nsolvejs/lib/derivativenumericOpt.js

Solve equations using numerical methods

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

module.exports = function (f, npoints, interval) {
  let x_n; let h; let h_n; let a; let b; let N; let y_a; let y_b; let y_n; let n;
  const x_pts = [];
  let x_n_1; let y_n_1; const
    df_dx = [];
  sortInterval(interval);
  N = npoints;
  a = interval[0];
  b = interval[1];
  y_a = f(a);
  y_b = f(b);
  x_n_1 = a;
  y_n_1 = y_a;
  h = (b - a) / N;
  h_n = h;
  n = 0;
  while (x_n_1 < b) {
    x_pts[n] = x_n_1;
    x_n = x_n_1 + h_n;
    y_n = f(x_n);
    df_dx[n] = [];
    df_dx[n] = [x_n, (y_n - y_n_1) / h_n];
    x_n_1 = x_n;
    y_n_1 = y_n;
    // h_n is calculated from the condition deltax^2+deltay^2=h^2 with
    // h=(b-a)/N.
    h_n = h / Math.sqrt(1 + df_dx[n][1]);
    n++;
  }
  return {
    dfdx_array: df_dx,
    xpoints: x_pts,
  };
};