Coverage for icet/tools/variable_transformation.py: 98%

1from itertools import combinations, permutations 

2from typing import List 

3 

4import numpy as np 

5from ase import Atoms 

6from icet.core.orbit import Orbit 

7from icet.core.orbit_list import OrbitList 

8from icet.core.lattice_site import LatticeSite 

9 

10 

11def _is_site_group_in_orbit(orbit: Orbit, site_group: List[LatticeSite]) -> bool: 

12 """Checks if a list of sites is found among the clusters in an orbit. 

13 The number of sites must match the order of the orbit. 

14 

15 Parameters 

16 ---------- 

17 orbit 

18 Orbit. 

19 site_group 

20 Sites to be searched for. 

21 """ 

22 

23 # Ensure that the number of sites matches the order of the orbit 

24 if len(site_group) != orbit.order: 24 ↛ 25line 24 didn't jump to line 25, because the condition on line 24 was never true

25 return False 

26 

27 # Check if the set of lattice sites is found among the equivalent sites 

28 if set(site_group) in [set(cl.lattice_sites) for cl in orbit.clusters]: 

29 return True 

30 

31 # Go through all clusters 

32 site_indices = [site.index for site in site_group] 

33 for cluster in orbit.clusters: 

34 cluster_site_indices = [s.index for s in cluster.lattice_sites] 

35 

36 # Skip if the site indices do not match 

37 if set(site_indices) != set(cluster_site_indices): 

38 continue 

39 

40 # Loop over all permutations of the lattice sites in cluster 

41 for cluster_site_group in permutations(cluster.lattice_sites): 

42 

43 # Skip all cases that include pairs of sites with different site indices 

44 if any(site1.index != site2.index 

45 for site1, site2 in zip(site_group, cluster_site_group)): 

46 continue 

47 

48 # If the relative offsets for all pairs of sites match, the two 

49 # clusters are equivalent 

50 relative_offsets = [site1.unitcell_offset - site2.unitcell_offset 

51 for site1, site2 in zip(site_group, cluster_site_group)] 

52 if all(np.array_equal(ro, relative_offsets[0]) for ro in relative_offsets): 

53 return True 

54 return False 

55 

56 

57def get_transformation_matrix(structure: Atoms, 

58 full_orbit_list: OrbitList) -> np.ndarray: 

59 r""" 

60 Determines the matrix that transforms the cluster functions in the form 

61 of spin variables, :math:`\sigma_i\in\{-1,1\}`, to their binary 

62 equivalents, :math:`x_i\in\{0,1\}`. The form is obtained by 

63 performing the substitution (:math:`\sigma_i=1-2x_i`) in the 

64 cluster expansion expression of the predicted property (commonly the energy). 

65 

66 Parameters 

67 ---------- 

68 structure 

69 Atomic configuration. 

70 full_orbit_list 

71 Full orbit list. 

72 """ 

73 # Go through all clusters associated with each active orbit and 

74 # determine its contribution to each orbit 

75 orbit_indices = range(len(full_orbit_list)) 

76 transformation = np.zeros((len(orbit_indices) + 1, 

77 len(orbit_indices) + 1)) 

78 transformation[0, 0] = 1.0 

79 for i, orb_index in enumerate(orbit_indices, 1): 

80 orbit = full_orbit_list.get_orbit(orb_index) 

81 repr_sites = orbit.representative_cluster.lattice_sites 

82 # add contributions to the lower order orbits to which the 

83 # subclusters belong 

84 for sub_order in range(orbit.order + 1): 

85 n_terms_target = len(list(combinations(orbit.representative_cluster.lattice_sites, 

86 sub_order))) 

87 n_terms_actual = 0 

88 if sub_order == 0: 

89 transformation[0, i] += 1.0 

90 n_terms_actual += 1 

91 if sub_order == orbit.order: 

92 transformation[i, i] += (-2.0) ** (sub_order) 

93 n_terms_actual += 1 

94 else: 

95 comb_sub_sites = combinations(repr_sites, sub_order) 

96 for sub_sites in comb_sub_sites: 

97 for j, sub_index in enumerate(orbit_indices, 1): 

98 sub_orbit = full_orbit_list.get_orbit(sub_index) 

99 if sub_orbit.order != sub_order: 

100 continue 

101 if _is_site_group_in_orbit(sub_orbit, sub_sites): 

102 transformation[j, i] += (-2.0) ** (sub_order) 

103 n_terms_actual += 1 

104 # If the number of contributions does not match the number of subclusters, 

105 # this orbit list is incompatible with the ground state finder 

106 # of subclusters 

107 if n_terms_actual != n_terms_target: 

108 raise ValueError('At least one cluster had subclusters that were not included' 

109 ' in the cluster space. This is typically caused by cutoffs' 

110 ' that are longer for a higher-order orbit than lower-order one' 

111 ' (such as 8 Angstrom for triplets and 6 Angstrom for pairs).' 

112 ' Please use a different cluster space for the ground state ' 

113 ' finder.') 

114 

115 return transformation 

116 

117 

118def transform_parameters(structure: Atoms, 

119 full_orbit_list: OrbitList, 

120 parameters: np.ndarray) -> np.ndarray: 

121 r""" 

122 Transforms the list of parameters, obtained using cluster functions in the 

123 form of of spin variables, :math:`\sigma_i\in\{-1,1\}`, to their 

124 equivalents for the case of binary variables, 

125 :math:`x_i\in\{0,1\}`. 

126 

127 Parameters 

128 ---------- 

129 structure 

130 Atomic configuration. 

131 full_orbit_list 

132 Full orbit list. 

133 parameters 

134 Parameter vector (spin variables). 

135 """ 

136 A = get_transformation_matrix(structure, full_orbit_list) 

137 return np.dot(A, parameters)