Part 3 - Point pattern analysis.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Python for spatial analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 3 - Point pattern analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Distance Based Statistical Method (G function, F function, Ripley K)\n",
    "- Point simulation\n",
    "\n",
    "I recommend an open-source python library for the statistical analysis of point patterns - [pointpats](https://pointpats.readthedocs.io/en/master/#point-pattern-analysis-pointpats). Although it's a subpackage of PySAL, you need to install it specially via 'pip install pointpats'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pointpats import PointPattern, distance_statistics, PoissonPointProcess\n",
    "import geopandas as gpd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1. Statistical analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "point_data = gpd.read_file('../Data/BJ6Ring_POI_point.shp',encoding='utf-8')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "point_data = point_data.sample(1000,random_state=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "pattern = PointPattern(point_data, coord_names=['wgs84_x','wgs84_y'])\n",
    "# The first parameter of PointPattern can be (n,p) array, n points with p>=2 attributes. \n",
    "# The default is that the first two columns are x and y coordinates.\n",
    "# Or, you can the name of the two attributes representing spatial coordinates."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Point Pattern\n",
      "1000 points\n",
      "Bounding rectangle [(116.0976455,39.704590036), (116.69697417,40.162781676)]\n",
      "Area of window: 0.27460738620632696\n",
      "Intensity estimate for window: 3641.5626462743703\n",
      "           wgs84_x    wgs84_y                   mark_0  \\\n",
      "375496  116.271069  39.921151                  Leisure   \n",
      "110068  116.359717  39.971339              Residential   \n",
      "249749  116.274537  39.887298       Daily Life Service   \n",
      "361390  116.301160  39.977463       Daily Life Service   \n",
      "260324  116.403919  39.888717  Government & Enterprise   \n",
      "\n",
      "                            mark_1  \n",
      "375496  POINT (116.27107 39.92115)  \n",
      "110068  POINT (116.35972 39.97134)  \n",
      "249749  POINT (116.27454 39.88730)  \n",
      "361390  POINT (116.30116 39.97746)  \n",
      "260324  POINT (116.40392 39.88872)  \n"
     ]
    }
   ],
   "source": [
    "pattern.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Mean Nearest Neighbor Distance Statistics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The mean distance ($\\overline d_{min}$) between points and their nearest neighbour is assumed to be normally distributed for completely spatial random (CSR) distribution. We can test whether the target distribution is the outcome of CSR or not."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
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       "        [2.73868322e-03],\n",
       "        [4.52926467e-03],\n",
       "        [3.48156883e-03],\n",
       "        [1.96390041e-02],\n",
       "        [6.08232030e-03],\n",
       "        [4.61561019e-03],\n",
       "        [9.77401578e-03],\n",
       "        [4.07891833e-03],\n",
       "        [8.05683836e-03],\n",
       "        [4.11143631e-03],\n",
       "        [1.89957946e-03],\n",
       "        [3.37609683e-03],\n",
       "        [2.03470685e-03],\n",
       "        [2.73868322e-03],\n",
       "        [5.10034340e-03],\n",
       "        [2.22794655e-03],\n",
       "        [6.70225297e-03],\n",
       "        [2.85405893e-03],\n",
       "        [2.43010300e-03],\n",
       "        [7.35102430e-04],\n",
       "        [1.19875424e-02],\n",
       "        [4.65613463e-03],\n",
       "        [6.20495148e-03],\n",
       "        [1.77463818e-02],\n",
       "        [3.73491703e-03],\n",
       "        [1.23651134e-02],\n",
       "        [1.48682732e-03],\n",
       "        [1.04448462e-02],\n",
       "        [4.65929459e-04],\n",
       "        [2.01497891e-03]]))"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pattern.knn() # the default is the one nearest neighbor"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Outcome: \n",
    "- tuple[0]: the id of the first nearest neighbour of each data point;\n",
    "- tuple[1]: corresponding distances"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([[ 47, 314],\n",
       "        [214, 100],\n",
       "        [437, 223],\n",
       "        ...,\n",
       "        [893, 841],\n",
       "        [330, 539],\n",
       "        [556, 159]]),\n",
       " array([[0.00517433, 0.00719137],\n",
       "        [0.00089308, 0.00097563],\n",
       "        [0.00519695, 0.00638598],\n",
       "        ...,\n",
       "        [0.01044485, 0.01370155],\n",
       "        [0.00046593, 0.00198717],\n",
       "        [0.00201498, 0.00998277]]))"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pattern.knn(2)   # the first two nearest neighbors and corresponding distances"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "       [2.73868322e-03],\n",
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       "       [6.70225297e-03],\n",
       "       [2.85405893e-03],\n",
       "       [2.43010300e-03],\n",
       "       [7.35102430e-04],\n",
       "       [1.19875424e-02],\n",
       "       [4.65613463e-03],\n",
       "       [6.20495148e-03],\n",
       "       [1.77463818e-02],\n",
       "       [3.73491703e-03],\n",
       "       [1.23651134e-02],\n",
       "       [1.48682732e-03],\n",
       "       [1.04448462e-02],\n",
       "       [4.65929459e-04],\n",
       "       [2.01497891e-03]])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pattern.nnd   # tuple[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pattern.min_nnd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.04351532361039509"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pattern.max_nnd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.005384654735421558"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pattern.mean_nnd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pattern.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Nearest Neighbor Analysis Functions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**$G$-function (event-event)** measures the proportion of nearest neighbor distances that are less than $d$. The target point $point_i$ only include those whose distance to the marginal is larger than $d$.\n",
    "\n",
    "$$G(d)=\\frac{\\sum_i^N I_i(d)}{N},\\ I_i(d)=\n",
    "\\left\\{ \n",
    "             \\begin{array}{cl}\n",
    "             1, & if\\ \\overline d_{min}(point_i)<d; \\\\\n",
    "             0, & else\n",
    "             \\end{array}\n",
    "\\right.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For CSR pattern, the expectation of $G-$function is:\n",
    "\n",
    "$$E[G(d)]=1-e^{-\\lambda\\pi d^2}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then we can calculate the max difference of the $G-$function between the target and the CSR distributions:\n",
    "\n",
    "$$\n",
    "D_d = max|E[G(d)]-G(d)|\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "gf = distance_statistics.G(pattern, intervals=20)\n",
    "gf.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "gf.plot(qq=True)   #quantile-quantile plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.        , 0.00217577, 0.00435153, 0.0065273 , 0.00870306,\n",
       "       0.01087883, 0.0130546 , 0.01523036, 0.01740613, 0.0195819 ,\n",
       "       0.02175766, 0.02393343, 0.02610919, 0.02828496, 0.03046073,\n",
       "       0.03263649, 0.03481226, 0.03698803, 0.03916379, 0.04133956,\n",
