def _area_interpolate(
source_df,
target_df,
extensive_variables=None,
intensive_variables=None,
tables=None,
allocate_total=True,
):
"""
Area interpolation for extensive and intensive variables.
Parameters
----------
source_df : geopandas.GeoDataFrame (required)
geodataframe with polygon geometries
target_df : geopandas.GeoDataFrame (required)
geodataframe with polygon geometries
extensive_variables : list, (optional)
columns in dataframes for extensive variables
intensive_variables : list, (optional)
columns in dataframes for intensive variables
tables : tuple (optional)
two 2-D numpy arrays
SU: area of intersection of source geometry i with union geometry j
UT: binary mapping of union geometry j to target geometry t
allocate_total : boolean
True if total value of source area should be allocated.
False if denominator is area of i. Note that the two cases
would be identical when the area of the source polygon is
exhausted by intersections. See Notes for more details.
Returns
-------
estimates : geopandas.GeoDataFrame
new geodaraframe with interpolated variables as columns and target_df geometry
as output geometry
Notes
-----
The assumption is both dataframes have the same coordinate reference system.
For an extensive variable, the estimate at target polygon j (default case) is:
v_j = \sum_i v_i w_{i,j}
w_{i,j} = a_{i,j} / \sum_k a_{i,k}
If the area of the source polygon is not exhausted by intersections with
target polygons and there is reason to not allocate the complete value of
an extensive attribute, then setting allocate_total=False will use the
following weights:
v_j = \sum_i v_i w_{i,j}
w_{i,j} = a_{i,j} / a_i
where a_i is the total area of source polygon i.
For an intensive variable, the estimate at target polygon j is:
v_j = \sum_i v_i w_{i,j}
w_{i,j} = a_{i,j} / \sum_k a_{k,j}
"""
source_df = source_df.copy()
target_df = target_df.copy()
if _check_crs(source_df, target_df):
pass
else:
return None
if tables is None:
SU, UT = _area_tables(source_df, target_df)
else:
SU, UT = tables
den = source_df["geometry"].area.values
if allocate_total:
den = SU.sum(axis=1)
den = den + (den == 0)
weights = np.dot(np.diag(1 / den), SU)
dfs = []
extensive = []
if extensive_variables:
for variable in extensive_variables:
vals = _nan_check(source_df, variable)
vals = _inf_check(source_df, variable)
estimates = np.dot(np.diag(vals), weights)
estimates = np.dot(estimates, UT)
estimates = estimates.sum(axis=0)
extensive.append(estimates)
extensive = np.array(extensive)
extensive = pd.DataFrame(extensive.T, columns=extensive_variables)
ST = np.dot(SU, UT)
area = ST.sum(axis=0)
den = np.diag(1.0 / (area + (area == 0)))
weights = np.dot(ST, den)
intensive = []
if intensive_variables:
for variable in intensive_variables:
vals = _nan_check(source_df, variable)
vals = _inf_check(source_df, variable)
vals.shape = (len(vals), 1)
est = (vals * weights).sum(axis=0)
intensive.append(est)
intensive = np.array(intensive)
intensive = pd.DataFrame(intensive.T, columns=intensive_variables)
if extensive_variables:
dfs.append(extensive)
if intensive_variables:
dfs.append(intensive)
df = pd.concat(dfs, axis=1)
df["geometry"] = target_df["geometry"].reset_index(drop=True)
df = gpd.GeoDataFrame(df.replace(np.inf, np.nan))
return df
def _area_interpolate_binning(
source_df,
target_df,
extensive_variables=None,
intensive_variables=None,
table=None,
allocate_total=True,
spatial_index="auto",
n_jobs=1,
categorical_variables=None,
):
"""
Area interpolation for extensive, intensive and categorical variables.
