dsmeanpn.c (2294B)
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/dsmeanpn.h" 20 #include "stdlib/blas/ext/base/dssum.h" 21 #include "stdlib/blas/ext/base/dsapxsum.h" 22 #include <stdint.h> 23 24 /** 25 * Computes the arithmetic mean of a single-precision floating-point strided array using a two-pass error correction algorithm with extended accumulation and returning an extended precision result. 26 * 27 * ## Method 28 * 29 * - This implementation uses a two-pass approach, as suggested by Neely (1966). 30 * 31 * ## References 32 * 33 * - 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). 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 X input array 38 * @param stride stride length 39 * @return output value 40 */ 41 double stdlib_strided_dsmeanpn( const int64_t N, const float *X, const int64_t stride ) { 42 double dN; 43 double mu; 44 double c; 45 46 if ( N <= 0 ) { 47 return 0.0 / 0.0; // NaN 48 } 49 if ( N == 1 || stride == 0 ) { 50 return X[ 0 ]; 51 } 52 dN = (double)N; 53 54 // Compute an estimate for the mean: 55 mu = stdlib_strided_dssum( N, X, stride ); 56 mu /= dN; 57 58 // Compute an error term: 59 c = stdlib_strided_dsapxsum( N, -mu, X, stride ); 60 c /= dN; 61 62 return mu + c; 63 }