using QuadGK
include("../math.jl")

# Testing ∫dp p u' u where u' and u' may have different l

function explicit_integral(np, lp, n, l, μω)
    integrand(p) = p * (-1)^(n + np) * 1/sqrt(μω) * ho_basis(l, n, 1/sqrt(μω) * p) * ho_basis(lp, np, 1/sqrt(μω) * p)
    (integral, _) = quadgk(integrand, 0, Inf; atol=1e-10)
    return integral
end

n_list = 0 : 5
l_list = 0 : 5
μω_list = [1, 2.66]

for np in n_list
    for n in n_list
        for lp in l_list
            for l in l_list
                for μω in μω_list
                    println("Checking n=$n, np=$np, l=$l, lp=$lp, μω=$μω")
                    expl = explicit_integral(np, lp, n, l, μω)
                    anal = integral(np, lp, n, l, μω)
                    @assert isapprox(expl, anal; atol=1e-8) "Explicit=$(expl) and analytical=$(anal)"
                end
            end
        end
    end
end

# Testing the full Racah's reduction formula

test_data = DelimitedFiles.readdlm("test/racah_test_data.csv", ',') # format = n1p, l1p, n2p, l2p, n1, l1, n2, l2, Λ, μ1ω1, μ2ω2, racah_matrix_element

for i in 1 : size(test_data)[1]
    n1p, l1p, n2p, l2p, n1, l1, n2, l2, Λ, μ1ω1, μ2ω2, racah_matrix_element = test_data[i, :]
    val = racahs_reduction_formula(Int(n1p), Int(l1p), Int(n2p), Int(l2p), Int(n1), Int(l1), Int(n2), Int(l2), Int(Λ), μ1ω1, μ2ω2)
    @assert isapprox(val, racah_matrix_element; atol=1e-8) "Formula=$(val) and test reference=$racah_matrix_element"
end