math/matrix.hpp

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#ifndef GENESIS_UTILS_MATH_MATRIX_H_
#define GENESIS_UTILS_MATH_MATRIX_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 "genesis/utils/math/statistics.hpp"
 
#include <cmath>
#include <limits>
#include <vector>
 
namespace genesis {
namespace utils {
 
// =================================================================================================
//     Min Max
// =================================================================================================
 
template< typename T >
MinMaxPair<T> matrix_minmax( Matrix<T> const& data, bool ignore_non_finite_values = true )
{
    // Edge case
    if( data.rows() == 0 || data.cols() == 0 ) {
        return {
            std::numeric_limits<double>::quiet_NaN(),
            std::numeric_limits<double>::quiet_NaN()
        };
    }
 
    // Init with first element
    auto ret = MinMaxPair<T>{
        std::numeric_limits<double>::infinity(),
        - std::numeric_limits<double>::infinity()
    };
 
    // Iterate
    size_t cnt = 0;
    for( auto const& e : data ) {
        if( std::isfinite( e ) || ! ignore_non_finite_values ) {
            ret.min = std::min( ret.min, e );
            ret.max = std::max( ret.max, e );
            ++cnt;
        }
    }
 
    // If we found no valid values at all, return nan.
    if( cnt == 0 ) {
        return {
            std::numeric_limits<double>::quiet_NaN(),
            std::numeric_limits<double>::quiet_NaN()
        };
    }
 
    return ret;
}
 
template< typename T >
std::vector<MinMaxPair<T>> matrix_col_minmax( Matrix<T> const& data, bool ignore_non_finite_values = true )
{
    auto ret = std::vector<MinMaxPair<T>>( data.cols(), {
        std::numeric_limits<double>::quiet_NaN(),
        std::numeric_limits<double>::quiet_NaN()
    });
 
    // Nothing to do.
    if( data.rows() == 0 ) {
        return ret;
    }
 
    // Iterate
    for( size_t c = 0; c < data.cols(); ++c ) {
        ret[ c ].min = std::numeric_limits<double>::infinity();
        ret[ c ].max = - std::numeric_limits<double>::infinity();
 
        size_t cnt = 0;
        for( size_t r = 0; r < data.rows(); ++r ) {
 
            // Find min and max of the column. If the value is not finite, skip it.
            auto const& e = data( r, c );
            if( std::isfinite( e ) || ! ignore_non_finite_values ) {
                ret[ c ].min = std::min( ret[ c ].min, data( r, c ) );
                ret[ c ].max = std::max( ret[ c ].max, data( r, c ) );
                ++cnt;
            }
        }
 
        // If we found no valid values at all, return nan.
        if( cnt == 0 ) {
            ret[ c ].min = std::numeric_limits<double>::quiet_NaN();
            ret[ c ].max = std::numeric_limits<double>::quiet_NaN();
        }
    }
 
    return ret;
}
 
template< typename T >
std::vector<MinMaxPair<T>> matrix_row_minmax( Matrix<T> const& data, bool ignore_non_finite_values = true )
{
    auto ret = std::vector<MinMaxPair<T>>( data.rows(), {
        std::numeric_limits<double>::quiet_NaN(),
        std::numeric_limits<double>::quiet_NaN()
    });
 
    // Nothing to do.
    if( data.cols() == 0 ) {
        return ret;
    }
 
    for( size_t r = 0; r < data.rows(); ++r ) {
        // Init with the first col.
        ret[ r ].min = std::numeric_limits<double>::infinity();
        ret[ r ].max = - std::numeric_limits<double>::infinity();
 
        // Go through all other cols. If the value is not finite, skip it.
        size_t cnt = 0;
        for( size_t c = 0; c < data.cols(); ++c ) {
            auto const& e = data( r, c );
            if( std::isfinite( e ) || ! ignore_non_finite_values ) {
                ret[ r ].min = std::min( ret[ r ].min, data( r, c ) );
                ret[ r ].max = std::max( ret[ r ].max, data( r, c ) );
                ++cnt;
            }
        }
 
