Heaviside Function

Evaluate the Heaviside function.

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}

Installation

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 available on the esm branch (see README).
If you are using Deno, visit the deno branch (see README for usage intructions).
For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the umd branch (see README).

The branches.md 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

var heaviside = require( '@stdlib/math-base-special-heaviside' );

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

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 ] ) );
}

Notice

This package is part of 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, see the main project repository.