Block and Poisson Kriging#

Centroid-based Poisson Kriging#

pyinterpolate.centroid_poisson_kriging(semivariogram_model: TheoreticalVariogram, point_support: PointSupport, unknown_block_index: str | Hashable, number_of_neighbors: int, neighbors_range: float = None, is_weighted_by_point_support=True, raise_when_negative_prediction=True, raise_when_negative_error=True, allow_lsa=False, negative_prediction_to_zero=False) → Dict[source]

Function performs centroid-based Poisson Kriging of blocks (areal) data.

Parameters:

semivariogram_modelTheoreticalVariogram: A fitted variogram.
point_supportPointSupport: The point support of polygons.
unknown_block_indexHashable: The id of the block with the unknown value.
number_of_neighborsint: The minimum number of neighbours that can potentially affect the unknown block.
neighbors_rangefloat, optional: The maximum range for neighbors search. If not provided then it is read from the semivariogram model.
is_weighted_by_point_supportbool, default = True: Are distances between blocks weighted by the point support?
raise_when_negative_predictionbool, default=True: Raise error when prediction is negative.
raise_when_negative_errorbool, default=True: Raise error when prediction error is negative.
allow_lsabool, default=False: Allows the approximation of kriging weights based on the OLS algorithm. We don’t recommend set it to True if you don’t know what are you doing. This parameter can be useful when you have clusters in your dataset, that can lead to singular or near-singular matrix creation.
negative_prediction_to_zerobool, default=False: While prediction is negative, then set it to 0.

Returns:

resultsDict: Block index, prediction, error: {"block id", "zhat", "sig"}

Raises:

ValueError: Raised when prediction or prediction error are negative.

Examples

>>> import os
>>> import geopandas as gpd
>>> from pyinterpolate import (
...     centroid_poisson_kriging,
...     Blocks,
...     ExperimentalVariogram,
...     PointSupport,
...     TheoreticalVariogram
... )
>>>
>>>
>>> FILENAME = 'cancer_data.gpkg'
>>> LAYER_NAME = 'areas'
>>> DS = gpd.read_file(FILENAME, layer=LAYER_NAME)
>>> AREA_VALUES = 'rate'
>>> AREA_INDEX = 'FIPS'
>>> AREA_GEOMETRY = 'geometry'
>>> PS_LAYER_NAME = 'points'
>>> PS_VALUES = 'POP10'
>>> PS_GEOMETRY = 'geometry'
>>> PS = gpd.read_file(FILENAME, layer=PS_LAYER_NAME)
>>>
>>> CANCER_DATA = {
...    'ds': DS,
...    'index_column_name': AREA_INDEX,
...    'value_column_name': AREA_VALUES,
...    'geometry_column_name': AREA_GEOMETRY
... }
>>> POINT_SUPPORT_DATA = {
...     'ps': PS,
...     'value_column_name': PS_VALUES,
...     'geometry_column_name': PS_GEOMETRY
... }
>>> BLOCKS = Blocks(**CANCER_DATA)
>>> indexes = BLOCKS.block_indexes
>>>
>>> PS = PointSupport(
...     points=POINT_SUPPORT_DATA['ps'],
...     ps_blocks=BLOCKS,
...     points_value_column=POINT_SUPPORT_DATA['value_column_name'],
...     points_geometry_column=POINT_SUPPORT_DATA['geometry_column_name']
... )
>>>
>>> EXPERIMENTAL = ExperimentalVariogram(
...     ds=BLOCKS.representative_points_array(),
...     step_size=40000,
...     max_range=300001
... )
>>>
>>> THEO = TheoreticalVariogram()
>>> THEO.autofit(
...     experimental_variogram=EXPERIMENTAL,
...     sill=150
... )
>>> centroid_pk = centroid_poisson_kriging(
...     semivariogram_model=THEO,
...     point_support=PS,
...     unknown_block_index=34017,
...     number_of_neighbors=8
... )
>>> print(centroid_pk)
{'block_id': 34017, 'zhat': 134.13113195517153, 'sig': 11.795520367595483}

Area-to-area Poisson Kriging#

pyinterpolate.area_to_area_pk(semivariogram_model: TheoreticalVariogram, point_support: PointSupport, unknown_block_index: str | Hashable, number_of_neighbors: int, neighbors_range: float = None, raise_when_negative_prediction=True, raise_when_negative_error=True, negative_prediction_to_zero=False) → dict[source]

Function predicts areal value in an unknown location based on the area-to-area Poisson Kriging

Parameters:

semivariogram_modelTheoreticalVariogram: A fitted variogram.
point_supportPointSupport: The point support of polygons.
unknown_block_indexHashable: The id of the block with the unknown value.
number_of_neighborsint: The minimum number of neighbours that can potentially affect the unknown block.
neighbors_rangefloat, optional: The maximum range for neighbors search. If not provided then it is read from the semivariogram model.
raise_when_negative_predictionbool, default=True: Raise error when prediction is negative.
raise_when_negative_errorbool, default=True: Raise error when prediction error is negative.
negative_prediction_to_zerobool, default=False: While prediction is negative, then set it to 0.

Returns:

resultsDict: Block index, prediction, error: {"block_id", "zhat", "sig"}

Raises:

ValueError: Raised when prediction or prediction error are negative.

