76 lines
2.6 KiB
Plaintext
76 lines
2.6 KiB
Plaintext
[/
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Copyright 2018 Nick Thompson
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Distributed under the Boost Software License, Version 1.0.
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(See accompanying file LICENSE_1_0.txt or copy at
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http://www.boost.org/LICENSE_1_0.txt).
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]
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[section:bivariate_statistics Bivariate Statistics]
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[heading Synopsis]
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``
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#include <boost/math/statistics/bivariate_statistics.hpp>
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namespace boost{ namespace math{ namespace statistics {
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template<class Container>
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auto covariance(Container const & u, Container const & v);
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template<class Container>
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auto means_and_covariance(Container const & u, Container const & v);
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template<class Container>
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auto correlation_coefficient(Container const & u, Container const & v);
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}}}
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``
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[heading Description]
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This file provides functions for computing bivariate statistics.
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[heading Covariance]
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Computes the population covariance of two datasets:
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std::vector<double> u{1,2,3,4,5};
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std::vector<double> v{1,2,3,4,5};
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double cov_uv = boost::math::statistics::covariance(u, v);
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The implementation follows [@https://doi.org/10.1109/CLUSTR.2009.5289161 Bennet et al].
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The data is not modified. Requires a random-access container.
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Works with real-valued inputs and does not work with complex-valued inputs.
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The algorithm used herein simultaneously generates the mean values of the input data /u/ and /v/.
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For certain applications, it might be useful to get them in a single pass through the data.
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As such, we provide `means_and_covariance`:
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std::vector<double> u{1,2,3,4,5};
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std::vector<double> v{1,2,3,4,5};
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auto [mu_u, mu_v, cov_uv] = boost::math::statistics::means_and_covariance(u, v);
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[heading Correlation Coefficient]
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Computes the [@https://en.wikipedia.org/wiki/Pearson_correlation_coefficient Pearson correlation coefficient] of two datasets /u/ and /v/:
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std::vector<double> u{1,2,3,4,5};
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std::vector<double> v{1,2,3,4,5};
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double rho_uv = boost::math::statistics::correlation_coefficient(u, v);
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// rho_uv = 1.
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The data must be random access and cannot be complex.
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If one or both of the datasets is constant, the correlation coefficient is an indeterminant form (0/0) and definitions must be introduced to assign it a value.
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We use the following: If both datasets are constant, then the correlation coefficient is 1.
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If one dataset is constant, and the other is not, then the correlation coefficient is zero.
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[heading References]
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* Bennett, Janine, et al. ['Numerically stable, single-pass, parallel statistics algorithms.] Cluster Computing and Workshops, 2009. CLUSTER'09. IEEE International Conference on. IEEE, 2009.
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[endsect]
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[/section:bivariate_statistics Bivariate Statistics]
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