npm package: @stdlib/blas-ext-base-gasumpw
Description: Calculate the sum of absolute values (L1 norm) of strided array elements using pairwise summation.
Author: The Stdlib Authors
Latest version: 0.3.1

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# gasumpw

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> Calculate the sum of absolute values ([_L1_ norm][l1norm]) of strided array elements using pairwise summation.

<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@b989712575768de8eab07dd05f635c636b46f278/lib/node_modules/@stdlib/blas/ext/base/gasumpw/docs/img/equation_l1norm.svg" alt="L1 norm definition.">
    <br>
</div>

<!-- </equation> -->

</section>

<!-- /.intro -->

<section class="installation">

## Installation

```bash
npm install @stdlib/blas-ext-base-gasumpw
```

</section>

<section class="usage">

## Usage

```javascript
var gasumpw = require( '@stdlib/blas-ext-base-gasumpw' );
```

#### gasumpw( N, x, strideX )

Computes the sum of absolute values ([_L1_ norm][l1norm]) of strided array elements using pairwise summation.

```javascript
var x = [ 1.0, -2.0, 2.0 ];

var v = gasumpw( x.length, x, 1 );
// returns 5.0
```

The function has the following parameters:

-   **N**: number of indexed elements.
-   **x**: input [`Array`][mdn-array] or [`typed array`][mdn-typed-array].
-   **strideX**: stride length.

The `N` and stride parameters determine which elements in the strided array are accessed at runtime. For example, to compute the sum of absolute values of every other element:

```javascript
var x = [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ];

var v = gasumpw( 4, x, 2 );
// returns 9.0
```

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 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 v = gasumpw( 4, x1, 2 );
// returns 9.0
```

#### gasumpw.ndarray( N, x, strideX, offsetX )

Computes the sum of absolute values ([_L1_ norm][l1norm]) of strided array elements using pairwise summation and alternative indexing semantics.

```javascript
var x = [ 1.0, -2.0, 2.0 ];

var v = gasumpw.ndarray( x.length, x, 1, 0 );
// returns 5.0
```

The function has the following additional parameters:

-   **offsetX**: 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 calculate the sum of absolute values of every other element starting from the second element:

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

var v = gasumpw.ndarray( 4, x, 2, 1 );
// returns 9.0
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

-   If `N <= 0`, both functions return `0.0`.
-   In general, pairwise summation is more numerically stable than ordinary recursive summation (i.e., "simple" summation), with slightly worse performance. While not the most numerically stable summation technique (e.g., compensated summation techniques such as the Kahan–Babuška-Neumaier algorithm are generally more numerically stable), pairwise summation strikes a reasonable balance between numerical stability and performance. If either numerical stability or performance is more desirable for your use case, consider alternative summation techniques.
-   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]).
-   Depending on the environment, the typed versions ([`dasumpw`][@stdlib/blas/ext/base/dasumpw], [`sasumpw`][@stdlib/blas/ext/base/sasumpw], etc.) are likely to be significantly more performant.

</section>

<!-- /.notes -->

<section class="examples">

## Examples

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

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

var x = discreteUniform( 10, -100, 100, {
    'dtype': 'float64'
});
console.log( x );

var v = gasumpw( x.length, x, 1 );
console.log( v );
```

</section>

<!-- /.examples -->

* * *

<section class="references">

## References

-   Higham, Nicholas J. 1993. "The Accuracy of Floating Point Summation." _SIAM Journal on Scientific Computing_ 14 (4): 783–99. doi:[10.1137/0914050][@higham:1993a].

</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/gasum`][@stdlib/blas/base/gasum]</span><span class="delimiter">: </span><span class="description">compute the sum of absolute values (L1 norm).</span>
-   <span class="package-name">[`@stdlib/blas-ext/base/dasumpw`][@stdlib/blas/ext/base/dasumpw]</span><span class="delimiter">: </span><span class="description">calculate the sum of absolute values (L1 norm) of double-precision floating-point strided array elements using pairwise summation.</span>
-   <span class="package-name">[`@stdlib/blas-ext/base/gsumpw`][@stdlib/blas/ext/base/gsumpw]</span><span class="delimiter">: </span><span class="description">calculate the sum of strided array elements using pairwise summation.</span>
-   <span class="package-name">[`@stdlib/blas-ext/base/sasumpw`][@stdlib/blas/ext/base/sasumpw]</span><span class="delimiter">: </span><span class="description">calculate the sum of absolute values (L1 norm) of single-precision floating-point strided array elements using pairwise summation.</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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[umd]: https://github.com/umdjs/umd
[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules

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

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

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

[@higham:1993a]: https://doi.org/10.1137/0914050

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

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

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

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

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