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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.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="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 -->

<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->

<section class="links">

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

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

[@stdlib/math/base/special/kronecker-delta]: https://github.com/stdlib-js/math/tree/main/base/special/kronecker-delta

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

</section>

<!-- /.links -->
