commons-math-interpolation/Cubic.js

A partial port of the Apache Commons Math Interpolation package, including Akima cubic spline interpolation and LOESS/LOWESS local regression.

import { checkStrictlyIncreasing, trimPoly, evaluatePolySegment } from "./Utils.js";
export function createCubicSplineInterpolator(xVals, yVals) {
    const segmentCoeffs = computeCubicPolyCoefficients(xVals, yVals);
    const xValsCopy = Float64Array.from(xVals);
    return (x) => evaluatePolySegment(xValsCopy, segmentCoeffs, x);
}
export function computeCubicPolyCoefficients(xVals, yVals) {
    if (xVals.length != yVals.length) {
        throw new Error("Dimension mismatch.");
    }
    if (xVals.length < 3) {
        throw new Error("Number of points is too small.");
    }
    checkStrictlyIncreasing(xVals);
    const n = xVals.length - 1;
    const h = new Float64Array(n);
    for (let i = 0; i < n; i++) {
        h[i] = xVals[i + 1] - xVals[i];
    }
    const mu = new Float64Array(n);
    const z = new Float64Array(n + 1);
    mu[0] = 0;
    z[0] = 0;
    for (let i = 1; i < n; i++) {
        const g = 2 * (xVals[i + 1] - xVals[i - 1]) - h[i - 1] * mu[i - 1];
        mu[i] = h[i] / g;
        z[i] = (3 * (yVals[i + 1] * h[i - 1] - yVals[i] * (xVals[i + 1] - xVals[i - 1]) + yVals[i - 1] * h[i]) /
            (h[i - 1] * h[i]) - h[i - 1] * z[i - 1]) / g;
    }
    const b = new Float64Array(n);
    const c = new Float64Array(n + 1);
    const d = new Float64Array(n);
    z[n] = 0;
    c[n] = 0;
    for (let i = n - 1; i >= 0; i--) {
        const dx = h[i];
        const dy = yVals[i + 1] - yVals[i];
        c[i] = z[i] - mu[i] * c[i + 1];
        b[i] = dy / dx - dx * (c[i + 1] + 2 * c[i]) / 3;
        d[i] = (c[i + 1] - c[i]) / (3 * dx);
    }
    const segmentCoeffs = new Array(n);
    for (let i = 0; i < n; i++) {
        const coeffs = new Float64Array(4);
        coeffs[0] = yVals[i];
        coeffs[1] = b[i];
        coeffs[2] = c[i];
        coeffs[3] = d[i];
        segmentCoeffs[i] = trimPoly(coeffs);
    }
    return segmentCoeffs;
}
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