From 8431b4b7e3390980dfed585825697ad6b37c6403 Mon Sep 17 00:00:00 2001
From: Nuwan Yapa <yapanuwan@gmail.com>
Date: Mon, 1 Jul 2024 12:01:41 -0400
Subject: [PATCH] Berggren R2R calculation

---
 calculations/3body_Berggren_R2R_EC.jl | 132 ++++++++++++++++++++++++++
 1 file changed, 132 insertions(+)
 create mode 100644 calculations/3body_Berggren_R2R_EC.jl

diff --git a/calculations/3body_Berggren_R2R_EC.jl b/calculations/3body_Berggren_R2R_EC.jl
new file mode 100644
index 0000000..a1a623a
--- /dev/null
+++ b/calculations/3body_Berggren_R2R_EC.jl
@@ -0,0 +1,132 @@
+using Arpack, SparseArrays, LRUCache
+using DelimitedFiles, Plots
+include("../ho_basis.jl")
+include("../p_space.jl")
+include("../berggren.jl")
+
+println("No of threads = ", Threads.nthreads())
+
+atol = 10^-5
+maxevals = 10^5
+
+training_ref = reverse([1.4750633616275919 - 0.0003021770706749637im
+    1.9567078295375822 - 0.0007646829108872369im
+    2.4351117758403076 - 0.001281037843108658im])
+
+exact_ref = reverse([4.076662025307587-0.012709842443350328im,
+    3.613318119833891-0.007335804709990623im,
+    3.1453431847006783-0.004030580410326795im,
+    2.672967129943755-0.00211498327461944im,
+    2.196542557810288-0.0010719835443437104im,
+    1.7164583929199813-0.0005455212208182736im,
+    1.233088227541505-0.0003070320106485624im])
+
+Λ = 0
+m = 1.0
+Va_of_r(r) = 2 * exp(-(r-3)^2 / (1.5)^2)
+Vb_of_r(r) = -exp(-(r/3)^2)
+
+# due to Jacobi coordinates
+μ1 = m * 1/2
+μ2 = m * 2/3
+
+vertices = [0, 2 - 0.1im, 3, 4]
+subdivisions = [16, 10, 10]
+ks, ws = get_mesh(vertices, subdivisions)
+
+jmax = 4
+tri((j1, j2)) = triangle_ineq(j1, j2, Λ)
+js = collect(Iterators.filter(tri, iter_prod(0:jmax, 0:jmax)))
+
+basis = iter_prod(js, zip(ks, ws), zip(ks, ws)) # basis = ((j1, j2), (k1, w1), (k2, w2))
+basis_size = length(js) * length(ks)^2
+weights_mat = spdiagm(repeat(kron(ws, ws), jmax + 1))
+@assert length(basis) == basis_size "Something wrong with the basis"
+println("Basis size = $basis_size")
+
+@time "T" begin
+    T_blocks = [kron_sum(get_T_matrix(ks, μ1), get_T_matrix(ks, μ2)) for _ in js]
+    T = blockdiag(sparse.(T_blocks)...)
+end
+
+@time "Va1" begin
+    Va_l(j, k, kp) = Vl_mat_elem(Va_of_r, j, k, kp; atol=atol, maxevals=maxevals, R_cutoff=16)
+    Va1_blocks = [kron(get_V_matrix((k, kp) -> Va_l(j1, k, kp), ks, ws), I(length(ks))) for (j1, _) in js]
+    Va1 = blockdiag(sparse.(Va1_blocks)...)
+end
+
+@time "Vb1" begin
+    Vb_l(j, k, kp) = Vl_mat_elem(Vb_of_r, j, k, kp; atol=atol, maxevals=maxevals, R_cutoff=16)
+    Vb1_blocks = [kron(get_V_matrix((k, kp) -> Vb_l(j1, k, kp), ks, ws), I(length(ks))) for (j1, _) in js]
+    Vb1 = blockdiag(sparse.(Vb1_blocks)...)
+end
+
+E_max = 40
+μω_global = 0.5
+μ1ω1 = μω_global * 1/2
+μ2ω2 = μω_global * 2
+
+@time "Va2_HO" Va2_HO =  get_jacobi_V2_matrix(Va_of_r, E_max, Λ, μω_global; atol=atol, maxevals=maxevals)
+@time "Vb2_HO" Vb2_HO =  get_jacobi_V2_matrix(Vb_of_r, E_max, Λ, μω_global; atol=atol, maxevals=maxevals)
+
+@time "W_right" W_right = get_W_matrix(basis, E_max, Λ, μ1ω1, μ2ω2; weights=true)
+@time "W_left" W_left = get_W_matrix(basis, E_max, Λ, μ1ω1, μ2ω2; weights=false)
+
+@time "Va2" Va2 = W_left * Va2_HO * transpose(W_right)
+@time "Vb2" Vb2 = W_left * Vb2_HO * transpose(W_right)
+
+@time "Ha" Ha = T + Va1 + Va2
+@time "Vb" Vb = Vb1 + Vb2
+@time "Eigenvalues" test_evals, _ = eigs(Ha, sigma=exact_ref[end], maxiter=5000, tol=1e-5, ritzvec=false, check=1)
+
+display(test_evals)
+
+# free memory
+Es = n1s = l1s = n2s = l2s = mask1 = mask2 = T1 = T2 = V1_cache = V_relative_cache = V1 = V_relative = U = V2 = nothing
+GC.gc()
+
+training_c = [1.1, 0.9, 0.7]
+extrapolating_c = 0.0 : 0.2 : 1.2
+
+exact = ComplexF64[]
+training = ComplexF64[]
+extrapolated = ComplexF64[]
+training_vecs = Vector{ComplexF64}[]
+
+for c in training_c
+    println("Training for c = $c")
+    global current_E = pop!(training_ref)
+
+    H = Ha + c .* Vb
+    evals, evecs = eigs(H, sigma=current_E, maxiter=5000, tol=1e-5, ritzvec=true, check=1)
+
+    global current_E = nearest(evals, current_E)
+    push!(training, current_E)
+    push!(training_vecs, evecs[:, nearestIndex(evals, current_E)])
+end
+
+EC_basis = hcat(training_vecs...)
+N_EC = transpose(EC_basis) * weights_mat * EC_basis
+Ha_EC = transpose(EC_basis) * weights_mat * Ha * EC_basis
+Vb_EC = transpose(EC_basis) * weights_mat * Vb * EC_basis
+
+for c in extrapolating_c
+    println("Extrapolating for c = $c")
+    global current_E = pop!(exact_ref)
+
+    H = Ha + c .* Vb
+    evals, _ = eigs(H, sigma=current_E, maxiter=5000, tol=1e-5, ritzvec=false, check=1)
+
+    global current_E = nearest(evals, current_E)
+    push!(exact, current_E)
+
+    # extrapolation
+    H_EC = Ha_EC + c .* Vb_EC
+    evals = eigvals(H_EC, N_EC)
+    push!(extrapolated, nearest(evals, current_E))
+end
+
+scatter(real.(training),imag.(training), label="training")
+scatter!(real.(exact),imag.(exact), label="exact")
+scatter!(real.(extrapolated),imag.(extrapolated), label="extrapolated")
+savefig("temp/Berggren_R2R.pdf")
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