variancepn.js (2488B)
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 25 26 // MAIN // 27 28 /** 29 * Computes the variance of a strided array using a two-pass algorithm. 30 * 31 * ## Method 32 * 33 * - This implementation uses a two-pass approach, as suggested by Neely (1966). 34 * 35 * ## References 36 * 37 * - 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). 38 * - 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). 39 * 40 * @param {PositiveInteger} N - number of indexed elements 41 * @param {number} correction - degrees of freedom adjustment 42 * @param {NumericArray} x - input array 43 * @param {integer} stride - stride length 44 * @returns {number} variance 45 * 46 * @example 47 * var x = [ 1.0, -2.0, 2.0 ]; 48 * var N = x.length; 49 * 50 * var v = variancepn( N, 1, x, 1 ); 51 * // returns ~4.3333 52 */ 53 function variancepn( N, correction, x, stride ) { 54 var mu; 55 var ix; 56 var M2; 57 var M; 58 var d; 59 var n; 60 var i; 61 62 n = N - correction; 63 if ( N <= 0 || n <= 0.0 ) { 64 return NaN; 65 } 66 if ( N === 1 || stride === 0 ) { 67 return 0.0; 68 } 69 // Compute an estimate for the mean: 70 mu = gsumpw( N, x, stride ) / N; 71 72 if ( stride < 0 ) { 73 ix = (1-N) * stride; 74 } else { 75 ix = 0; 76 } 77 // Compute the variance... 78 M2 = 0.0; 79 M = 0.0; 80 for ( i = 0; i < N; i++ ) { 81 d = x[ ix ] - mu; 82 M2 += d * d; 83 M += d; 84 ix += stride; 85 } 86 return (M2/n) - ((M/N)*(M/n)); 87 } 88 89 90 // EXPORTS // 91 92 module.exports = variancepn;