Add plot example for DiagonalReduction and RankSimplification transfo…

…rmations

docs/src/transformations.md

@@ -16,16 +16,43 @@ transform!
 # Example
 Here we show how can we reduce the complexity of the tensor network by applying a tranformation to it:
 ```@setup plot
+using Makie
+Makie.inline!(true)
+set_theme!(resolution=(800,200))
+
 using CairoMakie
-CairoMakie.activate!(type = "svg")
+using Tenet
+using NetworkLayout
 
 using Pkg
 Pkg.add("QuacIO")
+
+function smooth_annotation!(f; color=Makie.RGBAf(110 // 256, 170 // 256, 250 // 256, 60 // 256), xlims=[-2, 2], ylims=[-2, 2], offset_x=0.0, offset_y=0.0, radius_x=1.0, radius_y=1.0, num_waves=5, fluctuation_amplitude=0.1, phase_shift=0.0)
+    ax = Axis(f)
+    hidedecorations!(ax)
+    hidespines!(ax)
+
+    # Define limits of the plot
+    xlims!(ax, xlims...)
+    ylims!(ax, ylims...)
+
+    # Create a perturbed filled shape
+    theta = LinRange(0, 2π, 100)
+
+    fluctuations = fluctuation_amplitude .* sin.(num_waves .* theta .+ phase_shift)
+
+    # Apply the fluctuations and radius scaling
+    perturbed_radius_x = radius_x .+ fluctuations
+    perturbed_radius_y = radius_y .+ fluctuations
+
+    circle_points = [Point2f((perturbed_radius_x[i]) * cos(theta[i]) + offset_x,
+                              (perturbed_radius_y[i]) * sin(theta[i]) + offset_y) for i in 1:length(theta)]
+
+    poly!(ax, circle_points, color=color, closed=true)
+end
 ```
-```@example transformation
+```@example plot
 using QuacIO
-using CairoMakie
-using Tenet
 
 sites = [5, 6, 14, 15, 16, 17, 24, 25, 26, 27, 28, 32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 61, 62, 63, 64, 65, 66, 67, 72, 73, 74, 75, 76, 83, 84, 85, 94]
 circuit = QuacIO.parse(joinpath(@__DIR__, "sycamore_53_10_0.qasm"), format=QuacIO.Qflex(), sites=sites)
@@ -44,10 +71,130 @@ fig # hide
 
