# gnrm2
> Calculate the L2-norm of a vector.
The [L2-norm][l2-norm] is defined as
## Usage
```javascript
var gnrm2 = require( '@stdlib/blas/base/gnrm2' );
```
#### gnrm2( N, x, stride )
Computes the [L2-norm][l2-norm] of a vector `x`.
```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**: 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 floor = require( '@stdlib/math/base/special/floor' );
var x = [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ];
var N = floor( x.length / 2 );
var z = gnrm2( 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.
```javascript
var Float64Array = require( '@stdlib/array/float64' );
var floor = require( '@stdlib/math/base/special/floor' );
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 = floor( x0.length / 2 );
var z = gnrm2( N, x1, 2 );
// returns 5.0
```
If either `N` or `stride` 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 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 floor = require( '@stdlib/math/base/special/floor' );
var x = [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ];
var N = floor( x.length / 2 );
var z = gnrm2.ndarray( N, x, 2, 1 );
// returns 5.0
```
## 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.
## Examples
```javascript
var randu = require( '@stdlib/random/base/randu' );
var round = require( '@stdlib/math/base/special/round' );
var Float64Array = require( '@stdlib/array/float64' );
var gnrm2 = require( '@stdlib/blas/base/gnrm2' );
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 = gnrm2( x.length, x, 1 );
console.log( z );
```
[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/blas/base/dnrm2]: https://www.npmjs.com/package/@stdlib/blas/tree/main/base/dnrm2
[@stdlib/blas/base/snrm2]: https://www.npmjs.com/package/@stdlib/blas/tree/main/base/snrm2
