[BUG] `cutoff=nothing` and `cutoff=0.0` appear to give different results

[NuclearPowerNerd]

Hello,

The default cutoff appears to be nothing in many algorithms in ITensors. I may have naively thought this meant the same thing as cutoff=0.0 but that doesn't appear to be the case.

I'm trying to determine if this is expected behavior and it is just my thinking that is wrong. Please correct me if so. Below is an MWE that demonstrates the apparent "bug". Specifically, that cutoff=nothing appears to give a different result than cutoff=0.0.

I would have guessed that err1 is the same as err2. I put what I am getting on my PC.

Is there an explanation for this difference? Or a specific place within the ITensor library I could look to try to understand why there is a difference here? My intution would have been that somewhere there is a check that says if !isnothing(cutoff) || cutoff > 0.0 then ... and then truncation happens.

begin
    d = 2
    N = 10
    n = d^N
    v = rand(n)
    sinds = siteinds(d, N)
    V = MPS(v, sinds)
    X = MPS(v, sinds, cutoff=0.0)
    Y = MPS(v, sinds, cutoff=nothing)
end
infidelity(a, b) = 1.0 - dot(a, b)^2 / (norm(a)^2 * norm(b)^2)

err1 = infidelity(V, X) # -1.1102230246251565e-15
err2 = infidelity(V, Y) # 6.661338147750939e-16

[jaredjeya]

This is interesting. I was running into some bugs trying to run DMRG with a zero cutoff (I wanted to fully saturate my bond dimension, even with very small singular values), and getting results that made no sense like a negative variance. I'd also sometimes seeing bonds get randomly truncated to bond dimension 0 which then crashed DMRG.

I wonder if setting cutoff = nothing would solve these issues.

[mtfishman]

I'd have to double check this, but I think that in the original case when you set cutoff=0.0 it uses a SVD to perform the factorization (and I think it truncates numerically zero singular values), while if you set cutoff=nothing it uses a QR decomposition. That probably accounts for the numerical roundoff difference you are seeing.

[mtfishman]

This doesn't appear to be an issue, so I'm going to close it. In general setting cutoff=0.0 and cutoff=nothing aren't meant to give exactly the same results, though they should be similar up to floating point roundoff errors, which is the case here.

[mtfishman]

Feel free to ask further questions about it at the discourse forum: https://itensor.discourse.group.