diff --git a/calculations/3body_HO_B2R_ACCC.jl b/calculations/3body_HO_B2R_ACCC.jl new file mode 100644 index 0000000..93991cc --- /dev/null +++ b/calculations/3body_HO_B2R_ACCC.jl @@ -0,0 +1,66 @@ +using Roots, LinearAlgebra, Plots + +include("../EC.jl") +include("../common.jl") +include("../ho_basis.jl") + +V_of_r(r) = 2 * exp(-(r-3)^2 / (1.5)^2) +Λ = 0 +m = 1.0 + +ϕ = 0.1 +μω_global = 0.5 * exp(-2im * ϕ) +E_max = 40 + +H0 = get_3b_H_matrix(jacobi, V_of_r, μω_global, E_max, Λ, m, true, true) + +# Vp = perturbation to make the state artificially bound +Vp_of_r(r) = -exp(-(r/3)^2) +@time "Vp" Vp = get_3b_H_matrix(jacobi, Vp_of_r, μω_global, E_max, Λ, m, false, true) + +training_ref = -2.22 +extrapolating_ref = [4.076662025307587-0.012709842443350328im, + 3.613318119833891-0.007335804709990623im, + 3.1453431847006783-0.004030580410326795im, + 2.672967129943755-0.00211498327461944im, + 2.196542557810288-0.0010719835443437104im, + 1.7164583929199813-0.0005455212208182736im, + 1.233088227541505-0.0003070320106485624im] + +training_c = [2.6, 2.4, 2.2, 2.0, 1.8] +extrapolating_c = 0.0 : 0.2 : 1.2 + +EC = affine_EC(H0, Vp) +train!(EC, training_c; ref_eval=training_ref, CAEC=true) +extrapolate!(EC, extrapolating_c; ref_eval=extrapolating_ref) + +# determining c0 with EC +approx_c0 = 1.5 +quick_extrapolate(c) = minimum(abs2, get_extrapolated_evals(EC.H0_EC, EC.H1_EC, EC.N_EC, c, 1e-14)) +c0 = find_zero(quick_extrapolate, approx_c0) + +order::Int = ceil((length(training_c) - 1) / 2) # order of the Pade approximant + +# Solve coefficients as a linear system +training_k = alt_sqrt.(EC.training_E) +M_left_element(c, i) = alt_sqrt(c - c0)^i +M_left = M_left_element.(training_c, (0:order)') +M_right = -training_k .* M_left[:, 2:end] # remove the first column +M = hcat(M_left, M_right) # M = [M_left | M_right] +sol = M \ training_k +a = sol[1:order+1] +b = [1; sol[order+2:end]] + +# Pade approximant +polynomial(a, c) = sum(i -> a[i+1] * alt_sqrt(c - c0)^i, 0:order) +pade_approx(c) = polynomial(a, c) / polynomial(b, c) + +# Extrapolate +extrapolated_k = pade_approx.([extrapolating_c; training_c]) +extrapolated_E = extrapolated_k .^ 2 + +# Plotting +scatter(real.(EC.training_E), imag.(EC.training_E), label="training") +scatter!(real.(EC.exact_E), imag.(EC.exact_E), label="exact") +scatter!(real.(EC.extrapolated_E), imag.(EC.extrapolated_E), label="CAEC", m=:x) +scatter!(real.(extrapolated_E), imag.(extrapolated_E), label="ACCC", m=:+)