From 6d1ffa0c0c6d3fd43de0a3e29f939fa29e6b5e96 Mon Sep 17 00:00:00 2001
From: Nuwan Yapa <yapanuwan@gmail.com>
Date: Thu, 22 Feb 2024 19:24:59 -0500
Subject: [PATCH] XZ method for new system

---
 XZ_technique.jl | 32 +++++++++++++++++++-------------
 1 file changed, 19 insertions(+), 13 deletions(-)

diff --git a/XZ_technique.jl b/XZ_technique.jl
index bab5589..b037a49 100644
--- a/XZ_technique.jl
+++ b/XZ_technique.jl
@@ -4,11 +4,11 @@ include("p_space.jl")
 
 μ = 0.5
 l = 0
-V1 = -5
-R1 = sqrt(3)
-V2 = 2
-R2 = sqrt(10)
-n_max = 15
+V1 = -8.6
+R1 = 1.75
+V2 = 3.4
+R2 = 3.2
+n_max = 20
 
 ns = collect(0:n_max)
 ls = fill(l, n_max + 1)
@@ -16,29 +16,35 @@ ls = fill(l, n_max + 1)
 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))
 
-n_EC = 4
-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)
+n_EC = 16
+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_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 = 0.2 + 0.2im
+near_E_bound = 1.5 + 1.2im
 
 for (j, c) in enumerate(train_cs)
     H = T + c .* V
     evals, evecs = eigen(H)
-    i = argmin(abs.(evals .- near_E))
+    i = argmin(abs.(evals .- near_E_bound))
     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)
-    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_EC = transpose(EC_basis) * H * EC_basis
@@ -50,5 +56,5 @@ 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!(-0.2,0.3)
-ylims!(-0.3,0.3)
+xlims!(-0.5,2.0)
+ylims!(-1.5,1.5)