From edd63d8a316105d9e12325200ed21960ccad0f57 Mon Sep 17 00:00:00 2001
From: Nuwan Yapa <yapanuwan@gmail.com>
Date: Thu, 27 Jun 2024 15:11:48 -0400
Subject: [PATCH] Berggren basis with poles

---
 B2R_Berggren_poles.jl | 60 +++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 60 insertions(+)
 create mode 100644 B2R_Berggren_poles.jl

diff --git a/B2R_Berggren_poles.jl b/B2R_Berggren_poles.jl
new file mode 100644
index 0000000..8757ebb
--- /dev/null
+++ b/B2R_Berggren_poles.jl
@@ -0,0 +1,60 @@
+using Plots
+include("p_space.jl")
+
+# contour
+p, w = get_mesh([0, 0.4 - 0.15im, 0.8, 6], [128, 128, 128])
+
+# ResonanceEC: Eq. (20)
+V_system(c) = (p, q) -> c*(-5*g0(sqrt(3), p, q) + 2*g0(sqrt(10), p, q))
+
+# generating a Berggren basis with a pole using the same system
+basis_c = 0.6
+basis_E, berg_basis = eigen(get_H_matrix(V_system(basis_c), p, w); permute=false, scale=false)
+basis_p = sqrt.(basis_E)
+N_berg = sqrt.(diag(transpose(berg_basis .* w) * berg_basis))
+berg_basis = berg_basis ./ transpose(N_berg)
+berg_basis_w = berg_basis .* w
+
+training_points = range(1.1, 0.9, 5) # original: range(1.35, 0.9, 5)
+
+training_E = Vector{ComplexF64}(undef, length(training_points))
+EC_basis = Matrix{ComplexF64}(undef, length(p), length(training_points))
+
+# training
+for (j, c) in enumerate(training_points)
+    H = get_H_matrix(V_system(c), p, w)
+    H_berg = transpose(berg_basis_w) * H * berg_basis
+    evals, evecs = eigen(H_berg)
+    i = argmin(real.(evals))
+#    i = identify_pole_i(basis_p, evals)
+    training_E[j] = evals[i]
+    EC_basis[:, j] = evecs[:, i]
+end
+
+EC_basis = hcat(EC_basis, conj.(EC_basis)) # CA-EC
+N_EC = transpose(EC_basis) * EC_basis
+
+extrapolate_points = range(0.78, 0.45, 7) # original: range(0.75, 0.40, 8)
+
+exact_E = Vector{ComplexF64}(undef, length(extrapolate_points))
+extrapolate_E = Vector{ComplexF64}(undef, length(extrapolate_points))
+
+# extrapolating
+for (j, c) in enumerate(extrapolate_points)
+    exact_E[j] = quick_pole_E(V_system(c))
+
+    H = get_H_matrix(V_system(c), p, w)
+    H_berg = transpose(berg_basis_w) * H * berg_basis
+    H_EC = transpose(EC_basis) * H_berg * EC_basis
+    evals = eigvals(H_EC, N_EC)
+    i = argmin(abs.(evals .- exact_E[j]))
+    extrapolate_E[j] = evals[i]
+end
+
+scatter(real.(training_E), imag.(training_E), label="training")
+scatter!(real.(exact_E), imag.(exact_E), label="exact")
+scatter!(real.(extrapolate_E), imag.(extrapolate_E), label="extrapolated")
+scatter!(real.(basis_E), imag.(basis_E), m=:x, label="Berggren basis")
+xlims!(-0.3,0.3)
+ylims!(-0.120,0.020)
+savefig("temp/" * string(rand(UInt16)) * ".pdf")