Runtime polymorphism c++11 and operator overloading - c++11

Question

Let's say I am trying to implement some math vector class.
As vector interface will be used in multiple places: array based vector, matrices return columns and rows as vector interface objects and etc.
I would like to overload +,- operators for my vectors. Each operator should return new constructed object of some vector implementation class.
But as you know operator overloading should return a value or a reference. I can not return a value, as I need runtime polymorphism, so I am left with references. But to have a reference that does not die after the function call object should be created in the heap.
So how should I manage the situation?
P.S. I could create a shared_ptr and return a reference to containing value, but it does not look like a good practice.
typedef unsigned int vector_idx_t;
template <class T, vector_idx_t size>
class vector {
public:
virtual ~vector();
virtual T& operator[](const vector_idx_t idx) = 0;
virtual vector<T, size>& operator+ (const T& a) const = 0;
virtual vector<T, size>& operator- (const T& a) const = 0;
virtual vector<T, size>& operator* (const T& a) const = 0;
virtual vector<T, size>& operator/ (const T& a) const = 0;
virtual vector<T, size>& operator+ (const vector<T, size>& vec2) const = 0;
virtual vector<T, size>& operator- (const vector<T, size>& vec2) const = 0;
};
template <class T, vector_idx_t size>
class array_vector: public vector<T, size> {
private:
std::array<T, size> m_elements;
public:
array_vector();
array_vector(std::array<T, size> elements);
array_vector(const vector<T, size>& vec2);
array_vector(std::initializer_list<T> elems);
virtual ~array_vector();
virtual T& operator[](const vector_idx_t idx) {
return m_elements[idx];
}
virtual vector<T, size>& operator+ (const T& a) const {
std::array<T, size> e;
for (vector_idx_t i = 0; i < size; ++i) {
e[i] = m_elements[i] + a;
}
auto v = std::make_shared<array_vector<T, size>>(elems);
return *v;
}
};

Answer 1

I suggest a slight modification to your design for accommodating the polymorphic nature of the implementation.
Don't make vector polymorphic.
Use a Data class to contain the implementation specific details of vector.
Make Data polymorphic.
That will allow you to return vectors by value or by reference, as appropriate to an interface.

Answer 2

Polymorphism by subtype is not the answer to all problems. I understand what are you trying to do but I don't exactly understand why a polymorphic by template solution is not enough and you need to have virtual operators (which don't mix well at all with polymorphism by subtype).
You want to be able to define operations on mixed types of vectors so that you can compute results between real containers and proxy to containers.
This first of all should require that you have a basic final type that you need, a proxy to a matrix column is not a real container but rather a view of a container, so adding two of them should return a real container (eg. a container backed by an actual std::array?).
A similar design could be managed by something like
template<typename ContainerType, typename ElementType>
class vector_of : public ContainerType
{
public:
vector_of(const ContainerType& container) : ContainerType(container) { }
vector_of<ContainerType, ElementType> operator+(const ElementType& a) const
{
vector_of<ContainerType, ElementType> copy = vector_of<ContainerType,ElementType>(*this);
std::for_each(copy.begin(), copy.end(), [&a](ElementType& element) { element += a; });
}
template<typename T>
vector_of<ContainerType, ElementType> operator+(const vector_of<T, ElementType>& a) const
{
vector_of<ContainerType, ElementType> copy(*this);
auto it = copy.begin();
auto it2 = a.begin();
while (it != copy.end() && it2 != a.end())
{
*it += *it2;
++it;
++it2;
}
return copy;
}
};
The trick here is that operator+ is a template method which accepts a generic container of ElementType elements. The code assumes that these kind of containers provide a begin and end methods which return an iterator (which is a smart choice in any case because it works well with STL).
With you can do things like:
class MatrixRowProxy
{
private:
int* data;
size_t length;
public:
MatrixRowProxy(int* data, size_t length) : data(data), length(length) { }
int* begin() const { return data; }
int* end() const { return data + length; }
};
vector_of<std::array<int, 5>, int> base = vector_of<std::array<int, 5>, int>({ 1, 2, 3, 4, 5 });
vector_of<std::vector<int>, int> element = vector_of<std::vector<int>, int>({ 2, 3, 4, 5, 6 });
int* data = new int[5] { 10, 20, 30, 40, 50};
vector_of<MatrixRowProxy, int> proxy = vector_of<MatrixRowProxy, int>(MatrixRowProxy(data, 5));
auto result = base + element + proxy;
for (const auto& t : result)
std::cout << t << std::endl;
So you can add heterogeneous kinds of vectors without the need of any virtual method.
Of course these methods require to create a new resulting object in the methods. This is done by copying this into a new vector_of<ContainerType, ElementType>. Nothing prevents you from adding a third template argument like VectorFactory which takes care of this so that you could use vectors which are only wrappers also on LHS of such operators.