math-evalrational

evalrational

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

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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

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License

MIT license.

Copyright

Copyright © 2016. The Compute.io Authors..