91 lines
3.0 KiB
JavaScript
91 lines
3.0 KiB
JavaScript
/**
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* @license Apache-2.0
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*
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* Copyright (c) 2020 The Stdlib Authors.
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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'use strict';
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// MAIN //
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/**
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* Computes the variance of a strided array using a one-pass trial mean algorithm.
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*
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* ## Method
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*
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* - This implementation uses a one-pass trial mean approach, as suggested by Chan et al (1983).
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*
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* ## References
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*
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* - 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).
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* - 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).
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* - 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).
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* - 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).
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*
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* @param {PositiveInteger} N - number of indexed elements
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* @param {number} correction - degrees of freedom adjustment
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* @param {NumericArray} x - input array
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* @param {integer} stride - stride length
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* @returns {number} variance
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*
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* @example
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* var x = [ 1.0, -2.0, 2.0 ];
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* var N = x.length;
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*
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* var v = variancech( N, 1, x, 1 );
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* // returns ~4.3333
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*/
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function variancech( N, correction, x, stride ) {
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var mu;
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var ix;
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var M2;
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var M;
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var d;
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var n;
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var i;
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n = N - correction;
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if ( N <= 0 || n <= 0.0 ) {
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return NaN;
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}
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if ( N === 1 || stride === 0 ) {
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return 0.0;
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}
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if ( stride < 0 ) {
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ix = (1-N) * stride;
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} else {
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ix = 0;
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}
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// Use an estimate for the mean:
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mu = x[ ix ];
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ix += stride;
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// Compute the variance...
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M2 = 0.0;
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M = 0.0;
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for ( i = 1; i < N; i++ ) {
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d = x[ ix ] - mu;
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M2 += d * d;
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M += d;
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ix += stride;
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}
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return (M2/n) - ((M/N)*(M/n));
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}
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// EXPORTS //
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module.exports = variancech;
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