Function pcms::mls_interpolation

Function Documentation

Omega_h::Write<Omega_h::Real> pcms::mls_interpolation(const Omega_h::Reals source_values, const Omega_h::Reals source_coordinates, const Omega_h::Reals target_coordinates, const SupportResults &support, const Omega_h::LO &dim, const Omega_h::LO &degree, RadialBasisFunction bf, double lambda = 0, double tol = 1e-6, double decay_factor = 5.0)

Performs Moving Least Squares (MLS) interpolation at target points.

This function computes interpolated values at a set of target coordinates using Moving Least Squares (MLS) based on the provided source values and coordinates. It supports different radial basis functions (RBFs), polynomial degrees, spatial dimensions, optional regularization, and solver tolerance.

Note

  • All input arrays must reside in device memory (e.g., Kokkos device views).

  • Coordinate arrays must be correctly sized as num_points * dim.

  • Choose lambda and decay_factor carefully to balance accuracy and stability: a larger decay factor often requires a slightly higher lambda.

Parameters:

  • source_values – A flat array of source data values. Length should match the number of source points (num_sources).

  • source_coordinates – A flat array of source point coordinates of size num_sources * dim.

  • target_coordinates – A flat array of target point coordinates of size num_targets * dim.

  • support – A structure containing neighbor information for each target point in Compressed Sparse Row (CSR) format.

  • dim – Spatial dimension of the coordinate data (e.g., 2 or 3).

  • degree – Degree of the polynomial basis used in MLS.

  • bf – The radial basis function (RBF) used for weighting (e.g., Gaussian, C4).

  • lambda – Tikhonov regularization parameter (default: 0.0). A small positive value improves numerical stability for ill-conditioned local systems.

    • Well-conditioned systems: 1e-8 to 1e-6

    • Mildly ill-conditioned: 1e-5 to 1e-3

    • Highly ill-conditioned: 1e-2 to 1e-1

  • tol – Optional solver tolerance (default: 1e-6). Singular values below this threshold are ignored.

  • decay_factor – Controls the spread of the RBF influence width (default: 5.0).

    • 1–3 → wide influence (smooth interpolation)

    • 3–8 → moderate locality (balanced, recommended)

    • 8–20 → highly local behavior (sharp detail, possible conditioning issues)

Returns:

A Write<Real> array containing interpolated values at each target point. Length matches the number of target points.