05_spatial_weights.ipynb

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      "import pysal as ps\n",
      "import numpy as np\n",
      "%pylab inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      }
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     "cell_type": "heading",
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     "metadata": {},
     "source": [
      "Regular Lattice Weights "
     ]
    },
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     "input": [
      "w = ps.lat2W()"
     ],
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     "prompt_number": 2
    },
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     "cell_type": "code",
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     "cell_type": "markdown",
     "metadata": {},
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      "$s_0 = \\sum_i \\sum_j w_{i,j}$"
     ]
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      "w.s0"
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    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$pctnonzero = s_0 / n^2$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "w.s0 / w.n**2"
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      "Queen Contiguity"
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      "wq = ps.lat2W(rook=False)"
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    {
     "cell_type": "code",
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     "input": [
      "ps.w_difference?"
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    },
    {
     "cell_type": "code",
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     "input": [
      "wb.histogram"
     ],
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     "metadata": {},
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       "metadata": {},
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       "prompt_number": 25,
       "text": [
        "[(1, 4), (2, 12), (3, 0), (4, 9)]"
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     ],
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    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Spatial Lag"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$l_i = \\sum_{i,j} w_{i,j} y_j$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "y = np.arange(w.n)\n",
      "y"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
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        "array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,\n",
        "       17, 18, 19, 20, 21, 22, 23, 24])"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "wy = ps.lag_spatial(w,y)\n",
      "wy"
     ],
     "language": "python",
     "metadata": {},
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      {
       "metadata": {},
       "output_type": "pyout",
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        "array([  6.,   8.,  11.,  14.,  12.,  16.,  24.,  28.,  32.,  26.,  31.,\n",
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       ]
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    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "y *= 10"
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     "prompt_number": 30
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     "cell_type": "code",
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        "array([  0,  10,  20,  30,  40,  50,  60,  70,  80,  90, 100, 110, 120,\n",
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       ]
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     "cell_type": "code",
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      "wy = ps.lag_spatial(w,y)"
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    },
    {
     "cell_type": "markdown",
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     ]
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     "cell_type": "code",
     "collapsed": false,
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      "wry = ps.lag_spatial(w,y)"
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    {
     "cell_type": "code",
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        "\u001b[31mNAT.shp\u001b[m\u001b[m*    \u001b[31mmexico.csv\u001b[m\u001b[m* south.dbf   south.shp   usjoin.csv\r\n"
       ]
      }
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    {
     "cell_type": "code",
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     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 45,
       "text": [
        "0.0038620805880795125"
       ]
      }
     ],
     "prompt_number": 45
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "wsq = ps.queen_from_shapefile(\"data/south.shp\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 46
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "wsq.pct_nonzero"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 47,
       "text": [
        "0.004060701875466459"
       ]
      }
     ],
     "prompt_number": 47
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "wsouth.histogram"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 48,
       "text": [
        "[(1, 16),\n",
        " (2, 32),\n",
        " (3, 65),\n",
        " (4, 187),\n",
        " (5, 378),\n",
        " (6, 435),\n",
        " (7, 230),\n",
        " (8, 56),\n",
        " (9, 11),\n",
        " (10, 2)]"
       ]
      }
     ],
     "prompt_number": 48
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "wsq.histogram"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 49,
       "text": [
        "[(1, 16),\n",
        " (2, 29),\n",
        " (3, 54),\n",
        " (4, 141),\n",
        " (5, 306),\n",
        " (6, 437),\n",
        " (7, 319),\n",
        " (8, 86),\n",
        " (9, 18),\n",
        " (10, 5),\n",
        " (11, 1)]"
       ]
      }
     ],
     "prompt_number": 49
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "wh = np.array(wsouth.histogram)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 50
