evalrational

Compile a C function for evaluating a rational function.

Installation

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

Usage

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

compile( P, Q )

Compiles a C function for evaluating 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., double or float). Default: 'double'.
• name: function name. Default: 'evalpoly'.

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

/**
* 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
*
* @param x    value at which to evaluate the rational function
* @returns    evaluated rational function
*/
static double evalrational( const double x ) {
    double ax;
    double ix;
    double s1;
    double 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 {
        ix = 1.0 / x;
        s1 = 1.0 + (ix * (2.0 + (ix * 3.0)));
        s2 = -3.0 + (ix * (-2.0 + (ix * -1.0)));
    }
    return s1 / s2;
}

To generate a function having a custom name and supporting single-precision floating-point numbers, provide the corresponding options.

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

var opts = {
    'dtype': 'float',
    'name': 'rational123'
};
var str = compile( P, Q, opts );
// returns <string>

For the previous example, the output string would correspond to the following function:

/**
* 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
*
* @param x    value at which to evaluate the rational function
* @returns    evaluated rational function
*/
static float rational123( const float x ) {
    float ax;
    float ix;
    float s1;
    float s2;
    if ( x == 0.0f ) {
        return -3.0f;
    }
    if ( x < 0.0f ) {
        ax = -x;
    } else {
        ax = x;
    }
    if ( ax <= 1.0f ) {
        s1 = 3.0f + (x * (2.0f + (x * 1.0f)));
        s2 = -1.0f + (x * (-2.0f + (x * -3.0f)));
    } else {
        ix = 1.0f / x;
        s1 = 1.0f + (ix * (2.0f + (ix * 3.0f)));
        s2 = -3.0f + (ix * (-2.0f + (ix * -1.0f)));
    }
    return s1 / s2;
}

Notes

• The coefficients should be ordered in ascending degree, thus matching summation notation.
• 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-c' );

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 function for evaluating a rational function:
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.