107 lines
3.1 KiB
C
107 lines
3.1 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/dmeanvarpn.h"
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#include "stdlib/blas/ext/base/dsumpw.h"
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#include <stdint.h>
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/**
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* Computes the mean and variance of a double-precision floating-point strided array using a two-pass 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 correction degrees of freedom adjustment
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* @param X input array
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* @param strideX X stride length
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* @param Out output array
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* @param strideOut Out stride length
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*/
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void stdlib_strided_dmeanvarpn( const int64_t N, const double correction, const double *X, const int64_t strideX, double *Out, const int64_t strideOut ) {
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int64_t ix;
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int64_t io;
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int64_t i;
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double M2;
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double mu;
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double dN;
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double M;
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double d;
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double c;
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double n;
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if ( strideX < 0 ) {
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ix = (1-N) * strideX;
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} else {
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ix = 0;
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}
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if ( strideOut < 0 ) {
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io = -strideOut;
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} else {
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io = 0;
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}
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if ( N <= 0 ) {
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Out[ io ] = 0.0 / 0.0; // NaN
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Out[ io+strideOut ] = 0.0 / 0.0; // NaN
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return;
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}
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dN = (double)N;
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n = dN - correction;
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if ( N == 1 || strideX == 0 ) {
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Out[ io ] = X[ ix ];
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if ( n <= 0.0 ) {
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Out[ io+strideOut ] = 0.0 / 0.0; // NaN
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} else {
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Out[ io+strideOut ] = 0.0;
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}
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return;
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}
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// Compute an estimate for the mean:
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mu = stdlib_strided_dsumpw( N, X, strideX ) / dN;
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if ( mu != mu ) {
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Out[ io ] = 0.0 / 0.0; // NaN
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Out[ io+strideOut ] = 0.0 / 0.0; // NaN
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return;
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}
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// Compute the sum of squared differences from the mean...
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M2 = 0.0;
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M = 0.0;
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for ( i = 0; i < N; i++ ) {
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d = X[ ix ] - mu;
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M2 += d * d;
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M += d;
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ix += strideX;
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}
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// Compute an error term for the mean:
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c = M / dN;
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Out[ io ] = mu + c;
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if ( n <= 0.0 ) {
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Out[ io+strideOut ] = 0.0 / 0.0; // NaN
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} else {
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Out[ io+strideOut ] = (M2/n) - (c*(M/n));
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}
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return;
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}
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