time-to-botec

Benchmark sampling in different programming languages
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README.md (4151B)

      1 <!--
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      3 @license Apache-2.0
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      5 Copyright (c) 2018 The Stdlib Authors.
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      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
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     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 # Entropy
     22 
     23 > [Discrete uniform][discrete-uniform-distribution] distribution [entropy][entropy].
     24 
     25 <!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
     26 
     27 <section class="intro">
     28 
     29 The [entropy][entropy] (in [nats][nats]) for a [discrete uniform][discrete-uniform-distribution] random variable is
     30 
     31 <!-- <equation class="equation" label="eq:discrete_uniform_entropy" align="center" raw="h\left( X \right) = \ln(b-a+1)" alt="Entropy for a discrete uniform distribution."> -->
     32 
     33 <div class="equation" align="center" data-raw-text="h\left( X \right) = \ln(b-a+1)" data-equation="eq:discrete_uniform_entropy">
     34     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@591cf9d5c3a0cd3c1ceec961e5c49d73a68374cb/lib/node_modules/@stdlib/stats/base/dists/discrete-uniform/entropy/docs/img/equation_discrete_uniform_entropy.svg" alt="Entropy for a discrete uniform distribution.">
     35     <br>
     36 </div>
     37 
     38 <!-- </equation> -->
     39 
     40 where `a` is the minimum support and `b` is the maximum support. The parameters must satisfy `a < b`.
     41 
     42 </section>
     43 
     44 <!-- /.intro -->
     45 
     46 <!-- Package usage documentation. -->
     47 
     48 <section class="usage">
     49 
     50 ## Usage
     51 
     52 ```javascript
     53 var entropy = require( '@stdlib/stats/base/dists/discrete-uniform/entropy' );
     54 ```
     55 
     56 #### entropy( a, b )
     57 
     58 Returns the [entropy][entropy] of a [discrete uniform][discrete-uniform-distribution] distribution with minimum support `a` and maximum support `b` (in [nats][nats]).
     59 
     60 ```javascript
     61 var v = entropy( 0, 1 );
     62 // returns ~0.693
     63 
     64 v = entropy( 4, 12 );
     65 // returns ~2.197
     66 
     67 v = entropy( 2, 8 );
     68 // returns ~1.946
     69 ```
     70 
     71 If `a` or `b` is not an integer value, the function returns `NaN`.
     72 
     73 ```javascript
     74 var v = entropy( 0.1, 2 );
     75 // returns NaN
     76 
     77 v = entropy( 0, 2.2 );
     78 // returns NaN
     79 
     80 v = entropy( NaN, 2 );
     81 // returns NaN
     82 
     83 v = entropy( 2, NaN );
     84 // returns NaN
     85 ```
     86 
     87 If provided `a > b`, the function returns `NaN`.
     88 
     89 ```javascript
     90 var v = entropy( 3, 2 );
     91 // returns NaN
     92 
     93 v = entropy( -1, -2 );
     94 // returns NaN
     95 ```
     96 
     97 </section>
     98 
     99 <!-- /.usage -->
    100 
    101 <!-- Package usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
    102 
    103 <section class="notes">
    104 
    105 </section>
    106 
    107 <!-- /.notes -->
    108 
    109 <!-- Package usage examples. -->
    110 
    111 <section class="examples">
    112 
    113 ## Examples
    114 
    115 <!-- eslint no-undef: "error" -->
    116 
    117 ```javascript
    118 var randint = require( '@stdlib/random/base/discrete-uniform' );
    119 var entropy = require( '@stdlib/stats/base/dists/discrete-uniform/entropy' );
    120 
    121 var randa = randint.factory( 0, 10 );
    122 var randb = randint.factory();
    123 var a;
    124 var b;
    125 var v;
    126 var i;
    127 
    128 for ( i = 0; i < 10; i++ ) {
    129     a = randa();
    130     b = randb( a, a+randa() );
    131     v = entropy( a, b );
    132     console.log( 'a: %d, b: %d, H(X;a,b): %d', a.toFixed( 4 ), b.toFixed( 4 ), v.toFixed( 4 ) );
    133 }
    134 ```
    135 
    136 </section>
    137 
    138 <!-- /.examples -->
    139 
    140 <!-- Section to include cited references. If references are included, add a horizontal rule *before* the section. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
    141 
    142 <section class="references">
    143 
    144 </section>
    145 
    146 <!-- /.references -->
    147 
    148 <!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
    149 
    150 <section class="links">
    151 
    152 [discrete-uniform-distribution]: https://en.wikipedia.org/wiki/Discrete_uniform_distribution
    153 
    154 [entropy]: https://en.wikipedia.org/wiki/Entropy_%28information_theory%29
    155 
    156 [nats]: https://en.wikipedia.org/wiki/Nat_%28unit%29
    157 
    158 </section>
    159 
    160 <!-- /.links -->