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "bar(wh[:,0],wh[:,1])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 51,
       "text": [
        "<Container object of 10 artists>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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hHMlnwHFgLrAHSzSVSrmEkXp/lmjUik6WaC4BfiGu/zywDHgT2Aasju2rga1t9CFJGqd2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\nJEmSVMT/Abmn5IA9vs6mAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x109947910>"
       ]
      }
     ],
     "prompt_number": 51
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "whq = np.array(wsq.histogram)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 52
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "bar(whq[:,0],whq[:,1])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 53,
       "text": [
        "<Container object of 11 artists>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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4JUJZZl/L86Oc4ttUr9dPbmdZRpZlHQ5FktKS5zl5nk/79WWu6LQReBf4E0Jd/hAwH9gF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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10b1a65d0>"
       ]
      }
     ],
     "prompt_number": 53
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Distance Based Weights"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x,y = np.indices((5,5))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 54
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x.shape = (25,1)\n",
      "y.shape = (25,1)\n",
      "data = np.hstack([x,y])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 55
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 56,
       "text": [
        "array([[0, 0],\n",
        "       [0, 1],\n",
        "       [0, 2],\n",
        "       [0, 3],\n",
        "       [0, 4],\n",
        "       [1, 0],\n",
        "       [1, 1],\n",
        "       [1, 2],\n",
        "       [1, 3],\n",
        "       [1, 4],\n",
        "       [2, 0],\n",
        "       [2, 1],\n",
        "       [2, 2],\n",
        "       [2, 3],\n",
        "       [2, 4],\n",
        "       [3, 0],\n",
        "       [3, 1],\n",
        "       [3, 2],\n",
        "       [3, 3],\n",
        "       [3, 4],\n",
        "       [4, 0],\n",
        "       [4, 1],\n",
        "       [4, 2],\n",
        "       [4, 3],\n",
        "       [4, 4]])"
       ]
      }
     ],
     "prompt_number": 56
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "knn weights"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "wknn3 = ps.knnW(data, k = 3)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 57
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "wknn3[0]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 58,
       "text": [
        "{1: 1.0, 5: 1.0, 6: 1.0}"
       ]
      }
     ],
     "prompt_number": 58
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "wknn3.histogram"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 59,
       "text": [
        "[(3, 25)]"
       ]
      }
     ],
     "prompt_number": 59
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Distance Bands"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "wdb = ps.threshold_binaryW_from_array(data,2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 60
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "wdb[0]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 61,
       "text": [
        "{1: 1, 2: 1, 5: 1, 6: 1, 10: 1}"
       ]
      }
     ],
     "prompt_number": 61
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "wdb.histogram"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 62,
       "text": [
        "[(5, 4), (6, 0), (7, 8), (8, 4), (9, 0), (10, 4), (11, 4), (12, 1)]"
       ]
      }
     ],
     "prompt_number": 62
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "wdb.cardinalities"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 63,
       "text": [
        "{0: 5,\n",
        " 1: 7,\n",
        " 2: 8,\n",
        " 3: 7,\n",
        " 4: 5,\n",
        " 5: 7,\n",
        " 6: 10,\n",
        " 7: 11,\n",
        " 8: 10,\n",
        " 9: 7,\n",
        " 10: 8,\n",
        " 11: 11,\n",
        " 12: 12,\n",
        " 13: 11,\n",
        " 14: 8,\n",
        " 15: 7,\n",
        " 16: 10,\n",
        " 17: 11,\n",
        " 18: 10,\n",
        " 19: 7,\n",
        " 20: 5,\n",
        " 21: 7,\n",
        " 22: 8,\n",
        " 23: 7,\n",
        " 24: 5}"
       ]
      }
     ],
     "prompt_number": 63
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Writing to external files"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "w = ps.rook_from_shapefile('data/nat.shp')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 64
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "w.n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 65,
       "text": [
        "3085"
       ]
      }
     ],
     "prompt_number": 65
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "gal = ps.open('data/nat_copy.gal', 'w')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 66
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "gal.write(w)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 67
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "gal.close()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 68
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "gal = ps.open('data/nat_copy.gal', 'r')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 69
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "w1 = gal.read()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 70
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "w1.n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 71,
       "text": [
        "3085"
       ]
      }
     ],
     "prompt_number": 71
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "w.pct_nonzero == w1.pct_nonzero"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 72,
       "text": [
        "True"
       ]
      }
     ],
     "prompt_number": 72
    }
   ],
   "metadata": {}
  }
 ]
}