@stdlib/math-base-tools-fibpoly
v0.2.3TypeScript
Evaluate a Fibonacci polynomial.
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Published by The Stdlib Authors
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Fibonacci Polynomial
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> Evaluate a [Fibonacci polynomial][fibonacci-polynomials].
A [Fibonacci polynomial][fibonacci-polynomials] is expressed according to the following recurrence relation
Alternatively, if F(n,k) is the coefficient of x^k in F_n(x), then
where
We can extend [Fibonacci polynomials][fibonacci-polynomials] to negative n using the identity
Installation
``bash`
npm install @stdlib/math-base-tools-fibpoly
Usage
`javascript`
var fibpoly = require( '@stdlib/math-base-tools-fibpoly' );
#### fibpoly( n, x )
Evaluates a [Fibonacci polynomial][fibonacci-polynomials] at a value x.
`javascript`
var v = fibpoly( 5, 2.0 ); // => 2^4 + 3*2^2 + 1
// returns 29.0
#### fibpoly.factory( n )
Uses code generation to generate a function for evaluating a [Fibonacci polynomial][fibonacci-polynomials].
`javascript
var polyval = fibpoly.factory( 5 );
var v = polyval( 1.0 ); // => 1^4 + 3*1^2 + 1
// returns 5.0
v = polyval( 2.0 ); // => 2^4 + 3*2^2 + 1
// returns 29.0
`
Notes
- For hot code paths, a compiled function will be more performant than fibpoly().
- 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 fibpoly = require( '@stdlib/math-base-tools-fibpoly' );
var i;
// Compute the negaFibonacci and Fibonacci numbers...
for ( i = -77; i < 78; i++ ) {
console.log( 'F_%d = %d', i, fibpoly( 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/lucaspoly][@stdlib/math/base/tools/lucaspoly]: evaluate a Lucas 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 © 2016-2026. The Stdlib [Authors][stdlib-authors].
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[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-fibpoly/tree/deno
[deno-readme]: https://github.com/stdlib-js/math-base-tools-fibpoly/blob/deno/README.md
[umd-url]: https://github.com/stdlib-js/math-base-tools-fibpoly/tree/umd
[umd-readme]: https://github.com/stdlib-js/math-base-tools-fibpoly/blob/umd/README.md
[esm-url]: https://github.com/stdlib-js/math-base-tools-fibpoly/tree/esm
[esm-readme]: https://github.com/stdlib-js/math-base-tools-fibpoly/blob/esm/README.md
[branches-url]: https://github.com/stdlib-js/math-base-tools-fibpoly/blob/main/branches.md
[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/math-base-tools-fibpoly/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://www.npmjs.com/package/@stdlib/math-base-tools-evalpoly
[@stdlib/math/base/tools/lucaspoly]: https://www.npmjs.com/package/@stdlib/math-base-tools-lucaspoly