I am attempting to understand how some of the UBLAS libraries work. Currently I am looking at the implementation described in matrix_expression.hpp and specifically a small section of code that computes the outer product of a matrix. However, I am having some dificulty comprehending all of the code. I have read through the online documentation, and it has helped, but I am still unclear on many parts. So, if anyone could help me out by explaining to me how this operates I would be most grateful.

Below is the code I need help understanding. It is a function template that computes a product. What is confusing me is that I don't know what vector_matrix_binary_traits() and scalar_multiplies() do. I also don't understand, what BOOST_UBLAS_INLINE is supposed to accomplish. And lastly, what is value_type and expression_type ?

matrix_expression.hpp

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   // (outer_prod (v1, v2)) [i] [j] = v1 [i] * v2 [j]
    template<class E1, class E2>

    BOOST_UBLAS_INLINE
    typename vector_matrix_binary_traits<E1, E2, scalar_multiplies<typename E1::value_type, typename E2::value_type> >::result_type

    outer_prod (const vector_expression<E1> &e1,
                const vector_expression<E2> &e2) {

        BOOST_STATIC_ASSERT (E1::complexity == 0 && E2::complexity == 0);
        typedef typename vector_matrix_binary_traits<E1, E2, scalar_multiplies<typename E1::value_type, typename E2::value_type> >::expression_type expression_type;

        return expression_type (e1 (), e2 ());
    }
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