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|
import numpy as np
import pandas as pd
from libpysal.graph import Graph
from libpysal.graph._utils import _percentile_filtration_grouper
from numpy.typing import NDArray
from packaging.version import Version
from pandas import DataFrame, Series
from ..diversity import shannon_diversity, simpson_diversity
try:
from numba import njit
HAS_NUMBA = True
except (ModuleNotFoundError, ImportError):
HAS_NUMBA = False
from libpysal.common import jit as njit
from libpysal.graph._utils import (
_compute_stats,
_limit_range,
)
__all__ = [
"mean_deviation",
"describe_agg",
"describe_reached_agg",
"values_range",
"theil",
"simpson",
"shannon",
"gini",
"percentile",
]
def _get_grouper(y, graph):
return y.take(graph._adjacency.index.codes[1]).groupby(
graph._adjacency.index.codes[0]
)
@njit
def _interpolate(values, q):
weights = values[:, 0]
group = values[:, 1]
nan_tracker = np.isnan(group)
if nan_tracker.all():
return np.array([float(np.nan) for _ in q])
group = group[~nan_tracker]
sorter = np.argsort(group)
group = group[sorter]
weights = weights[~nan_tracker][sorter]
xs = np.cumsum(weights) - 0.5 * weights
xs = xs / weights.sum()
ys = group
interpolate = np.interp(
[x / 100 for x in q],
xs,
ys,
)
return interpolate
def _percentile_limited_group_grouper(y, group_index, q=(25, 75)):
"""Carry out a filtration of group members based on \\
quantiles, specified in ``q``"""
grouper = y.reset_index(drop=True).groupby(group_index)
if HAS_NUMBA:
to_keep = grouper.transform(
_limit_range, q[0], q[1], engine="numba"
).values.astype(bool)
else:
to_keep = grouper.transform(
lambda x: _limit_range(x.values, x.index, q[0], q[1])
).values.astype(bool)
filtered_grouper = y[to_keep].groupby(group_index[to_keep])
return filtered_grouper
def describe_agg(
y: NDArray[np.float64] | Series,
aggregation_key: NDArray[np.float64] | Series,
q: tuple[float, float] | list[float] | None = None,
statistics: list[str] | None = None,
) -> DataFrame:
"""Describe the distribution of values within the groups of an aggregation.
The desired statistics to compute can be passed to ``statistics``.
By default the statistics calculated are count,
sum, mean, median, std, nunique, mode.
Adapted from :cite:`hermosilla2012` and :cite:`feliciotti2018`.
Notes
-----
The numba package is used extensively in this function to accelerate the computation
of statistics. Without numba, these computations may become slow on large data.
Parameters
----------
y : Series | numpy.array
A Series or numpy.array containing values to analyse.
aggregation_key : Series | numpy.array
The unique ID that specifies the aggregation
of ``y`` objects to groups.
q : tuple[float, float] | None, optional
Tuple of percentages for the percentiles to compute. Values must be between 0
and 100 inclusive. When set, values below and above the percentiles will be
discarded before computation of the average. The percentiles are computed for
each neighborhood. By default None.
statistics : list[str]
A list of stats functions to pass to groupby.agg.
