https://github.com/stdlib-js/blas-ext-base-gcusumkbn2
Calculate the cumulative sum of strided array elements using a second-order iterative Kahan–Babuška algorithm.
https://github.com/stdlib-js/blas-ext-base-gcusumkbn2
accumulate blas compensated cumulative extended javascript kahan kbn math mathematics node node-js nodejs statistics stats stdlib strided sum summation total
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Calculate the cumulative sum of strided array elements using a second-order iterative Kahan–Babuška algorithm.
- Host: GitHub
- URL: https://github.com/stdlib-js/blas-ext-base-gcusumkbn2
- Owner: stdlib-js
- License: apache-2.0
- Created: 2021-06-15T16:39:36.000Z (almost 5 years ago)
- Default Branch: main
- Last Pushed: 2026-04-06T04:03:50.000Z (about 1 month ago)
- Last Synced: 2026-04-06T05:27:19.308Z (about 1 month ago)
- Topics: accumulate, blas, compensated, cumulative, extended, javascript, kahan, kbn, math, mathematics, node, node-js, nodejs, statistics, stats, stdlib, strided, sum, summation, total
- Language: JavaScript
- Homepage:
- Size: 998 KB
- Stars: 2
- Watchers: 2
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- Changelog: CHANGELOG.md
- Contributing: CONTRIBUTING.md
- License: LICENSE
- Code of conduct: CODE_OF_CONDUCT.md
- Citation: CITATION.cff
- Security: SECURITY.md
- Notice: NOTICE
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README
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# gcusumkbn2
[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url]
> Calculate the cumulative sum of strided array elements using a second-order iterative Kahan–Babuška algorithm.
## Installation
```bash
npm install @stdlib/blas-ext-base-gcusumkbn2
```
Alternatively,
- To load the package in a website via a `script` tag without installation and bundlers, use the [ES Module][es-module] available on the [`esm`][esm-url] branch (see [README][esm-readme]).
- If you are using Deno, visit the [`deno`][deno-url] branch (see [README][deno-readme] for usage intructions).
- For use in Observable, or in browser/node environments, use the [Universal Module Definition (UMD)][umd] build available on the [`umd`][umd-url] branch (see [README][umd-readme]).
The [branches.md][branches-url] file summarizes the available branches and displays a diagram illustrating their relationships.
To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.
## Usage
```javascript
var gcusumkbn2 = require( '@stdlib/blas-ext-base-gcusumkbn2' );
```
#### gcusumkbn2( N, sum, x, strideX, y, strideY )
Computes the cumulative sum of strided array elements using a second-order iterative Kahan–Babuška algorithm.
```javascript
var x = [ 1.0, -2.0, 2.0 ];
var y = [ 0.0, 0.0, 0.0 ];
gcusumkbn2( 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 ];
gcusumkbn2( 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 = gcusumkbn2( 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.
```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
gcusumkbn2( 4, 0.0, x1, -2, y1, 1 );
// y0 => [ 0.0, 0.0, 0.0, 4.0, 6.0, 4.0, 5.0, 0.0 ]
```
#### gcusumkbn2.ndarray( N, sum, x, strideX, offsetX, y, strideY, offsetY )
Computes the cumulative sum of strided array elements using a second-order iterative Kahan–Babuška algorithm and alternative indexing semantics.
```javascript
var x = [ 1.0, -2.0, 2.0 ];
var y = [ 0.0, 0.0, 0.0 ];
gcusumkbn2.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 ];
gcusumkbn2.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 ]
```
## 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 ([`dcusumkbn2`][@stdlib/blas/ext/base/dcusumkbn2], [`scusumkbn2`][@stdlib/blas/ext/base/scusumkbn2], etc.) are likely to be significantly more performant.
## Examples
```javascript
var discreteUniform = require( '@stdlib/random-array-discrete-uniform' );
var Float64Array = require( '@stdlib/array-float64' );
var gcusumkbn2 = require( '@stdlib/blas-ext-base-gcusumkbn2' );
var x = discreteUniform( 10, -100, 100, {
'dtype': 'float64'
});
var y = new Float64Array( x.length );
console.log( x );
console.log( y );
gcusumkbn2( x.length, 0.0, x, 1, y, -1 );
console.log( y );
```
* * *
## References
- Klein, Andreas. 2005. "A Generalized Kahan-Babuška-Summation-Algorithm." _Computing_ 76 (3): 279–93. doi:[10.1007/s00607-005-0139-x][@klein:2005a].
* * *
## See Also
- [`@stdlib/blas-ext/base/dcusumkbn2`][@stdlib/blas/ext/base/dcusumkbn2]: calculate the cumulative sum of double-precision floating-point strided array elements using a second-order iterative Kahan–Babuška algorithm.
- [`@stdlib/blas-ext/base/gcusum`][@stdlib/blas/ext/base/gcusum]: calculate the cumulative sum of strided array elements.
- [`@stdlib/blas-ext/base/gcusumkbn`][@stdlib/blas/ext/base/gcusumkbn]: calculate the cumulative sum of strided array elements using an improved Kahan–Babuška algorithm.
- [`@stdlib/blas-ext/base/scusumkbn2`][@stdlib/blas/ext/base/scusumkbn2]: calculate the cumulative sum of single-precision floating-point strided array elements using a second-order iterative Kahan–Babuška algorithm.
* * *
## 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 © 2016-2026. The Stdlib [Authors][stdlib-authors].
[npm-image]: http://img.shields.io/npm/v/@stdlib/blas-ext-base-gcusumkbn2.svg
[npm-url]: https://npmjs.org/package/@stdlib/blas-ext-base-gcusumkbn2
[test-image]: https://github.com/stdlib-js/blas-ext-base-gcusumkbn2/actions/workflows/test.yml/badge.svg?branch=main
[test-url]: https://github.com/stdlib-js/blas-ext-base-gcusumkbn2/actions/workflows/test.yml?query=branch:main
[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/blas-ext-base-gcusumkbn2/main.svg
[coverage-url]: https://codecov.io/github/stdlib-js/blas-ext-base-gcusumkbn2?branch=main
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[chat-url]: https://stdlib.zulipchat.com
[stdlib]: https://github.com/stdlib-js/stdlib
[stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors
[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-ext-base-gcusumkbn2/tree/deno
[deno-readme]: https://github.com/stdlib-js/blas-ext-base-gcusumkbn2/blob/deno/README.md
[umd-url]: https://github.com/stdlib-js/blas-ext-base-gcusumkbn2/tree/umd
[umd-readme]: https://github.com/stdlib-js/blas-ext-base-gcusumkbn2/blob/umd/README.md
[esm-url]: https://github.com/stdlib-js/blas-ext-base-gcusumkbn2/tree/esm
[esm-readme]: https://github.com/stdlib-js/blas-ext-base-gcusumkbn2/blob/esm/README.md
[branches-url]: https://github.com/stdlib-js/blas-ext-base-gcusumkbn2/blob/main/branches.md
[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/blas-ext-base-gcusumkbn2/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://github.com/stdlib-js/array-base-accessor
[@klein:2005a]: https://doi.org/10.1007/s00607-005-0139-x
[@stdlib/blas/ext/base/dcusumkbn2]: https://github.com/stdlib-js/blas-ext-base-dcusumkbn2
[@stdlib/blas/ext/base/gcusum]: https://github.com/stdlib-js/blas-ext-base-gcusum
[@stdlib/blas/ext/base/gcusumkbn]: https://github.com/stdlib-js/blas-ext-base-gcusumkbn
[@stdlib/blas/ext/base/scusumkbn2]: https://github.com/stdlib-js/blas-ext-base-scusumkbn2