Fibonacci Polynomial

Evaluate a Fibonacci polynomial.

A Fibonacci polynomial 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 to negative n using the identity

Installation

npm install @stdlib/math-base-tools-fibpoly

Usage

var fibpoly = require( '@stdlib/math-base-tools-fibpoly' );

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

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: evaluate a polynomial using double-precision floating-point arithmetic.
• @stdlib/math-base/tools/lucaspoly: evaluate a Lucas polynomial.

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.

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License

See LICENSE.

Copyright

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