       "       0.04351532, 0.04569109])"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# x values in the plot\n",
    "gf.d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.002, 0.259, 0.575, 0.75 , 0.837, 0.885, 0.923, 0.944, 0.955,\n",
       "       0.971, 0.974, 0.979, 0.985, 0.987, 0.992, 0.993, 0.996, 0.996,\n",
       "       0.997, 0.999, 1.   , 1.   ])"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# y values in the plot\n",
    "gf.G"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is obvious that the $G$ grows quicker than the CSR when $d$ is small, and then slowly increases at large $d$. It then comes a reasonable assumption that the points are clustered compared to CSR. Then we need to simulate CSR many times (such as >1000) to come to a final conclusion based on significant tests. We can use **Simulation Envelopes** to achieve such simulations and significance test."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<pointpats._deprecated_distance_statistics.Genv at 0x7fb5f458ea58>"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "realizations = PoissonPointProcess(pattern.window, pattern.n, 100, asPP=True) # simulate CSR 100 times\n",
    "genv = distance_statistics.Genv(pattern, intervals=20, realizations=realizations) # call Genv to generate simulation envelope\n",
    "genv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.        , 0.002     ],\n",
       "       [0.00217577, 0.259     ],\n",
       "       [0.00435153, 0.575     ],\n",
       "       [0.0065273 , 0.75      ],\n",
       "       [0.00870306, 0.837     ],\n",
       "       [0.01087883, 0.885     ],\n",
       "       [0.0130546 , 0.923     ],\n",
       "       [0.01523036, 0.944     ],\n",
       "       [0.01740613, 0.955     ],\n",
       "       [0.0195819 , 0.971     ],\n",
       "       [0.02175766, 0.974     ],\n",
       "       [0.02393343, 0.979     ],\n",
       "       [0.02610919, 0.985     ],\n",
       "       [0.02828496, 0.987     ],\n",
       "       [0.03046073, 0.992     ],\n",
       "       [0.03263649, 0.993     ],\n",
       "       [0.03481226, 0.996     ],\n",
       "       [0.03698803, 0.996     ],\n",
       "       [0.03916379, 0.997     ],\n",
       "       [0.04133956, 0.999     ],\n",
       "       [0.04351532, 1.        ],\n",
       "       [0.04569109, 1.        ]])"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "genv.observed"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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9qezvRRV/byr7e1E5wIsq/l7W4zzbqwR4UcnPCy8P/fWsLl+x1QjsoImgDDMGfvkFxo2zTv5Vq0LnzvDGG2TWqoGXuxens04T+lYoD7d5mHHdx5GamcqnH/+Lvotiqb7oNzzSUjlWJZgt9cLZE1SbnZVrsaNSCHv9A8lw5D8UDzehop8n5XN/bef51V3+rOd///qu5G+d2N3diqeNWJVtF0sEpW4aalUGGWO19Y8bB6tXQ+3a5Ez9H79dU4+FB5eycOGtVA+ozsIhC/H19OX+1g/S4GgVPluwmbXJhhq/VqD8T7P5ulFnfmjek9Q2HahWwQdfLw98Pd1o5+VBt9x2bE93fLzc8fM8u0079zU/bw8q+nri5+VebJ1+Srma1ghUybZsGTz/PKxaBSEh8NxzLOpSgzErnmF7/HY83TxpU6MDV1fsQW3P/myKTSblzx38+v4oxl17P7/2uIM21f1oEVKB5mHVaVqzgraLqzJJawSq9HrnHdi7F957j7W92jBm+bOs/mYJgT6hXBP0IqeONqLxz5vpt3URKb6r2frAeHrc1Ik/a7zBw3fexoSGdYv7EyhV4mmNQJUomdt3kP3gw2x4aiLbygUTvzOGLWmprDgxneOOn3HDlwpZAwlPaMUjW3/luqhlBJxKJjswCBk1CveXXyruj6BUiaQ1AlUixSWf5rdd8fx15BRxsfHsOGVIjz3E11E7+HDWUlZc1ZrAAG9qVfElw30919QYwuP1HqDL7E+pMPNRxN0dbr0Vhg3D4/rrwUP/nJUqDP2fo4pMZraDyJhEVkTHszw6nuijp2gRF81Tv39OFUcGU178hKvCa7Bp+DraZ67jyO4pzB/0A57unqSl7MBv+sdw+w3WVcL33gsTJkD16sX9sZQq9TQRKFsdPnGa5dHxLI8+xu+7E0jJyMbTXWhbtzJjT+yhx+yxULkyMnYs793VAuNujcaZF72JwymxxJ2KI7RiKH7HT8Azz0CPHjBpEjT9xzWKSqlC0kSgXCorx0Hk/iSW7zzG8r+sX/0ANSv6cnN4Dbo3CKJj/UAC5n4LL46Bjh1h/nxiOckzP95NvUr1GN99PDc1uIkbk6vi/spUeOUVa4bPbdugfv3i/YBKXYE0EajLduJ0Fgv+PMzy6HhW7T5+5ld/mzqVebZ1I7o3rEpY1YC/x93PmQODB0PnzqR8/yWvbXid11e/jsM4eK7LcwCICO6/r4aZM+GxxyA4WJOAUjbRUUOq0FIzspm5ej/TVuzhZHo2wRV86N6wKt0bBtGpfiAB3uf5nfHFFzBkCHTuzO5Zb9Pz+1s4cOIAA5oO4NWIZ6k99XNo0QIGDrTm8M/IgHLliv7DKXWF0VFDyqXSs3L4bE0MU5fvISE1k56NqvJozzCah1S4+NW2s2fD0KHQpQu7Z71Nt29uIDMnk1VDl9Np4TaI6AHHj8NTT1mJwMvrHxO6KaVcTxOByrfMbAdfbzjIu0t2c+RkOp3qV+GJ6xvSqnal/B1g6VLo2pXdn7x1JgmsC5lI3RsfgL/+gm7d4I03oHVrez+IUuosmgjUJeU4DHM3HeKtJTs5mHiaVrUrMvmuFnSsF5i/A2RkgLc3TJvGniM76PZlLzJzMtlQ/ilqD37Ymtp57lxrumedv0epIqeJQF2Qw2FYsPUIk3+NZk98Kk1qlOfjEU3p3jAo/xOuzZ4N48dbcwbVrEmFStW5OvBqpvveZSWBzp1h0SLw9bX1syilLkwTgfoHYwzLoo/x+qKdbD98kvpVA/jf4Fb0blIdt4JOoVy/PjRrxkG3FKrlZBLoF8jipq9ZzUCNGsG8eZoElCpmmgjUWVbvPs7rv0Sz8UAytSv7MfnOFtwSXrPgc+hv3Wpd9NW2Ladmz6TDlKu5vt71fHTLR9Yyja1bW7WFihXt+SBKqXzTRKAA2H88lf/+sJXfdh2nenkfXr6tGXdEhBRubdmZM+Gee6wT/YABlPMux/ju4+lQoam1tkDDhrB8uas/glKqkDQRlHE5DsPHv+/j9V+i8XRz4z83Xs2Q9qGFn7P/449h5Ei49lp2d27C4Zjf6BLahXsbDbL6A7p2hbfecu2HUEpdFk0EZdiuo6d46psoNh9Mpmejqrx0WzOqV/Ap/AE/+siaDO6669g943W6fdUbL3cvokdH4+XrCzfcAJ06ue4DKKVcQhNBGZSV42Daij28s2Q3/t7uvD0gnJtb1Li8pRdzk8D117P7w0l0+6o3mTmZLBq0AK/Dx6zVxV580XUfQinlMpoIypith04w9psoth8+yY3Ng5lwcxMCA7wv76Bffvl3Epjx+pnrBJYNW0rTF6dbr0dF6ZTRSpVQmgjKiIzsHN5dspupK/ZQ2d+L94e0pndTF5yYDxyA++6DDh3OTgLDl9H0w3nw3nswZowmAaVKME0EZcDGA0mM/SaK3cdS6N86hP/e2JgKfp6uOfhDD4HDwb53Jp6dBH5cC889Z80yOmmSa8pSStlCE8EV7HRmDm/8Es2M3/cRXN6HmXe3oXvDqq4tZPJkDq9fRucVw/5OAmv2WrWEXr2svgO3QgxBVUoVGU0EV6g/9iTw7++iiElIY0j72jzduxHlfFxUCwA4cQLKl4cGDViQuoqcwzlWEth1Au66y7pg7JtvdPZQpUoBXY/gCpOakc3LP+/g87UHCK3ixyu3N6dDvSquLSQzE9q3h7Zt4f33rXIzU/Hftd+6VqBqVVi1CoKCXFuuUqrQdD2CMiIrx8H9n27g9z3HubdzXZ64viG+XoW8MOxi3N1hwACOhlRk0+6F9K7fG//UTOjd25o3aNEiTQJKlSLaeHuFMMYwft42Vu0+zmv9mvOfvo3tSQLGWIlg7FjGld/IHV/fQUJagjVn0OOPw8KF1vrCSqlSQxPBFWLm6v18vvYAD3Srxx0RtewpJDXVavpZuBCAt3u/zeKhi6mS4WatIzBmDDRvbk/ZSinbaCK4Aiz76xgvzN/O9Y2rMbZXQ/sKevJJ+OMPTrplcSrjFN4e3rT7M9GqAaxfb1+5SilbaSIo5f46cpJHvtjE1cHleWtAeMHXC8ivBQusjuExY7j/1GxaT29NZk6mtbrYXXdpTUCpUszWRCAivUUkWkR2i8i/z/N6bRFZJiKbRCRKRG6wM54rzfGUDEbOjMTPy50Zw9vg52VT339CgjWtdNOm/Dy8I3O2zmFo86F4uXtZC89Mn24tRamUKpVsSwQi4g5MAfoAjYGBItL4nN3+A3xljGkJDAD+Z1c8V5r0rBzumxVJQmoGHw6PuLxZQy/GGHjwQUhIIGXGVO5f/BhNqzbl6cBboH9/iIuzp1ylVJGxc/hoW2C3MWYvgIjMAW4BtufZxwDlnY8rAHpWyQdjDE9/G8XGA8lMHdyK5iE2rvI1ezZ8/TW8/DJj42cTdyqOb+/4Bq+hj8HmzeChI5CVKu3sbBqqCRzM8zzWuS2v8cAQEYkFfgYeOd+BROQ+EYkUkcj4+Hg7Yi1V3l26mx82x/FUr4b0aRZsX0EHD8LDD0PHjqy8qz1TI6fyWLvHaLtsp7XC2CuvWBePKaVKteLuLB4IzDTGhAA3AJ+KyD9iMsZMN8ZEGGMigsr4hUrzo+KY/OtObm9Zk4e617O3sFGjIDubjI8+YNTPD1C3Yl1eaPE4PPGEdWXxqFH2lq+UKhJ21usPAXkHtIc4t+U1EugNYIz5Q0R8gEDgmI1xlVqbDybzxFdbiAitxP/1a3Z5C8nkx/PPQ2wsE2I/Y2fCTn4d+iv+41+CxET49VedTE6pK4Sd/5PXA2EiUldEvLA6g+eds88BoCeAiFwN+ADa9nMeh5JPc+8nkVQt7820oa3x9rDhquFcGRnWfceOHOzVgUmrJzEifATXHvWHadPgscegRQv7yldKFSnbagTGmGwRGQ0sAtyBj4wx20RkIhBpjJkHPAF8ICKPY3UcjzClbRa8IpCSkc3ImevJyMrhi1HtqHK5K4pdTFaWdfXwjTfC+PHUqlCLnwf9TOuqLaDL9VCzJowfb1/5SqkiZ+uQD2PMz1idwHm3PZ/n8XZAVzO/iByH4V9zNrHz6Ck+vrstYdXK2VxgDnTsCM2bk5yeTEWfilxX7zp4803YsgW+/RbK2RyDUqpIaSNvCffqwr9YvOMY429uQrcGRdBR7uMDb7/N7u7NCX0rlC/+/MLanpkJt98Ot91mfwxKqSKliaAEm7PuANNX7mVYh1CGdahjb2FZWdC3L6xbB0Bl38oMajqIrqFdrdefftpaaMbuDmqlVJHTRFBCrd5znP/M3UqXsECe73vuBdk2+PRT+OknOHoUsBLB1L5Tqbn+L2s7aBJQ6gqliaAESsvMZvTsTdQN9GfK4FZ4uNv8z5SdDS+9BK1aEdetFdfOupbt8c4LwCdPhqeesvZRSl2RdH6AEuiHzXEkpmby/pDWlHflOsMXMns27N0Lc+cyesEj/H7wdzzdnOV+/z0cOqRTSSh1BdMaQQljjGHWHzE0ql6ONnUq2V9gTg68+CK0aMG39bP4/q/vGd9tPGFpPnDqlLX4fN269sehlCo2+jOvhNkQk8SOwyd5+bYiuHIY4MsvYdcuMubMZvTCR2hZvSVPdBgDPa6FpCRrYjm9glipK5omghLmkz9iKOfjwa0ta9hfWG5toGlTPqqTyJG/jjCn3xw8PpsNK1fCBx9oElCqDNBEUIIcO5XOwq2HGdq+jn2LzOT17bewYweOL77gjbX/oV3NdnQNaAJP9rcuKrvnHvtjUEoVO/25V4LMWXeQrBzD0A6hRVPgBx/A1VfzXRNhT9IexnYaizzzjNUkNHWq1gaUKiO0RlBCZOU4mL32AF3CAqkb6F80hc6bh9m/n9dWDSeschi3HA+EDz+0FqnXNYiVKjP0J18J8ev2oxw5mW7/FcRgLT+ZlQW+vhyqWY79yft5sv0Y3Ec/ArVqwbhx9seglCoxNBGUELP+2E/Nir70aFQEK37Nnw8NG8KuXYSUDyHmXzHcHRsEUVHWqmMBAfbHoJQqMTQRlAA7j55izd5EhrQPxd2tCIaMVqgArVqRVK0C2Y5sfD198XzzbahdG+680/7ylVIlivYRlACf/hGDl4cbd7WpdemdXaFrV+jalce+H8aWo1vYdP8m3MaNsy4g0yuIlSpz9H99MTuVnsV3G2O5qXkNKvt72VuYMfC//8Fdd0FgIP2u7kfbmm1xEzfo2dPespVSJZY2DRWz7zYeIjUzh2FFMWR08WIYPRq++w6AWxrdwuhqN8Hjj8ORI/aXr5QqkTQRFCNjDJ+uiaFFSAVa1Kpod2EwYQLUqkXSnTczYfkEEtISYNUqax3irCx7y1dKlViaCIrRH3sS2H0shaFFMWR0+XL4/Xd4+mne//Njxq8YT+zJWBg8GOLirGGjSqkySfsIitEnf+ynkp8nfZsH21/YxIkQHEz68MG8/X4jetXrRQvv2tZrFW2ujSilSjStERSTuOTT/Lr9KHe1qY2Pp7u9ha1cadUInn6aT6O/5mjqUZ5uO8a6evjpp+0tWylV4mmNoJjMXnsAAwxuV9v+wl54AapVI2fkPbw+M4LWwa3pvu4YxMZaQ0mVUmWaJoJikJGdw5z1B+jZqCq1KvvZW9jq1dZooddfZ97BxexM2MmX/eYgw16FRo2gTx97y1dKlXiaCIrBgj+PcDwls2jmFXrhBQgMxNx/P6/OuZarKl1Fv6NVYNMmmD5dZxhVSmkiKA6z/thP3UB/OtcPtL+w8eMhNpZVCZtYe2gtU26YgvuEtyAoCIYOtb98pVSJpz8Hi9jWQyfYeCCZIe1DcSuKeYXatYN+/Zi0ehKBfoHc7d0efvrJurDMx8f+8pVSJZ4mgiL26R8x+Hq60791iL0FbdwIo0bBsWMAPN3paabcMAXf9963EsCDD9pbvlKq1NBEUISS0zKZu/kQt7asSQVfT3sL27TJmm7a2xuATrU7cWdQd5g1C4YPt5qGlFIKTQRF6uvIWDKyHUUzr9DIkbBvH4ckhQfnP2hdRbx5M/j6WnMLKaWUkyaCIuJwGD5bG0ObOpW4Ori8vYXt2GHd+/iwJnYNs6JmkZWTBddfD4cPW4vSKKWUk62JQER6i0i0iOwWkX9fYJ87RWS7iGwTkdl2xlOcVuyKJyYhzf4howgpoBcAACAASURBVNu2QZMm1tBQoF/jfhx54gh1T3tbE89pB7FS6hy2JQIRcQemAH2AxsBAEWl8zj5hwDNAJ2NME+BfdsVT3Gat3k9QOW96Nalub0GTJ1vNP/36cSzV6igu5+kP11yjw0WVUudlZ42gLbDbGLPXGJMJzAFuOWefUcAUY0wSgDHmmI3xFJsDCWks3xnPwLa18fKw8StPToY5c2DQIDIqBNByWkue/OVJcDjg2WdhyBD7ylZKlVp2XlBWEziY53ks0O6cfRoAiMjvgDsw3hiz8NwDich9wH0AtWsXwdw8LvbZ2hjcRBjU1ubYP/sM0tLggQeY/eds4k7F0ateL2v5yeHD7S1bKVVqFXdnsQcQBnQHBgIfiMg/5kQ2xkw3xkQYYyKCStmwx9OZOXy5/iC9m1SnegUb2+eNsRaYad0aR6uWTFo9ifDq4Vx7MhDeeANSU+0rWylVqtmZCA4BeVc7CXFuyysWmGeMyTLG7AN2YiWGK8aPW+I4cTqLoXYPGV29GrZuhQce4KedP7Hj+A7GdhyLvPaatRZBTo695SulSi07E8F6IExE6oqIFzAAmHfOPnOxagOISCBWU9FeG2MqUsYYZq3ZT4NqAbSrW9newt5/H8qXhwEDeG31a4RWCOWOcu3g66+tK4zL2zxkVSlVatmWCIwx2cBoYBGwA/jKGLNNRCaKyM3O3RYBCSKyHVgGPGWMSbArpqK26WAyWw+dZFiHOojYOK9QQoJ1wh8yhNVJUaw6sIoxHcbg8e4UEIHHHrOvbKVUqWfr7KPGmJ+Bn8/Z9nyexwYY47xdcRb8eRgvDzdua1nT3oK2b7d+8d9/P1PWv0oF7wrcc1U/+OBquPNOXY9YKXVRxd1ZfEVbvz+J8JCK+HvbPNt3ly5w6BBJYbX4dvu3DG42mIBZc+DUKXjiCXvLVkqVepoIbHI6M4dtcSdoXaeSvQUlJlodwZ6ebI/fToBXACObDYO33oLu3aFVK3vLV0qVepoIbLIlNpmsHENEqM2J4MEHoW1bMIZOtTsR90QcrVbtsdYj1tqAUiofdIUym2yISQKgtd2JYMAAiI8nJSsVP08/vNw8resGGjaEG26wt2yl1BVBE4FNIvcnElY1gIp+XvYWdNttADy74FEW711M1ANb8HjpJWtaCV2PWCmVD5oIbOBwGDbEJHFj8xr2FZKTA2+/DYMGQfXq9Kjbg+CAYDzcPaF3b/vKVUpdcQr0k1FE/J2ziqqL2HUshZPp2fb2D/zyi9UHsHIlALc2upVnGt9nTS536NwLuJVS6sIumghExE1EBonITyJyDPgLOOxcP2CSiNQvmjBLl/X7EwGIsHPE0LRpULUq3Horc7bO4UjKEVi1Cl57zRpJpJRS+XSpGsEyoB7WmgHVjTG1jDFVgc7AGuBVEdG5jc+xISaJoHLe1K7sZ08BsbHw449wzz3EpB1m0LeDeD/yfbjlFmsFsmbN7ClXKXVFulQfwbXGmKxzNxpjEoFvgW9FxOZV2Euf9fsTiQitZN+0Eh9+aM02OmoUMzfPBODu5s5ppkvZ7KxKqeJ3qRpBORGpfKEbwPkSRVl29GQ6sUmniahj0yRz2dlWIujVC0fdOny8+WOuvepaQv8zCW6+2UoQSilVAJdKBBuASOd9PNY00bucjzfYG1rpFLnfun7Ato7in36yOoPvv58le5cQcyKG+xoNgc8/h4oVrUnmlFKqAC6aCIwxdY0xVwGLgZuMMYHGmCpAX+CXogiwtFm/PxFfT3ca17Bp2uf334caNaBvX2ZsmkFl38rcsi0bTp6Ee+6xp0yl1BUtv8NH2ztnEgXAGLMA6GhPSKXbhpgkwmtVxNPdhou59u2DRYtg1CgSMk/w/V/fM6TZEDxnzoJ69aBbN9eXqZS64uX3bBUnIv8RkTrO23NAnJ2BlUapGdlsP3zSvmGj2dnWtNL33svsP2eTmZPJAxWvhRUrrNqANgsppQohv4lgIBAEfA9853w80K6gSqvNB5PJcRj7OorDwmDOHEzNmszYNIPWwa25ev4aayoJXZxeKVVI+ZpiwjlcVJe5uoTI/UmIQMvaFV1/8E2bwMcHrr6atKw06leuT58618GEidCnD9S0efEbpdQV61JXFn8gIue9Osk53cQ9IjLYntBKn8iYRBpWK0d5HxsurXjmGWs2UYcDfy9/vrnzG0bGh0BcnHYSK6Uuy6VqBFOA/zqTwVasYaM+QBhQHvgI+NzWCEuJ7BwHG2OSuL1ViD0FzJoFe/ZwOieDg0kHaVClgbUtKAj69rWnTKVUmXDRRGCM2QzcKSIBQAQQDKQBO4wxO4sgvlLjryOnSM3Msa+juGpVqFqV76I+Z8j3Q1g/aj0R06fDjh3gZfNU10qpK9qlmoZuEZGHjTEpxpjlwOPAW8BCEelfFAGWFrkL0bi8ozg93frF75xltOdVPXm3z7u0Cm4FFSpA+/auLU8pVeZcatTQWGBenudeWDWD7sCDNsVUKkXGJBFcwYeaFX1de+BvvrGuJs6yZvKoHlCd0W0exm3AQJg717VlKaXKpEv1EXgZYw7meb7KGJMAJIiIv41xlTqR+xPtWZZy2jRr2Og11zBryyy83b25q3pPiI6GhATXl6eUKnMulQjOOrMZY0bnearTXDodSj7N4RPptHF1s9DWrdYaA6+/Tg6G55Y+R7Oqzbir6V3WcFKdYE4p5QKXahpaKyKjzt0oIvcD6+wJqfSJdC5E4/IawbRpVkfw8OH8sucXYk/GMqrxUDh1yrqKWNckVkq5wKVqBI8Dc0VkELDRua014A3camdgpUnk/iQCvD1oVL2c6w6ammoND73jDggMZMbSGQT6BXLTxhToXB2ioqz5hZRS6jJdavjoMaCjiPQAmjg3/2SMWWp7ZKXI+v2JtKxdEQ9XTjT35ZfWjKIPPEB8ajzzoucxuu1oPF74BGrVgquucl1ZSqkyLb9TTCwF9OR/HifTs4g+eoreTau79sDvvw9NmkCnTny25i2yHFk8GHAN/P6mtS6xTjCnlHIRbWS+TJsOJGMMru0o3roV1q+HUaMwwIxNM2hXsx1hP/wG7u4wdKjrylJKlXmaCC5T5P5E3N2E8FounGiuTh34+GMYNIh1h9axLX4bI5sNh08+sS4uq+7i2odSqkzTRHCZIvcn0Ti4PP7e+Wply5+AABgxAoKCmLFpBn6efgw+WBGOHYORI11XjlJKYXMiEJHeIhItIrtF5N8X2a+fiBgRibAzHlfLynGw6WCSa4eNrl0Lb71ljRoCutTuwnNdnsNv1hcQHGxNOa2UUi5kWyIQEXes2Uv7AI2BgSLS+Dz7lcNa62CtXbHYZXvcSdKzHK6daO6nn2DcuDPXCAxtMZRn698NP/9sLT7j4cKah1JKYW+NoC2w2xiz1xiTCcwBbjnPfi8ArwLpNsZii8jcieZCXdhRPHEi7NwJvr58s/0bkk4nwZIl4HDA3Xe7rhyllHKyMxHUBPLOUxTr3HaGiLQCahljfrrYgUTkPhGJFJHI+Ph410daSJH7Ewmp5Ev1Cj6uOWDulBHVqrEvaR93fH0H0zZMgyFD4OBBaNDANeUopVQexdbOICJuwGRgxKX2NcZMB6YDRERElIgJdowxRMYk0bl+oOsOevvt1tXCr79O3Up12XDfBmqVcy50o0tRKqVsYmeN4BBQK8/zEOe2XOWApsByEdkPtAfmlZYO4wOJacSfynBdR/HhwzBvnrUusVOr4FYEPf4cDBvmmjKUUuo87EwE64EwEakrIl7AAPKsbWCMOWGMCTTG1DHG1AHWADcbYyJtjMllIvfnLkTjokQwe7bVDzB0KIt2L+LuH+4mIS3BqgmE2LT8pVJKYWMiMMZkA6OBRcAO4CtjzDYRmSgiN9tVblGJjEminI8HDaq6aKK5WbOgbVto2JCpkVNZsGsB5b3Lw/jx8PLLrilDKaXOw9Y+AmPMz8DP52x7/gL7drczFlfLXYjGzc0Fc/5ERVm3997jSMoR5u+czxMdnsBzzTprKUp398svQymlLkCvLC6E5LRMdh1Lcd38Qp9+al0fcNddzNoyixyTwwO+XaBzZ2tNAqWUspEmgkLIXajeJR3FOTnw+edw442YKlWYsWkGnWt3pu53S8HT01qPQCmlbKSJoBAiY5LwcBNahLhgorklS6wRQ0OHsurAKnYm7GRU0+FWLeHmmyFIVwRVStlLE0EhRO5PpGnNCvh6uaDtftYsqFgR+vZlxqYZlPMqx537/OD4cbjnnss/vlJKXYImggLKyM5hS+wJIlx1/cBLL8Hs2Zww6Xy9/WsGNh2Iz6zZ1rDRXr1cU4ZSSl2EzmBWQFsPnSQz20GEqzqKQ0MhNJQ5kdNIy0rjgRo3w4Kb4emndbSQUqpIaI2ggCL3JwIu6ij+739h4UIAetXvxeTrJxP+6586wZxSqkhpjaCAImOSqFPFj6By3pd3oLQ0a8Uxd3fo3Zs6FevwePt/wYhG0KULhIW5JmCllLoETQQFYIxhQ0wSPRpVvfyD+fnBvn2QkcHHmz6mWkA1bghoqbUBpVSR00RQAHuPp5KYmnn5HcXGWCd8d3eMry9v/PEGTao24Yb+N1hrEeTkuCZgpZTKB+0jKIANZyaau8yO4k2brInk/vgDEWHT/Zt4r8cbkJ4OIroKmVKqSGkiKID1+xOp5OdJvSD/yzvQp59CYiI0bIgxBk93T4LmLYYaNazmIqWUKkKaCApgQ4y1UL3IZUw0l51tTTndty8xbqeo+3Zdlu1bBk2aWGsS16njsniVUio/tA0in46nZLD3eCp3tql16Z0v5pdf4NgxGDqUjzd/zIETB7iq0lVQNxTatHFNsEopVQBaI8inDWcWqr/MjuJPP4XKlcnp3YuPNn3EdfWuI/SP7bBtmwuiVEqpgtMaQT5tiEnCy8ONZiEVCn+Qkydh7ly45x4Wx67k4MmDvNHzNehzL7RsCfPnuy5gpdQFZWVlERsbS3p6enGH4nI+Pj6EhITg6emZ7/doIsin9fsTaV6zAt4elzHtwzffWCODhg1jxqY3qOJbhVsP+EFcHLz7ruuCVUpdVGxsLOXKlaNOnTqX1+dXwhhjSEhIIDY2lrp16+b7fdo0lA/pWTlsPXSC1pe7PvGnn0JYGMebXsXcv+YypPkQPD/5FAIDoW9f1wSrlLqk9PR0qlSpckUlAQARoUqVKgWu6WgiyIctB5PJyjG0Cb2M6wdiY2H5chg2jM/+/JwsRxb31b4dfvgBhgwBLy+XxauUurQrLQnkKszn0qahfIh0xYpkNWvCmjWYWrWY8UMv2tRoQ+PFmyErS9cdUEoVK60R5EPk/kTqVw2gkv9l/GoXgXbt2Mhhth7bysjwe2DGDIiIgGbNXBesUqpUOHr0KIMGDeKqq66idevWdOjQge+//75YYtFEcAk5DmuiucsaNrpxI9x/Pxw+TKvgVqwcsZLBOY0hKkonmFOqDDLGcOutt9K1a1f27t3Lhg0bmDNnDrGxscUSjzYNXcLmg8mcTM+mY/3Awh9k2zb49lt49VVEhC6hXeD1R8DbGwYOdF2wSqkCm/DjNrbHnXTpMRvXKM+4m5pc8PWlS5fi5eXFAw88cGZbaGgojzzyiEvjyC+tEVzCiuhjuAl0DbuMRDB0KMTF8fWhXxn982jSstKgfHmrNlDJRUteKqVKjW3bttGqVaviDuMMrRFcwvKd8YTXqkhFv0L2D5w+Db6+4OXFzoSd/HbgN3w9fK21ipVSxe5iv9yLysMPP8yqVavw8vJi/fr1RV6+1ggu4nhKBlGxJ+je8DIWohk+HK6/HoDnuj7Hxvs2Itu2WWsSKKXKpCZNmrBx48Yzz6dMmcKSJUuIj48vlng0EVzEyp3WP0r3hkGFO0ByMsybB40akZCWAID7oTho3hzefNNVYSqlSpkePXqQnp7O1KlTz2xLS0srtng0EVzE8uh4AgO8aFqjkPMLzZkDGRlkDx5E06lNGfvrWKhSBT76CPr3d22wSqlSQ0SYO3cuK1asoG7durRt25bhw4fz6quvFks82kdwATkOw8pd8fRoVBU3t0JcgZiTA5MnQ6tW/FT+CEdSjtCldhdrreIRI1wer1KqdAkODmbOnDnFHQagNYIL2hKbTHJaVuH7B77/Hnbtgmee4cPNMwgOCKZPUhV46y1ITXVtsEopdRlsTQQi0ltEokVkt4j8+zyvjxGR7SISJSJLRCTUzngKYnl0fOGHjRoDr7wCYWHEXduOn3f9zPAWw/H43/swfjy4af5VSpUctp2RRMQdmAL0ARoDA0Wk8Tm7bQIijDHNgW+A1+yKp6BWRB8r/LDRxYthwwYYO5ZP/vwMh3Fwb707rGmoBwywhpMqpVQJYedP07bAbmPMXmNMJjAHuCXvDsaYZcaY3K7yNUCIjfHkW0JKBlGHLmPY6CuvQI0aOIYMZsamGXQL7Ua9xRusawp0gjmlVAljZyKoCRzM8zzWue1CRgILzveCiNwnIpEiElkU42xX7orHmEIOGz1+HLZvhzFjWHlkLXuS9jCy5UhrpFCTJrousVKqxCkRo4ZEZAgQAXQ73+vGmOnAdICIiAjbr8S6rGGjgYGwbx8Yw2vf9aOyb2X6SxNYswbeeMOahVQppUoQO2sEh4BaeZ6HOLedRUSuBZ4DbjbGZNgYT77kOAwrd8bTNSyo4MNGk5Ks9QV8fDjmOMX6uPWM7TgW38/mgIeHtQCNUkoBR44cYcCAAdSrV4/WrVtzww03sHPnTh599FGaNm1Ks2bNaNOmDfv27QOgTp06NGvWjObNm9OtWzdiYmJcFoudNYL1QJiI1MVKAAOAQXl3EJGWwDSgtzHmmI2x5FtUbDJJaVl0K0yz0BNPWL/8//yTqv5V2fvoXtxzHNC/obUUZdXLmKpCKXXFMMZw2223MXz48DPXEmzZsoUvv/ySuLg4oqKicHNzIzY2Fn9//zPvW7ZsGYGBgYwbN44XX3yRDz74wCXx2JYIjDHZIjIaWAS4Ax8ZY7aJyEQg0hgzD5gEBABfO5dXO2CMudmumPLj72GjhUgE/ftDq1YcOR1PkF8Q5bzLWVNMHD2qncRKlWDdZ3a/