Returns
-------
DataFrame
Examples
--------
>>> path = momepy.datasets.get_path("bubenec")
>>> buildings = geopandas.read_file(path, layer="buildings")
>>> streets = geopandas.read_file(path, layer="streets")
>>> buildings["street_index"] = momepy.get_nearest_street(buildings, streets)
>>> buildings.head()
uID geometry street_index
0 1 POLYGON ((1603599.221 6464369.816, 1603602.984... 0.0
1 2 POLYGON ((1603042.88 6464261.498, 1603038.961 ... 33.0
2 3 POLYGON ((1603044.65 6464178.035, 1603049.192 ... 10.0
3 4 POLYGON ((1603036.557 6464141.467, 1603036.969... 8.0
4 5 POLYGON ((1603082.387 6464142.022, 1603081.574... 8.0
>>> momepy.describe_agg(buildings.area, buildings["street_index"]).head() # doctest: +SKIP
count mean median std min max sum nunique mode
street_index
0.0 9.0 366.827019 339.636871 266.747247 68.336193 800.045495 3301.443174 9.0 68.336193
1.0 1.0 618.447036 618.447036 NaN 618.447036 618.447036 618.447036 1.0 618.447036
2.0 12.0 504.523575 535.973108 318.660691 92.280807 1057.998520 6054.282903 12.0 92.280807
5.0 5.0 1150.865099 1032.693716 580.660030 673.015192 2127.752228 5754.325496 5.0 673.015192
6.0 7.0 662.179187 662.192603 291.397747 184.798661 1188.294675 4635.254306 7.0 184.798661
The result can be directly assigned a columns of the ``streets`` GeoDataFrame.
To eliminate the effect of outliers, you can take into account only values within a
specified percentile range (``q``). At the same time, you can specify only a subset
of statistics to compute:
>>> momepy.describe_agg(
... buildings.area,
... buildings["street_index"],
... q=(10, 90),
... statistics=["mean", "std"],
... ).head()
mean std
street_index
0.0 347.580212 219.797123
1.0 618.447036 NaN
2.0 476.592190 206.011102
5.0 984.519359 203.718644
6.0 652.432194 32.829824
""" # noqa: E501
if Version(pd.__version__) <= Version("2.1.0"):
raise ImportError("pandas 2.1.0 or newer is required to use this function.")
# series indice needs renaming, since multiindices
# without explicit names cannot be joined
if isinstance(y, np.ndarray):
y = pd.Series(y)
if isinstance(aggregation_key, np.ndarray):
aggregation_key = pd.Series(aggregation_key)
# aggregate data
if q is None:
grouper = y.groupby(aggregation_key)
else:
grouper = _percentile_limited_group_grouper(y, aggregation_key, q=q)
stats = _compute_stats(grouper, to_compute=statistics)
# fill only counts with zeros, other stats are NA
if "count" in stats.columns:
stats.loc[:, "count"] = stats.loc[:, "count"].fillna(0)
return stats
def describe_reached_agg(
y: NDArray[np.float64] | Series,
graph_index: NDArray[np.float64] | Series,
graph: Graph,
q: tuple[float, float] | list[float] | None = None,
statistics: list[str] | None = None,
) -> DataFrame:
"""Describe the distribution of values reached on a neighbourhood graph.
Given a neighborhood graph or a grouping, computes the descriptive statistics
of values reached. Optionally, the values can be limited to a certain
quantile range before computing the statistics.
The statistics calculated are count, sum, mean, median, std, nunique, mode.
The desired statistics to compute can be passed to ``statistics``
The neighbourhood is defined in ``graph``. If ``graph`` is ``None``,
the function will assume topological distance ``0`` (element itself)
and ``result_index`` is required in order to arrange the results.
If ``graph``, the results are arranged according to the spatial weights ordering.
Adapted from :cite:`hermosilla2012` and :cite:`feliciotti2018`.
Notes
-----
The numba package is used extensively in this function to accelerate the computation
of statistics. Without numba, these computations may become slow on large data.
Parameters
----------
y : Series | numpy.array
A Series or numpy.array containing values to analyse.
graph_index : Series | numpy.array
The unique ID that specifies the aggregation
of ``y`` objects to ``graph`` groups.
graph : libpysal.graph.Graph (default None)
A spatial weights matrix of the element ``y`` is grouped into.
q : tuple[float, float] | None, optional
Tuple of percentages for the percentiles to compute. Values must be between 0
and 100 inclusive. When set, values below and above the percentiles will be
discarded before computation of the average. The percentiles are computed for
each neighborhood. By default None.
statistics : list[str]
A list of stats functions to pass to groupby.agg.