        // If we found no valid values at all, return nan.
        if( cnt == 0 ) {
            ret[ r ].min = std::numeric_limits<double>::quiet_NaN();
            ret[ r ].max = std::numeric_limits<double>::quiet_NaN();
        }
    }
 
    return ret;
}
 
template< typename T >
T matrix_sum( Matrix<T> const& data, bool ignore_non_finite_values = true )
{
    // Get row sums.
    auto sum = T{};
    for( auto const& e : data ) {
        if( std::isfinite( e ) || ! ignore_non_finite_values ) {
            sum += e;
        }
    }
    return sum;
}
 
template< typename T >
std::vector<T> matrix_row_sums( Matrix<T> const& data, bool ignore_non_finite_values = true )
{
    // Get row sums.
    auto row_sums = std::vector<T>( data.rows(), T{} );
    for( size_t i = 0; i < data.rows(); ++i ) {
        for( size_t j = 0; j < data.cols(); ++j ) {
            auto const& e = data( i, j );
            if( std::isfinite( e ) || ! ignore_non_finite_values ) {
                row_sums[ i ] += e;
            }
        }
    }
    return row_sums;
}
 
template< typename T >
std::vector<T> matrix_col_sums( Matrix<T> const& data, bool ignore_non_finite_values = true )
{
    // Get col sums.
    auto col_sums = std::vector<T>( data.cols(), T{} );
    for( size_t i = 0; i < data.rows(); ++i ) {
        for( size_t j = 0; j < data.cols(); ++j ) {
            auto const& e = data( i, j );
            if( std::isfinite( e ) || ! ignore_non_finite_values ) {
                col_sums[ j ] += e;
            }
        }
    }
    return col_sums;
}
 
// =================================================================================================
//     Normalization and Standardization
// =================================================================================================
 
std::vector<MinMaxPair<double>> normalize_cols( Matrix<double>& data );
 
std::vector<MinMaxPair<double>> normalize_rows( Matrix<double>& data );
 
std::vector<MeanStddevPair> standardize_cols(
    Matrix<double>& data,
    bool            scale_means = true,
    bool            scale_std = true
);
 
std::vector<MeanStddevPair> standardize_rows(
    Matrix<double>& data,
    bool            scale_means = true,
    bool            scale_std = true
);
 
std::vector<size_t> filter_constant_columns(
    Matrix<double>& data,
    double          epsilon = 1e-5
);
 
// =================================================================================================
//     Correlation and Covariance
// =================================================================================================
 
Matrix<double> correlation_matrix( Matrix<double> const& data );
 
Matrix<double> covariance_matrix( Matrix<double> const& data );
 
Matrix<double> sums_of_squares_and_cross_products_matrix( Matrix<double> const& data );
 
// =================================================================================================
//     Sorting
// =================================================================================================
 
template< typename T >
Matrix<T> matrix_sort_by_row_sum_symmetric( Matrix<T> const& data )
{
    if( data.rows() != data.cols() ) {
        throw std::runtime_error( "Symmetric sort only works on square matrices." );
    }
 
    auto result = Matrix<T>( data.rows(), data.cols() );
    auto row_sums = matrix_row_sums( data );
    auto si = sort_indices( row_sums.begin(), row_sums.end() );
 
    for( size_t i = 0; i < data.rows(); ++i ) {
        for( size_t j = 0; j < data.cols(); ++j ) {
            result( i, j ) = data( si[i], si[j] );
        }
    }
 
    return result;
}
 
template< typename T >
Matrix<T> matrix_sort_by_col_sum_symmetric( Matrix<T> const& data )
{
    if( data.rows() != data.cols() ) {
        throw std::runtime_error( "Symmetric sort only works on square matrices." );
    }
 
    auto result = Matrix<T>( data.rows(), data.cols() );
    auto col_sums = matrix_col_sums( data );
    auto si = sort_indices( col_sums.begin(), col_sums.end() );
 
    for( size_t i = 0; i < data.rows(); ++i ) {
        for( size_t j = 0; j < data.cols(); ++j ) {
            result( i, j ) = data( si[i], si[j] );
        }
    }
 
    return result;
}
 
template< typename T >
Matrix<T> matrix_sort_diagonal_symmetric( Matrix<T> const& data )
{
    if( data.rows() != data.cols() ) {
        throw std::runtime_error( "Symmetric sort only works on square matrices." );
    }
 
    // Find the row and col that contains the max element in the rest of the matrix,
    // that is, excluding the first rows and cols according to start.
    auto find_max = []( Matrix<T> const& mat, size_t start ){
        size_t max_r = start;
        size_t max_c = start;
        for( size_t r = start; r < mat.rows(); ++r ) {
            for( size_t c = start; c < mat.cols(); ++c ) {
                if( mat(r, c) > mat( max_r, max_c ) ) {
                    max_r = r;
                    max_c = c;
                }
            }
        }
        return std::make_pair( max_r, max_c );
    };
 
    // Sort by swapping rows and cols.
    auto mat = data;
    assert( mat.rows() == mat.cols() );
    for( size_t i = 0; i < mat.rows(); ++i ) {
        auto const max_pair = find_max( mat, i );
        matrix_swap_rows( mat, i, max_pair.first );
        matrix_swap_cols( mat, i, max_pair.second );
    }
    return mat;
}
 
