{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline\n",
    "import pysal as ps\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "ntw = ps.Network(ps.examples.get_path('geodanet/streets.shp'))\n",
    "\n",
    "#Snap a point pattern to the network\n",
    "ntw.snapobservations(ps.examples.get_path('geodanet/crimes.shp'), 'crimes', attribute=True)\n",
    "ntw.snapobservations(ps.examples.get_path('geodanet/schools.shp'), 'schools', attribute=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "####A network is composed of a single topological representation of a road and $n$ point patterns which are snapped to the network."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'crimes': <pysal.network.network.PointPattern instance at 0x107fb1710>,\n",
       " 'schools': <pysal.network.network.PointPattern instance at 0x107fc1b90>}"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ntw.pointpatterns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['__doc__',\n",
       " '__init__',\n",
       " '__module__',\n",
       " 'dist_to_node',\n",
       " 'npoints',\n",
       " 'obs_to_edge',\n",
       " 'obs_to_node',\n",
       " 'points',\n",
       " 'snapped_coordinates']"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dir(ntw.pointpatterns['crimes'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#####Attributes for every point pattern\n",
    "\n",
    "1. dist_to_node dict keyed by pointid with the value being a dict in the form {node: distance to node, node: distance to node}\n",
    "2. obs_to_edge dict keyed by edge with the value being a dict in the form {pointID:(x-coord, y-coord), pointID:(x-coord, y-coord), ... }\n",
    "3. obs_to_node\n",
    "4. points geojson like representation of the point pattern.  Includes properties if read with attributes=True\n",
    "5. snapped_coordinates dict keyed by pointid with the value being (x-coord, y-coord)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "####Counts per edge are important, but should not be precomputed since we have different representations of the network (digitized and graph currently).  (Relatively) Uniform segmentation still needs to be done."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.6822429906542058"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "counts = ntw.count_per_edge(ntw.pointpatterns['crimes'].obs_to_edge,\n",
    "                            graph=False)\n",
    "sum(counts.values()) / float(len(counts.keys()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Segmentation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "n200 = ntw.segment_edges(200.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.0354609929078014"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "counts = n200.count_per_edge(n200.pointpatterns['crimes'].obs_to_edge, graph=False)\n",
    "sum(counts.values()) / float(len(counts.keys()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Visualization of the shapefile derived, unsegmented network with nodes in a larger, semi-opaque form and the distance segmented network with small, fully opaque nodes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a085350>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import networkx as nx\n",
    "figsize(10,10)\n",
    "\n",
    "g = nx.Graph()\n",
    "for e in ntw.edges:\n",
    "    g.add_edge(*e)\n",
    "for n, p in ntw.node_coords.iteritems():\n",
    "    g.node[n] = p\n",
    "nx.draw(g, ntw.node_coords, node_size=300, alpha=0.5)\n",
    "\n",
    "g = nx.Graph()\n",
    "for e in n200.edges:\n",
    "    g.add_edge(*e)\n",
    "for n, p in n200.node_coords.iteritems():\n",
    "    g.node[n] = p\n",
    "nx.draw(g, n200.node_coords, node_size=25, alpha=1.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#####Moran's I using the digitized network"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['EI', 'EI_sim', 'I', 'VI_norm', 'VI_rand', 'VI_sim', '_Moran__calc', '_Moran__moments', '__doc__', '__init__', '__module__', 'n', 'p_norm', 'p_rand', 'p_sim', 'p_z_sim', 'permutations', 'seI_norm', 'seI_rand', 'seI_sim', 'sim', 'w', 'y', 'z', 'z2ss', 'z_norm', 'z_rand', 'z_sim']\n"
     ]
    }
   ],
   "source": [
    "#Binary Adjacency\n",
    "#ntw.contiguityweights(graph=False)\n",
    "\n",
    "w = ntw.contiguityweights(graph=False)\n",
    "\n",
    "\n",
    "#Build the y vector\n",
    "#edges = ntw.w.neighbors.keys()\n",
    "edges = w.neighbors.keys()\n",
    "y = np.zeros(len(edges))\n",
    "for i, e in enumerate(edges):\n",
    "    if e in counts.keys():\n",
    "        y[i] = counts[e]\n",
    "\n",
    "#Moran's I\n",
    "#res = ps.esda.moran.Moran(y, ntw.w, permutations=99)\n",
    "res = ps.esda.moran.Moran(y, w, permutations=99)\n",
    "print dir(res)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "####Moran's I using the graph representation to generate the W\n",
    "\n",
    "Note that we have to regenerate the counts per edge, since the graph will have less edges."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['EI', 'EI_sim', 'I', 'VI_norm', 'VI_rand', 'VI_sim', '_Moran__calc', '_Moran__moments', '__doc__', '__init__', '__module__', 'n', 'p_norm', 'p_rand', 'p_sim', 'p_z_sim', 'permutations', 'seI_norm', 'seI_rand', 'seI_sim', 'sim', 'w', 'y', 'z', 'z2ss', 'z_norm', 'z_rand', 'z_sim']\n"
     ]
    }
   ],
   "source": [
    "counts = ntw.count_per_edge(ntw.pointpatterns['crimes'].obs_to_edge, graph=True)\n",
    "\n",
    "#Binary Adjacency\n",
    "#ntw.contiguityweights(graph=True)\n",
    "w = ntw.contiguityweights(graph=True)\n",
    "#Build the y vector\n",
    "#edges = ntw.w.neighbors.keys()\n",
    "edges = w.neighbors.keys()\n",
    "y = np.zeros(len(edges))\n",
    "for i, e in enumerate(edges):\n",
    "    if e in counts.keys():\n",
    "        y[i] = counts[e]\n",
    "\n",
    "#Moran's I\n",
