geomesher.area_weighted#

Area Weighted Interpolation based on tobler.

Module Contents#

geomesher.area_weighted.area_interpolate(source_df, target_df, extensive_variables=None, intensive_variables=None, categorical_variables=None, table=None, allocate_total=True, spatial_index='auto')[source]#

Area interpolation for extensive, intensive and categorical variables.

Parameters:

  • source_df (geopandas.GeoDataFrame) – The source dataframe to get values from.

  • target_df (geopandas.GeoDataFrame) – The target dataframe to interpolate the values from source_df.

  • extensive_variables (list, optional) – Columns in dataframes for extensive variables, defaults to None.

  • intensive_variables (list, optional) – Columns in dataframes for intensive variables, defaults to None.

  • categorical_variables (list, optional) – Columns in dataframes for categorical variables, defaults to None.

  • table (scipy.sparse.csr_matrix, optional) – Area allocation source-target correspondence table. If not provided, it will be built from source_df and target_df.

  • allocate_total (boolean, optional) – 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. Defaults to True.

  • spatial_index (str, optional) – Spatial index to use to build the allocation of area from source to target tables, defaults to auto. It currently supports 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 query on the shorter table.

Returns:

geopandas.GeoDataFrame – new geodaraframe with interpolated variables as columns and target_df geometry as output geometry

Return type:

geopandas.GeoDataFrame

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:

\[ \begin{align}\begin{aligned}v_j = \sum_i v_i w_{i,j}\\w_{i,j} = \frac{a_{i,j}}{\sum_k a_{i,k}}\end{aligned}\end{align} \]

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:

\[ \begin{align}\begin{aligned}v_j = \sum_i v_i w_{i,j}\\w_{i,j} = \frac{a_{i,j}}{a_i}\end{aligned}\end{align} \]

where \(a_i\) is the total area of source polygon \(i\). For an intensive variable, the estimate at target polygon \(j\) is:

\[ \begin{align}\begin{aligned}v_j = \sum_i v_i w_{i,j}\\w_{i,j} = \frac{a_{i,j}}{\sum_k a_{k,j}}\end{aligned}\end{align} \]

For categorical variables, the estimate returns ratio of presence of each unique category.