ndarray.js (2495B)
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 * @param {NonNegativeInteger} offset - starting index 37 * @returns {number} variance 38 * 39 * @example 40 * var Float64Array = require( '@stdlib/array/float64' ); 41 * var floor = require( '@stdlib/math/base/special/floor' ); 42 * 43 * var x = new Float64Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] ); 44 * var N = floor( x.length / 2 ); 45 * 46 * var v = dvarmpn( N, 1.25, 1, x, 2, 1 ); 47 * // returns 6.25 48 */ 49 function dvarmpn( N, mean, correction, x, stride, offset ) { 50 var ix; 51 var M2; 52 var M; 53 var d; 54 var n; 55 var i; 56 57 n = N - correction; 58 if ( N <= 0 || n <= 0.0 ) { 59 return NaN; 60 } 61 if ( N === 1 || stride === 0 ) { 62 return 0.0; 63 } 64 ix = offset; 65 M2 = 0.0; 66 M = 0.0; 67 for ( i = 0; i < N; i++ ) { 68 d = x[ ix ] - mean; 69 M2 += d * d; 70 M += d; 71 ix += stride; 72 } 73 return (M2/n) - ((M/N)*(M/n)); 74 } 75 76 77 // EXPORTS // 78 79 module.exports = dvarmpn;