Operators

[JoeyT1994]

This code adds operators into the mix, specifically the ability to build derivative operators by constructing stencils which are operators that perform the mapping: f(x,y,z, ...) -> a*f(x+h, y, z, ...) + b*f(x, y, z, ...) + c*f(x-h, y, z, ...) where a,b,c are arbitrary scalars and h = 1/(2^L) with L the number of bits in the dimension where the derivative is being taken. The derivative can be taken in any dimension you wish.

Currently this operator is only supported on trees but a simple modification can be done to make it work on any graph (by taking a spanning tree of that graph).

Tests are included.
Slight refactor of the TensorNetworkFunctionals.jl file to streamline the module interface.

[emstoudenmire]

The stencil idea is really nice. Are yall planning to lift the limitation on only passing three numbers?

[JoeyT1994]

The stencil idea is really nice. Are yall planning to lift the limitation on only passing three numbers?

I think so! It seems straightforward enough to do shift by any multiple of (1/2^{L}) so that would allow us to create stencils for even higher order derivatives.

[ryanlevy]

LGTM, could you just add some comments/docstrings on the itensornetworkutils.jl functions and either in this one or another PR we can address the numerical type "safety"

[JoeyT1994]

@ryanlevy Sure let me add some comments because those functions are ambiguous (and probably need better naming)