using DFTK
using LinearAlgebra

struct ElementCustomPotential <: DFTK.Element
    pot_real::Function      # Real potential
    pot_fourier::Function   # Fourier potential
end

function DFTK.local_potential_fourier(el::ElementCustomPotential, q::Real)
    return el.pot_fourier(q)
end
function DFTK.local_potential_real(el::ElementCustomPotential, r::Real)
    return el.pot_real(r)
end

a = 10
lattice = a .* [[1 0 0.]; [0 0 0]; [0 0 0]];

x1 = 0.2
x2 = 0.8;

L = 0.5;

pot_real(x) = exp(-(x/L)^2)
pot_fourier(q::T) where {T <: Real} = exp(- (q*L)^2 / 4);

nucleus = ElementCustomPotential(pot_real, pot_fourier)
atoms = [nucleus => [x1*[1,0,0], x2*[1,0,0]]];

C = 1.0
α = 2;
n_electrons = 1  # Increase this for fun
terms = [Kinetic(),
         AtomicLocal(),
         PowerNonlinearity(C, α),
]
model = Model(lattice; atoms=atoms, n_electrons=n_electrons, terms=terms,
              spin_polarization=:spinless);  # use "spinless electrons"

basis = PlaneWaveBasis(model; Ecut=500, kgrid=(1, 1, 1))
ρ = zeros(eltype(basis), basis.fft_size..., 1)
scfres = self_consistent_field(basis, tol=1e-8, ρ=ρ)
scfres.energies

hcat(compute_forces(scfres)...)

tot_local_pot = DFTK.total_local_potential(scfres.ham)[:, 1, 1]; # use only dimension 1

ρ = scfres.ρ[:, 1, 1, 1]  # converged density, first spin component
ψ_fourier = scfres.ψ[1][:, 1];    # first kpoint, all G components, first eigenvector
ψ = G_to_r(basis, basis.kpoints[1], ψ_fourier)[:, 1, 1]
ψ /= (ψ[div(end, 2)] / abs(ψ[div(end, 2)]));

using Plots
x = a * vec(first.(DFTK.r_vectors(basis)))
p = plot(x, real.(ψ), label="real(ψ)")
plot!(p, x, imag.(ψ), label="imag(ψ)")
plot!(p, x, ρ, label="ρ")
plot!(p, x, tot_local_pot, label="tot local pot")