Parameters
----------
source_df : geopandas.GeoDataFrame
target_df : geopandas.GeoDataFrame
extensive_variables : list
[Optional. Default=None] Columns in dataframes for extensive variables
intensive_variables : list
[Optional. Default=None] Columns in dataframes for intensive variables
table : scipy.sparse.dok_matrix
[Optional. Default=None] Area allocation source-target correspondence
table. If not provided, it will be built from `source_df` and
`target_df` using `tobler.area_interpolate._area_tables_binning`
allocate_total : boolean
[Optional. Default=True] True if total value of source area should be
allocated. False if denominator is area of i. Note that the two cases
would be identical when the area of the source polygon is exhausted by
intersections. See Notes for more details.
spatial_index : str
[Optional. Default="auto"] Spatial index to use to build the
allocation of area from source to target tables. It currently support
the following values:
- "source": build the spatial index on `source_df`
- "target": build the spatial index on `target_df`
- "auto": attempts to guess the most efficient alternative.
Currently, this option uses the largest table to build the
index, and performs a `bulk_query` on the shorter table.
This argument is ignored if n_jobs>1 (or n_jobs=-1).
n_jobs : int
[Optional. Default=1] Number of processes to run in parallel to
generate the area allocation. If -1, this is set to the number of CPUs
available. If `table` is passed, this is ignored.
NOTE: as of Jan'21 multi-core functionality requires master versions
of `pygeos` and `geopandas`.
categorical_variables : list
[Optional. Default=None] Columns in dataframes for categorical variables
Returns
-------
estimates : geopandas.GeoDataFrame
new geodaraframe with interpolated variables as columns and target_df geometry
as output geometry
Notes
-----
The assumption is both dataframes have the same coordinate reference system.
For an extensive variable, the estimate at target polygon j (default case) is:
.. math::
v_j = \\sum_i v_i w_{i,j}
w_{i,j} = a_{i,j} / \\sum_k a_{i,k}
If the area of the source polygon is not exhausted by intersections with
target polygons and there is reason to not allocate the complete value of
an extensive attribute, then setting allocate_total=False will use the
following weights:
.. math::
v_j = \\sum_i v_i w_{i,j}
w_{i,j} = a_{i,j} / a_i
where a_i is the total area of source polygon i.
For an intensive variable, the estimate at target polygon j is:
.. math::
v_j = \\sum_i v_i w_{i,j}
w_{i,j} = a_{i,j} / \\sum_k a_{k,j}
For categorical variables, the estimate returns ratio of presence of each
unique category.
"""
source_df = source_df.copy()
target_df = target_df.copy()
if _check_crs(source_df, target_df):
pass
else:
return None
if table is None:
if n_jobs == 1:
table = _area_tables_binning(source_df, target_df, spatial_index)
else:
table = _area_tables_binning_parallel(source_df,
target_df,
n_jobs=n_jobs)
den = source_df.area.values
if allocate_total:
den = np.asarray(table.sum(axis=1))
den = den + (den == 0)
den = 1.0 / den
n = den.shape[0]
den = den.reshape((n, ))
den = diags([den], [0])
weights = den.dot(table) # row standardize table
dfs = []
extensive = []
if extensive_variables:
for variable in extensive_variables:
vals = _nan_check(source_df, variable)
vals = _inf_check(source_df, variable)
estimates = diags([vals], [0]).dot(weights)
estimates = estimates.sum(axis=0)
extensive.append(estimates.tolist()[0])
extensive = np.asarray(extensive)
extensive = np.array(extensive)
extensive = pd.DataFrame(extensive.T, columns=extensive_variables)
area = np.asarray(table.sum(axis=0))
den = 1.0 / (area + (area == 0))
n, k = den.shape
den = den.reshape((k, ))
den = diags([den], [0])
weights = table.dot(den)
intensive = []
if intensive_variables:
for variable in intensive_variables:
vals = _nan_check(source_df, variable)
vals = _inf_check(source_df, variable)
n = vals.shape[0]
vals = vals.reshape((n, ))
estimates = diags([vals], [0])
estimates = estimates.dot(weights).sum(axis=0)
intensive.append(estimates.tolist()[0])
intensive = np.asarray(intensive)
intensive = pd.DataFrame(intensive.T, columns=intensive_variables)
if categorical_variables:
categorical = {}
for variable in categorical_variables:
unique = source_df[variable].unique()
for value in unique:
mask = source_df[variable] == value
categorical[f"{variable}_{value}"] = np.asarray(
table[mask].sum(axis=0))[0]
categorical = pd.DataFrame(categorical)
categorical = categorical.div(target_df.area.values, axis="rows")
if extensive_variables:
dfs.append(extensive)
if intensive_variables:
dfs.append(intensive)
if categorical_variables:
dfs.append(categorical)
df = pd.concat(dfs, axis=1)
df["geometry"] = target_df[target_df.geometry.name].reset_index(drop=True)
df = gpd.GeoDataFrame(df.replace(np.inf, np.nan))
return df
def _area_interpolate_binning(
source_df,
target_df,
extensive_variables=None,
intensive_variables=None,
table=None,
allocate_total=True,
):
"""
Area interpolation for extensive and intensive variables.
