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# snrm2

> Calculate the L2-norm of a single-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@247c6b352fc1002f11ba3e7ed389f067380a8a87/lib/node_modules/@stdlib/blas/base/snrm2/docs/img/equation_l2_norm.svg" alt="L2-norm definition.">
    <br>
</div>

<!-- </equation> -->

</section>

<!-- /.intro -->

<section class="usage">

## Usage

```javascript
var snrm2 = require( '@stdlib/blas/base/snrm2' );
```

#### snrm2( N, x, stride )

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

```javascript
var Float32Array = require( '@stdlib/array/float32' );

var x = new Float32Array( [ 1.0, -2.0, 2.0 ] );

var z = snrm2( x.length, x, 1 );
// returns 3.0
```

The function has the following parameters:

-   **N**: number of indexed elements.
-   **x**: input [`Float32Array`][@stdlib/array/float32].
-   **stride**: index increment for `x`.

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

```javascript
var Float32Array = require( '@stdlib/array/float32' );

var x = new Float32Array( [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ] );

var z = snrm2( 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 Float32Array = require( '@stdlib/array/float32' );

var x0 = new Float32Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
var x1 = new Float32Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element

var z = snrm2( 4, x1, 2 );
// returns 5.0
```

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

#### snrm2.ndarray( N, x, stride, offset )

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

```javascript
var Float32Array = require( '@stdlib/array/float32' );

var x = new Float32Array( [ 1.0, -2.0, 2.0 ] );

var z = snrm2.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 Float32Array = require( '@stdlib/array/float32' );

var x = new Float32Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );

var z = snrm2.ndarray( 4, x, 2, 1 );
// returns 5.0
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

-   If `N <= 0`, both functions return `0.0`.
-   `snrm2()` corresponds to the [BLAS][blas] level 1 function [`snrm2`][snrm2].

</section>

<!-- /.notes -->

<section class="examples">

## Examples

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

```javascript
var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
var snrm2 = require( '@stdlib/blas/base/snrm2' );

var opts = {
    'dtype': 'float32'
};
var x = discreteUniform( 10, 0, 100, opts );
console.log( x );

var out = snrm2( 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/snrm2.h"
```

#### c_snrm2( N, \*X, stride )

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

```c
const float x[] = { 1.0f, 2.0f, 2.0f, -7.0f, -2.0f, 3.0f, 4.0f, 2.0f };

float norm = c_snrm2( 4, x, 2 );
// returns 5.0f
```

The function accepts the following arguments:

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

```c
float c_snrm2( const CBLAS_INT N, const float *X, const CBLAS_INT stride );
```

#### c_snrm2_ndarray( N, \*X, stride, offset )

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

```c
const float x[] = { 1.0f, 2.0f, 2.0f, -7.0f, -2.0f, 3.0f, 4.0f, 2.0f };

float norm = c_snrm2_ndarray( 4, x, 2, 0 );
// returns 5.0f
```

The function accepts the following arguments:

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

```c
float c_snrm2_ndarray( const CBLAS_INT N, const float *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/snrm2.h"
#include <stdio.h>

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

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

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

    // Compute the L2-norm:
    float l2 = c_snrm2( N, x, strideX );

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

    // Compute the L2-norm:
    l2 = c_snrm2_ndarray( N, x, -strideX, 7 );

    // Print the result:
    printf( "L2-norm: %f\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/dnrm2`][@stdlib/blas/base/dnrm2]</span><span class="delimiter">: </span><span class="description">calculate the L2-norm of a double-precision floating-point vector.</span>
-   <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>

</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="links">

[l2-norm]: https://en.wikipedia.org/wiki/Euclidean_distance

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

[snrm2]: http://www.netlib.org/lapack/explore-html/df/d28/group__single__blas__level1.html

[@stdlib/array/float32]: https://www.npmjs.com/package/@stdlib/array-float32

[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> -->

[@stdlib/blas/base/dnrm2]: https://github.com/stdlib-js/blas/tree/main/base/dnrm2

[@stdlib/blas/base/gnrm2]: https://github.com/stdlib-js/blas/tree/main/base/gnrm2

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

</section>

<!-- /.links -->
