integrate-adaptive-simpson

WebJar for integrate-adaptive-simpson

License	MIT
GroupId	org.webjars.npm
ArtifactId	integrate-adaptive-simpson
Last Version	1.1.1
Release Date	Aug 9, 2016
Type	jar
Description	integrate-adaptive-simpson WebJar for integrate-adaptive-simpson
Project URL	http://webjars.org
Source Code Management	https://github.com/scijs/integrate-adaptive-simpson

Download integrate-adaptive-simpson

Filename	Size
integrate-adaptive-simpson-1.1.1.pom
integrate-adaptive-simpson-1.1.1.jar	13 KB
integrate-adaptive-simpson-1.1.1-sources.jar	22 bytes
integrate-adaptive-simpson-1.1.1-javadoc.jar	22 bytes

How to add to project

Apache Maven

<!-- https://jarcasting.com/artifacts/org.webjars.npm/integrate-adaptive-simpson/ -->
<dependency>
    <groupId>org.webjars.npm</groupId>
    <artifactId>integrate-adaptive-simpson</artifactId>
    <version>1.1.1</version>
</dependency>

Gradle Groovy

// https://jarcasting.com/artifacts/org.webjars.npm/integrate-adaptive-simpson/
implementation 'org.webjars.npm:integrate-adaptive-simpson:1.1.1'

Gradle Kotlin

// https://jarcasting.com/artifacts/org.webjars.npm/integrate-adaptive-simpson/
implementation ("org.webjars.npm:integrate-adaptive-simpson:1.1.1")

Apache Buildr

'org.webjars.npm:integrate-adaptive-simpson:jar:1.1.1'

Apache Ivy

<dependency org="org.webjars.npm" name="integrate-adaptive-simpson" rev="1.1.1">
  <artifact name="integrate-adaptive-simpson" type="jar" />
</dependency>

Groovy Grape

@Grapes(
@Grab(group='org.webjars.npm', module='integrate-adaptive-simpson', version='1.1.1')
)

Scala SBT

libraryDependencies += "org.webjars.npm" % "integrate-adaptive-simpson" % "1.1.1"

Leiningen

[org.webjars.npm/integrate-adaptive-simpson "1.1.1"]

Dependencies

There are no dependencies for this project. It is a standalone project that does not depend on any other jars.

Project Modules

There are no modules declared in this project.

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 = require('integrate-adaptive-simpson');

function f (x) {
  return Math.cos(1 / x) / x;
}

integrate(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.

Versions

Version
1.1.1 Aug 9, 2016