5D59G/TlyY5Pntl/RPgIRoSP4Hjacfp/dfZMActHLL/osZYtW4anp+dZ01C3aNGCJUuWEBwcjJtziHlIyPnHz3To0IF33nnnkjHnl619BMaYn4Gfz9n2fJ7H19pZfmEs3xlPi1oVC7ca2Q03YIyh/8dd8PX05dehv0JQkNUk1KeP64NVSpVKW7dupXXr1v/Yfuedd9K5c2d+++03evbsyZAhQ2jZsuU/9lu4cCG33nqry+IpEZ3FJUVCSgZRscn8q2eDAr4xwZpE7rHHIDCQx9s/jsHZp92hg3VTSpVYl/oFf7H9A/0CC/z+CwkJCSE6OpqlS5eydOlSevbsyddff03Pnj0BuOaaa0hMTCQgIIAXXnjBJWWCTjFxlt92HS/csNH33rPWFzh2DBGhX+N+9G/cH+bPh2Jaek4pVXI1adKEDRs2nPc1b29v+vTpw6RJk3j22WeZO3fumdeWLVtGTEwM4eHhjBs3zmXxaCLIY3n0Mar4e9GsZgGGjaakwDvvwC23sND7IBNXTCQ9Ox3S061+gTFj7AtYKVUq9ejRg4yMDKZPn35mW1RUFCtWrCAuLg4Ah8NBVFQUoaFnz7zj4eHBW2+9xaxZs0hMTHRJPJoInBwOw8pdx+naoIDDRj/8EBITcTw9ln8v/jefRn2Kh5sH+PjAunUwaZJ9QSulSiUR4fvvv2fx4sXUq1ePJk2a8MwzzxAVFcVNN91E06ZNad68OR4eHowePfof7w8ODmbgwIFMmTLFJfFoH4FT1KETJKZmFqxZKDPTukisWze+qxDHlqNb+Oy2z/A4nQH+HlCnjm3xKqVKtxo1avDVV1/9Y/uFFrDfv3//Wc/fffddl8WiicBpefQxRKBLQYaNfv45xMaSM30azy97ksZBjRnQ5C7o3ccaLTR7tn0BK6WUi2jTkNPy6HhahFSkcn6HjToc8OqrEB7OnBqJ7Di+gwndJ+C+cJE1+2j79vYGrJRSLqI1AiAxNZMtsck81jMs/2+aOxeio8mZ/TnjV46jRbUW3F7/JugXDg0awIMP2hewUkq5kCYC4Lczs43mcwqI3IVn6tVjVv1Udu/czQ8DfsDtgw/hr7+sq4k9Pe0NWimlXEQTAVazUGV/L5rnd9ioCEyZQlZCPBN+f4g2NdpwU1BnGNcAevSw5hVSSqlSosz3ETjOzDYaWLBho23aMD80g5gTMbxwzQvIyy9DYqJONa2UKnXKfCL489AJElIz898stGEDjBwJR49y29W3se7edVxPPeuisnvugfBwewNWSl0RAgIC/rFt/Pjx1KxZk/DwcBo1asSDDz6Iw+GwPZYynwiWR8cjAl0b5HPYaFQULFhAhqf11bWp2QZ5+mnw8gIXzv2hlCqbHn/8cTZv3sz27dv5888/WbFihe1llvk+guU7j9G8IMNG776b1P630HhGS57p/AwPtL4fWrWCTp0gONjeYJVS9uje/dL79O0LTz759/4jRli348etKejzWr78skPKzMwkPT2dSpUqXfaxLqVM1wiSUjPZfDCZ7vmtDezaBcaQ7m64/qrraV6tudUf8NxzOqeQUsol3nzzTcLDwwkODqZBgwaEF0Fzc5muERRokfpDh6zF5196iSpPPcUHN39gXUuw9hvo1087iJUqzQr6Cz7v/oGBLqkB5Hr88cd58sknycrKon///syZM4cBAwa47PjnU6ZrBMuj46nk50nzkIqX3nnyZHA4mNfUi7Wxa61t06ZZk8oZY2+gSqkyx9PTk969e7Ny5UrbyyqzieDMsNEGQbhfathoYiJMm0bGHbczbMs4/m/V/1nb58+3agVuZfZrVErZxBjD77//Tr169Wwvq8yewf4eNpqPZqEpUyA1lek9K3Ii4wQvNfsXJCeDu7t2ECulCiUtLY2QkJAzt8mTJwN/9xE0bdqUnJwcHnroIdtjKbN9BGeGjV5qttEtW2DyZDL6XM8zx2ZzV5O7aDJppjWx3O7d1roDSilVQBe6PmD8+PFFGwhluEawfOcxmtesQJUA7wvvtHGjNWVEQABv3lmb09mn+b9Kd8Ann8DgwZoElFJXhDKZCHKHjXa72NXEkZHQsycEBHDsp6+ZeOhzhjQbTN2J71hrDTz7bNEFrJRSNiqTiSBfw0ZnzoRKlWDFCl48NJvMnExePdUBVq6EiROhQgHWNVZKqRKsTCaCFc5hoy3ON2w0t93u7bfJ+G05T0S/y7vr3uX+piOoPvEN61qCe+8t2oCVUspGZS4ROByGFTvj6RJ2nmGjK1da00XExoK7O1lBlZm/az4PRTzEW3vCYM8ea3ZRjzLbx66UugKVuTPa1riLDBv19sb4+DBv13yuqzaMAK8AIkdFUu5UBgyuD717Q69eRR+0UkrZqMzVCM4722hMjHXfrh1bvp/KrSsfZPqG6QCU8y4HEyZASopVG1BKKRfYv38/TZs2PWvb+PHjef311xkxYgR169Y9Mx31hAkTbI2lDCYCa9hoYO6w0YULoVEjkqa+CUB4cEuWDFvCI83uhSNHrH0GDLCmkmjcuJiiVkqVNZMmTWLz5s1s3ryZTz75hH379tlWVplqGkpOs4aNju7hXKT+p58wt9/OkdqVaXXwab492I6OtTrSI7Q7NGxo9Rd8+aU1xXSnTsUau1LKRiVwGupc6enpAPj7+7vsmOcqUzWClbuO48gdNvrDD5jbbiM62Ismtx9hWHBvWv9vrjWBnJsb/Pe/8PDDxR2yUqqMeuqppwgPDyckJIQBAwZQtWo+V1EshDJVI1gefcwaNrp2CY5BA9gQDK91ySLqj3BCfvsRfH6FoSOsJqBhw4o7XKVUUSmGaajlAlPX526fNGkS/fv3JyUlhZ49e7J69Wo6duxY4HLyw9YagYj0FpFoEdktIv8+z+veIvKl8/W1IlLHrlhyZxt9KH4tDLiTXeVzqGC8+PqzDEL+OmR1CB84oP0ASqkiUaVKFZKSks7alpiYSGBg4FnbAgIC6N69O6tWrbItFtsSgYi4A1OAPkBjYKCInHuWHQkkGWPqA28Cr9oVz7a4k3T7/SNGvvc8WWJomAhhAbVh+nRr1NDzz1tTRyilVBEICAggODiYpUuXAlYSWLhwIZ07dz5rv+zsbNauXWvrdNR21gjaAruNMXuNMZnAHOCWc/a5BfjE+fgboKdcqL50mVau38Gri+bgBpxu1RR+/BHZth1GjQJfXzuKVEqpi5o1axYvvPAC4eHh9OjRg3Hjxp054ef2ETRv3pxmzZpx++232xaHnX0ENYGDeZ7HAu0utI8xJltETgBVgON5dxKR+4D7AGrXrl2oYAZc15LfHn+Y8Bv6UKnnjYU6hlJKuVLjxo1ZtmzZP7bPnDmzSOMoFZ3FxpjpwHSAiIiIQq0LWSXAm2veeM+lcSml1JXAzqahQ0CtPM9DnNvOu4+IeAAVgAQbY1JKKXUOOxPBeiBMROqKiBcwAJh3zj7zgOHOx/2BpcboSvBKKftdqaeawnwu2xKBMSYbGA0sAnYAXxljtonIRBG52bnbDKCKiOwGxgD/GGKqlFKu5uPjQ0JCwhWXDIwxJCQk4FPA1ROltH0RERERJjIysrjDUEqVYllZWcTGxp6ZvuFK4uPjQ0hICJ6enmdtF5ENxpiI872nVHQWK6WUK3l6elK3bt3iDqPEKFNzDSmllPonTQRKKVXGaSJQSqkyrtR1FotIPBBTyLcHcs5Vy2WYfhd/0+/Cot/D367E7yLUGHPeCdVKXSK4HCISeaFe87JGv4u/6Xdh0e/hb2Xtu9CmIaWUKuM0ESilVBlX1hLB9OIOoATR7+Jv+l1Y9Hv4W5n6LspUH4FSSql/Kms1AqWUUufQRKCUUmXcFZMIRKS3iESLyG4R+ccspiLiLSJfoUud1gAAA7JJREFUOl////buHsSOKgzj+P8hSz78QCEgqFF3A0FJLBQxaUyjiChoVrRIo5YGsbAIxLgWq4WgjRYWtnYJBgILtgoSiyhZN4QgCRuzYGIRUBA2gdi8FnOEyyVF9p65c5wzzw+GPXfuzPCel3vnvTtzOHNa0uzIe0fT+guSXugy7rZNmgdJ2yV9L2ldUhVP8MnIxfOSzkg6l/4+23XsbcvIxV5JK2k5K+nVrmNvU855Ir3/cPqOHO4q5k5ERO8XYBNwCdgJbAbOArvHtnkH+Cq1DwLHU3t32n4LMJeOs6l0nwrk4U7gGeAQ8GXpvhTOxZPAA6n9OHC1dH8K5uIOYCa17weu/fe6b0tOHkbePwF8Axwu3Z82l1r+I9gLrEbEbxHxD3AMODC2zQHg69Q+ATwnSWn9sYi4GRGXgdV0vD6aOA8RcT0iTgG1zMubk4tfIuKPtP48sE3Slk6ino6cXNyI5tkiAFuBPo8uyTlPIGkeuEzzmahKLYXgQeD3kddX0rpbbpM+2H8D229z377IyUNt2srFa8ByRNycUpxdyMqFpH2SzgPngEMjhaFvJs6DpLuAI8BHHcTZuVoKgVnrJO0BPgXeLh1LSRFxOiL2AE8DRyVt7PFXdVgEPo+I9dKBTEMtheAq8NDI6x1p3S23kTQD3AP8eZv79kVOHmqTlQtJO4CTwJsRcWnq0U5XK5+LiPgVWKe5b9JHOXnYB3wmaQ14D/hA0rvTDrgrtRSCn4FdkuYkbaa5ybM0ts0S8FZqvw58F83dnyXgYBotMAfsAn7qKO625eShNhPnQtK9wLfA+xHxY2cRT09OLubSCRFJjwCPAWvdhN26ifMQEfsjYjYiZoEvgE8ioorRdUAdo4bSeewl4CLNqICFtO5j4JXU3kpzt3+V5kS/c2TfhbTfBeDF0n0pmIc14C+aX31XGBtR0bdl0lwAHwLXgZWR5b7S/SmUizdobo6uAMvAfOm+lMjD2DEWqWzUkKeYMDMbuFouDZmZ2YRcCMzMBs6FwMxs4FwIzMwGzoXAzGzgXAjMWiZpsbrZKa1qLgRmZgPnQmDWAkkLki5KOgU8Wjoes42YKR2AWd9JeopmuoInaL5Ty8CZokGZbYALgVm+/cDJiLgBIGl8/hqz/zVfGjIzGzgXArN8PwDzkrZJuht4uXRAZhvhS0NmmSJiWdJxmmfgXqOZ7tisNzz7qJnZwPnSkJnZwLkQmJkNnAuBmdnAuRCYmQ2cC4GZ2cC5EJiZDZwLgZnZwP0LgAk/ek0ETMUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "genv.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The $G$ curve is obviously outside and upon the CSR significant curves, so we can conclude that the points are outcomes of cluster point process."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**$F$-function (point-event)** is similar to the $G-$function, but the distance is not to the points in target events, but to the points coming from CSR process."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ff = distance_statistics.F(pattern, intervals=20)\n",
    "ff.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ff.plot(qq=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<pointpats._deprecated_distance_statistics.Fenv at 0x7fb5f451d5f8>"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fenv = distance_statistics.Fenv(pattern, intervals=20, realizations=realizations) # call Genv to generate simulation envelope\n",
    "fenv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fenv.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**$J-$function** is based on these two functions. One of its advantage is that it is based on the non-CSR null hypothesis. When $J<1$, the points are clustered; if $J=1$, the underlying process is a random point process; when $J>1$, it is a regular process.\n",
    "\n",
    "$$\n",
    "J(d) = \\frac{1-G(d)}{1-F(d)}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/xxy/Environment/anaconda3/envs/py36/lib/python3.6/site-packages/pointpats/_deprecated_distance_statistics.py:239: RuntimeWarning: invalid value encountered in true_divide\n",
      "  self.ev = self.j / self.j\n"
     ]
    },
    {
     "data": {
