various fixes and improvements

Author: lkdvos

src/bimodulesector.jl

@@ -3,7 +3,7 @@ struct BimoduleSector{Name} <: Sector
     j::Int
     label::Int
 end
-
+BimoduleSector{Name}(data::NTuple{3,Int}) where {Name} = BimoduleSector{Name}(data...)
 const A4Object = BimoduleSector{:A4}
 
 # Utility implementations
@@ -12,7 +12,9 @@ function Base.isless(a::I, b::I) where {I<:BimoduleSector}
     return isless((a.i, a.j, a.label), (b.i, b.j, b.label))
 end
 Base.hash(a::BimoduleSector, h::UInt) = hash(a.i, hash(a.j, hash(a.label, h)))
-Base.convert(::Type{BimoduleSector{Name}}, d::NTuple{3,Int}) = BimoduleSector{Name}(d...)
+function Base.convert(::Type{BimoduleSector{Name}}, d::NTuple{3,Int}) where {Name}
+    return BimoduleSector{Name}(d...)
+end
 
 Base.IteratorSize(::Type{SectorValues{<:BimoduleSector}}) = Base.SizeUnknown()
 
@@ -39,14 +41,6 @@ function TensorKitSectors.:⊗(a::A4Object, b::A4Object)
                                 numlabels(A4Object, a.i, b.j)))
 end
 
-# TODO: can I assume A4Irrep(i, i, 1) is identity?
-function Base.conj(a::A4Object)
-    i, j = a.i, a.j
-    label = findfirst(x -> Nsymbol(a, A4Irrep(j, i, x), A4Irrep(i, i, 1)) == 1,
-                      1:numlabels(A4Object, j, i))
-    return A4Object(j, i, label)
-end
-
 # Data from files
 # ---------------
 const artifact_path = joinpath(artifact"fusiondata", "MultiTensorKit.jl-data-v0.1.0")
@@ -62,35 +56,113 @@ function extract_Nsymbol(::Type{A4Object})
             a, b, c = parse.(Int, split(string(k)[2:(end - 1)], ", "))
             y[(a, b, c)] = v
         end
+        return y
+    end
+end
+
+const Ncache = IdDict{Type{<:BimoduleSector},Array{Dict{NTuple{3,Int},Int},3}}()
+
+function _get_Ncache(::Type{T}) where {T<:BimoduleSector}
+    global Ncache
+    return get!(Ncache, T) do
+        return extract_Nsymbol(T)
     end
 end
 
-const A4_Ncache = extract_Nsymbol(A4Object)
 function TensorKitSectors.Nsymbol(a::I, b::I, c::I) where {I<:A4Object}
     # TODO: should this error or return 0?
     (a.j == b.i && a.i == c.i && b.j == c.j) ||
         throw(ArgumentError("invalid fusion channel"))
     i, j, k = a.i, a.j, b.j
-    return get(A4_Ncache[i, j, k], (a.label, b.label, c.label), 0)
+    return get(_get_Ncache(I)[i, j, k], (a.label, b.label, c.label), 0)
+end
+
+# TODO: can we define dual for modules?
+const Dualcache = IdDict{Type{<:BimoduleSector},Vector{Tuple{Int,Vector{Int}}}}()
+
+function _get_dual_cache(::Type{T}) where {T<:BimoduleSector}
+    global Dualcache
+    return get!(Dualcache, T) do
+        return extract_dual(T)
+    end
+end
+
+function extract_dual(::Type{A4Object})
+    N = _get_Ncache(A4Object)
+    ncats = size(N, 1)
+    return map(1:ncats) do i
+        Niii = N[i, i, i]
+        nobj = maximum(first, keys(Niii))
+
+        # find identity object:
+        # I x I -> I, a x I -> a, I x a -> a
+        I = findfirst(1:nobj) do u
+            get(Niii, (u, u, u), 0) == 1 || return false
+            for j in 1:nobj
+                get(Niii, (j, u, j), 0) == 1 || return false
+                get(Niii, (u, j, j), 0) == 1 || return false
+            end
+            return true
+        end
+
+        # find duals
+        # a x abar -> I
+        duals = map(1:nobj) do j
+            return findfirst(1:nobj) do k
+                return get(Niii, (j, k, I), 0) == 1
+            end
+        end
+
+        return I, duals
+    end
+end
+
+function Base.one(a::A4Object)
+    a.i == a.j || error("don't know how to define one for modules")
+    global Dualcache
+    return A4Object(i, i, get(Dualcache, T)[1])
+end
+
+function Base.conj(a::A4Object)
+    a.i == a.j || error("don't know how to define dual for modules")
+    global Dualcache
+    return A4Object(i, i, get(Dualcache, T)[2][i])
 end
 
