Arbitrary floating-point types

Since DFTK is completely generic in the floating-point type in its routines, there is no reason to perform the computation using double-precision arithmetic (i.e.Float64). Other floating-point types such as Float32 (single precision) are readily supported as well. On top of that we already reported[HLC2020] calculations in DFTK using elevated precision from DoubleFloats.jl or interval arithmetic using IntervalArithmetic.jl. In this example, however, we will concentrate on single-precision computations with Float32. The setup of such a reduced-precision calculation is basically identical to the regular case, since Julia automatically compiles all routines of DFTK at the precision, which is used for the lattice vectors. Apart from setting up the model with an explicit cast of the lattice vectors to Float32, there is thus no change in user code required:

using DFTK

# Setup silicon lattice
a = 10.263141334305942  # lattice constant in Bohr
lattice = a / 2 .* [[0 1 1.]; [1 0 1.]; [1 1 0.]]
Si = ElementPsp(:Si, psp=load_psp(:Si, functional="lda"))
atoms = [Si => [ones(3)/8, -ones(3)/8]]

# Cast to Float32, setup model and basis
model = model_DFT(Array{Float32}(lattice), atoms, [:lda_x, :lda_c_vwn])
Ecut = 7
basis = PlaneWaveBasis(model, Ecut, kgrid=[4, 4, 4])

# Run the SCF
scfres = self_consistent_field(basis, tol=1e-4);
n     Energy            Eₙ-Eₙ₋₁     ρout-ρin   Diag
---   ---------------   ---------   --------   ----
  1   -7.907553672791         NaN   1.95e-01    4.1
  2   -7.912325859070   -4.77e-03   2.98e-02    2.0
  3   -7.912410259247   -8.44e-05   3.21e-03    1.0

To check the calculation has really run in Float32, we check the energies and density are expressed in this floating-point type:

scfres.energies
Energy breakdown:
    Kinetic             3.0811601 
    AtomicLocal         -2.1866393
    AtomicNonlocal      1.7370193 
    Ewald               -8.3978930
    PspCorrection       -0.2946220
    Hartree             0.5437461 
    Xc                  -2.3951817

    total               -7.912410259247
eltype(scfres.energies.total)
Float32
eltype(scfres.ρ.real)
Float32
  • HLC2020M. F. Herbst, A. Levitt, E. Cancès. A posteriori error estimation for the non-self-consistent Kohn-Sham equations ArXiv 2004.13549