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About stdlib...

We believe in a future in which the web is a preferred environment for numerical computation. To help realize this future, we've built stdlib. stdlib is a standard library, with an emphasis on numerical and scientific computation, written in JavaScript (and C) for execution in browsers and in Node.js.

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

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Evaluate the Heaviside function.

The Heaviside function is defined as

$$H(x) = \begin{cases} 1 & \textrm{if}\ x \gt 0 \\ 0 & \textrm{if}\ x \lt 0\end{cases}$$

and is discontinuous at 0. Depending on the context, the Heaviside function may be defined as a continuous function. To define the Heaviside function such that the function has rotational symmetry,

$$H(x) = \begin{cases} x & \textrm{if}\ x \gt 0 \\ \frac{1}{2} & \textrm{if}\ x = 0 \\ 0 & \textrm{if}\ x \lt 0\end{cases}$$

To define the Heaviside function as a left-continuous function,

$$H(x) = \begin{cases} x & \textrm{if}\ x \gt 0 \\ 0 & \textrm{if}\ x \leq 0\end{cases}$$

To define the Heaviside function as a right-continuous function,

$$H(x) = \begin{cases} x & \textrm{if}\ x \geq 0 \\ 0 & \textrm{if}\ x \lt 0\end{cases}$$

Usage

import heaviside from 'https://cdn.jsdelivr.net/gh/stdlib-js/math-base-special-heaviside@esm/index.mjs';

heaviside( x[, continuity] )

Evaluates the Heaviside function.

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.

var v = heaviside( 0.0 );
// returns NaN

To define the Heaviside function as a continuous function, set the continuity parameter.

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

<!DOCTYPE html>
<html lang="en">
<body>
<script type="module">

import linspace from 'https://cdn.jsdelivr.net/gh/stdlib-js/array-base-linspace@esm/index.mjs';
import heaviside from 'https://cdn.jsdelivr.net/gh/stdlib-js/math-base-special-heaviside@esm/index.mjs';

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 ] ) );
}

</script>
</body>
</html>

See Also

Notice

This package is part of stdlib, a standard library 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, see the main project repository.

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License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.