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# gnrm2

> Calculate the L2-norm of a vector.

<section class="intro">

The [L2-norm][l2-norm] is defined as

<!-- <equation class="equation" label="eq:l2_norm" align="center" raw="\|\mathbf{x}\|_2 = \sqrt{x_0^2 + x_1^2 + \ldots + x_{N-1}^2}" alt="L2-norm definition."> -->

<div class="equation" align="center" data-raw-text="\|\mathbf{x}\|_2 = \sqrt{x_0^2 + x_1^2 + \ldots + x_{N-1}^2}" data-equation="eq:l2_norm">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@f8997c489e47eb1a9d993ef4ab3a522a095331f5/lib/node_modules/@stdlib/blas/base/gnrm2/docs/img/equation_l2_norm.svg" alt="L2-norm definition.">
    <br>
</div>

<!-- </equation> -->

</section>

<!-- /.intro -->

<section class="usage">

## Usage

```javascript
var gnrm2 = require( '@stdlib/blas/base/gnrm2' );
```

#### gnrm2( N, x, stride )

Computes the [L2-norm][l2-norm] of a vector.

```javascript
var x = [ 1.0, -2.0, 2.0 ];

var z = gnrm2( x.length, x, 1 );
// returns 3.0
```

The function has the following parameters:

-   **N**: number of indexed elements.
-   **x**: input [`Array`][mdn-array] or [`typed array`][mdn-typed-array].
-   **stride**: stride length.

The `N` and stride parameters determine which elements in the strided array are accessed at runtime. For example, to compute the [L2-norm][l2-norm] of every other element:

```javascript
var x = [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ];

var z = gnrm2( 4, x, 2 );
// returns 5.0
```

Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views.

<!-- eslint-disable stdlib/capitalized-comments -->

```javascript
var Float64Array = require( '@stdlib/array/float64' );

var x0 = new Float64Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element

var z = gnrm2( 4, x1, 2 );
// returns 5.0
```

If `N` is less than or equal to `0`, the function returns `0`.

#### gnrm2.ndarray( N, x, stride, offset )

Computes the [L2-norm][l2-norm] of a vector using alternative indexing semantics.

```javascript
var x = [ 1.0, -2.0, 2.0 ];

var z = gnrm2.ndarray( x.length, x, 1, 0 );
// returns 3.0
```

The function has the following additional parameters:

-   **offset**: starting index.

While [`typed array`][mdn-typed-array] views mandate a view offset based on the underlying buffer, the offset parameter supports indexing semantics based on a starting index. For example, to calculate the [L2-norm][l2-norm] for every other value in the strided array starting from the second value:

```javascript
var x = [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ];

var z = gnrm2.ndarray( 4, x, 2, 1 );
// returns 5.0
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

-   If `N <= 0`, both functions return `0.0`.
-   `gnrm2()` corresponds to the [BLAS][blas] level 1 function [`dnrm2`][dnrm2] with the exception that this implementation works with any array type, not just Float64Arrays. Depending on the environment, the typed versions ([`dnrm2`][@stdlib/blas/base/dnrm2], [`snrm2`][@stdlib/blas/base/snrm2], etc.) are likely to be significantly more performant.
-   Both functions support array-like objects having getter and setter accessors for array element access (e.g., [`@stdlib/array/base/accessor`][@stdlib/array/base/accessor]).

</section>

<!-- /.notes -->

<section class="examples">

## Examples

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

```javascript
var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
var gnrm2 = require( '@stdlib/blas/base/gnrm2' );

var opts = {
    'dtype': 'float64'
};
var x = discreteUniform( 10, -100, 100, opts );
console.log( x );

var out = gnrm2( x.length, x, 1 );
console.log( out );
```

</section>

<!-- /.examples -->

* * *

<section class="references">

## References

-   Blue, James L. 1978. "A Portable Fortran Program to Find the Euclidean Norm of a Vector." _ACM Transactions on Mathematical Software_ 4 (1). New York, NY, USA: Association for Computing Machinery: 15–23. doi:[10.1145/355769.355771][@blue:1978a].
-   Anderson, Edward. 2017. "Algorithm 978: Safe Scaling in the Level 1 BLAS." _ACM Transactions on Mathematical Software_ 44 (1). New York, NY, USA: Association for Computing Machinery: 1–28. doi:[10.1145/3061665][@anderson:2017a].

</section>

<!-- /.references -->

<!-- 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/blas/base/dnrm2`][@stdlib/blas/base/dnrm2]</span><span class="delimiter">: </span><span class="description">calculate the L2-norm of a double-precision floating-point vector.</span>
-   <span class="package-name">[`@stdlib/blas/base/snrm2`][@stdlib/blas/base/snrm2]</span><span class="delimiter">: </span><span class="description">calculate the L2-norm of a single-precision floating-point vector.</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">

[l2-norm]: https://en.wikipedia.org/wiki/Euclidean_distance

[blas]: http://www.netlib.org/blas

[dnrm2]: http://www.netlib.org/lapack/explore-html/de/da4/group__double__blas__level1.html

[mdn-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array

[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray

[@stdlib/array/base/accessor]: https://www.npmjs.com/package/@stdlib/array-base-accessor

[@stdlib/blas/base/dnrm2]: https://github.com/stdlib-js/blas/tree/main/base/dnrm2

[@stdlib/blas/base/snrm2]: https://github.com/stdlib-js/blas/tree/main/base/snrm2

[@blue:1978a]: https://doi.org/10.1145/355769.355771

[@anderson:2017a]: https://doi.org/10.1145/3061665

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

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

</section>

<!-- /.links -->
