npm package: @stdlib/blas-base-dnrm2
Description: Calculate the L2-norm of a double-precision floating-point vector.
Author: The Stdlib Authors
Latest version: 0.4.1

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# dnrm2

[![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 double-precision floating-point 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@f766d7eeb56ff14cbceeeeef03d7f7b88c467515/lib/node_modules/@stdlib/blas/base/dnrm2/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-dnrm2
```

</section>

<section class="usage">

## Usage

```javascript
var dnrm2 = require( '@stdlib/blas-base-dnrm2' );
```

#### dnrm2( N, x, stride )

Computes the [L2-norm][l2-norm] of a double-precision floating-point vector `x`.

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

var x = new Float64Array( [ 1.0, -2.0, 2.0 ] );

var z = dnrm2( 3, x, 1 );
// returns 3.0
```

The function has the following parameters:

-   **N**: number of indexed elements.
-   **x**: input [`Float64Array`][@stdlib/array/float64].
-   **stride**: index increment for `x`.

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

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

var x = new Float64Array( [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ] );

var z = dnrm2( 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 = dnrm2( 4, x1, 2 );
// returns 5.0
```

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

#### dnrm2.ndarray( N, x, stride, offset )

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

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

var x = new Float64Array( [ 1.0, -2.0, 2.0 ] );

var z = dnrm2.ndarray( 3, x, 1, 0 );
// returns 3.0
```

The function has the following additional parameters:

-   **offset**: starting index for `x`.

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 `x` starting from the second value

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

var x = new Float64Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );

var z = dnrm2.ndarray( 4, x, 2, 1 );
// returns 5.0
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

-   If `N <= 0`, both functions return `0.0`.
-   `dnrm2()` corresponds to the [BLAS][blas] level 1 function [`dnrm2`][dnrm2].

</section>

<!-- /.notes -->

<section class="examples">

## Examples

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

```javascript
var discreteUniform = require( '@stdlib/random-array-discrete-uniform' );
var dnrm2 = require( '@stdlib/blas-base-dnrm2' );

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

var out = dnrm2( x.length, x, 1 );
console.log( out );
```

</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/blas/base/dnrm2.h"
```

#### c_dnrm2( N, \*X, stride )

Computes the L2-norm of a double-precision floating-point vector.

```c
const double x[] = { 1.0, -2.0, 2.0 };

double v = c_dnrm2( 3, x, 1 );
// returns 3.0
```

The function accepts the following arguments:

-   **N**: `[in] CBLAS_INT` number of indexed elements.
-   **X**: `[in] double*` input array.
-   **stride**: `[in] CBLAS_INT` index increment for `X`.

```c
double c_dnrm2( const CBLAS_INT N, const double *X, const CBLAS_INT stride );
```

#### c_dnrm2_ndarray( N, \*X, stride, offset )

Computes the L2-norm of a double-precision floating-point vector using alternative indexing semantics.

```c
const double x[] = { 1.0, -2.0, 2.0 };

double v = c_dnrm2_ndarray( 3, x, -1, 2 );
// returns 3.0
```

The function accepts the following arguments:

-   **N**: `[in] CBLAS_INT` number of indexed elements.
-   **X**: `[in] double*` input array.
-   **stride**: `[in] CBLAS_INT` index increment for `X`.
-   **offset**: `[in] CBLAS_INT` starting index for `X`.

```c
double c_dnrm2_ndarray( const CBLAS_INT N, const double *X, const CBLAS_INT stride, const CBLAS_INT offset );
```

</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/blas/base/dnrm2.h"
#include <stdio.h>

int main( void ) {
    // Create a strided array:
    const double x[] = { 1.0, -2.0, 3.0, -4.0, 5.0, -6.0, 7.0, -8.0 };

    // Specify the number of elements:
    const int N = 8;

    // Specify a stride:
    const int strideX = 1;

    // Compute the L2-norm:
    double l2 = c_dnrm2( N, x, strideX );

    // Print the result:
    printf( "L2-norm: %lf\n", l2 );

    // Compute the L2-norm:
    l2 = c_dnrm2_ndarray( N, x, -strideX, N-1 );

    // Print the result:
    printf( "L2-norm: %lf\n", l2 );
}
```

</section>

<!-- /.examples -->

</section>

<!-- /.c -->

* * *

<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/gnrm2`][@stdlib/blas/base/gnrm2]</span><span class="delimiter">: </span><span class="description">calculate the L2-norm of a 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="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

[![Chat][chat-image]][chat-url]

---

## License

See [LICENSE][stdlib-license].


## Copyright

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

</section>

<!-- /.stdlib -->

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[umd]: https://github.com/umdjs/umd
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[deno-url]: https://github.com/stdlib-js/blas-base-dnrm2/tree/deno
[deno-readme]: https://github.com/stdlib-js/blas-base-dnrm2/blob/deno/README.md
[umd-url]: https://github.com/stdlib-js/blas-base-dnrm2/tree/umd
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[branches-url]: https://github.com/stdlib-js/blas-base-dnrm2/blob/main/branches.md

[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/blas-base-dnrm2/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

[@stdlib/array/float64]: https://www.npmjs.com/package/@stdlib/array-float64

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

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

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

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

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

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</section>

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