{
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  {
   "cell_type": "code",
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   "id": "0c88261c-c8d4-4638-a727-60d833b7d111",
   "metadata": {
    "execution": {
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Author: eli knaap\n",
      "\n"
     ]
    }
   ],
   "source": [
    "%load_ext watermark\n",
    "%watermark -a 'eli knaap'\n",
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "\n",
    "from libpysal import examples\n",
    "from esda import correlogram\n",
    "\n",
    "import geopandas as gpd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "68d86eb6-8595-48f0-a244-8889c59e770d",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-08-05T22:38:09.920052Z",
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     "shell.execute_reply.started": "2023-08-05T22:38:09.920043Z"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "sac = gpd.read_file(examples.load_example(\"Sacramento1\").get_path(\"sacramentot2.shp\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "2650732f-b704-4af8-bfee-ccd8c75cf133",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-08-05T22:38:10.131596Z",
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     "shell.execute_reply.started": "2023-08-05T22:38:10.131587Z"
    },
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   },
   "outputs": [],
   "source": [
    "sac = sac.to_crs(sac.estimate_utm_crs())  # now in meters)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "d3b1de58-3fb4-4874-ae5b-63f5e03f869d",
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    "execution": {
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[31mSignature:\u001b[39m\n",
      "correlogram(\n",
      "    geometry: geopandas.geoseries.GeoSeries,\n",
      "    variable: str | list | pandas.core.series.Series | \u001b[38;5;28;01mNone\u001b[39;00m,\n",
      "    support: list | \u001b[38;5;28;01mNone\u001b[39;00m = \u001b[38;5;28;01mNone\u001b[39;00m,\n",
      "    statistic: collections.abc.Callable | str = <\u001b[38;5;28;01mclass\u001b[39;00m \u001b[33m'esda.moran.Moran'\u001b[39m>,\n",
      "    distance_type: str = \u001b[33m'band'\u001b[39m,\n",
      "    weights_kwargs: dict = \u001b[38;5;28;01mNone\u001b[39;00m,\n",
      "    stat_kwargs: dict = \u001b[38;5;28;01mNone\u001b[39;00m,\n",
      "    select_numeric: bool = \u001b[38;5;28;01mFalse\u001b[39;00m,\n",
      "    n_jobs: int = -\u001b[32m1\u001b[39m,\n",
      "    n_bins: int | \u001b[38;5;28;01mNone\u001b[39;00m = \u001b[32m50\u001b[39m,\n",
      ") -> pandas.core.frame.DataFrame\n",
      "\u001b[31mDocstring:\u001b[39m\n",
      "Generate a spatial correlogram\n",
      "\n",
      "A spatial profile is a set of spatial autocorrelation statistics calculated for\n",
      "a set of increasing distances. It is a useful exploratory tool for examining\n",
      "how the relationship between spatial units changes over different notions of scale.\n",
      "\n",
      "Parameters\n",
      "----------\n",
      "geometry : gpd.GeoSeries\n",
      "    geodataframe holding spatial and attribute data\n",
      "variable: pd.Series or list\n",
      "    pandas series matching input geometries\n",
      "support : list or None\n",
      "    list of values at which to compute the autocorrelation statistic\n",
      "statistic : callable or str\n",
      "    statistic to be computed for a range of libpysal.Graph specifications.\n",
      "    This should be a class with a signature like `Statistic(y,w, **kwargs)`\n",
      "    where y is a  array and w is a libpysal.weights.W object\n",
      "    Generally, this is a class from pysal's `esda` package\n",
      "    defaults to esda.Moran, which computes the Moran's I statistic. If\n",
      "    'lowess' is provided, a non-parametric correlogram is computed using\n",
      "    lowess regression on the spatial-covariation model, see Notes.\n",
      "distance_type : str, optional\n",
      "    which concept of distance to increment. Options are {`band`, `knn`}.\n",
      "    by default 'band' (for `libpysal.weights.DistanceBand` weights)\n",
      "weights_kwargs : dict\n",
      "    additional keyword arguments passed to the libpysal.weights.W class\n",
      "stat_kwargs : dict\n",
      "    additional keyword arguments passed to the `esda` autocorrelation statistic class.\n",
