pyinterp.RTree.kriging

Contents

pyinterp.RTree.kriging#

RTree.kriging(coordinates: ndarray, *, radius: float | None = None, k: int = 9, covariance: str | None = None, drift_function: str | None = None, sigma: float = 1.0, alpha: float = 1000000.0, nugget: float = 0.0, within: bool = True, num_threads: int = 0) → tuple[ndarray, ndarray][source]#

Interpolate the values of a point using kriging.

Parameters:

  • coordinates – Array of shape (n, 3) or (n, 2) containing observation coordinates. Here n is the number of observations and each row represents a coordinate in the order x, y, and optionally z. If the matrix shape is (n, 2), the z-coordinate is assumed to be zero. The coordinate system depends on the instance configuration: If ecef=True, coordinates are in the Cartesian coordinate system (ECEF). Otherwise, coordinates are in the geodetic system (longitude, latitude, altitude) in degrees, degrees, and meters, respectively.

  • radius – The maximum radius of the search (m).

  • k – The number of nearest neighbors to be used for calculating the interpolated value. Defaults to 9.

  • covariance –

    The covariance function, based on the distance between points. This parameter can take one of the following values:

    • matern_12: \(\sigma^2\exp\left(-\frac{d}{\rho} \right)\)

    • matern_32: \(\sigma^2\left(1+\frac{\sqrt{3}d}{ \rho}\right)\exp\left(-\frac{\sqrt{3}d}{\rho} \right)\)

    • matern_52: \(\sigma^2\left(1+\frac{\sqrt{5}d}{ \rho}+\frac{5d^2}{3\rho^2}\right) \exp\left(-\frac{ \sqrt{5}d}{\rho} \right)\)

    • cauchy: \(\sigma^2 \left(1 + \frac{d}{\rho} \right)^{-1}\)

    • gaussian: \(\sigma^2 \exp \left(-\frac{d^2}{ \rho^2} \right)\)

    • spherical: \(\sigma^2 \left(1 - \frac{3d}{2r} + \frac{3d^3}{2r^3} \right) \left(\frac{d}{r} \le 1 \right)\)

    • linear: \(\sigma^2 \left(1 - \frac{d}{r} \right) \left(\frac{d}{r} \le 1 \right)\)

  • drift_function –

    The drift (trend) function to be used for universal kriging. This parameter can take one of the following values:

    • linear: \(m(x,y,z) = \beta_0 + \beta_1 x + \beta_2 y + \beta_3 z\)

    • quadratic: \(m(x,y,z) = \beta_0 + \beta_1 x + \beta_2 y + \beta_3 z + \beta_4 x^2 + \beta_5 y^2 + \beta_6 z^2 + \beta_7 xy + \beta_8 xz + \beta_9 yz\)

    Defaults to None (simple kriging with known mean 0).

  • sigma – The sill (magnitude) parameter \(\sigma\) of the covariance function. Determines the overall scale (maximum covariance).

  • alpha – The range parameter \(\rho\). Determines how quickly the covariance decays with distance. Units must match the distance units used internally (geodetic/ECEF -> meters, pure Cartesian -> user units).

  • nugget – Nugget effect (added to the covariance matrix diagonal). Accounts for measurement error or unresolved microscale variability. Must be \(\ge 0\).

  • within – If true, the method ensures that the neighbors found are located around the point of interest (prevents extrapolation).

  • num_threads – Number of threads to use. 0 uses all available, 1 disables parallelism (useful for debugging).

Returns:

The interpolated value and the number of neighbors used in the calculation.

Note

  • If drift_function is None, simple kriging with known mean 0 is applied.

  • If drift_function is provided, universal kriging augments the system with the corresponding trend basis functions.

  • alpha corresponds to the range parameter \(\rho\) controlling spatial correlation extent.

Contents