Kd/indexing tests

benchmarks/indexing_example_short.jl

@@ -0,0 +1,272 @@
+using SpinGlassPEPS
+using MetaGraphs
+using LightGraphs
+using Test
+using TensorCast
+
+function make_particular_tensors(D)
+    h1 = D[(1,1)]
+    h2 = D[(2,2)]
+    J12 = D[(1,2)]
+    J23 = D[(2,3)]
+    h3 = D[(3,3)]
+
+    if D[(1, 2)] == 0.652
+        A1ex = reshape([exp(h1+h2-J12) 0. exp(-h1+h2+J12) 0.; 0. exp(h1-h2+J12) 0. exp(-h1-h2-J12)], (1,1,2,1,4))
+        A2ex = reshape([exp(h3-J23) exp(-h3+J23); exp(h3+J23) exp(-h3-J23)],(2,1,1,1,2))
+        C = [exp(h1+h2-J12+h3-J23) exp(h1-h2+J12+h3+J23) exp(-h1+h2+J12+h3-J23) exp(-h1-h2-J12+h3+J23); exp(h1+h2-J12-h3+J23) exp(h1-h2+J12-h3-J23) exp(-h1+h2+J12-h3+J23) exp(-h1-h2-J12-h3-J23)]
+    else
+        A1ex = reshape([exp(-h1-h2-J12) 0. 0. exp(h1-h2+J12); 0. exp(h1+h2-J12) exp(-h1+h2+J12) 0.], (1,1,2,1,4))
+        A2ex = reshape([exp(-h3-J23) exp(h3+J23); exp(-h3+J23) exp(h3-J23)],(2,1,1,1,2))
+        C = [exp(-h1-h2-J12-h3-J23) exp(h1+h2-J12-h3+J23) exp(-h1+h2+J12-h3+J23) exp(h1-h2+J12-h3-J23); exp(-h1-h2-J12+h3+J23) exp(h1+h2-J12+h3-J23) exp(-h1+h2+J12+h3-J23) exp(h1-h2+J12+h3+J23)]
+    end
+    A1ex, A2ex, C
+end
+
+function show_dificult_example(C, fg)
+
+    println("states of T1  ", get_prop(fg, 1, :spectrum).states)
+    println("x")
+    println("states of T2  ", get_prop(fg, 2, :spectrum).states)
+    println("D2, tensor with beta = 1")
+    display(C)
+    println()
+
+    println("D2, tensor with beta = $β")
+    display(C.^β)
+    println()
+end
+
+@testset "Test if the solution of the tensor agreeds with the BF" begin
+
+    #      grid
+    #     A1    |    A2
+    #           |
+    #   1 -- 2 -|- 3
+
+
+    D1 = Dict((1, 2) => 0.652,(2, 3) => 0.73,(3, 3) => 0.592,(2, 2) => 0.704,(1, 1) => 0.868)
+    D2 = Dict((1, 2) => -0.9049,(2, 3) => 0.2838,(3, 3) => -0.7928,(2, 2) => 0.1208,(1, 1) => -0.3342)
+
+    for D in [D1, D2]
+
+        m = 1
+        n = 2
+        t = 2
+
+        L = m * n * t
+        g_ising = ising_graph(D, L)
+
+        # brute force solution
+        bf = brute_force(g_ising; num_states = 1)
+        states = bf.states[1]
+        sol_A1 = states[[1,2]]
+        sol_A2 = states[[3]]
+
+        #particular form of peps tensors
+        update_cells!(
+          g_ising,
+          rule = square_lattice((m, 1, n, 1, t)),
+        )
+
+        fg = factor_graph(
+            g_ising,
+            Dict(1=>4, 2=>2),
+            energy=energy,
+            spectrum = brute_force
+        )
+
+        for origin ∈ (:NW, :SW)
+
+            β = 2.
