    "from shapely.geometry import Polygon"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Example 1: 3x3 lattice"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Inputs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd7424a7a20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "geometry = [\n",
    "    Polygon([(x, y),\n",
    "             (x, y+1),\n",
    "             (x+1, y+1),\n",
    "             (x+1, y)]) for y in range(3) for x in range(3)\n",
    "]\n",
    "\n",
    "areas_gdf = gpd.GeoDataFrame(\n",
    "    {\"values\": [726.7, 623.6, 487.3,\n",
    "                200.4, 245.0, 481.0,\n",
    "                170.9, 225.9, 226.9]},\n",
    "    geometry=geometry)\n",
    "areas_gdf.plot(column=\"values\")\n",
    "plt.gca().invert_yaxis()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Clustering"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step 1\n",
      "Init with:  [{0, 1, 3, 6, 7}, {8, 2, 4, 5}]\n",
      "=============================================\n",
      "step 2\n",
      "obj_value: 4086.8\n",
      "[{0, 1, 3, 6, 7}, {8, 2, 4, 5}]\n",
      "-----------------------------------\n",
      "step 3\n",
      "step 4\n",
      "step 5\n",
      "step 5 loop\n",
      "  move 7 from {0, 1, 3, 6, 7} to {8, 2, 4, 5}\n",
      "step 4\n",
      "step 5\n",
      "step 5 loop\n",
      "  move 6 from {0, 1, 3, 6} to {8, 2, 4, 5, 7}\n",
      "step 4\n",
      "step 5\n",
      "step 5 loop\n",
      "  move 3 from {0, 1, 3} to {2, 4, 5, 6, 7, 8}\n",
      "step 4\n",
      "step 5\n",
      "step 5 loop\n",
      "step 5 loop\n",
      "step 3\n",
      "step 4\n",
      "step 5\n",
      "step 5 loop\n",
      "step 5 loop\n",
      "step 5 loop\n",
      "  move 2 from {2, 3, 4, 5, 6, 7, 8} to {0, 1}\n",
      "step 4\n",
      "step 5\n",
      "step 5 loop\n",
      "step 5 loop\n",
      "  move 5 from {3, 4, 5, 6, 7, 8} to {0, 1, 2}\n",
      "step 4\n",
      "step 5\n",
      "step 5 loop\n",
      "step 5 loop\n",
      "step 5 loop\n",
      "=============================================\n",
      "step 2\n",
      "obj_value: 1222.8\n",
      "[{0, 1, 2, 5}, {3, 4, 6, 7, 8}]\n",
      "-----------------------------------\n",
      "step 3\n",
      "step 4\n",
      "step 5\n",
      "step 5 loop\n",
      "step 5 loop\n",
      "step 3\n",
      "step 4\n",
      "step 5\n",
      "step 5 loop\n",
      "step 5 loop\n",
      "step 5 loop\n"
     ]
    }
   ],
   "source": [
    "regions_dict1 = azp(areas=areas_gdf,\n",
    "                    data=[\"values\"],\n",
    "                    num_regions=2,\n",
    "                    contiguity=\"rook\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAQIAAAD8CAYAAACcoKqNAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd7424ab2e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "areas_gdf[\"region\"] = pd.Series(regions_dict1)\n",
    "areas_gdf.plot(column=\"region\", cmap='tab20c')\n",
    "plt.gca().invert_yaxis()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Example 2: A tricky toy example"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Inputs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Clusterpy's AZP algorithm is having trouble with the following toy example.](http://yogabonito-gsoc.blogspot.com/2017/07/clusterpy-infinite-loop-in-azp.html) It gets caught in an infinite loop jumping back and forth between the only two feasible solutions (which happen to be both optimal). Let's see whether the AZP algorithm of PySAL `region` suffers from the same problem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fd7422f8a20>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAX0AAACSCAYAAACpHBqyAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nGKteEXakAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd73ea5c7b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "squares = [\n",
    "    Polygon([(x,   0),\n",
    "             (x,   1),\n",
    "             (x+1, 1),\n",
    "             (x+1, 0)]) for x in range(3)\n",
    "]\n",
    "values = [0, 1, 0]\n",
    "squares_gdf = gpd.GeoDataFrame({\"values\": values},\n",
    "                           geometry=squares)\n",
    "squares_gdf.plot(column=\"values\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Clustering"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step 1\n",
      "Init with:  [{0}, {1, 2}]\n",
      "=============================================\n",
