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# Dirac Delta

> 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.rawgit.com/stdlib-js/stdlib/7e0a95722efd9c771b129597380c63dc6715508b/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.rawgit.com/stdlib-js/stdlib/7e0a95722efd9c771b129597380c63dc6715508b/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="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 linspace = require( '@stdlib/array/linspace' );
var diracDelta = require( '@stdlib/math/base/special/dirac-delta' );

var x = linspace( -1.0, 1.0, 101 );
var i;

for ( i = 0; i < x.length; i++ ) {
    console.log( 'dirac(%d) = %d', x[ i ], diracDelta( x[ i ] ) );
}
```

</section>

<!-- /.examples -->

<section class="links">

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

</section>

<!-- /.links -->
