#NumMeth Lab 5 (Simpsons/Rekt/Trap) COMPLETE

var K1 = 1.0/3.0;
var K2 = 1.0/15.0;

function fx(x) { return Math.pow(x, 4) - 12*Math.pow(x, 3) + 15*Math.pow(x, 2) - 6; }

function simpsons(f, a, b, n) {
    var h = (b - a) / n;
    var r, s = 0.0, m = 0;

    for (var x = a; x <= b; x += h) {
        r = f(x);
        if (x == a || x == b) {
            s += r;
        } else {
            m = !m;
            s += r * (m + 1) * 2.0;
        }
    }

    return s * (h / 3.0);
}

function rektangles(f, a, b, n) {
    var h = (b - a) / n;
    var s = 0.0;

    for (var i = 0; i < n; i++)
        s += f(a + h*(i + 0.5));

    return s * h;
}

function trapezoids(f, a, b, n) {
    var h = (b - a) / n;
    var s = 0.0;

    for (var i = 1; i <= n-1; i++)
        s += f(a + i*h);

    return (h/2) * (f(a) + f(b) + 2*s);
}

function lab5Main() {
    var a = 0, b = 1;
    steps = 1;
    epsilon = 0.001;
    rektStop = false, trapStop = false, simpStop = false;

    do {
        rektDelta = K1 * Math.abs(rektangles(fx, a, b, 2*steps) - rektangles(fx, a, b, steps));
        trapDelta = K1 * Math.abs(trapezoids(fx, a, b, 2*steps) - trapezoids(fx, a, b, steps));
        simpDelta = K2 * Math.abs(simpsons(fx, a, b, 2*steps) - simpsons(fx, a, b, steps));

        if (rektDelta < epsilon && !rektStop) {
            rektStop = true;
            rektSteps = 2*steps;
        }
        if (trapDelta < epsilon && !trapStop) {
            trapStop = true;
            trapSteps = 2*steps;
        }
        if (simpDelta < epsilon && !simpStop) {
            simpStop = true;
            simpSteps = 2*steps;
        }

        steps *= 2;

    } while (!(rektStop && trapStop && simpStop));

    rektStr = "rektangles I=" + rektangles(fx, a, b, rektSteps) + " n=" + rektSteps;
    trapStr = "trapezoids I=" + trapezoids(fx, a, b, trapSteps) + " n=" + trapSteps;
    simpStr = "simpsons   I=" + simpsons(fx, a, b, simpSteps) + " n=" + simpSteps;

    console.log(rektStr);
    console.log(trapStr);
    console.log(simpStr);
}