lambert-w-function


This is efficient and zero-dependency JavaScript implementations for the Lambert W function on the principal branch W_0.

Please note that this library does not support complex numbers and only supports the principal branch.

Currently there are three implementations:

* Naive implementation (desmos) that make use of iterative method to furnish (relatively poor) approximate solution.
* The work of Roberto Iacono and John P. Boyd with a maximum relative error 5E-3. This is the default and the one you should use.
* Implementation provided by xmodar for log(x) as input.

Installation

From npm via npm

``bash
npm install lambert-w-function
yarn add lambert-w-function
bun add lambert-w-function
pnpm add lambert-w-function
`

Import

For CommonJS

`js
const {
lambertW0, // same as lambertW0_IaconoBoyd
lambertW0_IaconoBoyd,
lambertW0Log, // same as lambertW0Log_xmodar
lambertW0Log_xmodar,
lambertW0_SimpleIteration_LT_E,
lambertW0_SimpleIteration_GT_E,
W0_LIMIT_POINT
} = require('lambert-w-function')
`

otherwise

`js
import { ... } from 'lambert-w-function'
`

Usage / Documentation

$3

An approximation with a maximum relative error 5E-3. Same as lambertW0Log if is_x_log set to true.

`js
lambertW0(x: number, is_x_log = false): number
`

$3

Computes W(y) where y is of the form log(x).

`js
// See: https://gist.github.com/xmodar/baa392fc2bec447d10c2c20bbdcaf687
lambertW0Log(logX: number): number
`

$3

Simple iterative Lambert W function approximation for (x <= Math.E). Note that it won't raise an error if x is greater than E.

`js
lambertW0_SimpleIteration_LT_E(x: number, iterations = 10): number
`

$3

Simple iterative Lambert W function approximation for (x > Math.E). Note that it won't raise an error if x is less than E.

`js
lambertW0_SimpleIteration_GT_E(x: number, iterations = 10): number
``

License

This project is licensed under the MIT License meaning you're free to use, modify, and distribute it however you like. Go build something awesome.