time-to-botec

Benchmark sampling in different programming languages
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dvariancech.c (3063B)

      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 #include "stdlib/stats/base/dvariancech.h"
     20 #include <stdint.h>
     21 
     22 /**
     23 * Computes the variance of a double-precision floating-point strided array using a one-pass trial mean algorithm.
     24 *
     25 * ## Method
     26 *
     27 * -   This implementation uses a one-pass trial mean approach, as suggested by Chan et al (1983).
     28 *
     29 * ## References
     30 *
     31 * -   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).
     32 * -   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).
     33 * -   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).
     34 * -   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).
     35 *
     36 * @param N           number of indexed elements
     37 * @param correction  degrees of freedom adjustment
     38 * @param X           input array
     39 * @param stride      stride length
     40 * @return            output value
     41 */
     42 double stdlib_strided_dvariancech( const int64_t N, const double correction, const double *X, const int64_t stride ) {
     43 	int64_t ix;
     44 	int64_t i;
     45 	double dN;
     46 	double mu;
     47 	double M2;
     48 	double M;
     49 	double n;
     50 	double d;
     51 
     52 	dN = (double)N;
     53 	n = dN - correction;
     54 	if ( N <= 0 || n <= 0.0 ) {
     55 		return 0.0 / 0.0; // NaN
     56 	}
     57 	if ( N == 1 || stride == 0 ) {
     58 		return 0.0;
     59 	}
     60 	if ( stride < 0 ) {
     61 		ix = (1-N) * stride;
     62 	} else {
     63 		ix = 0;
     64 	}
     65 	// Use an estimate for the mean:
     66 	mu = X[ ix ];
     67 	ix += stride;
     68 
     69 	// Compute the variance...
     70 	M2 = 0.0;
     71 	M = 0.0;
     72 	for ( i = 1; i < N; i++ ) {
     73 		d = X[ ix ] - mu;
     74 		M2 += d * d;
     75 		M += d;
     76 		ix += stride;
     77 	}
     78 	return (M2/n) - ((M/dN)*(M/n));
     79 }