def _calc(self, Y, w, k):
wY = lag_spatial(w, Y)
dx = Y[:, -1] - Y[:, 0]
dy = wY[:, -1] - wY[:, 0]
self.wY = wY
self.Y = Y
r = np.sqrt(dx * dx + dy * dy)
theta = np.arctan2(dy, dx)
neg = theta < 0.0
utheta = theta * (1 - neg) + neg * (2 * np.pi + theta)
counts, bins = np.histogram(utheta, self.cuts)
results = {}
results['counts'] = counts
results['theta'] = theta
results['bins'] = bins
results['r'] = r
results['lag'] = wY
results['dx'] = dx
results['dy'] = dy
return results
def moran_loc_bv_scatterplot(moran_loc_bv, p=None,
ax=None, scatter_kwds=None, fitline_kwds=None):
"""
Moran Bivariate Scatterplot with option of coloring of Local Moran Statistics
Parameters
----------
moran_loc : esda.moran.Moran_Local_BV instance
Values of Moran's I Local Autocorrelation Statistics
p : float, optional
If given, the p-value threshold for significance. Points will
be colored by significance. By default it will not be colored.
Default =None.
ax : Matplotlib Axes instance, optional
If given, the Moran plot will be created inside this axis.
Default =None.
scatter_kwds : keyword arguments, optional
Keywords used for creating and designing the scatter points.
Default =None.
fitline_kwds : keyword arguments, optional
Keywords used for creating and designing the moran fitline.
Default =None.
Returns
-------
fig : Matplotlib Figure instance
Bivariate Moran Local scatterplot figure
ax : matplotlib Axes instance
Axes in which the figure is plotted
Examples
--------
Imports
>>> import matplotlib.pyplot as plt
>>> import geopandas as gpd
>>> import libpysal.api as lp
>>> from libpysal import examples
>>> from esda.moran import Moran_Local_BV
>>> from splot.esda import moran_loc_bv_scatterplot
Load data and calculate Moran Local statistics
>>> link = examples.get_path('Guerry.shp')
>>> gdf = gpd.read_file(link)
>>> x = gdf['Suicids'].values
>>> y = gdf['Donatns'].values
>>> w = lp.Queen.from_dataframe(gdf)
>>> w.transform = 'r'
>>> m = Moran_Local_BV(x, y, w)
Plot
>>> moran_loc_bv_scatterplot(m)
Customize plot
>>> moran_loc_bv_scatterplot(m, p=0.05,
... fitline_kwds=dict(color='#4393c3')))
>>> plt.show()
"""
# to set default as an empty dictionary that is later filled with defaults
if scatter_kwds is None:
scatter_kwds = dict()
if fitline_kwds is None:
fitline_kwds = dict()
if p is not None:
if not isinstance(moran_loc_bv, Moran_Local_BV):
raise ValueError("`moran_loc_bv` is not a\n" +
"esda.moran.Moran_Local_BV instance")
if 'color' in scatter_kwds or 'cmap' in scatter_kwds:
warnings.warn("To change the color use cmap with a colormap of 5,\n" +
"c defines the LISA category, color will interfere with c")
# colors
spots_bv = moran_hot_cold_spots(moran_loc_bv, p)
hmap = colors.ListedColormap(['#bababa', '#d7191c', '#abd9e9',
'#2c7bb6', '#fdae61'])
# define customization
scatter_kwds.setdefault('alpha', 0.6)
scatter_kwds.setdefault('s', 40)
fitline_kwds.setdefault('alpha', 0.9)
# get fig and ax
fig, ax = _create_moran_fig_ax(ax, figsize=(7,7))
# set labels
ax.set_xlabel('Attribute')
ax.set_ylabel('Spatial Lag')
ax.set_title('Moran BV Local Scatterplot')
# plot and set standards
lag = lp.lag_spatial(moran_loc_bv.w, moran_loc_bv.zy)
fit = OLS(moran_loc_bv.zy[:, None], lag[:, None])
# v- and hlines
ax.axvline(0, alpha=0.5, color='k', linestyle='--')
ax.axhline(0, alpha=0.5, color='k', linestyle='--')
if p is not None:
fitline_kwds.setdefault('color', 'k')
scatter_kwds.setdefault('cmap', hmap)
scatter_kwds.setdefault('c', spots_bv)
ax.plot(lag, fit.predy, **fitline_kwds)
ax.scatter(moran_loc_bv.zx, fit.predy,
**scatter_kwds)
else:
scatter_kwds.setdefault('color', splot_colors['moran_base'])
fitline_kwds.setdefault('color', splot_colors['moran_fit'])
ax.plot(lag, fit.predy, **fitline_kwds)
ax.scatter(moran_loc_bv.zy, fit.predy, **scatter_kwds)
return fig, ax
def moran_scatterplot(moran, zstandard=True, ax=None,
scatter_kwds=None, fitline_kwds=None):
"""
Global Moran's I Scatterplot.
