npm package: @stdlib/math-base-special-dirac-delta
Description: Evaluate the Dirac delta function.
Author: The Stdlib Authors
Latest version: 0.2.4

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# Dirac Delta

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] <!-- [![dependencies][dependencies-image]][dependencies-url] -->

> Evaluate the [Dirac delta function][dirac-delta-function].

<section class="intro">

The [Dirac delta function][dirac-delta-function] may be loosely defined as

<!-- <equation class="equation" label="eq:dirac_delta" align="center" raw="\delta = \begin{cases} \infty & \textrm{if}\ x = 0 \\ 0 & \textrm{if}\ x \neq 0\end{cases}" alt="Dirac delta function."> -->

<div class="equation" align="center" data-raw-text="\delta = \begin{cases} \infty &amp; \textrm{if}\ x = 0 \\ 0 &amp; \textrm{if}\ x \neq 0\end{cases}" data-equation="eq:dirac_delta">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bb29798906e119fcb2af99e94b60407a270c9b32/lib/node_modules/@stdlib/math/base/special/dirac-delta/docs/img/equation_dirac_delta.svg" alt="Dirac delta function.">
    <br>
</div> -->

<!-- </equation> -->

and is constrained to satisfy the identity

<!-- <equation class="equation" label="eq:dirac_delta_integral" align="center" raw="\int^{+\infty}_{-\infty} \delta(x)\ dx = 1" alt="Dirac delta function integral."> -->

<!-- <div class="equation" align="center" data-raw-text="\int^{+\infty}_{-\infty} \delta(x)\ dx = 1" data-equation="eq:dirac_delta_integral">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bb29798906e119fcb2af99e94b60407a270c9b32/lib/node_modules/@stdlib/math/base/special/dirac-delta/docs/img/equation_dirac_delta_integral.svg" alt="Dirac delta function integral.">
    <br>
</div>

<!-- </equation> -->

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`.

</section>

<!-- /.intro -->

<section class="installation">

## Installation

```bash
npm install @stdlib/math-base-special-dirac-delta
```

</section>

<section class="usage">

## 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
```

</section>

<!-- /.usage -->

<section class="examples">

## Examples

<!-- eslint no-undef: "error" -->

```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 );
```

</section>

<!-- /.examples -->

<!-- C interface documentation. -->

* * *

<section class="c">

## C APIs

<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->

<section class="intro">

</section>

<!-- /.intro -->

<!-- C usage documentation. -->

<section class="usage">

### 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 );
```

</section>

<!-- /.usage -->

<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->

<section class="notes">

</section>

<!-- /.notes -->

<!-- C API usage examples. -->

<section class="examples">

### Examples

```c
#include "stdlib/math/base/special/dirac_delta.h"
#include <stdlib.h>
#include <stdio.h>

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 );
    }
}
```

</section>

<!-- /.examples -->

</section>

<!-- /.c -->

<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->

<section class="related">

* * *

## See Also

-   <span class="package-name">[`@stdlib/math-base/special/kronecker-delta`][@stdlib/math/base/special/kronecker-delta]</span><span class="delimiter">: </span><span class="description">evaluate the Kronecker delta.</span>

</section>

<!-- /.related -->

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<section class="main-repo" >

* * *

## 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 &copy; 2016-2026. The Stdlib [Authors][stdlib-authors].

</section>

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[dirac-delta-function]: https://en.wikipedia.org/wiki/Dirac_delta_function

<!-- <related-links> -->

[@stdlib/math/base/special/kronecker-delta]: https://www.npmjs.com/package/@stdlib/math-base-special-kronecker-delta

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</section>

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