R2R EC implemented

calculations/EC-R2R-S.jl

@@ -0,0 +1,67 @@
+using Plots, Arpack
+
+include("../helper.jl")
+include("../Hamiltonian.jl")
+
+mode = cpu_tensor
+T = Float32 # single-precision mode
+
+V_r2(c) = r2 -> c * (-5 * exp(-r2/3) + 2 * exp(-r2/10))
+
+d = 3
+n = 2
+N = 48
+L = 30
+ϕ = pi/6
+n_imag = 1
+s = system{T}(d, n, N, L)
+
+train_cs = range(0.78, 0.45, length=5)
+train_ref = reverse([0.05387926313545913-0.008900278182520881im,
+    0.11254295298924327-0.020515067379548786im,
+    0.16060154707503538-0.03716539208626717im,
+    0.19741353362674618-0.05994519982799412im,
+    0.2219100763497223-0.08959449893439568im])
+
+extrapolate_cs = range(0.38, 0.22, length=5)
+extrapolate_ref = reverse([0.23165109150003316-0.12052751440975719im,
+    0.23190549514995962-0.1406687118589838im,
+    0.22763660218046278-0.1626190970863793im,
+    0.21807104244164865-0.18635600686249373im,
+    0.2020979906072586-0.21180157628258728im])
+
+training_E = ComplexF64[]
+training_vec = Array[]
+exact_E = ComplexF64[]
+extrapolated_E = ComplexF64[]
+
+for c in train_cs
+    println("Training c=", c)
+    H = Hamiltonian{T}(s, V_r2(c), ϕ, n_imag, mode)
+    @time evals, evecs, info = eig(H, 20, resonances = true)
+    i = nearestIndex(evals, pop!(train_ref))
+    push!(training_E, evals[i])
+    push!(training_vec, evecs[i])
+end
+
+N_EC = [sum(x .* y) for (x, y) in Iterators.product(training_vec, training_vec)]
+
+for c in extrapolate_cs
+    println("Extrapolating c=", c)
+    H = Hamiltonian{T}(s, V_r2(c), ϕ, n_imag, mode)
+    @time evals, _, info = eig(H, 40, resonances = true)
+    nearestE = nearest(evals, pop!(extrapolate_ref))
+    push!(exact_E, nearestE)
+    
+    # EC extrapolation
+    H_training_vec = H.(training_vec)
+    H_EC = [sum(x .* y) for (x, y) in Iterators.product(training_vec, H_training_vec)]
+
+    evals = eigvals(H_EC, N_EC)
+    push!(extrapolated_E, nearestE)
+end
+
+scatter(real.(training_E), imag.(training_E), label="training")
+scatter!(real.(exact_E), imag.(exact_E), label="exact")
+scatter!(real.(extrapolated_E), imag.(extrapolated_E), label="extrapolated")
+savefig("temp/EC-R2R-S.pdf")

helper.jl

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+"Index of the nearest value in a list to a given reference point"
+nearestIndex(list::Array, ref) = argmin(norm.(list .- ref))
+
+"Nearest value in a list to a given reference point"
+nearest(list::Array, ref) = list[nearestIndex(list, ref)]