ndarray.js (3526B)
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 * @param {NonNegativeInteger} offset - starting index 42 * @returns {number} variance 43 * 44 * @example 45 * var floor = require( '@stdlib/math/base/special/floor' ); 46 * 47 * var x = [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0, NaN, NaN ]; 48 * var N = floor( x.length / 2 ); 49 * 50 * var v = nanvariancech( N, 1, x, 2, 1 ); 51 * // returns 6.25 52 */ 53 function nanvariancech( N, correction, x, stride, offset ) { 54 var mu; 55 var ix; 56 var M2; 57 var nc; 58 var M; 59 var d; 60 var v; 61 var n; 62 var i; 63 64 if ( N <= 0 ) { 65 return NaN; 66 } 67 if ( N === 1 || stride === 0 ) { 68 v = x[ offset ]; 69 if ( v === v && N-correction > 0.0 ) { 70 return 0.0; 71 } 72 return NaN; 73 } 74 ix = offset; 75 76 // Find an estimate for the mean... 77 for ( i = 0; i < N; i++ ) { 78 v = x[ ix ]; 79 if ( v === v ) { 80 mu = v; 81 break; 82 } 83 ix += stride; 84 } 85 if ( i === N ) { 86 return NaN; 87 } 88 ix += stride; 89 i += 1; 90 91 // Compute the variance... 92 M2 = 0.0; 93 M = 0.0; 94 n = 1; 95 for ( i; i < N; i++ ) { 96 v = x[ ix ]; 97 if ( v === v ) { 98 d = v - mu; 99 M2 += d * d; 100 M += d; 101 n += 1; 102 } 103 ix += stride; 104 } 105 nc = n - correction; 106 if ( nc <= 0.0 ) { 107 return NaN; 108 } 109 return (M2/nc) - ((M/n)*(M/nc)); 110 } 111 112 113 // EXPORTS // 114 115 module.exports = nanvariancech;