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.

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#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.

download source: utst1.cpp

This compiles on Lucid Lynx with the following CMakeLists.txt:

cmake_minimum_required(VERSION 2.6)
PROJECT(utst1)
find_package( Boost )
if(Boost_FOUND)
    include_directories(${Boost_INCLUDE_DIRS})
endif()
ADD_EXECUTABLE(utst1 utst1.cpp)
target_link_libraries(utst1 ${Boost_LIBRARIES})