time-to-botec

Benchmark sampling in different programming languages
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README.md (3123B)

      1 <!--
      2 
      3 @license Apache-2.0
      4 
      5 Copyright (c) 2018 The Stdlib Authors.
      6 
      7 Licensed under the Apache License, Version 2.0 (the "License");
      8 you may not use this file except in compliance with the License.
      9 You may obtain a copy of the License at
     10 
     11    http://www.apache.org/licenses/LICENSE-2.0
     12 
     13 Unless required by applicable law or agreed to in writing, software
     14 distributed under the License is distributed on an "AS IS" BASIS,
     15 WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
     16 See the License for the specific language governing permissions and
     17 limitations under the License.
     18 
     19 -->
     20 
     21 # beta
     22 
     23 > [Beta function][beta-function].
     24 
     25 <section class="intro">
     26 
     27 The [beta function][beta-function], also called the Euler integral, is defined as
     28 
     29 <!-- <equation class="equation" label="eq:beta_function" align="center" raw="\operatorname{Beta}(x,y) = \int_0^1t^{x-1}(1-t)^{y-1}\,\mathrm{d}t" alt="Equation for the beta function."> -->
     30 
     31 <div class="equation" align="center" data-raw-text="\operatorname{Beta}(x,y) = \int_0^1t^{x-1}(1-t)^{y-1}\,\mathrm{d}t" data-equation="eq:beta_function">
     32     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bb29798906e119fcb2af99e94b60407a270c9b32/lib/node_modules/@stdlib/math/base/special/beta/docs/img/equation_beta_function.svg" alt="Equation for the beta function.">
     33     <br>
     34 </div>
     35 
     36 <!-- </equation> -->
     37 
     38 The [beta function][beta-function] is related to the [Gamma function][gamma-function] via the following equation
     39 
     40 <!-- <equation class="equation" label="eq:beta_function2" align="center" raw="\operatorname{Beta}(x,y)=\dfrac{\Gamma(x)\,\Gamma(y)}{\Gamma(x+y)} \!" alt="Beta function expressed in terms of the Gamma function."> -->
     41 
     42 <div class="equation" align="center" data-raw-text="\operatorname{Beta}(x,y)=\dfrac{\Gamma(x)\,\Gamma(y)}{\Gamma(x+y)} \!" data-equation="eq:beta_function2">
     43     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bb29798906e119fcb2af99e94b60407a270c9b32/lib/node_modules/@stdlib/math/base/special/beta/docs/img/equation_beta_function2.svg" alt="Beta function expressed in terms of the Gamma function.">
     44     <br>
     45 </div>
     46 
     47 <!-- </equation> -->
     48 
     49 </section>
     50 
     51 <!-- /.intro -->
     52 
     53 <section class="usage">
     54 
     55 ## Usage
     56 
     57 ```javascript
     58 var beta = require( '@stdlib/math/base/special/beta' );
     59 ```
     60 
     61 #### beta( x, y )
     62 
     63 Evaluates the [beta function][beta-function].
     64 
     65 ```javascript
     66 var val = beta( 0.0, 0.5 );
     67 // returns Infinity
     68 
     69 val = beta( 1.0, 1.0 );
     70 // returns 1.0
     71 
     72 val = beta( -1.0, 2.0 );
     73 // returns NaN
     74 
     75 val = beta( 5.0, 0.2 );
     76 // returns ~3.382
     77 
     78 val = beta( 4.0, 1.0 );
     79 // returns 0.25
     80 ```
     81 
     82 </section>
     83 
     84 <!-- /.usage -->
     85 
     86 <section class="examples">
     87 
     88 ## Examples
     89 
     90 <!-- eslint no-undef: "error" -->
     91 
     92 ```javascript
     93 var beta = require( '@stdlib/math/base/special/beta' );
     94 var x;
     95 var y;
     96 
     97 for ( x = 0; x < 10; x++ ) {
     98     for ( y = 10; y > 0; y-- ) {
     99         console.log( 'x: %d, \t y: %d, \t f(x,y): %d', x, y, beta( x, y ) );
    100     }
    101 }
    102 ```
    103 
    104 </section>
    105 
    106 <!-- /.examples -->
    107 
    108 <section class="links">
    109 
    110 [beta-function]: http://en.wikipedia.org/wiki/Beta_function
    111 
    112 [gamma-function]: https://en.wikipedia.org/wiki/Gamma_function
    113 
    114 </section>
    115 
    116 <!-- /.links -->