using LinearAlgebra, SparseArrays, Arpack
include("helper.jl")
include("p_space.jl")
include("ho_basis.jl")

println("No of threads = ", Threads.nthreads())
atol = 10^-5
maxevals = 10^5
R_cutoff = 16

Λ = 0
m = 1.0
μ1 = m * 1/2
μ2 = m * 2/3

target = 4.0766890719636875 - 0.012758927741074495im

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)

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")

# generate Berggren bases
berg_bases = Vector{Matrix{ComplexF64}}(undef, jmax + 1)
berg_Es = Vector{Vector{ComplexF64}}(undef, jmax + 1)
for j in 0:jmax
    berg_E, berg_basis = eigen(get_H_matrix((k, kp) -> V_l(j, k, kp), ks, ws); permute=false, scale=false)
    N_berg = diag(transpose(berg_basis .* ws) * berg_basis)
    berg_basis = berg_basis ./ transpose(sqrt.(N_berg))
    berg_bases[1 + j] = berg_basis
    berg_Es[1 + j] = berg_E
end
to_berg_basis(mat, j) = transpose(berg_bases[1 + j] .* ws) * mat * berg_bases[1 + j]

@time "U_berggren" begin
    U_blocks = [kron(berg_bases[1 + j1], berg_bases[1 + j2]) for (j1, j2) in js]
    U = blockdiag(sparse.(U_blocks)...)
end

@time "T" begin
    T_blocks = [kron_sum(to_berg_basis(get_T_matrix(ks, μ1), j1), to_berg_basis(get_T_matrix(ks, μ2), j2)) for (j1, j2) in js]
    T = blockdiag(sparse.(T_blocks)...)
end

@time "V1" begin
    V1_blocks = [kron(to_berg_basis(get_V_matrix((k, kp) -> V_l(j1, k, kp), ks, ws), j1), I(length(ks))) for (j1, _) in js]
    V1 = blockdiag(sparse.(V1_blocks)...)
end

E_max = 30
μω_global = 0.5
μ1ω1 = μω_global * 1/2
μ2ω2 = μω_global * 2

@time "V2_HO" V2_HO =  get_jacobi_V2_matrix(V_of_r, E_max, Λ, μω_global)

@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=true)

@time "V2_p" V2_p = W_left * V2_HO * transpose(W_right)
@time "V2" V2 = transpose(U) * V2_p * U

@time "H" H = T + V1 + V2

@time "Eigenvalues" evals, _ = eigs(H, sigma=target, maxiter=5000, tol=1e-5, ritzvec=false, check=1)
display(evals)