Inverse Distance Weighting (IDW)#

pyinterpolate.inverse_distance_weighting(unknown_location: ArrayLike, known_locations: ArrayLike = None, known_values: ArrayLike = None, known_geometries: ArrayLike = None, no_neighbors=-1, power=2.0) → float[source]

Inverse Distance Weighting with a given set of points and the unknown location.

Parameters:
unknown_locationIterable

Array or list with coordinates of the unknown point. Its length is N-1 (number of dimensions). The unknown location shape should be the same as the known_points parameter shape, if not, then new dimension is added once - vector of points [x, y] becomes [[x, y]] for 2-dimensional data.

known_locationsnumpy array, optional

The known locations: [x, y, value].

known_valuesArrayLike, optional

Observation in the i-th geometry (from known_geometries). Optional parameter, if not given then known_locations must be provided.

known_geometriesArrayLike, optional

Array or similar structure with geometries. It must have the same length as known_values. Optional parameter, if not given then known_locations must be provided. Point type geometry.

no_neighborsint, default = -1

If default value (-1) then all known points will be used to estimate value at the unknown location. Can be any number within the limits [2, len(known_points)],

powerfloat, default = 2.

Power value must be larger or equal to 0. It controls weight assigned to each known point. Larger power means stronger influence of the closest neighbors, but it decreases faster.

Returns:
resultfloat

The estimated value.

Raises:
ValueError

Power parameter set to be smaller than 0.

ValueError

Less than 2 neighbours or more than the number of known_points neighbours are given in the number_of_neighbours parameter.

Examples

>>> unknown_pos = (10, 10)
>>> locs = np.array([
...     [11, 1, 1],
...     [23, 2, 2],
...     [33, 3, 3],
...     [14, 44, 4],
...     [13, 10, 9],
...     [12, 55, 35],
...     [11, 9, 7]
... ])
>>> pred = inverse_distance_weighting(
...     unknown_locations=unknown_pos,
...     known_values=locs[:, -1],
...     known_geometries=locs[:, :-1],
...     no_neighbors=2
... )
>>> print(pred)
7.286311587314138

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