      "    For example for faster results with no statistical inference, set the number\n",
      "    of permutations to zero with stat_kwargs={permutations: 0}\n",
      "select_numeric : bool\n",
      "    if True, only return numeric attributes from the original class. This is useful\n",
      "    e.g. to prevent lists inside a \"cell\" of a dataframe\n",
      "n_jobs : int\n",
      "    number of jobs to pass to joblib. If -1 (default), all cores will be used\n",
      "n_bins : int\n",
      "    number of distance bands or k-nearest neighbor values to use if\n",
      "    `support` is not provided. Ignored if `support` is provided.\n",
      "    by default 10. If `distance_type` is 'knn', the number of neighbors\n",
      "    will be capped at n-1, where n is the number of observations. Further,\n",
      "    if n-1 is not divisible by `n_bins`, the actual number of bins will be\n",
      "    may be off by one bin.\n",
      "\n",
      "Returns\n",
      "-------\n",
      "outputs : pandas.DataFrame\n",
      "    table of autocorrelation statistics at increasing distance bandwidths\n",
      "\n",
      "Notes\n",
      "-----\n",
      "The nonparametric correlogram uses a lowess regression\n",
      "to estimate the spatial-covariation model:\n",
      "\n",
      "    zi*zj = f(d_{ij}) + e_ij\n",
      "\n",
      "where f is a smooth function of distance d_{ij} between points i and j.\n",
      "This function requires the statsmodels package to be installed.\n",
      "\n",
      "For the nonparametric correlogram, a precomputed distance matrix can\n",
      "be used. To do this, set\n",
      "stat_kwargs={'metric':'precomputed', 'coordinates':distance_matrix}\n",
      "where `distance_matrix` is a square matrix of pairwise distances that\n",
      "aligns with the `geometry` rows.\n",
      "\u001b[31mFile:\u001b[39m      ~/Dropbox/work/dev/esda/esda/correlogram.py\n",
      "\u001b[31mType:\u001b[39m      function"
     ]
    }
   ],
   "source": [
    "correlogram?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "90fc27f4-1f71-4a39-bcd1-339fa27fa3b4",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-08-05T22:38:10.253267Z",
     "iopub.status.busy": "2023-08-05T22:38:10.253180Z",
     "iopub.status.idle": "2023-08-05T22:38:10.283353Z",
     "shell.execute_reply": "2023-08-05T22:38:10.282850Z",
     "shell.execute_reply.started": "2023-08-05T22:38:10.253257Z"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "from esda import Moran, Geary, G"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d77ee874-e889-4d60-a039-434906696451",
   "metadata": {},
   "source": [
    "## Distance Bands"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "ab615631-b083-4700-b402-8dd8343cc790",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-08-05T22:38:10.283933Z",
     "iopub.status.busy": "2023-08-05T22:38:10.283848Z",
     "iopub.status.idle": "2023-08-05T22:38:10.313104Z",
     "shell.execute_reply": "2023-08-05T22:38:10.312763Z",
     "shell.execute_reply.started": "2023-08-05T22:38:10.283925Z"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Create a liste of distances between 500 and 5000 (meters, here) in increments of 500\n",
    "\n",
    "distances = [i+500 for i in range(0,5000, 500)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "049e4002-52a1-4205-9238-bfdb175f04ff",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-08-05T22:38:10.315016Z",
     "iopub.status.busy": "2023-08-05T22:38:10.314723Z",
     "iopub.status.idle": "2023-08-05T22:38:10.343152Z",
     "shell.execute_reply": "2023-08-05T22:38:10.342713Z",
     "shell.execute_reply.started": "2023-08-05T22:38:10.315005Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[500, 1000, 1500, 2000, 2500, 3000, 3500, 4000, 4500, 5000]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "distances"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d5642b21-6e3c-46ed-8c6f-5ada5baec96d",
   "metadata": {},
   "source": [
    "The correlogram will compute an autocorrelation statistic (Moran's $I$ by default) at each distance threshold. Plotting this statistic against distance reveals how spatial similarity changes over distance (similar in concept to a variogram)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9d546402-f9c8-407c-945e-b72979fc9df8",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "prof = correlogram(\n",
    "    sac.centroid,\n",
    "    sac.HH_INC,\n",
    "    distances,\n",
