dnanvariancech.c (3451B)
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/dnanvariancech.h" 20 #include <stdint.h> 21 22 /** 23 * Computes the variance of a double-precision floating-point strided array ignoring `NaN` values and 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_dnanvariancech( const int64_t N, const double correction, const double *X, const int64_t stride ) { 43 int64_t ix; 44 int64_t n; 45 int64_t i; 46 double M2; 47 double mu; 48 double nc; 49 double dn; 50 double M; 51 double d; 52 double v; 53 54 if ( N <= 0 ) { 55 return 0.0 / 0.0; // NaN 56 } 57 if ( N == 1 || stride == 0 ) { 58 v = X[ 0 ]; 59 if ( v == v && (double)N-correction > 0.0 ) { 60 return 0.0; 61 } 62 return 0.0 / 0.0; // NaN 63 } 64 if ( stride < 0 ) { 65 ix = (1-N) * stride; 66 } else { 67 ix = 0; 68 } 69 // Find an estimate for the mean... 70 for ( i = 0; i < N; i++ ) { 71 v = X[ ix ]; 72 if ( v == v ) { 73 mu = v; 74 break; 75 } 76 ix += stride; 77 } 78 if ( i == N ) { 79 return 0.0 / 0.0; // NaN 80 } 81 ix += stride; 82 i += 1; 83 84 // Compute the variance... 85 M2 = 0.0; 86 M = 0.0; 87 n = 1; 88 for (; i < N; i++ ) { 89 v = X[ ix ]; 90 if ( v == v ) { 91 d = v - mu; 92 M2 += d * d; 93 M += d; 94 n += 1; 95 } 96 ix += stride; 97 } 98 dn = (double)n; 99 nc = dn - correction; 100 if ( nc <= 0.0 ) { 101 return 0.0 / 0.0; // NaN 102 } 103 return (M2/nc) - ((M/dn)*(M/nc)); 104 }