integrate-adaptive-simpson

Compute a definite integral of one variable using Simpson's Rule with adaptive quadrature

Introduction

This module computes the definite integral

Install

$ npm install integrate-adaptive-simpson

Example

To compute the definite integral

var integrate = require('integrate-adaptive-simpson');
 
function f (x) {
  return Math.cos(1 / x) / x);
}
 
intiegrate(f, 0.01, 1, 1e-8);
// => -0.3425527480294604

To integrate a vector function, you may import the vectorized version. To compute a contour integral of, say, about , that is,

var integrate = require('integrate-adaptive-simpson/vector');
 
integrate(function (f, theta) {
  // z = unit circle:
  var c = Math.cos(theta);
  var s = Math.sin(theta);
 
  // dz:
  var dzr = -s;
  var dzi = c;
 
  // 1 / z at this point on the unit circle:
  var fr = c / (c * c + s * s);
  var fi = -s / (c * c + s * s);
 
  // Multiply f(z) * dz:
  f[0] = fr * dzr - fi * dzi;
  f[1] = fr * dzi + fi * dzr;
}, 0, Math.PI * 2);
 
// => [ 0, 6.283185307179586 ]

API

require('integrate-adaptive-simpson')( f, a, b [, tol, maxdepth]] )

Compute the definite integral of scalar function f from a to b.

Arguments:

• f: The function to be integrated. A function of one variable that returns a value.
• a: The lower limit of integration, .
• b: The upper limit of integration, .
• tol: The relative error required for an interval to be subdivided, based on Richardson extraplation. Default tolerance is 1e-8. Be careful—the total accumulated error may be significantly less and result in more function evaluations than necessary.
• maxdepth: The maximum recursion depth. Default depth is 20. If reached, computation continues and a warning is output to the console.

Returns: The computed value of the definite integral.

require('integrate-adaptive-simpson/vector')( f, a, b [, tol, maxdepth]] )

Compute the definite integral of vector function f from a to b.

Arguments:

• f: The function to be integrated. The first argument is an array of length n into which the output must be written. The second argument is the scalar value of the independent variable.
• a: The lower limit of integration, .
• b: The upper limit of integration, .
• tol: The relative error required for an interval to be subdivided, based on Richardson extraplation. Default tolerance is 1e-8.
• maxdepth: The maximum recursion depth. Default depth is 20. If reached, computation continues and a warning is output to the console.

Returns: An Array representing The computed value of the definite integral.

References

Colins, C., Romberg Integration and Adaptive Quadrature Course Notes.

License

(c) 2015 Scijs Authors. MIT License.