Parameters
----------
moran : esda.moran.Moran instance
Values of Moran's I Global Autocorrelation Statistics
zstandard : bool, optional
If True, Moran Scatterplot will show z-standardized attribute and
spatial lag values. Default =True.
ax : Matplotlib Axes instance, optional
If given, the Moran plot will be created inside this axis.
Default =None.
scatter_kwds : keyword arguments, optional
Keywords used for creating and designing the scatter points.
Default =None.
fitline_kwds : keyword arguments, optional
Keywords used for creating and designing the moran fitline.
Default =None.
Returns
-------
fig : Matplotlib Figure instance
Moran scatterplot figure
ax : matplotlib Axes instance
Axes in which the figure is plotted
Examples
--------
Imports
>>> import matplotlib.pyplot as plt
>>> import libpysal.api as lp
>>> from libpysal import examples
>>> import geopandas as gpd
>>> from esda.moran import Moran
>>> from splot.esda import moran_scatterplot
Load data and calculate weights
>>> link_to_data = examples.get_path('Guerry.shp')
>>> gdf = gpd.read_file(link_to_data)
>>> y = gdf['Donatns'].values
>>> w = lp.Queen.from_dataframe(gdf)
>>> w.transform = 'r'
Calculate Global Moran
>>> moran = Moran(y, w)
plot
>>> moran_scatterplot(moran)
>>> plt.show()
customize plot
>>> fig, ax = moran_scatterplot(moran, zstandard=False,
... fitline_kws=dict(color='#4393c3'))
>>> ax.set_xlabel('Donations')
>>> plt.show()
"""
# to set default as an empty dictionary that is later filled with defaults
if scatter_kwds is None:
scatter_kwds = dict()
if fitline_kwds is None:
fitline_kwds = dict()
# define customization defaults
scatter_kwds.setdefault('alpha', 0.6)
scatter_kwds.setdefault('color', splot_colors['moran_base'])
scatter_kwds.setdefault('s', 40)
fitline_kwds.setdefault('alpha', 0.9)
fitline_kwds.setdefault('color', splot_colors['moran_fit'])
# get fig and ax
fig, ax = _create_moran_fig_ax(ax, figsize=(7, 7))
# set labels
ax.set_xlabel('Attribute')
ax.set_ylabel('Spatial Lag')
ax.set_title('Moran Scatterplot' +
' (' + str(round(moran.I, 2)) + ')')
# plot and set standards
if zstandard is True:
lag = lp.lag_spatial(moran.w, moran.z)
fit = OLS(moran.z[:, None], lag[:, None])
# plot
ax.scatter(moran.z, lag, **scatter_kwds)
ax.plot(lag, fit.predy, **fitline_kwds)
# v- and hlines
ax.axvline(0, alpha=0.5, color='k', linestyle='--')
ax.axhline(0, alpha=0.5, color='k', linestyle='--')
else:
lag = lp.lag_spatial(moran.w, moran.y)
b, a = np.polyfit(moran.y, lag, 1)
# plot
ax.scatter(moran.y, lag, **scatter_kwds)
ax.plot(moran.y, a + b*moran.y, **fitline_kwds)
# dashed vert at mean of the attribute
ax.vlines(moran.y.mean(), lag.min(), lag.max(), alpha=0.5,
linestyle='--')
# dashed horizontal at mean of lagged attribute
ax.hlines(lag.mean(), moran.y.min(), moran.y.max(), alpha=0.5,
linestyle='--')
return fig, ax
def plot_local_autocorrelation(moran_loc, gdf, attribute, p=0.05,
region_column=None, mask=None,
mask_color='#636363', quadrant=None,
legend=True, scheme='Quantiles',
cmap='YlGnBu', figsize=(15, 4),
scatter_kwds=None, fitline_kwds=None):
'''
Produce three-plot visualisation of Moran Scatteprlot, LISA cluster
and Choropleth maps, with Local Moran region and quadrant masking
Parameters
----------
moran_loc : esda.moran.Moran_Local instance
Values of Moran's Local Autocorrelation Statistic
gdf : geopandas dataframe
The Dataframe containing information to plot the two maps.
