README.md (6342B)
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 # dsmeanpw 22 23 > Calculate the [arithmetic mean][arithmetic-mean] of a single-precision floating-point strided array using pairwise summation 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@bef48a7ab1318364d0bf178f0e69d081a61688c3/lib/node_modules/@stdlib/stats/base/dsmeanpw/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 dsmeanpw = require( '@stdlib/stats/base/dsmeanpw' ); 48 ``` 49 50 #### dsmeanpw( N, x, stride ) 51 52 Computes the [arithmetic mean][arithmetic-mean] of a single-precision floating-point strided array `x` using pairwise summation 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 = dsmeanpw( 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 = dsmeanpw( 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 = dsmeanpw( N, x1, 2 ); 97 // returns 1.25 98 ``` 99 100 #### dsmeanpw.ndarray( N, x, stride, offset ) 101 102 Computes the [arithmetic mean][arithmetic-mean] of a single-precision floating-point strided array using pairwise summation 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 = dsmeanpw.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 = dsmeanpw.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 - In general, pairwise summation is more numerically stable than ordinary recursive summation (i.e., "simple" summation), with slightly worse performance. While not the most numerically stable summation technique (e.g., compensated summation techniques such as the Kahan–Babuška-Neumaier algorithm are generally more numerically stable), pairwise summation strikes a reasonable balance between numerical stability and performance. If either numerical stability or performance is more desirable for your use case, consider alternative summation techniques. 142 143 </section> 144 145 <!-- /.notes --> 146 147 <section class="examples"> 148 149 ## Examples 150 151 <!-- eslint no-undef: "error" --> 152 153 ```javascript 154 var randu = require( '@stdlib/random/base/randu' ); 155 var round = require( '@stdlib/math/base/special/round' ); 156 var Float32Array = require( '@stdlib/array/float32' ); 157 var dsmeanpw = require( '@stdlib/stats/base/dsmeanpw' ); 158 159 var x; 160 var i; 161 162 x = new Float32Array( 10 ); 163 for ( i = 0; i < x.length; i++ ) { 164 x[ i ] = round( (randu()*100.0) - 50.0 ); 165 } 166 console.log( x ); 167 168 var v = dsmeanpw( x.length, x, 1 ); 169 console.log( v ); 170 ``` 171 172 </section> 173 174 <!-- /.examples --> 175 176 * * * 177 178 <section class="references"> 179 180 ## References 181 182 - Higham, Nicholas J. 1993. "The Accuracy of Floating Point Summation." _SIAM Journal on Scientific Computing_ 14 (4): 783–99. doi:[10.1137/0914050][@higham:1993a]. 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 [@higham:1993a]: https://doi.org/10.1137/0914050 197 198 </section> 199 200 <!-- /.links -->