using LinearAlgebra, Plots
include("../helper.jl")
include("../ho_basis.jl")
include("../p_space.jl")

μω_gen = 0.5 * exp(-1im * 0.47 * pi)
μ = 0.5
l = 0
V1 = -5
R1 = sqrt(3)
V2 = 2
R2 = sqrt(10)
n_max = 15

ns = collect(0:n_max)
ls = fill(l, n_max + 1)

T = get_sp_T_matrix(ns, ls; μω_gen=μω_gen, μ=μ)
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)

n_EC = 8
train_cs = (0.7 .+ 0.05 * randn(n_EC)) - 1im * (0.2 .+ 0.05 * randn(n_EC))
target_cs = range(0.77, 0.22, 6)

train_E = zeros(ComplexF64, n_EC)
EC_basis = zeros(ComplexF64, (n_max + 1, length(train_cs)))
exact_E = zeros(ComplexF64, length(target_cs))
extrapolate_E = similar(exact_E)

near_E = 0.2 + 0.2im

for (j, c) in enumerate(train_cs)
    H = T + c .* V
    evals, evecs = eigen(H)
    i = argmin(abs.(evals .- near_E))
    train_E[j] = evals[i]
    EC_basis[:, j] = evecs[:, i]
end

EC_basis = gram_schmidt!(EC_basis)

for (j, c) in enumerate(target_cs)
    exact_E[j] = quick_pole_E((p, q) -> c*(V1*g0(R1, p, q) + V2*g0(R2, p, q)), μ; cs_angle=0.5)

    H = T + c .* V
    H_EC = transpose(EC_basis) * H * EC_basis
    evals = eigvals(H_EC)
    i = argmin(abs.(evals .- exact_E[j]))
    extrapolate_E[j] = evals[i]
end

scatter(real.(train_E), imag.(train_E), label="training")
scatter!(real.(exact_E), imag.(exact_E), label="exact")
scatter!(real.(extrapolate_E), imag.(extrapolate_E), label="extrapolated")
xlims!(-0.2,0.3)
ylims!(-0.3,0.3)