Optimize ttn_svd (#157)

Author: b-kloss

Project.toml

@@ -46,7 +46,7 @@ ITensorNetworksEinExprsExt = "EinExprs"
 AbstractTrees = "0.4.4"
 Combinatorics = "1"
 Compat = "3, 4"
-DataGraphs = "0.1.7"
+DataGraphs = "0.1.13"
 DataStructures = "0.18"
 Dictionaries = "0.4"
 Distributions = "0.25.86"

src/treetensornetworks/opsum_to_ttn.jl

@@ -6,36 +6,25 @@ using ITensors.NDTensors: Block, maxdim, nblocks, nnzblocks
 using ITensors.Ops: Op, OpSum
 using NamedGraphs: degrees, is_leaf, vertex_path
 using StaticArrays: MVector
-
+using NamedGraphs: boundary_edges
 # convert ITensors.OpSum to TreeTensorNetwork
 
 # 
 # Utility methods
 # 
 
-# linear ordering of vertices in tree graph relative to chosen root, chosen outward from root
-function find_index_in_tree(site, g::AbstractGraph, root_vertex)
-  ordering = reverse(post_order_dfs_vertices(g, root_vertex))
-  return findfirst(x -> x == site, ordering)
-end
-function find_index_in_tree(o::Op, g::AbstractGraph, root_vertex)
-  return find_index_in_tree(ITensors.site(o), g, root_vertex)
+function align_edges(edges, reference_edges)
+  return intersect(Iterators.flatten(zip(edges, reverse.(edges))), reference_edges)
 end
 
-# determine 'support' of product operator on tree graph
-function span(t::Scaled{C,Prod{Op}}, g::AbstractGraph) where {C}
-  spn = eltype(g)[]
-  nterms = length(t)
-  for i in 1:nterms, j in i:nterms
-    path = vertex_path(g, ITensors.site(t[i]), ITensors.site(t[j]))
-    spn = union(spn, path)
-  end
-  return spn
+function align_and_reorder_edges(edges, reference_edges)
+  return intersect(reference_edges, align_edges(edges, reference_edges))
 end
 
-# determine whether an operator string crosses a given graph vertex
-function crosses_vertex(t::Scaled{C,Prod{Op}}, g::AbstractGraph, v) where {C}
-  return v ∈ span(t, g)
+function split_at_vertex(g::AbstractGraph, v)
+  g = copy(g)
+  rem_vertex!(g, v)
+  return Set.(connected_components(g))
 end
 
 # 
@@ -45,7 +34,7 @@ end
 """
     ttn_svd(os::OpSum, sites::IndsNetwork, root_vertex, kwargs...)
 
-Construct a dense TreeTensorNetwork from a symbolic OpSum representation of a
+Construct a TreeTensorNetwork from a symbolic OpSum representation of a
 Hamiltonian, compressing shared interaction channels.
 """
 function ttn_svd(os::OpSum, sites::IndsNetwork, root_vertex; kwargs...)
@@ -71,9 +60,9 @@ function ttn_svd(
   thishasqns = any(v -> hasqns(sites[v]), vertices(sites))
 
   # traverse tree outwards from root vertex
-  vs = reverse(post_order_dfs_vertices(sites, root_vertex))                                 # store vertices in fixed ordering relative to root
+  vs = _default_vertex_ordering(sites, root_vertex)
   # ToDo: Add check in ttn_svd that the ordering matches that of find_index_in_tree, which is used in sorteachterm #fermion-sign!
-  es = reverse(reverse.(post_order_dfs_edges(sites, root_vertex)))                          # store edges in fixed ordering relative to root
+  es = _default_edge_ordering(sites, root_vertex)                          # store edges in fixed ordering relative to root
   # some things to keep track of
   degrees = Dict(v => degree(sites, v) for v in vs)                                           # rank of every TTN tensor in network
   Vs = Dict(e => Dict{QN,Matrix{coefficient_type}}() for e in es)                                    # link isometries for SVD compression of TTN
@@ -105,6 +94,8 @@ function ttn_svd(
   for v in vs
     is_internal[v] = isempty(sites[v])
     if isempty(sites[v])
+      # FIXME: This logic only works for trivial flux, breaks for nonzero flux
+      # ToDo: add assert or fix and add test!
       sites[v] = [Index(Hflux => 1)]
     end
   end
@@ -118,35 +109,65 @@ function ttn_svd(
   # build compressed finite state machine representation
   for v in vs
     # for every vertex, find all edges that contain this vertex
-    edges = filter(e -> dst(e) == v || src(e) == v, es)
+    edges = align_and_reorder_edges(incident_edges(sites, v), es)
+
     # use the corresponding ordering as index order for tensor elements at this site
     dim_in = findfirst(e -> dst(e) == v, edges)
     edge_in = (isnothing(dim_in) ? [] : edges[dim_in])
     dims_out = findall(e -> src(e) == v, edges)
     edges_out = edges[dims_out]
 
