xkcd’s Geothemic Meandian

geothemic_meandian.js

// https://xkcd.com/2435/
// Usage: geothemic meandian = g(array, epsilon, [iterations = 3])

function g(a, epsilon, iterations) {
    if (a.length < 1) { return NaN; }
    iterations = (Number.isFinite(iterations) && iterations > 0) ? iterations : 3;
    let geothmetic = Array.from(a);
    while (range(geothmetic) > epsilon) {
        geothmetic = f(geothmetic);
    }
    return geothmetic[0];
}

function f(a) {
    return [amean(a), gmean(a), median(a)];
}

function range(a) {
    if (a.length < 1) { return NaN; }
    let min = Number.MAX_SAFE_INTEGER;
    let max = Number.MIN_SAFE_INTEGER;
    a.forEach(x => {
        min = Math.min(min, x);
        max = Math.max(max, x);
    });
    return max - min;
}

function amean(a) {
    if (a.length < 1) { return NaN; }
    let sum = 0;
    a.forEach(x => { sum += x; });
    return sum / a.length;
}

function gmean(a) {
    if (a.length < 1) { return NaN; }
    let prod = 1;
    a.forEach(x => { prod = prod * x; });
    return Math.pow(prod, 1 / a.length);
}

function median(a) {
    if (a.length < 1) { return NaN; }
    a.sort();
    let pivot = Math.floor(a.length / 2);
    if (a.length % 2 == 0) {
        return (a[pivot - 1] + a[pivot]) / 2;
    } else {
        return a[pivot];
    }
}