attribute : str
Column name of attribute which should be depicted in Choropleth map.
p : float, optional
The p-value threshold for significance. Points and polygons will
be colored by significance. Default = 0.05.
region_column: string, optional
Column name containing mask region of interest. Default = None
mask: str, optional
Identifier or name of the region to highlight. Default = None
mask_color: str, optional
Color of mask. Default = '#636363'
quadrant : int, optional
Quadrant 1-4 in scatterplot masking values in LISA cluster and
Choropleth maps. Default = None
figsize: tuple, optional
W, h of figure. Default = (15,4)
legend: boolean, optional
If True, legend for maps will be depicted. Default = True
scheme: str, optional
Name of PySAL classifier to be used. Default = 'Quantiles'
cmap: str, optional
Name of matplotlib colormap used for plotting the Choropleth.
Default = 'YlGnBU'
scatter_kwds : keyword arguments, optional
Keywords used for creating and designing the scatter points.
Default =None.
fitline_kwds : keyword arguments, optional
Keywords used for creating and designing the moran fitline
in the scatterplot. Default =None.
Returns
-------
fig : Matplotlib figure instance
Moran Scatterplot, LISA cluster map and Choropleth.
axs : list of Matplotlib axes
Lisat of Matplotlib axes plotted.
Examples
--------
Imports
>>> import matplotlib.pyplot as plt
>>> import libpysal.api as lp
>>> from libpysal import examples
>>> import geopandas as gpd
>>> from esda.moran import Moran_Local
>>> from splot.esda import plot_local_autocorrelation
Data preparation and analysis
>>> link = examples.get_path('Guerry.shp')
>>> gdf = gpd.read_file(link)
>>> y = gdf['Donatns'].values
>>> w = lp.Queen.from_dataframe(gdf)
>>> w.transform = 'r'
>>> moran_loc = Moran_Local(y, w)
Plotting with quadrant mask and region mask
>>> fig = plot_local_autocorrelation(moran_loc, gdf, 'HOVAL', p=0.05,
... region_column='POLYID',
... mask=['1', '2', '3'], quadrant=1)
>>> plt.show()
'''
fig, axs = plt.subplots(1, 3, figsize=figsize,
subplot_kw={'aspect': 'equal'})
# Moran Scatterplot
if isinstance (moran_loc, Moran_Local):
moran_loc_scatterplot(moran_loc, p=p, ax=axs[0],
scatter_kwds=scatter_kwds, fitline_kwds=fitline_kwds)
else:
moran_loc_bv_scatterplot(moran_loc, p=p, ax=axs[0],
scatter_kwds=scatter_kwds, fitline_kwds=fitline_kwds)
axs[0].set_aspect('auto')
# Lisa cluster map
# TODO: Fix legend_kwds: display boxes instead of points
lisa_cluster(moran_loc, gdf, p=p, ax=axs[1], legend=legend,
legend_kwds={'loc': 'upper left',
'bbox_to_anchor': (0.92, 1.05)})
axs[1].set_aspect('equal')
# Choropleth for attribute
gdf.plot(column=attribute, scheme=scheme, cmap=cmap,
legend=legend, legend_kwds={'loc': 'upper left',
'bbox_to_anchor': (0.92, 1.05)},
ax=axs[2], alpha=1)
axs[2].set_axis_off()
axs[2].set_aspect('equal')
# MASKING QUADRANT VALUES
if quadrant is not None:
# Quadrant masking in Scatterplot
mask_angles = {1: 0, 2: 90, 3: 180, 4: 270} # rectangle angles
# We don't want to change the axis data limits, so use the current ones
xmin, xmax = axs[0].get_xlim()
ymin, ymax = axs[0].get_ylim()
# We are rotating, so we start from 0 degrees and
# figured out the right dimensions for the rectangles for other angles
mask_width = {1: abs(xmax),
2: abs(ymax),
3: abs(xmin),
4: abs(ymin)}
mask_height = {1: abs(ymax),
2: abs(xmin),
3: abs(ymin),
4: abs(xmax)}
axs[0].add_patch(patches.Rectangle((0, 0), width=mask_width[quadrant],
height=mask_height[quadrant],
angle=mask_angles[quadrant],
color='grey', zorder=-1, alpha=0.8))
# quadrant selection in maps
non_quadrant = ~(moran_loc.q == quadrant)
