## Matrix determinant with Boost::uBLAS

Boost uBLAS provides BLAS functionality, but doesn't have a function for computing the determinant of a matrix. Googling for this turns up a few code snippets, but it's best to document this completely here now since I got it to work, and it will be useful for opencamlib sooner or later.

```1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 #include <boost /numeric/ublas/matrix.hpp> #include </boost><boost /numeric/ublas/io.hpp> #include </boost><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><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; }```

I'm trying the WP-syntax plugin here for the first time. The include statements are garbled, but otherwise it seems to work.

```cmake_minimum_required(VERSION 2.6)