[ENH] Start sketching out merge lattice and tensor class

[adam2392]

Closes: #27

Useful links: https://godbolt.org/z/crbY5ae8n

[adam2392]

Okay so in order to go towards the MergeLattice, we first want a MVP of the Tensor class. Looking at the taco's documentation: http://tensor-compiler.org/docs/tensors.html, and the Tensor class, the main functionalities look like:

1. constructor with arbitrary template types [x]
2. insert: inserting a value at a specific index in the tensor
3. pack: I don't see why this would be needed since we define the data structures during compile-time? But maybe I'm wrong.
4. querying basic metadata of the tensor, such as get_dimension, get_levels

Is there any other explicit functionality we would like? Perhaps convert_format, which gets passed in a tuple of level types, which are used to construct new levels? E.g. convert (dense, dense) into (compressed, hashed) or something like that?

Error-checking

During construction of the tensor, Hameer, you mentioned we should do some error-checking. Should we work on this now, or possibly table it until we connect this with the MergeLattice?

[adam2392]

A few questions:

1. How do we get data/pointer-to-the-next-level at a specific index if they don't support locate? Do we just iterate?

To iterate, is this the right pseudocode? The get_data function for writing/reading would be a runtime method right?

// E.g. 3D tensor, then write non-zero value to (i,j,k) location
// at a high level in the Tensor need to access the levels to use the append_init, append_*
// methods
//
// for idx != i:
//     append(j, ithlevel)
//     for jdx <= j:
//         append(k, jthlevel)
//         for kdx <= k:
//             append(value, kthlevel)

2. Re enhancing container_traits.hpp, what sort of functions should we provide the container_traits struct? We need to provide an implementation so that someone could plug in an arbitrary set of containers right?

E.g. would it be these?

template <typename size_type>
        constexpr void resize(size_type count)
        {
        }

        template <typename T>
        constexpr void push_back(const T& value)
        {
        }

        template <typename size_type, typename Elem>
        constexpr Elem operator[](size_type pos)
        {
        }