npm package: @stdlib/blas-base-gasum
Description: Compute the sum of absolute values (L1 norm).
Author: The Stdlib Authors
Latest version: 0.3.1

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# gasum

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] <!-- [![dependencies][dependencies-image]][dependencies-url] -->

> 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="installation">

## Installation

```bash
npm install @stdlib/blas-base-gasum
```

</section>

<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 -->

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<section class="main-repo" >

* * *

## Notice

This package is part of [stdlib][stdlib], a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop [stdlib][stdlib], see the main project [repository][stdlib].

#### Community

[![Chat][chat-image]][chat-url]

---

## License

See [LICENSE][stdlib-license].


## Copyright

Copyright &copy; 2016-2026. The Stdlib [Authors][stdlib-authors].

</section>

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[stdlib]: https://github.com/stdlib-js/stdlib

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[umd]: https://github.com/umdjs/umd
[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules

[deno-url]: https://github.com/stdlib-js/blas-base-gasum/tree/deno
[deno-readme]: https://github.com/stdlib-js/blas-base-gasum/blob/deno/README.md
[umd-url]: https://github.com/stdlib-js/blas-base-gasum/tree/umd
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[esm-url]: https://github.com/stdlib-js/blas-base-gasum/tree/esm
[esm-readme]: https://github.com/stdlib-js/blas-base-gasum/blob/esm/README.md
[branches-url]: https://github.com/stdlib-js/blas-base-gasum/blob/main/branches.md

[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/blas-base-gasum/main/LICENSE

[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://www.npmjs.com/package/@stdlib/blas-base-dasum

[@stdlib/blas/base/sasum]: https://www.npmjs.com/package/@stdlib/blas-base-sasum

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

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