npm package: @stdlib/blas-ext-base-gcusumkbn
Description: Calculate the cumulative sum of strided array elements using an improved Kahan–Babuška algorithm.
Author: The Stdlib Authors
Latest version: 0.3.1

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# gcusumkbn

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> Calculate the cumulative sum of strided array elements using an improved Kahan–Babuška algorithm.

<section class="intro">

</section>

<!-- /.intro -->

<section class="installation">

## Installation

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

</section>

<section class="usage">

## Usage

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

#### gcusumkbn( N, sum, x, strideX, y, strideY )

Computes the cumulative sum of strided array elements using an improved Kahan–Babuška algorithm.

```javascript
var x = [ 1.0, -2.0, 2.0 ];
var y = [ 0.0, 0.0, 0.0 ];

gcusumkbn( x.length, 0.0, x, 1, y, 1 );
// y => [ 1.0, -1.0, 1.0 ]

x = [ 1.0, -2.0, 2.0 ];
y = [ 0.0, 0.0, 0.0 ];

gcusumkbn( x.length, 10.0, x, 1, y, 1 );
// y => [ 11.0, 9.0, 11.0 ]
```

The function has the following parameters:

-   **N**: number of indexed elements.
-   **sum**: initial sum.
-   **x**: input [`Array`][mdn-array] or [`typed array`][mdn-typed-array].
-   **strideX**: stride length for `x`.
-   **y**: output [`Array`][mdn-array] or [`typed array`][mdn-typed-array].
-   **strideY**: stride length for `y`.

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

```javascript
var x = [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ];
var y = [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ];

var v = gcusumkbn( 4, 0.0, x, 2, y, 1 );
// y => [ 1.0, 3.0, 1.0, 5.0, 0.0, 0.0, 0.0, 0.0 ]
```

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' );

// Initial arrays...
var x0 = new Float64Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
var y0 = new Float64Array( x0.length );

// Create offset views...
var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
var y1 = new Float64Array( y0.buffer, y0.BYTES_PER_ELEMENT*3 ); // start at 4th element

gcusumkbn( 4, 0.0, x1, -2, y1, 1 );
// y0 => <Float64Array>[ 0.0, 0.0, 0.0, 4.0, 6.0, 4.0, 5.0, 0.0 ]
```

#### gcusumkbn.ndarray( N, sum, x, strideX, offsetX, y, strideY, offsetY )

Computes the cumulative sum of strided array elements using an improved Kahan–Babuška algorithm and alternative indexing semantics.

```javascript
var x = [ 1.0, -2.0, 2.0 ];
var y = [ 0.0, 0.0, 0.0 ];

gcusumkbn.ndarray( x.length, 0.0, x, 1, 0, y, 1, 0 );
// y => [ 1.0, -1.0, 1.0 ]
```

The function has the following additional parameters:

-   **offsetX**: starting index for `x`.
-   **offsetY**: starting index for `y`.

While [`typed array`][mdn-typed-array] views mandate a view offset based on the underlying buffer, offset parameters support indexing semantics based on starting indices. For example, to calculate the cumulative sum of every other element in the strided input array starting from the second element and to store in the last `N` elements of the strided output array starting from the last element:

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

gcusumkbn.ndarray( 4, 0.0, x, 2, 1, y, -1, y.length-1 );
// y => [ 0.0, 0.0, 0.0, 0.0, 5.0, 1.0, -1.0, 1.0 ]
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

-   If `N <= 0`, both functions return `y` unchanged.
-   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 ([`dcusum`][@stdlib/blas/ext/base/dcusum], [`scusum`][@stdlib/blas/ext/base/scusum], 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 Float64Array = require( '@stdlib/array-float64' );
var gcusumkbn = require( '@stdlib/blas-ext-base-gcusumkbn' );

var x = discreteUniform( 10, -100, 100, {
    'dtype': 'float64'
});
var y = new Float64Array( x.length );

console.log( x );
console.log( y );

gcusumkbn( x.length, 0.0, x, 1, y, -1 );
console.log( y );
```

</section>

<!-- /.examples -->

* * *

<section class="references">

## References

-   Neumaier, Arnold. 1974. "Rounding Error Analysis of Some Methods for Summing Finite Sums." _Zeitschrift Für Angewandte Mathematik Und Mechanik_ 54 (1): 39–51. doi:[10.1002/zamm.19740540106][@neumaier:1974a].

</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-ext/base/dcusumkbn`][@stdlib/blas/ext/base/dcusumkbn]</span><span class="delimiter">: </span><span class="description">calculate the cumulative sum of double-precision floating-point strided array elements using an improved Kahan–Babuška algorithm.</span>
-   <span class="package-name">[`@stdlib/blas-ext/base/gcusum`][@stdlib/blas/ext/base/gcusum]</span><span class="delimiter">: </span><span class="description">calculate the cumulative sum of strided array elements.</span>
-   <span class="package-name">[`@stdlib/blas-ext/base/gcusumkbn2`][@stdlib/blas/ext/base/gcusumkbn2]</span><span class="delimiter">: </span><span class="description">calculate the cumulative sum of strided array elements using a second-order iterative Kahan–Babuška algorithm.</span>
-   <span class="package-name">[`@stdlib/blas-ext/base/scusumkbn`][@stdlib/blas/ext/base/scusumkbn]</span><span class="delimiter">: </span><span class="description">calculate the cumulative sum of single-precision floating-point strided array elements using an improved Kahan–Babuška algorithm.</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>

<!-- /.stdlib -->

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

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

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

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

[@neumaier:1974a]: https://doi.org/10.1002/zamm.19740540106

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

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

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

[@stdlib/blas/ext/base/gcusumkbn2]: https://www.npmjs.com/package/@stdlib/blas-ext-base-gcusumkbn2

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

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