@stdlib/math-base-tools-evalrational
v0.2.3TypeScript
Evaluate a rational function using double-precision floating-point arithmetic.
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Published by The Stdlib Authors
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evalrational
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> Evaluate a [rational function][rational-function] using double-precision floating-point arithmetic.
A [rational function][rational-function] f(x) is defined as
where both P(x) and Q(x) are polynomials in x. A [polynomial][polynomial] in x can be expressed
where c_n, c_{n-1}, ..., c_0 are constants.
Installation
``bash`
npm install @stdlib/math-base-tools-evalrational
Usage
`javascript`
var evalrational = require( '@stdlib/math-base-tools-evalrational' );
#### evalrational( P, Q, x )
Evaluates a [rational function][rational-function] at a value x using double-precision floating-point arithmetic.
`javascript
var P = [ -6.0, -5.0 ];
var Q = [ 3.0, 0.5 ];
var v = evalrational( P, Q, 6.0 ); // => ( -66^0 - 56^1 ) / ( 36^0 + 0.56^1 ) = (-6-30)/(3+3)
// returns -6.0
`
For polynomials of different degree, the coefficient array for the lower degree [polynomial][polynomial] should be padded with zeros.
`javascript
// 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 ); // => ( -66^0 - 56^1 + 46^2 + 26^3 ) / ( 36^0 + 0.56^1 + 06^2 + 06^3 ) = (-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][rational-function] using double-precision floating-point arithmetic.
`javascript
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 ); // => (2010^0 + 810^1 + 310^2) / (1010^0 + 910^1 + 110^2) = (20+80+300)/(10+90+100)
// returns 2.0
v = rational( 2.0 ); // => (202^0 + 82^1 + 32^2) / (102^0 + 92^1 + 12^2) = (20+16+12)/(10+18+4)
// returns 1.5
`
Notes
- The coefficients P and Q are expected to be arrays of the same length.evalrational()
- For hot code paths in which coefficients are invariant, a compiled function will be more performant than .
- 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 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][@stdlib/math/base/tools/evalpoly]: evaluate a polynomial using double-precision floating-point arithmetic.
*
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]
---
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-evalrational/tree/deno
[deno-readme]: https://github.com/stdlib-js/math-base-tools-evalrational/blob/deno/README.md
[umd-url]: https://github.com/stdlib-js/math-base-tools-evalrational/tree/umd
[umd-readme]: https://github.com/stdlib-js/math-base-tools-evalrational/blob/umd/README.md
[esm-url]: https://github.com/stdlib-js/math-base-tools-evalrational/tree/esm
[esm-readme]: https://github.com/stdlib-js/math-base-tools-evalrational/blob/esm/README.md
[branches-url]: https://github.com/stdlib-js/math-base-tools-evalrational/blob/main/branches.md
[polynomial]: https://en.wikipedia.org/wiki/Polynomial
[rational-function]: https://en.wikipedia.org/wiki/Rational_function
[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