time-to-botec

Benchmark sampling in different programming languages
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README.md (4576B)

      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
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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 # incrcovariance
     22 
     23 > Compute an [unbiased sample covariance][covariance] incrementally.
     24 
     25 <section class="intro">
     26 
     27 For unknown population means, the [unbiased sample covariance][covariance] is defined as
     28 
     29 <!-- <equation class="equation" label="eq:unbiased_sample_covariance_unknown_means" align="center" raw="\operatorname{cov_n} = \frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x}_n)(y_i - \bar{y}_n)" alt="Equation for the unbiased sample covariance for unknown population means."> -->
     30 
     31 <div class="equation" align="center" data-raw-text="\operatorname{cov_n} = \frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x}_n)(y_i - \bar{y}_n)" data-equation="eq:unbiased_sample_covariance_unknown_means">
     32     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@49d8cabda84033d55d7b8069f19ee3dd8b8d1496/lib/node_modules/@stdlib/stats/incr/covariance/docs/img/equation_unbiased_sample_covariance_unknown_means.svg" alt="Equation for the unbiased sample covariance for unknown population means.">
     33     <br>
     34 </div>
     35 
     36 <!-- </equation> -->
     37 
     38 For known population means, the [unbiased sample covariance][covariance] is defined as
     39 
     40 <!-- <equation class="equation" label="eq:unbiased_sample_covariance_known_means" align="center" raw="\operatorname{cov_n} = \frac{1}{n} \sum_{i=0}^{n-1} (x_i - \mu_x)(y_i - \mu_y)" alt="Equation for the unbiased sample covariance for known population means."> -->
     41 
     42 <div class="equation" align="center" data-raw-text="\operatorname{cov_n} = \frac{1}{n} \sum_{i=0}^{n-1} (x_i - \mu_x)(y_i - \mu_y)" data-equation="eq:unbiased_sample_covariance_known_means">
     43     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@27e2a43c70db648bb5bbc3fd0cdee050c25adc0b/lib/node_modules/@stdlib/stats/incr/covariance/docs/img/equation_unbiased_sample_covariance_known_means.svg" alt="Equation for the unbiased sample covariance for known population means.">
     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 incrcovariance = require( '@stdlib/stats/incr/covariance' );
     59 ```
     60 
     61 #### incrcovariance( \[mx, my] )
     62 
     63 Returns an accumulator `function` which incrementally computes an [unbiased sample covariance][covariance].
     64 
     65 ```javascript
     66 var accumulator = incrcovariance();
     67 ```
     68 
     69 If the means are already known, provide `mx` and `my` arguments.
     70 
     71 ```javascript
     72 var accumulator = incrcovariance( 3.0, -5.5 );
     73 ```
     74 
     75 #### accumulator( \[x, y] )
     76 
     77 If provided input values `x` and `y`, the accumulator function returns an updated [unbiased sample covariance][covariance]. If not provided input values `x` and `y`, the accumulator function returns the current [unbiased sample covariance][covariance].
     78 
     79 ```javascript
     80 var accumulator = incrcovariance();
     81 
     82 var v = accumulator( 2.0, 1.0 );
     83 // returns 0.0
     84 
     85 v = accumulator( 1.0, -5.0 );
     86 // returns 3.0
     87 
     88 v = accumulator( 3.0, 3.14 );
     89 // returns 4.07
     90 
     91 v = accumulator();
     92 // returns 4.07
     93 ```
     94 
     95 </section>
     96 
     97 <!-- /.usage -->
     98 
     99 <section class="notes">
    100 
    101 ## Notes
    102 
    103 -   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.
    104 
    105 </section>
    106 
    107 <!-- /.notes -->
    108 
    109 <section class="examples">
    110 
    111 ## Examples
    112 
    113 <!-- eslint no-undef: "error" -->
    114 
    115 ```javascript
    116 var randu = require( '@stdlib/random/base/randu' );
    117 var incrcovariance = require( '@stdlib/stats/incr/covariance' );
    118 
    119 var accumulator;
    120 var x;
    121 var y;
    122 var i;
    123 
    124 // Initialize an accumulator:
    125 accumulator = incrcovariance();
    126 
    127 // For each simulated datum, update the unbiased sample covariance...
    128 for ( i = 0; i < 100; i++ ) {
    129     x = randu() * 100.0;
    130     y = randu() * 100.0;
    131     accumulator( x, y );
    132 }
    133 console.log( accumulator() );
    134 ```
    135 
    136 </section>
    137 
    138 <!-- /.examples -->
    139 
    140 <section class="links">
    141 
    142 [covariance]: https://en.wikipedia.org/wiki/Covariance
    143 
    144 </section>
    145 
    146 <!-- /.links -->