Variogram

Variogram fits an empirical semivariogram from source points and chooses the best-fitting model from spherical, exponential, and Gaussian options. Kriging always uses a fitted variogram; the other estimators use one to derive radius when it is omitted (see Variogram fitting).

apbase.Map fits the variogram for you. Use Variogram directly when you want to inspect the fitted curve or control the fitting step.

from apbase.variogram import Variogram

variogram = Variogram(n_lags=50, max_pairs=100_000).fit(x, y, z)
gamma = variogram.evaluate(distances)

use apbase::variogram::{Variogram, VariogramOptions};

let mut variogram = Variogram::new(VariogramOptions { n_lags: 50, max_pairs: 100_000, ..Default::default() })?;
variogram.fit(&x, &y, &z)?;
let gamma = variogram.evaluate(&distances)?;

Parameters

x, y : array_like : Source coordinates passed to fit. Variogram does not convert longitude/latitude: pass projected coordinates.

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

n_lags : int, default 50 : Number of distance bins used to build the empirical semivariogram.

max_pairs : int, default 100_000 : Maximum point pairs sampled while building the empirical semivariogram. 0 uses every eligible pair, subject to the native ceiling.

max_distance : float, default 0.0 : Maximum pair distance considered. 0.0 lets the native kernel choose the extent from the data.

distance : array_like : Distances passed to evaluate; returns semivariance for each distance.

What fit does

fit computes the empirical semivariogram, estimates the nugget, partial sill, and range for each candidate model, and keeps the fit with the lowest weighted error. evaluate(distance) returns the fitted model's semivariance at arbitrary distances, which is useful for inspecting the curve directly.

See Variogram fitting for the math behind the empirical estimator and the fitting procedure, and Ordinary kriging for how the fitted model feeds into the kriging system.