      "step 2\n",
      "obj_value: 1.0\n",
      "[{0}, {1, 2}]\n",
      "-----------------------------------\n",
      "step 3\n",
      "step 4\n",
      "step 5\n",
      "step 5 loop\n",
      "  move 1 from {1, 2} to {0}\n",
      "step 4\n",
      "step 5\n",
      "step 3\n",
      "step 4\n",
      "step 5\n",
      "step 5 loop\n",
      "  move 1 from {0, 1} to {2}\n",
      "step 4\n",
      "step 5\n"
     ]
    }
   ],
   "source": [
    "regions_dict2 = azp(areas=squares_gdf,\n",
    "                    data=\"values\",\n",
    "                    num_regions=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAX0AAACSCAYAAACpHBqyAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd742437a20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "squares_gdf[\"region\"] = pd.Series(regions_dict2)\n",
    "squares_gdf.plot(column=\"region\", cmap='tab20c')\n",
    "plt.gca().invert_yaxis()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "No infinite loop in `region`'s implementation. Nice!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# Example 3: Islands"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "islands_geometry = [\n",
    "    Polygon([(x, y),\n",
    "             (x, y+1),\n",
    "             (x+1, y+1),\n",
    "             (x+1, y)]) for y in range(3) for x in range(3)\n",
    "] + [\n",
    "    Polygon([(x, y),\n",
    "             (x, y+1),\n",
    "             (x+1, y+1),\n",
    "             (x+1, y)]) for y in range(4,6) for x in range(5,8)\n",
    "]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "islands_gdf = gpd.GeoDataFrame(\n",
    "    {\"values\": [726.7, 623.6, 487.3,\n",
    "                200.4, 245.0, 481.0,\n",
    "                170.9, 225.9, 226.9] +\n",
    "               [100,   120,   190,\n",
    "                175,   185,   210]},\n",
    "    geometry=islands_geometry)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAUEAAAD8CAYAAADpLRYuAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd73ea9f470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "islands_gdf.plot(column=\"values\")\n",
    "plt.gca().invert_yaxis()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step 1\n",
      "Init with:  [{0, 1, 2, 3, 4, 5, 6}, {8, 7}]\n",
      "=============================================\n",
      "step 2\n",
      "obj_value: 5513.2\n",
      "[{0, 1, 2, 3, 4, 5, 6}, {8, 7}]\n",
      "-----------------------------------\n",
      "step 3\n",
      "step 4\n",
      "step 5\n",
      "step 5 loop\n",
      "  move 6 from {0, 1, 2, 3, 4, 5, 6} to {8, 7}\n",
      "step 4\n",
      "step 5\n",
      "step 5 loop\n",
      "  move 3 from {0, 1, 2, 3, 4, 5} to {8, 6, 7}\n",
      "step 4\n",
      "step 5\n",
      "step 5 loop\n",
      "step 5 loop\n",
      "step 5 loop\n",
      "  move 4 from {0, 1, 2, 4, 5} to {8, 3, 6, 7}\n",
      "step 4\n",
      "step 5\n",
      "step 5 loop\n",
      "step 5 loop\n",
      "step 3\n",
      "step 4\n",
      "step 5\n",
      "step 5 loop\n",
      "step 5 loop\n",
      "step 5 loop\n",
      "=============================================\n",
      "step 2\n",
      "obj_value: 1222.8\n",
      "[{0, 1, 2, 5}, {8, 3, 4, 6, 7}]\n",
      "-----------------------------------\n",
      "step 3\n",
      "step 4\n",
      "step 5\n",
      "step 5 loop\n",
      "step 5 loop\n",
      "step 5 loop\n",
      "step 3\n",
      "step 4\n",
      "step 5\n",
      "step 5 loop\n",
      "step 5 loop\n",
      "Init with:  [{9, 10, 11, 12, 13, 14}]\n",
      "=============================================\n",
      "step 2\n",
      "obj_value: 770.0\n",
      "[{9, 10, 11, 12, 13, 14}]\n",
      "-----------------------------------\n",
      "step 3\n",
      "step 4\n",
      "step 5\n"
     ]
    }
   ],
   "source": [
    "regions_dict3 = azp(areas=islands_gdf,\n",
    "                    data=[\"values\"],\n",
    "                    num_regions=3,\n",
    "                    contiguity=\"rook\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAUEAAAD8CAYAAADpLRYuAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ntP8GaFAuNfo1NOIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd73e9f1b70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "islands_gdf[\"region\"] = pd.Series(regions_dict3)\n",
    "islands_gdf.plot(column=\"region\", cmap='tab20c')\n",
    "plt.gca().invert_yaxis()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}