evalrational

Compile a module for evaluating a rational function.

Usage

var compile = require( '@stdlib/math/base/tools/evalrational-compile' );

compile( P, Q )

Compiles a module string containing an exported function which evaluates a rational function having coefficients P and Q.

var P = [ 3.0, 2.0, 1.0 ];
var Q = [ -1.0, -2.0, -3.0 ];

var str = compile( P, Q );
// returns <string>

In the example above, the output string would correspond to the following module:

'use strict';

// MAIN //

/**
* Evaluates a rational function, i.e., the ratio of two polynomials described by the coefficients stored in \\(P\\) and \\(Q\\).
*
* ## Notes
*
* -   Coefficients should be sorted in ascending degree.
* -   The implementation uses [Horner's rule][horners-method] for efficient computation.
*
* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method
*
*
* @private
* @param {number} x - value at which to evaluate the rational function
* @returns {number} evaluated rational function
*/
function evalrational( x ) {
    var ax;
    var s1;
    var s2;
    if ( x === 0.0 ) {
        return -3.0;
    }
    if ( x < 0.0 ) {
        ax = -x;
    } else {
        ax = x;
    }
    if ( ax <= 1.0 ) {
        s1 = 3.0 + (x * (2.0 + (x * 1.0))); // eslint-disable-line max-len
        s2 = -1.0 + (x * (-2.0 + (x * -3.0))); // eslint-disable-line max-len
    } else {
        x = 1.0 / x;
        s1 = 1.0 + (x * (2.0 + (x * 3.0))); // eslint-disable-line max-len
        s2 = -3.0 + (x * (-2.0 + (x * -1.0))); // eslint-disable-line max-len
    }
    return s1 / s2;
}


// EXPORTS //

module.exports = evalrational;

The coefficients should be ordered in ascending degree, thus matching summation notation.

Notes

  • The function is intended for non-browser environments for the purpose of generating module files.

Examples

var randu = require( '@stdlib/random/base/randu' );
var round = require( '@stdlib/math/base/special/round' );
var Float64Array = require( '@stdlib/array/float64' );
var compile = require( '@stdlib/math/base/tools/evalrational-compile' );

var sign;
var str;
var P;
var Q;
var i;

// Create two arrays of random coefficients...
P = new Float64Array( 10 );
Q = new Float64Array( 10 );
for ( i = 0; i < P.length; i++ ) {
    if ( randu() < 0.5 ) {
        sign = -1.0;
    } else {
        sign = 1.0;
    }
    P[ i ] = sign * round( randu()*100.0 );
    Q[ i ] = sign * round( randu()*100.0 );
}

// Compile a module for evaluating a rational function:
str = compile( P, Q );
console.log( str );