integrate-adaptive-simpson
Compute a definite integral of one variable using Simpson's Rule with adaptive quadrature
Introduction
This module computes the definite integral
using Romberg Integration based on Simpson's Rule. That is, it uses Richardson Extrapolation to estimate the error and recursively subdivide intervals until the error tolerance is met. The code is adapted from the pseudocode in Romberg Integration and Adaptive Quadrature.Install
$ npm install integrate-adaptive-simpson
Example
To compute the definite integral
execute:var integrate = ; { return Math / x);} ;// => -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 = ; ; // => [ 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 is1e-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 is20
. 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 lengthn
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 is1e-8
.maxdepth
: The maximum recursion depth. Default depth is20
. 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.