Examples

>>> import os
>>> import geopandas as gpd
>>> from pyinterpolate import (
...     area_to_area_pk,
...     Blocks,
...     ExperimentalVariogram,
...     PointSupport,
...     TheoreticalVariogram
... )
>>>
>>>
>>> FILENAME = 'cancer_data.gpkg'
>>> LAYER_NAME = 'areas'
>>> DS = gpd.read_file(FILENAME, layer=LAYER_NAME)
>>> AREA_VALUES = 'rate'
>>> AREA_INDEX = 'FIPS'
>>> AREA_GEOMETRY = 'geometry'
>>> PS_LAYER_NAME = 'points'
>>> PS_VALUES = 'POP10'
>>> PS_GEOMETRY = 'geometry'
>>> PS = gpd.read_file(FILENAME, layer=PS_LAYER_NAME)
>>>
>>> CANCER_DATA = {
...    'ds': DS,
...    'index_column_name': AREA_INDEX,
...    'value_column_name': AREA_VALUES,
...    'geometry_column_name': AREA_GEOMETRY
... }
>>> POINT_SUPPORT_DATA = {
...     'ps': PS,
...     'value_column_name': PS_VALUES,
...     'geometry_column_name': PS_GEOMETRY
... }
>>> BLOCKS = Blocks(**CANCER_DATA)
>>> indexes = BLOCKS.block_indexes
>>>
>>> PS = PointSupport(
...     points=POINT_SUPPORT_DATA['ps'],
...     ps_blocks=BLOCKS,
...     points_value_column=POINT_SUPPORT_DATA['value_column_name'],
...     points_geometry_column=POINT_SUPPORT_DATA['geometry_column_name']
... )
>>>
>>> EXPERIMENTAL = ExperimentalVariogram(
...     ds=BLOCKS.representative_points_array(),
...     step_size=40000,
...     max_range=300001
... )
>>>
>>> THEO = TheoreticalVariogram()
>>> THEO.autofit(
...     experimental_variogram=EXPERIMENTAL,
...     sill=150
... )
>>> ata_pk = area_to_area_pk(
...     semivariogram_model=THEO,
...     point_support=PS,
...     unknown_block_index=34017,
...     number_of_neighbors=8
... )
>>> print(ata_pk)
{'block_id': 34017, 'zhat': 133.89984110553695, 'sig': 5.9614557671535335}

Area-to-point Poisson Kriging#

pyinterpolate.area_to_point_pk(semivariogram_model: TheoreticalVariogram, point_support: PointSupport, unknown_block_index: str | Hashable, number_of_neighbors: int, neighbors_range: float = None, raise_when_negative_prediction=True, raise_when_negative_error=True, err_to_nan=True, negative_prediction_to_zero=False)[source]

Function predicts point-support value in the unknown location based on the area-to-point Poisson Kriging

Parameters:

semivariogram_modelTheoreticalVariogram: A fitted variogram.
point_supportPointSupport: The point support of polygons.
unknown_block_indexHashable: The id of the block with the unknown value.
number_of_neighborsint: The minimum number of neighbours that can potentially affect the unknown block.
neighbors_rangefloat, optional: The maximum range for neighbors search. If not provided then it is read from the semivariogram model.
raise_when_negative_predictionbool, default=True: Raise error when prediction is negative.
raise_when_negative_errorbool, default=True: Raise error when prediction error is negative.
err_to_nanbool, default=True: When point interpolation returns ValueError then set prediction or variance error to NaN.
negative_prediction_to_zerobool, default=False: While prediction is negative, then set it to 0.

Returns:

resultsDict[numpy array]: `{"block_id": [["x", "y", "zhat", "sig"], ...]}

Raises:

ValueError: Prediction or prediction error are negative.

Examples

>>> import os
>>> import geopandas as gpd
>>> from pyinterpolate import (
...     area_to_point_pk,
...     Blocks,
...     ExperimentalVariogram,
...     PointSupport,
...     TheoreticalVariogram
... )
>>>
>>>
>>> FILENAME = 'cancer_data.gpkg'
>>> LAYER_NAME = 'areas'
>>> DS = gpd.read_file(FILENAME, layer=LAYER_NAME)
>>> AREA_VALUES = 'rate'
>>> AREA_INDEX = 'FIPS'
>>> AREA_GEOMETRY = 'geometry'
>>> PS_LAYER_NAME = 'points'
>>> PS_VALUES = 'POP10'
>>> PS_GEOMETRY = 'geometry'
>>> PS = gpd.read_file(FILENAME, layer=PS_LAYER_NAME)
>>>
>>> CANCER_DATA = {
...    'ds': DS,
...    'index_column_name': AREA_INDEX,
...    'value_column_name': AREA_VALUES,
...    'geometry_column_name': AREA_GEOMETRY
... }
>>> POINT_SUPPORT_DATA = {
...     'ps': PS,
...     'value_column_name': PS_VALUES,
...     'geometry_column_name': PS_GEOMETRY
... }
>>> BLOCKS = Blocks(**CANCER_DATA)
>>> indexes = BLOCKS.block_indexes
>>>
>>> PS = PointSupport(
...     points=POINT_SUPPORT_DATA['ps'],
...     ps_blocks=BLOCKS,
...     points_value_column=POINT_SUPPORT_DATA['value_column_name'],
...     points_geometry_column=POINT_SUPPORT_DATA['geometry_column_name']
... )
>>>
>>> EXPERIMENTAL = ExperimentalVariogram(
...     ds=BLOCKS.representative_points_array(),
...     step_size=40000,
...     max_range=300001
... )
>>>
>>> THEO = TheoreticalVariogram()
>>> THEO.autofit(
...     experimental_variogram=EXPERIMENTAL,
...     sill=150
... )
>>> atp_pk = area_to_point_pk(
...     semivariogram_model=THEO,
...     point_support=PS,
...     unknown_block_index=34017,
...     number_of_neighbors=8
... )
>>> print(atp_pk)
{34017: array([[1.82287362e+06, 4.06124500e+05, 1.34010668e+02, 5.47866897e+00]])}

Block and Poisson Kriging#

Centroid-based Poisson Kriging#

Area-to-area Poisson Kriging#

Area-to-point Poisson Kriging#

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