README.md (6312B)
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 # dsmeanpn 22 23 > Calculate the [arithmetic mean][arithmetic-mean] of a single-precision floating-point strided array using a two-pass error correction algorithm with extended accumulation and returning an extended precision result. 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@6453bd4f7916e1518ccdbbc20396ba7d13a348ba/lib/node_modules/@stdlib/stats/base/dsmeanpn/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 dsmeanpn = require( '@stdlib/stats/base/dsmeanpn' ); 48 ``` 49 50 #### dsmeanpn( N, x, stride ) 51 52 Computes the [arithmetic mean][arithmetic-mean] of a single-precision floating-point strided array `x` using a two-pass error correction algorithm with extended accumulation and returning an extended precision result. 53 54 ```javascript 55 var Float32Array = require( '@stdlib/array/float32' ); 56 57 var x = new Float32Array( [ 1.0, -2.0, 2.0 ] ); 58 var N = x.length; 59 60 var v = dsmeanpn( N, x, 1 ); 61 // returns ~0.3333 62 ``` 63 64 The function has the following parameters: 65 66 - **N**: number of indexed elements. 67 - **x**: input [`Float32Array`][@stdlib/array/float32]. 68 - **stride**: index increment for `x`. 69 70 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`, 71 72 ```javascript 73 var Float32Array = require( '@stdlib/array/float32' ); 74 var floor = require( '@stdlib/math/base/special/floor' ); 75 76 var x = new Float32Array( [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ] ); 77 var N = floor( x.length / 2 ); 78 79 var v = dsmeanpn( N, x, 2 ); 80 // returns 1.25 81 ``` 82 83 Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views. 84 85 <!-- eslint-disable stdlib/capitalized-comments --> 86 87 ```javascript 88 var Float32Array = require( '@stdlib/array/float32' ); 89 var floor = require( '@stdlib/math/base/special/floor' ); 90 91 var x0 = new Float32Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] ); 92 var x1 = new Float32Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element 93 94 var N = floor( x0.length / 2 ); 95 96 var v = dsmeanpn( N, x1, 2 ); 97 // returns 1.25 98 ``` 99 100 #### dsmeanpn.ndarray( N, x, stride, offset ) 101 102 Computes the [arithmetic mean][arithmetic-mean] of a single-precision floating-point strided array using a two-pass error correction algorithm with extended accumulation and alternative indexing semantics and returning an extended precision result. 103 104 ```javascript 105 var Float32Array = require( '@stdlib/array/float32' ); 106 107 var x = new Float32Array( [ 1.0, -2.0, 2.0 ] ); 108 var N = x.length; 109 110 var v = dsmeanpn.ndarray( N, x, 1, 0 ); 111 // returns ~0.33333 112 ``` 113 114 The function has the following additional parameters: 115 116 - **offset**: starting index for `x`. 117 118 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 119 120 ```javascript 121 var Float32Array = require( '@stdlib/array/float32' ); 122 var floor = require( '@stdlib/math/base/special/floor' ); 123 124 var x = new Float32Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] ); 125 var N = floor( x.length / 2 ); 126 127 var v = dsmeanpn.ndarray( N, x, 2, 1 ); 128 // returns 1.25 129 ``` 130 131 </section> 132 133 <!-- /.usage --> 134 135 <section class="notes"> 136 137 ## Notes 138 139 - If `N <= 0`, both functions return `NaN`. 140 - Accumulated intermediate values are stored as double-precision floating-point numbers. 141 142 </section> 143 144 <!-- /.notes --> 145 146 <section class="examples"> 147 148 ## Examples 149 150 <!-- eslint no-undef: "error" --> 151 152 ```javascript 153 var randu = require( '@stdlib/random/base/randu' ); 154 var round = require( '@stdlib/math/base/special/round' ); 155 var Float32Array = require( '@stdlib/array/float32' ); 156 var dsmeanpn = require( '@stdlib/stats/base/dsmeanpn' ); 157 158 var x; 159 var i; 160 161 x = new Float32Array( 10 ); 162 for ( i = 0; i < x.length; i++ ) { 163 x[ i ] = round( (randu()*100.0) - 50.0 ); 164 } 165 console.log( x ); 166 167 var v = dsmeanpn( x.length, x, 1 ); 168 console.log( v ); 169 ``` 170 171 </section> 172 173 <!-- /.examples --> 174 175 * * * 176 177 <section class="references"> 178 179 ## References 180 181 - 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]. 182 - 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]. 183 184 </section> 185 186 <!-- /.references --> 187 188 <section class="links"> 189 190 [arithmetic-mean]: https://en.wikipedia.org/wiki/Arithmetic_mean 191 192 [@stdlib/array/float32]: https://www.npmjs.com/package/@stdlib/array-float32 193 194 [mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray 195 196 [@neely:1966a]: https://doi.org/10.1145/365719.365958 197 198 [@schubert:2018a]: https://doi.org/10.1145/3221269.3223036 199 200 </section> 201 202 <!-- /.links -->