add cg2fp

src/nonlocal.jl

@@ -117,12 +117,12 @@ end
 export tsirelson_bound
 
 """
-    fp2cg(V::Array{T,4}) where {T <: Real}
+    fp2cg(V::Array{T,4}, behaviour::Bool = false) where {T <: Real}
 
 Takes a bipartite Bell functional `V` in full probability notation and transforms it
-to Collins-Gisin notation.
+to Collins-Gisin notation. If `behaviour` is `true` do instead the transformation for behaviours. Doesn't assume normalization.
 """
-function fp2cg(V::AbstractArray{T,4}) where {T<:Real}
+function fp2cg(V::AbstractArray{T,4}, behaviour::Bool = false) where {T}
     oa, ob, ia, ib = size(V)
     alice_pars = ia * (oa - 1) + 1
     bob_pars = ib * (ob - 1) + 1
@@ -131,21 +131,82 @@ function fp2cg(V::AbstractArray{T,4}) where {T<:Real}
 
     CG = zeros(T, alice_pars, bob_pars)
 
-    CG[1, 1] = sum(V[oa, ob, :, :])
-    for a = 1:oa-1, x = 1:ia
-        CG[aindex(a, x), 1] = sum(V[a, ob, x, :] - V[oa, ob, x, :])
-    end
-    for b = 1:ob-1, y = 1:ib
-        CG[1, bindex(b, y)] = sum(V[oa, b, :, y] - V[oa, ob, :, y])
-    end
-    for a = 1:oa-1, b = 1:ob-1, x = 1:ia, y = 1:ib
-        CG[aindex(a, x), bindex(b, y)] = V[a, b, x, y] - V[a, ob, x, y] - V[oa, b, x, y] + V[oa, ob, x, y]
+    if ~behaviour
+        CG[1, 1] = sum(V[oa, ob, :, :])
+        for a = 1:oa-1, x = 1:ia
+            CG[aindex(a, x), 1] = sum(V[a, ob, x, :] - V[oa, ob, x, :])
+        end
+        for b = 1:ob-1, y = 1:ib
+            CG[1, bindex(b, y)] = sum(V[oa, b, :, y] - V[oa, ob, :, y])
+        end
+        for a = 1:oa-1, b = 1:ob-1, x = 1:ia, y = 1:ib
+            CG[aindex(a, x), bindex(b, y)] = V[a, b, x, y] - V[a, ob, x, y] - V[oa, b, x, y] + V[oa, ob, x, y]
+        end
+    else
+        CG[1, 1] = sum(V) / (ia * ib)
+        for x = 1:ia, a = 1:oa-1
+            CG[aindex(a, x), 1] = sum(V[a, b, x, y] for b = 1:ob, y = 1:ib) / ib
+        end
+        for y = 1:ib, b = 1:ob-1
+            CG[1, bindex(b, y)] = sum(V[a, b, x, y] for a = 1:oa, x = 1:ia) / ia
+        end
+        for x = 1:ia, y = 1:ib
+            CG[aindex(1, x):aindex(oa - 1, x), bindex(1, y):bindex(ob - 1, y)] = V[1:oa-1, 1:ob-1, x, y]
+        end
     end
-
     return CG
 end
 export fp2cg
 
+"""
+    cg2fp(CG::Matrix, behaviour::Bool = false)
+
+Takes a bipartite Bell functional `CG` in Collins-Gisin notation and transforms it
+to full probability notation. `scenario` is a vector detailing the number of inputs and outputs, in the order [oa, ob, ia, ib]. If `behaviour` is `true` do instead the transformation for behaviours. Doesn't assume normalization.
+"""
+function cg2fp(CG::Matrix{T}, scenario::Vector{<:Integer}, behaviour::Bool = false) where {T}
+    oa, ob, ia, ib = scenario
+    aindex(a, x) = 1 + a + (x - 1) * (oa - 1)
+    bindex(b, y) = 1 + b + (y - 1) * (ob - 1)
+
+    V = Array{T,4}(undef, (oa, ob, ia, ib))
+
+    if ~behaviour
+        for x = 1:ia, y = 1:ib
+            V[oa, ob, x, y] = CG[1, 1] / (ia * ib)
+        end
+        for x = 1:ia, y = 1:ib, b = 1:ob-1
+            V[oa, b, x, y] = CG[1, 1] / (ia * ib) + CG[1, bindex(b, y)] / ia
+        end
+        for x = 1:ia, y = 1:ib, a = 1:oa-1
+            V[a, ob, x, y] = CG[1, 1] / (ia * ib) + CG[aindex(a, x), 1] / ib
+        end
+        for x = 1:ia, y = 1:ib, a = 1:oa-1, b = 1:ob-1
+            V[a, b, x, y] =
+                CG[1, 1] / (ia * ib) +
+                CG[aindex(a, x), 1] / ib +
+                CG[1, bindex(b, y)] / ia +
+                CG[aindex(a, x), bindex(b, y)]
+        end
+    else
+        for x = 1:ia, y = 1:ib
+            V[1:oa-1, 1:ob-1, x, y] = CG[aindex(1, x):aindex(oa - 1, x), bindex(1, y):bindex(ob - 1, y)]
+            V[1:oa-1, ob, x, y] =
+                CG[aindex(1, x):aindex(oa - 1, x), 1] -
+                sum(CG[aindex(1, x):aindex(oa - 1, x), bindex(1, y):bindex(ob - 1, y)]; dims = 2)
+            V[oa, 1:ob-1, x, y] =
+                CG[1, bindex(1, y):bindex(ob - 1, y)] -
+                vec(sum(CG[aindex(1, x):aindex(oa - 1, x), bindex(1, y):bindex(ob - 1, y)]; dims = 1))
+            V[oa, ob, x, y] =
+                CG[1, 1] - sum(CG[aindex(1, x):aindex(oa - 1, x), 1]) -
+                sum(CG[1, bindex(1, y):bindex(ob - 1, y)]) +
+                sum(CG[aindex(1, x):aindex(oa - 1, x), bindex(1, y):bindex(ob - 1, y)])
+        end
+    end
+    return V
+end
+export cg2fp
+
 """
     probability_tensor(rho::Hermitian, all_Aax::Vector{Measurement}...)
 

test/nonlocal.jl

@@ -19,4 +19,8 @@ end
     Aax = povm(mub(2))
     @test correlation_tensor(state_phiplus(), Aax, 2) ≈ Diagonal([1, 1, -1, 1])
     @test correlation_tensor(state_phiplus(), Aax, 2; marg = false) ≈ Diagonal([1, 1, -1])
+    scenario = [2,3,4,5]
+    cg = randn(scenario[3]*(scenario[1]-1) + 1, scenario[4]*(scenario[2]-1) + 1)
+    @test fp2cg(cg2fp(cg,scenario)) ≈ cg
+    @test fp2cg(cg2fp(cg,scenario,true),true) ≈ cg
 end