      "image/png": 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5H/VNbUGXIiLSbxEdI3D3R9x9mrtPcfd/Dz/3dXdfEr7v7v5P7l7h7rPc/YFI1hNpF1aMpbPLefLNqDz4SUTiVNCDxTFlVnEOY0el8fgadQ+JSPRQEAyhhATjgooxPLOhlpb2zqDLERHpFwXBELtwxhia2ztZ9tbeoEsREekXBcEQO2VSAdlpSTyuSehEJEooCIZYSlIC50wfzdJ1e+js0iR0IjLyKQgi4MIZY9h3qI2VW/cHXYqIyLtSEETAWdOKSElM4HGdZSwiUaBfQWBmeWY2w8wmm5nC411kpyXznqkFPK5rFIhIFOjzS93Mcszsn81sNbAC+CmwGNhqZr81s3OGq8hodGHFWLbta2L97oNBlyIiclRH+3X/EKFppM9w9+nufnp4BtBS4HbgcjO7fliqjELnV4SuUaCTy0RkpEvqa4G7X3CUZSuBlRGpKEaMzk5jTmkuj6/dxWfPi8oJVUUkTvQZBGY292gvdPdVQ19ObLlwxlhuf/RNauqbKc5ND7ocEZFeHa1r6L/CtzuBF4G7gLvD9++MfGnR78KKMYCuUSAiI1ufQeDu57j7OcBOYG54fOAkYA5HXmBGejG5KIupo7N4TOMEIjKC9edQ0OnuvvrwA3d/Azg+ciXFlveeMI7lVXVsqm0MuhQRkV71JwheN7N7zOzs8O1u4PVIFxYrPnrqRFKSErjnuc1BlyIi0qv+BMF1wBrgH8K3teHnpB8Ks1L5wNwSHl5Vzd7G1qDLERE5wrsGgbu3uPv33f2K8O377t4yHMXFik+dMYm2ji5+tXxr0KWIiBzhaGcW/8nMLjOz5F6WTQ5fe/iTkS0vNkwpyuL848dw3/ItNLfpgjUiMrIcbY/gBuAM4E0ze9nMHjGzp8xsM6HpJla5+73DUmUMuPHMyexvauehVdVBlyIi8g5HO7N4F/Al4EtmVgaMBZqBDe7ePCzVxZCTy/KYXZrLz56r4sPzJ5CYYEGXJCICHL1r6KCZHTCzA4SOEnoCeA7YbWa1ZrbCzM4brkKjnZlx4xmT2VLXxBNrdV6BiIwcR9sjyO5rmZklAjOB/w3/lX64aMYYSvPTufu5KhbOHBt0OSIiwAAvTOPune7+GvCjIa4npiUlJnD9gkms3LqflVv3BV2OiAgwyCuUuftPh6qQePGheaXkpCdz97M6wUxERgZdbWyYZaYm8dFTJ/DY2l1s2Xso6HJERBQEQbj2tDKSExK4Z1lV0KWIiCgIgjB6VBqXzR7P71fV0NTWEXQ5IhLnFAQBuXJeCYfaOnUpSxEJnIIgICeX5VOSl87DOtNYRAKmIAhIQoLx/jnFPL9xL7saNIefiAQnokFgZgvNbL2ZbTSzLx+l3QfMzM1sXiTrGWmumFtCl8MfXtUF30QkOBELgvDZx3cCFwMVwDVmVtFLu2xC1zl4MVK1jFSTCjOZOyGXh1dW4+5BlyMicSqSewTzgY3uXuXubcADwOW9tPsm8B0gLvtH3j+3hLf2NLJmx4GgSxGROBXJICgGtnd7XB1+7m1mNhcodfe/HG1FZnajmVWaWWVtbe3QVxqgy04YT0piggaNRSQwgQ0Wm1kC8N/A59+trbvf5e7z3H1eUVFR5IsbRjkZyZxfMZolr+6gvbMr6HJEJA5FMghqgNJuj0vCzx2WTWjm0qfNbAtwKrAk3gaMAd4/p4S6Q208uyG29nZEJDpEMgheBsrNbJKZpQBXA0sOL3T3BncvdPcydy8DVgCL3L0ygjWNSGdNLyI/M0XdQyISiIgFgbt3ALcAjwHrgMXuviZ8reNFkXrfaJScmMCi2eNZunYPDU3tQZcjInEmomME7v6Iu09z9ynu/u/h577u7kt6aXt2PO4NHPaBuSW0dXbx59U7gi5FROKMziweIWYWj6J8dBa/W6WTy0RkeCkIRggz4wMnlbBy635dp0BEhpWCYAR534nFmMHvNGgsIsNIQTCCjM1J46xpRdzx1Ea+9NBr1NQ3B12SiMQBBcEI84OrTuS6BZP4wys7OOd7T/PNP6+lrrE16LJEJIZZtE12Nm/ePK+sjP2Di2rqm/nh0g08tLKa9OREbjhzMp86YzJZqUlBlyYiUcjMVrp7ryfsao9ghCrOTee7H5zN4/94JmdOK+IHS9/iQz9ZTmtHZ9CliUiMURCMcFNHZ/Pjj57ETz46l3U7D/DDpW8FXZKIxBgFQZRYOHMcV84r4SfPbGLVtv1BlyMiMURBEEX+5b0VjMtJ5wuLX6O5TV1EIjI0FARRJDstme9+8ASq9h7iPx9bH3Q5IhIjFARRZsHUQj5+2kTufX4zK6rqgi5HRGKAgiAKffni45hYkMEXH3qNxtaOoMsRkSinIIhCGSlJ/NeHZlO9v5lvP7Iu6HJEJMopCKLUvLJ8bjhjMr95cRtPvrk76HJEJIopCKLYP10wjWljsvjkLyq5+b6VrK5uCLokEYlCCoIolpacyOKbTuPvz53K85v2ctkdy7j23pd4afO+oEsTkSiiuYZixIGWdu5bvpV7l22m7lAb88vyufXi4zhpYl7QpYnICKC5huLAqLRkPnPOVJbdei7/elkF2/Y1cc1dK/jrG7uCLk1ERjgFQYxJT0nkugWT+OvnzmBG8Sg+/b8rWVy5PeiyRGQEUxDEqNyMFH59/SksmFrIlx56nXueqwq6JBEZoRQEMSwzNYl7rp3HJbPG8q2/rON7j60n2saERCTydJWTGJealMiPrplLdupq7nhqIw3N7fzbohkkJFjQpYnICKEgiAOJCcbtH5hFbkYyP322iv1NbXzvQ7NJS04MujQRGQEUBHHCzPjKJceTn5nCfzz6JjsbWrj74/PIz0wJujQRCZjGCOLMTWdN4c4Pz2V1TQNX/M/zVNU2Bl2SiARMQRCHLj1hHPffcCqNLR28/8cv8KKmsxaJawqCOHXSxDx+/+kF5Gem8LGfvcQfXqkJuiQRCYiCII5NKMjgd3/3HuZMyOVzD77KF377Gi9s2ktnlw4xFYknGiyOc7kZKdx3/Sl8+5F1LK7czkMrqxmdncqlJ4xj0ezxnFiai5kONRWJZRGddM7MFgI/BBKBe9z99h7L/wn4FNAB1AKfdPetR1unJp2LnOa2Tv725m7+9NoOnnqzlrbOLkrz0/nM2VO5ev6EoMsTkUE42qRzEQsCM0sENgAXANXAy8A17r62W5tzgBfdvcnM/g44292vOtp6FQTD40BLO4+9sYsHXt7Oyq37uWZ+KbctmkFqks49EIlGQc0+Oh/Y6O5V7t4GPABc3r2Buz/l7k3hhyuAkgjWI8dgVFoyH5pXyuKbTuMz50zh/pe2c81dK9hzoCXo0kRkiEUyCIqB7tNeVoef68v1wKO9LTCzG82s0swqa2trh7BEeTeJCcYXLzqOOz88l3U7D/LeHy1j1bb9QZclIkNoRBw1ZGYfBeYB/9nbcne/y93nufu8oqKi4S1OgNC5B7//zHtITU7g6p+u4MGXtwVdkogMkUgGQQ1Q2u1xSfi5dzCz84GvAovcvTWC9cggHTd2FH+65XROmZzPrQ+v5mt/WE1bR1fQZYnIIEUyCF4Gys1skpmlAFcDS7o3MLM5wE8JhcCeCNYiQyQ3I4Wff+JkbjprMr9esY2r7lrOzobmoMsSkUGIWBC4ewdwC/AYsA5Y7O5rzOwbZrYo3Ow/gSzgt2b2qpkt6WN1MoIkJSbwlYuP58cfmcuGXQe57EfLWL5J01SIRCtdvF4GZeOeg9x030q21DVx68Lp3HDGZJ2AJjIC6eL1EjFTR2fzx1tO58KKMXz7kTe55TevUHtQQz0i0URTTMigZaUm8T8fmctdz1bxnb++yV9W72RyYSYnTczj5LJ8TirLY3JhpvYUREYoBYEMCTPjprOmcNb0Ip5eX0vlln08sW43v11ZDUB+ZgpnTy9i0ezxLJhaSHKidkZFRgoFgQyp48aO4rixo+CsKXR1OVV7G6ncsp8XN+/jibW7+d2qGvIzU7hk1lgWzS5m3sQ8XT9ZJGAaLJZh09rRyTPra1ny2g6WrttNS3sX43LSmDshj4kFGZQVZDIh/Hd0dqoCQmQIHW2wWHsEMmxSkxK5cMZYLpwxlkOtHSxdt5tHV+9i3c4DPLZmFx3droOQnpzIeceP5pOnT2LuhLwAqxaJfdojkBGho7OLnQ0tbKk7xJa6Jt7ceYAlr+7gYGsHJ5bmct2CMi6ZNU5jCyIDFMg01JGiIIgfja0dPLyyml+8sIXNew8xdlQaHzttIqdOzqc0P4OirFQdiSTSTwoCiWpdXc7TG/bw8+e38Nxbe99+Pi05gdK8DErzM5hYkMEnF0yiND8jwEpFRi4FgcSM7fua2LinkW37mti+ryn0d38zm2obyUlP5r7r54eOWhKRd9BgscSM0vyMXn/1b9h9kI/97EWu/Mlyfn7dyZw0MT+A6kSik0beJCZMG5PNQze/h4KsVD5yz4s8tV6T2Yr0l4JAYkZpfgaLbzqNKUVZ3PDLSv746hGXvxCRXqhrSGJKUXYq9994Kp/6ZSWfe/BV6pvauerkUhLMSLDQpTeH+kijw4e+1tQ3U7O/mer9zdQ3tzFnQh6nTy0kPzNlSN9PZKhpsFhiUkt7J7f85hWWrtvd6/KUpASuOLGYz55fTnFu+jGtd3VNA69s288r2+pZXdPAzoYWOrve+f9RWnICLe1dmMGs4hzOLC/izGlFzJmQq3MhJBA6akjiUkdnFw+trKbuUBvuTpdDlztdXc7uA638/pVQ19GHT5nAp8+ZwujstCPW0djawfJNdTy/cS+rtu1n7Y4Db58BPSE/gxNKcphUmElJXjrFuRkU56UzLieN5MQEXq+u57m39vLshlpe2V5PZ5czKi2Jm8+ewicXTCItOXFYt4fENwWBSC9q6pu548m3WFxZTXKice17yrjpzCnsbGjmmQ21PLuhlpVb99Pe6aQnJzK7NIe5E/KYMyGPE0tzKcpO7fd7NTS3s3zTXn5bWc3f3tzD+Jw0Pn/hdK6YU6w5lWRYKAhEjmLL3kP88G9v8Yfw4PLh/yWOHzeKM6cVclZ5ESeV5ZGaNDS/4JdvquPbj6xjdU0DFeNG8c+XHM/p5YVDsm6RvigIRPphw+6DPLyqmvLR2ZxZXsjoUUd2FQ2Vri7nT6/v4Lt/XU9NfTPzy/IpGnXkHkZWShLvm1PMqZPzNZ2GDIqCQGSEamnv5FfLt/C7VTW0d3YdsXzPwVYOtnQwdXQWHzt1IlfMLWZUWvLwFypRT0EgEqVa2jv58+s7uW/FVl7bXk9GSiLvm1PMB+YWMzo7jazUJLLSkt5xJFJTWwfb9jWxta6JrXWH2FrXRGNrB5MLs5g2JovyMVlMLMjU0UtxRkEgEgNer67n1yu28sdXd9Da8c69h9SkBLLTQqcF7W1se8ey3IxkMlOS2NHQ/Pb4R3KiMakwk3E56bR1dNHc3knL27cuCrJS+IfzyrmgYoy6pGKEgkAkhtQ3tbGiah8HW9ppbO2gsaWDxrbQ384upzQ/gwnhGVkn5meSkxHqSmpu62RTbSMbdh/krT2NvLX7IHsOtpKWlEhqcgLpyYmkJSeSlpxA5db9VNUeYv6kfL56yfHMLs0N+FPLYCkIROSYtHd28cDL2/nBExuoO9TGotnj+eJF04+Y8K+zy9nf1EZnl1OYlUqiDoUdsRQEIjIgB1va+ekzVdyzrIquLjhrehGHWjvY29hKXWMb+5ra3u5uSkwwxmSnMjYnjXE56eG/aZTkZVCSl05pXgaj0pPU1RQQBYGIDMrOhma+/8QGKrfsJz8zhYKsFAqyUinMDP1NSDB2N7Sws6GFXQea2dnQws76FprbO9+xnqzUJEry0pldksu17ymjYryuHTFcFAQiMuzcnfqmdmrqQxPxVe9vevvvC5vqaGrr5D1TCrj+9EmcM320zrCOMF2YRkSGnZmRl5lCXmYKM4tz3rGsoamd+1/exi9f2ML1v6xkcmEm1y0o4/TyIhpbOjjQ0k5DczsHmts50NJOfVM79c3t1De1Ud/Uzv6mdhqa2o44eurdFOelc9rkAk6dUsDJZflkpeorELRHICIBau/s4tE3dvGzZZt5bXt9n+2SEozcjGRy0pPJy0ghNyOZ3IwU0pL7fy6EO7y1u5FXtgTAOqUAAAbiSURBVIfmj0pMME4oyeG0yQXkZ6ZwoKXj7eA50BwKo5K8dM6aVsTpUwspyOr/3FIjkbqGRGREc3de2V7P5tpDjEoPfeGPSk9iVFoyo9KTyUxJHLJB5ua2Tiq37mP5pjqWV9XxenXD29OIZ6eF3jMnPZms1CQ27DlIfVM7ZjBzfA5nlBdy5rQi5k7IIyUpuk7IUxCIiPShqa2D9k4nKzXpiMNfO7ucN2oaeHZDLc++VcuqbaHpxNOSE5g3MZ9TJ+dz2pQCZhXnjvhgCCwIzGwh8EMgEbjH3W/vsTwV+BVwElAHXOXuW462TgWBiATlQEt7aE9iUx0rqup4c9dBANKTEzlpYh65Gcm0dXTR2tEV/ttJa0cXvX3NmsEJJblcOmscp07OJynCU34EEgRmlghsAC4AqoGXgWvcfW23Np8GTnD3m83sauAKd7/qaOtVEIjISLHvUBsvba5jRdU+Xtq8j5b2TlKSEkhNTiQ1MYHU5ARSEhN67dZq6+yicss+mto6yc9M4aIZY7hk1jhOm1wQkVAI6qih+cBGd68KF/EAcDmwtluby4HbwvcfAu4wM/No668SkbiUn5nCwpnjWDhz3IBe39zWyTMb9vCX1bv446s7uP+l7eRmJFPUx8D0Z88r57LZ4wdTcq8iGQTFwPZuj6uBU/pq4+4dZtYAFAB7uzcysxuBGwEmTJgQqXpFRIZVekri20HS0t7JMxtq+du63TS2dvTaPic9MlOQR8VBtO5+F3AXhLqGAi5HRGTIpSUnctGMsVw0Y+ywv3ckRydqgNJuj0vCz/XaxsySgBxCg8YiIjJMIhkELwPlZjbJzFKAq4ElPdosAa4N3/8g8KTGB0REhlfEuobCff63AI8ROnz0XndfY2bfACrdfQnwM+A+M9sI7CMUFiIiMowiOkbg7o8Aj/R47uvd7rcAH4pkDSIicnQj+1Q4ERGJOAWBiEicUxCIiMQ5BYGISJyLutlHzawW2DrAlxfS46xl0TbpQdvjSNomR4rGbTLR3Yt6WxB1QTAYZlbZ16RL8Urb5J20PY6kbXKkWNsm6hoSEYlzCgIRkTgXb0FwV9AFjEDaJu+k7XEkbZMjxdQ2iasxAhEROVK87RGIiEgPCgIRkTgXM0FgZgvNbL2ZbTSzL/eyPNXMHgwvf9HMyrot+0r4+fVmdtFw1h0pA90eZlZgZk+ZWaOZ3THcdUfSILbJBWa20sxWh/+eO9y1R8ogtsl8M3s1fHvNzK4Y7tojYTDfI+HlE8L/73xhuGoeEu4e9TdC01xvAiYDKcBrQEWPNp8GfhK+fzXwYPh+Rbh9KjApvJ7EoD9TgNsjEzgduBm4I+jPMkK2yRxgfPj+TKAm6M8zArZJBpAUvj8O2HP4cbTeBrM9ui1/CPgt8IWgP8+x3GJlj2A+sNHdq9y9DXgAuLxHm8uBX4bvPwScZ2YWfv4Bd291983AxvD6otmAt4e7H3L3ZUDL8JU7LAazTV5x9x3h59cA6WbW+9XFo8tgtkmTux++sG4aEAtHnQzmewQzex+wmdC/kagSK0FQDGzv9rg6/FyvbcL/gBuAgn6+NtoMZnvEqqHaJh8AVrl7a4TqHE6D2iZmdoqZrQFWAzd3C4ZoNeDtYWZZwK3Avw1DnUMuVoJAJOLMbAbwHeCmoGsZCdz9RXefAZwMfMXM0oKuKUC3Ad9398agCxmIWAmCGqC02+OS8HO9tjGzJCAHqOvna6PNYLZHrBrUNjGzEuD3wMfdfVPEqx0eQ/LvxN3XAY2Exk+i2WC2xynAd81sC/A54J/Dl+qNCrESBC8D5WY2ycxSCA3iLOnRZglwbfj+B4EnPTS6swS4Onw0wCSgHHhpmOqOlMFsj1g14G1iZrnAX4Avu/vzw1Zx5A1mm0wKfxFiZhOB44Atw1N2xAx4e7j7Ge5e5u5lwA+Ab7t79Bx1F/Ro9VDdgEuADYRG/b8afu4bwKLw/TRCo/kbCX3RT+722q+GX7ceuDjozzICtscWYB+hX3nV9DhyIlpvA90mwNeAQ8Cr3W6jg/48AW+TjxEaFH0VWAW8L+jPEuT26LGO24iyo4Y0xYSISJyLla4hEREZIAWBiEicUxCIiMQ5BYGISJxTEIiIxDkFgcgQM7Pbom72SYlrCgIRkTinIBAZAmb2VTPbYGbLgOlB1yNyLJKCLkAk2pnZSYSmIziR0P9Tq4CVgRYlcgwUBCKDdwbwe3dvAjCznvPTiIxo6hoSEYlzCgKRwXsWeJ+ZpZtZNnBZ0AWJHAt1DYkMkruvMrMHCV3jdg+h6YxFooZmHxURiXPqGhIRiXMKAhGROKcgEBGJcwoCEZE4pyAQEYlzCgIRkTinIBARiXP/H28vaeb+ggliAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "jf = distance_statistics.J(pattern, intervals=50)\n",
    "jf.plot()  \n",
    "# The warning may due to F(d) becoming 1 in CSR process, but I do not find out how to fix it until now. This also influence the belowed Jenv calculations. \n",
