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Filename : determinant_impl.hpp
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//Copyright (c) 2008-2016 Emil Dotchevski and Reverge Studios, Inc.

//Distributed under the Boost Software License, Version 1.0. (See accompanying
//file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

#ifndef BOOST_QVM_3DCF6B90AE0E11DE9A315BE555D89593
#define BOOST_QVM_3DCF6B90AE0E11DE9A315BE555D89593

#include <boost/qvm/inline.hpp>
#include <boost/qvm/mat_traits_array.hpp>
#include <boost/qvm/static_assert.hpp>

namespace
boost
    {
    namespace
    qvm
        {
        namespace
        qvm_detail
            {
            template <int N>
            struct
            det_size
                {
                };

            template <class M>
            BOOST_QVM_INLINE_TRIVIAL
            typename mat_traits<M>::scalar_type
            determinant_impl_( M const & a, det_size<2> )
                {
                return
                    mat_traits<M>::template read_element<0,0>(a) * mat_traits<M>::template read_element<1,1>(a) -
                    mat_traits<M>::template read_element<1,0>(a) * mat_traits<M>::template read_element<0,1>(a);
                }

            template <class M,int N>
            BOOST_QVM_INLINE_RECURSION
            typename mat_traits<M>::scalar_type
            determinant_impl_( M const & a, det_size<N> )
                {
                typedef typename mat_traits<M>::scalar_type T;
                T m[N-1][N-1];
                T det=T(0);
                for( int j1=0; j1!=N; ++j1 )
                    {
                    for( int i=1; i!=N; ++i )
                        {
                        int j2 = 0;
                        for( int j=0; j!=N; ++j )
                            {
                            if( j==j1 )
                                continue;
                            m[i-1][j2] = mat_traits<M>::read_element_idx(i,j,a);
                            ++j2;
                            }
                        }
                    T d=determinant_impl_(m,det_size<N-1>());
                    if( j1&1 )
                        d=-d;
                    det += mat_traits<M>::read_element_idx(0,j1,a) * d;
                    }
                return det;
                }

            template <class M>
            BOOST_QVM_INLINE_TRIVIAL
            typename mat_traits<M>::scalar_type
            determinant_impl( M const & a )
                {
                BOOST_QVM_STATIC_ASSERT(mat_traits<M>::rows==mat_traits<M>::cols);
                return determinant_impl_(a,det_size<mat_traits<M>::rows>());
                }
            }
        }
    }

#endif