Returns
-------
DataFrame
Examples
--------
>>> from libpysal import graph
>>> path = momepy.datasets.get_path("bubenec")
>>> buildings = geopandas.read_file(path, layer="buildings")
>>> streets = geopandas.read_file(path, layer="streets")
>>> buildings["street_index"] = momepy.get_nearest_street(buildings, streets)
>>> buildings.head()
uID geometry street_index
0 1 POLYGON ((1603599.221 6464369.816, 1603602.984... 0.0
1 2 POLYGON ((1603042.88 6464261.498, 1603038.961 ... 33.0
2 3 POLYGON ((1603044.65 6464178.035, 1603049.192 ... 10.0
3 4 POLYGON ((1603036.557 6464141.467, 1603036.969... 8.0
4 5 POLYGON ((1603082.387 6464142.022, 1603081.574... 8.0
>>> queen_contig = graph.Graph.build_contiguity(streets, rook=False)
>>> queen_contig
<Graph of 35 nodes and 148 nonzero edges indexed by
[0, 1, 2, 3, 4, ...]>
>>> momepy.describe_reached_agg(
... buildings.area,
... buildings["street_index"],
... queen_contig,
... ).head() # doctest: +SKIP
count mean median std min max sum nunique mode
0 43.0 643.595418 633.692589 412.563790 53.851509 2127.752228 27674.602973 43.0 53.851509
1 41.0 735.058515 662.921280 381.827737 51.246377 2127.752228 30137.399128 41.0 51.246377
2 50.0 636.304006 625.190488 450.182157 53.851509 2127.752228 31815.200298 50.0 53.851509
3 6.0 405.782514 370.352071 334.848563 57.138700 863.828420 2434.695086 6.0 57.138700
4 1.0 683.514930 683.514930 NaN 683.514930 683.514930 683.514930 1.0 683.514930
The result can be directly assigned a columns of the ``streets`` GeoDataFrame.
To eliminate the effect of outliers, you can take into account only values within a
specified percentile range (``q``). At the same time, you can specify only a subset
of statistics to compute:
>>> momepy.describe_reached_agg(
... buildings.area,
... buildings["street_index"],
... queen_contig,
... q=(10, 90),
... statistics=["mean", "std"],
... ).head()
mean std
0 619.104840 250.369496
1 721.441808 216.516469
2 597.379925 297.213321
3 378.431992 274.631290
4 683.514930 NaN
""" # noqa: E501
if Version(pd.__version__) <= Version("2.1.0"):
raise ImportError("pandas 2.1.0 or newer is required to use this function.")
# series indice needs renaming, since multiindices
# without explicit names cannot be joined
if isinstance(y, np.ndarray):
y = pd.Series(y, name="obs_index")
else:
y = y.rename_axis("obs_index")
if isinstance(graph_index, np.ndarray):
graph_index = pd.Series(graph_index, name="neighbor")
else:
graph_index = graph_index.rename("neighbor")
# aggregate data
df_multi_index = y.to_frame().set_index(graph_index, append=True).swaplevel()
combined_index = graph.adjacency.index.join(df_multi_index.index).dropna()
if q is None:
grouper = y.loc[combined_index.get_level_values(-1)].groupby(
combined_index.get_level_values(0)
)
else:
grouper = _percentile_filtration_grouper(y, combined_index, q=q)
stats = _compute_stats(grouper, statistics)
result = pd.DataFrame(
np.full((graph.unique_ids.shape[0], stats.shape[1]), np.nan),
index=graph.unique_ids,
)
result.loc[stats.index.values] = stats.values
result.columns = stats.columns
# fill only counts with zeros, other stats are NA
if "count" in result.columns:
result.loc[:, "count"] = result.loc[:, "count"].fillna(0)
result.index.name = None
return result
def values_range(
y: Series | NDArray[np.float64], graph: Graph, q: tuple | list = (0, 100)
) -> Series:
"""Calculates the range of values within neighbours defined in ``graph``.