+    # for every site w except v, determine the incident edge to v that lies 
+    # in the edge_path(w,v)
+    subgraphs = split_at_vertex(sites, v)
+    _boundary_edges = align_edges(
+      [only(boundary_edges(underlying_graph(sites), subgraph)) for subgraph in subgraphs],
+      edges,
+    )
+    which_incident_edge = Dict(
+      Iterators.flatten([
+        subgraphs[i] .=> ((_boundary_edges[i]),) for i in eachindex(subgraphs)
+      ]),
+    )
+
     # sanity check, leaves only have single incoming or outgoing edge
     @assert !isempty(dims_out) || !isnothing(dim_in)
     (isempty(dims_out) || isnothing(dim_in)) && @assert is_leaf(sites, v)
 
     for term in os
       # loop over OpSum and pick out terms that act on current vertex
-      crosses_vertex(term, sites, v) || continue
+
+      factors = ITensors.terms(term)
+      if v in ITensors.site.(factors)
+        crosses_vertex = true
+      else
+        crosses_vertex =
+          !isone(
+            length(Set([which_incident_edge[site] for site in ITensors.site.(factors)]))
+          )
+      end
+      #if term doesn't cross vertex, skip it
+      crosses_vertex || continue
+
+      # filter out factor that acts on current vertex
+      onsite = filter(t -> (ITensors.site(t) == v), factors)
+      not_onsite_factors = setdiff(factors, onsite)
 
       # filter out factors that come in from the direction of the incoming edge
       incoming = filter(
-        t -> edge_in ∈ edge_path(sites, ITensors.site(t), v), ITensors.terms(term)
+        t -> which_incident_edge[ITensors.site(t)] == edge_in, not_onsite_factors
       )
+
       # also store all non-incoming factors in standard order, used for channel merging
       not_incoming = filter(
-        t -> edge_in ∉ edge_path(sites, ITensors.site(t), v), ITensors.terms(term)
+        t -> (ITensors.site(t) == v) || which_incident_edge[ITensors.site(t)] != edge_in,
+        factors,
       )
-      # filter out factor that acts on current vertex
-      onsite = filter(t -> (ITensors.site(t) == v), ITensors.terms(term))
+
       # for every outgoing edge, filter out factors that go out along that edge
       outgoing = Dict(
-        e => filter(t -> e ∈ edge_path(sites, v, ITensors.site(t)), ITensors.terms(term))
-        for e in edges_out
+        e => filter(t -> which_incident_edge[ITensors.site(t)] == e, not_onsite_factors) for
+        e in edges_out
       )
 
       # compute QNs
@@ -246,7 +267,8 @@ function ttn_svd(
 
   for v in vs
     # redo the whole thing like before
-    edges = filter(e -> dst(e) == v || src(e) == v, es)
+    # ToDo: use neighborhood instead of going through all edges, see above
+    edges = align_and_reorder_edges(incident_edges(sites, v), es)
     dim_in = findfirst(e -> dst(e) == v, edges)
     dims_out = findall(e -> src(e) == v, edges)
     # slice isometries at this vertex
@@ -340,9 +362,10 @@ function ttn_svd(
       if is_internal[v]
         H[v] += iT
       else
-        if hasqns(iT)
-          @assert flux(iT * Op) == Hflux
-        end
+        #ToDo: Remove this assert since it seems to be costly
+        #if hasqns(iT)
+        #  @assert flux(iT * Op) == Hflux
+        #end
         H[v] += (iT * Op)
       end
     end
@@ -409,12 +432,24 @@ function computeSiteProd(sites::IndsNetwork{V,<:Index}, ops::Prod{Op})::ITensor
   return T
 end
 
+function _default_vertex_ordering(g::AbstractGraph, root_vertex)
+  return reverse(post_order_dfs_vertices(g, root_vertex))
+end
+
+function _default_edge_ordering(g::AbstractGraph, root_vertex)
+  return reverse(reverse.(post_order_dfs_edges(g, root_vertex)))
+end
+
 # This is almost an exact copy of ITensors/src/opsum_to_mpo_generic:sorteachterm except for the site ordering being
 # given via find_index_in_tree
 # changed `isless_site` to use tree vertex ordering relative to root
 function sorteachterm(os::OpSum, sites::IndsNetwork{V,<:Index}, root_vertex::V) where {V}
   os = copy(os)
-  findpos(op::Op) = find_index_in_tree(op, sites, root_vertex)
+
+  # linear ordering of vertices in tree graph relative to chosen root, chosen outward from root
+  ordering = _default_vertex_ordering(sites, root_vertex)
+  site_positions = Dict(zip(ordering, 1:length(ordering)))
+  findpos(op::Op) = site_positions[ITensors.site(op)]
   isless_site(o1::Op, o2::Op) = findpos(o1) < findpos(o2)
   N = nv(sites)
   for n in eachindex(os)