time-to-botec

Benchmark sampling in different programming languages
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README.md (4503B)

      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 > [Gamma][gamma-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 [gamma][gamma-distribution] random variable with shape parameter `α > 0` and rate parameter `β > 0` is
     30 
     31 <!-- <equation class="equation" label="eq:gamma_entropy" align="center" raw="h\left( X \right) = \alpha \,-\, \ln \beta \,+\, \ln[\Gamma(\alpha)] \,+\, (1 \,-\, \alpha)\psi(\alpha)" alt="Differential entropy for a gamma distribution."> -->
     32 
     33 <div class="equation" align="center" data-raw-text="h\left( X \right) = \alpha \,-\, \ln \beta \,+\, \ln[\Gamma(\alpha)] \,+\, (1 \,-\, \alpha)\psi(\alpha)" data-equation="eq:gamma_entropy">
     34     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/gamma/entropy/docs/img/equation_gamma_entropy.svg" alt="Differential entropy for a gamma distribution.">
     35     <br>
     36 </div>
     37 
     38 <!-- </equation> -->
     39 
     40 where `Γ` and `Ψ` denote the [gamma][gamma-function] and [digamma][digamma] function, respectively.
     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/gamma/entropy' );
     54 ```
     55 
     56 #### entropy( alpha, beta )
     57 
     58 Returns the [differential entropy][entropy] of a [gamma][gamma-distribution] distribution with shape parameter `alpha` and rate parameter `beta` (in [nats][nats]).
     59 
     60 ```javascript
     61 var v = entropy( 1.0, 1.0 );
     62 // returns 1.0
     63 
     64 v = entropy( 4.0, 12.0 );
     65 // returns ~-0.462
     66 
     67 v = entropy( 8.0, 2.0 );
     68 // returns ~1.723
     69 ```
     70 
     71 If provided `NaN` as any argument, the function returns `NaN`.
     72 
     73 ```javascript
     74 var v = entropy( NaN, 2.0 );
     75 // returns NaN
     76 
     77 v = entropy( 2.0, NaN );
     78 // returns NaN
     79 ```
     80 
     81 If provided `alpha <= 0`, the function returns `NaN`.
     82 
     83 ```javascript
     84 var v = entropy( 0.0, 1.0 );
     85 // returns NaN
     86 
     87 v = entropy( -1.0, 1.0 );
     88 // returns NaN
     89 ```
     90 
     91 If provided `beta <= 0`, the function returns `NaN`.
     92 
     93 ```javascript
     94 var v = entropy( 1.0, 0.0 );
     95 // returns NaN
     96 
     97 v = entropy( 1.0, -1.0 );
     98 // returns NaN
     99 ```
    100 
    101 </section>
    102 
    103 <!-- /.usage -->
    104 
    105 <!-- Package usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
    106 
    107 <section class="notes">
    108 
    109 </section>
    110 
    111 <!-- /.notes -->
    112 
    113 <!-- Package usage examples. -->
    114 
    115 <section class="examples">
    116 
    117 ## Examples
    118 
    119 <!-- eslint no-undef: "error" -->
    120 
    121 ```javascript
    122 var randu = require( '@stdlib/random/base/randu' );
    123 var EPS = require( '@stdlib/constants/float64/eps' );
    124 var entropy = require( '@stdlib/stats/base/dists/gamma/entropy' );
    125 
    126 var alpha;
    127 var beta;
    128 var v;
    129 var i;
    130 
    131 for ( i = 0; i < 10; i++ ) {
    132     alpha = ( randu()*10.0 ) + EPS;
    133     beta = ( randu()*10.0 ) + EPS;
    134     v = entropy( alpha, beta );
    135     console.log( 'α: %d, β: %d, h(X;α,β): %d', alpha.toFixed( 4 ), beta.toFixed( 4 ), v.toFixed( 4 ) );
    136 }
    137 ```
    138 
    139 </section>
    140 
    141 <!-- /.examples -->
    142 
    143 <!-- 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. -->
    144 
    145 <section class="references">
    146 
    147 </section>
    148 
    149 <!-- /.references -->
    150 
    151 <!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
    152 
    153 <section class="links">
    154 
    155 [gamma-distribution]: https://en.wikipedia.org/wiki/Gamma_distribution
    156 
    157 [entropy]: https://en.wikipedia.org/wiki/Entropy_%28information_theory%29
    158 
    159 [nats]: https://en.wikipedia.org/wiki/Nat_%28unit%29
    160 
    161 [gamma-function]: https://en.wikipedia.org/wiki/Gamma_function
    162 
    163 [digamma]: https://en.wikipedia.org/wiki/Digamma_function
    164 
    165 </section>
    166 
    167 <!-- /.links -->