pyinterp.RTree.universal_kriging

RTree.universal_kriging(coordinates: ndarray, radius: float | None = None, k: int = 9, covariance: str | None = None, sigma: float = 1.0, alpha: float = 1000000.0, within: bool = True, num_threads: int = 0) → tuple[ndarray, ndarray]

Interpolate the values of a point using universal kriging.

Parameters:

• coordinates – a matrix of shape (n, 3), where n is the number of observations and 3 represents the coordinates in theorder: x, y, and z. If the matrix shape is (n, 2), the z-coordinate is assumed to be zero. The coordinates (x, y, z) are in the Cartesian coordinate system (ECEF) if the instance is configured to use this system (ecef keyword set to True during construction). Otherwise, the coordinates are in the geodetic system (longitude, latitude, and 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: \(\sigma^2\left(1+\frac{\sqrt{5}d}{ \rho}+\frac{5d^2}{3\rho^2}\right) \exp\left(-\frac{ \sqrt{5}d}{\rho} \right)\)

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

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

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

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

• sigma – The sigma parameter of the covariance function. Defaults to 1.0. Determines the overall scale of the covariance function. It represents the maximum possible covariance between two points.

• alpha – The alpha parameter of the covariance function. Defaults to 1_000_000.0. Determines the rate at which the covariance decreases. It represents the spatial scale of the covariance function and can be used to control the smoothness of the spatial dependence structure.

• within – If true, the method ensures that the neighbors found are located around the point of interest. In other words, this parameter ensures that the calculated values will not be extrapolated. Defaults to true.

• num_threads – The number of threads to use for the computation. If 0 all CPUs are used. If 1 is given, no parallel computing code is used at all, which is useful for debugging. Defaults to 0.

Returns:

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