Adapted from :cite:`dibble2017`.
Notes
-----
The index of ``y`` must match the index along which the ``graph`` is
built.
Parameters
----------
y : Series
A DataFrame or Series containing the values to be analysed.
graph : libpysal.graph.Graph
A spatial weights matrix for the data.
q : tuple, list, optional (default (0,100)))
A two-element sequence containing floats between 0 and 100 (inclusive)
that are the percentiles over which to compute the range.
The order of the elements is not important.
Returns
-------
Series
A Series containing resulting values.
Examples
--------
>>> from libpysal import graph
>>> path = momepy.datasets.get_path("bubenec")
>>> buildings = geopandas.read_file(path, layer="buildings")
>>> buildings.head()
uID geometry
0 1 POLYGON ((1603599.221 6464369.816, 1603602.984...
1 2 POLYGON ((1603042.88 6464261.498, 1603038.961 ...
2 3 POLYGON ((1603044.65 6464178.035, 1603049.192 ...
3 4 POLYGON ((1603036.557 6464141.467, 1603036.969...
4 5 POLYGON ((1603082.387 6464142.022, 1603081.574...
Define spatial graph:
>>> knn5 = graph.Graph.build_knn(buildings.centroid, k=5)
>>> knn5
<Graph of 144 nodes and 720 nonzero edges indexed by
[0, 1, 2, 3, 4, ...]>
Range of building area within 5 nearest neighbors:
>>> momepy.values_range(buildings.area, knn5)
focal
0 559.745602
1 444.997770
2 10651.932677
3 365.239452
4 339.585788
...
139 769.179096
140 721.444718
141 996.921755
142 119.708607
143 798.344284
Length: 144, dtype: float64
To eliminate the effect of outliers, you can take into account only values within a
specified percentile range (``q``).
>>> momepy.values_range(buildings.area, knn5, q=(25, 75))
focal
0 258.656230
1 113.990829
2 2878.811586
3 92.005635
4 87.637833
...
139 587.139513
140 325.726611
141 621.315615
142 34.446110
143 488.967863
Length: 144, dtype: float64
"""
stats = percentile(y, graph, q=q)
return stats[max(q)] - stats[min(q)]
def theil(y: Series, graph: Graph, q: tuple | list | None = None) -> Series:
"""Calculates the Theil measure of inequality of values within neighbours defined in
``graph``.
Uses ``inequality.theil.Theil`` under the hood. Requires '`inequality`' package.
.. math::
T = \\sum_{i=1}^n \\left(
\\frac{y_i}{\\sum_{i=1}^n y_i} \\ln \\left[
N \\frac{y_i} {\\sum_{i=1}^n y_i}
\\right]
\\right)
Notes
-----
The index of ``y`` must match the index along which the ``graph`` is
built.
Parameters
----------
y : Series
A DataFrame or Series containing the values to be analysed.
graph : libpysal.graph.Graph
A spatial weights matrix for the data.
q : tuple, list, optional (default (0,100)))
A two-element sequence containing floats between 0 and 100 (inclusive)
that are the percentiles over which to compute the range.
The order of the elements is not important.
Returns
-------
Series
A Series containing resulting values.
Examples
--------
>>> from libpysal import graph
>>> path = momepy.datasets.get_path("bubenec")
>>> buildings = geopandas.read_file(path, layer="buildings")
>>> buildings.head()
uID geometry
0 1 POLYGON ((1603599.221 6464369.816, 1603602.984...
1 2 POLYGON ((1603042.88 6464261.498, 1603038.961 ...
2 3 POLYGON ((1603044.65 6464178.035, 1603049.192 ...
3 4 POLYGON ((1603036.557 6464141.467, 1603036.969...
4 5 POLYGON ((1603082.387 6464142.022, 1603081.574...
