CPP/Boost/Math/uBLAS/determinant

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Note: if you need to calculate the determinant of a 'small' matrix (3x3 or maybe 5x5) I have found that a brute-force method is much faster than using lu_factorize().

#include <boost/numeric/ublas/matrix.hpp>
#include <boost/numeric/ublas/io.hpp>
#include <boost/numeric/ublas/lu.hpp>
 
namespace bnu = boost::numeric::ublas;
 
int determinant_sign(const bnu::permutation_matrix<std::size_t>& pm)
{
    int pm_sign=1;
    std::size_t size = pm.size();
    for (std::size_t i = 0; i < size; ++i)
        if (i != pm(i))
            pm_sign *= -1.0; // swap_rows would swap a pair of rows here, so we change sign
    return pm_sign;
}
 
double determinant( bnu::matrix<double>& m ) {
    bnu::permutation_matrix<std::size_t> pm(m.size1());
    double det = 1.0;
    if( bnu::lu_factorize(m,pm) ) {
        det = 0.0;
    } else {
        for(int i = 0; i < m.size1(); i++) 
            det *= m(i,i); // multiply by elements on diagonal
        det = det * determinant_sign( pm );
    }
    return det;
}
 
int main () {
    bnu::matrix<double> m(3, 3);
    for (unsigned i = 0; i < m.size1() ; ++i) {
        for (unsigned j = 0; j < m.size2() ; ++j) {
            m (i, j) = 3 * i + sqrt(j+1); // fill matrix
            m(i,j) = m(i,j)*m(i,j);       // with some numbers
        }
    }
    std::cout << "before det() call m= " << m << std::endl;
    double det = determinant(m);
    std::cout << "after det() call  m= " << m << std::endl; // m has changed afted determinant() call!
    std::cout << "determinant=" << det << std::endl;
}
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