time-to-botec

Benchmark sampling in different programming languages
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variancech.js (3057B)

      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 strided array using a one-pass trial mean algorithm.
     25 *
     26 * ## Method
     27 *
     28 * -   This implementation uses a one-pass trial mean approach, as suggested by Chan et al (1983).
     29 *
     30 * ## References
     31 *
     32 * -   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).
     33 * -   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).
     34 * -   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).
     35 * -   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).
     36 *
     37 * @param {PositiveInteger} N - number of indexed elements
     38 * @param {number} correction - degrees of freedom adjustment
     39 * @param {NumericArray} x - input array
     40 * @param {integer} stride - stride length
     41 * @returns {number} variance
     42 *
     43 * @example
     44 * var x = [ 1.0, -2.0, 2.0 ];
     45 * var N = x.length;
     46 *
     47 * var v = variancech( N, 1, x, 1 );
     48 * // returns ~4.3333
     49 */
     50 function variancech( N, correction, x, stride ) {
     51 	var mu;
     52 	var ix;
     53 	var M2;
     54 	var M;
     55 	var d;
     56 	var n;
     57 	var i;
     58 
     59 	n = N - correction;
     60 	if ( N <= 0 || n <= 0.0 ) {
     61 		return NaN;
     62 	}
     63 	if ( N === 1 || stride === 0 ) {
     64 		return 0.0;
     65 	}
     66 	if ( stride < 0 ) {
     67 		ix = (1-N) * stride;
     68 	} else {
     69 		ix = 0;
     70 	}
     71 	// Use an estimate for the mean:
     72 	mu = x[ ix ];
     73 	ix += stride;
     74 
     75 	// Compute the variance...
     76 	M2 = 0.0;
     77 	M = 0.0;
     78 	for ( i = 1; i < N; i++ ) {
     79 		d = x[ ix ] - mu;
     80 		M2 += d * d;
     81 		M += d;
     82 		ix += stride;
     83 	}
     84 	return (M2/n) - ((M/N)*(M/n));
     85 }
     86 
     87 
     88 // EXPORTS //
     89 
     90 module.exports = variancech;