evalrational

Compile a module for evaluating a rational function.

Installation

npm install @stdlib/math-base-tools-evalrational-compile

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;

Notes

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

Examples

var discreteUniform = require( '@stdlib/random-array-discrete-uniform' );
var compile = require( '@stdlib/math-base-tools-evalrational-compile' );

// Create arrays of random coefficients:
var P = discreteUniform( 10, -100, 100 );
var Q = discreteUniform( 10, -100, 100 );

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

Notice

This package is part of stdlib, a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop stdlib, see the main project repository.

Community

License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.