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# Kronecker Delta

> Evaluate the [Kronecker delta][kronecker-delta].

<section class="intro">

The [Kronecker delta][kronecker-delta] is defined as

<!-- <equation class="equation" label="eq:kronecker_delta" align="center" raw="\delta_{ij} = \begin{cases} 1 & \textrm{if}\ i = j \\ 0 & \textrm{if}\ i \neq j\end{cases}" alt="Kronecker delta."> -->

<div class="equation" align="center" data-raw-text="\delta_{ij} = \begin{cases} 1 &amp; \textrm{if}\ i = j \\ 0 &amp; \textrm{if}\ i \neq j\end{cases}" data-equation="eq:kronecker_delta">
    <img src="https://cdn.rawgit.com/stdlib-js/stdlib/7e0a95722efd9c771b129597380c63dc6715508b/lib/node_modules/@stdlib/math/base/special/kronecker-delta/docs/img/equation_kronecker_delta.svg" alt="Kronecker delta.">
    <br>
</div>

<!-- </equation> -->

</section>

<!-- /.intro -->

<section class="usage">

## Usage

```javascript
var kroneckerDelta = require( '@stdlib/math/base/special/kronecker-delta' );
```

#### kroneckerDelta( i, j )

Evaluates the [Kronecker delta][kronecker-delta].

```javascript
var v = kroneckerDelta( 3.14, 3.14 );
// returns 1.0

v = kroneckerDelta( 3.14, 0.0 );
// returns 0.0

v = kroneckerDelta( NaN, 3.14 );
// returns NaN

v = kroneckerDelta( 3.14, NaN );
// returns NaN

v = kroneckerDelta( NaN, NaN );
// returns NaN
```

</section>

<!-- /.usage -->

<section class="examples">

## Examples

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

```javascript
var linspace = require( '@stdlib/array/linspace' );
var kroneckerDelta = require( '@stdlib/math/base/special/kronecker-delta' );

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

for ( i = 0; i < x.length; i++ ) {
    console.log( 'kronecker(%d,%d) = %d', x[ i ], 0.0, kroneckerDelta( x[ i ], 0.0 ) );
}
```

</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/kronecker_delta.h
```

#### stdlib_base_kronecker_delta( i, j )

Evaluates the Kronecker delta.

```c
double v = stdlib_base_kronecker_delta( 3.0, 3.0 );
// returns 1.0
```

The function accepts the following arguments:

-   **i**: `[in] double` input value.
-   **j**: `[in] double` input value.

```c
double stdlib_base_kronecker_delta( const double i, const double j );
```

</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/kronecker_delta.h"
#include <stdio.h>

int main() {
    double x[] = { 3.0, 4.0, 5.0, 5.0 };

    double y;
    int i;
    for ( i = 0; i < 4; i += 2 ) {
        y = stdlib_base_kronecker_delta( x[ i ], x[ i+1 ] );
        printf( "kronecker_delta(%lf, %lf) = %lf\n", x[ i ], x[ i+1 ], y );
    }
}
```

</section>

<!-- /.examples -->

</section>

<!-- /.c -->

<section class="links">

[kronecker-delta]: https://en.wikipedia.org/wiki/Kronecker_delta

</section>

<!-- /.links -->
