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

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

Import

For CommonJS

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

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

Usage / Documentation

lambertW0

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

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

lambertW0Log

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

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

lambertW0_SimpleIteration_LT_E

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

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

lambertW0_SimpleIteration_GT_E

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

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.