From 5dbc19bf06537f3ddafde3878c7f97e5623ffe75 Mon Sep 17 00:00:00 2001
From: Nuwan Yapa <yapanuwan@gmail.com>
Date: Tue, 25 Nov 2025 17:51:42 -0500
Subject: [PATCH] XZ comparison in p-space vs HO

---
 calculations/XZ/p_space_vs_HO.jl | 39 +++++++++++++++-----------------
 1 file changed, 18 insertions(+), 21 deletions(-)

diff --git a/calculations/XZ/p_space_vs_HO.jl b/calculations/XZ/p_space_vs_HO.jl
index eb9ac04..fbc2637 100644
--- a/calculations/XZ/p_space_vs_HO.jl
+++ b/calculations/XZ/p_space_vs_HO.jl
@@ -4,20 +4,6 @@ include("../../EC.jl")
 include("../../ho_basis.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
 
 angle = 0.0 * pi
@@ -29,12 +15,15 @@ V2 = 2
 R2 = sqrt(10)
 
 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
 
+target_c = 0.5
+exact_E = 0.20845136860234303 - 0.07100640993695649im
+
 # HO basis
 
-HO_Es = zeros(ComplexF64, n_EC)
+global EC_HO
 begin
     println("HO basis calculation")
     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)
     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
 
 # p-space
 
-p_space_Es = zeros(ComplexF64, n_EC)
+global EC_p_space
 begin
     println("p-space calculation")
     vertices = [0, 4 * exp(-1im * angle)]
@@ -62,13 +53,19 @@ begin
     V = get_V_matrix(V_mat_elem, ks, ws)
     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
 
 # Plotting
 
-scatter(real.(HO_Es), imag.(HO_Es), label="HO basis", marker=:circle, color=:blue)
-scatter!(real.(p_space_Es), imag.(p_space_Es), label="p-space", marker=:circle, color=:red)
+scatter([real(exact_E)], [imag(exact_E)], label="Exact", marker=:circle, markercolor=:white)
+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)")
 ylabel!("Im(E)")
 savefig("temp/2b_p_space_vs_HO.pdf")
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