Struct PolyharmonicSpline 

pub struct PolyharmonicSpline { /* private fields */ }

A polyharmonic spline interpolator for arbitrary-dimension data.

Given n data points in d dimensions with scalar values, the polyharmonic spline builds an interpolant (or smoothing approximation) using radial basis functions augmented with a polynomial of degree <= order - 1.

Examples

use scirs2_interpolate::polyharmonic::PolyharmonicSpline;

// 2D scattered data
let points = vec![
    vec![0.0, 0.0],
    vec![1.0, 0.0],
    vec![0.0, 1.0],
    vec![1.0, 1.0],
];
let values = vec![0.0, 1.0, 1.0, 2.0];

let spline = PolyharmonicSpline::fit(&points, &values, 2, 0.0)
    .expect("should fit successfully");

// Evaluate at a query point
let result = spline.evaluate(&[0.5, 0.5]).expect("should evaluate");
assert!((result - 1.0).abs() < 1e-8);

Implementations

impl PolyharmonicSpline

pub fn fit( points: &[Vec<f64>], values: &[f64], order: usize, smoothing: f64, ) -> InterpolateResult<Self>

Fit a polyharmonic spline to scattered data.

Arguments

• points - Data point coordinates, n points each of dimension d.
• values - Function values at the data points (length n).
• order - Order of the polyharmonic kernel (>= 1).
  • order = 1: phi(r) = r
  • order = 2: phi(r) = r^2 log(r) (thin-plate spline)
  • order = 3: phi(r) = r^3
• smoothing - Regularization parameter (>= 0). When 0, exact interpolation is performed. Larger values produce smoother results.

Errors

Returns an error if:

• points is empty
• points and values have different lengths
• The linear system is singular

pub fn thin_plate_spline( points: &[Vec<f64>], values: &[f64], smoothing: f64, ) -> InterpolateResult<Self>

Create a thin-plate spline interpolator (order = 2).

This is a convenience method equivalent to fit(points, values, 2, smoothing).

pub fn evaluate(&self, query: &[f64]) -> InterpolateResult<f64>

Evaluate the polyharmonic spline at a single query point.

Errors

Returns an error if the query point dimension does not match the data point dimension.

pub fn evaluate_batch( &self, queries: &[Vec<f64>], ) -> InterpolateResult<Vec<f64>>

Evaluate the polyharmonic spline at multiple query points.

Returns a vector of interpolated values, one per query point.

pub fn order(&self) -> usize

Return the order of the polyharmonic kernel.

pub fn dim(&self) -> usize

Return the dimension of the data points.

pub fn num_points(&self) -> usize

Return the number of data points.

pub fn weights(&self) -> &[f64]

Return the RBF weights.

pub fn poly_coefficients(&self) -> &[f64]

Return the polynomial coefficients.