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https://github.com/stdlib-js/math-base-tools-lucaspoly
Evaluate a Lucas polynomial.
https://github.com/stdlib-js/math-base-tools-lucaspoly
eval evalpoly evaluate fib fibo fibonacci javascript lucas math mathematics negalucas node node-js nodejs number poly polynomial polyval stdlib
Last synced: about 1 month ago
JSON representation
Evaluate a Lucas polynomial.
- Host: GitHub
- URL: https://github.com/stdlib-js/math-base-tools-lucaspoly
- Owner: stdlib-js
- License: apache-2.0
- Created: 2021-06-15T17:17:09.000Z (over 3 years ago)
- Default Branch: main
- Last Pushed: 2024-11-01T10:55:52.000Z (about 2 months ago)
- Last Synced: 2024-11-18T15:45:54.069Z (about 1 month ago)
- Topics: eval, evalpoly, evaluate, fib, fibo, fibonacci, javascript, lucas, math, mathematics, negalucas, node, node-js, nodejs, number, poly, polynomial, polyval, stdlib
- Language: JavaScript
- Homepage: https://github.com/stdlib-js/stdlib
- Size: 1.12 MB
- Stars: 2
- Watchers: 3
- 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
Awesome Lists containing this project
README
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!
# Lucas Polynomial
[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url]
> Evaluate a [Lucas polynomial][fibonacci-polynomials].
A [Lucas polynomial][fibonacci-polynomials] is expressed according to the following recurrence relation
```math
L_n(x) = \begin{cases}2 & \textrm{if}\ n = 0\\x & \textrm{if}\ n = 1\\x \cdot L_{n-1}(x) + L_{n-2}(x) & \textrm{if}\ n \geq 2\end{cases}
```
Alternatively, if `L(n,k)` is the coefficient of `x^k` in `L_n(x)`, then
```math
L_n(x) = \sum_{k = 0}^n L(n,k) x^k
```
We can extend [Lucas polynomials][fibonacci-polynomials] to negative `n` using the identity
```math
L_{-n}(x) = (-1)^{n} L_n(x)
```
## Installation
```bash
npm install @stdlib/math-base-tools-lucaspoly
```
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 lucaspoly = require( '@stdlib/math-base-tools-lucaspoly' );
```
#### lucaspoly( n, x )
Evaluates a [Lucas polynomial][fibonacci-polynomials] at a value `x`.
```javascript
var v = lucaspoly( 5, 2.0 ); // => 2^5 + 5*2^3 + 5*2
// returns 82.0
```
#### lucaspoly.factory( n )
Uses code generation to generate a `function` for evaluating a [Lucas polynomial][fibonacci-polynomials].
```javascript
var polyval = lucaspoly.factory( 5 );
var v = polyval( 1.0 ); // => 1^5 + 5*1^3 + 5
// returns 11.0
v = polyval( 2.0 ); // => 2^5 + 5*2^3 + 5*2
// returns 82.0
```
## Notes
- For hot code paths, a compiled function will be more performant than `lucaspoly()`.
- While code generation can boost performance, its use may be problematic in browser contexts enforcing a strict [content security policy][mdn-csp] (CSP). If running in or targeting an environment with a CSP, avoid using code generation.
## Examples
```javascript
var lucaspoly = require( '@stdlib/math-base-tools-lucaspoly' );
var i;
// Compute the negaLucas and Lucas numbers...
for ( i = -76; i < 77; i++ ) {
console.log( 'L_%d = %d', i, lucaspoly( i, 1.0 ) );
}
```
* * *
## See Also
- [`@stdlib/math-base/tools/evalpoly`][@stdlib/math/base/tools/evalpoly]: evaluate a polynomial using double-precision floating-point arithmetic.
- [`@stdlib/math-base/tools/fibpoly`][@stdlib/math/base/tools/fibpoly]: evaluate a Fibonacci polynomial.
* * *
## 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-base-tools-lucaspoly.svg
[npm-url]: https://npmjs.org/package/@stdlib/math-base-tools-lucaspoly
[test-image]: https://github.com/stdlib-js/math-base-tools-lucaspoly/actions/workflows/test.yml/badge.svg?branch=main
[test-url]: https://github.com/stdlib-js/math-base-tools-lucaspoly/actions/workflows/test.yml?query=branch:main
[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/math-base-tools-lucaspoly/main.svg
[coverage-url]: https://codecov.io/github/stdlib-js/math-base-tools-lucaspoly?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-base-tools-lucaspoly/tree/deno
[deno-readme]: https://github.com/stdlib-js/math-base-tools-lucaspoly/blob/deno/README.md
[umd-url]: https://github.com/stdlib-js/math-base-tools-lucaspoly/tree/umd
[umd-readme]: https://github.com/stdlib-js/math-base-tools-lucaspoly/blob/umd/README.md
[esm-url]: https://github.com/stdlib-js/math-base-tools-lucaspoly/tree/esm
[esm-readme]: https://github.com/stdlib-js/math-base-tools-lucaspoly/blob/esm/README.md
[branches-url]: https://github.com/stdlib-js/math-base-tools-lucaspoly/blob/main/branches.md
[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/math-base-tools-lucaspoly/main/LICENSE
[fibonacci-polynomials]: https://en.wikipedia.org/wiki/Fibonacci_polynomials
[mdn-csp]: https://developer.mozilla.org/en-US/docs/Web/HTTP/CSP
[@stdlib/math/base/tools/evalpoly]: https://github.com/stdlib-js/math-base-tools-evalpoly
[@stdlib/math/base/tools/fibpoly]: https://github.com/stdlib-js/math-base-tools-fibpoly