@stdlib/math-base-tools-continued-fraction

Continued fraction approximation.

https://github.com/stdlib-js/math-base-tools-continued-fraction

Science Score: 44.0%

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Low similarity (14.5%) to scientific vocabulary

Keywords

expansion fraction javascript math mathematics node node-js nodejs series stdlib

Last synced: 6 months ago · JSON representation ·

Repository

Continued fraction approximation.

Basic Info

Host: GitHub
Owner: stdlib-js
License: apache-2.0
Language: JavaScript
Default Branch: main
Homepage: https://github.com/stdlib-js/stdlib
Size: 435 KB

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Stars: 1
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expansion fraction javascript math mathematics node node-js nodejs series stdlib

Created over 4 years ago · Last pushed 6 months ago

Metadata Files

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!

continued-fraction

$NPM version$ $Build Status$ $Coverage Status$

Continued fraction approximation.

## Installation ```bash npm install @stdlib/math-base-tools-continued-fraction ``` 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 continuedFraction = require( '@stdlib/math-base-tools-continued-fraction' ); ``` #### continuedFraction( generator\[, options ] ) Evaluates the continued fraction described by the supplied `generator` argument. `generator` can be either a function which returns an array with two elements, the `a` and `b` terms of the fraction, or an ES6 [Generator object][es6-generator]. By default, the function computes ```math \frac{a_1}{b_1+\frac{a_2}{b_2+\frac{a_3}{b_3+\frac{a_4}{b_4}+\ldots}}} ``` Using an ES6 [Generator object][es6-generator]: ```javascript // Continued fraction for (e-1)^(-1): var gen = generator(); var out = continuedFraction( gen ); // returns ~0.582 function* generator() { var i = 0; while ( true ) { i += 1; yield [ i, i ]; } } ``` Alternatively, one can use a closure to achieve the same goal: ```javascript // Continued fraction for (e-1)^(-1): var gen = generator(); var out = continuedFraction( gen ); // returns ~0.582 function generator() { var i = 0; return gen; function gen() { i += 1; return [ i, i ]; } } ``` The function accepts the following `options`: - **maxIter**: `integer` denoting the maximum number of times the supplied generator object will be called. Default: `1000000`. - **tolerance**: `number` primitive specifying the used tolerance to assess convergence. Default: `2.22e-16`. - **keep**: `boolean` primitive indicating whether to keep the `b0` term in the continued fraction. Default: `false`. To evaluate ```math b_0 + \frac{a_1}{b_1+\frac{a_2}{b_2+\frac{a_3}{b_3+\frac{a_4}{b_4}+\ldots}}} ``` set the `keep` option to `true`. ```javascript var out = continuedFraction( generator(), { 'keep': true }); // returns ~1.718 function generator() { var i = 0; return gen; function gen() { i += 1; return [ i, i ]; } } ``` To change the maximum number of iterations, set the `maxIter` option. ```javascript var out = continuedFraction( generator(), { 'maxIter': 10 }); // returns ~0.582 function generator() { var i = 0; return gen; function gen() { i += 1; return [ i, i ]; } } ``` The default tolerance of `2.22e-16` to assess convergence can be changed via the `tolerance` option. ```javascript var out = continuedFraction( generator(), { 'tolerance': 1e-1 }); // returns ~0.579 function generator() { var i = 0; return gen; function gen() { i += 1; return [ i, i ]; } } ```

## Examples ```javascript var continuedFraction = require( '@stdlib/math-base-tools-continued-fraction' ); var out; function* generator() { while ( true ) { yield [ 1, 1 ]; } } function closure() { var ones = [ 1, 1 ]; return gen; function gen() { return ones; } } out = continuedFraction( generator(), { 'keep': true }); console.log( 'Golden ratio (generator): %d,', out ); out = continuedFraction( closure(), { 'keep': true }); console.log( 'Golden ratio (closure): %d', out ); ```

* * * ## 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].

Owner

Name: stdlib
Login: stdlib-js
Kind: organization

Website: https://stdlib.io
Twitter: stdlibjs
Repositories: 3,692
Profile: https://github.com/stdlib-js

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
  metadata from this file.

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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Total packages: 1
Total downloads:
- npm 110,013 last-month
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Total dependent packages: 8
Total dependent repositories: 17
Total versions: 10
Total maintainers: 4

npmjs.org: @stdlib/math-base-tools-continued-fraction

Continued fraction approximation.

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

Versions: 10
Dependent Packages: 8
Dependent Repositories: 17
Downloads: 110,013 Last month
Docker Downloads: 24

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Downloads: 0.6%

Dependent packages count: 2.5%

Dependent repos count: 2.9%

Average: 7.2%

Stargazers count: 14.5%

Forks count: 15.4%

Maintainers (4)

planeshifter rreusser stdlib-bot kgryte

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type: opencollective
url: https://opencollective.com/stdlib

Last synced: 6 months ago

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@stdlib/random-base-randu ^0.0.x development
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@stdlib/types ^0.0.x

@stdlib/math-base-tools-continued-fraction

Science Score: 44.0%

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continued-fraction

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