Coverage for /builds/hweiske/ase/ase/optimize/cellawarebfgs.py: 98.57%

1import time 

2from typing import IO, Optional, Union 

3 

4import numpy as np 

5 

6from ase import Atoms 

7from ase.geometry import cell_to_cellpar 

8from ase.optimize import BFGS 

9from ase.optimize.optimize import Dynamics 

10from ase.units import GPa 

11 

12 

13def calculate_isotropic_elasticity_tensor(bulk_modulus, poisson_ratio, 

14 suppress_rotation=0): 

15 """ 

16 Parameters: 

17 bulk_modulus Bulk Modulus of the isotropic system used to set up the 

18 Hessian (in ASE units (eV/Å^3)). 

19 

20 poisson_ratio Poisson ratio of the isotropic system used to set up the 

21 initial Hessian (unitless, between -1 and 0.5). 

22 

23 suppress_rotation The rank-2 matrix C_ijkl.reshape((9,9)) has by 

24 default 6 non-zero eigenvalues, because energy is 

25 invariant to orthonormal rotations of the cell 

26 vector. This serves as a bad initial Hessian due to 3 

27 zero eigenvalues. Suppress rotation sets a value for 

28 those zero eigenvalues. 

29 

30 Returns C_ijkl 

31 """ 

32 

33 # https://scienceworld.wolfram.com/physics/LameConstants.html 

34 _lambda = 3 * bulk_modulus * poisson_ratio / (1 + 1 * poisson_ratio) 

35 _mu = _lambda * (1 - 2 * poisson_ratio) / (2 * poisson_ratio) 

36 

37 # https://en.wikipedia.org/wiki/Elasticity_tensor 

38 g_ij = np.eye(3) 

39 

40 # Construct 4th rank Elasticity tensor for isotropic systems 

41 C_ijkl = _lambda * np.einsum('ij,kl->ijkl', g_ij, g_ij) 

42 C_ijkl += _mu * (np.einsum('ik,jl->ijkl', g_ij, g_ij) + 

43 np.einsum('il,kj->ijkl', g_ij, g_ij)) 

44 

45 # Supplement the tensor with suppression of pure rotations that are right 

46 # now 0 eigenvalues. 

47 # Loop over all basis vectors of skew symmetric real matrix 

48 for i, j in ((0, 1), (0, 2), (1, 2)): 

49 Q = np.zeros((3, 3)) 

50 Q[i, j], Q[j, i] = 1, -1 

51 C_ijkl += (np.einsum('ij,kl->ijkl', Q, Q) 

52 * suppress_rotation / 2) 

53 

54 return C_ijkl 

55 

56 

57class CellAwareBFGS(BFGS): 

58 def __init__( 

59 self, 

60 atoms: Atoms, 

61 restart: Optional[str] = None, 

62 logfile: Union[IO, str] = '-', 

63 trajectory: Optional[str] = None, 

64 append_trajectory: bool = False, 

65 maxstep: Optional[float] = None, 

66 master: Optional[bool] = None, 

67 bulk_modulus: Optional[float] = 145 * GPa, 

68 poisson_ratio: Optional[float] = 0.3, 

69 alpha: Optional[float] = None, 

70 long_output: Optional[bool] = False, 

71 ): 

72 self.bulk_modulus = bulk_modulus 

73 self.poisson_ratio = poisson_ratio 

74 self.long_output = long_output 

75 BFGS.__init__(self, atoms=atoms, restart=restart, logfile=logfile, 

76 trajectory=trajectory, maxstep=maxstep, master=master, 

77 alpha=alpha, append_trajectory=append_trajectory) 

78 assert not isinstance(atoms, Atoms) 

79 if hasattr(atoms, 'exp_cell_factor'): 

80 assert atoms.exp_cell_factor == 1.0 

81 

82 def initialize(self): 

83 BFGS.initialize(self) 

84 C_ijkl = calculate_isotropic_elasticity_tensor( 

85 self.bulk_modulus, 

86 self.poisson_ratio, 

87 suppress_rotation=self.alpha) 

88 cell_H = self.H0[-9:, -9:] 

89 ind = np.where(self.atoms.mask.ravel() != 0)[0] 

90 cell_H[np.ix_(ind, ind)] = C_ijkl.reshape((9, 9))[ 

91 np.ix_(ind, ind)] * self.atoms.atoms.cell.volume 

92 

93 def converged(self, forces=None): 

94 if forces is None: 

95 forces = self.atoms.atoms.get_forces() 

96 stress = self.atoms.atoms.get_stress() 

97 return np.max(np.sum(forces**2, axis=1))**0.5 < self.fmax and \ 

98 np.max(np.abs(stress)) < self.smax 

99 

100 def run(self, fmax=0.05, smax=0.005, steps=None): 

101 """ call Dynamics.run and keep track of fmax""" 

102 self.fmax = fmax 

103 self.smax = smax 

104 if steps is not None: 

105 self.max_steps = steps 

106 return Dynamics.run(self) 

107 

108 def log(self, forces=None): 

109 if forces is None: 

110 forces = self.atoms.atoms.get_forces() 

111 fmax = (forces ** 2).sum(axis=1).max() ** 0.5 

112 e = self.optimizable.get_potential_energy() 

113 T = time.localtime() 

114 smax = abs(self.atoms.atoms.get_stress()).max() 

115 volume = self.atoms.atoms.cell.volume 

116 if self.logfile is not None: 

117 name = self.__class__.__name__ 

118 if self.nsteps == 0: 

119 args = (" " * len(name), 

120 "Step", "Time", "Energy", "fmax", "smax", "volume") 

121 msg = "\n%s %4s %8s %15s %15s %15s %15s" % args 

122 if self.long_output: 

123 msg += ("%8s %8s %8s %8s %8s %8s" % 

124 ('A', 'B', 'C', 'α', 'β', 'γ')) 

125 msg += '\n' 

126 self.logfile.write(msg) 

127 

128 ast = '' 

129 args = (name, self.nsteps, T[3], T[4], T[5], e, ast, fmax, smax, 

130 volume) 

131 msg = ("%s: %3d %02d:%02d:%02d %15.6f%1s %15.6f %15.6f %15.6f" % 

132 args) 

133 if self.long_output: 

134 msg += ("%8.3f %8.3f %8.3f %8.3f %8.3f %8.3f" % 

135 tuple(cell_to_cellpar(self.atoms.atoms.cell))) 

136 msg += '\n' 

137 self.logfile.write(msg) 

138 

139 self.logfile.flush()