npm package: @stdlib/blas-base-dznrm2
Description: Compute the L2-norm of a complex double-precision floating-point vector.
Author: The Stdlib Authors
Latest version: 0.2.1

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# dznrm2

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

> Compute the L2-norm of a complex double-precision floating-point vector.

<section class="installation">

## Installation

```bash
npm install @stdlib/blas-base-dznrm2
```

</section>

<section class="usage">

## Usage

```javascript
var dznrm2 = require( '@stdlib/blas-base-dznrm2' );
```

#### dznrm2( N, x, strideX )

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

```javascript
var Complex128Array = require( '@stdlib/array-complex128' );

var x = new Complex128Array( [ 0.3, 0.1, 0.5, 0.0, 0.0, 0.5, 0.0, 0.2 ] );

var norm = dznrm2( 4, x, 1 );
// returns ~0.8
```

The function has the following parameters:

-   **N**: number of indexed elements.
-   **x**: input [`Complex128Array`][@stdlib/array/complex128].
-   **strideX**: index increment for `x`.

The `N` and stride parameters determine which elements in the strided array are accessed at runtime. For example, to traverse every other value,

```javascript
var Complex128Array = require( '@stdlib/array-complex128' );

var x = new Complex128Array( [ -2.0, 1.0, 3.0, -5.0, 4.0, 0.0, -1.0, -3.0 ] );

var norm = dznrm2( 2, x, 2 );
// returns ~4.6
```

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

```javascript
var Complex128Array = require( '@stdlib/array-complex128' );

// Initial array:
var x0 = new Complex128Array( [ 1.0, -2.0, 3.0, -4.0, 5.0, -6.0 ] );

// Create an offset view:
var x1 = new Complex128Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element

// Compute the L2-norm:
var norm = dznrm2( 2, x1, 1 );
// returns ~9.3
```

#### dznrm2.ndarray( N, x, strideX, offset )

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

```javascript
var Complex128Array = require( '@stdlib/array-complex128' );

var x = new Complex128Array( [ 0.3, 0.1, 0.5, 0.0, 0.0, 0.5, 0.0, 0.2 ] );

var norm = dznrm2.ndarray( 4, x, 1, 0 );
// returns ~0.8
```

The function has the following additional parameters:

-   **offsetX**: 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 start from the second index,

```javascript
var Complex128Array = require( '@stdlib/array-complex128' );

var x = new Complex128Array( [ 1.0, -2.0, 3.0, -4.0, 5.0, -6.0 ] );

var norm = dznrm2.ndarray( 2, x, 1, 1 );
// returns ~9.3
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

-   If `N <= 0`, both functions return `0.0`.
-   `dznrm2()` corresponds to the [BLAS][blas] level 1 function [`dznrm2`][dznrm2].

</section>

<!-- /.notes -->

<section class="examples">

## Examples

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

```javascript
var discreteUniform = require( '@stdlib/random-base-discrete-uniform' );
var filledarrayBy = require( '@stdlib/array-filled-by' );
var Complex128 = require( '@stdlib/complex-float64-ctor' );
var dznrm2 = require( '@stdlib/blas-base-dznrm2' );

function rand() {
    return new Complex128( discreteUniform( 0, 10 ), discreteUniform( -5, 5 ) );
}

var x = filledarrayBy( 10, 'complex128', rand );
console.log( x.toString() );

// Computes the L2-norm:
var norm = dznrm2( x.length, x, 1 );
console.log( norm );
```

</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/dznrm2.h"
```

#### c_dznrm2( N, \*X, strideX )

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

```c
const double X[] = { 0.3, 0.1, 0.5, 0.0, 0.0, 0.5, 0.0, 0.2 };

double norm = c_dznrm2( 4, (void *)X, 1 );
// returns 0.8
```

The function accepts the following arguments:

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

```c
double c_dznrm2( const CBLAS_INT N, const void *X, const CBLAS_INT strideX );
```

#### c_dznrm2_ndarray( N, \*X, strideX, offsetX )

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

```c
const double X[] = { 0.3, 0.1, 0.5, 0.0, 0.0, 0.5, 0.0, 0.2 };

double norm = c_dznrm2_ndarray( 4, (void *)X, 1, 0 );
// returns 0.8
```

The function accepts the following arguments:

-   **N**: `[in] CBLAS_INT` number of indexed elements.
-   **X**: `[in] void*` input array.
-   **strideX**: `[in] CBLAS_INT` index increment for `X`.
-   **offsetX**: `[in] CBLAS_INT` starting index for `X`.

```c
double c_dznrm2_ndarray( const CBLAS_INT N, const void *X, const CBLAS_INT strideX, const CBLAS_INT offsetX );
```

</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/dznrm2.h"
#include <stdio.h>

int main( void ) {
    // Create a strided array of interleaved real and imaginary components:
    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 = 4;

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

    // Compute the L2-norm:
    double norm = c_dznrm2( N, (void *)X, strideX );

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

    // Compute the L2-norm using alternative indexing semantics:
    norm = c_dznrm2_ndarray( N, (void *)X, -strideX, N-1 );

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

</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">

</section>

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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-dznrm2/main/LICENSE

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

[dznrm2]: https://netlib.org/lapack/explore-html//d1/d2a/group__nrm2_ga7f9f9febc6dc1836c9f5e7c1aa00b743.html

[@stdlib/array/complex128]: https://www.npmjs.com/package/@stdlib/array-complex128

[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

</section>

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