Heaviside Function

Evaluate the Heaviside function.

The Heaviside function is defined as

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,

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

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

Installation

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

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 ] ) );
}

See Also

• @stdlib/math-base/special/ramp: evaluate the ramp function.

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.

Community

License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.