pyinterp.RTree.radial_basis_function

RTree.radial_basis_function(coordinates: ndarray, radius: float | None = None, k: int = 9, rbf: str | None = None, epsilon: float | None = None, smooth: float = 0, within: bool = True, num_threads: int = 0) → tuple[ndarray, ndarray][source]

Interpolate values using radial basis function interpolation.

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). Defaults to the maximum distance between two points.

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

  • rbf –

    The radial basis function, based on the radius, \(r\) given by the distance between points. This parameter can take one of the following values:

    • cubic: \(\varphi(r) = r^3\)

    • gaussian: \(\varphi(r) = e^{-(\dfrac{r} {\varepsilon})^2}\)

    • inverse_multiquadric: \(\varphi(r) = \dfrac{1} {\sqrt{1+(\dfrac{r}{\varepsilon})^2}}\)

    • linear: \(\varphi(r) = r\)

    • multiquadric: \(\varphi(r) = \sqrt{1+( \dfrac{r}{\varepsilon})^2}\)

    • thin_plate: \(\varphi(r) = r^2 \ln(r)\)

    Defaults to multiquadric.

  • epsilon – adjustable constant for gaussian or multiquadrics functions. Default to the average distance between nodes.

  • smooth – values greater than zero increase the smoothness of the approximation. Default to 0 (interpolation).

  • 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.