Max-P-Regions exact

max_p_regions_exact.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "from matplotlib import pyplot as plt\n",
    "import libpysal as ps\n",
    "import geopandas as gpd\n",
    "from shapely.geometry import Polygon"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Making the lattice"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We are generating a 3x3 lattice: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{0: [3, 1],\n",
       " 1: [0, 4, 2],\n",
       " 2: [1, 5],\n",
       " 3: [0, 6, 4],\n",
       " 4: [1, 3, 7, 5],\n",
       " 5: [2, 4, 8],\n",
       " 6: [3, 7],\n",
       " 7: [4, 6, 8],\n",
       " 8: [5, 7]}"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lat_w = ps.weights.util.lat2W(nrows=3, ncols=3, rook=True, id_type=\"int\")\n",
    "neighbor_dict = lat_w.neighbors\n",
    "neighbor_dict"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Defining the data (_hardcoded_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{0: 350.2,\n",
       " 1: 400.5,\n",
       " 2: 430.8,\n",
       " 3: 490.4,\n",
       " 4: 410.9,\n",
       " 5: 450.4,\n",
       " 6: 560.1,\n",
       " 7: 500.7,\n",
       " 8: 498.6}"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "value_list = [350.2, 400.5, 430.8,\n",
    "              490.4, 410.9, 450.4,\n",
    "              560.1, 500.7, 498.6]\n",
    "value_dict = {area: value \n",
    "              for area, value in zip(neighbor_dict.keys(),\n",
    "                                     value_list)}\n",
    "value_dict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{0: 30, 1: 25, 2: 31, 3: 28, 4: 32, 5: 30, 6: 35, 7: 27, 8: 33}"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "spatially_extensive_attr_list = [30, 25, 31,\n",
    "                                 28, 32, 30,\n",
    "                                 35, 27, 33]\n",
    "spatially_extensive_attr_dict = {area: value \n",
    "    for area, value in zip(neighbor_dict.keys(),\n",
    "                           spatially_extensive_attr_list)}\n",
    "spatially_extensive_attr_dict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f509123acc0>"
      ]
     },
     "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",
    "gdf = gpd.GeoDataFrame(\n",
    "    {\"values\": value_list},\n",
    "    geometry=geometry)\n",
    "gdf.plot(column=\"values\")\n",
    "plt.gca().invert_yaxis()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Solving the Max-p-Regions Problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "from region.max_p_regions.exact import MaxPExact"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "start solving with <pulp.solvers.COIN_CMD object at 0x7f5092f37278>\n",
      "solved\n"
     ]
    }
   ],
   "source": [
    "maxp = MaxPExact()\n",
    "#%timeit -n1 maxp.fit_from_dict(neighbor_dict, value_dict, spatially_extensive_attr_dict, threshold=120, solver=\"cbc\")\n",
    "maxp.fit_from_dict(neighbor_dict, value_dict, spatially_extensive_attr_dict, threshold=120, solver=\"cbc\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{0: 0, 1: 0, 2: 0, 3: 7, 4: 0, 5: 0, 6: 7, 7: 7, 8: 7}"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "maxp.labels_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f509118e3c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from region.util import array_from_dict_values\n",
    "labels_arr = array_from_dict_values(maxp.labels_)\n",
    "gdf[\"region\"] = labels_arr\n",
    "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
}