    "    Moran\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5187da59-aba0-465d-9fa7-e22794c8eb1a",
   "metadata": {},
   "source": [
    "`prof` is a dataframe of autocorrelation statistics indexed by distance. It includes all attributes created by the esda autocorrelation statistic class (e.g. [Moran](https://pysal.org/esda/generated/esda.Moran.html#esda.Moran), [Geary](https://pysal.org/esda/generated/esda.Geary.html#esda.Geary), or [Geits-Ord G](https://pysal.org/esda/generated/esda.G.html#esda.G)). The row index for each statistic is the distance at which it was computed"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "af5bad37-874a-483b-a692-a3ae205416f8",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-08-05T22:38:11.719943Z",
     "iopub.status.busy": "2023-08-05T22:38:11.719810Z",
     "iopub.status.idle": "2023-08-05T22:38:11.764412Z",
     "shell.execute_reply": "2023-08-05T22:38:11.764069Z",
     "shell.execute_reply.started": "2023-08-05T22:38:11.719928Z"
    },
    "tags": []
   },
   "outputs": [
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       "      <td>1.668694e-05</td>\n",
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       "      <td>999</td>\n",
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       "      <td>1.260604e+11</td>\n",
       "      <td>-0.002488</td>\n",
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       "2500  <libpysal.weights.distance.DistanceBand object...           999  403   \n",
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       "1000  [0.27506115837390277, 0.21948138443207246, -0....  1.260604e+11   \n",
       "1500  [0.27506115837390277, 0.21948138443207246, -0....  1.260604e+11   \n",
       "2000  [0.27506115837390277, 0.21948138443207246, -0....  1.260604e+11   \n",
       "2500  [0.27506115837390277, 0.21948138443207246, -0....  1.260604e+11   \n",
       "\n",
       "            EI   VI_norm  seI_norm   VI_rand  ...     z_rand        p_norm  \\\n",
       "500  -0.002488  0.497534  0.705361  0.496239  ...   0.086188  9.314058e-01   \n",
       "1000 -0.002488  0.014259  0.119409  0.014221  ...   4.147088  3.447621e-05   \n",
       "1500 -0.002488  0.004586  0.067719  0.004574  ...   6.763620  1.430242e-11   \n",
       "2000 -0.002488  0.002164  0.046515  0.002158  ...  12.164298  5.846476e-34   \n",
       "2500 -0.002488  0.001481  0.038483  0.001477  ...  13.102771  3.974924e-39   \n",
       "\n",
       "            p_rand                                                sim  p_sim  \\\n",
       "500   9.313166e-01  [-0.041149125017795225, 0.8047828919464444, 0....  0.465   \n",
       "1000  3.367309e-05  [0.01407910066509541, -0.09399265148441757, -0...  0.001   \n",
       "1500  1.345857e-11  [-0.028776580865062164, 0.07946937157388524, 0...  0.001   \n",
       "2000  4.815656e-34  [-0.0566559868640034, 0.06456200403436937, -0....  0.001   \n",
       "2500  3.174519e-39  [-0.03272028047068946, -0.025327634962963246, ...  0.001   \n",
       "\n",
       "        EI_sim   seI_sim    VI_sim      z_sim       p_z_sim  \n",
       "500  -0.017506  0.693436  0.480854   0.109214  4.565164e-01  \n",
       "1000 -0.007273  0.120349  0.014484   4.149132  1.668694e-05  \n",
       "1500 -0.003352  0.067581  0.004567   6.781418  5.950106e-12  \n",
       "2000 -0.000508  0.047756  0.002281  11.791263  2.164994e-32  \n",
       "2500 -0.002785  0.039315  0.001546  12.816543  6.623787e-38  \n",
       "\n",
       "[5 rows x 23 columns]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prof.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fc0196ce-f47d-424b-8ca6-2ef56c25193b",
   "metadata": {},
   "source": [
    "Often, it is easiest to visualize the statistic, and the pandas `plot` function will plot a column against the dataframe's index by default"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d82a3e65-4cfd-43d7-990c-2dde5fb23ee9",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-08-05T22:38:11.764940Z",
     "iopub.status.busy": "2023-08-05T22:38:11.764861Z",
     "iopub.status.idle": "2023-08-05T22:38:12.073150Z",
     "shell.execute_reply": "2023-08-05T22:38:12.072868Z",
     "shell.execute_reply.started": "2023-08-05T22:38:11.764931Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: >"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = prof.I.plot()\n",
    "ax.set_xlabel(\"distance (m)\")\n",
