meanpn.js (2267B)
1 /** 2 * @license Apache-2.0 3 * 4 * Copyright (c) 2020 The Stdlib Authors. 5 * 6 * Licensed under the Apache License, Version 2.0 (the "License"); 7 * you may not use this file except in compliance with the License. 8 * You may obtain a copy of the License at 9 * 10 * http://www.apache.org/licenses/LICENSE-2.0 11 * 12 * Unless required by applicable law or agreed to in writing, software 13 * distributed under the License is distributed on an "AS IS" BASIS, 14 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 15 * See the License for the specific language governing permissions and 16 * limitations under the License. 17 */ 18 19 'use strict'; 20 21 // MODULES // 22 23 var gsumpw = require( '@stdlib/blas/ext/base/gsumpw' ); 24 var gapxsumpw = require( '@stdlib/blas/ext/base/gapxsumpw' ); 25 26 27 // MAIN // 28 29 /** 30 * Computes the arithmetic mean of a strided array using a two-pass error correction algorithm. 31 * 32 * ## Method 33 * 34 * - This implementation uses a two-pass approach, as suggested by Neely (1966). 35 * 36 * ## References 37 * 38 * - 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](https://doi.org/10.1145/365719.365958). 39 * - 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](https://doi.org/10.1145/3221269.3223036). 40 * 41 * @param {PositiveInteger} N - number of indexed elements 42 * @param {NumericArray} x - input array 43 * @param {integer} stride - stride length 44 * @returns {number} arithmetic mean 45 * 46 * @example 47 * var x = [ 1.0, -2.0, 2.0 ]; 48 * var N = x.length; 49 * 50 * var v = meanpn( N, x, 1 ); 51 * // returns ~0.3333 52 */ 53 function meanpn( N, x, stride ) { 54 var mu; 55 var c; 56 57 if ( N <= 0 ) { 58 return NaN; 59 } 60 if ( N === 1 || stride === 0 ) { 61 return x[ 0 ]; 62 } 63 // Compute an estimate for the meanpn: 64 mu = gsumpw( N, x, stride ) / N; 65 66 // Compute an error term: 67 c = gapxsumpw( N, -mu, x, stride ) / N; 68 69 return mu + c; 70 } 71 72 73 // EXPORTS // 74 75 module.exports = meanpn;