62 lines
1.6 KiB
Julia
62 lines
1.6 KiB
Julia
using LinearAlgebra, Plots
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include("ho_basis.jl")
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include("p_space.jl")
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ω = 0.25
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μ = 0.5
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l = 0
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V1 = -8.6
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R1 = 1.75
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V2 = 3.4
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R2 = 3.2
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n_max = 20
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ns = collect(0:n_max)
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ls = fill(l, n_max + 1)
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T = sp_T_matrix(ns, ls; ω=ω, μ=μ)
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V = V1 .* V_Gaussian.(R1, l, ns, transpose(ns); ω=ω) + V2 .* V_Gaussian.(R2, l, ns, transpose(ns); ω=ω)
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n_EC = 8
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train_cs = (2.2 - 0.7im) .+ (0.1 .* randn(n_EC)) .+ (0.1im * randn(n_EC))
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target_cs = range(2.0, 0.8, 6)
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train_E = zeros(ComplexF64, n_EC)
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EC_basis = zeros(ComplexF64, (n_max + 1, length(train_cs)))
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exact_E = zeros(ComplexF64, length(target_cs))
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extrapolate_E = similar(exact_E)
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near_E_bound = 1.5 + 1.2im
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for (j, c) in enumerate(train_cs)
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H = T + c .* V
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evals, evecs = eigen(H)
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i = argmin(abs.(evals .- near_E_bound))
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train_E[j] = evals[i]
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EC_basis[:, j] = evecs[:, i]
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end
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N_EC = transpose(EC_basis) * EC_basis
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near_E_res = 1.5 - 0.4im
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for (j, c) in enumerate(target_cs)
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mesh_p, mesh_w = get_mesh([0, 8 * exp(-0.5im)], 256)
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p_space_H = get_H_matrix((p, q) -> c*(V1*g0(R1, p, q) + V2*g0(R2, p, q)), mesh_p, mesh_w, μ)
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evals = eigvals(p_space_H)
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i = argmin(abs.(evals .- near_E_res))
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exact_E[j] = evals[i]
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H = T + c .* V
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H_EC = transpose(EC_basis) * H * EC_basis
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evals = eigvals(H_EC, N_EC)
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i = argmin(abs.(evals .- exact_E[j]))
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extrapolate_E[j] = evals[i]
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end
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scatter(real.(train_E), imag.(train_E), label="training")
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scatter!(real.(exact_E), imag.(exact_E), label="exact")
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scatter!(real.(extrapolate_E), imag.(extrapolate_E), label="extrapolated")
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xlims!(-0.5,2.0)
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ylims!(-1.5,1.5)
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