Evaluate the 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}
npm install @stdlib/math-base-special-heaviside
Alternatively,
script
tag without installation and bundlers, use the ES Module available on the esm
branch (see README).deno
branch (see README for usage intructions).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.
var heaviside = require( '@stdlib/math-base-special-heaviside' );
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
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 ] ) );
}
@stdlib/math-base/special/ramp
: evaluate the ramp function.
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.
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See LICENSE.
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