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math-base-special-heavisidef

Evaluate the Heaviside function for a single-precision floating-point number.

https://github.com/stdlib-js/math-base-special-heavisidef

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digital-signal-processing discontinuous dist distribution dsp heavisidef javascript math mathematics node node-js nodejs ramp stdlib step-function unit-step-function
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Evaluate the Heaviside function for a single-precision floating-point number.

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digital-signal-processing discontinuous dist distribution dsp heavisidef javascript math mathematics node node-js nodejs ramp stdlib step-function unit-step-function
Created about 1 year ago · Last pushed 9 months ago
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README.md

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Heaviside Function

NPM version Build Status Coverage Status <!-- dependencies -->

Evaluate the Heaviside function for a single-precision floating-point number.

The [Heaviside function][heaviside-function] is defined as ```math 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][heaviside-function] may be defined as a continuous function. To define the [Heaviside function][heaviside-function] such that the function has rotational symmetry, ```math 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][heaviside-function] as a left-continuous function, ```math H(x) = \begin{cases} x & \textrm{if}\ x \gt 0 \\ 0 & \textrm{if}\ x \leq 0\end{cases} ``` To define the [Heaviside function][heaviside-function] as a right-continuous function, ```math H(x) = \begin{cases} x & \textrm{if}\ x \geq 0 \\ 0 & \textrm{if}\ x \lt 0\end{cases} ```
## Installation ```bash npm install @stdlib/math-base-special-heavisidef ``` Alternatively, - To load the package in a website via a `script` tag without installation and bundlers, use the [ES Module][es-module] available on the [`esm`][esm-url] branch (see [README][esm-readme]). - If you are using Deno, visit the [`deno`][deno-url] branch (see [README][deno-readme] for usage intructions). - For use in Observable, or in browser/node environments, use the [Universal Module Definition (UMD)][umd] build available on the [`umd`][umd-url] branch (see [README][umd-readme]). The [branches.md][branches-url] 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 ```javascript var heavisidef = require( '@stdlib/math-base-special-heavisidef' ); ``` #### heavisidef( x\[, continuity] ) Evaluates the [Heaviside function][heaviside-function] for a single-precision floating-point number. ```javascript var v = heavisidef( 3.14 ); // returns 1.0 v = heavisidef( -3.14 ); // returns 0.0 v = heavisidef( 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 = heavisidef( 0.0 ); // returns NaN ``` To define the [Heaviside function][heaviside-function] as a continuous function, set the `continuity` parameter. ```javascript var v = heavisidef( 0.0, 'half-maximum' ); // returns 0.5 v = heavisidef( 0.0, 'left-continuous' ); // returns 0.0 v = heavisidef( 0.0, 'right-continuous' ); // returns 1.0 ```
## Examples ```javascript var uniform = require( '@stdlib/random-array-uniform' ); var logEachMap = require( '@stdlib/console-log-each-map' ); var heavisidef = require( '@stdlib/math-base-special-heavisidef' ); var opts = { 'dtype': 'float32' }; var x = uniform( 100, -10.0, 10.0, opts ); logEachMap( 'H(%0.4f) = %0.4f', x, heavisidef ); ```
## C APIs
### Usage ```c #include "stdlib/math/base/special/heavisidef.h" ``` #### stdlib_base_heavisidef( x, continuity ) Evaluates the [Heaviside function][heaviside-function] for a single-precision floating-point number. ```c float y = stdlib_base_heavisidef( 0.0f, STDLIB_BASE_HEAVISIDEF_CONTINUITY_HALF_MAXIMUM ); // returns 0.5f y = stdlib_base_heavisidef( 0.0f, STDLIB_BASE_HEAVISIDEF_CONTINUITY_LEFT_CONTINUOUS ); // returns 0.0f ``` The function accepts the following arguments: - **x**: `[in] float` input value. - **continuity**: `[in] enum STDLIB_BASE_HEAVISIDEF_CONTINUITY` continuity option. The `continuity` parameter may be one of the following values: - `STDLIB_BASE_HEAVISIDEF_CONTINUITY_HALF_MAXIMUM`: if `x == 0`, the function returns `0.5`. - `STDLIB_BASE_HEAVISIDEF_CONTINUITY_LEFT_CONTINUOUS`: if `x == 0`, the function returns `0.0`. - `STDLIB_BASE_HEAVISIDEF_CONTINUITY_RIGHT_CONTINUOUS`: if `x == 0`, the function returns `1.0`. - `STDLIB_BASE_HEAVISIDEF_CONTINUITY_DISCONTINUOUS`: if `x == 0`, the function returns `NaN`. If provided a `continuity` argument which is not one of the enumeration constants listed above, the function returns `NaN` for `x == 0`, behaving like the discontinuous case. ```c float stdlib_base_heavisidef( const float x, const enum STDLIB_BASE_HEAVISIDEF_CONTINUITY continuity ); ```
### Examples ```c #include "stdlib/math/base/special/heavisidef.h" #include int main( void ) { const float x[] = { -4.0f, -3.0f, -2.0f, -1.0f, 0.0f, 1.0f, 2.0f, 3.0f, 4.0f, 5.0f }; float y; int i; for ( i = 0; i < 10; i++ ) { y = stdlib_base_heavisidef( x[ i ], STDLIB_BASE_HEAVISIDEF_CONTINUITY_HALF_MAXIMUM ); printf( "H(%f) = %f\n", x[ i ], y ); } } ```

* * * ## 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 [![Chat][chat-image]][chat-url] --- ## License See [LICENSE][stdlib-license]. ## Copyright Copyright © 2016-2025. The Stdlib [Authors][stdlib-authors].

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Standard library for JavaScript.

Citation (CITATION.cff) 

cff-version: 1.2.0
title: stdlib
message: >-
  If you use this software, please cite it using the
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type: software

authors:
  - name: The Stdlib Authors
    url: https://github.com/stdlib-js/stdlib/graphs/contributors

repository-code: https://github.com/stdlib-js/stdlib
url: https://stdlib.io

abstract: |
  Standard library for JavaScript and Node.js.

keywords:
  - JavaScript
  - Node.js
  - TypeScript
  - standard library
  - scientific computing
  - numerical computing
  - statistical computing

license: Apache-2.0 AND BSL-1.0

date-released: 2016

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