https://github.com/stdlib-js/math-base-special-dirac-delta
Evaluate the Dirac delta function.
https://github.com/stdlib-js/math-base-special-dirac-delta
continuous delta dirac dist distribution impulse javascript kronecker math mathematics node node-js nodejs spike stdlib
Last synced: 2 months ago
JSON representation
Evaluate the Dirac delta function.
- Host: GitHub
- URL: https://github.com/stdlib-js/math-base-special-dirac-delta
- Owner: stdlib-js
- License: apache-2.0
- Created: 2021-06-14T16:38:31.000Z (over 4 years ago)
- Default Branch: main
- Last Pushed: 2025-04-07T07:05:52.000Z (6 months ago)
- Last Synced: 2025-06-20T21:13:10.422Z (4 months ago)
- Topics: continuous, delta, dirac, dist, distribution, impulse, javascript, kronecker, math, mathematics, node, node-js, nodejs, spike, stdlib
- Language: Python
- Homepage: https://github.com/stdlib-js/stdlib
- Size: 425 KB
- Stars: 1
- Watchers: 3
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- Changelog: CHANGELOG.md
- Contributing: CONTRIBUTING.md
- License: LICENSE
- Code of conduct: CODE_OF_CONDUCT.md
- Citation: CITATION.cff
- Security: SECURITY.md
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README
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# Dirac Delta
[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url]
> Evaluate the [Dirac delta function][dirac-delta-function].
The [Dirac delta function][dirac-delta-function] may be loosely defined as
```math
\delta = \begin{cases} \infty & \textrm{if}\ x = 0 \\ 0 & \textrm{if}\ x \neq 0\end{cases}
```
and is constrained to satisfy the identity
```math
\int^{+\infty}_{-\infty} \delta(x)\ dx = 1
```
Note that the [Dirac delta function][dirac-delta-function] is **not** a function in the traditional sense, as any real-valued function which is zero everywhere except at a single point, must have an integral equal to `0`.
## Installation
```bash
npm install @stdlib/math-base-special-dirac-delta
```
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 diracDelta = require( '@stdlib/math-base-special-dirac-delta' );
```
#### diracDelta( x )
Evaluates the [Dirac delta function][dirac-delta-function].
```javascript
var v = diracDelta( 0.0 );
// returns Infinity
v = diracDelta( 3.14 );
// returns 0.0
v = diracDelta( NaN );
// returns NaN
```
## Examples
```javascript
var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var diracDelta = require( '@stdlib/math-base-special-dirac-delta' );
var opts = {
'dtype': 'float64'
};
var x = uniform( 100, -1.0, 1.0, opts );
logEachMap( 'dirac(%0.4f) = %0.4f', x, diracDelta );
```
* * *
## C APIs
### Usage
```c
#include "stdlib/math/base/special/dirac_delta.h"
```
#### stdlib_base_dirac_delta( x )
Evaluates the [Dirac delta function][dirac-delta-function].
```c
double x = stdlib_base_dirac_delta( 0.0 );
// returns Infinity
x = stdlib_base_dirac_delta( 3.14 );
// returns 0.0
```
The function accepts the following arguments:
- **x**: `[in] double` input value.
```c
double stdlib_base_dirac_delta( const double x );
```
### Examples
```c
#include "stdlib/math/base/special/dirac_delta.h"
#include
#include
int main( void ) {
const double x[] = { -1.0, -0.5, 0.0, 0.5, 1.0, 3.14, 2.0 };
double v;
int i;
for ( i = 0; i < 7; i++ ) {
v = stdlib_base_dirac_delta( x[ i ] );
printf( "dirac(%lf) = %lf\n", x[ i ], v );
}
}
```
* * *
## See Also
- [`@stdlib/math-base/special/kronecker-delta`][@stdlib/math/base/special/kronecker-delta]: evaluate the Kronecker delta.
* * *
## 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].
[npm-image]: http://img.shields.io/npm/v/@stdlib/math-base-special-dirac-delta.svg
[npm-url]: https://npmjs.org/package/@stdlib/math-base-special-dirac-delta
[test-image]: https://github.com/stdlib-js/math-base-special-dirac-delta/actions/workflows/test.yml/badge.svg?branch=main
[test-url]: https://github.com/stdlib-js/math-base-special-dirac-delta/actions/workflows/test.yml?query=branch:main
[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/math-base-special-dirac-delta/main.svg
[coverage-url]: https://codecov.io/github/stdlib-js/math-base-special-dirac-delta?branch=main
[chat-image]: https://img.shields.io/gitter/room/stdlib-js/stdlib.svg
[chat-url]: https://app.gitter.im/#/room/#stdlib-js_stdlib:gitter.im
[stdlib]: https://github.com/stdlib-js/stdlib
[stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors
[umd]: https://github.com/umdjs/umd
[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules
[deno-url]: https://github.com/stdlib-js/math-base-special-dirac-delta/tree/deno
[deno-readme]: https://github.com/stdlib-js/math-base-special-dirac-delta/blob/deno/README.md
[umd-url]: https://github.com/stdlib-js/math-base-special-dirac-delta/tree/umd
[umd-readme]: https://github.com/stdlib-js/math-base-special-dirac-delta/blob/umd/README.md
[esm-url]: https://github.com/stdlib-js/math-base-special-dirac-delta/tree/esm
[esm-readme]: https://github.com/stdlib-js/math-base-special-dirac-delta/blob/esm/README.md
[branches-url]: https://github.com/stdlib-js/math-base-special-dirac-delta/blob/main/branches.md
[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/math-base-special-dirac-delta/main/LICENSE
[dirac-delta-function]: https://en.wikipedia.org/wiki/Dirac_delta_function
[@stdlib/math/base/special/kronecker-delta]: https://github.com/stdlib-js/math-base-special-kronecker-delta