ndarray.js (2614B)
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 gsumpw = require( '@stdlib/blas/ext/base/gsumpw' ).ndarray; 24 25 26 // MAIN // 27 28 /** 29 * Computes the variance of a strided array using a two-pass algorithm. 30 * 31 * ## Method 32 * 33 * - This implementation uses a two-pass approach, as suggested by Neely (1966). 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 * - 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). 39 * 40 * @param {PositiveInteger} N - number of indexed elements 41 * @param {number} correction - degrees of freedom adjustment 42 * @param {NumericArray} x - input array 43 * @param {integer} stride - stride length 44 * @param {NonNegativeInteger} offset - starting index 45 * @returns {number} variance 46 * 47 * @example 48 * var floor = require( '@stdlib/math/base/special/floor' ); 49 * 50 * var x = [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ]; 51 * var N = floor( x.length / 2 ); 52 * 53 * var v = variancepn( N, 1, x, 2, 1 ); 54 * // returns 6.25 55 */ 56 function variancepn( N, correction, x, stride, offset ) { 57 var mu; 58 var ix; 59 var M2; 60 var M; 61 var d; 62 var n; 63 var i; 64 65 n = N - correction; 66 if ( N <= 0 || n <= 0.0 ) { 67 return NaN; 68 } 69 if ( N === 1 || stride === 0 ) { 70 return 0.0; 71 } 72 // Compute an estimate for the mean: 73 mu = gsumpw( N, x, stride, offset ) / N; 74 75 // Compute the variance... 76 ix = offset; 77 M2 = 0.0; 78 M = 0.0; 79 for ( i = 0; i < N; i++ ) { 80 d = x[ ix ] - mu; 81 M2 += d * d; 82 M += d; 83 ix += stride; 84 } 85 return (M2/n) - ((M/N)*(M/n)); 86 } 87 88 89 // EXPORTS // 90 91 module.exports = variancepn;