npm package: @stdlib/blas-ext-base-ndarray-gcusumpw
Description: Compute the cumulative sum of a one-dimensional ndarray using pairwise summation.
Author: The Stdlib Authors
Latest version: 0.1.1

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# gcusumpw

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> Compute the cumulative sum of a one-dimensional ndarray using pairwise summation.

<section class="intro">

</section>

<!-- /.intro -->

<section class="installation">

## Installation

```bash
npm install @stdlib/blas-ext-base-ndarray-gcusumpw
```

</section>

<section class="usage">

## Usage

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

#### gcusumpw( arrays )

Computes the cumulative sum of a one-dimensional ndarray using pairwise summation.

```javascript
var ndarray2array = require( '@stdlib/ndarray-to-array' );
var scalar2ndarray = require( '@stdlib/ndarray-base-from-scalar' );
var ndarray = require( '@stdlib/ndarray-base-ctor' );

var xbuf = [ 1.0, 3.0, 4.0, 2.0 ];
var x = new ndarray( 'generic', xbuf, [ 4 ], [ 1 ], 0, 'row-major' );

var ybuf = [ 0.0, 0.0, 0.0, 0.0 ];
var y = new ndarray( 'generic', ybuf, [ 4 ], [ 1 ], 0, 'row-major' );

var initial = scalar2ndarray( 0.0, 'generic', 'row-major' );

var v = gcusumpw( [ x, y, initial ] );
// returns <ndarray>

var bool = ( v === y );
// returns true

var arr = ndarray2array( v );
// returns [ 1.0, 4.0, 8.0, 10.0 ]
```

The function has the following parameters:

-   **arrays**: array-like object containing a one-dimensional input ndarray, a one-dimensional output ndarray, and a zero-dimensional ndarray containing the initial sum.

</section>

<!-- /.usage -->

<section class="notes">

## Notes

-   If provided an empty one-dimensional input ndarray, the function returns the output ndarray unchanged.
-   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.

</section>

<!-- /.notes -->

<section class="examples">

## Examples

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

```javascript
var discreteUniform = require( '@stdlib/random-array-discrete-uniform' );
var ndarray = require( '@stdlib/ndarray-base-ctor' );
var zerosLike = require( '@stdlib/ndarray-zeros-like' );
var scalar2ndarray = require( '@stdlib/ndarray-from-scalar' );
var ndarray2array = require( '@stdlib/ndarray-to-array' );
var gcusumpw = require( '@stdlib/blas-ext-base-ndarray-gcusumpw' );

var xbuf = discreteUniform( 10, -50, 50, {
    'dtype': 'generic'
});
var x = new ndarray( 'generic', xbuf, [ xbuf.length ], [ 1 ], 0, 'row-major' );
console.log( ndarray2array( x ) );

var y = zerosLike( x );
console.log( ndarray2array( y ) );

var initial = scalar2ndarray( 100.0, {
    'dtype': 'generic'
});

var v = gcusumpw( [ x, y, initial ] );
console.log( ndarray2array( 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 -->

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<section class="related">

</section>

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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].

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---

## License

See [LICENSE][stdlib-license].


## Copyright

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

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

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