README.md (6315B)
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 # dsnanmeanwd 22 23 > Calculate the [arithmetic mean][arithmetic-mean] of a single-precision floating-point strided array, ignoring `NaN` values, using Welford's 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@0d925ed05a6925fe1e213f07851ac761bf6aba96/lib/node_modules/@stdlib/stats/base/dsnanmeanwd/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 dsnanmeanwd = require( '@stdlib/stats/base/dsnanmeanwd' ); 48 ``` 49 50 #### dsnanmeanwd( N, x, stride ) 51 52 Computes the [arithmetic mean][arithmetic-mean] of a single-precision floating-point strided array `x`, ignoring `NaN` values, using Welford's 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, NaN, 2.0 ] ); 58 var N = x.length; 59 60 var v = dsnanmeanwd( 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, NaN ] ); 77 var N = floor( x.length / 2 ); 78 79 var v = dsnanmeanwd( 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, NaN ] ); 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 = dsnanmeanwd( N, x1, 2 ); 97 // returns 1.25 98 ``` 99 100 #### dsnanmeanwd.ndarray( N, x, stride, offset ) 101 102 Computes the [arithmetic mean][arithmetic-mean] of a single-precision floating-point strided array, ignoring `NaN` values and using Welford's algorithm with extended accumulation and alternative indexing semantics. 103 104 ```javascript 105 var Float32Array = require( '@stdlib/array/float32' ); 106 107 var x = new Float32Array( [ 1.0, -2.0, NaN, 2.0 ] ); 108 var N = x.length; 109 110 var v = dsnanmeanwd.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, NaN ] ); 125 var N = floor( x.length / 2 ); 126 127 var v = dsnanmeanwd.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 - If every indexed element is `NaN`, both functions return `NaN`. 141 - Accumulated intermediate values are stored as double-precision floating-point numbers. 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 dsnanmeanwd = require( '@stdlib/stats/base/dsnanmeanwd' ); 158 159 var x; 160 var i; 161 162 x = new Float32Array( 10 ); 163 for ( i = 0; i < x.length; i++ ) { 164 if ( randu() < 0.2 ) { 165 x[ i ] = NaN; 166 } else { 167 x[ i ] = round( (randu()*100.0) - 50.0 ); 168 } 169 } 170 console.log( x ); 171 172 var v = dsnanmeanwd( x.length, x, 1 ); 173 console.log( v ); 174 ``` 175 176 </section> 177 178 <!-- /.examples --> 179 180 * * * 181 182 <section class="references"> 183 184 ## References 185 186 - Welford, B. P. 1962. "Note on a Method for Calculating Corrected Sums of Squares and Products." _Technometrics_ 4 (3). Taylor & Francis: 419–20. doi:[10.1080/00401706.1962.10490022][@welford:1962a]. 187 - van Reeken, A. J. 1968. "Letters to the Editor: Dealing with Neely's Algorithms." _Communications of the ACM_ 11 (3): 149–50. doi:[10.1145/362929.362961][@vanreeken:1968a]. 188 189 </section> 190 191 <!-- /.references --> 192 193 <section class="links"> 194 195 [arithmetic-mean]: https://en.wikipedia.org/wiki/Arithmetic_mean 196 197 [@stdlib/array/float32]: https://www.npmjs.com/package/@stdlib/array-float32 198 199 [mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray 200 201 [@welford:1962a]: https://doi.org/10.1080/00401706.1962.10490022 202 203 [@vanreeken:1968a]: https://doi.org/10.1145/362929.362961 204 205 </section> 206 207 <!-- /.links -->