time-to-botec

Benchmark sampling in different programming languages
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README.md (3983B)

      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 > [Laplace][laplace-distribution] distribution [differential 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 [differential entropy][entropy] (in [nats][nats]) for a [Laplace][laplace-distribution] random variable with location `μ` and scale `b > 0` is
     30 
     31 <!-- <equation class="equation" label="eq:laplace_entropy" align="center" raw="h\left( X \right) = \ln(2be)" alt="Differential entropy for a Laplace distribution."> -->
     32 
     33 <div class="equation" align="center" data-raw-text="h\left( X \right) = \ln(2be)" data-equation="eq:laplace_entropy">
     34     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/laplace/entropy/docs/img/equation_laplace_entropy.svg" alt="Differential entropy for a Laplace distribution.">
     35     <br>
     36 </div>
     37 
     38 <!-- </equation> -->
     39 
     40 where `e` is [Euler's number][e].
     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/laplace/entropy' );
     54 ```
     55 
     56 #### entropy( mu, b )
     57 
     58 Returns the [differential entropy][entropy] for a [Laplace][laplace-distribution] distribution with location parameter `mu` and scale parameter `b` (in [nats][nats]).
     59 
     60 ```javascript
     61 var y = entropy( 2.0, 1.0 );
     62 // returns ~1.693
     63 
     64 y = entropy( 0.0, 1.0 );
     65 // returns ~1.693
     66 
     67 y = entropy( -1.0, 4.0 );
     68 // returns ~3.079
     69 ```
     70 
     71 If provided `NaN` as any argument, the function returns `NaN`.
     72 
     73 ```javascript
     74 var y = entropy( NaN, 1.0 );
     75 // returns NaN
     76 
     77 y = entropy( 0.0, NaN );
     78 // returns NaN
     79 ```
     80 
     81 If provided `b <= 0`, the function returns `NaN`.
     82 
     83 ```javascript
     84 var y = entropy( 0.0, 0.0 );
     85 // returns NaN
     86 
     87 y = entropy( 0.0, -1.0 );
     88 // returns NaN
     89 ```
     90 
     91 </section>
     92 
     93 <!-- /.usage -->
     94 
     95 <!-- Package usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
     96 
     97 <section class="notes">
     98 
     99 </section>
    100 
    101 <!-- /.notes -->
    102 
    103 <!-- Package usage examples. -->
    104 
    105 <section class="examples">
    106 
    107 ## Examples
    108 
    109 <!-- eslint no-undef: "error" -->
    110 
    111 ```javascript
    112 var randu = require( '@stdlib/random/base/randu' );
    113 var entropy = require( '@stdlib/stats/base/dists/laplace/entropy' );
    114 
    115 var mu;
    116 var b;
    117 var y;
    118 var i;
    119 
    120 for ( i = 0; i < 10; i++ ) {
    121     mu = ( randu()*10.0 ) - 5.0;
    122     b = randu() * 20.0;
    123     y = entropy( mu, b );
    124     console.log( 'µ: %d, b: %d, h(X;µ,b): %d', mu.toFixed( 4 ), b.toFixed( 4 ), y.toFixed( 4 ) );
    125 }
    126 ```
    127 
    128 </section>
    129 
    130 <!-- /.examples -->
    131 
    132 <!-- 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. -->
    133 
    134 <section class="references">
    135 
    136 </section>
    137 
    138 <!-- /.references -->
    139 
    140 <!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
    141 
    142 <section class="links">
    143 
    144 [e]: https://en.wikipedia.org/wiki/E_%28mathematical_constant%29
    145 
    146 [laplace-distribution]: https://en.wikipedia.org/wiki/Laplace_distribution
    147 
    148 [entropy]: https://en.wikipedia.org/wiki/Entropy_%28information_theory%29
    149 
    150 [nats]: https://en.wikipedia.org/wiki/Nat_%28unit%29
    151 
    152 </section>
    153 
    154 <!-- /.links -->