    "ax.set_ylabel(\"Moran's I\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "746f27c2-664b-4d75-abb2-5b202d96c4ab",
   "metadata": {},
   "source": [
    "Autocorrelation statistics differ in concept, so the shape of the spatial correlogram statistic will vary considerably, based on which statistic is created. For example, we can also plot Geary's $C$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "511b4ce9-9c68-4142-a6b7-f202b39a9951",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-08-05T22:38:12.073772Z",
     "iopub.status.busy": "2023-08-05T22:38:12.073633Z",
     "iopub.status.idle": "2023-08-05T22:38:12.251370Z",
     "shell.execute_reply": "2023-08-05T22:38:12.250906Z",
     "shell.execute_reply.started": "2023-08-05T22:38:12.073764Z"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "prof = correlogram(\n",
    "    sac.centroid,\n",
    "    sac.HH_INC,\n",
    "    distances,\n",
    "    statistic=Geary\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8586e477-faac-434c-90e3-fbc34e044375",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-08-05T22:38:12.252069Z",
     "iopub.status.busy": "2023-08-05T22:38:12.251970Z",
     "iopub.status.idle": "2023-08-05T22:38:12.354317Z",
     "shell.execute_reply": "2023-08-05T22:38:12.353996Z",
     "shell.execute_reply.started": "2023-08-05T22:38:12.252060Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: >"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = prof.C.plot()\n",
    "ax.set_xlabel(\"distance (m)\")\n",
    "ax.set_ylabel(\"Geary's C\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "39390947-1cd9-4a4a-9e9b-71bb7c493b39",
   "metadata": {},
   "source": [
    "...Or Getis-Ord $G$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d9984fc2-400b-4561-9158-c2a28ac25476",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-08-05T22:38:12.355011Z",
     "iopub.status.busy": "2023-08-05T22:38:12.354787Z",
     "iopub.status.idle": "2023-08-05T22:38:12.480568Z",
     "shell.execute_reply": "2023-08-05T22:38:12.480260Z",
     "shell.execute_reply.started": "2023-08-05T22:38:12.355001Z"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "prof = correlogram(\n",
    "    sac.centroid,\n",
    "    sac.HH_INC,\n",
    "    distances,\n",
    "    statistic=G\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "61cb28fd-2e07-44df-8b25-b11b4b06e9f4",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-08-05T22:38:12.481090Z",
     "iopub.status.busy": "2023-08-05T22:38:12.481003Z",
     "iopub.status.idle": "2023-08-05T22:38:12.589553Z",
     "shell.execute_reply": "2023-08-05T22:38:12.589289Z",
     "shell.execute_reply.started": "2023-08-05T22:38:12.481081Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: >"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = prof.G.plot()\n",
    "ax.set_xlabel(\"distance (m)\")\n",
    "ax.set_ylabel(\"Getis-Ord G\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f7d77976",
   "metadata": {},
   "source": [
    "You can also leave the distance thresholds unspecified, and the correlogram will estimate over a reasonable range of distances:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8189ff3a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: >"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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hqmGKDOOfLICug994gI/ZX1WvmYuytbGgUkE26c4pg/Sz8X04vAOgy6GkAD5k7Z5y3bZovUprXHJEhOp/p4/Q+AE9rI4FAJagpAA+wBijRV/s1f3v5qjJYzQoOVrP3jhaGd0jrY4GAJahpAAWq29063dvb9U/1+2TxPoTADiC34KAhUprXPrxi+u860/mTxmkn7L+BAAkUVIAy+wtq9WMv63RnrI6OSJC9eR1I3R+f9afAMARlBTAApv3VeqWF9aqrLZBaXERevHWs9S3RzerYwGAT6GkAJ1s2fYSzXppveoa3BqaEqMXbhmjxGgubw8A30VJATrRa+sKdNcbW+T2GJ3fP0ELbxilbty9GACOid+OQCcwxujJT3fqj0t2SJKuHJGq3//XMIWFBFmcDAB8FyUF6GBuj9Hv3t6ql77MlyTddkFf3Tl5IGfwAMBJUFKADnSowa05izdoSc4B2WzSfdOGasa5mVbHAgC/QEkBOoizvlG3vLBW2XsrFBYSpCeuHa4pWT2tjgUAfoOSAnSAQw1u/ej/mgtKTHiInr95jMZkxlsdCwD8CiUFaGcNTR7d9lK21u6pUHR4iF756TkamuKwOhYA+B1OLQDakdtj9MvXNmn59oMKDw3S324eQ0EBgDaipADtxJjms3je3VSkkCCbFt4wikM8AHAaKClAO/nDR9v10pf5stmkx64ZrokDE62OBAB+jZICtIO/rNilp5fvkiQ9fMUZmnZmisWJAMD/UVKA07R4Tb4WfLhNkjR/yiBdd3aGxYkAIDBQUoDT8P7mYt395hZJ0swJfXXbBX0tTgQAgYOSArTRih0HNe/VDTJGmn5WhuZPGWh1JAAIKJQUoA025Fdo5j+y1eg2mjqspx66Iot78QBAO6OkAK20r6JOP/n7Oh1qdGvCgB567IfDFRxEQQGA9kZJAVqhxtWkH7+4TqU1DRrcM0ZPXz9SYSH8MwKAjsBvV+AUuT1Gc17ZoG37q9Uj2q7nZ4xWlJ07SwBAR6GkAKfokQ++1qfbSmQPCdJfbxqtlNgIqyMBQECjpACn4KUv9+r5lXmSpD/+8EydmR5rbSAA6AIoKcBJrMwt1e/