evalrational

Usage

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

compile( P, Q[, options] )

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>

The function supports the following options:

• dtype: input argument floating-point data type (e.g., float64 or float32). Default: 'float64'.

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)));
        s2 = -1.0 + (x * (-2.0 + (x * -3.0)));
    } else {
        x = 1.0 / x;
        s1 = 1.0 + (x * (2.0 + (x * 3.0)));
        s2 = -3.0 + (x * (-2.0 + (x * -1.0)));
    }
    return s1 / s2;
}


// EXPORTS //

module.exports = evalrational;

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

By default, the function assumes double-precision floating-point arithmetic. To emulate single-precision floating-point arithmetic, set the dtype option to 'float32'.

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

var str = compile( P, Q, {
    'dtype': 'float32'
});
// returns <string>

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

'use strict';

// MODULES //

var float64ToFloat32 = require( '@stdlib/number/float64/base/to-float32' );


// 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 = float64ToFloat32(3.0 + float64ToFloat32(x * float64ToFloat32(2.0 + float64ToFloat32(x * 1.0)))); // eslint-disable-line max-len
        s2 = float64ToFloat32(-1.0 + float64ToFloat32(x * float64ToFloat32(-2.0 + float64ToFloat32(x * -3.0)))); // eslint-disable-line max-len
    } else {
        x = float64ToFloat32( 1.0 / x );
        s1 = float64ToFloat32(1.0 + float64ToFloat32(x * float64ToFloat32(2.0 + float64ToFloat32(x * 3.0)))); // eslint-disable-line max-len
        s2 = float64ToFloat32(-3.0 + float64ToFloat32(x * float64ToFloat32(-2.0 + float64ToFloat32(x * -1.0)))); // eslint-disable-line max-len
    }
    return float64ToFloat32( s1 / s2 );
}


// EXPORTS //

module.exports = evalrational;