npm package: @stdlib/math-base-special-heaviside
Description: Evaluate the Heaviside function.
Author: The Stdlib Authors
Latest version: 0.2.3

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# Heaviside Function

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] <!-- [![dependencies][dependencies-image]][dependencies-url] -->

> Evaluate the [Heaviside function][heaviside-function].

<section class="intro">

The [Heaviside function][heaviside-function] is defined as

<!-- <equation class="equation" label="eq:heaviside_function" align="center" raw="H(x) = \begin{cases} 1 & \textrm{if}\ x \gt 0 \\ 0 & \textrm{if}\ x \lt 0\end{cases}" alt="Heaviside function."> -->

<div class="equation" align="center" data-raw-text="H(x) = \begin{cases} 1 &amp; \textrm{if}\ x \gt 0 \\ 0 &amp; \textrm{if}\ x \lt 0\end{cases}" data-equation="eq:heaviside_function">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bb29798906e119fcb2af99e94b60407a270c9b32/lib/node_modules/@stdlib/math/base/special/heaviside/docs/img/equation_heaviside_function.svg" alt="Heaviside function.">
    <br>
</div> -->

<!-- </equation> -->

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,

<!-- <equation class="equation" label="eq:heaviside_function_half_maximum" align="center" raw="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}" alt="Heaviside function half-maximum."> -->

<!-- <div class="equation" align="center" data-raw-text="H(x) = \begin{cases} x &amp; \textrm{if}\ x \gt 0 \\ \frac{1}{2} &amp; \textrm{if}\ x = 0 \\ 0 &amp; \textrm{if}\ x \lt 0\end{cases}" data-equation="eq:heaviside_function_half_maximum">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bb29798906e119fcb2af99e94b60407a270c9b32/lib/node_modules/@stdlib/math/base/special/heaviside/docs/img/equation_heaviside_function_half_maximum.svg" alt="Heaviside function half-maximum.">
    <br>
</div> -->

<!-- </equation> -->

To define the [Heaviside function][heaviside-function] as a left-continuous function,

<!-- <equation class="equation" label="eq:heaviside_function_left_continuous" align="center" raw="H(x) = \begin{cases} x & \textrm{if}\ x \gt 0 \\ 0 & \textrm{if}\ x \leq 0\end{cases}" alt="Heaviside function left-continuous."> -->

<!-- <div class="equation" align="center" data-raw-text="H(x) = \begin{cases} x &amp; \textrm{if}\ x \gt 0 \\ 0 &amp; \textrm{if}\ x \leq 0\end{cases}" data-equation="eq:heaviside_function_left_continuous">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bb29798906e119fcb2af99e94b60407a270c9b32/lib/node_modules/@stdlib/math/base/special/heaviside/docs/img/equation_heaviside_function_left_continuous.svg" alt="Heaviside function left-continuous.">
    <br>
</div> -->

<!-- </equation> -->

To define the [Heaviside function][heaviside-function] as a right-continuous function,

<!-- <equation class="equation" label="eq:heaviside_function_right_continuous" align="center" raw="H(x) = \begin{cases} x & \textrm{if}\ x \geq 0 \\ 0 & \textrm{if}\ x \lt 0\end{cases}" alt="Heaviside function right-continuous."> -->

<!-- <div class="equation" align="center" data-raw-text="H(x) = \begin{cases} x &amp; \textrm{if}\ x \geq 0 \\ 0 &amp; \textrm{if}\ x \lt 0\end{cases}" data-equation="eq:heaviside_function_right_continuous">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bb29798906e119fcb2af99e94b60407a270c9b32/lib/node_modules/@stdlib/math/base/special/heaviside/docs/img/equation_heaviside_function_right_continuous.svg" alt="Heaviside function right-continuous.">
    <br>
</div>

<!-- </equation> -->

</section>

<!-- /.intro -->

<section class="installation">

## Installation

```bash
npm install @stdlib/math-base-special-heaviside
```

</section>

<section class="usage">

## 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
```

</section>

<!-- /.usage -->

<section class="examples">

## Examples

<!-- eslint no-undef: "error" -->

```javascript
var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var heaviside = require( '@stdlib/math-base-special-heaviside' );

var opts = {
    'dtype': 'float64'
};
var x = uniform( 101, -10.0, 10.0, opts );

logEachMap( 'H(%0.4f) = %0.4f', x, heaviside );
```

</section>

<!-- /.examples -->

<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->

<section class="related">

* * *

## See Also

-   <span class="package-name">[`@stdlib/math-base/special/ramp`][@stdlib/math/base/special/ramp]</span><span class="delimiter">: </span><span class="description">evaluate the ramp function.</span>

</section>

<!-- /.related -->

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<section class="main-repo" >

* * *

## 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

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---

## License

See [LICENSE][stdlib-license].


## Copyright

Copyright &copy; 2016-2026. The Stdlib [Authors][stdlib-authors].

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[heaviside-function]: https://en.wikipedia.org/wiki/Heaviside_step_function

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