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XZ method for new system

This commit is contained in:
Nuwan Yapa 2024-02-22 19:24:59 -05:00
parent 33281b2832
commit 6d1ffa0c0c
1 changed files with 19 additions and 13 deletions
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32
XZ_technique.jl
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@ -4,11 +4,11 @@ include("p_space.jl")
μ = 0.5 μ = 0.5
l = 0 l = 0
V1 = -5 V1 = -8.6
R1 = sqrt(3) R1 = 1.75
V2 = 2 V2 = 3.4
R2 = sqrt(10) R2 = 3.2
n_max = 15 n_max = 20
ns = collect(0:n_max) ns = collect(0:n_max)
ls = fill(l, n_max + 1) ls = fill(l, n_max + 1)
@ -16,29 +16,35 @@ ls = fill(l, n_max + 1)
T = 1/μ * sp_T_matrix(ns, ls) T = 1/μ * sp_T_matrix(ns, ls)
V = V1 .* V_Gaussian.(R1, l, ns, transpose(ns)) + V2 .* V_Gaussian.(R2, l, ns, transpose(ns)) V = V1 .* V_Gaussian.(R1, l, ns, transpose(ns)) + V2 .* V_Gaussian.(R2, l, ns, transpose(ns))
n_EC = 4 n_EC = 16
train_cs = (0.7 .+ 0.05 * randn(n_EC)) - 1im * (0.2 .+ 0.05 * randn(n_EC)) train_cs = (2.2 - 0.7im) .+ (0.1 .* randn(n_EC)) .+ (0.1im * randn(n_EC))
target_cs = range(0.77, 0.22, 6) target_cs = range(2.0, 0.8, 6)
train_E = zeros(ComplexF64, n_EC) train_E = zeros(ComplexF64, n_EC)
EC_basis = zeros(ComplexF64, (n_max + 1, length(train_cs))) EC_basis = zeros(ComplexF64, (n_max + 1, length(train_cs)))
exact_E = zeros(ComplexF64, length(target_cs)) exact_E = zeros(ComplexF64, length(target_cs))
extrapolate_E = similar(exact_E) extrapolate_E = similar(exact_E)
near_E = 0.2 + 0.2im near_E_bound = 1.5 + 1.2im
for (j, c) in enumerate(train_cs) for (j, c) in enumerate(train_cs)
H = T + c .* V H = T + c .* V
evals, evecs = eigen(H) evals, evecs = eigen(H)
i = argmin(abs.(evals .- near_E)) i = argmin(abs.(evals .- near_E_bound))
train_E[j] = evals[i] train_E[j] = evals[i]
EC_basis[:, j] = evecs[:, i] EC_basis[:, j] = evecs[:, i]
end end
N_EC = transpose(EC_basis) * EC_basis N_EC = transpose(EC_basis) * EC_basis
near_E_res = 1.5 - 0.4im
for (j, c) in enumerate(target_cs) 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) mesh_p, mesh_w = get_mesh([0, 8 * exp(-0.5im)], 256)
p_space_H = get_H_matrix((p, q) -> c*(V1*g0(R1, p, q) + V2*g0(R2, p, q)), mesh_p, mesh_w, μ)
evals = eigvals(p_space_H)
i = argmin(abs.(evals .- near_E_res))
exact_E[j] = evals[i]
H = T + c .* V H = T + c .* V
H_EC = transpose(EC_basis) * H * EC_basis H_EC = transpose(EC_basis) * H * EC_basis
@ -50,5 +56,5 @@ end
scatter(real.(train_E), imag.(train_E), label="training") scatter(real.(train_E), imag.(train_E), label="training")
scatter!(real.(exact_E), imag.(exact_E), label="exact") scatter!(real.(exact_E), imag.(exact_E), label="exact")
scatter!(real.(extrapolate_E), imag.(extrapolate_E), label="extrapolated") scatter!(real.(extrapolate_E), imag.(extrapolate_E), label="extrapolated")
xlims!(-0.2,0.3) xlims!(-0.5,2.0)
ylims!(-0.3,0.3) ylims!(-1.5,1.5)