    "# If you know, please contact me."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "ename": "IndexError",
     "evalue": "index 52 is out of bounds for axis 0 with size 52",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mIndexError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-79-617de1075f31>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mjenv\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdistance_statistics\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mJenv\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpattern\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mintervals\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m50\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mrealizations\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mrealizations\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      2\u001b[0m \u001b[0mjenv\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/Environment/anaconda3/envs/py36/lib/python3.6/site-packages/pointpats/_deprecated_distance_statistics.py\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, pp, n, intervals, dmin, dmax, d, pct, realizations)\u001b[0m\n\u001b[1;32m    928\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0md\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0md\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    929\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpct\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpct\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 930\u001b[0;31m         \u001b[0msuper\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mJenv\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__init__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpp\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mrealizations\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mrealizations\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mname\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m\"J\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    931\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    932\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mcalc\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/Environment/anaconda3/envs/py36/lib/python3.6/site-packages/pointpats/_deprecated_distance_statistics.py\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, *args, **kwargs)\u001b[0m\n\u001b[1;32m    633\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    634\u001b[0m         \u001b[0;31m# do realizations\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 635\u001b[0;31m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmapper\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m\"realizations\"\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    636\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    637\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mmapper\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mrealizations\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/Environment/anaconda3/envs/py36/lib/python3.6/site-packages/pointpats/_deprecated_distance_statistics.py\u001b[0m in \u001b[0;36mmapper\u001b[0;34m(self, realizations)\u001b[0m\n\u001b[1;32m    649\u001b[0m                     \u001b[0mdiff\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0md\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mj\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    650\u001b[0m                     \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdiff\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 651\u001b[0;31m                         \u001b[0mj\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0md\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mdiff\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0minf\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maxis\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    652\u001b[0m                 \u001b[0mres\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mj\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    653\u001b[0m             \u001b[0mres\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mres\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mIndexError\u001b[0m: index 52 is out of bounds for axis 0 with size 52"
     ]
    }
   ],
   "source": [
    "# jenv = distance_statistics.Jenv(pattern, intervals=50, realizations=realizations)\n",
    "# jenv.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The $J(d)$ is obviously under $J(d)=1$, so we can conclude that the underlining process has a large propability to be a cluster process."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There also has **$S-$function** as $S(d)=\\sum_{i=1}^N[F(d_i)-G(d_i)]$ or $S(d)=\\sum_{i=1}^N|F(d_i)-G(d_i)|$, which is quite similar to $J-$function to compare the $F(d)$ and $G(d)$. The latter is better under most circumstances because the positive and negative values can not be added to be zero. It seems that the $S-$function is not included in the package."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Second-order point pattern analysis "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The $F-$function, $G-$function, and their combinations only consider the nearest distances which rely on a single spatial scale. We can call them `the first-order measurement'. Acturally, we can use all the points including higher order neighbors to consider distances between all target points. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$K-$function is related to the expect number of points within a specific circle.\n",
    "\n",
    "$$\n",
    "K(d)=A\\sum_{i=1,i\\neq j}^N\\sum_{j=1}^Nh_i(d)I_d(i,j)/N^2\n",
    "$$\n",
    "$A$ is the area of target zones; $h_i(d)=1$ if the circle with point $i$ as centre and $d$ as its radius located completely within the study area, otherwise $h_i(d)$ equals to the reciprocal intersected areas; $I_d(i,j)$ is 1 when $d_{ij}\\leq d$, else 0; $N$ is the total number of points.\n",
    "\n",
    "If the target points are generated from a CSR process, the expect point number will follow Poisson distribution. The expect number of points within a circle with $d$ as its radius is $n\\pit^2/A$.\n",
    "\n",
    "We can also compare target process with CSR via $L-$function:\n",
    "\n",
    "$$\n",
    "L(d)=\\sqrt{K(d)/\\pi}-d\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "kf = distance_statistics.K(pattern)\n",
    "kf.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "kenv = distance_statistics.Kenv(pattern, intervals=20, realizations=realizations)\n",
    "kenv.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "lf = distance_statistics.L(pattern)\n",
    "lf.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "lenv = distance_statistics.Lenv(pattern, intervals=20, realizations=realizations)\n",
    "lenv.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2. Simulating point process"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Random pattern ($N$-conditioned, $\\lambda$-conditioned)\n",
    "- Cluster pattern\n",
    "- Regular pattern\n",
    "\n",
    "All refer to https://nbviewer.jupyter.org/github/pysal/pointpats/blob/master/notebooks/process.ipynb."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pointpats import PoissonPointProcess, PoissonClusterPointProcess, Window, poly_from_bbox, PointPattern\n",
    "import libpysal as ps\n",
    "from libpysal.cg import shapely_ext\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SHAPEFILE WARNING: Polygon 3 topology has been fixed. (ccw -> cw)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/xxy/Environment/anaconda3/envs/py36/lib/python3.6/site-packages/libpysal/io/iohandlers/pyShpIO.py:174: RuntimeWarning: SHAPEFILE WARNING: Polygon 3 topology has been fixed. (ccw -> cw)\n",
