57 lines
1.5 KiB
Julia
57 lines
1.5 KiB
Julia
using LinearAlgebra, Plots
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include("../helper.jl")
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include("../ho_basis.jl")
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include("../p_space.jl")
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μω_gen = 0.5 * exp(-1im * 0.47 * pi)
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μ = 0.5
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l = 0
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V1 = -5
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R1 = sqrt(3)
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V2 = 2
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R2 = sqrt(10)
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n_max = 15
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ns = collect(0:n_max)
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ls = fill(l, n_max + 1)
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T = get_sp_T_matrix(ns, ls; μω_gen=μω_gen, μ=μ)
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V = V1 .* V_Gaussian.(R1, l, ns, transpose(ns); μω_gen=μω_gen) + V2 .* V_Gaussian.(R2, l, ns, transpose(ns); μω_gen=μω_gen)
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n_EC = 8
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train_cs = (0.7 .+ 0.05 * randn(n_EC)) - 1im * (0.2 .+ 0.05 * randn(n_EC))
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target_cs = range(0.77, 0.22, 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 = 0.2 + 0.2im
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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))
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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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EC_basis = gram_schmidt!(EC_basis)
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for (j, c) in enumerate(target_cs)
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exact_E[j] = quick_pole_E((p, q) -> c*(V1*g0(R1, p, q) + V2*g0(R2, p, q)), μ; cs_angle=0.5)
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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)
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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!(-0.2,0.3)
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ylims!(-0.3,0.3)
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