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    math-evalrational

    1.0.0 • Public • Published

    evalrational

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    Evaluates a rational function, i.e. the ratio of two polynomials.

    A rational function f(x) is defined as

    Rational function definition.

    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

    Polynomial expression.

    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)
     
    = 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

    MIT license.

    Copyright

    Copyright © 2016. The Compute.io Authors..

    Install

    npm i math-evalrational

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    Version

    1.0.0

    License

    MIT

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