From cfd2eddad1bc65a05354b0dd010bebbe8a09edc5 Mon Sep 17 00:00:00 2001
From: Nuwan Yapa <yapanuwan@gmail.com>
Date: Fri, 8 Mar 2024 11:54:04 -0500
Subject: [PATCH] Revert "XZ method for new system"

This reverts commit 6d1ffa0c0c6d3fd43de0a3e29f939fa29e6b5e96.
---
 XZ_technique.jl | 32 +++++++++++++-------------------
 1 file changed, 13 insertions(+), 19 deletions(-)

diff --git a/XZ_technique.jl b/XZ_technique.jl
index 711c59a..a4e5158 100644
--- a/XZ_technique.jl
+++ b/XZ_technique.jl
@@ -2,14 +2,14 @@ using LinearAlgebra, Plots
 include("ho_basis.jl")
 include("p_space.jl")
 
-ω = 0.5 * exp(-1im * 0.3 * pi)
+ω = 0.5 * exp(-1im * 0.47 * pi)
 μ = 0.5
 l = 0
-V1 = -8.6
-R1 = 1.75
-V2 = 3.4
-R2 = 3.2
-n_max = 20
+V1 = -5
+R1 = sqrt(3)
+V2 = 2
+R2 = sqrt(10)
+n_max = 15
 
 ns = collect(0:n_max)
 ls = fill(l, n_max + 1)
@@ -18,34 +18,28 @@ T = sp_T_matrix(ns, ls; ω=ω, μ=μ)
 V = V1 .* V_Gaussian.(R1, l, ns, transpose(ns); ω=ω) + V2 .* V_Gaussian.(R2, l, ns, transpose(ns); ω=ω)
 
 n_EC = 8
-train_cs = (2.2 - 0.7im) .+ (0.1 .* randn(n_EC)) .+ (0.1im * randn(n_EC))
-target_cs = range(2.0, 0.8, 6)
+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_bound = 1.5 + 1.2im
+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_bound))
+    i = argmin(abs.(evals .- near_E))
     train_E[j] = evals[i]
     EC_basis[:, j] = evecs[:, i]
 end
 
 N_EC = transpose(EC_basis) * EC_basis
 
-near_E_res = 1.5 - 0.4im
-
 for (j, c) in enumerate(target_cs)
-    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]
+    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
@@ -57,5 +51,5 @@ 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!(-0.5,2.0)
-ylims!(-1.5,1.5)
+xlims!(-0.2,0.3)
+ylims!(-0.3,0.3)