Inverse distance weighting (IDW)

IDW estimates each target value as a distance-weighted average of nearby source points. Most users can let apbase.Map handle it: the automatic pipeline compares IDW with ordinary kriging and keeps IDW when it has the lower leave-one-out RMSE for the current dataset.

from apbase.idw import IDW

idw = IDW(power=2.0, max_neighbors=40, min_neighbors=3).fit(x, y, z)
z_targets = idw.interpolate(targets)  # targets: (n, 2) array

use apbase::idw::{IDW, IDWOptions};

let mut idw = IDW::new(IDWOptions { power: 2.0, max_neighbors: 40, min_neighbors: 3, ..Default::default() })?;
idw.fit(&x, &y, &z)?;
let z_targets = idw.interpolate(&targets)?; // targets: (n, 2) array or a fitted Grid

Parameters

x, y : array_like : Source coordinates passed to fit. IDW does not convert longitude/latitude: pass projected coordinates, in the same unit as radius.

z : array_like : Source values. Must have the same length as x and y.

targets : array_like or Grid : Target coordinates passed to interpolate: an (n_targets, 2) array, a fitted Grid, or point geometries (a list of Shapely points, or a GeoSeries/GeoDataFrame).

radius : float, optional : Local search radius. If omitted, it is derived from a fitted variogram (see Variogram fitting).

power : float, default 2.0 : Distance exponent. Higher values give more weight to nearby points.

max_neighbors : int, default 40 : Maximum source points used per target.

min_neighbors : int, default 3 : Minimum source points within radius. When fewer are found, the max_neighbors nearest points are used regardless of distance.

When IDW wins over kriging

IDW is a deterministic weighted average. It is fast, makes no distributional assumptions, and behaves predictably when data is sparse. Ordinary kriging also uses the spatial correlation captured by the variogram. It can be more accurate when that structure is well fitted, but it costs more and is more sensitive to a poor fit. apbase.Map and apbase.create_map compare both methods on your data, so you do not need to choose manually.

See Inverse distance weighting (IDW) for the weighting formula itself.