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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!

Fibonacci Polynomial

NPM version Build Status Coverage Status

Evaluate a Fibonacci polynomial.

A Fibonacci polynomial is expressed according to the following recurrence relation

$$F_n(x) = \begin{cases}0 & \textrm{if}\ n = 0\\1 & \textrm{if}\ n = 1\\x \cdot F_{n-1}(x) + F_{n-2}(x) & \textrm{if}\ n \geq 2\end{cases}$$

Alternatively, if F(n,k) is the coefficient of x^k in F_n(x), then

$$F_n(x) = \sum_{k = 0}^n F(n,k) x^k$$

where

$$F(n,k) = {{\frac{n+k-1}{2}} \choose {k}}$$

We can extend Fibonacci polynomials to negative n using the identity

$$F_{-n}(x) = (-1)^{n-1} F_n(x)$$

Usage

To use in Observable,

fibpoly = require( 'https://cdn.jsdelivr.net/gh/stdlib-js/math-base-tools-fibpoly@umd/browser.js' )

To vendor stdlib functionality and avoid installing dependency trees for Node.js, you can use the UMD server build:

var fibpoly = require( 'path/to/vendor/umd/math-base-tools-fibpoly/index.js' )

To include the bundle in a webpage,

<script type="text/javascript" src="https://cdn.jsdelivr.net/gh/stdlib-js/math-base-tools-fibpoly@umd/browser.js"></script>

If no recognized module system is present, access bundle contents via the global scope:

<script type="text/javascript">
(function () {
    window.fibpoly;
})();
</script>

fibpoly( n, x )

Evaluates a Fibonacci polynomial at a value x.

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.

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 (CSP). If running in or targeting an environment with a CSP, avoid using code generation.

Examples

<!DOCTYPE html>
<html lang="en">
<body>
<script type="text/javascript" src="https://cdn.jsdelivr.net/gh/stdlib-js/math-base-tools-fibpoly@umd/browser.js"></script>
<script type="text/javascript">
(function () {

var i;

// Compute the negaFibonacci and Fibonacci numbers...
for ( i = -77; i < 78; i++ ) {
    console.log( 'F_%d = %d', i, fibpoly( i, 1.0 ) );
}

})();
</script>
</body>
</html>

See Also

Notice

This package is part of 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, see the main project repository.

Community

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License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.