62 lines
2.2 KiB
C
62 lines
2.2 KiB
C
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/**
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* @license Apache-2.0
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*
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* Copyright (c) 2020 The Stdlib Authors.
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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#include "stdlib/stats/base/smeanpn.h"
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#include "stdlib/blas/ext/base/ssumpw.h"
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#include "stdlib/blas/ext/base/sapxsumpw.h"
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#include <stdint.h>
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/**
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* Computes the arithmetic mean of a single-precision floating-point strided array using a two-pass error correction algorithm.
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*
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* ## Method
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*
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* - This implementation uses a two-pass approach, as suggested by Neely (1966).
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*
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* ## References
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*
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* - 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).
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* - 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).
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*
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* @param N number of indexed elements
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* @param X input array
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* @param stride stride length
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* @return output value
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*/
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float stdlib_strided_smeanpn( const int64_t N, const float *X, const int64_t stride ) {
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double dN;
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float mu;
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float c;
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if ( N <= 0 ) {
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return 0.0 / 0.0; // NaN
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}
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if ( N == 1 || stride == 0 ) {
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return X[ 0 ];
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}
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dN = (double)N;
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// Compute an estimate for the mean:
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mu = (double)stdlib_strided_ssumpw( N, X, stride ) / dN;
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// Compute an error term:
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c = (double)stdlib_strided_sapxsumpw( N, -mu, X, stride ) / dN;
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return mu + c;
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}
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