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XZ comparison in p-space vs HO

This commit is contained in:
Nuwan Yapa 2025-11-25 17:51:42 -05:00
parent 59c22cd3bc
commit 5dbc19bf06
1 changed files with 18 additions and 21 deletions
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39
calculations/XZ/p_space_vs_HO.jl
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@ -4,20 +4,6 @@ include("../../EC.jl")
include("../../ho_basis.jl") include("../../ho_basis.jl")
include("../../p_space.jl") include("../../p_space.jl")
function solve_E(H0, H1, c_vals, near_E)
out_E = ComplexF64[]
for c in c_vals
println("Solving for c = $c")
H = H0 + c .* H1
evals, _ = eigs(H, sigma=near_E, maxiter=5000, ritzvec=false, check=1)
new_E = nearest(evals, near_E)
push!(out_E, new_E)
end
return out_E
end
# paramters of the system # paramters of the system
angle = 0.0 * pi angle = 0.0 * pi
@ -29,12 +15,15 @@ V2 = 2
R2 = sqrt(10) R2 = sqrt(10)
n_EC = 8 n_EC = 8
train_cs = (0.7 .+ 0.05 * randn(n_EC)) - 1im * (0.2 .+ 0.05 * randn(n_EC)) train_cs = (0.7 .+ 0.03 * randn(n_EC)) - 1im * (0.2 .+ 0.03 * randn(n_EC))
near_E = 0.2 + 0.2im near_E = 0.2 + 0.2im
target_c = 0.5
exact_E = 0.20845136860234303 - 0.07100640993695649im
# HO basis # HO basis
HO_Es = zeros(ComplexF64, n_EC) global EC_HO
begin begin
println("HO basis calculation") println("HO basis calculation")
μω_gen = 0.5 * exp(-1im * angle) μω_gen = 0.5 * exp(-1im * angle)
@ -45,12 +34,14 @@ begin
T = get_sp_T_matrix(ns, ls; μω_gen=μω_gen, μ=μ) 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) 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)
HO_Es .= solve_E(T, V, train_cs, near_E) global EC_HO = affine_EC(T, V)
train!(EC_HO, train_cs; ref_eval=near_E, CAEC=false)
extrapolate!(EC_HO, [target_c]; precalculated_exact_E=[exact_E])
end end
# p-space # p-space
p_space_Es = zeros(ComplexF64, n_EC) global EC_p_space
begin begin
println("p-space calculation") println("p-space calculation")
vertices = [0, 4 * exp(-1im * angle)] vertices = [0, 4 * exp(-1im * angle)]
@ -62,13 +53,19 @@ begin
V = get_V_matrix(V_mat_elem, ks, ws) V = get_V_matrix(V_mat_elem, ks, ws)
T = get_T_matrix(ks, μ) T = get_T_matrix(ks, μ)
p_space_Es .= solve_E(T, V, train_cs, near_E) global EC_p_space = affine_EC(T, V)
train!(EC_p_space, train_cs; ref_eval=near_E, CAEC=false)
extrapolate!(EC_p_space, [target_c]; precalculated_exact_E=[exact_E])
end end
# Plotting # Plotting
scatter(real.(HO_Es), imag.(HO_Es), label="HO basis", marker=:circle, color=:blue) scatter([real(exact_E)], [imag(exact_E)], label="Exact", marker=:circle, markercolor=:white)
scatter!(real.(p_space_Es), imag.(p_space_Es), label="p-space", marker=:circle, color=:red) scatter!(real.(EC_HO.training_E), imag.(EC_HO.training_E), label="HO basis training", marker=:circle, color=:blue)
scatter!(real.(EC_HO.extrapolated_E), imag.(EC_HO.extrapolated_E), label="HO basis extrapolated", marker=:x, color=:blue)
scatter!(real.(EC_p_space.training_E), imag.(EC_p_space.training_E), label="p-space training", marker=:circle, color=:red)
scatter!(real.(EC_p_space.extrapolated_E), imag.(EC_p_space.extrapolated_E), label="p-space extrapolated", marker=:x, color=:red)
plot!(legend=:bottomleft)
xlabel!("Re(E)") xlabel!("Re(E)")
ylabel!("Im(E)") ylabel!("Im(E)")
savefig("temp/2b_p_space_vs_HO.pdf") savefig("temp/2b_p_space_vs_HO.pdf")