time-to-botec

README.md (5458B)

---

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 # evalrational
 
 > Evaluate a [rational function][rational-function].
 
 <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="usage">
 
 ## Usage
 
 ```javascript
 var evalrational = require( '@stdlib/math/base/tools/evalrational' );
 ```
 
 #### evalrational( P, Q, x )
 
 Evaluates a [rational function][rational-function] at a value `x`. The coefficients `P` and `Q` are expected to be arrays of the **same** length.
 
 ```javascript
 var P = [ -6.0, -5.0 ];
 var Q = [ 3.0, 0.5 ];
 
 var v = evalrational( 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
 // 2x^3 + 4x^2 - 5x^1 - 6x^0 => degree 4
 var P = [ -6.0, -5.0, 4.0, 2.0 ];
 
 // 0.5x^1 + 3x^0 => degree 2
 var Q = [ 3.0, 0.5, 0.0, 0.0 ]; // zero-padded
 
 var v = evalrational( 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.
 
 #### evalrational.factory( P, Q )
 
 Uses code generation to in-line coefficients and return a `function` for evaluating a [rational function][rational-function].
 
 ```javascript
 var P = [ 20.0, 8.0, 3.0 ];
 var Q = [ 10.0, 9.0, 1.0 ];
 
 var rational = evalrational.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
 
 -   For hot code paths in which coefficients are invariant, a compiled function will be more performant than `evalrational()`.
 -   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 randu = require( '@stdlib/random/base/randu' );
 var round = require( '@stdlib/math/base/special/round' );
 var Float64Array = require( '@stdlib/array/float64' );
 var evalrational = require( '@stdlib/math/base/tools/evalrational' );
 
 var rational;
 var sign;
 var len;
 var P;
 var Q;
 var v;
 var i;
 
 // Create two arrays of random coefficients...
 len = 10;
 P = new Float64Array( len );
 Q = new Float64Array( len );
 for ( i = 0; i < len; i++ ) {
     if ( randu() < 0.5 ) {
         sign = -1.0;
     } else {
         sign = 1.0;
     }
     P[ i ] = sign * round( randu()*100 );
     Q[ i ] = sign * round( randu()*100 );
 }
 
 // Evaluate the rational function at random values...
 for ( i = 0; i < 100; i++ ) {
     v = randu() * 100.0;
     console.log( 'f(%d) = %d', v, evalrational( P, Q, v ) );
 }
 
 // Generate an `evalrational` function...
 rational = evalrational.factory( P, Q );
 for ( i = 0; i < 100; i++ ) {
     v = (randu()*100.0) - 50.0;
     console.log( 'f(%d) = %d', v, rational( v ) );
 }
 ```
 
 </section>
 
 <!-- /.examples -->
 
 <section class="links">
 
 [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
 
 </section>
 
 <!-- /.links -->