nsolvejs/lib/bisection.js

Solve equations using numerical methods

const sortInterval = require('./sortInterval');

const _ = {};
_.clone = require('../utils/clone');

function bisection(f, interval, options) {
  if (!f) return;

  if (typeof options === 'number') options = arguments[3];

  options = options || {
    presicion: 0.001,
    nstepsmax: 100000,
  };
  options.presicion = options.presicion || 0.001;
  options.nstepsmax = options.nstepsmax || 100000;
  const { presicion } = options;
  interval = _.clone(interval, true);
  let A; let B; let test; let x; let
    y;
  sortInterval(interval);
  A = {
    x: interval[0],
    y: f(interval[0]),
  };
  B = {
    x: interval[1],
    y: f(interval[1]),
  };
  test = A.y * B.y > 0;
  if (test) {
    x = (A.x + B.x) / 2;
    y = f(x);
    test = A.y * y > 0;
    if (!test) {
      B.x = x;
      B.y = y;
    } else {
      A.x = x;
      A.y = y;
    }
  }
  test = A.y * B.y > 0;
  if (test) return;

  let Root;
  let n = 1;
  const nmax = options.nstepsmax;
  while (!Root && n < nmax) {
    n++;
    x = (A.x + B.x) / 2;
    y = f(x);
    if (Math.abs(y) <= presicion) Root = x;

    test = A.y * y > 0;
    if (!test) {
      B.x = x;
      B.y = y;
    } else {
      A.x = x;
      A.y = y;
    }
  }
  return {
    Root,
    numSteps: n,
    method: 'bisection',
  };
}

module.exports = bisection;