Parameters
----------
source_df : geopandas.GeoDataFrame
target_df : geopandas.GeoDataFrame
extensive_variables : list
columns in dataframes for extensive variables
intensive_variables : list
columns in dataframes for intensive variables
table : scipy.sparse.dok_matrix
allocate_total : boolean
True if total value of source area should be allocated.
False if denominator is area of i. Note that the two cases
would be identical when the area of the source polygon is
exhausted by intersections. See Notes for more details.
Returns
-------
estimates : geopandas.GeoDataFrame
new geodaraframe with interpolated variables as columns and target_df geometry
as output geometry
Notes
-----
The assumption is both dataframes have the same coordinate reference system.
For an extensive variable, the estimate at target polygon j (default case) is:
.. math::
v_j = \\sum_i v_i w_{i,j}
w_{i,j} = a_{i,j} / \\sum_k a_{i,k}
If the area of the source polygon is not exhausted by intersections with
target polygons and there is reason to not allocate the complete value of
an extensive attribute, then setting allocate_total=False will use the
following weights:
.. math::
v_j = \\sum_i v_i w_{i,j}
w_{i,j} = a_{i,j} / a_i
where a_i is the total area of source polygon i.
For an intensive variable, the estimate at target polygon j is:
.. math::
v_j = \\sum_i v_i w_{i,j}
w_{i,j} = a_{i,j} / \\sum_k a_{k,j}
"""
source_df = source_df.copy()
target_df = target_df.copy()
if _check_crs(source_df, target_df):
pass
else:
return None
if table is None:
table = _area_tables_binning(source_df, target_df)
den = source_df["geometry"].area.values
if allocate_total:
den = np.asarray(table.sum(axis=1))
den = den + (den == 0)
den = 1.0 / den
n = den.shape[0]
den = den.reshape((n, ))
den = diags([den], [0])
weights = den.dot(table) # row standardize table
dfs = []
extensive = []
if extensive_variables:
for variable in extensive_variables:
vals = _nan_check(source_df, variable)
vals = _inf_check(source_df, variable)
estimates = diags([vals], [0]).dot(weights)
estimates = estimates.sum(axis=0)
extensive.append(estimates.tolist()[0])
extensive = np.asarray(extensive)
extensive = np.array(extensive)
extensive = pd.DataFrame(extensive.T, columns=extensive_variables)
area = np.asarray(table.sum(axis=0))
den = 1.0 / (area + (area == 0))
n, k = den.shape
den = den.reshape((k, ))
den = diags([den], [0])
weights = table.dot(den)
intensive = []
if intensive_variables:
for variable in intensive_variables:
vals = _nan_check(source_df, variable)
vals = _inf_check(source_df, variable)
n = vals.shape[0]
vals = vals.reshape((n, ))
estimates = diags([vals], [0])
estimates = estimates.dot(weights).sum(axis=0)
intensive.append(estimates.tolist()[0])
intensive = np.asarray(intensive)
intensive = pd.DataFrame(intensive.T, columns=intensive_variables)
if extensive_variables:
dfs.append(extensive)
if intensive_variables:
dfs.append(intensive)
df = pd.concat(dfs, axis=1)
df["geometry"] = target_df["geometry"].reset_index(drop=True)
df = gpd.GeoDataFrame(df.replace(np.inf, np.nan))
return df