N-dimensional tensor based on std::vector

Question

I want to define n-dimensional data structure using std::vector. I have a problem with definition of operator(). Lets have a look at a sample 2D structure

class my_data {

public:
  my_data (size_t N, size_t M) : tab(N*M), _N(N), _M(M) {}

  const double& operator() (size_t i, size_t j) const {
     return tab.at(i * M + j);
  }

  double& operator() (size_t i, size_t j) {
     return tab.at(i * M + j);
  }

private:
   std::vector<double> tab;
   size_t _N;
   size_t _M;

};

I would like to define such a structures for any dimension using templates , but I don't know if it is possible. So basically what I would like to have is something like that

my_data<4> vec (1,2,3,4);

defines 4D 'tensor' with sizes 1,2,3,4 (number of all elements 1*2*3*4). You can now access and change values by typing

vec (0,0,0,0) = 2.0;

Answer 1

The below solution uses some of the C++14 and C++1z features, but they can be easily ported to C++11:

#include <vector>
#include <utility>
#include <array>
#include <cstddef>

namespace detail
{
    template <typename T, typename S>
    class my_data;

    template <typename T, std::size_t... Is>
    class my_data<T, std::index_sequence<Is...>>
    {
    public:
        my_data(decltype(Is)... size)
            : t((size * ...)), s{{ size... }}
        {}

        T& operator()(decltype(Is)... i)
        {            
            return t.at(index({{ i... }}));
        }

        const T& operator()(decltype(Is)... i) const
        {            
            return t.at(index({{ i... }}));
        }

    private:
        std::size_t index(const std::array<std::size_t, sizeof...(Is)>& a) const
        {
            std::size_t ind = a[0];
            for (std::size_t i = 1; i < a.size(); ++i)
            {
                ind = ind * s[i] + a[i];
            }
            return ind;
        }

        std::vector<T> t;
        const std::array<std::size_t, sizeof...(Is)> s;
    };
}

template <typename T, std::size_t N>
using my_data = detail::my_data<T, std::make_index_sequence<N>>;

Test:

int main()
{        
    my_data<double, 4> vec(1,2,3,4);
    vec(0,0,0,0) = 2.0;
}

DEMO

DEMO (C++11)