# dnrm2
> Calculate the L2-norm of a double-precision floating-point vector.
The [L2-norm][l2-norm] is defined as
## 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.
```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
```
## Notes
- If `N <= 0`, both functions return `0.0`.
- `dnrm2()` corresponds to the [BLAS][blas] level 1 function [`dnrm2`][dnrm2].
## Examples
```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 );
```
* * *
## C APIs
### 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( 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 );
```
### Examples
```c
#include "stdlib/blas/base/dnrm2.h"
#include
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 );
}
```
[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
[@stdlib/blas/base/gnrm2]: https://github.com/stdlib-js/blas/tree/main/base/gnrm2
[@stdlib/blas/base/snrm2]: https://github.com/stdlib-js/blas/tree/main/base/snrm2