      "  warn(\"SHAPEFILE WARNING: Polygon %d topology has been fixed. (ccw -> cw)\" % (self.pos), RuntimeWarning)\n"
     ]
    }
   ],
   "source": [
    "# open the virginia polygon shapefile\n",
    "va = ps.io.open('../Data/Beijing6Ring_Polygon.shp')\n",
    "polys = [shp for shp in va]\n",
    "# Create the exterior polygons for VA from the union of the county shapes\n",
    "state = shapely_ext.cascaded_union(polys)\n",
    "# create window from virginia state boundary\n",
    "window = Window(state.parts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Random pattern \n",
    "\n",
    "$N$-conditioned"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(5)\n",
    "samples = PoissonPointProcess(window, 200, 1, conditioning=False, asPP=False)  \n",
    "# by specifying \"asPP\" false, we can generate a point series\n",
    "# by specifying \"asPP\" true, or we will directly get a point pattern, samples.realizations[0] will be like <pointpats.pointpattern.PointPattern at 0x7fb5f41af208> instead of an array series. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[116.22423069,  39.8584922 ],\n",
       "       [116.2147703 ,  39.77007168],\n",
       "       [116.38924415,  39.82470785],\n",
       "       [116.46563369,  39.85878493],\n",
       "       [116.56111948,  39.97673101],\n",
       "       [116.4078297 ,  40.06597873],\n",
       "       [116.2705647 ,  39.99301402],\n",
       "       [116.2030034 ,  39.7671771 ],\n",
       "       [116.54410667,  40.04440774],\n",
       "       [116.36007022,  39.93135016],\n",
       "       [116.18478665,  40.00218483],\n",
       "       [116.63174664,  39.93703505],\n",
       "       [116.25649612,  39.77131787],\n",
       "       [116.34330106,  40.00112844],\n",
       "       [116.2701184 ,  40.16948534],\n",
       "       [116.4761904 ,  40.06370432],\n",
       "       [116.44587178,  39.77776319],\n",
       "       [116.45831595,  39.74779612],\n",
       "       [116.25137551,  40.14140542],\n",
       "       [116.26306117,  40.13157485],\n",
       "       [116.24379996,  40.05343658],\n",
       "       [116.2896189 ,  40.05894655],\n",
       "       [116.1760252 ,  39.75901663],\n",
       "       [116.18930996,  40.08391223],\n",
       "       [116.20343289,  39.8873121 ],\n",
       "       [116.21343021,  40.10021538],\n",
       "       [116.52020074,  39.76788195],\n",
       "       [116.56954718,  40.04861272],\n",
       "       [116.10093725,  39.97269499],\n",
       "       [116.44452467,  40.06367064],\n",
       "       [116.4060054 ,  40.15651984],\n",
       "       [116.48300806,  39.87405511],\n",
       "       [116.69720707,  39.93098224],\n",
       "       [116.24721235,  39.85393222],\n",
       "       [116.58378192,  40.0503123 ],\n",
       "       [116.62589107,  39.83555599],\n",
       "       [116.37752377,  39.80407385],\n",
       "       [116.69463314,  39.90240919],\n",
       "       [116.33383063,  39.75084411],\n",
       "       [116.59074099,  39.78822811],\n",
       "       [116.42519613,  40.09828511],\n",
       "       [116.56418306,  39.87048797],\n",
       "       [116.38708864,  39.79582754],\n",
       "       [116.14032511,  39.96903549],\n",
       "       [116.15576504,  39.99736592],\n",
       "       [116.24234869,  40.12129537],\n",
       "       [116.47803499,  39.81837412],\n",
       "       [116.43735173,  39.95645316],\n",
       "       [116.48025866,  40.03320749],\n",
       "       [116.58960748,  40.08087747],\n",
       "       [116.65199394,  39.99760765],\n",
       "       [116.1450801 ,  39.81501076],\n",
       "       [116.31035845,  39.83166376],\n",
       "       [116.42513534,  39.9669979 ],\n",
       "       [116.11840973,  39.9752632 ],\n",
       "       [116.20358964,  40.12079562],\n",
       "       [116.31310189,  40.00828926],\n",
       "       [116.23804139,  39.91921558],\n",
       "       [116.57919269,  39.83800953],\n",
       "       [116.30481286,  39.8596821 ],\n",
       "       [116.48243978,  40.06700875],\n",
       "       [116.39234343,  39.77583433],\n",
       "       [116.4481399 ,  39.75661758],\n",
       "       [116.15591283,  39.86998901],\n",
       "       [116.60921239,  39.78991346],\n",
       "       [116.30105522,  39.85022507],\n",
       "       [116.14918319,  39.72927583],\n",
       "       [116.32420814,  39.90161605],\n",
       "       [116.40283553,  40.08355861],\n",
       "       [116.6820191 ,  39.90611114],\n",
       "       [116.31683974,  39.90684813],\n",
       "       [116.09439434,  39.70300466],\n",
       "       [116.61921653,  39.82510688],\n",
       "       [116.15555255,  39.72613934],\n",
       "       [116.61319193,  40.10898898],\n",
       "       [116.40555037,  40.03650534],\n",
       "       [116.36335206,  40.09289256],\n",
       "       [116.44140039,  40.13308996],\n",
       "       [116.34153496,  39.90008756],\n",
       "       [116.20471074,  39.89986549],\n",
       "       [116.36695128,  39.97279299],\n",
       "       [116.52211986,  39.85902558],\n",
       "       [116.29239632,  39.87223589],\n",
       "       [116.30969867,  39.86242182],\n",
       "       [116.33924457,  40.04469556],\n",
       "       [116.2912846 ,  39.70825561],\n",
       "       [116.41297027,  39.95394821],\n",
       "       [116.68453035,  39.94479212],\n",
       "       [116.55690229,  39.83337157],\n",
       "       [116.52652176,  39.82309494],\n",
       "       [116.56200118,  39.91770423],\n",
       "       [116.31820355,  40.14524173],\n",
       "       [116.23516102,  40.03897327],\n",
       "       [116.22391455,  39.75610464],\n",
       "       [116.31193871,  40.12176661],\n",
       "       [116.58862381,  39.90391035],\n",
       "       [116.36529427,  40.0399876 ],\n",
       "       [116.59039293,  40.00680956],\n",
       "       [116.25039644,  40.06207455],\n",
       "       [116.23668917,  39.91381707],\n",
       "       [116.13942377,  39.92496586],\n",
       "       [116.19218215,  39.86972573],\n",
       "       [116.20772516,  40.1199385 ],\n",
       "       [116.59130434,  39.79659977],\n",
       "       [116.58860603,  40.05330569],\n",
       "       [116.45177821,  40.08133153],\n",
       "       [116.27410606,  39.87818982],\n",
       "       [116.59815702,  40.05711026],\n",
       "       [116.49516156,  40.09945582],\n",
       "       [116.69775029,  39.8737124 ],\n",
       "       [116.15330965,  39.79825859],\n",
       "       [116.44654116,  39.8684533 ],\n",
       "       [116.37959236,  40.00664727],\n",
       "       [116.49073517,  39.81462275],\n",
       "       [116.23653518,  40.10651893],\n",
       "       [116.42381855,  40.06064765],\n",
       "       [116.31262646,  39.84553391],\n",
       "       [116.6394246 ,  39.93453294],\n",
       "       [116.37124156,  40.11413537],\n",
       "       [116.34603814,  39.92534271],\n",
       "       [116.47874077,  39.9927392 ],\n",
       "       [116.41325597,  39.85610253],\n",
       "       [116.68208603,  39.91717348],\n",
       "       [116.39437527,  39.94203249],\n",
       "       [116.21750909,  39.90774356],\n",
       "       [116.46082749,  39.83482128],\n",
       "       [116.55038439,  39.77358509],\n",
       "       [116.55489843,  39.85506126],\n",
       "       [116.22206572,  39.86568313],\n",
       "       [116.3503634 ,  40.08236312],\n",
       "       [116.34925612,  40.12453477],\n",
       "       [116.28409559,  40.13397169],\n",
       "       [116.31301223,  39.89434188],\n",
       "       [116.38275933,  40.12591772],\n",
       "       [116.42249187,  39.97471836],\n",
       "       [116.16995494,  39.74997829],\n",
       "       [116.27371461,  40.05714986],\n",
       "       [116.17126577,  39.97529669],\n",