    "#res = ps.esda.moran.Moran(y, ntw.w, permutations=99)\n",
    "res = ps.esda.moran.Moran(y, w, permutations=99)\n",
    "\n",
    "\n",
    "print dir(res)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Moran's I using the segmented network and intensities instead of counts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['EI', 'EI_sim', 'I', 'VI_norm', 'VI_rand', 'VI_sim', '_Moran__calc', '_Moran__moments', '__doc__', '__init__', '__module__', 'n', 'p_norm', 'p_rand', 'p_sim', 'p_z_sim', 'permutations', 'seI_norm', 'seI_rand', 'seI_sim', 'sim', 'w', 'y', 'z', 'z2ss', 'z_norm', 'z_rand', 'z_sim']\n"
     ]
    }
   ],
   "source": [
    "#Binary Adjacency\n",
    "#n200.contiguityweights(graph=False)\n",
    "w = n200.contiguityweights(graph=False)\n",
    "\n",
    "\n",
    "#Compute the counts\n",
    "counts = n200.count_per_edge(n200.pointpatterns['crimes'].obs_to_edge, graph=False)\n",
    "\n",
    "#Build the y vector and convert from raw counts to intensities\n",
    "#edges = n200.w.neighbors.keys()\n",
    "edges = w.neighbors.keys()\n",
    "y = np.zeros(len(edges))\n",
    "for i, e in enumerate(edges):\n",
    "    if e in counts.keys():\n",
    "        length = n200.edge_lengths[e]\n",
    "        y[i] = counts[e] / length\n",
    "      \n",
    "#Moran's I\n",
    "#res = ps.esda.moran.Moran(y, n200.w, permutations=99)\n",
    "res = ps.esda.moran.Moran(y, w, permutations=99)\n",
    "\n",
    "\n",
    "print dir(res)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Timings for distance based methods, e.g. G-function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.19567084312\n"
     ]
    }
   ],
   "source": [
    "import time\n",
    "t1 = time.time()\n",
    "n0 = ntw.allneighbordistances(ntw.pointpatterns['crimes'])\n",
    "print time.time()-t1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "11.2402291298\n"
     ]
    }
   ],
   "source": [
    "import time\n",
    "t1 = time.time()\n",
    "n1 = n200.allneighbordistances(n200.pointpatterns['crimes'])\n",
    "print time.time()-t1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that the first time these methods are called, the underlying node-to-node shortest path distance matrix has to be calculated. Subsequent calls will not require this, and will be much faster:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.136250972748\n"
     ]
    }
   ],
   "source": [
    "import time\n",
    "t1 = time.time()\n",
    "n0 = ntw.allneighbordistances(ntw.pointpatterns['crimes'])\n",
    "print time.time()-t1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.160092830658\n"
     ]
    }
   ],
   "source": [
    "import time\n",
    "t1 = time.time()\n",
    "n1 = n200.allneighbordistances(n200.pointpatterns['crimes'])\n",
    "print time.time()-t1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "####Simulate a point pattern on the network\n",
    "\n",
    "Need to supply a count of the number of points and a distirbution (default is uniform).  Generally this will not be called by the user, since the simulation will be used for Monte Carlo permutation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<pysal.network.network.SimulatedPointPattern instance at 0x1208e2878>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "npts = ntw.pointpatterns['crimes'].npoints\n",
    "sim = ntw.simulate_observations(npts)\n",
    "sim"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "####Create a nearest neighbor matrix using the crimes point pattern\n",
    "\n",
    "Right now, both the G and K functions generate a full distance matrix.  This is because, I know that the full generation is correct and I believe that the truncated generated, e.g. nearest neighbor, has a big."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### G-function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "gres = ps.NetworkG(ntw,\n",
    "                         ntw.pointpatterns['crimes'],\n",
    "                         permutations = 99)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x10bb0d690>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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       "u+reDPxV0juxPf7ZM1yzPemjw9743De5PvNGbH/RMG9+buB32EGoTdgWUVkv1h0GnATCM7zmrbqH\n",
       "YBP+L9gR8qJerPtHV90bgQ7u/tw6WVopFdR87shNpZTyJk2CSqmgpklQKRXUNAkqpYKaJkGlVFDT\n",
       "JKiUCmqaBJVSQU2ToFIqqP0/uwZUr/oksQYAAAAASUVORK5CYII=\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10aedb510>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figsize(5,5)\n",
    "plot(gres.xaxis, gres.observed, 'b-', linewidth=1.5, label='Observed')\n",
    "plot(gres.xaxis, gres.upperenvelope, 'r--', label='Upper')\n",
    "plot(gres.xaxis, gres.lowerenvelope, 'k--', label='Lower')\n",
    "legend(loc='best')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###K-function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/serge/Dropbox/p/pysal/src/pysal/pysal/network/analysis.py:142: RuntimeWarning: invalid value encountered in less_equal\n",
      "  y[i] = len(nearest[nearest <= s])\n"
     ]
    }
   ],
   "source": [
    "kres = ps.NetworkK(ntw,\n",
    "                         ntw.pointpatterns['crimes'],\n",
    "                         permutations=99)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x12143c7d0>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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       "hBAuSHIUQggXJDkKIYQL/w/TVxujD//IPwAAAABJRU5ErkJggg==\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10aeb22d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figsize(5,5)\n",
    "plot(kres.xaxis, kres.observed, 'b-', linewidth=1.5, label='Observed')\n",
    "plot(kres.xaxis, kres.upperenvelope, 'r--', label='Upper')\n",
    "plot(kres.xaxis, kres.lowerenvelope, 'k--', label='Lower')\n",
    "legend(loc='best')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
