example of BCs

examples/boundary_conditions.jl

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+using Test
+using ITensorNumericalAnalysis
+
+using Graphs: SimpleGraph, uniform_tree
+using NamedGraphs: NamedGraph
+using ITensors: ITensors, Index, siteinds, dim, tags, replaceprime!, MPO, MPS, inner
+using ITensorNetworks: ITensorNetwork, dmrg, ttn, maxlinkdim
+using Dictionaries: Dictionary
+using Random: seed!
+
+using UnicodePlots
+
+#Solve the 2D Laplace equation on a random tree
+seed!(1234)
+L = 12
+g = NamedGraph(SimpleGraph(uniform_tree(L)))
+
+s = continuous_siteinds(g; map_dimension=2)
+
+ψ_fxy = const_itn(s; c=1)
+@show maxlinkdim(ψ_fxy)
+
+Zero_X = zero_point_op(s, [0, 1], 1)
+Zero_Y = zero_point_op(s, [0, 1], 2)
+Zero_X = truncate(Zero_X; cutoff=1e-14)
+Zero_Y = truncate(Zero_Y; cutoff=1e-14)
+
+maxdim = 4
+cutoff = 0e-8 #0e-16
+ϕ_fxy = copy(ψ_fxy)
+ϕ_fxy = operate([Zero_X, Zero_Y], ϕ_fxy; cutoff, maxdim, normalize=true)
+@show maxlinkdim(ϕ_fxy)
+
+n_grid = 100
+x_vals, y_vals = grid_points(s, n_grid, 1), grid_points(s, n_grid, 2)
+vals = zeros((length(x_vals), length(y_vals)))
+for (i, x) in enumerate(x_vals)
+  for (j, y) in enumerate(y_vals)
+    vals[i, j] = real(calculate_fxyz(ϕ_fxy, [x, y]; alg="exact"))
+  end
+end
+
+println("Here is the heatmap of the 2D function")
+show(heatmap(vals; xfact=0.01, yfact=0.01, xoffset=0, yoffset=0, colormap=:inferno))
+
+n_grid = 100
+x_vals = grid_points(s, n_grid, 1)
+y = 0.5
+vals2 = zeros(length(x_vals))
+for (i, x) in enumerate(x_vals)
+  vals2[i] = real(calculate_fxyz(ϕ_fxy, [x, y]; alg="exact"))
+end
+
+lp = lineplot(x_vals, vals2; name="cut x=$x")
+
+y_vals = grid_points(s, n_grid, 2)
+x = 0.5
+vals3 = zeros(length(y_vals))
+for (i, y) in enumerate(y_vals)
+  vals3[i] = real(calculate_fxyz(ϕ_fxy, [x, y]; alg="exact"))
+end
+
+println("Here is a cut of the function at x = $x or y = $y")
+show(lineplot!(lp, y_vals, vals3; name="cut y=$y"))