Implement inner(x,A,y) for TTN via BP.
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inner(x,A,y) for TTN via BP.
| O = O * ydag[v] * A[v] * x[v] | ||
| end | ||
| return O[] | ||
| blf = BilinearFormNetwork(A, ydag, x) |
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I don't think we should be using a form here, that is mostly meant for optimization.
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Is your goal to make a tensor network out of the network y, A, and x? If so, you can use disjoint_union.
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Yes, as far as I understand the BilinearFormNetwork just stacks the network here.
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Ok, let's do that without going through BilinearFormNetwork.
| ) | ||
| end | ||
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| function contract_with_BP( |
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contract_with_BP isn't a good function name, what about overloading ITensors.contract(::Algorithm"bp", kwargs...) and running with contract(itn; alg="bp", kwargs...).
| end | ||
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| function contract_with_BP( | ||
| T::Type, |
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I'm confused by this part of the interface, why can you set the element type in this way?
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This is not the right way to do it. Basically, due to the log in this implementation, we need to promote the scalars of which the element type is taken to complex. Then the idea was that contract_with_BP returns a complex scalar, unless you specify a type, in which case it converts the scalar to the specified type. This should of course be handled differently for a proper implementation as contract with BP backend.
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Ok. I think contract_with_BP as it stands is too far away from being a library function, so we should think about how to deal with that before continuing forward with this PR.
| if !is_tree(partitioned_graph(pg)) && outputlevel > 0 | ||
| println("Partitioned graph is not a tree, result will be approximate!!") | ||
| end |
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Let's remove this, I think this is inherent if someone selects that they are using BP.
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Yes, but it may be good to allow to pass a flag like assert_exact=true, to check that the BP will indeed be exact for the contraction (for the case of contracting TTNs)?
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Let's think about the design of that, but I don't think we have to address that in this PR. I agree with the sentiment that we don't want to secretly perform approximate contractions but give users the impression that we are doing exact contractions.
| for pv in partitionvertices(pg) | ||
| incoming_mts = incoming_messages(bp_cache, [pv]) | ||
| local_state = ITensor[itn[v] for v in vertices(pg, pv)] | ||
| log_numerator += log(complex(ITensors.contract(vcat(incoming_mts, local_state))[])) |
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| log_numerator += log(complex(ITensors.contract(vcat(incoming_mts, local_state))[])) | |
| log_numerator += log(complex(contract(vcat(incoming_mts, local_state))[])) |
| for pe in partitionedges(pg) | ||
| log_denominator += log( | ||
| complex( | ||
| ITensors.contract(vcat(message(bp_cache, pe), message(bp_cache, reverse(pe))))[] |
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| ITensors.contract(vcat(message(bp_cache, pe), message(bp_cache, reverse(pe))))[] | |
| contract(vcat(message(bp_cache, pe), message(bp_cache, reverse(pe))))[] |
| log_numerator, log_denominator = 0, 0 | ||
| for pv in partitionvertices(pg) | ||
| incoming_mts = incoming_messages(bp_cache, [pv]) | ||
| local_state = ITensor[itn[v] for v in vertices(pg, pv)] |
| end | ||
| return O[] | ||
| blf = BilinearFormNetwork(A, ydag, x) | ||
| blf_scalar_bp = contract_with_BP( |
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If we just use contract here, then we can allow an alg keyword argument to get passed from inner, and users can control what algorithm is used to contract the network.
To handle partitioning in the more general case, something we could do is that instead of passing an ITensorNetwork and a partitioning, we pass a PartitionedGraph to contract, then it is up to the contract backends to contract the partitioned tensor network (either using or ignoring the partitioning).
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Closing in favor of first writing a better designed |
This implements
inner(x,A,y)forx,A,yallAbstractTTNwith the same underlying graph, passing through the BP-backend. It addresses a performance issue of the previous implementation for certainTTN, leading to higher than necessary scaling in some situations (due to the traversal order). Thanks @JoeyT1994 for providing thecontract_with_BPcode.Tests have been added to
test_forms.jlto verify the correctness of the implementation.This is not intended as a complete overhaul of the current implementations of
inner,expectetc, which could be addressed in future PRs.