README.md (4145B)
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 # incrmhmean 22 23 > Compute a moving [harmonic mean][harmonic-mean] incrementally. 24 25 <section class="intro"> 26 27 The [harmonic mean][harmonic-mean] of positive real numbers `x_0, x_1, ..., x_{n-1}` is defined as 28 29 <!-- <equation class="equation" label="eq:harmonic_mean" align="center" raw="\begin{align}H &= \frac{n}{\frac{1}{x_0} + \frac{1}{x_1} + \cdots + \frac{1}{x_{n-1}}} \\ &= \frac{n}{\sum_{i=0}^{n-1} \frac{1}{x_i}} \\ &= \biggl( \frac{\sum_{i=0}^{n-1} \frac{1}{x_i}}{n} \biggr)^{-1}\end{align}" alt="Equation for the harmonic mean."> --> 30 31 <div class="equation" align="center" data-raw-text="\begin{align}H &= \frac{n}{\frac{1}{x_0} + \frac{1}{x_1} + \cdots + \frac{1}{x_{n-1}}} \\ &= \frac{n}{\sum_{i=0}^{n-1} \frac{1}{x_i}} \\ &= \biggl( \frac{\sum_{i=0}^{n-1} \frac{1}{x_i}}{n} \biggr)^{-1}\end{align}" data-equation="eq:harmonic_mean"> 32 <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@0a561712608b99b59d9243f7d478a2e2a019a130/lib/node_modules/@stdlib/stats/incr/mhmean/docs/img/equation_harmonic_mean.svg" alt="Equation for the harmonic mean."> 33 <br> 34 </div> 35 36 <!-- </equation> --> 37 38 </section> 39 40 <!-- /.intro --> 41 42 <section class="usage"> 43 44 ## Usage 45 46 ```javascript 47 var incrmhmean = require( '@stdlib/stats/incr/mhmean' ); 48 ``` 49 50 #### incrmhmean( window ) 51 52 Returns an accumulator `function` which incrementally computes a moving [harmonic mean][harmonic-mean]. The `window` parameter defines the number of values over which to compute the moving [harmonic mean][harmonic-mean]. 53 54 ```javascript 55 var accumulator = incrmhmean( 3 ); 56 ``` 57 58 #### accumulator( \[x] ) 59 60 If provided an input value `x`, the accumulator function returns an updated [harmonic mean][harmonic-mean]. If not provided an input value `x`, the accumulator function returns the current [harmonic-mean][harmonic-mean]. 61 62 ```javascript 63 var accumulator = incrmhmean( 3 ); 64 65 var v = accumulator(); 66 // returns null 67 68 // Fill the window... 69 v = accumulator( 2.0 ); // [2.0] 70 // returns 2.0 71 72 v = accumulator( 1.0 ); // [2.0, 1.0] 73 // returns ~1.33 74 75 v = accumulator( 3.0 ); // [2.0, 1.0, 3.0] 76 // returns ~1.64 77 78 // Window begins sliding... 79 v = accumulator( 7.0 ); // [1.0, 3.0, 7.0] 80 // returns ~2.03 81 82 v = accumulator( 5.0 ); // [3.0, 7.0, 5.0] 83 // returns ~4.44 84 85 v = accumulator(); 86 // returns ~4.44 87 ``` 88 89 </section> 90 91 <!-- /.usage --> 92 93 <section class="notes"> 94 95 ## Notes 96 97 - 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 **at least** `W-1` 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. 98 - As `W` values are needed to fill the window buffer, the first `W-1` returned values are calculated from smaller sample sizes. Until the window is full, each returned value is calculated from all provided values. 99 100 </section> 101 102 <!-- /.notes --> 103 104 <section class="examples"> 105 106 ## Examples 107 108 <!-- eslint no-undef: "error" --> 109 110 ```javascript 111 var randu = require( '@stdlib/random/base/randu' ); 112 var incrmhmean = require( '@stdlib/stats/incr/mhmean' ); 113 114 var accumulator; 115 var v; 116 var i; 117 118 // Initialize an accumulator: 119 accumulator = incrmhmean( 5 ); 120 121 // For each simulated datum, update the moving harmonic mean... 122 for ( i = 0; i < 100; i++ ) { 123 v = randu() * 100.0; 124 accumulator( v ); 125 } 126 console.log( accumulator() ); 127 ``` 128 129 </section> 130 131 <!-- /.examples --> 132 133 <section class="links"> 134 135 [harmonic-mean]: https://en.wikipedia.org/wiki/Harmonic_mean 136 137 </section> 138 139 <!-- /.links -->