time-to-botec

Benchmark sampling in different programming languages
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README.md (3807B)

      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 # increwvariance
     22 
     23 > Compute an [exponentially weighted variance][moving-average] incrementally.
     24 
     25 <section class="intro">
     26 
     27 An [exponentially weighted variance][moving-average] can be defined recursively as
     28 
     29 <!-- <equation class="equation" label="eq:exponentially_weighted_variance" align="center" raw="S_n = \begin{cases} 0 & \textrm{if}\ n = 0 \\ (1 - \alpha) (S_{n-1} + \alpha(x_n - \mu_{n-1})^2) & \textrm{if}\ n > 0 \end{cases}" alt="Recursive definition for computing an exponentially weighted variance."> -->
     30 
     31 <div class="equation" align="center" data-raw-text="S_n = \begin{cases} 0 &amp; \textrm{if}\ n = 0 \\ (1 - \alpha) (S_{n-1} + \alpha(x_n - \mu_{n-1})^2) &amp; \textrm{if}\ n &gt; 0 \end{cases}" data-equation="eq:exponentially_weighted_variance">
     32     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@12be48682a7c25918504f886cbb80051c6ec8240/lib/node_modules/@stdlib/stats/incr/ewvariance/docs/img/equation_exponentially_weighted_variance.svg" alt="Recursive definition for computing an exponentially weighted variance.">
     33     <br>
     34 </div>
     35 
     36 <!-- </equation> -->
     37 
     38 where `μ` is the [exponentially weighted mean][@stdlib/stats/incr/ewmean].
     39 
     40 </section>
     41 
     42 <!-- /.intro -->
     43 
     44 <section class="usage">
     45 
     46 ## Usage
     47 
     48 ```javascript
     49 var increwvariance = require( '@stdlib/stats/incr/ewvariance' );
     50 ```
     51 
     52 #### increwvariance( alpha )
     53 
     54 Returns an accumulator `function` which incrementally computes an [exponentially weighted variance][moving-average], where `alpha` is a smoothing factor between `0` and `1`.
     55 
     56 ```javascript
     57 var accumulator = increwvariance( 0.5 );
     58 ```
     59 
     60 #### accumulator( \[x] )
     61 
     62 If provided an input value `x`, the accumulator function returns an updated variance. If not provided an input value `x`, the accumulator function returns the current variance.
     63 
     64 ```javascript
     65 var accumulator = increwvariance( 0.5 );
     66 
     67 var v = accumulator();
     68 // returns null
     69 
     70 v = accumulator( 2.0 );
     71 // returns 0.0
     72 
     73 v = accumulator( 1.0 );
     74 // returns 0.25
     75 
     76 v = accumulator( 3.0 );
     77 // returns 0.6875
     78 
     79 v = accumulator();
     80 // returns 0.6875
     81 ```
     82 
     83 </section>
     84 
     85 <!-- /.usage -->
     86 
     87 <section class="notes">
     88 
     89 ## Notes
     90 
     91 -   Input values are **not** type checked. If provided `NaN` or a value which, when used in computations, results in `NaN`, the accumulated value is `NaN` for **all** future invocations. If non-numeric inputs are possible, you are advised to type check and handle accordingly **before** passing the value to the accumulator function.
     92 
     93 </section>
     94 
     95 <!-- /.notes -->
     96 
     97 <section class="examples">
     98 
     99 ## Examples
    100 
    101 <!-- eslint no-undef: "error" -->
    102 
    103 ```javascript
    104 var randu = require( '@stdlib/random/base/randu' );
    105 var increwvariance = require( '@stdlib/stats/incr/ewvariance' );
    106 
    107 var accumulator;
    108 var v;
    109 var i;
    110 
    111 // Initialize an accumulator:
    112 accumulator = increwvariance( 0.5 );
    113 
    114 // For each simulated datum, update the exponentially weighted variance...
    115 for ( i = 0; i < 100; i++ ) {
    116     v = randu() * 100.0;
    117     accumulator( v );
    118 }
    119 console.log( accumulator() );
    120 ```
    121 
    122 </section>
    123 
    124 <!-- /.examples -->
    125 
    126 <section class="links">
    127 
    128 [moving-average]: https://en.wikipedia.org/wiki/Moving_average
    129 
    130 [@stdlib/stats/incr/ewmean]: https://www.npmjs.com/package/@stdlib/stats/tree/main/incr/ewmean
    131 
    132 </section>
    133 
    134 <!-- /.links -->