dsvariancepn.c (2560B)
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/dsvariancepn.h" 20 #include "stdlib/blas/ext/base/dssum.h" 21 #include <stdint.h> 22 23 /** 24 * Computes the variance of a single-precision floating-point strided array using a two-pass algorithm with extended accumulation and returning an extended precision result. 25 * 26 * ## Method 27 * 28 * - This implementation uses a two-pass approach, as suggested by Neely (1966). 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 * - 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). 34 * 35 * @param N number of indexed elements 36 * @param correction degrees of freedom adjustment 37 * @param X input array 38 * @param stride stride length 39 * @return output value 40 */ 41 double stdlib_strided_dsvariancepn( const int64_t N, const float correction, const float *X, const int64_t stride ) { 42 int64_t ix; 43 int64_t i; 44 double dN; 45 double mu; 46 double M2; 47 double M; 48 double n; 49 double d; 50 51 dN = (double)N; 52 n = dN - (double)correction; 53 if ( N <= 0 || n <= 0 ) { 54 return 0.0 / 0.0; // NaN 55 } 56 if ( N == 1 || stride == 0 ) { 57 return 0.0; 58 } 59 // Compute an estimate for the mean: 60 mu = stdlib_strided_dssum( N, X, stride ) / dN; 61 62 if ( stride < 0 ) { 63 ix = (1-N) * stride; 64 } else { 65 ix = 0; 66 } 67 // Compute the variance... 68 M2 = 0.0; 69 M = 0.0; 70 for ( i = 0; i < N; i++ ) { 71 d = (double)X[ ix ] - mu; 72 M2 += d * d; 73 M += d; 74 ix += stride; 75 } 76 return (M2/n) - ((M/dN)*(M/n)); 77 }