mask_quadrant = gdf[non_quadrant]
df_quadrant = gdf.iloc[~non_quadrant]
union2 = df_quadrant.unary_union.boundary
# LISA Cluster mask and cluster boundary
mask_quadrant.plot(column=attribute, scheme=scheme, color='white',
ax=axs[1], alpha=0.7, zorder=1)
gpd.GeoSeries([union2]).plot(linewidth=2, ax=axs[1], color='darkgrey')
# CHOROPLETH MASK
mask_quadrant.plot(column=attribute, scheme=scheme, color='white',
ax=axs[2], alpha=0.7, zorder=1)
gpd.GeoSeries([union2]).plot(linewidth=2, ax=axs[2], color='darkgrey')
# REGION MASKING
if region_column is not None:
# masking inside axs[0] or Moran Scatterplot
ix = gdf[region_column].isin(mask)
df_mask = gdf[ix]
x_mask = moran_loc.z[ix]
y_mask = lp.lag_spatial(moran_loc.w, moran_loc.z)[ix]
axs[0].plot(x_mask, y_mask, color=mask_color, marker='o',
markersize=14, alpha=.8, linestyle="None", zorder=-1)
# masking inside axs[1] or Lisa cluster map
union = df_mask.unary_union.boundary
gpd.GeoSeries([union]).plot(linewidth=2, ax=axs[1], color=mask_color)
# masking inside axs[2] or Chloropleth
gpd.GeoSeries([union]).plot(linewidth=2, ax=axs[2], color=mask_color)
return fig, axs
def moran_bv_scatterplot(moran_bv, ax=None, scatter_kwds=None, fitline_kwds=None):
"""
Bivariate Moran Scatterplot.
Parameters
----------
moran_bv : esda.moran.Moran_BV instance
Values of Bivariate Moran's I Autocorrelation Statistics
ax : Matplotlib Axes instance, optional
If given, the Moran plot will be created inside this axis.
Default =None.
scatter_kwds : keyword arguments, optional
Keywords used for creating and designing the scatter points.
Default =None.
fitline_kwds : keyword arguments, optional
Keywords used for creating and designing the moran fitline.
Default =None.
Returns
-------
fig : Matplotlib Figure instance
Bivariate moran scatterplot figure
ax : matplotlib Axes instance
Axes in which the figure is plotted
Examples
--------
Imports
>>> import matplotlib.pyplot as plt
>>> import libpysal.api as lp
>>> from libpysal import examples
>>> import geopandas as gpd
>>> from esda.moran import Moran_BV
>>> from splot.esda import moran_bv_scatterplot
Load data and calculate weights
>>> link_to_data = examples.get_path('Guerry.shp')
>>> gdf = gpd.read_file(link_to_data)
>>> x = gdf['Suicids'].values
>>> y = gdf['Donatns'].values
>>> w = lp.Queen.from_dataframe(gdf)
>>> w.transform = 'r'
Calculate Bivariate Moran
>>> moran_bv = Moran_BV(x, y, w)
plot
>>> moran_bv_scatterplot(moran_bv)
>>> plt.show()
customize plot
>>> moran_bv_scatterplot(moran_bv, zstandard=False,
... fitline_kwds=dict(color='#4393c3'))
>>> plt.show()
"""
# to set default as an empty dictionary that is later filled with defaults
if scatter_kwds is None:
scatter_kwds = dict()
if fitline_kwds is None:
fitline_kwds = dict()
# define customization
scatter_kwds.setdefault('alpha', 0.6)
scatter_kwds.setdefault('color', splot_colors['moran_base'])
scatter_kwds.setdefault('s', 40)
fitline_kwds.setdefault('alpha', 0.9)
fitline_kwds.setdefault('color', splot_colors['moran_fit'])
# get fig and ax
fig, ax = _create_moran_fig_ax(ax, figsize=(7,7))
# set labels
ax.set_xlabel('Attribute X')
ax.set_ylabel('Spatial Lag of Y')
ax.set_title('Bivariate Moran Scatterplot' +
' (' + str(round(moran_bv.I, 2)) + ')')
# plot and set standards
lag = lp.lag_spatial(moran_bv.w, moran_bv.zy)
fit = OLS(moran_bv.zy[:, None], lag[:, None])
# plot
ax.scatter(moran_bv.zx, lag, **scatter_kwds)
ax.plot(lag, fit.predy, **fitline_kwds)
# v- and hlines
ax.axvline(0, alpha=0.5, color='k', linestyle='--')
ax.axhline(0, alpha=0.5, color='k', linestyle='--')
return fig, ax