@bmancini55/finance/lib/math-newton-raphson.ts

Finance utilities for JavaScript

/**
 * Performs the Newton-Raphson iteration to find an approximate root of a real-valued
 * function.
 *
 * @param fx function f(x)
 * @param gx derivative of f(x)
 * @param x0 initial guess
 * @param n optional number of iterations, default is 10
 * @param e optional tolerable error, default is 1e-8
 */
export function calcNewtonRaphson(
  fx: (v: number) => number,
  gx: (v: number) => number,
  x0: number,
  n: number = 10,
  e: number = 1e-8
) {
  for (let i = 0; i < n; i++) {
    const gx0 = gx(x0);

    // console.log('x0', x0);
    // console.log('fx0', Math.abs(fx(x0)));
    // console.log('gx0', gx0);

    // check if g(x0) === 0 and error if it is
    if (Math.abs(gx0) < 1e-30) {
      return 0;
    }

    // calculate x1
    const x1 = x0 - fx(x0) / gx0;

    // check if f(x1) is inside error requirement
    const fx1 = fx(x1);
    if (Math.abs(fx1) <= e) {
      return x1;
    }

    // if not try to iterate again
    x0 = x1;
  }

  return 0;
}