 # Transformations
 
+## Rank simplification
+!!! warn ""
+    This transformation is always used by default when visualizing a `TensorNetwork` with `plot`.
 ```@docs
 Tenet.HyperindConverter
+```
+
+## Diagonal reduction
+```@example plot
+    fig = Figure() #hide
+
+    data = zeros(Float64, 2, 2, 2, 2) #hide
+    for i in 1:2 #hide
+        for j in 1:2 #hide
+            for k in 1:2 #hide
+                data[i, i, j, k] = k #hide
+            end #hide
+        end #hide
+    end #hide
+
+    A = Tensor(data, (:i, :j, :k, :l)) #hide
+    B = Tensor(rand(2, 2), (:i, :m)) #hide
+    C = Tensor(rand(2, 2), (:j, :n)) #hide
+
+    bg_blue = Makie.RGBAf(110 // 256, 170 // 256, 250 // 256, 50 // 256) #hide
+    orange = Makie.RGBf(240 // 256, 180 // 256, 100 // 256) #hide
+    red = Makie.RGBf(240 // 256, 90 // 256, 70 // 256) #hide
+
+    tn = TensorNetwork([A, B, C]) #hide
+    reduced = transform(tn, Tenet.DiagonalReduction) #hide
+
+    smooth_annotation!( #hide
+        fig[1, 1]; #hide
+        color = bg_blue, #hide
+        xlims = [-2, 2], #hide
+        ylims = [-2, 2], #hide
+        offset_x = -0.21, #hide
+        offset_y = -0.42, #hide
+        radius_x = 0.38, #hide
+        radius_y = 0.8, #hide
+        num_waves = 6, #hide
+        fluctuation_amplitude = 0.02, #hide
+        phase_shift = 0.0) #hide
+    plot!(fig[1, 1], tn, layout=Spring(iterations=1000, C=0.5, seed=100); node_color=[red, orange, orange, :black, :black,:black, :black]) #hide
+
+    smooth_annotation!( #hide
+        fig[1, 2]; #hide
+        color = bg_blue, #hide
+        xlims = [-2, 2], #hide
+        ylims = [-2, 2], #hide
+        offset_x = 0.1, #hide
+        offset_y = -0.35, #hide
+        radius_x = 0.38, #hide
+        radius_y = 1.1, #hide
+        num_waves = 5, #hide
+        fluctuation_amplitude = 0.02, #hide
+        phase_shift = 1.9) #hide
+    plot!(fig[1, 2], reduced, layout=Spring(iterations=1000, C=0.5, seed=100),  node_color=[orange, orange, red, :black, :black, :black, :black, :black]) #hide
+
+    Label(fig[1, 1, Bottom()], "Original Tensor Network") #hide
+    Label(fig[1, 2, Bottom()], "Transformed Tensor Network") #hide
+
+    fig #hide
+```
+
+```@docs
 Tenet.DiagonalReduction
-Tenet.RankSimplification
+```
+
+## Rank reduction
+```@docs
+Tenet.RankReduction
+```
+
+```@example plot
+    fig = Figure() #hide
+
+    A = Tensor(rand(2, 2, 2, 2), (:i, :j, :k, :l)) #hide
+    B = Tensor(rand(2, 2), (:i, :m)) #hide
+    C = Tensor(rand(2, 2, 2), (:m, :n, :o)) #hide
+    E = Tensor(rand(2, 2, 2, 2), (:o, :p, :q, :j)) #hide
+
+    bg_blue = Makie.RGBAf(110 // 256, 170 // 256, 250 // 256, 50 // 256) #hide
+    orange = Makie.RGBf(240 // 256, 180 // 256, 100 // 256) #hide
+    red = Makie.RGBf(240 // 256, 90 // 256, 70 // 256) #hide
+
+    tn = TensorNetwork([A, B, C, E]) #hide
+    reduced = transform(tn, Tenet.RankSimplification) #hide
+
+    smooth_annotation!( #hide
+        fig[1, 1]; #hide
+        color = bg_blue, #hide
+        xlims = [-2, 2], #hide
+        ylims = [-2, 2], #hide
+        offset_x = -0.32, #hide
+        offset_y = -0.5, #hide
+        radius_x = 0.25, #hide
+        radius_y = 0.94, #hide
+        num_waves = 6, #hide
+        fluctuation_amplitude = 0.01, #hide
+        phase_shift = 0.0) #hide
+    plot!(fig[1, 1], tn, layout=Spring(iterations=1000, C=0.5, seed=20); node_color=[orange, red, orange, orange, :black, :black, :black, :black, :black]) #hide
+
+    smooth_annotation!( #hide
+        fig[1, 2]; #hide
+        color = bg_blue, #hide
+        xlims = [-2, 2], #hide
+        ylims = [-2, 2], #hide
+        offset_x = 0.12, #hide
+        offset_y = -0.62, #hide
+        radius_x = 0.18, #hide
+        radius_y = 0.46, #hide
+        num_waves = 5, #hide
+        fluctuation_amplitude = 0.01, #hide
+        phase_shift = 0) #hide
+    plot!(fig[1, 2], reduced, layout=Spring(iterations=1000, C=0.5, seed=1); node_color=[red, orange, orange, :black, :black, :black, :black, :black]) #hide
+
+    Label(fig[1, 1, Bottom()], "Original Tensor Network") #hide
+    Label(fig[1, 2, Bottom()], "Transformed Tensor Network") #hide
+
+    fig #hide
+```
+
+```@docs
 Tenet.AntiDiagonalGauging
 Tenet.ColumnReduction
 Tenet.SplitSimplification