Fix BP convergence metric for complex networks

[JoeyT1994]

This PR alters the message_diff function in BP to do a better convergence test.

Specifically, it defines it as 1 - |<m_{e, t+1}|m_{e, t}>|^{2} where |m_{e, t}> is the message tensor (reshaped as a vector) on edge e at iteration t and |m_{e, t}> is the message tensor (reshaped as a vector) on edge e at the subsequent iteration.

It is analogous to the infidelity measure for a quantum wavefunction and a strict lower bound on the trace distance,
i.e. 1 - |<m_{e, t+1}|m_{e, t}>|^{2} <= 0.5*Tr(|m_{e, t}><m_{e, t}| - |m_{e, t+1}><m_{e, t+1}|)

Importantly, it is independent of a "phase" factor e^i\theta difference between the two messages, something which I believe the Euclidean distance isn't and therefore would run into trouble with complex numbers.

[mtfishman]

Good point about the Euclidean distance, I think the Euclidean distance would be something like 1 - real(dot(lhs / norm(lhs), rhs / norm(rhs))) which as you say would not be invariant under multiplying lhs or rhs by a phase factor.

[mtfishman]

For some terminology, this measure is related to the cosine similarity, and the cosine distance which is defined in Distances.jl, but only for real numbers so far.

[mtfishman]

Thanks! Nice to see the BP code getting more robust.