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interpolation.jl
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interpolation.jl
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using Test
using DFTK
using DFTK: interpolate_density, transfer_blochwave, compute_transfer_matrix
using LinearAlgebra
include("testcases.jl")
@testset "Interpolation of density" begin
lattice = Array{Float64}(I, 3, 3)
N = 20
f(n) = cos(2π*(n-1)/N)
grid_in = (N, N, N)
grid_out = (N+20, N-5, N+2)
ρin = [f(i)*f(j)+f(k) for i = 1:N, j = 1:N, k = 1:N]
# Test interpolation
ρout = interpolate_density(ρin, grid_in, grid_out, lattice, lattice)
ρin2 = interpolate_density(ρout, grid_out, grid_in, lattice, lattice)
@test maximum(abs.(ρin2-ρin)) < .01
# Test supercell
ρout = interpolate_density(ρin, grid_in, grid_in, lattice, 2lattice)
ρout1 = interpolate_density(ρout, grid_in, grid_in, 2lattice, 4lattice)
ρout2 = interpolate_density(ρin, grid_in, grid_in, lattice, 4lattice)
@test maximum(abs.(ρout2 - ρout1)) < sqrt(eps())
ρout = interpolate_density(ρin, grid_in, grid_in, lattice, 2lattice)
ρout1 = interpolate_density(ρout, grid_in, grid_out, 2lattice, 4lattice)
ρout2 = interpolate_density(ρin, grid_in, grid_out, lattice, 4lattice)
@test maximum(abs.(ρout2 - ρout1)) < .01
end
@testset "Transfer of blochwave" begin
tol = 1e-7
Ecut = 5
Si = ElementPsp(silicon.atnum, psp=load_psp(silicon.psp))
model = model_LDA(silicon.lattice, [Si => silicon.positions])
kgrid = [2, 2, 2]
basis = PlaneWaveBasis(model; Ecut, kgrid)
ψ = self_consistent_field(basis; tol=tol, callback=identity).ψ
## Testing transfers from basis to a bigger_basis and backwards
# Transfer to bigger basis then same basis (both interpolations are
# tested then)
bigger_basis = PlaneWaveBasis(model; Ecut=(Ecut + 5), kgrid)
ψ_b = transfer_blochwave(ψ, basis, bigger_basis)
ψ_bb = transfer_blochwave(ψ_b, bigger_basis, basis)
@test norm(ψ - ψ_bb) < eps(eltype(basis))
T = compute_transfer_matrix(basis, bigger_basis) # transfer
Tᵇ = compute_transfer_matrix(bigger_basis, basis) # back-transfer
Tψ = [Tk * ψk for (Tk, ψk) in zip(T, ψ)]
TᵇTψ = [Tᵇk * Tψk for (Tᵇk, Tψk) in zip(Tᵇ, Tψ)]
@test norm(ψ - TᵇTψ) < eps(eltype(basis))
# TᵇT should be the identity and TTᵇ should be a projection
TᵇT = [Tᵇk * Tk for (Tk, Tᵇk) in zip(T, Tᵇ)]
@test all(M -> maximum(abs, M-I) < eps(eltype(basis)), TᵇT)
TTᵇ = [Tk * Tᵇk for (Tk, Tᵇk) in zip(T, Tᵇ)]
@test all(M -> M ≈ M*M, TTᵇ)
# Transfer between same basis (not very useful, but is worth testing)
bigger_basis = PlaneWaveBasis(model; Ecut, kgrid)
ψ_b = transfer_blochwave(ψ, basis, bigger_basis)
ψ_bb = transfer_blochwave(ψ_b, bigger_basis, basis)
@test norm(ψ-ψ_bb) < eps(eltype(basis))
end