dvarmpn.js (2377B)
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 double-precision floating-point strided array provided a known mean and using Neely's correction algorithm. 25 * 26 * ## References 27 * 28 * - 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). 29 * - 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). 30 * 31 * @param {PositiveInteger} N - number of indexed elements 32 * @param {number} mean - mean 33 * @param {number} correction - degrees of freedom adjustment 34 * @param {Float64Array} x - input array 35 * @param {integer} stride - stride length 36 * @returns {number} variance 37 * 38 * @example 39 * var Float64Array = require( '@stdlib/array/float64' ); 40 * 41 * var x = new Float64Array( [ 1.0, -2.0, 2.0 ] ); 42 * 43 * var v = dvarmpn( x.length, 1.0/3.0, 1, x, 1 ); 44 * // returns ~4.3333 45 */ 46 function dvarmpn( N, mean, correction, x, stride ) { 47 var ix; 48 var M2; 49 var M; 50 var d; 51 var n; 52 var i; 53 54 n = N - correction; 55 if ( N <= 0 || n <= 0.0 ) { 56 return NaN; 57 } 58 if ( N === 1 || stride === 0 ) { 59 return 0.0; 60 } 61 if ( stride < 0 ) { 62 ix = (1-N) * stride; 63 } else { 64 ix = 0; 65 } 66 M2 = 0.0; 67 M = 0.0; 68 for ( i = 0; i < N; i++ ) { 69 d = x[ ix ] - mean; 70 M2 += d * d; 71 M += d; 72 ix += stride; 73 } 74 return (M2/n) - ((M/N)*(M/n)); 75 } 76 77 78 // EXPORTS // 79 80 module.exports = dvarmpn;