time-to-botec/js/node_modules/@stdlib/blas/base/dnrm2/README.md

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# dnrm2

> 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="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 N = 3;

var z = dnrm2( N, 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 floor = require( '@stdlib/math/base/special/floor' );

var x = new Float64Array( [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ] );
var N = floor( x.length / 2 );

var z = dnrm2( N, 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 N = 4;

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

If either `N` or `stride` 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 N = 3;

var z = dnrm2.ndarray( N, 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 floor = require( '@stdlib/math/base/special/floor' );

var x = new Float64Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
var N = floor( x.length / 2 );

var z = dnrm2.ndarray( N, 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 randu = require( '@stdlib/random/base/randu' );
var round = require( '@stdlib/math/base/special/round' );
var Float64Array = require( '@stdlib/array/float64' );
var dnrm2 = require( '@stdlib/blas/base/dnrm2' );

var x;
var i;

x = new Float64Array( 10 );
for ( i = 0; i < x.length; i++ ) {
    x[ i ] = round( randu()*100.0 );
}
console.log( x );

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

</section>

<!-- /.examples -->

<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

[@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

</section>

<!-- /.links -->