dvarmpn.c (2283B)
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/dvarmpn.h" 20 #include <stdint.h> 21 22 /** 23 * Computes the variance of a double-precision floating-point strided array provided a known mean and using Neely's correction algorithm. 24 * 25 * ## References 26 * 27 * - 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). 28 * - 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). 29 * 30 * @param N number of indexed elements 31 * @param mean mean 32 * @param correction degrees of freedom adjustment 33 * @param X input array 34 * @param stride stride length 35 * @return output value 36 */ 37 double stdlib_strided_dvarmpn( const int64_t N, const double mean, const double correction, const double *X, const int64_t stride ) { 38 int64_t ix; 39 int64_t i; 40 double dN; 41 double M2; 42 double M; 43 double n; 44 double d; 45 46 dN = (double)N; 47 n = dN - correction; 48 if ( N <= 0 || n <= 0.0 ) { 49 return 0.0 / 0.0; // NaN 50 } 51 if ( N == 1 || stride == 0 ) { 52 return 0.0; 53 } 54 if ( stride < 0 ) { 55 ix = (1-N) * stride; 56 } else { 57 ix = 0; 58 } 59 M2 = 0.0; 60 M = 0.0; 61 for ( i = 0; i < N; i++ ) { 62 d = X[ ix ] - mean; 63 M2 += d * d; 64 M += d; 65 ix += stride; 66 } 67 return (M2/n) - ((M/dN)*(M/n)); 68 }