80 lines
3.0 KiB
C
80 lines
3.0 KiB
C
|
/**
|
|||
|
|
* @license Apache-2.0
|
|||
|
|
*
|
|||
|
|
* Copyright (c) 2020 The Stdlib Authors.
|
|||
|
|
*
|
|||
|
|
* Licensed under the Apache License, Version 2.0 (the "License");
|
|||
|
|
* you may not use this file except in compliance with the License.
|
|||
|
|
* You may obtain a copy of the License at
|
|||
|
|
*
|
|||
|
|
* http://www.apache.org/licenses/LICENSE-2.0
|
|||
|
|
*
|
|||
|
|
* Unless required by applicable law or agreed to in writing, software
|
|||
|
|
* distributed under the License is distributed on an "AS IS" BASIS,
|
|||
|
|
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
|
|||
|
|
* See the License for the specific language governing permissions and
|
|||
|
|
* limitations under the License.
|
|||
|
|
*/
|
|||
|
|
|
|||
|
|
#include "stdlib/stats/base/dvariancech.h"
|
|||
|
|
#include <stdint.h>
|
|||
|
|
|
|||
|
|
/**
|
|||
|
|
* Computes the variance of a double-precision floating-point strided array using a one-pass trial mean algorithm.
|
|||
|
|
*
|
|||
|
|
* ## Method
|
|||
|
|
*
|
|||
|
|
* - This implementation uses a one-pass trial mean approach, as suggested by Chan et al (1983).
|
|||
|
|
*
|
|||
|
|
* ## References
|
|||
|
|
*
|
|||
|
|
* - 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).
|
|||
|
|
* - 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).
|
|||
|
|
* - 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).
|
|||
|
|
* - 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).
|
|||
|
|
*
|
|||
|
|
* @param N number of indexed elements
|
|||
|
|
* @param correction degrees of freedom adjustment
|
|||
|
|
* @param X input array
|
|||
|
|
* @param stride stride length
|
|||
|
|
* @return output value
|
|||
|
|
*/
|
|||
|
|
double stdlib_strided_dvariancech( const int64_t N, const double correction, const double *X, const int64_t stride ) {
|
|||
|
|
int64_t ix;
|
|||
|
|
int64_t i;
|
|||
|
|
double dN;
|
|||
|
|
double mu;
|
|||
|
|
double M2;
|
|||
|
|
double M;
|
|||
|
|
double n;
|
|||
|
|
double d;
|
|||
|
|
|
|||
|
|
dN = (double)N;
|
|||
|
|
n = dN - correction;
|
|||
|
|
if ( N <= 0 || n <= 0.0 ) {
|
|||
|
|
return 0.0 / 0.0; // NaN
|
|||
|
|
}
|
|||
|
|
if ( N == 1 || stride == 0 ) {
|
|||
|
|
return 0.0;
|
|||
|
|
}
|
|||
|
|
if ( stride < 0 ) {
|
|||
|
|
ix = (1-N) * stride;
|
|||
|
|
} else {
|
|||
|
|
ix = 0;
|
|||
|
|
}
|
|||
|
|
// Use an estimate for the mean:
|
|||
|
|
mu = X[ ix ];
|
|||
|
|
ix += stride;
|
|||
|
|
|
|||
|
|
// Compute the variance...
|
|||
|
|
M2 = 0.0;
|
|||
|
|
M = 0.0;
|
|||
|
|
for ( i = 1; i < N; i++ ) {
|
|||
|
|
d = X[ ix ] - mu;
|
|||
|
|
M2 += d * d;
|
|||
|
|
M += d;
|
|||
|
|
ix += stride;
|
|||
|
|
}
|
|||
|
|
return (M2/n) - ((M/dN)*(M/n));
|
|||
|
|
}
|