e/kqS9MvvDdBlw7iaLAB0BkoKcAI7S2p020vZcnuMrhieotkX9rM6EgB0GZQU4Dgqahv0oxfXqrq+SaN6xenR/xrGtVAAoBNRUoBjaGjy6GeLsrW3rE5pcRH6y42jFB4abHUsAOhSKCnAdxhjdM+bW7Qmr1zd7CH6281jlNDNbnUsAOhyKCnAd/z18zy9lr1PQTbpyetGaEBStNWRAKBLoqQA3/Ll7jI9+u9tkqTfXjZEFwxMtDgRAHRdlBTgsJLqes1+ZYPcHqMrR6Tq5nMzrY4EAF0aJQWQ1OT26PaXN+hgtUsDkrrp4Su5qzEAWI2SAkj645Id+jKvXFFhwVp4wyhFhnFPHgCwGiUFXd6SnANauHyXJOn3Vw1T3x7dLE4EAJAoKeji8svq9Mt/bpQk3XxuJpe8BwAf0uqSUlhYqBtuuEHdu3dXZGSkhg8fruzs7I7IBnSo+ka3fv5ytpz1TRqREatfXzrY6kgAgG9p1YH3iooKnXfeeZo4caI+/PBDJSYmateuXYqNje2geEDHuf/dHG0tdCo+KkxPXTdSYSFMLAKAL2lVSfn973+v9PR0vfDCC95tmZmZ7Z0J6HCvZ+/TK2vyZbNJj18zXCmxEVZHAgB8R6v+6/jOO+9o9OjRuvrqq5WYmKgRI0boueeeO+FzXC6XnE5niwdgpW37nbrnrS2SpLmT+mv8gB4WJwIAHEurSsru3bu1cOFC9e/fXx999JFmzpypOXPm6O9///txn7NgwQI5HA7vIz09/bRDA21VXd+o2xatV32jR+MH9NCcC/tbHQkAcBw2Y4w51Z3DwsI0evRorVq1yrttzpw5Wrt2rVavXn3M57hcLrlcLu/nTqdT6enpqqqqUkxMzGlEB1rHGKPZr2zQ+5uLleII13tzzld8VJjVsQDALzidTjkcjk59/27VTErPnj01ZMiQFtsGDx6s/Pz84z7HbrcrJiamxQOwwmvZ+/T+5mKFBNn05PUjKSgA4ONaVVLOO+88bd++vcW2HTt2qFevXu0aCmhve0prdd87X0mSfnnxQI3MiLM4EQDgZFpVUn7xi1/oiy++0COPPKKdO3fq5Zdf1rPPPqtZs2Z1VD7gtDW6PZq7eIPqGtw6p0+8fjq+j9WRAACnoFUlZcyYMXrzzTf1yiuvKCsrSw8++KAef/xxXX/99R2VDzhtf16aq037qhQTHqI//XC4goO4cSAA+INW30Xtsssu02WXXdYRWYB29+XuMj21fKckacEPhnE9FADwI1xiEwGr6lCj7vjnJhkjXT0qTVOH9bQ6EgCgFSgpCEjGGP3mra0qrDykXt0jde/3h1odCQDQSpQUBKS3Nhbq3U1FCg6y6fFrhqubvdVHNgEAFqOkIODkl9Xpt281n248b1J/jeB0YwDwS5QUBJQmt0fzXt2gGleTxmTG6ecT+1kdCQDQRpQUBJQnl+3U+vxKRdtD9Ng1nG4MAP6MkoKAkb23XE98kitJeujKLKXFRVqcCABwOigpCAh1DU2a9+pGeYx05YhUXT481epIAIDTRElBQPjz0lwVlB9SamyE7r+c040BIBBQUuD3vi526q8r8yRJD14xVDHhoRYnAgC0B0oK/JrHY/TrN7fI7TG6JCtZFw5KsjoSAKCdUFLg1xavLdCG/EpFhQXrd9OGWB0HANCOKCnwWwerXXr0w68lSb+8eKB6Orh5IAAEEkoK/NbD7+fIWd+krNQYzTg30+o4AIB2RkmBX1qZW6q3NhYpyCY9cuUZXLQNAAIQJQV+p77Rrd++vVWSdNPYTA1Li7U2EACgQ1BS4HeeXr5LeaW1Soqx65cXD7A6DgCgg1BS4Fd2HazRM8t3SZLunTZU0VwTBQACFiUFfsMYo3ve3KIGt0cXDOyhS7KSrY4EAOhAlBT4jTfWF+qL3eUKDw3Sg5dnyWZjsSwABDJKCvxCZV2DHv6g+Zoocyb1V3o8dzgGgEBHSYFfePTDbSqvbdCApG76yfl9rI4DAOgElBT4vOy95Vq8tkBS8zVRQoP5sQWAroDf9vBpTW6P7nmz+Zoo14xO1+jMeIsTAQA6CyUFPu0fX+zVtv3VckSEav4lg6yOAwDoRJQU+KwSZ73+9PEOSdKdUwYqPirM4kQAgM5ESYHPWvDhNlW7mnRmmkPXjsmwOg4AoJNRUuCTvthdpjc3FMpmkx68IosbCAJAF0RJgc9pdHv0u8M3ELzurAxuIAgAXRQlBT7n//6zRzsO1Cg+Kky/mjzQ6jgAAItQUuBT9lfV6/GlzYtl75oySLGRLJYFgK6KkgKf8tD7OaptcGtkRqyuGpVmdRwAgIUoKfAZ/9lZqvc2FyvIJj1weZaCWCwLAF0aJQU+oaHpm8WyN57TS1mpDosTAQCsRkmBT3h+ZZ52HaxVQrcw3XExi2UBAJQU+IDCykN64pNcSdLdlwyWIyLU4kQAAF9ASYHlHnovR4ca3RqTGacfjEy1Og4AwEdQUmCpz3Yc1Idb9ys4yKYHr8iSzcZiWQBAM0oKLNPo9uj+d7+SJM0Ym6lByTEWJwIA+BJKCizz4qo92nWwVt2jwjT3ov5WxwEA+BhKCixRWuPSn5c2L5b91eSBLJYFAByFkgJL/PHj7ap2NSkrNUZXj063Og4AwAdRUtDpthZWafHaAknSvdOGKpgrywIAjoGSgk5ljNF973wlY6Tvn5miMZnxVkcCAPgoSgo61bubi7Vub4UiQoN196WDrI4DAPBhlBR0mrqGJi344GtJ0m0X9FVPR4TFiQAAvoySgk7zzPJdKq6qV1pchH46vo/VcQAAPo6Sgk5RUF6nv3y2W5J0z6WDFR4abHEiAICvo6SgUyz48Gu5mjw6p0+8pmQlWx0HAOAHKCnocKt2leqDLfsVZGs+5Zj78wAATgUlBR2qye3RA+/mSJKuP7uXBvfk/jwAgFNDSUGHemVtgbbtr5YjIlR3fG+A1XEAAH6EkoIOU1nXoD9+vF2SdMf3BiguKsziRAAAf0JJQYd5fGmuKusaNSCpm64/O8PqOAAAP0NJQYfYcaBa//hir6TmxbIhwfyoAQBah3cOtDtjjB58L0duj9HkoUk6r1+C1ZEAAH6IkoJ2tyTngD7PLVVYcJDuuXSI1XEAAH6KkoJ25Wpy66H3m+/P8+Pzeyuje6TFiQAA/oqSgnb1t5V7lF9ep8Rou34+sZ/VcQAAfoySgnZT4qzXk5/mSpLmTxmkbvYQixMBAPwZJQXt5r8/2q7aBreGp8fqyhGpVscBAPg5SgraxaaCSv0re58k6d5pQxQUxP15AACnh5KC02aM0X3vfiVJ+sHIVI3IiLM4EQAgEFBScNre3likDfmVigwL1vwpg6yOAwAIEJQUnJZaV5MWfNh8yvGsif2UFBNucSIAQKCgpOC0LFy+SwecLqXHR+hH43pbHQcAEEBOq6QsWLBANptN8+bNa6c48CcF5XV69vPdkqR7Lh2i8NBgixMBAAJJm0vK2rVr9eyzz2rYsGHtmQd+5JEPvlZDk0fn9u2uyUOTrI4DAAgwbSopNTU1uv766/Xcc88pLo4zObqiVbtK9eHW/QqyNd/l2GbjlGMAQPtqU0mZNWuWpk6dqosuuuik+7pcLjmdzhYP+De3x+jB95oXy95wTi8NTI62OBEAIBC1+rrlixcv1vr167V27dpT2n/BggW6//77Wx0MvuuN9fv0dbFTMeEh+sVFA6yOAwAIUK2aSSkoKNDcuXO1aNEihYef2qmmd999t6qqqryPgoKCNgWFbzjU4Nb/fLxdkjT7wn6KiwqzOBEAIFC1aiYlOztbJSUlGjVqlHeb2+3WZ599pieffFIul0vBwS3P8LDb7bLb7e2TFpZ7fuVuHXC6lBoboZvGZlodBwAQwFpVUiZNmqQtW7a02HbLLbdo0KBBmj9//lEFBYGltMalZ1Y0n3J855SBnHIMAOhQrSop0dHRysrKarEtKipK3bt3P2o7As+fl+aqxtWkM1IdmjYsxeo4AIAAxxVncUp2HazRy2vyJUm/vnQwdzkGAHS4Vp/d813Lly9vhxjwdY9+uE1uj9FFgxM1tm93q+MAALoAZlJwUmvyyrUk54CCg2y66xLucgwA6ByUFJyQMUYPf9B84bZrxqSrXyIXbgMAdA5KCk7ovc3F2lRQqciwYM27qL/VcQAAXQglBcflanLrvz/aJkn62fi+Sow+tQv4AQDQHigpOK5/rN6rgvJDSoy26yfje1sdBwDQxVBScExVdY363093SpJ+efEARYad9olgAAC0CiUFx/TkslxVHWrUwKRoXTUq3eo4AIAuiJKCoxSU1+nFVXslSXddOkjBXLgNAGABSgqO8oePtqvB7dF5/brrggE9rI4DAOiiKCloYWthld7ZVCSbTbr7ksGy2ZhFAQBYg5KCFv77o+2SpMvPTFFWqsPiNACAroySAq9Vu0r12Y6DCgmy6Y7vDbQ6DgCgi6OkQFLz5e//+9/NsyjXnZ2hjO6RFicCAHR1lBRIkj7OOaCNBZWKCA3W7Av7WR0HAABKCiS3x+gPh9ei/Ghcby5/DwDwCZQU6I31+7SzpEaxkaH66YQ+VscBAEASJaXLczW59fjSXEnSzy/oq5jwUIsTAQDQjJLSxb30Rb4KKw8pOSZcN43NtDoOAABelJQurMbVpCeXNd9EcN5F/RUeGmxxIgAAvkFJ6cL++vluldc2qE9ClK4alWZ1HAAAWqCkdFFlNS4999luSdL/mzxQIcH8KAAAfAvvTF3UU8t2qbbBrTNSHbokK9nqOAAAHIWS0gXtq6jToi/2SpLunDKQmwgCAHwSJaULenxprhrcHp3bt7vG9UuwOg4AAMdESelicg9U6431+yRJd04ZxCwKAMBnUVK6mP/5eLs8RpoyNFnD02OtjgMAwHFRUrqQjQWV+uirAwqySf9v8gCr4wAAcEKUlC7ksSU7JEk/GJmmfonRFqcBAODEKCldRPbecq3YcVAhQTbNubC/1XEAADgpSkoX8diS5psIXjUqTRndIy1OAwDAyVFSuoA1eeVaubNUocE2zZrYz+o4AACcEkpKF3BkLcrVo9OVHs8sCgDAP1BSAtzqXWVavbtMYcFBzKIAAPwKJSWAGWP02NLmWZRrxqQrNTbC4kQAAJw6SkoAW72rTGvyyhUWEqSfT+xrdRwAAFqFkhKgjDH60+G1KNedlaGeDmZRAAD+hZISoD7PLdW6vRWyhwTptguYRQEA+B9KSgD69lqU68/upaSYcIsTAQDQepSUALR8x0FtyK9UeGiQZl7Qx+o4AAC0CSUlwBhj9PjhtSg3ntNLidHMogAA/BMlJcB8uq1Em/ZVKSI0WD+bwFoUAID/oqQEkG+vRZlxbqYSutktTgQAQNtRUgLIkpwD2lroVFRYsH46nrUoAAD/RkkJEB6P0WNLm+90fPN5mYqPCrM4EQAAp4eSEiA+ztmvr4ud6mYP0U/OZxYFAOD/KCkBwBijJz7ZKUm65bxMxUYyiwIA8H+UlACwbHuJcoqb16Lcel5vq+MAANAuKCl+7tuzKDeM7aU41qIAAAIEJcXP/WdnmTYWVMoeEqQfj2MtCgAgcFBS/Nz/ftp8Rs/0szLUI5rrogAAAgclxY+tySvXl3nlCgsO0s8mMIsCAAgslBQ/dmQW5arRaerpiLA4DQAA7YuS4qc2FlTq89xSBQfZdBv36AEABCBKip968tPmM3quGJ6q9PhIi9MAAND+KCl+KKfIqaVfH5DNJs2ayCwKACAwUVL80FPLmmdRLhuWoj49ulmcBgCAjkFJ8TM7S6r1wdZiScyiAAACGyXFzzy1bJeMkSYPTdKg5Bir4wAA0GEoKX5kb1mt3t5YKEmaPbG/xWkAAOhYlBQ/snD5LnmMdMHAHjojzWF1HAAAOhQlxU8UVh7S6+v3SZJuv5BZFABA4KOk+Im/rNilRrfRuX27a1SvOKvjAADQ4SgpfqDEWa/FawskSbMv7GdxGgAAOgclxQ889/luNTR5NKpXnMb26W51HAAAOgUlxceV1zZo0Rf5kppnUWw2m8WJAADoHK0qKQsWLNCYMWMUHR2txMREXXHFFdq+fXtHZYOkF/6Tp0ONbmWlxuiCAT2sjgMAQKdpVUlZsWKFZs2apS+++EJLlixRU1OTLr74YtXW1nZUvi7NWd+o/1u1R5I0eyKzKACAriWkNTv/+9//bvH5Cy+8oMTERGVnZ2v8+PHtGgzSP1bvVXV9k/ondtPFQ5KtjgMAQKc6rTUpVVVVkqT4+Ph2CYNvHGpw628r8yRJP5/YV0FBzKIAALqWVs2kfJsxRnfccYfGjRunrKys4+7ncrnkcrm8nzudzra+ZJfyypp8ldU2KCM+UtOGpVgdBwCATtfmmZTZs2dr8+bNeuWVV06434IFC+RwOLyP9PT0tr5kl+FqcuvZz3ZLkmZO6KuQYE7CAgB0PW1697v99tv1zjvvaNmyZUpLSzvhvnfffbeqqqq8j4KCgjYF7UreWF+o/c56JceE679GpVodBwAAS7TqcI8xRrfffrvefPNNLV++XL179z7pc+x2u+x2e5sDdjVNbo8WLt8lSfrJ+D6yhwRbnAgAAGu0qqTMmjVLL7/8st5++21FR0dr//79kiSHw6GIiIgOCdjVvLe5WPnldYqPCtP0szg0BgDoulp1uGfhwoWqqqrSBRdcoJ49e3ofr776akfl61I8HqOnlu2UJP1oXG9FhrV5XTMAAH6v1Yd70HE+ztmv3JIaRYeH6MaxvayOAwCApThtxEcYY/Tk4VmUGWMzFRMeanEiAACsRUnxESt2HNTWQqciQoN167iTL0gGACDQUVJ8xJG1KNednaH4qDCL0wAAYD1Kig/4cneZ1u6pUFhwkH46vo/VcQAA8AmUFB9wZC3KVaPTlBQTbnEaAAB8AyXFYpsKKvV5bqmCg2y6bUJfq+MAAOAzKCkWO7IW5fLhKUqPj7Q4DQAAvoOSYqGviqr0cc4B2WzSzy9gFgUAgG+jpFjoiU9yJUnThqWoX2K0xWkAAPAtlBSLfFVUpY++ap5FmTOpn9VxAADwOZQUizCLAgDAiVFSLMAsCgAAJ0dJsQCzKAAAnBwlpZMxiwIAwKmhpHQyZlEAADg1lJROxCwKAACnjpLSif68lFkUAABOFSWlk2wt/ObqsnMm9bc6DgAAPo+S0kmOrEX5/pkp6pfYzeI0AAD4PkpKJ/j2LMrtFzKLAgDAqaCkdAJmUQAAaD1KSgdjFgUAgLahpHQwZlEAAGgbSkoHYhYFAIC2o6R0IGZRAABoO0pKB1mfX8EsCgAAp4GS0gGMMXrovRxJ0lUj05hFAQCgDSgpHeC9zcVan1+pyLBg/b/JA62OAwCAX6KktLP6Rrce/XCbJGnmhL5Kigm3OBEAAP6JktLOXvjPHhVWHlJyTLh+cn4fq+MAAOC3KCntqLTGpaeW7ZQk3TlloCLCgi1OBACA/6KktKPHluxQjatJZ6Q6dMXwVKvjAADg1ygp7WTHgWq9siZfkvSbqYMVFGSzOBEAAP6NktJOHn7/a3mMNGVoss7u093qOAAA+D1KSjtYvr1EK3YcVGiwTXdfOsjqOAAABARKymlqcnv08PtfS5JuPjdTvbpHWZwIAIDAQEk5TYvXFii3pEZxkaGazeXvAQBoN5SU0+Csb9RjS3ZIkuZdNECOiFCLEwEAEDgoKafh6WW7VFbboD49onTd2RlWxwEAIKBQUtqooLxOf1uZJ0m659LBCg1mKAEAaE+8s7bR7/+9TQ1uj87r110XDkq0Og4AAAGHktIGX+4u03ubi2WzSfdcOkQ2GxduAwCgvVFSWulQg1t3vr5ZknTtmAwNSYmxOBEAAIGJktJKf/x4u/aW1amnI5wLtwEA0IEoKa2QvbdCz/+nebHsI1eeoZhwTjkGAKCjUFJOUX2jW3f+a5OMkX4wMlUTWSwLAECHoqScoseX5mrXwVr1iLbrd5cNsToOAAABj5JyCjYVVOrZz3ZJkh6+IkuxkWEWJwIAIPBRUk7C1eTWnf/aLI+Rpp2ZoouHJlsdCQCALoGSchJPfbpT2w9Uq3tUmO7//lCr4wAA0GVQUk7gq6IqPb28+TDPA5dnKT6KwzwAAHQWSspxNLo9+tVrm9XkMZoyNFmXnsFhHgAAOhMl5TieWb5LOcVOxUaG6oErhnLpewAAOhkl5Ri276/WE5/mSpLunTZEidHhFicCAKDroaR8R5Pbozv/tUmNbqNJgxJ1xfBUqyMBANAlUVK+4w8fbdemfVWKDg/Rw1eewWEeAAAsQkn5luc+262/fLZbkvTg5VlKdnCYBwAAq1BSDvtX9j49/MHXkqT5UwbpihEc5gEAwEqUFElLcw5o/uubJUk/HtdbMyf0sTgRAADo8iXly91lmvXyerk9Rj8YmapfXzqYdSgAAPiALl1Scoqc+vGL6+Rq8mjSoET9/r+GKSiIggIAgC/osiVlb1mtbvrbGlW7mjQmM05PXT9SocFddjgAAPA5XfJducRZrxufX6PSGpcGJUfrrzPGKDw02OpYAADgW7pcSak61Kib/rZG+eV1yoiP1N9vPUuOiFCrYwEAgO/oUiWlvtGtn7y4Ttv2Vyuhm13/+NFZSozhWigAAPiiEKsDdAa3x+i9zUX68ye52n2wVtH2EL146xj16h5ldTQAAHAcbZpJefrpp9W7d2+Fh4dr1KhR+vzzz9s7V7twe4ze2lCo7z22QnMXb9Tug7WKjQzVX2eM1tAUh9XxAADACbR6JuXVV1/VvHnz9PTTT+u8887TX/7yF11yySXKyclRRkZGR2RstSa3R+9sKtKTn+7U7tJaSVJsZKh+cn4f3TS2l6LDWYMCAICvsxljTGuecPbZZ2vkyJFauHChd9vgwYN1xRVXaMGCBSd9