JarCastingevalrational
Evaluates a rational function, i.e. the ratio of two polynomials.
A rational function f(x) is defined as
where both P(x) and Q(x) are polynomials in x.
Installation
$ npm install math-evalrational
Usage
var evalrational = require( 'math-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, -5 ];
var Q = [ 3, 0.5 ];
var v = evalrational( P, Q, 6 );
// returns -6 => ( -6*6^0 - 5*6^1 ) / ( 3*6^0 + 0.5*6^1 ) = (-6-30)/(3+3)
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, -5, 4, 2 ];
// 0.5x^1 + 3x^0 => degree 2
var Q = [ 3, 0.5, 0, 0 ]; // zero-padded
var v = evalrational( P, Q, 6 );
// returns 90 => ( -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)
Coefficients should be ordered in ascending degree. For example, for a polynomial
the coefficients would be
[c_0, c_1, ..., c_(n-1), c_n]
matching the summation notation.
evalrational.factory( P, Q )
Uses code generation to in-line coefficients and return a reusable function for evaluating a rational function.
var P = [ 20, 8, 3 ];
var Q = [ 10, 9, 1 ];
var rational = evalrational.factory( P, Q );
var v = rational( 10 );
// returns 2 => (20*10^0 + 8*10^1 + 3*10^2) / (10*10^0 + 9*10^1 + 1*10^2) = (20+80+300)/(10+90+100)
v = rational( 2 );
// returns 1.5 => (20*2^0 + 8*2^1 + 3*2^2) / (10*2^0 + 9*2^1 + 1*2^2) = (20+16+12)/(10+18+4)
Note: For hot code paths in which coefficients are invariant, the generated function will be more performant than the main export.
Examples
var round = require( 'math-round' );
var evalrational = require( 'math-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 ( Math.random() < 0.5 ) {
sign = -1;
} else {
sign = 1;
}
P[ i ] = sign * round( Math.random()*100 );
Q[ i ] = sign * round( Math.random()*100 );
}
// Evaluate the rational function at random values...
for ( i = 0; i < 100; i++ ) {
v = Math.random() * 100;
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 = Math.random()*100 - 50;
console.log( 'f(%d) = %d', v, rational( v ) );
}
To run the example code from the top-level application directory,
$ node ./examples/index.js
Tests
Unit
This repository uses tape for unit tests. To run the tests, execute the following command in the top-level application directory:
$ make test
All new feature development should have corresponding unit tests to validate correct functionality.
Test Coverage
This repository uses Istanbul as its code coverage tool. To generate a test coverage report, execute the following command in the top-level application directory:
$ make test-cov
Istanbul creates a ./reports/coverage directory. To access an HTML version of the report,
$ make view-cov
Browser Support
This repository uses Testling for browser testing. To run the tests in a (headless) local web browser, execute the following command in the top-level application directory:
$ make test-browsers
To view the tests in a local web browser,
$ make view-browser-tests
License
Copyright
Copyright © 2016. The Compute.io Authors..
