nanvariancech.js (3392B)
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 // MAIN // 22 23 /** 24 * Computes the variance of a strided array ignoring `NaN` values and using a one-pass trial mean algorithm. 25 * 26 * ## Method 27 * 28 * - This implementation uses a one-pass trial mean approach, as suggested by Chan et al (1983). 29 * 30 * ## References 31 * 32 * - 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). 33 * - Ling, Robert F. 1974. "Comparison of Several Algorithms for Computing Sample Means and Variances." _Journal of the American Statistical Association_ 69 (348). American Statistical Association, Taylor & Francis, Ltd.: 859–66. doi:[10.2307/2286154](https://doi.org/10.2307/2286154). 34 * - Chan, Tony F., Gene H. Golub, and Randall J. LeVeque. 1983. "Algorithms for Computing the Sample Variance: Analysis and Recommendations." _The American Statistician_ 37 (3). American Statistical Association, Taylor & Francis, Ltd.: 242–47. doi:[10.1080/00031305.1983.10483115](https://doi.org/10.1080/00031305.1983.10483115). 35 * - 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). 36 * 37 * @param {PositiveInteger} N - number of indexed elements 38 * @param {number} correction - degrees of freedom adjustment 39 * @param {NumericArray} x - input array 40 * @param {integer} stride - stride length 41 * @returns {number} variance 42 * 43 * @example 44 * var x = [ 1.0, -2.0, NaN, 2.0 ]; 45 * 46 * var v = nanvariancech( x.length, 1, x, 1 ); 47 * // returns ~4.3333 48 */ 49 function nanvariancech( N, correction, x, stride ) { 50 var mu; 51 var ix; 52 var M2; 53 var nc; 54 var M; 55 var d; 56 var v; 57 var n; 58 var i; 59 60 if ( N <= 0 ) { 61 return NaN; 62 } 63 if ( N === 1 || stride === 0 ) { 64 v = x[ 0 ]; 65 if ( v === v && N-correction > 0.0 ) { 66 return 0.0; 67 } 68 return NaN; 69 } 70 if ( stride < 0 ) { 71 ix = (1-N) * stride; 72 } else { 73 ix = 0; 74 } 75 // Find an estimate for the mean... 76 for ( i = 0; i < N; i++ ) { 77 v = x[ ix ]; 78 if ( v === v ) { 79 mu = v; 80 break; 81 } 82 ix += stride; 83 } 84 if ( i === N ) { 85 return NaN; 86 } 87 ix += stride; 88 i += 1; 89 90 // Compute the variance... 91 M2 = 0.0; 92 M = 0.0; 93 n = 1; 94 for ( i; i < N; i++ ) { 95 v = x[ ix ]; 96 if ( v === v ) { 97 d = v - mu; 98 M2 += d * d; 99 M += d; 100 n += 1; 101 } 102 ix += stride; 103 } 104 nc = n - correction; 105 if ( nc <= 0.0 ) { 106 return NaN; 107 } 108 return (M2/nc) - ((M/n)*(M/nc)); 109 } 110 111 112 // EXPORTS // 113 114 module.exports = nanvariancech;