vtPplMPhUFVVlWJiYlqf+ASa3B69vbFITy7bqbzvlJMZ52aqm71LHN0CAKDddeT79/G06l27oaFB2dnZuuuuu1psv/jii7Vq1apjPsflcsnlcnk/dzqdbYh5Yk1uj97aWKQnP83VnrI6SVJcZKh+Mr6PbhpLOQEAwB+16t27tLRUbrdbSUlJLbYnJSVp//79x3zOggULdP/997c94SmocTXpvne+Uo2rSXGRofrp+L66cWwvygkAAH6sTe/i3723jTHmuPe7ufvuu3XHHXd4P3c6nUpPT2/Lyx5XbGSY5k7qL7cxuvGcXoqinAAA4Pda9W6ekJCg4ODgo2ZNSkpKjppdOcJut8tut7c94Sn6yXjuXAwAQCBp1SnIYWFhGjVqlJYsWdJi+5IlS3Tuuee2azAAANC1tfq4yB133KEbb7xRo0eP1tixY/Xss88qPz9fM2fO7Ih8AACgi2p1SbnmmmtUVlamBx54QMXFxcrKytIHH3ygXr16dUQ+AADQRbX6Oimny4rzrAEAwOmx4v27S91gEAAA+A9KCgAA8EmUFAAA4JMoKQAAwCdRUgAAgE+ipAAAAJ9ESQEAAD6JkgIAAHwSJQUAAPikVl8W/3QducCt0+ns7JcGAABtdOR9uzMvVN/pJaW6ulqSlJ6e3tkvDQAATlN1dbUcDkenvFan37vH4/GoqKhI0dHRstlsp/39nE6n0tPTVVBQwL2AWoFxaxvGrW0Yt7Zh3NqGcWubk42bMUbV1dVKSUlRUFDnrBbp9JmUoKAgpaWltfv3jYmJ4YexDRi3tmHc2oZxaxvGrW0Yt7Y50bh11gzKESycBQAAPomSAgAAfJLflxS73a57771Xdrvd6ih+hXFrG8atbRi3tmHc2oZxaxtfHLdOXzgLAABwKvx+JgUAAAQmSgoAAPBJlBQAAOCTKCkAAMAn+X1Jefrpp9W7d2+Fh4dr1KhR+vzzz62O1CEWLFigMWPGKDo6WomJibriiiu0ffv2FvsYY3TfffcpJSVFERERuuCCC/TVV1+12Mflcun2229XQkKCoqKi9P3vf1/79u1rsU9FRYVuvPFGORwOORwO3XjjjaqsrGyxT35+vqZNm6aoqCglJCRozpw5amho6JC/e3tasGCBbDab5s2b593GuB1bYWGhbrjhBnXv3l2RkZEaPny4srOzvV9n3I7W1NSk3/zmN+rdu7ciIiLUp08fPfDAA/J4PN59GDfps88+07Rp05SSkiKbzaa33nqrxdd9bYy2bNmiCRMmKCIiQqmpqXrggQc69f41R5xo3BobGzV//nydccYZioqKUkpKim666SYVFRW1+B5+N27Gjy1evNiEhoaa5557zuTk5Ji5c+eaqKgos3fvXqujtbvJkyebF154wWzdutVs3LjRTJ061WRkZJiamhrvPo8++qiJjo42r7/+utmyZYu55pprTM+ePY3T6fTuM3PmTJOammqWLFli1q9fbyZOnGjOPPNM09TU5N1nypQpJisry6xatcqsWrXKZGVlmcsuu8z79aamJpOVlWUmTpxo1q9fb5YsWWJSUlLM7NmzO2cw2mjNmjUmMzPTDBs2zMydO9e7nXE7Wnl5uenVq5e5+eabzZdffmny8vLM0qVLzc6dO737MG5He+ihh0z37t3Ne++9Z/Ly8sxrr71munXrZh5//HHvPoybMR988IG55557zOuvv24kmTfffLPF131pjKqqqkxSUpK59tprzZYtW8zrr79uoqOjzf/8z/903AAdx4nGrbKy0lx00UXm1VdfNdu2bTOrV682Z599thk1alSL7+Fv4+bXJeWss84yM2fObLFt0KBB5q677rIoUecpKSkxksyKFSuMMcZ4PB6TnJxsHn30Ue8+9fX1xuFwmGeeecYY0/xDHBoaahYvXuzdp7Cw0AQFBZl///vfxhhjcnJyjCTzxRdfePdZvXq1kWS2bdtmjGn+hxIUFGQKCwu9+7zyyivGbrebqqqqjvtLn4bq6mrTv39/s2TJEjNhwgRvSWHcjm3+/Plm3Lhxx/0643ZsU6dONbfeemuLbT/4wQ/MDTfcYIxh3I7lu2+2vjZGTz/9tHE4HKa+vt67z4IFC0xKSorxeDztOBKtc6xy911r1qwxkrz/cffHcfPbwz0NDQ3Kzs7WxRdf3GL7xRdfrFWrVlmUqvNUVVVJkuLj4yVJeXl52r9/f4vxsNvtmjBhgnc8srOz1djY2GKflJQUZWVlefdZvXq1HA6Hzj77bO8+55xzjhwOR4t9srKylJKS4t1n8uTJcrlcLQ4H+JJZs2Zp6tSpuuiii1psZ9yO7Z133tHo0aN19dVXKzExUSNGjNBzzz3n/Trjdmzjxo3TJ598oh07dkiSNm3apJUrV+rSSy+VxLidCl8bo9WrV2vChAktLnA2efJkFRUVac+ePe0/AO2oqqpKNptNsbGxkvxz3Py2pJSWlsrtdispKanF9qSkJO3fv9+iVJ3DGKM77rhD48aNU1ZWliR5/84nGo/9+/crLCxMcXFxJ9wnMTHxqNdMTExssc93XycuLk5hYWE+OfaLFy/W+vXrtWDBgqO+xrgd2+7du7Vw4UL1799fH330kWbOnKk5c+bo73//uyTG7Xjmz5+v6dOna9CgQQoNDdWIESM0b948TZ8+XRLjdip8bYyOtc+Rz315HOvr63XXXXfpuuuu894s0B/HrdPvgtzebDZbi8+NMUdtCzSzZ8/W5s2btXLlyqO+1pbx+O4+x9q/Lfv4goKCAs2dO1cff/yxwsPDj7sf49aSx+PR6NGj9cgjj0iSRowYoa+++koLFy7UTTfd5N2PcWvp1Vdf1aJFi/Tyyy9r6NCh2rhxo+bNm6eUlBTNmDHDux/jdnK+NEbHynK85/qCxsZGXXvttfJ4PHr66adPur8vj5vfzqQkJCQoODj4qEZWUlJyVHsLJLfffrveeecdLVu2TGlpad7tycnJko5uqN8ej+TkZDU0NKiiouKE+xw4cOCo1z148GCLfb77OhUVFWpsbPS5sc/OzlZJSYlGjRqlkJAQhYSEaMWKFXriiScUEhJy3Gbf1cetZ8+eGjJkSIttgwcPVn5+viR+3o7nV7/6le666y5de+21OuOMM3TjjTfqF7/4hXcWj3E7OV8bo2PtU1JSIuno2R5f0NjYqB/+8IfKy8vTkiVLvLMokn+Om9+WlLCwMI0aNUpLlixpsX3JkiU699xzLUrVcYwxmj17tt544w19+umn6t27d4uv9+7dW8nJyS3Go6GhQStWrPCOx6hRoxQaGtpin+LiYm3dutW7z9ixY1VVVaU1a9Z49/nyyy9VVVXVYp+tW7equLjYu8/HH38su92uUaNGtf9f/jRMmjRJW7Zs0caNG72P0aNH6/rrr9fGjRvVp08fxu0YzjvvvKNOcd+xY4d69eoliZ+346mrq1NQUMtfq8HBwd5TkBm3k/O1MRo7dqw+++yzFqfXfvzxx0pJSVFmZmb7D8BpOFJQcnNztXTpUnXv3r3F1/1y3E55ia0POnIK8vPPP29ycnLMvHnzTFRUlNmzZ4/V0drdbbfdZhwOh1m+fLkpLi72Purq6rz7PProo8bhcJg33njDbNmyxUyfPv2Yp+2lpaWZpUuXmvXr15sLL7zwmKefDRs2zKxevdqsXr3anHHGGcc8/WzSpElm/fr1ZunSpSYtLc0nTm08Fd8+u8cYxu1Y1qxZY0JCQszDDz9scnNzzUsvvWQiIyPNokWLvPswbkebMWOGSU1N9Z6C/MYbb5iEhARz5513evdh3JrPttuwYYPZsGGDkWT+9Kc/mQ0bNnjPQvGlMaqsrDRJSUlm+vTpZsuWLeaNN94wMTExlpyCfKJxa2xsNN///vdNWlqa2bhxY4v3CZfL5f0e/jZufl1SjDHmqaeeMr169TJhYWFm5MiR3lNyA42kYz5eeOEF7z4ej8fce++9Jjk52djtdjN+/HizZcuWFt/n0KFDZvbs2SY+Pt5ERESYyy67zOTn57fYp6yszFx//fUmOjraREdHm+uvv95UVFS02Gfv3r1m6tSpJiIiwsTHx5vZs2e3ONXMl323pDBux/buu++arKwsY7fbzaBBg8yzzz7b4uuM29GcTqeZO3euycjIMOHh4aZPnz7mnnvuafEmwbgZs2zZsmP+PpsxY4YxxvfGaPPmzeb88883drvdJCcnm/vuu8+S049PNG55eXnHfZ9YtmyZ93v427jZjLHgsnkAAAAn4bdrUgAAQGCjpAAAAJ9ESQEAAD6JkgIAAHwSJQUAAPgkSgoAAPBJlBQAAOCTKCkAAMAnUVIAAIBPoqQAAACfREkBAAA+iZICAAB80v8Hd2H8MoPvKHQAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "prof = correlogram(\n",
