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# gasum

> Compute the sum of [absolute values][@stdlib/math/base/special/abs] ([_L1_ norm][l1norm]).

<section class="intro">

The [_L1_ norm][l1norm] is defined as

<!-- <equation class="equation" label="eq:l1norm" align="center" raw="\|\mathbf{x}\|_1 = \sum_{i=0}^{n-1} \vert x_i \vert" alt="L1 norm definition."> -->

<div class="equation" align="center" data-raw-text="\|\mathbf{x}\|_1 = \sum_{i=0}^{n-1} \vert x_i \vert" data-equation="eq:l1norm">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@30de397fadee10fa175a8332ae1447737f201818/lib/node_modules/@stdlib/blas/base/gasum/docs/img/equation_l1norm.svg" alt="L1 norm definition.">
    <br>
</div>

<!-- </equation> -->

</section>

<!-- /.intro -->

<section class="usage">

## Usage

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

#### gasum( N, x, stride )

Computes the sum of [absolute values][@stdlib/math/base/special/abs].

```javascript
var x = [ -2.0, 1.0, 3.0, -5.0, 4.0, 0.0, -1.0, -3.0 ];

var sum = gasum( x.length, x, 1 );
// returns 19.0
```

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.

The `N` and `stride` parameters determine which elements in `x` are used to compute the sum. For example, to sum every other value,

```javascript
var x = [ -2.0, 1.0, 3.0, -5.0, 4.0, 0.0, -1.0, -3.0 ];

var sum = gasum( 4, x, 2 );
// returns 10.0
```

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' );

// Initial array...
var x0 = new Float64Array( [ 1.0, -2.0, 3.0, -4.0, 5.0, -6.0 ] );

// Create an offset view...
var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element

// Sum every other value...
var sum = gasum( 3, x1, 2 );
// returns 12.0
```

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

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

Computes the sum of [absolute values][@stdlib/math/base/special/abs] using alternative indexing semantics.

```javascript
var x = [ -2.0, 1.0, 3.0, -5.0, 4.0, 0.0, -1.0, -3.0 ];

var sum = gasum.ndarray( x.length, x, 1, 0 );
// returns 19.0
```

The function has the following additional parameters:

-   **offset**: 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 sum the last three elements,

```javascript
var Float64Array = require( '@stdlib/array/float64' );

var x = new Float64Array( [ 1.0, -2.0, 3.0, -4.0, 5.0, -6.0 ] );

var sum = gasum.ndarray( 3, x, 1, x.length-3 );
// returns 15.0

// Using a negative stride to sum from the last element:
sum = gasum.ndarray( 3, x, -1, x.length-1 );
// returns 15.0
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

-   If `N <= 0`, both functions return `0`.
-   `gasum()` corresponds to the [BLAS][blas] level 1 function [`dasum`][dasum] with the exception that this implementation works with any array type, not just Float64Arrays. Depending on the environment, the typed versions ([`dasum`][@stdlib/blas/base/dasum], [`sasum`][@stdlib/blas/base/sasum], etc.) are likely to be significantly more performant.
-   Both functions support array-like objects having getter and setter accessors for array element access (e.g., [`@stdlib/array/base/accessor`][@stdlib/array/base/accessor]).

</section>

<!-- /.notes -->

<section class="examples">

## Examples

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

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

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

var y = gasum( x.length, x, 1 );
console.log( y );
```

</section>

<!-- /.examples -->

<!-- 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/dasum`][@stdlib/blas/base/dasum]</span><span class="delimiter">: </span><span class="description">compute the sum of absolute values (L1 norm).</span>
-   <span class="package-name">[`@stdlib/blas/base/sasum`][@stdlib/blas/base/sasum]</span><span class="delimiter">: </span><span class="description">compute the sum of absolute values (L1 norm).</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">

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

[dasum]: 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

[l1norm]: https://en.wikipedia.org/wiki/Norm_%28mathematics%29

[@stdlib/math/base/special/abs]: https://www.npmjs.com/package/@stdlib/math-base-special-abs

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

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

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

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

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

</section>

<!-- /.links -->
