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https://github.com/stdlib-js/math-base-special-heaviside
Evaluate the Heaviside function.
https://github.com/stdlib-js/math-base-special-heaviside
digital-signal-processing discontinuous dist distribution dsp heaviside javascript math mathematics node node-js nodejs ramp stdlib step-function unit-step-function
Last synced: 3 months ago
JSON representation
Evaluate the Heaviside function.
- Host: GitHub
- URL: https://github.com/stdlib-js/math-base-special-heaviside
- Owner: stdlib-js
- License: apache-2.0
- Created: 2021-06-14T16:38:03.000Z (over 3 years ago)
- Default Branch: main
- Last Pushed: 2024-10-01T04:17:59.000Z (4 months ago)
- Last Synced: 2024-10-05T20:44:18.381Z (4 months ago)
- Topics: digital-signal-processing, discontinuous, dist, distribution, dsp, heaviside, javascript, math, mathematics, node, node-js, nodejs, ramp, stdlib, step-function, unit-step-function
- Language: JavaScript
- Homepage: https://github.com/stdlib-js/stdlib
- Size: 350 KB
- Stars: 2
- Watchers: 3
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- Changelog: CHANGELOG.md
- Contributing: CONTRIBUTING.md
- License: LICENSE
- Code of conduct: CODE_OF_CONDUCT.md
- Citation: CITATION.cff
- Security: SECURITY.md
Awesome Lists containing this project
README
About stdlib...
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The library is fully decomposable, being architected in such a way that you can swap out and mix and match APIs and functionality to cater to your exact preferences and use cases.
When you use stdlib, you can be absolutely certain that you are using the most thorough, rigorous, well-written, studied, documented, tested, measured, and high-quality code out there.
To join us in bringing numerical computing to the web, get started by checking us out on GitHub, and please consider financially supporting stdlib. We greatly appreciate your continued support!
# Heaviside Function
[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url]
> Evaluate the [Heaviside function][heaviside-function].
The [Heaviside function][heaviside-function] is defined as
```math
H(x) = \begin{cases} 1 & \textrm{if}\ x \gt 0 \\ 0 & \textrm{if}\ x \lt 0\end{cases}
```
and is discontinuous at `0`. Depending on the context, the [Heaviside function][heaviside-function] may be defined as a continuous function. To define the [Heaviside function][heaviside-function] such that the function has rotational symmetry,
```math
H(x) = \begin{cases} x & \textrm{if}\ x \gt 0 \\ \frac{1}{2} & \textrm{if}\ x = 0 \\ 0 & \textrm{if}\ x \lt 0\end{cases}
```
To define the [Heaviside function][heaviside-function] as a left-continuous function,
```math
H(x) = \begin{cases} x & \textrm{if}\ x \gt 0 \\ 0 & \textrm{if}\ x \leq 0\end{cases}
```
To define the [Heaviside function][heaviside-function] as a right-continuous function,
```math
H(x) = \begin{cases} x & \textrm{if}\ x \geq 0 \\ 0 & \textrm{if}\ x \lt 0\end{cases}
```
## Installation
```bash
npm install @stdlib/math-base-special-heaviside
```
Alternatively,
- To load the package in a website via a `script` tag without installation and bundlers, use the [ES Module][es-module] available on the [`esm`][esm-url] branch (see [README][esm-readme]).
- If you are using Deno, visit the [`deno`][deno-url] branch (see [README][deno-readme] for usage intructions).
- For use in Observable, or in browser/node environments, use the [Universal Module Definition (UMD)][umd] build available on the [`umd`][umd-url] branch (see [README][umd-readme]).
The [branches.md][branches-url] file summarizes the available branches and displays a diagram illustrating their relationships.
To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.
## Usage
```javascript
var heaviside = require( '@stdlib/math-base-special-heaviside' );
```
#### heaviside( x\[, continuity] )
Evaluates the [Heaviside function][heaviside-function].
```javascript
var v = heaviside( 3.14 );
// returns 1.0
v = heaviside( -3.14 );
// returns 0.0
v = heaviside( NaN );
// returns NaN
```
The `continuity` parameter may be one of the following values:
- `'half-maximum'`: if `x == 0`, the function returns `0.5`.
- `'left-continuous'`: if `x == 0`, the function returns `0.0`.
- `'right-continuous'`: if `x == 0`, the function returns `1.0`.
By default, the function is discontinuous at `0`.
```javascript
var v = heaviside( 0.0 );
// returns NaN
```
To define the [Heaviside function][heaviside-function] as a continuous function, set the `continuity` parameter.
```javascript
var v = heaviside( 0.0, 'half-maximum' );
// returns 0.5
v = heaviside( 0.0, 'left-continuous' );
// returns 0.0
v = heaviside( 0.0, 'right-continuous' );
// returns 1.0
```
## Examples
```javascript
var linspace = require( '@stdlib/array-base-linspace' );
var heaviside = require( '@stdlib/math-base-special-heaviside' );
var x = linspace( -10.0, 10.0, 101 );
var i;
for ( i = 0; i < x.length; i++ ) {
console.log( 'H(%d) = %d', x[ i ], heaviside( x[ i ] ) );
}
```
* * *
## See Also
- [`@stdlib/math-base/special/ramp`][@stdlib/math/base/special/ramp]: evaluate the ramp function.
* * *
## Notice
This package is part of [stdlib][stdlib], a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.
For more information on the project, filing bug reports and feature requests, and guidance on how to develop [stdlib][stdlib], see the main project [repository][stdlib].
#### Community
[![Chat][chat-image]][chat-url]
---
## License
See [LICENSE][stdlib-license].
## Copyright
Copyright © 2016-2024. The Stdlib [Authors][stdlib-authors].
[npm-image]: http://img.shields.io/npm/v/@stdlib/math-base-special-heaviside.svg
[npm-url]: https://npmjs.org/package/@stdlib/math-base-special-heaviside
[test-image]: https://github.com/stdlib-js/math-base-special-heaviside/actions/workflows/test.yml/badge.svg?branch=main
[test-url]: https://github.com/stdlib-js/math-base-special-heaviside/actions/workflows/test.yml?query=branch:main
[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/math-base-special-heaviside/main.svg
[coverage-url]: https://codecov.io/github/stdlib-js/math-base-special-heaviside?branch=main
[chat-image]: https://img.shields.io/gitter/room/stdlib-js/stdlib.svg
[chat-url]: https://app.gitter.im/#/room/#stdlib-js_stdlib:gitter.im
[stdlib]: https://github.com/stdlib-js/stdlib
[stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors
[umd]: https://github.com/umdjs/umd
[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules
[deno-url]: https://github.com/stdlib-js/math-base-special-heaviside/tree/deno
[deno-readme]: https://github.com/stdlib-js/math-base-special-heaviside/blob/deno/README.md
[umd-url]: https://github.com/stdlib-js/math-base-special-heaviside/tree/umd
[umd-readme]: https://github.com/stdlib-js/math-base-special-heaviside/blob/umd/README.md
[esm-url]: https://github.com/stdlib-js/math-base-special-heaviside/tree/esm
[esm-readme]: https://github.com/stdlib-js/math-base-special-heaviside/blob/esm/README.md
[branches-url]: https://github.com/stdlib-js/math-base-special-heaviside/blob/main/branches.md
[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/math-base-special-heaviside/main/LICENSE
[heaviside-function]: https://en.wikipedia.org/wiki/Heaviside_step_function
[@stdlib/math/base/special/ramp]: https://github.com/stdlib-js/math-base-special-ramp