@fvictorio/newton-raphson-method/lib/index.js

Find zeros of a function using the Newton-Raphson method

'use strict';
var __importDefault = (this && this.__importDefault) || function (mod) {
    return (mod && mod.__esModule) ? mod : { "default": mod };
};
Object.defineProperty(exports, "__esModule", { value: true });
const big_js_1 = __importDefault(require("big.js"));
big_js_1.default.DP = 100;
function newtonRaphson(f, x0, options, fp) {
    var x1, y, yp, tol, maxIter, iter, yph, ymh, yp2h, ym2h, h, hr, verbose;
    options = options || {};
    tol = new big_js_1.default(options.tolerance === undefined ? 1e-7 : options.tolerance);
    maxIter = options.maxIterations === undefined ? 20 : options.maxIterations;
    h = new big_js_1.default(options.h === undefined ? 1e-4 : options.h);
    verbose = options.verbose === undefined ? false : options.verbose;
    hr = new big_js_1.default(1).div(h);
    x0 = new big_js_1.default(x0);
    iter = 0;
    while (iter++ < maxIter) {
        // Compute the value of the function:
        y = f(x0);
        if (fp) {
            yp = fp(x0);
        }
        else {
            // Needs numerical derivatives:
            yph = f(x0.plus(h));
            ymh = f(x0.minus(h));
            yp2h = f(x0.plus(h.mul(2)));
            ym2h = f(x0.minus(h.mul(2)));
            yp = ym2h
                .minus(yp2h)
                .plus(new big_js_1.default(8).mul(yph.minus(ymh)))
                .mul(hr)
                .div(12);
        }
        // Update the guess:
        x1 = x0.minus(y.div(yp));
        // Check for convergence:
        if (x1
            .minus(x0)
            .abs()
            .lte(tol.mul(x1.abs()))) {
            if (verbose) {
                console.log('Newton-Raphson: converged to x = ' + x1 + ' after ' + iter + ' iterations');
            }
            return x1;
        }
        // Transfer update to the new guess:
        x0 = x1;
    }
    if (verbose) {
        console.log('Newton-Raphson: Maximum iterations reached (' + maxIter + ')');
    }
    return false;
}
exports.newtonRaphson = newtonRaphson;