svariancech.js (3466B)
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 float64ToFloat32 = require( '@stdlib/number/float64/base/to-float32' ); 24 25 26 // MAIN // 27 28 /** 29 * Computes the variance of a single-precision floating-point strided array using a one-pass trial mean algorithm. 30 * 31 * ## Method 32 * 33 * - This implementation uses a one-pass trial mean approach, as suggested by Chan et al (1983). 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 * - 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). 39 * - 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). 40 * - 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). 41 * 42 * @param {PositiveInteger} N - number of indexed elements 43 * @param {number} correction - degrees of freedom adjustment 44 * @param {Float32Array} x - input array 45 * @param {integer} stride - stride length 46 * @returns {number} variance 47 * 48 * @example 49 * var Float32Array = require( '@stdlib/array/float32' ); 50 * 51 * var x = new Float32Array( [ 1.0, -2.0, 2.0 ] ); 52 * var N = x.length; 53 * 54 * var v = svariancech( N, 1, x, 1 ); 55 * // returns ~4.3333 56 */ 57 function svariancech( N, correction, x, stride ) { 58 var mu; 59 var ix; 60 var M2; 61 var M; 62 var d; 63 var n; 64 var i; 65 66 n = N - correction; 67 if ( N <= 0 || n <= 0.0 ) { 68 return NaN; 69 } 70 if ( N === 1 || stride === 0 ) { 71 return 0.0; 72 } 73 if ( stride < 0 ) { 74 ix = (1-N) * stride; 75 } else { 76 ix = 0; 77 } 78 // Use an estimate for the mean: 79 mu = x[ ix ]; 80 ix += stride; 81 82 // Compute the variance... 83 M2 = 0.0; 84 M = 0.0; 85 for ( i = 1; i < N; i++ ) { 86 d = float64ToFloat32( x[ ix ] - mu ); 87 M2 = float64ToFloat32( M2 + float64ToFloat32( d*d ) ); 88 M = float64ToFloat32( M + d ); 89 ix += stride; 90 } 91 return float64ToFloat32( float64ToFloat32(M2/n) - float64ToFloat32( float64ToFloat32(M/N)*float64ToFloat32(M/n) ) ); // eslint-disable-line max-len 92 } 93 94 95 // EXPORTS // 96 97 module.exports = svariancech;