pca.hpp

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#ifndef GENESIS_UTILS_MATH_PCA_H_
#define GENESIS_UTILS_MATH_PCA_H_
 
/*
    Genesis - A toolkit for working with phylogenetic data.
    Copyright (C) 2014-2019 Lucas Czech and HITS gGmbH
 
    This program is free software: you can redistribute it and/or modify
    it under the terms of the GNU General Public License as published by
    the Free Software Foundation, either version 3 of the License, or
    (at your option) any later version.
 
    This program is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    GNU General Public License for more details.
 
    You should have received a copy of the GNU General Public License
    along with this program.  If not, see <http://www.gnu.org/licenses/>.
 
    Contact:
    Lucas Czech <lucas.czech@h-its.org>
    Exelixis Lab, Heidelberg Institute for Theoretical Studies
    Schloss-Wolfsbrunnenweg 35, D-69118 Heidelberg, Germany
*/
 
#include "genesis/utils/containers/matrix.hpp"
 
#include <vector>
 
namespace genesis {
namespace utils {
 
// ================================================================================================
//     Settings for Functions
// ================================================================================================
 
enum class PcaStandardization
{
    kCorrelation,
 
    kCovariance,
 
    kSSCP
};
 
// ================================================================================================
//     Structs for Storing Results
// ================================================================================================
 
struct TridiagonalDecompositionData
{
    std::vector<double> eigenvalues;
    std::vector<double> intermediates;
};
 
struct PcaData
{
    std::vector<double> eigenvalues;
    Matrix<double>      eigenvectors;
    Matrix<double>      projection;
};
 
// ================================================================================================
//     Helper Functions
// ================================================================================================
 
TridiagonalDecompositionData reduce_to_tridiagonal_matrix(
    Matrix<double>& data
);
 
void tridiagonal_ql_algorithm(
    Matrix<double>&               data,
    TridiagonalDecompositionData& tri,
    size_t                        max_iterations = 1000
);
 
// ================================================================================================
//     Principal Component Analysis
// ================================================================================================
 
PcaData principal_component_analysis(
    Matrix<double> const& data,
    size_t                components      = 0,
    PcaStandardization    standardization = PcaStandardization::kCorrelation
);
 
} // namespace utils
} // namespace genesis
 
#endif // include guard