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!

evalrational

Evaluate a rational function using double-precision floating-point arithmetic.

A rational function f(x) is defined as

$$f(x) = \frac{P(x)}{Q(x)}$$

where both P(x) and Q(x) are polynomials in x. A polynomial in x can be expressed

$$c_nx^n + c_{n-1}x^{n-1} + \ldots + c_1x^1 + c_0 = \sum_{i=0}^{n} c_ix^i$$

where c_n, c_{n-1}, ..., c_0 are constants.

Installation

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

Alternatively,

• To load the package in a website via a script tag without installation and bundlers, use the ES Module available on the esm branch (see README).
• If you are using Deno, visit the deno branch (see README for usage intructions).
• For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the umd branch (see README).

The branches.md 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

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

evalrational( P, Q, x )

Evaluates a rational function at a value x using double-precision floating-point arithmetic.

var P = [ -6.0, -5.0 ];
var Q = [ 3.0, 0.5 ];

var v = evalrational( P, Q, 6.0 ); // => ( -6*6^0 - 5*6^1 ) / ( 3*6^0 + 0.5*6^1 ) = (-6-30)/(3+3)
// returns -6.0

For polynomials of different degree, the coefficient array for the lower degree polynomial should be padded with zeros.

// 2x^3 + 4x^2 - 5x^1 - 6x^0 => degree 4
var P = [ -6.0, -5.0, 4.0, 2.0 ];

// 0.5x^1 + 3x^0 => degree 2
var Q = [ 3.0, 0.5, 0.0, 0.0 ]; // zero-padded

var v = evalrational( P, Q, 6.0 ); // => ( -6*6^0 - 5*6^1 + 4*6^2 + 2*6^3 ) / ( 3*6^0 + 0.5*6^1 + 0*6^2 + 0*6^3 ) = (-6-30+144+432)/(3+3)
// returns 90.0

Coefficients should be ordered in ascending degree, thus matching summation notation.

evalrational.factory( P, Q )

Uses code generation to in-line coefficients and return a function for evaluating a rational function using double-precision floating-point arithmetic.

var P = [ 20.0, 8.0, 3.0 ];
var Q = [ 10.0, 9.0, 1.0 ];

var rational = evalrational.factory( P, Q );

var v = rational( 10.0 ); // => (20*10^0 + 8*10^1 + 3*10^2) / (10*10^0 + 9*10^1 + 1*10^2) = (20+80+300)/(10+90+100)
// returns 2.0

v = rational( 2.0 ); // => (20*2^0 + 8*2^1 + 3*2^2) / (10*2^0 + 9*2^1 + 1*2^2) = (20+16+12)/(10+18+4)
// returns 1.5

Notes

• The coefficients P and Q are expected to be arrays of the same length.
• For hot code paths in which coefficients are invariant, a compiled function will be more performant than evalrational().
• 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 discreteUniform = require( '@stdlib/random-array-discrete-uniform' );
var uniform = require( '@stdlib/random-base-uniform' );
var evalrational = require( '@stdlib/math-base-tools-evalrational' );

// Create two arrays of random coefficients...
var P = discreteUniform( 10, -100, 100 );
var Q = discreteUniform( 10, -100, 100 );

// Evaluate the rational function at random values...
var v;
var i;
for ( i = 0; i < 100; i++ ) {
    v = uniform( 0.0, 100.0 );
    console.log( 'f(%d) = %d', v, evalrational( P, Q, v ) );
}

// Generate an `evalrational` function...
var rational = evalrational.factory( P, Q );
for ( i = 0; i < 100; i++ ) {
    v = uniform( -50.0, 50.0 );
    console.log( 'f(%d) = %d', v, rational( v ) );
}

---

See Also

• @stdlib/math-base/tools/evalpoly: evaluate a 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.

Community

---

Copyright

Copyright © 2016-2024. The Stdlib Authors.