Variable dimension dynamic array in C++ - c++

Question

I would like to implement a STL-like tensor template in C++, which needs overload operator[] to access its elements, which may looks like this:
Tensor<double,2> tensor2
{
{1,2,3},
{4,5,6}
};
std::cout<< tensor2[1][2]<<'\n';
For low dimensions, it may be easy to use some thing like
std::vector<std::vector<int>>
But this would not be easy to use for higher dimensions.
Also I would like to implement product between tensors and contraction between dimensions in one tensor.

Answer 1

I implemented the multi-dimensional array with some very basic operations. Since Boost.MultiArray offers a far better solution, my implementation is just for demonstration.
namespace DataStructures
{
struct ExtentList //Discribe extents of dimensions for MultiArray
{
std::vector<size_t> dimensions;
ExtentList() = default;
template<typename Iterator, typename SFINAE = std::enable_if_t<std::_Is_iterator_v<Iterator>>>
ExtentList(Iterator begin, Iterator end) : dimensions(begin, end) {}
//operator[] used to initialize the extents
ExtentList& operator[](size_t n) { dimensions.push_back(n); return *this; }
ExtentList after_front() const { return ExtentList(++dimensions.cbegin(), dimensions.cend()); }
//at() used to access extents
size_t at(size_t n) const { return dimensions.at(n); }
};
static ExtentList Extents;
template<
typename ElemType, //Underlying Type
size_t Dimension, //Dimension of MultiArray
typename ElementAllocator = std::allocator<ElemType>, //Allocator for elements
template<typename, typename> typename ContainerType = std::vector, //Underlying container type
template<typename> typename ContainerAllocator = std::allocator> //Allocator for container
class MultiArray
{
//Necessary for contructor with ExtentList
friend class MultiArray<ElemType, Dimension + 1U, ElementAllocator, ContainerType, ContainerAllocator>;
using value_type = typename
std::conditional_t<
Dimension == 1U,
ElemType,
MultiArray<ElemType, Dimension - 1U, ElementAllocator, ContainerType, ContainerAllocator>>;
using allocator_type = typename
std::conditional_t<
Dimension == 1U,
ElementAllocator,
ContainerAllocator<value_type>>;
ContainerType<value_type, allocator_type> data;
public:
MultiArray() = default;
MultiArray(size_t n, const value_type& val) : data(n, val) {}
template<typename SFINAE = std::enable_if_t<(Dimension == 1U)>>
MultiArray(ExtentList extents, const ElemType& elem) : data(extents.at(0), elem) {}
template<typename SFINAE = std::enable_if_t<(Dimension >= 2U)>, typename SFINAE2 = SFINAE>
MultiArray(ExtentList extents, const ElemType& elem) : data(extents.at(0), value_type(extents.after_front(), elem)) {}
MultiArray(std::initializer_list<value_type> ilist) : data(ilist) {}
template<typename ... SizeType>
MultiArray(size_t N, SizeType... args) : data(N, value_type(args...)) {}
value_type& operator[](size_t n) { return data[n]; }
void push_back(const value_type& elem) { data.push_back(elem); }
};
}
The idea is to implement the multi-dimensional array with recursive template, so subscription and list initialization operations are allowed.
namespace DS = DataStructures;
DS::MultiArray<int, 2> matrix_2d
{
{ 1,2,3 },
{ 4,5,6 },
{ 7,8,9 }
};
for (size_t i = 0; i != 3; ++i)
for (size_t j = 0; j != 3; ++j)
std::cout << matrix_2d[i][j] << ' ';
DS::MultiArray<int, 3> matrix_3d(DS::Extents[10][10][10], 0);
size_t sum = 0;
for (size_t i = 0; i != DS::Extents.at(0); ++i)
for (size_t j = 0; j != DS::Extents.at(1); ++j)
for (size_t k = 0; k != DS::Extents.at(2); ++k)
sum += (matrix_3d[i][j][k] = i * 100 + j * 10 + k);
std::cout << sum << '\n' << matrix_3d[9][9][9] << '\n';
The idea of ExtentList comes from Boost. It is better than variable function parameter list or variable template.