From c0e2b0c91098d827f828fd90453d5dcc2096852a Mon Sep 17 00:00:00 2001
From: Nuwan Yapa <yapanuwan@gmail.com>
Date: Thu, 5 Dec 2024 20:11:46 -0500
Subject: [PATCH] p1p2 matrix test (failing)

---
 test/p1p2_matrix.jl | 57 +++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 57 insertions(+)
 create mode 100644 test/p1p2_matrix.jl

diff --git a/test/p1p2_matrix.jl b/test/p1p2_matrix.jl
new file mode 100644
index 0000000..78f2d48
--- /dev/null
+++ b/test/p1p2_matrix.jl
@@ -0,0 +1,57 @@
+using LinearAlgebra, SparseArrays, Plots
+include("../p_space.jl")
+include("../ho_basis.jl")
+include("../berggren.jl")
+
+println("No of threads = ", Threads.nthreads())
+atol = 10^-5
+maxevals = 10^5
+R_cutoff = 16
+
+Λ = 0
+m = 1.0
+μ = m/2 # due to simple relative coordinates
+
+vertices = [0, 2 - 0.2im, 3, 4]
+subdivisions = [15, 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
+@assert length(basis) == basis_size "Something wrong with the basis"
+println("Basis size = $basis_size")
+
+V_of_r(r) =  2 * exp(-(r-3)^2 / (1.5)^2)
+V_l(j, k, kp) = Vl_mat_elem(V_of_r, j, k, kp; atol=atol, maxevals=maxevals, R_cutoff=R_cutoff)
+
+# generate p-space bases (actually identity matrices)
+@time "p-space bases" ps_bases = [Matrix(spdiagm(1 ./ sqrt.(ws))) for _ in 0:jmax]
+
+# generate Berggren bases
+@time "Berggren bases" begin
+    berg_bases = Vector{Matrix{ComplexF64}}(undef, jmax + 1)
+    for j in 0:jmax
+        _, berg_basis = eigen(get_H_matrix((k, kp) -> V_l(j, k, kp), ks, ws, μ); permute=false, scale=false)
+        N_berg = sum(berg_basis.^2 .* ws, dims=1)
+        berg_bases[1 + j] = berg_basis ./ transpose(sqrt.(N_berg))
+    end
+end
+
+@time "BB tranform matrix" begin
+    U_blocks = [kron(berg_bases[1 + j1] .* ws, berg_bases[1 + j2] .* ws) for (j1, j2) in js]
+    U = blockdiag(sparse.(U_blocks)...)
+end
+
+@time "In p-space" T_cross_PS = get_2p_p1p2_matrix(length(ks), js, Λ, ps_bases, ps_bases, ws)
+@time "In BB" T_cross_BB = get_2p_p1p2_matrix(length(ks), js, Λ, berg_bases, berg_bases, ws)
+
+@time "Basis transform" T_cross_transformed = transpose(U) * T_cross_PS * U
+
+diff = abs.(T_cross_transformed .- T_cross_BB)
+println("Max error = $(maximum(diff))")
+
+#@time "In in HO" T_cross_HO = get_2p_p1p2_matrix(n1s, l1s, n2s, l2s, Λ, μω, μω; dtype=ComplexF64)