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https://github.com/stdlib-js/math-iter-utils-continued-fraction

Evaluate the terms of a continued fraction.
https://github.com/stdlib-js/math-iter-utils-continued-fraction

approximation continued fraction iterable iterate iterator javascript math mathematics node node-js nodejs stdlib

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Evaluate the terms of a continued fraction.

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README 

        



  

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# iterContinuedFraction



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



> Evaluate the terms of a continued fraction.



A **generalized continued fraction** has the form



```math

x = b_0 + \frac{a_1}{b_1+\frac{a_2}{b_2+\frac{a_3}{b_3+\frac{a_4}{b_4+\ldots}}}}

```



If `a_i = 1` for all `i`, the above expression reduces to a **simple continued fraction**.



```math

x = b_0 + \frac{1}{b_1+\frac{1}{b_2+\frac{1}{b_3+\frac{1}{b_4+\ldots}}}}

```



where the values `b_i` are called the **coefficients** or **terms** of the continued fraction.



## Installation



```bash

npm install @stdlib/math-iter-utils-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 iterContinuedFraction = require( '@stdlib/math-iter-utils-continued-fraction' );

```



#### iterContinuedFraction( iterator\[, options] )



Evaluates the terms of a continued fraction.



```javascript

var array2iterator = require( '@stdlib/array-to-iterator' );



var arr = array2iterator( [ 3, 4, 12, 4 ] );



var v = iterContinuedFraction( arr );

// returns ~3.245

```



The function supports the following `options`:



-   **iter**: maximum number of iterations. Default: `1e308`.

-   **tol**: tolerance at which to terminate further evaluation of the continued fraction. Default: [floating-point epsilon][@stdlib/constants/float64/eps].



To explicitly cap the maximum number of iterations, set the `iter` option.



```javascript

var array2iterator = require( '@stdlib/array-to-iterator' );



var arr = array2iterator( [ 3, 4, 12, 4 ] );



var opts = {

    'iter': 2

};

var v = iterContinuedFraction( arr, opts );

// returns 3.25

```



The function terminates continued fraction evaluation once the difference between continued fraction approximations is sufficiently small. The default tolerance is [floating-point epsilon][@stdlib/constants/float64/eps] (`~2.22e-16`). Once an update to a continued fraction approximation is less than or equal to this tolerance, the function terminates evaluation. To adjust the tolerance (e.g., to return a rough approximation), set the `tol` option.



```javascript

var iterContinuedFractionSeq = require( '@stdlib/math-iter-sequences-continued-fraction' );



var opts = {

    'tol': 1.0e-7

};

var it = iterContinuedFractionSeq( 3.141592653589793, opts );

// returns 



var v = iterContinuedFraction( it );

// returns ~3.14159292

```



## Notes



-   If an iterated value is non-numeric (including `NaN`), the function returns `NaN`. If non-numeric iterated values are possible, you are advised to provide an [`iterator`][mdn-iterator-protocol] which type checks and handles non-numeric values accordingly.



## Examples



```javascript

var iterContinuedFractionSeq = require( '@stdlib/math-iter-sequences-continued-fraction' );

var PI = require( '@stdlib/constants-float64-pi' );

var iterContinuedFraction = require( '@stdlib/math-iter-utils-continued-fraction' );



// Create an iterator for returning the list of continued fraction terms:

var it = iterContinuedFractionSeq( PI );



// Reconstitute the original value:

var v = iterContinuedFraction( it );

// returns 



console.log( 'Value: %d.', v );

```



* * *



## See Also



-   [`@stdlib/math-iter/sequences/continued-fraction`][@stdlib/math/iter/sequences/continued-fraction]: create an iterator which generates a list of all continued fraction terms which can be obtained given the precision of a provided number.



* * *



## 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 © 2016-2024. The Stdlib [Authors][stdlib-authors].



[npm-image]: http://img.shields.io/npm/v/@stdlib/math-iter-utils-continued-fraction.svg

[npm-url]: https://npmjs.org/package/@stdlib/math-iter-utils-continued-fraction



[test-image]: https://github.com/stdlib-js/math-iter-utils-continued-fraction/actions/workflows/test.yml/badge.svg?branch=main

[test-url]: https://github.com/stdlib-js/math-iter-utils-continued-fraction/actions/workflows/test.yml?query=branch:main



[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/math-iter-utils-continued-fraction/main.svg

[coverage-url]: https://codecov.io/github/stdlib-js/math-iter-utils-continued-fraction?branch=main



[chat-image]: https://img.shields.io/gitter/room/stdlib-js/stdlib.svg

[chat-url]: https://app.gitter.im/#/room/#stdlib-js_stdlib:gitter.im



[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/math-iter-utils-continued-fraction/tree/deno

[deno-readme]: https://github.com/stdlib-js/math-iter-utils-continued-fraction/blob/deno/README.md

[umd-url]: https://github.com/stdlib-js/math-iter-utils-continued-fraction/tree/umd

[umd-readme]: https://github.com/stdlib-js/math-iter-utils-continued-fraction/blob/umd/README.md

[esm-url]: https://github.com/stdlib-js/math-iter-utils-continued-fraction/tree/esm

[esm-readme]: https://github.com/stdlib-js/math-iter-utils-continued-fraction/blob/esm/README.md

[branches-url]: https://github.com/stdlib-js/math-iter-utils-continued-fraction/blob/main/branches.md



[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/math-iter-utils-continued-fraction/main/LICENSE



[mdn-iterator-protocol]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Iteration_protocols#The_iterator_protocol



[@stdlib/constants/float64/eps]: https://github.com/stdlib-js/constants-float64-eps



[@stdlib/math/iter/sequences/continued-fraction]: https://github.com/stdlib-js/math-iter-sequences-continued-fraction