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.
A rational function f(x) is defined as
where both P(x) and Q(x) are polynomials in x. A polynomial in x can be expressed
where c_n, c_{n-1}, ..., c_0 are constants.
Installation
npm install @stdlib/math-base-tools-evalrationalUsage
var evalrational = require( '@stdlib/math-base-tools-evalrational' );evalrational( P, Q, x )
Evaluates a rational function at a value x. The coefficients P and Q are expected to be arrays of the same length.
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 -6.0For 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 90.0Coefficients 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.
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 1.5Notes
- 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.
var randu = require( '@stdlib/random-base-randu' );
var round = require( '@stdlib/math-base-special-round' );
var Float64Array = require( '@stdlib/array-float64' );
var evalrational = require( '@stdlib/math-base-tools-evalrational' );
var rational;
var sign;
var len;
var P;
var Q;
var v;
var i;
// Create two arrays of random coefficients...
len = 10;
P = new Float64Array( len );
Q = new Float64Array( len );
for ( i = 0; i < len; i++ ) {
if ( randu() < 0.5 ) {
sign = -1.0;
} else {
sign = 1.0;
}
P[ i ] = sign * round( randu()*100 );
Q[ i ] = sign * round( randu()*100 );
}
// Evaluate the rational function at random values...
for ( i = 0; i < 100; i++ ) {
v = randu() * 100.0;
console.log( 'f(%d) = %d', v, evalrational( P, Q, v ) );
}
// Generate an `evalrational` function...
rational = evalrational.factory( P, Q );
for ( i = 0; i < 100; i++ ) {
v = (randu()*100.0) - 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.