Coverage for gpaw/test/tetrahedron/test_improved.py: 100%

1"""Test ITM with half-filled 1-d cosine band.""" 

2from math import pi 

3import pytest 

4import numpy as np 

5from gpaw.tetrahedron import TetrahedronMethod 

6from gpaw.dos import DOSCalculator 

7 

8 

9def f(N: int, i: bool): 

10 rcell = np.diag([1, 0.1, 0.1]) 

11 k = (np.linspace(-0.5, 0.5, N, endpoint=False) + 0.5 / N) * 2 * pi 

12 e = -np.cos(k)[:, np.newaxis] 

13 f = np.empty((N, 1)) 

14 w = np.zeros(N) + 1 / N 

15 t = TetrahedronMethod(rcell, (N, 1, 1), improved=i) 

16 ef, _ = t._calculate(0.5, e, w, f) 

17 wfs = WFS(e, ef) 

18 dos = DOSCalculator(wfs, cell=np.linalg.inv(rcell)) 

19 dosef = dos.raw_dos([ef], spin=0, width=0.0)[0] 

20 return f.sum() / N, (f * e).sum() / N, ef, dosef 

21 

22 

23class WFS: 

24 def __init__(self, e, ef): 

25 self.eig_skn = e[np.newaxis] 

26 self.fermi_level = ef 

27 self.size = (len(e), 1, 1) 

28 self.bz2ibz_map = None 

29 

30 def weights(self): 

31 n = self.size[0] 

32 return np.zeros(n) + 1 / n 

33 

34 def eigenvalues(self): 

35 return self.eig_skn 

36 

37 

38@pytest.mark.serial 

39def test_tm_1d(): 

40 # Improved: 

41 nelectrons, eband, efermi, dosefermi = f(100, True) 

42 assert nelectrons == pytest.approx(0.5, abs=1e-9) 

43 assert eband == pytest.approx(-1 / pi, abs=1e-5) 

44 assert efermi == pytest.approx(0.0, abs=1e-9) 

45 assert dosefermi == pytest.approx(1 / pi, abs=1e-4) 

46 

47 # Standard: 

48 nelectrons, eband100, efermi, dosefermi = f(100, not True) 

49 assert nelectrons == pytest.approx(0.5, abs=1e-9) 

50 assert efermi == pytest.approx(0.0, abs=1e-9) 

51 assert dosefermi == pytest.approx(1 / pi, abs=1e-4) 

52 

53 # ebands converges as 1/N^2. 

54 # Extrapolate to infinite number of k-points: 

55 eband80 = f(80, not True)[1] 

56 eband = np.polyval(np.polyfit([100**-2, 80**-2], 

57 [eband100, eband80], 1), 0.0) 

58 assert eband == pytest.approx(-1 / pi, abs=1e-7)