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Viewing file:     MonotonicInterpolant.js (2.67 KB)      -rw-r--r--

export default class MonotonicInterpolant {
    constructor(xs, ys) {
        const { length } = xs;
        // Rearrange xs and ys so that xs is sorted
        const indexes = [];
        for (let i = 0; i < length; i++) {
            indexes.push(i);
        }
        indexes.sort((a, b) => (xs[a] < xs[b] ? -1 : 1));
        // Get consecutive differences and slopes
        const dys = [];
        const dxs = [];
        const ms = [];
        let dx;
        let dy;
        for (let i = 0; i < length - 1; i++) {
            dx = xs[i + 1] - xs[i];
            dy = ys[i + 1] - ys[i];
            dxs.push(dx);
            dys.push(dy);
            ms.push(dy / dx);
        }
        // Get degree-1 coefficients
        const c1s = [ms[0]];
        for (let i = 0; i < dxs.length - 1; i++) {
            const m2 = ms[i];
            const mNext = ms[i + 1];
            if (m2 * mNext <= 0) {
                c1s.push(0);
            }
            else {
                dx = dxs[i];
                const dxNext = dxs[i + 1];
                const common = dx + dxNext;
                c1s.push((3 * common) / ((common + dxNext) / m2 + (common + dx) / mNext));
            }
        }
        c1s.push(ms[ms.length - 1]);
        // Get degree-2 and degree-3 coefficients
        const c2s = [];
        const c3s = [];
        let m;
        for (let i = 0; i < c1s.length - 1; i++) {
            m = ms[i];
            const c1 = c1s[i];
            const invDx = 1 / dxs[i];
            const common = c1 + c1s[i + 1] - m - m;
            c2s.push((m - c1 - common) * invDx);
            c3s.push(common * invDx * invDx);
        }
        this.xs = xs;
        this.ys = ys;
        this.c1s = c1s;
        this.c2s = c2s;
        this.c3s = c3s;
    }
    interpolate(x) {
        const { xs, ys, c1s, c2s, c3s } = this;
        // The rightmost point in the dataset should give an exact result
        let i = xs.length - 1;
        if (x === xs[i]) {
            return ys[i];
        }
        // Search for the interval x is in, returning the corresponding y if x is one of the original xs
        let low = 0;
        let high = c3s.length - 1;
        let mid;
        while (low <= high) {
            mid = Math.floor(0.5 * (low + high));
            const xHere = xs[mid];
            if (xHere < x) {
                low = mid + 1;
            }
            else if (xHere > x) {
                high = mid - 1;
            }
            else {
                return ys[mid];
            }
        }
        i = Math.max(0, high);
        // Interpolate
        const diff = x - xs[i];
        const diffSq = diff * diff;
        return ys[i] + c1s[i] * diff + c2s[i] * diffSq + c3s[i] * diff * diffSq;
    }
}