About stdlib...

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!

gasumpw

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url]

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

The [_L1_ norm][l1norm] is defined as

Installation

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

`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.

`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`

`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.

`Examples`

`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 );`

*

`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`

[npm-image]: http://img.shields.io/npm/v/@stdlib/blas-ext-base-gasumpw.svg [npm-url]: https://npmjs.org/package/@stdlib/blas-ext-base-gasumpw

[test-image]: https://github.com/stdlib-js/blas-ext-base-gasumpw/actions/workflows/test.yml/badge.svg?branch=v0.3.1 [test-url]: https://github.com/stdlib-js/blas-ext-base-gasumpw/actions/workflows/test.yml?query=branch:v0.3.1

[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/blas-ext-base-gasumpw/main.svg [coverage-url]: https://codecov.io/github/stdlib-js/blas-ext-base-gasumpw?branch=main

[chat-image]: https://img.shields.io/badge/zulip-join_chat-brightgreen.svg [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-gasumpw/tree/deno [deno-readme]: https://github.com/stdlib-js/blas-ext-base-gasumpw/blob/deno/README.md [umd-url]: https://github.com/stdlib-js/blas-ext-base-gasumpw/tree/umd [umd-readme]: https://github.com/stdlib-js/blas-ext-base-gasumpw/blob/umd/README.md [esm-url]: https://github.com/stdlib-js/blas-ext-base-gasumpw/tree/esm [esm-readme]: https://github.com/stdlib-js/blas-ext-base-gasumpw/blob/esm/README.md [branches-url]: https://github.com/stdlib-js/blas-ext-base-gasumpw/blob/main/branches.md

[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

[@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


  
    About stdlib...
  

  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!

`gasumpw`

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url]

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

The [_L1_ norm][l1norm] is defined as

`Installation`

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

`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.

`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 `

`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.

`Examples`

`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 ); `

*

`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`

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`

[npm-image]: http://img.shields.io/npm/v/@stdlib/blas-ext-base-gasumpw.svg [npm-url]: https://npmjs.org/package/@stdlib/blas-ext-base-gasumpw

[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/blas-ext-base-gasumpw/main.svg [coverage-url]: https://codecov.io/github/stdlib-js/blas-ext-base-gasumpw?branch=main

[chat-image]: https://img.shields.io/badge/zulip-join_chat-brightgreen.svg [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

[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

[@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

@stdlib/blas-ext-base-gasumpw

gasumpw

Installation

Usage

Notes

Examples

References

See Also

Notice

License

Copyright

@stdlib/blas-ext-base-gasumpw

gasumpw

Installation

Usage

Notes

Examples

References

See Also

Notice

License

Copyright

`Usage`

`Notes`

`Examples`

`References`

`See Also`

`Notice`

`License`

`Copyright`

`@stdlib/blas-ext-base-gasumpw`

`gasumpw`

`Installation`

`Usage`

`Notes`

`Examples`

`References`

`See Also`

`Notice`

`License`

`Copyright`