    "    sac.centroid,\n",
    "    sac.HH_INC,\n",
    "    statistic=G\n",
    ")\n",
    "ax = prof.G.plot()\n",
    "ax.set_xlabel(\"distance (m)\")\n",
    "ax.set_ylabel(\"Getis-Ord G\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9d885279-a3d6-45bf-ad17-2eff155cff76",
   "metadata": {},
   "source": [
    "## KNN Distance"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3db93010-f7d2-45f2-8121-c8ebf0ae71a9",
   "metadata": {},
   "source": [
    "It is also possible to consider different concepts of *distance*. For example, rather than stepping through increments of Euclidean distance/length at each interval, we could instead step through increments of nearest-neighbors.\n",
    "\n",
    "Instead of adding neighbors using sequential distances of 500 meters, here we will step through the 50 nearest neighbors, adding one neighbor at a time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "42a8033a-9058-4e92-80c9-939a13e83a5b",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-08-05T22:38:12.590257Z",
     "iopub.status.busy": "2023-08-05T22:38:12.590111Z",
     "iopub.status.idle": "2023-08-05T22:38:12.620312Z",
     "shell.execute_reply": "2023-08-05T22:38:12.620010Z",
     "shell.execute_reply.started": "2023-08-05T22:38:12.590247Z"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "kdists = list(range(1,50))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "772cc3aa-1aae-4faf-bac1-b51b4d774a9e",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-08-05T22:38:12.652697Z",
     "iopub.status.busy": "2023-08-05T22:38:12.652620Z",
     "iopub.status.idle": "2023-08-05T22:38:13.009186Z",
     "shell.execute_reply": "2023-08-05T22:38:13.008871Z",
     "shell.execute_reply.started": "2023-08-05T22:38:12.652690Z"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "kcorr = correlogram(sac.centroid, sac.HH_INC, kdists, distance_type='knn')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fd15a2dc-437e-436d-af31-745b09369209",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-08-05T22:38:13.009837Z",
     "iopub.status.busy": "2023-08-05T22:38:13.009749Z",
     "iopub.status.idle": "2023-08-05T22:38:13.115678Z",
     "shell.execute_reply": "2023-08-05T22:38:13.115409Z",
     "shell.execute_reply.started": "2023-08-05T22:38:13.009828Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: >"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = kcorr.I.plot()\n",
    "ax.set_xlabel(\"number of nearest neighbors\")\n",
    "ax.set_ylabel(\"Moran's I\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6ce895b3-7af7-4c16-94b0-7f4a724e55ea",
   "metadata": {},
   "source": [
    "# Nonparametric"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e31a4e2e",
   "metadata": {},
   "source": [
    "Finally it is also possible to fit a non-parametric curve to estimate spatial autocorrelation as a function of distance. This is done using a LOWESS smoother, which fits a locally-weighted polynomial regression to the data based on the following regression: \n",
    "\n",
    "$$ z_iz_j = f(d_{ij}) + u_{ij}$$\n",
    "\n",
    "where $z_i$ and $z_j$ are standardized values of the variable of interest at locations $i$ and $j$, $d_{ij}$ is the distance between locations $i$ and $j$, and $u_{ij}$ is an error term. The function $f$ is estimated using a LOWESS smoother, which fits a locally-weighted polynomial regression to the data.\n",
    "\n",
    "This can be interpreted as the correlation between observations separated by *approximately* the distance on the horizontal axis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "cd4fb7fa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Correlation between pairs\\napproximately this separation')"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nonparametric = correlogram(sac.centroid, sac.HH_INC, statistic='lowess')\n",
    "ax = nonparametric.lowess.plot()\n",
    "ax.set_xlabel(\"Distance (m)\")\n",
    "ax.set_ylabel(\"Correlation between pairs\\napproximately this separation\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c99a4c51",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Analysis",
   "language": "python",
   "name": "analysis"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.11"
  },
  "widgets": {
   "application/vnd.jupyter.widget-state+json": {
    "state": {},
    "version_major": 2,
    "version_minor": 0
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}