Unnecessary repeat calculations in dynamics code

[cerisola]

As part of issue #2 about speeding up dynamics, I have noticed some unnecessary repeated calculations being done in the dynamics code. In particular, when computing the super operator the total Hamiltonian is created and diagonalised multiple times.

For example, in the super operator creation function, the following loop is run:

    for i in 1:dim(n)
        trans = transitions(prm, ang, n, i)
        ωb = trans[1]
        ATr = trans[2]
        len = length(ωb)
        ATot = sum(ATr[j] for j = 1:len)
        χ = (π/2)*sum(spectral_density_Ohm(ωb[j], prm)[i]*coth((ωb[j])/(2*T))*ATr[j] for j = 1:len) 
        Θ = (π/2)*sum(spectral_density_Ohm(ωb[j], prm)[i]*ATr[j] for j = 1:len)
        supop += - ℒ(ATot)*(ℒ(χ) - ℛ(χ)) + ℛ(ATot)*(ℒ(χ) - ℛ(χ)) + ℒ(ATot)*(ℒ(Θ) + ℛ(Θ)) - ℛ(ATot)*(ℒ(Θ) + ℛ(Θ))
    end

the function transitions is called multiple times. Inside of each call this code is run:

    H = HTot(prm, ang, n)
    A = jump(n)[i]
    d = hspace_size(n)
    table = zeros(d, d)
    bohr_freqs = Float64[]
    jump_ops = Any[]
    eval = eigen(H).values
    evec = eigen(H).vectors

which means that for each call to transitions, the total Hamiltonina is computed and diagonals (twice of each call). This is probably a leading cause for the heavy slowdown when going to more levels in the RCs.