@stdlib/math-base-tools-evalrationalf
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Evaluate a rational function using single-precision floating-point arithmetic.
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# evalrationalf
[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] <!-- [![dependencies][dependencies-image]][dependencies-url] -->
> Evaluate a [rational function][rational-function] using single-precision floating-point arithmetic.
<section class="intro">
A [rational function][rational-function] `f(x)` is defined as
<!-- <equation class="equation" label="eq:rational_function" align="center" raw="f(x) = \frac{P(x)}{Q(x)}" alt="Rational function definition."> -->
<div class="equation" align="center" data-raw-text="f(x) = \frac{P(x)}{Q(x)}" data-equation="eq:rational_function">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@7e0a95722efd9c771b129597380c63dc6715508b/lib/node_modules/@stdlib/math/base/tools/evalrational/docs/img/equation_rational_function.svg" alt="Rational function definition.">
<br>
</div> -->
<!-- </equation> -->
where both `P(x)` and `Q(x)` are polynomials in `x`. A [polynomial][polynomial] in `x` can be expressed
<!-- <equation class="equation" label="eq:polynomial" align="center" raw="c_nx^n + c_{n-1}x^{n-1} + \ldots + c_1x^1 + c_0 = \sum_{i=0}^{n} c_ix^i" alt="Polynomial expression."> -->
<!-- <div class="equation" align="center" data-raw-text="c_nx^n + c_{n-1}x^{n-1} + \ldots + c_1x^1 + c_0 = \sum_{i=0}^{n} c_ix^i" data-equation="eq:polynomial">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@7e0a95722efd9c771b129597380c63dc6715508b/lib/node_modules/@stdlib/math/base/tools/evalrational/docs/img/equation_polynomial.svg" alt="Polynomial expression.">
<br>
</div>
<!-- </equation> -->
where `c_n, c_{n-1}, ..., c_0` are constants.
</section>
<!-- /.intro -->
<section class="installation">
## Installation
```bash
npm install @stdlib/math-base-tools-evalrationalf
```
</section>
<section class="usage">
## Usage
```javascript
var evalrationalf = require( '@stdlib/math-base-tools-evalrationalf' );
```
#### evalrationalf( P, Q, x )
Evaluates a [rational function][rational-function] at a value `x` using single-precision floating-point arithmetic.
```javascript
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][polynomial] should be padded with zeros.
```javascript
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][rational-function] using single-precision floating-point arithmetic.
```javascript
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
```
</section>
<!-- /.usage -->
<section class="notes">
## 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][mdn-csp] (CSP). If running in or targeting an environment with a CSP, avoid using code generation.
</section>
<!-- /.notes -->
<section class="examples">
## Examples
<!-- eslint no-undef: "error" -->
```javascript
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 ) );
}
```
</section>
<!-- /.examples -->
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<section class="related">
</section>
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<section class="main-repo" >
* * *
## Notice
This package is part of [stdlib][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][stdlib], see the main project [repository][stdlib].
#### Community
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---
## Copyright
Copyright © 2016-2024. The Stdlib [Authors][stdlib-authors].
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[branches-url]: https://github.com/stdlib-js/math-base-tools-evalrationalf/blob/main/branches.md
[polynomial]: https://en.wikipedia.org/wiki/Polynomial
[rational-function]: https://en.wikipedia.org/wiki/Rational_function
[mdn-csp]: https://developer.mozilla.org/en-US/docs/Web/HTTP/CSP
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