Define spatial graph:
>>> knn5 = graph.Graph.build_knn(buildings.centroid, k=5)
>>> knn5
<Graph of 144 nodes and 720 nonzero edges indexed by
[0, 1, 2, 3, 4, ...]>
Theil index of building area within 5 nearest neighbors:
>>> momepy.theil(buildings.area, knn5)
focal
0 0.106079
1 0.023256
2 0.800522
3 0.016015
4 0.013829
...
139 0.547522
140 0.041755
141 0.098827
142 0.159690
143 0.068131
Length: 144, dtype: float64
To eliminate the effect of outliers, you can take into account only values within a
specified percentile range (``q``).
>>> momepy.theil(buildings.area, knn5, q=(25, 75))
focal
0 1.144550e-02
1 3.121656e-06
2 1.295882e-02
3 1.772730e-07
4 2.913017e-06
...
139 5.402548e-01
140 6.658486e-03
141 3.330720e-02
142 1.433583e-03
143 2.096421e-02
Length: 144, dtype: float64
"""
try:
from inequality.theil import Theil
except ImportError as err:
raise ImportError("The 'inequality' package is required.") from err
if q:
grouper = _percentile_filtration_grouper(y, graph._adjacency.index, q=q)
else:
grouper = _get_grouper(y, graph)
result = grouper.apply(lambda x: Theil(x.values).T)
result.index = graph.unique_ids
return result
def simpson(
y: Series,
graph: Graph,
binning: str = "HeadTailBreaks",
gini_simpson: bool = False,
inverse: bool = False,
categorical: bool = False,
**classification_kwds,
) -> Series:
"""Calculates the Simpson's diversity index of values within neighbours defined in
``graph``.
Uses ``mapclassify.classifiers`` under the hood for binning.
Requires ``mapclassify>=.2.1.0`` dependency.
.. math::
\\lambda=\\sum_{i=1}^{R} p_{i}^{2}
Adapted from :cite:`feliciotti2018`.
Notes
-----
The index of ``y`` must match the index along which the ``graph`` is
built.
Parameters
----------
y : Series
A DataFrame or Series containing the values to be analysed.
graph : libpysal.graph.Graph
A spatial weights matrix for the data.
binning : str (default 'HeadTailBreaks')
One of mapclassify classification schemes. For details see
`mapclassify API documentation <http://pysal.org/mapclassify/api.html>`_.
gini_simpson : bool (default False)
Return Gini-Simpson index instead of Simpson index (``1 - λ``).
inverse : bool (default False)
Return Inverse Simpson index instead of Simpson index (``1 / λ``).
categorical : bool (default False)
Treat values as categories (will not use ``binning``).
**classification_kwds : dict
Keyword arguments for the classification scheme.
For details see `mapclassify documentation <https://pysal.org/mapclassify>`_.
Returns
-------
Series
A Series containing resulting values.
Examples
--------
>>> from libpysal import graph
>>> path = momepy.datasets.get_path("bubenec")
>>> buildings = geopandas.read_file(path, layer="buildings")
>>> buildings.head()
uID geometry
0 1 POLYGON ((1603599.221 6464369.816, 1603602.984...
1 2 POLYGON ((1603042.88 6464261.498, 1603038.961 ...
2 3 POLYGON ((1603044.65 6464178.035, 1603049.192 ...
3 4 POLYGON ((1603036.557 6464141.467, 1603036.969...
4 5 POLYGON ((1603082.387 6464142.022, 1603081.574...
Define spatial graph:
>>> knn5 = graph.Graph.build_knn(buildings.centroid, k=5)
>>> knn5
<Graph of 144 nodes and 720 nonzero edges indexed by
[0, 1, 2, 3, 4, ...]>
Simpson index of building area within 5 nearest neighbors:
>>> momepy.simpson(buildings.area, knn5)
focal
0 1.00
1 0.68
2 0.36
3 0.68
4 0.68
...