+
+            x, y = m, n
+            peps = PepsNetwork(x, y, fg, β, origin)
+            pp = PEPSRow(peps, 1)
+
+
+            # the solution without cutting off
+            M1 = pp[1][1,1,:,1,:]
+            M2 = pp[2][:,1,1,1,:]
+            @reduce MM[a,b] |= sum(x) M1[x,a] * M2[x,b]
+
+            _, inds = findmax(MM)
+
+            A1ex, A2ex, C = make_particular_tensors(D)
+
+            @test pp[1] ≈ A1ex.^β
+            @test pp[2] ≈ A2ex.^β
+            @test MM ≈ transpose(C.^β)
+
+
+            # peps solution, first tensor
+            Aa1 = pp[1]
+            Aa2 = MPO(pp)[2]
+
+            @reduce A12[l, u, d, uu, rr, dd, σ] |= sum(x) Aa1[l, u, x, d, σ] * Aa2[x, uu, rr, dd]
+            A12 = dropdims(A12, dims=(1,2,3,4,5,6))
+            _, spins = findmax(A12)
+
+            #solution from the first tensor
+            st = get_prop(fg, 1, :spectrum).states
+            @test st[spins] == sol_A1
+            @test st[inds[1]] == sol_A1
+
+            # reading projector
+            p1, en, p2 = projectors(fg, 1, 2)
+            if D[(1, 2)] == 0.652
+                @test p1 == [1.0 0.0; 0.0 1.0; 1.0 0.0; 0.0 1.0]
+                @test en == [0.73 -0.73; -0.73 0.73]
+                @test p2 == [1.0 0.0; 0.0 1.0]
+            end
+            r1, rn, r2 = projectors(fg, 2, 1)
+            @test p1 == r2
+            @test p2 == r1
+            @test en == rn
+            @test projectors(fg, 3, 1) == (ones(1,1), ones(1,1), ones(1,1))
+
+            @reduce C[a, b, c, d] := sum(x) p1[$spins, x] * pp[$2][x, a, b, c, d]
+            _, s = findmax(C[1,1,1,:])
+
+            # solution form the second tensor
+            st = get_prop(fg, 2, :spectrum).states
+            @test st[s] == sol_A2
+            @test st[inds[2]] == sol_A2
+        end
+    end
+end
+
+@testset "larger example" begin
+    #      grid
+    #     A1    |    A2
+    #           |
+    #   1 -- 3 -|- 5 -- 7
+    #   |    |  |  |    |
+    #   |    |  |  |    |
+    #   2 -- 4 -|- 6 -- 8
+    #           |
+
+   D = Dict((5, 7) => -0.0186,(5, 6) => 0.0322,(2, 2) => -0.5289544745642463,(4, 4) => -0.699,(4, 6) => 0.494,(3, 3) => -0.4153941108520631,(8, 8) => 0.696,(6, 8) => 0.552,(1, 3) => -0.739,(7, 8) => -0.0602,(2, 4) => -0.0363,(1, 1) => 0.218,(7, 7) => -0.931,(1, 2) => 0.162,(6, 6) => 0.567,(5, 5) => -0.936,(3, 4) => 0.0595,(3, 5) => -0.9339)
+
+
+    m = 1
+    n = 2
+    t = 4
+
+
+    L = m * n * t
+
+    g_ising = ising_graph(D, L)
+
+    update_cells!(
+      g_ising,
+      rule = square_lattice((m, 1, n, 1, t)),
+    )
+
+    fg1 = factor_graph(
+        g_ising,
+        Dict(1=>16, 2=>16),
+        energy=energy,
+        spectrum = brute_force,
+    )
+
+    fg2 = factor_graph(
+        g_ising,
+        Dict(1=>16, 2=>16),
+        energy=energy,
+        spectrum = full_spectrum,
+    )
+
+    for fg in [fg1, fg2]
+
+        #Partition function
+        β = 2.
+        states = collect.(all_states(rank_vec(g_ising)))
+
+        ρ = exp.(-β .* energy.(states, Ref(g_ising)))
+        Z = sum(ρ)
+        @test gibbs_tensor(g_ising, β)  ≈ ρ ./ Z
+
+        for origin ∈ (:NW, :SW, :WS, :WN, :NE, :EN, :SE, :ES)
+
+            peps = PepsNetwork(m, n, fg, β, origin)
+
+            ψ = MPO(PEPSRow(peps, 1))
+
+            for i ∈ 2:peps.i_max
+                W = MPO(PEPSRow(peps, i))
+                M = MPO(peps, i-1, i)
+
+                ψ = (ψ * M) * W
+
+                @test length(W) == peps.j_max
+                for A ∈ ψ @test size(A, 2) == 1 end
+                @test size(ψ[1], 1) == 1 == size(ψ[peps.j_max], 3)
+            end
+            for A ∈ ψ @test size(A, 4) == 1 end
+            #println("ψ ", ψ)
+
+            ZZ = []
+            for A ∈ ψ
+                #println("A ", A)
+                push!(ZZ, dropdims(A, dims=(2, 4)))
+                #println("ZZ ", ZZ)
+            end
+            @test Z ≈ prod(ZZ)[]
+        end
+
+
+        origin = :NW
+
+        x, y = m, n
+        peps = PepsNetwork(x, y, fg, β, origin)
+        pp = PEPSRow(peps, 1)
+
+
+        # brute force solution
+        bf = brute_force(g_ising; num_states = 1)
+        states = bf.states[1]
+
+        cluster = props(fg, 1)[:cluster]
+        println(cluster.vertices)
+
+        cluster = props(fg, 2)[:cluster]
+        println(cluster.vertices)
+        sol_A1 = states[[1,2,3,4]]
+        sol_A2 = states[[5,6,7,8]]
+
+        Aa1 = pp[1]
+
+        # A2 traced
+        # index 1 (left is not trivial)
+
+        Aa2 = MPO(pp)[2]
+
+        # contraction of A1 with A2
+        #
+        #              .           .
+        #            .           .
+        #   A1 -- A2      =  A12
+        #
+
+        @reduce A12[l, u, d, uu, rr, dd, σ] |= sum(x) Aa1[l, u, x, d, σ] * Aa2[x, uu, rr, dd]
+
+        A12 = dropdims(A12, dims=(1,2,3,4,5,6))
+
+        _, spins = findmax(A12)
+
+        st = get_prop(fg, 1, :spectrum).states
+
+        @test st[spins] == sol_A1
+
+        p1, _, _ = projectors(fg, 1, 2)
+
+        @reduce C[a, b, c, d] := sum(x) p1[$spins, x] * pp[$2][x, a, b, c, d]
+
+        _, s = findmax(C[1,1,1,:])
+
+        st = get_prop(fg, 2, :spectrum).states
+
+        @test st[s] == sol_A2
+    end
+end