From a569302ca2253d15943ff4114556ca9f9fd317d0 Mon Sep 17 00:00:00 2001
From: ysyapa <ysyapa@ncsu.edu>
Date: Tue, 23 Jan 2024 18:54:44 +0000
Subject: [PATCH] Exact values for comparison

---
 EC_test.ipynb | 7 ++++++-
 p_space.jl    | 6 ++++++
 2 files changed, 12 insertions(+), 1 deletion(-)

diff --git a/EC_test.ipynb b/EC_test.ipynb
index 2daa773..061d003 100644
--- a/EC_test.ipynb
+++ b/EC_test.ipynb
@@ -57,10 +57,14 @@
    "outputs": [],
    "source": [
     "extrapolate_points = range(0.40, 0.20, 5)\n",
-    "extrapolate_E = Vector{ComplexF64}(undef, length(extrapolate_points))\n",
     "ref_E = 0.2 - 0.1im\n",
     "\n",
+    "exact_E = Vector{ComplexF64}(undef, length(extrapolate_points))\n",
+    "extrapolate_E = Vector{ComplexF64}(undef, length(extrapolate_points))\n",
+    "\n",
     "for (j, c) in enumerate(extrapolate_points)\n",
+    "    exact_E[j] = quick_pole_E(V_system(c))\n",
+    "\n",
     "    EC_basis_w = EC_basis .* w\n",
     "    H = get_H_matrix(V_system(c), p, w)\n",
     "    H_EC = transpose(EC_basis) * H * EC_basis\n",
@@ -72,6 +76,7 @@
     "end\n",
     "\n",
     "scatter(real.(training_E), imag.(training_E), label=\"training\")\n",
+    "scatter!(real.(exact_E), imag.(exact_E), label=\"exact\")\n",
     "scatter!(real.(extrapolate_E), imag.(extrapolate_E), label=\"extrapolated\")\n",
     "plot!(real.(mesh_E), imag.(mesh_E), label=\"contour\")\n",
     "xlims!(0,1)"
diff --git a/p_space.jl b/p_space.jl
index 2883769..3915930 100644
--- a/p_space.jl
+++ b/p_space.jl
@@ -39,4 +39,10 @@ function identify_pole_i(p, evals, μ=0.5)
         end
     end
     return current_i
+end
+
+function quick_pole_E(V_pq, μ=0.5; cs_angle=0.5, cutoff=8.0, meshpoints=256)
+    p, w = get_mesh([0, cutoff * exp(-1im * cs_angle)], meshpoints)
+    evals = eigvals(get_H_matrix(V_pq, p, w))
+    return evals[identify_pole_i(p, evals)]
 end
\ No newline at end of file