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evalrationalf

Evaluate a rational function using single-precision floating-point arithmetic.

A rational function f(x) is defined as

$$f(x) = \frac{P(x)}{Q(x)}$$

where both P(x) and Q(x) are polynomials in x. A polynomial in x can be expressed

$$c_nx^n + c_{n-1}x^{n-1} + \ldots + c_1x^1 + c_0 = \sum_{i=0}^{n} c_ix^i$$

where c_n, c_{n-1}, ..., c_0 are constants.

Installation

npm install @stdlib/math-base-tools-evalrationalf

Alternatively,

• To load the package in a website via a script tag without installation and bundlers, use the ES Module available on the esm branch (see README).
• If you are using Deno, visit the deno branch (see README for usage intructions).
• For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the umd branch (see README).

The branches.md file summarizes the available branches and displays a diagram illustrating their relationships.

To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.

Usage

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

evalrationalf( P, Q, x )

Evaluates a rational function at a value x using single-precision floating-point arithmetic.

var Float32Array = require( '@stdlib/array-float32' );

var P = new Float32Array( [ -6.0, -5.0 ] );
var Q = new Float32Array( [ 3.0, 0.5 ] );

var v = evalrationalf( P, Q, 6.0 ); // => ( -6*6^0 - 5*6^1 ) / ( 3*6^0 + 0.5*6^1 ) = (-6-30)/(3+3)
// returns -6.0

For polynomials of different degree, the coefficient array for the lower degree polynomial should be padded with zeros.

var Float32Array = require( '@stdlib/array-float32' );

// 2x^3 + 4x^2 - 5x^1 - 6x^0 => degree 4
var P = new Float32Array( [ -6.0, -5.0, 4.0, 2.0 ] );

// 0.5x^1 + 3x^0 => degree 2
var Q = new Float32Array( [ 3.0, 0.5, 0.0, 0.0 ] ); // zero-padded

var v = evalrationalf( P, Q, 6.0 ); // => ( -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)
// returns ~90.0

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

evalrationalf.factory( P, Q )

Uses code generation to in-line coefficients and return a function for evaluating a rational function using single-precision floating-point arithmetic.

var Float32Array = require( '@stdlib/array-float32' );

var P = new Float32Array( [ 20.0, 8.0, 3.0 ] );
var Q = new Float32Array( [ 10.0, 9.0, 1.0 ] );

var rational = evalrationalf.factory( P, Q );

var v = rational( 10.0 ); // => (20*10^0 + 8*10^1 + 3*10^2) / (10*10^0 + 9*10^1 + 1*10^2) = (20+80+300)/(10+90+100)
// returns 2.0

v = rational( 2.0 ); // => (20*2^0 + 8*2^1 + 3*2^2) / (10*2^0 + 9*2^1 + 1*2^2) = (20+16+12)/(10+18+4)
// returns 1.5

Notes

• The coefficients P and Q are expected to be arrays of the same length.
• For hot code paths in which coefficients are invariant, a compiled function will be more performant than evalrationalf().
• While code generation can boost performance, its use may be problematic in browser contexts enforcing a strict content security policy (CSP). If running in or targeting an environment with a CSP, avoid using code generation.

## Examples

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

// Create two arrays of random coefficients...
var opts = {
    'dtype': 'float32'
};
var P = discreteUniform( 10, -100, 100, opts );
var Q = discreteUniform( 10, -100, 100, opts );

// Evaluate the rational function at random values...
var v;
var i;
for ( i = 0; i < 100; i++ ) {
    v = uniform( 0.0, 100.0 );
    console.log( 'f(%d) = %d', v, evalrationalf( P, Q, v ) );
}

// Generate an `evalrationalf` function...
var rational = evalrationalf.factory( P, Q );
for ( i = 0; i < 100; i++ ) {
    v = uniform( -50.0, 50.0 );
    console.log( 'f(%d) = %d', v, rational( v ) );
}

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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.

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