README.md (6010B)
1 <!-- 2 3 @license Apache-2.0 4 5 Copyright (c) 2020 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 # meanpn 22 23 > Calculate the [arithmetic mean][arithmetic-mean] of a strided array using a two-pass error correction algorithm. 24 25 <section class="intro"> 26 27 The [arithmetic mean][arithmetic-mean] is defined as 28 29 <!-- <equation class="equation" label="eq:arithmetic_mean" align="center" raw="\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i" alt="Equation for the arithmetic mean."> --> 30 31 <div class="equation" align="center" data-raw-text="\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i" data-equation="eq:arithmetic_mean"> 32 <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@7158616c9399e313d462e91b1a5c0f82d090c372/lib/node_modules/@stdlib/stats/base/meanpn/docs/img/equation_arithmetic_mean.svg" alt="Equation for the arithmetic 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 meanpn = require( '@stdlib/stats/base/meanpn' ); 48 ``` 49 50 #### meanpn( N, x, stride ) 51 52 Computes the [arithmetic mean][arithmetic-mean] of a strided array `x` using a two-pass error correction algorithm. 53 54 ```javascript 55 var x = [ 1.0, -2.0, 2.0 ]; 56 var N = x.length; 57 58 var v = meanpn( N, x, 1 ); 59 // returns ~0.3333 60 ``` 61 62 The function has the following parameters: 63 64 - **N**: number of indexed elements. 65 - **x**: input [`Array`][mdn-array] or [`typed array`][mdn-typed-array]. 66 - **stride**: index increment for `x`. 67 68 The `N` and `stride` parameters determine which elements in `x` are accessed at runtime. For example, to compute the [arithmetic mean][arithmetic-mean] of every other element in `x`, 69 70 ```javascript 71 var floor = require( '@stdlib/math/base/special/floor' ); 72 73 var x = [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ]; 74 var N = floor( x.length / 2 ); 75 76 var v = meanpn( N, x, 2 ); 77 // returns 1.25 78 ``` 79 80 Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views. 81 82 <!-- eslint-disable stdlib/capitalized-comments --> 83 84 ```javascript 85 var Float64Array = require( '@stdlib/array/float64' ); 86 var floor = require( '@stdlib/math/base/special/floor' ); 87 88 var x0 = new Float64Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] ); 89 var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element 90 91 var N = floor( x0.length / 2 ); 92 93 var v = meanpn( N, x1, 2 ); 94 // returns 1.25 95 ``` 96 97 #### meanpn.ndarray( N, x, stride, offset ) 98 99 Computes the [arithmetic mean][arithmetic-mean] of a strided array using a two-pass error correction algorithm and alternative indexing semantics. 100 101 ```javascript 102 var x = [ 1.0, -2.0, 2.0 ]; 103 var N = x.length; 104 105 var v = meanpn.ndarray( N, x, 1, 0 ); 106 // returns ~0.33333 107 ``` 108 109 The function has the following additional parameters: 110 111 - **offset**: starting index for `x`. 112 113 While [`typed array`][mdn-typed-array] views mandate a view offset based on the underlying `buffer`, the `offset` parameter supports indexing semantics based on a starting index. For example, to calculate the [arithmetic mean][arithmetic-mean] for every other value in `x` starting from the second value 114 115 ```javascript 116 var floor = require( '@stdlib/math/base/special/floor' ); 117 118 var x = [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ]; 119 var N = floor( x.length / 2 ); 120 121 var v = meanpn.ndarray( N, x, 2, 1 ); 122 // returns 1.25 123 ``` 124 125 </section> 126 127 <!-- /.usage --> 128 129 <section class="notes"> 130 131 ## Notes 132 133 - If `N <= 0`, both functions return `NaN`. 134 - Depending on the environment, the typed versions ([`dmeanpn`][@stdlib/stats/base/dmeanpn], [`smeanpn`][@stdlib/stats/base/smeanpn], etc.) are likely to be significantly more performant. 135 136 </section> 137 138 <!-- /.notes --> 139 140 <section class="examples"> 141 142 ## Examples 143 144 <!-- eslint no-undef: "error" --> 145 146 ```javascript 147 var randu = require( '@stdlib/random/base/randu' ); 148 var round = require( '@stdlib/math/base/special/round' ); 149 var Float64Array = require( '@stdlib/array/float64' ); 150 var meanpn = require( '@stdlib/stats/base/meanpn' ); 151 152 var x; 153 var i; 154 155 x = new Float64Array( 10 ); 156 for ( i = 0; i < x.length; i++ ) { 157 x[ i ] = round( (randu()*100.0) - 50.0 ); 158 } 159 console.log( x ); 160 161 var v = meanpn( x.length, x, 1 ); 162 console.log( v ); 163 ``` 164 165 </section> 166 167 <!-- /.examples --> 168 169 * * * 170 171 <section class="references"> 172 173 ## References 174 175 - Neely, Peter M. 1966. "Comparison of Several Algorithms for Computation of Means, Standard Deviations and Correlation Coefficients." _Communications of the ACM_ 9 (7). Association for Computing Machinery: 496–99. doi:[10.1145/365719.365958][@neely:1966a]. 176 - Schubert, Erich, and Michael Gertz. 2018. "Numerically Stable Parallel Computation of (Co-)Variance." In _Proceedings of the 30th International Conference on Scientific and Statistical Database Management_. New York, NY, USA: Association for Computing Machinery. doi:[10.1145/3221269.3223036][@schubert:2018a]. 177 178 </section> 179 180 <!-- /.references --> 181 182 <section class="links"> 183 184 [arithmetic-mean]: https://en.wikipedia.org/wiki/Arithmetic_mean 185 186 [mdn-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array 187 188 [mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray 189 190 [@stdlib/stats/base/dmeanpn]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dmeanpn 191 192 [@stdlib/stats/base/smeanpn]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/smeanpn 193 194 [@neely:1966a]: https://doi.org/10.1145/365719.365958 195 196 [@schubert:2018a]: https://doi.org/10.1145/3221269.3223036 197 198 </section> 199 200 <!-- /.links -->