Variogram

Variogram fits an empirical semivariogram from source points and chooses the best-fitting model from spherical, exponential, and gaussian options. IDW, Kriging, and SpatialFilter use it internally when radius is omitted, but you can also inspect it directly.

For normal map generation, apbase.Map fits and reuses the variogram before comparing IDW and kriging. 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)

Parameters

x, y : array_like : Source coordinates passed to fit.

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 uses the native default extent.

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

What fit does

fit computes the empirical semivariogram, estimates nugget, sill, and range for each candidate model, and keeps the fit with the lowest weighted error. evaluate(distances) 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.