Coverage for gpaw/test/ralda/test_pbe_deriv.py: 100%

1import pytest 

2import numpy as np 

3from gpaw.xc.fxc_kernels import get_pbe_fxc_and_intermediate_derivatives 

4 

5 

6def eps_unif_x(kf_g): 

7 return -3 * kf_g / (4.0 * np.pi) 

8 

9 

10# (We test "small" and "large" densities separately) 

11@pytest.mark.parametrize( 

12 'n_g', [ 

13 np.linspace(0.001, 0.02, 10000), 

14 np.linspace(0.02, 0.5, 1000) 

15 ]) 

16def test_pbe_x_derivs(n_g): 

17 # Here we test d(fxc(n))/dn. We create a linspace of n and 

18 # calculate all the derivatives. However we put a dummy (constant) 

19 # value for s2_g (the gradient) which makes the numerics sensitive 

20 # (I think) for small densities. 

21 # 

22 # This test guards against the problem observed in #723. 

23 dn = n_g[1] - n_g[0] 

24 # (assuming np.linspace) 

25 

26 gradn2 = np.ones_like(n_g) 

27 kf_g = (3. * np.pi**2 * n_g)**(1 / 3.) 

28 s2_g = gradn2 / (4 * kf_g**2 * n_g**2) 

29 

30 fxc_g, F_g, Fn_g, Fnn_g = get_pbe_fxc_and_intermediate_derivatives( 

31 n_g, s2_g) 

32 

33 def numderiv(y_g): 

34 return (y_g[1:] - y_g[:-1]) / dn 

35 

36 E_g = n_g * eps_unif_x(kf_g) * F_g 

37 d2Edn2_num = numderiv(numderiv(E_g)) 

38 

39 assert fxc_g[1:-1] == pytest.approx(d2Edn2_num, abs=1e-4, rel=1e-4) 

40 # We could also test the other derivatives (Fn, Fnn) 

41 # but that's probably not highest priority.