 function extract_Fsymbol(::Type{A4Object})
-    return mapreduce(vcat, 1:12) do i
-        filename = joinpath(artifact_path, "A4", "Fsymbol$i.json")
-        @assert isfile(filename)
+    return mapreduce((x, y) -> cat(x, y; dims=1), 1:12) do i
+        filename = joinpath(artifact_path, "A4", "Fsymbol_$i.json")
+        @assert isfile(filename) "cannot find $filename"
         json_string = read(filename, String)
         Farray_part = copy(JSON3.read(json_string))
-        return map(reshape(Farray_part, 12, 12, 12, 12)) do x
-            y = Dict{NTuple{6,Int},ComplexF64}()
-            for (k, v) in x
-                a, b, c, d, e, f = parse.(Int, split(string(k)[2:(end - 1)], ", "))
-                y[(a, b, c, d, e, f)] = v
+        return map(enumerate(Farray_part[Symbol(i)])) do (I, x)
+            j, k, l = Tuple(CartesianIndices((12, 12, 12))[I])
+            y = Dict{NTuple{6,Int},Array{ComplexF64,4}}()
+            for (key, v) in x
+                a, b, c, d, e, f = parse.(Int, split(string(key)[2:(end - 1)], ", "))
+                a_ob, b_ob, c_ob, d_ob, e_ob, f_ob = A4Object.(((i, j, a), (j, k, b),
+                                                                (k, l, c), (i, l, d),
+                                                                (i, j, e), (j, l, f)))
+                y[(a, b, c, d, e, f)] = reshape(v,
+                                                (Nsymbol(a_ob, b_ob, e_ob),
+                                                 Nsymbol(e_ob, c_ob, d_ob),
+                                                 Nsymbol(b_ob, c_ob, f_ob),
+                                                 Nsymbol(a_ob, f_ob, d_ob)))
             end
         end
     end
 end
 
-const A4_Fcache = extract_Fsymbol(A4Object)
+const Fcache = IdDict{Type{<:BimoduleSector},
+                      Array{Dict{NTuple{6,Int},Array{ComplexF64,4}},4}}()
+
+function _get_Fcache(::Type{T}) where {T<:BimoduleSector}
+    global Fcache
+    return get!(Fcache, T) do
+        return extract_Fsymbol(T)
+    end
+end
+
 function TensorKitSectors.Fsymbol(a::I, b::I, c::I, d::I, e::I,
                                   f::I) where {I<:A4Object}
     # TODO: should this error or return 0?
@@ -99,7 +171,7 @@ function TensorKitSectors.Fsymbol(a::I, b::I, c::I, d::I, e::I,
         throw(ArgumentError("invalid fusion channel"))
 
     i, j, k, l = a.i, a.j, b.j, c.j
-    return get(A4_Fcache[i, j, k, l],
+    return get(_get_Fcache(I)[i, j, k, l],
                (a.label, b.label, c.label, d.label, e.label, f.label)) do
         return zeros(sectorscalartype(A4Object),
                      (Nsymbol(a, b, e), Nsymbol(e, c, d), Nsymbol(b, c, f),