       "       [116.28350952,  39.93950717],\n",
       "       [116.50740381,  40.05782194],\n",
       "       [116.45919048,  40.09427361],\n",
       "       [116.43415116,  39.85673909],\n",
       "       [116.42660193,  39.87449149],\n",
       "       [116.48459017,  39.97870389],\n",
       "       [116.46815436,  40.08525299],\n",
       "       [116.45123699,  39.9742063 ],\n",
       "       [116.46145936,  39.90500023],\n",
       "       [116.30647931,  39.99951147],\n",
       "       [116.46121099,  40.08015711],\n",
       "       [116.27826374,  40.00825935],\n",
       "       [116.23887144,  39.79041832],\n",
       "       [116.32650274,  39.80472785],\n",
       "       [116.64741645,  40.029553  ],\n",
       "       [116.39707521,  39.89203549],\n",
       "       [116.5032079 ,  40.12573131],\n",
       "       [116.63637088,  39.83428823],\n",
       "       [116.12289585,  39.9522351 ],\n",
       "       [116.26929259,  39.82802865],\n",
       "       [116.1967925 ,  40.15026065],\n",
       "       [116.11557472,  39.82451939],\n",
       "       [116.29844153,  40.01801437],\n",
       "       [116.65371208,  39.86171469],\n",
       "       [116.2432599 ,  40.02153551],\n",
       "       [116.15674614,  39.99064619],\n",
       "       [116.39227897,  39.9937406 ],\n",
       "       [116.37894998,  39.9111167 ],\n",
       "       [116.51277015,  39.90843207],\n",
       "       [116.59281737,  39.76556424],\n",
       "       [116.22727439,  39.74672251],\n",
       "       [116.21206591,  39.76478072],\n",
       "       [116.34965821,  40.1410128 ],\n",
       "       [116.61171343,  40.01520737],\n",
       "       [116.20466465,  39.98812917],\n",
       "       [116.51376886,  39.79297729],\n",
       "       [116.63061519,  39.94878816],\n",
       "       [116.26982801,  40.16211771],\n",
       "       [116.25409132,  40.07505186],\n",
       "       [116.10031713,  39.72310685],\n",
       "       [116.62642857,  39.86635568],\n",
       "       [116.18958677,  39.75441265],\n",
       "       [116.2592491 ,  39.8209504 ],\n",
       "       [116.23930512,  40.01868494],\n",
       "       [116.65783184,  39.84776937],\n",
       "       [116.13729169,  39.93702153],\n",
       "       [116.29525183,  39.83009512],\n",
       "       [116.50817949,  39.88857633],\n",
       "       [116.18928042,  39.87310682],\n",
       "       [116.44452197,  39.97294154],\n",
       "       [116.34975625,  39.72797199],\n",
       "       [116.46244948,  39.75554906],\n",
       "       [116.30160568,  39.71576968],\n",
       "       [116.21774811,  40.13154241],\n",
       "       [116.69071947,  39.86694137],\n",
       "       [116.36465367,  39.81145781],\n",
       "       [116.28570759,  40.08216269],\n",
       "       [116.53768344,  40.00291499],\n",
       "       [116.25168795,  40.09056485],\n",
       "       [116.4036625 ,  39.91923816],\n",
       "       [116.47447544,  40.13585033],\n",
       "       [116.55306641,  39.82057908]])"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "samples.realizations[0] # simulated event points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [],
   "source": [
    "# build a point pattern from the simulated point series\n",
    "pp_csr = PointPattern(samples.realizations[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pp_csr.plot(window=True, hull=True, title='Random Point Pattern')  # hull, window - whether draw the maximum bounding polygon and rectangle"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pp_csr.plot(window=False, hull=False, title='Random Point Pattern')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\lambda$-conditioned (The function will calculate the intensity $\\lambda$ according to your input N(=200, in our example), we will obtain points with similar intensities, but not strictly with similar point numbers.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<pointpats.process.PoissonPointProcess at 0x7fb5f41914e0>"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# by specifying \"conditioning\" True, we can simulate a lamda-conditioned CSR\n",
    "np.random.seed(5)\n",
    "samples = PoissonPointProcess(window, 200, 1, conditioning=True, asPP=True)\n",
    "samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<pointpats.pointpattern.PointPattern at 0x7fb5f418de80>"
      ]
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pp_csr = samples.realizations[0] # simulated point pattern\n",
    "pp_csr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pp_csr.plot(window=True, hull=True, title='Random Point Pattern')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "188"
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pp_csr.n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<pointpats.process.PoissonPointProcess at 0x7fb5f40bf4a8>"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "samples = PoissonPointProcess(window, 100, 1, conditioning=True, asPP=True)\n",
    "samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<pointpats.pointpattern.PointPattern at 0x7fb5f40fb710>"
      ]
     },
     "execution_count": 122,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pp_csr = samples.realizations[0] # simulated point pattern\n",
    "pp_csr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pp_csr.plot(window=True, hull=True, title='Random Point Pattern')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "101"
      ]
     },
     "execution_count": 124,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pp_csr.n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Cluster pattern"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are two sources of clustering:\n",
    "\n",
    "-Contagion: presence of events at one location affects probability of events at another location (**correlated point process**)\n",
    "-Heterogeneity: intensity $\\lambda$ varies with location (**heterogeneous Poisson point process**)\n",
    "\n",
    "The PoissonClusterPointProcess seems mainly focus on the first one."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First generate parent points using CSR generation, based on both $N-$conditioned and $\\lambda-$conditioned by set `conditioning' parameter True or False. Then we generate offspring events independently around the parents within a circle of radius $r$ centered on the parent. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<pointpats.process.PoissonClusterPointProcess at 0x7fb5f3ef4da0>"
      ]
     },
     "execution_count": 173,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "csamples = PoissonClusterPointProcess(window, 200, 5, 0.05, 1, asPP=True, conditioning=False)\n",
    "# parameter: total number-200, parents-5, offsprings-200/5, radius-0.05, realization nums-1\n",
    "csamples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{0: 5}"
      ]
     },
     "execution_count": 174,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "csamples.num_parents "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "40"
      ]
     },
     "execution_count": 175,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "csamples.children"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 176,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<pointpats.pointpattern.PointPattern at 0x7fb64976cba8>"
      ]
     },
     "execution_count": 176,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pp_pcp = csamples.realizations[0]\n",
    "pp_pcp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 177,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pp_pcp.plot(window=True, hull=True, title='Clustered Point Pattern') #plot the first realization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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  "kernelspec": {
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