139 0.68
140 0.44
141 0.44
142 1.00
143 0.52
Length: 144, dtype: float64
In some occasions, you may want to override the binning method:
>>> momepy.simpson(buildings.area, knn5, binning="fisher_jenks", k=8)
focal
0 0.28
1 0.68
2 0.36
3 0.68
4 0.68
...
139 0.44
140 0.28
141 0.28
142 1.00
143 0.20
Length: 144, dtype: float64
See also
--------
momepy.simpson_diversity : Calculates the Simpson's diversity index of data.
"""
if not categorical:
try:
from mapclassify import classify
except ImportError as err:
raise ImportError(
"The 'mapclassify >= 2.4.2` package is required."
) from err
bins = classify(y, scheme=binning, **classification_kwds).bins
else:
bins = None
def _apply_simpson_diversity(values):
return simpson_diversity(
values,
bins,
categorical=categorical,
)
result = graph.apply(y, _apply_simpson_diversity)
if gini_simpson:
result = 1 - result
elif inverse:
result = 1 / result
return result
def shannon(
y: Series,
graph: Graph,
binning: str = "HeadTailBreaks",
categorical: bool = False,
categories: list | None = None,
**classification_kwds,
) -> Series:
"""Calculates the Shannon index of values within neighbours defined in
``graph``.
Uses ``mapclassify.classifiers`` under the hood
for binning. Requires ``mapclassify>=.2.1.0`` dependency.
.. math::
H^{\\prime}=-\\sum_{i=1}^{R} p_{i} \\ln p_{i}
Notes
-----
The index of ``y`` must match the index along which the ``graph`` is
built.
Parameters
----------
y : Series
A DataFrame or Series containing the values to be analysed.
graph : libpysal.graph.Graph
A spatial weights matrix for the data.
binning : str (default 'HeadTailBreaks')
One of mapclassify classification schemes. For details see
`mapclassify API documentation <http://pysal.org/mapclassify/api.html>`_.
categorical : bool (default False)
Treat values as categories (will not use binning).
categories : list-like (default None)
A list of categories. If ``None``, ``values.unique()`` is used.
**classification_kwds : dict
Keyword arguments for classification scheme
For details see `mapclassify documentation <https://pysal.org/mapclassify>`_.
Returns
-------
Series
A Series containing resulting values.
Examples
--------
>>> from libpysal import graph
>>> path = momepy.datasets.get_path("bubenec")
>>> buildings = geopandas.read_file(path, layer="buildings")
>>> buildings.head()
uID geometry
0 1 POLYGON ((1603599.221 6464369.816, 1603602.984...
1 2 POLYGON ((1603042.88 6464261.498, 1603038.961 ...
2 3 POLYGON ((1603044.65 6464178.035, 1603049.192 ...
3 4 POLYGON ((1603036.557 6464141.467, 1603036.969...
4 5 POLYGON ((1603082.387 6464142.022, 1603081.574...
Define spatial graph:
>>> knn5 = graph.Graph.build_knn(buildings.centroid, k=5)
>>> knn5
<Graph of 144 nodes and 720 nonzero edges indexed by
[0, 1, 2, 3, 4, ...]>
Shannon index of building area within 5 nearest neighbors:
>>> momepy.shannon(buildings.area, knn5)
focal
0 -0.000000
1 0.500402
2 1.054920
3 0.500402
4 0.500402
...
139 0.500402
140 0.950271
141 0.950271
142 -0.000000
143 0.673012
Length: 144, dtype: float64
In some occasions, you may want to override the binning method:
>>> momepy.shannon(buildings.area, knn5, binning="fisher_jenks", k=8)
focal
0 1.332179
1 0.500402
2 1.054920
3 0.500402
4 0.500402
...
139 0.950271
140 1.332179
141 1.332179
142 -0.000000
143 1.609438
Length: 144, dtype: float64
"""
if not categories:
categories = y.unique()
if not categorical:
try:
from mapclassify import classify
except ImportError as err:
raise ImportError(
"The 'mapclassify >= 2.4.2` package is required."
