npm package: @stdlib/blas-base-gnrm2
Description: Calculate the L2-norm of a vector.
Author: The Stdlib Authors
Latest version: 0.3.1

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# gnrm2

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

> 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="installation">

## Installation

```bash
npm install @stdlib/blas-base-gnrm2
```

</section>

<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 -->

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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

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---

## License

See [LICENSE][stdlib-license].


## Copyright

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

</section>

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[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/blas-base-gnrm2/main/LICENSE

[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://www.npmjs.com/package/@stdlib/blas-base-dnrm2

[@stdlib/blas/base/snrm2]: https://www.npmjs.com/package/@stdlib/blas-base-snrm2

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

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

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