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compute_density.jl
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compute_density.jl
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using Test
using LinearAlgebra
using DFTK
import DFTK: total_local_potential
include("testcases.jl")
# TODO Once we have converged SCF densities in a file it would be better to instead / also
# test the energies of these densities and compare them directly to the reference
# energies obtained in the data files
if mpi_nprocs() == 1 # not easy to distribute
@testset "Using BZ symmetry yields identical density" begin
function get_bands(testcase, kcoords, ksymops, symmetries, atoms; Ecut=5, tol=1e-8, n_rounds=1)
kwargs = ()
n_bands = div(testcase.n_electrons, 2, RoundUp)
if testcase.temperature !== nothing
kwargs = (temperature=testcase.temperature, smearing=DFTK.Smearing.FermiDirac())
n_bands = div(testcase.n_electrons, 2, RoundUp) + 4
end
model = model_DFT(testcase.lattice, atoms, :lda_xc_teter93; kwargs...)
basis = PlaneWaveBasis(model, Ecut, kcoords, ksymops, symmetries)
ham = Hamiltonian(basis; ρ=guess_density(basis, atoms))
res = diagonalize_all_kblocks(lobpcg_hyper, ham, n_bands; tol=tol)
occ, εF = DFTK.compute_occupation(basis, res.λ)
ρnew = compute_density(basis, res.X, occ)
for it in 1:n_rounds
ham = Hamiltonian(basis; ρ=ρnew)
res = diagonalize_all_kblocks(lobpcg_hyper, ham, n_bands; tol=tol, ψguess=res.X)
occ, εF = DFTK.compute_occupation(basis, res.λ)
ρnew = compute_density(basis, res.X, occ)
end
ham, res.X, res.λ, ρnew, occ
end
function test_orthonormality(basis, ψ; tol=1e-8)
n_k = length(ψ)
n_states = size(ψ[1], 2)
n_fft = prod(basis.fft_size)
for (ik, kpt) in enumerate(basis.kpoints)
# Fourier-transform the wave functions to real space
ψk = ψ[ik]
ψk_real = cat((DFTK.G_to_r(basis, kpt, ψik) for ψik in eachcol(ψk))..., dims=4)
T = real(eltype(ψk_real))
ψk_real_mat = reshape(ψk_real, n_fft, n_states)
ψk_real_overlap = adjoint(ψk_real_mat) * ψk_real_mat
nondiag = ψk_real_overlap - I * (n_fft / basis.model.unit_cell_volume)
@test maximum(abs.(nondiag)) < tol
end
end
function test_full_vs_irreducible(testcase, kgrid_size; Ecut=5, tol=1e-8, n_ignore=0,
kshift=[0, 0, 0], eigenvectors=true)
spec = ElementPsp(testcase.atnum, psp=load_psp(testcase.psp))
atoms = [spec => testcase.positions]
kfull, sym_full, symmetries = bzmesh_uniform(kgrid_size, kshift=kshift)
res = get_bands(testcase, kfull, sym_full, symmetries, atoms; Ecut=Ecut, tol=tol)
ham_full, ψ_full, eigenvalues_full, ρ_full, occ_full = res
test_orthonormality(ham_full.basis, ψ_full, tol=tol)
symmetries = DFTK.symmetry_operations(testcase.lattice, atoms)
kcoords, ksymops, symmetries = bzmesh_ir_wedge(kgrid_size, symmetries, kshift=kshift)
res = get_bands(testcase, kcoords, ksymops, symmetries, atoms; Ecut=Ecut, tol=tol)
ham_ir, ψ_ir, eigenvalues_ir, ρ_ir, occ_ir = res
test_orthonormality(ham_ir.basis, ψ_ir, tol=tol)
@test ham_full.basis.fft_size == ham_ir.basis.fft_size
# Test density is the same in both schemes, and symmetric wrt the basis symmetries
@test maximum(abs.(ρ_ir - ρ_full)) < 10tol
@test maximum(abs, DFTK.symmetrize_ρ(ham_ir.basis, ρ_ir; symmetries=symmetries) - ρ_ir) < tol
# Test local potential is the same in both schemes
@test maximum(abs, total_local_potential(ham_ir) - total_local_potential(ham_full)) < tol
# Test equivalent k-points have the same orbital energies
for (ik, k) in enumerate(kcoords)
for symop in ksymops[ik]
ikfull = findfirst(1:length(kfull)) do idx
all(isinteger, kfull[idx] - symop.S * k)
end
@test ikfull !== nothing
# Orbital energies should agree (by symmetry)
# The largest few are ignored, because the results between the
# full kpoints and the reduced kpoints are sometimes a little unstable
# (since we actually use different guesses)
range = 1:length(eigenvalues_full[ikfull]) - n_ignore
@test eigenvalues_full[ikfull][range] ≈ eigenvalues_ir[ik][range] atol=tol
end
end
if eigenvectors
# Test applying the symmetry transformation to the irreducible k-points
# yields an eigenfunction of the Hamiltonian
# Also check that the accumulated partial densities are equal
# to the returned density.
ρsum = zeros(eltype(ψ_ir[1]), ham_ir.basis.fft_size)
n_ρ = 0
for (ik, k) in enumerate(kcoords)
Hk_ir = ham_ir.blocks[ik]
for symop in ksymops[ik]
Skpoint, ψSk = DFTK.apply_symop(symop, ham_ir.basis, Hk_ir.kpoint, ψ_ir[ik])
ikfull = findfirst(1:length(kfull)) do idx
all(isinteger, round.(kfull[idx] - Skpoint.coordinate, digits=10))
end
@test !isnothing(ikfull)
Hk_full = ham_full.blocks[ikfull]
range = 1:length(eigenvalues_ir[ik]) - n_ignore
for iband in range
ψnSk = ψSk[:, iband]
residual = norm(Hk_full * ψnSk - eigenvalues_ir[ik][iband] * ψnSk)
@test residual < 10tol
end # iband
end # symop
end # k
end # eigenvectors
end
test_full_vs_irreducible(silicon, [3, 2, 3], Ecut=5, tol=1e-10)
test_full_vs_irreducible(silicon, [3, 3, 3], Ecut=5, tol=1e-6)
test_full_vs_irreducible(silicon, [3, 3, 3], Ecut=5, tol=1e-6, kshift=[1/2, 1/2, 1/2])
test_full_vs_irreducible(silicon, [3, 3, 3], Ecut=5, tol=1e-6, kshift=[1/2, 0, 1/2])
test_full_vs_irreducible(silicon, [3, 3, 3], Ecut=5, tol=1e-6, kshift=[0, 1/2, 0])
test_full_vs_irreducible(silicon, [2, 3, 4], Ecut=5, tol=1e-6)
test_full_vs_irreducible(magnesium, [2, 3, 4], Ecut=5, tol=1e-6, n_ignore=1)
test_full_vs_irreducible(aluminium, [1, 3, 5], Ecut=3, tol=1e-5, n_ignore=3,
eigenvectors=false)
# That's pretty expensive:
# test_full_vs_irreducible([4, 4, 4], Ecut=5, tol=1e-6)
end
end