) from err
bins = classify(y, scheme=binning, **classification_kwds).bins
else:
bins = categories
def _apply_shannon(values):
return shannon_diversity(values, bins, categorical, categories)
return graph.apply(y, _apply_shannon)
def gini(y: Series, graph: Graph, q: tuple | list | None = None) -> Series:
"""Calculates the Gini index of values within neighbours defined in ``graph``.
Uses ``inequality.gini.Gini`` under the hood. Requires '`inequality`' package.
Notes
-----
The index of ``y`` must match the index along which the ``graph`` is
built.
Parameters
----------
y : Series
A DataFrame or Series containing the values to be analysed.
graph : libpysal.graph.Graph
A spatial weights matrix for the data.
q : tuple, list, optional (default (0,100)))
A two-element sequence containing floats between 0 and 100 (inclusive)
that are the percentiles over which to compute the range.
The order of the elements is not important.
Returns
-------
Series
A Series containing resulting values.
Examples
--------
>>> from libpysal import graph
>>> path = momepy.datasets.get_path("bubenec")
>>> buildings = geopandas.read_file(path, layer="buildings")
>>> buildings.head()
uID geometry
0 1 POLYGON ((1603599.221 6464369.816, 1603602.984...
1 2 POLYGON ((1603042.88 6464261.498, 1603038.961 ...
2 3 POLYGON ((1603044.65 6464178.035, 1603049.192 ...
3 4 POLYGON ((1603036.557 6464141.467, 1603036.969...
4 5 POLYGON ((1603082.387 6464142.022, 1603081.574...
Define spatial graph:
>>> knn5 = graph.Graph.build_knn(buildings.centroid, k=5)
>>> knn5
<Graph of 144 nodes and 720 nonzero edges indexed by
[0, 1, 2, 3, 4, ...]>
Gini index of building area within 5 nearest neighbors:
>>> momepy.gini(buildings.area, knn5)
focal
0 0.228493
1 0.102110
2 0.605867
3 0.085589
4 0.080435
...
139 0.525724
140 0.156737
141 0.239009
142 0.259808
143 0.204820
Length: 144, dtype: float64
To eliminate the effect of outliers, you can take into account only values within a
specified percentile range (``q``).
>>> momepy.gini(buildings.area, knn5, q=(25, 75))
focal
0 0.073817
1 0.001264
2 0.077521
3 0.000321
4 0.001264
...
139 0.505618
140 0.055096
141 0.130501
142 0.025522
143 0.110987
Length: 144, dtype: float64
"""
try:
from inequality.gini import Gini
except ImportError as err:
raise ImportError("The 'inequality' package is required.") from err
if y.min() < 0:
raise ValueError(
"Values contain negative numbers. Normalise data before"
"using momepy.Gini."
)
if q:
grouper = _percentile_filtration_grouper(y, graph._adjacency.index, q=q)
else:
grouper = _get_grouper(y, graph)
result = grouper.apply(lambda x: Gini(x.values).g)
result.index = graph.unique_ids
return result
def percentile(
y: Series,
graph: Graph,
q: tuple | list = [25, 50, 75],
) -> DataFrame:
"""Calculates linearly weighted percentiles of ``y`` values using
the neighbourhoods and weights defined in ``graph``.
The specific interpolation method implemented is "hazen".
Parameters
----------
y : Series
A Series containing the values to be analysed.
graph : libpysal.graph.Graph
A spatial weights matrix for the data.
q : array-like (default [25, 50, 75])
The percentiles to return.
Returns
-------
Dataframe
A Dataframe with columns as the results for each percentile
Examples
--------
>>> from libpysal import graph
>>> path = momepy.datasets.get_path("bubenec")
>>> buildings = geopandas.read_file(path, layer="buildings")
>>> buildings.head()
uID geometry
0 1 POLYGON ((1603599.221 6464369.816, 1603602.984...
