@stdlib/blas-ext-base-gapxsumpw

Adds a constant to each strided array element and computes the sum using pairwise summation.

https://github.com/stdlib-js/blas-ext-base-gapxsumpw

Science Score: 57.0%

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Keywords

array blas extended javascript math mathematics node node-js nodejs pairwise pw statistics stats stdlib strided strided-array sum summation total typed

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Adds a constant to each strided array element and computes the sum using pairwise summation.

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Host: GitHub
Owner: stdlib-js
License: apache-2.0
Language: JavaScript
Default Branch: main
Homepage: https://github.com/stdlib-js/stdlib
Size: 638 KB

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array blas extended javascript math mathematics node node-js nodejs pairwise pw statistics stats stdlib strided strided-array sum summation total typed

Created over 4 years ago · Last pushed 6 months ago

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Readme Changelog Contributing License Code of conduct Citation Security

We believe in a future in which the web is a preferred environment for numerical computation. To help realize this future, we've built stdlib. stdlib is a standard library, with an emphasis on numerical and scientific computation, written in JavaScript (and C) for execution in browsers and in Node.js.

The library is fully decomposable, being architected in such a way that you can swap out and mix and match APIs and functionality to cater to your exact preferences and use cases.

When you use stdlib, you can be absolutely certain that you are using the most thorough, rigorous, well-written, studied, documented, tested, measured, and high-quality code out there.

To join us in bringing numerical computing to the web, get started by checking us out on GitHub, and please consider financially supporting stdlib. We greatly appreciate your continued support!

gapxsumpw

Add a scalar constant to each strided array element and compute the sum using pairwise summation.

## Installation ```bash npm install @stdlib/blas-ext-base-gapxsumpw ``` 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 gapxsumpw = require( '@stdlib/blas-ext-base-gapxsumpw' ); ``` #### gapxsumpw( N, alpha, x, strideX ) Adds a scalar constant to each strided array element and computes the sum using pairwise summation. ```javascript var x = [ 1.0, -2.0, 2.0 ]; var v = gapxsumpw( x.length, 5.0, x, 1 ); // returns 16.0 ``` The function has the following parameters: - **N**: number of indexed elements. - **alpha**: scalar constant. - **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 access every other element: ```javascript var x = [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ]; var v = gapxsumpw( 4, 5.0, x, 2 ); // returns 25.0 ``` 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' ); 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 = gapxsumpw( 4, 5.0, x1, 2 ); // returns 25.0 ``` #### gapxsumpw.ndarray( N, alpha, x, strideX, offsetX ) Adds a scalar constant to each strided array element and computes the sum using pairwise summation and alternative indexing semantics. ```javascript var x = [ 1.0, -2.0, 2.0 ]; var v = gapxsumpw.ndarray( x.length, 5.0, x, 1, 0 ); // returns 16.0 ``` 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 access 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 = gapxsumpw.ndarray( 4, 5.0, x, 2, 1 ); // returns 25.0 ```

## 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 ([`dapxsumpw`][@stdlib/blas/ext/base/dapxsumpw], [`sapxsumpw`][@stdlib/blas/ext/base/sapxsumpw], etc.) are likely to be significantly more performant.

## Examples ```javascript var discreteUniform = require( '@stdlib/random-array-discrete-uniform' ); var gapxsumpw = require( '@stdlib/blas-ext-base-gapxsumpw' ); var x = discreteUniform( 10, -100, 100, { 'dtype': 'float64' }); console.log( x ); var v = gapxsumpw( x.length, 5.0, x, 1 ); console.log( v ); ```

## 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].

* * * ## 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 © 2016-2025. The Stdlib [Authors][stdlib-authors].

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Standard library for JavaScript.

Citation (CITATION.cff)

cff-version: 1.2.0
title: stdlib
message: >-
  If you use this software, please cite it using the
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type: software

authors:
  - name: The Stdlib Authors
    url: https://github.com/stdlib-js/stdlib/graphs/contributors

repository-code: https://github.com/stdlib-js/stdlib
url: https://stdlib.io

abstract: |
  Standard library for JavaScript and Node.js.

keywords:
  - JavaScript
  - Node.js
  - TypeScript
  - standard library
  - scientific computing
  - numerical computing
  - statistical computing

license: Apache-2.0 AND BSL-1.0

date-released: 2016

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npmjs.org: @stdlib/blas-ext-base-gapxsumpw

Adds a constant to each strided array element and computes the sum using pairwise summation.

Homepage: https://stdlib.io
License: Apache-2.0
Latest release: 0.2.2
published over 1 year ago

Versions: 14
Dependent Packages: 5
Dependent Repositories: 4
Downloads: 21,170 Last month

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planeshifter rreusser stdlib-bot kgryte

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@stdlib/blas-ext-base-gapxsumpw

Science Score: 57.0%

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