Ordinary kriging

Kriging fits or accepts a variogram model and uses local ordinary kriging to estimate target values. Most users can let apbase.Map decide whether it is the better option: the pipeline compares kriging with IDW and keeps it only when it has the lower leave-one-out RMSE.

from apbase.kriging import Kriging

kriging = Kriging(max_neighbors=40, min_neighbors=3).fit(x, y, z)
z_targets = kriging.interpolate(targets)  # targets: (n, 2) array

use apbase::kriging::{Kriging, KrigingOptions};

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

Parameters

x, y : array_like : Source coordinates passed to fit. Kriging 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 the fitted variogram (see Variogram fitting).

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.

model_values : array_like, optional : Precomputed variogram model (Variogram.model_values). If provided, fit uses it instead of fitting a new variogram.

What "local" and "ordinary" mean here

Local means that each target is estimated from nearby source points within radius, capped at max_neighbors, rather than from the entire dataset. This keeps the linear system small and the method scalable. Ordinary means that the process mean is treated as unknown and constant within each local neighborhood. Simple kriging, by contrast, assumes the mean is known.

See Ordinary kriging for the full derivation (the linear system solved per target and why it produces the best linear unbiased estimate) and Variogram fitting for the variogram models.