1 2 POLYGON ((1603042.88 6464261.498, 1603038.961 ...
2 3 POLYGON ((1603044.65 6464178.035, 1603049.192 ...
3 4 POLYGON ((1603036.557 6464141.467, 1603036.969...
4 5 POLYGON ((1603082.387 6464142.022, 1603081.574...
Define spatial graph:
>>> knn5 = graph.Graph.build_knn(buildings.centroid, k=5)
>>> knn5
<Graph of 144 nodes and 720 nonzero edges indexed by
[0, 1, 2, 3, 4, ...]>
Percentiles of building area within 5 nearest neighbors:
>>> momepy.percentile(buildings.area, knn5).head()
25 50 75
focal
0 347.252959 427.819360 605.909188
1 621.834862 641.629131 735.825691
2 622.262074 903.746689 3501.073660
3 621.834862 641.629131 713.840496
4 621.834862 641.987211 709.472695
Optionally, you can specify which percentile values shall be computed.
>>> momepy.percentile(buildings.area, knn5, q=[10, 90]).head()
10 90
focal
0 123.769329 683.514930
1 564.160901 1009.158671
2 564.160901 11216.093578
3 564.160901 929.400353
4 564.160901 903.746689
"""
weights = graph._adjacency.values
vals = y.loc[graph._adjacency.index.get_level_values(1)]
vals = np.vstack((weights, vals)).T
vals = DataFrame(vals, columns=["weights", "values"])
grouper = vals.groupby(graph._adjacency.index.get_level_values(0))
q = tuple(q)
stats = grouper.apply(lambda x: _interpolate(x.values, q))
result = DataFrame(np.stack(stats), columns=q, index=stats.index)
result.loc[graph.isolates] = np.nan
return result
def mean_deviation(y: Series, graph: Graph) -> Series:
"""Calculate the mean deviation of each ``y`` value and its graph neighbours.
.. math::
\\frac{1}{n}\\sum_{i=1}^n dev_i=\\frac{dev_1+dev_2+\\cdots+dev_n}{n}
Parameters
----------
y : Series
A Series containing the values to be analysed.
graph : libpysal.graph.Graph
Graph representing spatial relationships between elements.
Returns
-------
Series
Examples
--------
>>> from libpysal import graph
>>> path = momepy.datasets.get_path("bubenec")
>>> buildings = geopandas.read_file(path, layer="buildings")
>>> buildings.head()
uID geometry
0 1 POLYGON ((1603599.221 6464369.816, 1603602.984...
1 2 POLYGON ((1603042.88 6464261.498, 1603038.961 ...
2 3 POLYGON ((1603044.65 6464178.035, 1603049.192 ...
3 4 POLYGON ((1603036.557 6464141.467, 1603036.969...
4 5 POLYGON ((1603082.387 6464142.022, 1603081.574...
Define spatial graph:
>>> knn5 = graph.Graph.build_knn(buildings.centroid, k=5)
>>> knn5
<Graph of 144 nodes and 720 nonzero edges indexed by
[0, 1, 2, 3, 4, ...]>
Mean deviation of building area and area of 5 nearest neighbors:
>>> momepy.mean_deviation(buildings.area, knn5)
0 281.179149
1 10515.948995
2 2240.706061
3 230.360732
4 68.719810
...
139 259.180720
140 517.496703
141 331.849751
142 25.297225
143 654.691897
Length: 144, dtype: float64
"""
inp = graph._adjacency.index.get_level_values(0)
res = graph._adjacency.index.get_level_values(1)
itself = inp == res
inp = inp[~itself]
res = res[~itself]
left = y.loc[inp].reset_index(drop=True)
right = y.loc[res].reset_index(drop=True)
deviations = (left - right).abs()
vals = deviations.groupby(inp).mean()
result = Series(np.nan, index=y.index)
result.loc[vals.index] = vals.values
return result
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