// =================================================================================================
//     Matrix Addition
// =================================================================================================
 
template< typename T = double, typename A = double, typename B = double >
Matrix<T> matrix_addition( Matrix<A> const& a, Matrix<B> const& b )
{
    if( a.rows() != b.rows() || a.cols() != b.cols() ) {
        throw std::runtime_error( "Cannot add matrices with different dimensions." );
    }
 
    auto result = Matrix<T>( a.rows(), a.cols() );
    for( size_t r = 0; r < a.rows(); ++r ) {
        for( size_t c = 0; c < a.cols(); ++c ) {
            result( r, c ) = a( r, c ) + b( r, c );
        }
    }
    return result;
}
 
template< typename T = double, typename A = double, typename B = double >
Matrix<T> matrix_addition( Matrix<A> const& matrix, B const& scalar )
{
    auto result = Matrix<T>( matrix.rows(), matrix.cols() );
    for( size_t r = 0; r < matrix.rows(); ++r ) {
        for( size_t c = 0; c < matrix.cols(); ++c ) {
            result( r, c ) = matrix( r, c ) + scalar;
        }
    }
    return result;
}
 
template< typename T = double, typename A = double, typename B = double >
Matrix<T> matrix_subtraction( Matrix<A> const& a, Matrix<B> const& b )
{
    if( a.rows() != b.rows() || a.cols() != b.cols() ) {
        throw std::runtime_error( "Cannot add matrices with different dimensions." );
    }
 
    auto result = Matrix<T>( a.rows(), a.cols() );
    for( size_t r = 0; r < a.rows(); ++r ) {
        for( size_t c = 0; c < a.cols(); ++c ) {
            result( r, c ) = a( r, c ) - b( r, c );
        }
    }
    return result;
}
 
// =================================================================================================
//     Matrix Multiplication
// =================================================================================================
 
template< typename T = double, typename A = double, typename B = double >
Matrix<T> matrix_multiplication( Matrix<A> const& a, Matrix<B> const& b )
{
    if( a.cols() != b.rows() ) {
        throw std::runtime_error( "Cannot multiply matrices if a.cols() != b.rows()." );
    }
 
    // Simple and naive. Fast enough for the few occasions were we need this.
    // If Genesis at some point starts to need more elaborate matrix operations, it might be
    // worth including some proper library for this.
    auto result = Matrix<T>( a.rows(), b.cols() );
    for( size_t r = 0; r < a.rows(); ++r ) {
        for( size_t c = 0; c < b.cols(); ++c ) {
            result( r, c ) = 0.0;
            for( size_t j = 0; j < a.cols(); ++j ) {
                result( r, c ) += a( r, j ) * b( j, c );
            }
        }
    }
 
    return result;
}
 
template< typename T = double, typename A = double, typename B = double >
std::vector<T> matrix_multiplication( std::vector<A> const& a, Matrix<B> const& b )
{
    if( a.size() != b.rows() ) {
        throw std::runtime_error( "Cannot multiply vector with matrix if a.size() != b.rows()." );
    }
 
    auto result = std::vector<T>( b.cols(), 0.0 );
    for( size_t c = 0; c < b.cols(); ++c ) {
        for( size_t j = 0; j < a.size(); ++j ) {
            result[ c ] += a[ j ] * b( j, c );
        }
    }
 
    return result;
}
 
template< typename T = double, typename A = double, typename B = double >
std::vector<T> matrix_multiplication( Matrix<A> const& a, std::vector<B> const& b )
{
    if( a.cols() != b.size() ) {
        throw std::runtime_error( "Cannot multiply matrix with vector if a.cols() != b.size()." );
    }
 
    auto result = std::vector<T>( a.rows(), 0.0 );
    for( size_t r = 0; r < a.rows(); ++r ) {
        for( size_t j = 0; j < a.cols(); ++j ) {
            result[ r ] += a( r, j ) * b[ j ];
        }
    }
 
    return result;
}
 
template< typename T = double, typename A = double, typename B = double >
Matrix<T> matrix_multiplication( Matrix<A> const& matrix, B const& scalar )
{
    auto result = Matrix<T>( matrix.rows(), matrix.cols() );
    for( size_t r = 0; r < matrix.rows(); ++r ) {
        for( size_t c = 0; c < matrix.cols(); ++c ) {
            result( r, c ) = matrix( r, c ) * scalar;
        }
    }
    return result;
}
 
} // namespace utils
} // namespace genesis
 
#endif // include guard