Coverage for /builds/ericyuan00000/ase/ase/utils/forcecurve.py: 78.63%

1# fmt: off 

2 

3from collections import namedtuple 

4 

5import numpy as np 

6 

7from ase.geometry import find_mic 

8 

9 

10def fit_raw(energies, forces, positions, cell=None, pbc=None): 

11 """Calculates parameters for fitting images to a band, as for 

12 a NEB plot.""" 

13 energies = np.array(energies) - energies[0] 

14 n_images = len(energies) 

15 fit_energies = np.empty((n_images - 1) * 20 + 1) 

16 fit_path = np.empty((n_images - 1) * 20 + 1) 

17 

18 path = [0] 

19 for i in range(n_images - 1): 

20 dR = positions[i + 1] - positions[i] 

21 if cell is not None and pbc is not None: 

22 dR, _ = find_mic(dR, cell, pbc) 

23 path.append(path[i] + np.sqrt((dR**2).sum())) 

24 

25 lines = [] # tangent lines 

26 lastslope = None 

27 for i in range(n_images): 

28 if i == 0: 

29 direction = positions[i + 1] - positions[i] 

30 dpath = 0.5 * path[1] 

31 elif i == n_images - 1: 

32 direction = positions[-1] - positions[-2] 

33 dpath = 0.5 * (path[-1] - path[-2]) 

34 else: 

35 direction = positions[i + 1] - positions[i - 1] 

36 dpath = 0.25 * (path[i + 1] - path[i - 1]) 

37 

38 direction /= np.linalg.norm(direction) 

39 slope = -(forces[i] * direction).sum() 

40 x = np.linspace(path[i] - dpath, path[i] + dpath, 3) 

41 y = energies[i] + slope * (x - path[i]) 

42 lines.append((x, y)) 

43 

44 if i > 0: 

45 s0 = path[i - 1] 

46 s1 = path[i] 

47 x = np.linspace(s0, s1, 20, endpoint=False) 

48 c = np.linalg.solve(np.array([(1, s0, s0**2, s0**3), 

49 (1, s1, s1**2, s1**3), 

50 (0, 1, 2 * s0, 3 * s0**2), 

51 (0, 1, 2 * s1, 3 * s1**2)]), 

52 np.array([energies[i - 1], energies[i], 

53 lastslope, slope])) 

54 y = c[0] + x * (c[1] + x * (c[2] + x * c[3])) 

55 fit_path[(i - 1) * 20:i * 20] = x 

56 fit_energies[(i - 1) * 20:i * 20] = y 

57 

58 lastslope = slope 

59 

60 fit_path[-1] = path[-1] 

61 fit_energies[-1] = energies[-1] 

62 return ForceFit(path, energies, fit_path, fit_energies, lines) 

63 

64 

65class ForceFit(namedtuple('ForceFit', ['path', 'energies', 'fit_path', 

66 'fit_energies', 'lines'])): 

67 """Data container to hold fitting parameters for force curves.""" 

68 

69 def plot(self, ax=None): 

70 import matplotlib.pyplot as plt 

71 if ax is None: 

72 ax = plt.gca() 

73 

74 ax.plot(self.path, self.energies, 'o') 

75 for x, y in self.lines: 

76 ax.plot(x, y, '-g') 

77 ax.plot(self.fit_path, self.fit_energies, 'k-') 

78 ax.set_xlabel(r'path [Å]') 

79 ax.set_ylabel('energy [eV]') 

80 Ef = max(self.energies) - self.energies[0] 

81 Er = max(self.energies) - self.energies[-1] 

82 dE = self.energies[-1] - self.energies[0] 

83 ax.set_title(r'$E_\mathrm{{f}} \approx$ {:.3f} eV; ' 

84 r'$E_\mathrm{{r}} \approx$ {:.3f} eV; ' 

85 r'$\Delta E$ = {:.3f} eV'.format(Ef, Er, dE)) 

86 return ax 

87 

88 

89def fit_images(images): 

90 """Fits a series of images with a smoothed line for producing a standard 

91 NEB plot. Returns a `ForceFit` data structure; the plot can be produced 

92 by calling the `plot` method of `ForceFit`.""" 

93 R = [atoms.positions for atoms in images] 

94 E = [atoms.get_potential_energy() for atoms in images] 

95 F = [atoms.get_forces() for atoms in images] # XXX force consistent??? 

96 A = images[0].cell 

97 pbc = images[0].pbc 

98 return fit_raw(E, F, R, A, pbc) 

99 

100 

101def force_curve(images, ax=None): 

102 """Plot energies and forces as a function of accumulated displacements. 

103 

104 This is for testing whether a calculator's forces are consistent with 

105 the energies on a set of geometries where energies and forces are 

106 available.""" 

107 

108 if ax is None: 

109 import matplotlib.pyplot as plt 

110 ax = plt.gca() 

111 

112 nim = len(images) 

113 

114 accumulated_distances = [] 

115 accumulated_distance = 0.0 

116 

117 # XXX force_consistent=True will work with some calculators, 

118 # but won't work if images were loaded from a trajectory. 

119 energies = [atoms.get_potential_energy() 

120 for atoms in images] 

121 

122 for i in range(nim): 

123 atoms = images[i] 

124 f_ac = atoms.get_forces() 

125 

126 if i < nim - 1: 

127 rightpos = images[i + 1].positions 

128 else: 

129 rightpos = atoms.positions 

130 

131 if i > 0: 

132 leftpos = images[i - 1].positions 

133 else: 

134 leftpos = atoms.positions 

135 

136 disp_ac, _ = find_mic(rightpos - leftpos, cell=atoms.cell, 

137 pbc=atoms.pbc) 

138 

139 def total_displacement(disp): 

140 disp_a = (disp**2).sum(axis=1)**.5 

141 return sum(disp_a) 

142 

143 dE_fdotr = -0.5 * np.vdot(f_ac.ravel(), disp_ac.ravel()) 

144 

145 linescale = 0.45 

146 

147 disp = 0.5 * total_displacement(disp_ac) 

148 

149 if i == 0 or i == nim - 1: 

150 disp *= 2 

151 dE_fdotr *= 2 

152 

153 x1 = accumulated_distance - disp * linescale 

154 x2 = accumulated_distance + disp * linescale 

155 y1 = energies[i] - dE_fdotr * linescale 

156 y2 = energies[i] + dE_fdotr * linescale 

157 

158 ax.plot([x1, x2], [y1, y2], 'b-') 

159 ax.plot(accumulated_distance, energies[i], 'bo') 

160 ax.set_ylabel('Energy [eV]') 

161 ax.set_xlabel('Accumulative distance [Å]') 

162 accumulated_distances.append(accumulated_distance) 

163 accumulated_distance += total_displacement(rightpos - atoms.positions) 

164 

165 ax.plot(accumulated_distances, energies, ':', zorder=-1, color='k') 

166 return ax 

167 

168 

169def plotfromfile(*fnames): 

170 from ase.io import read 

171 nplots = len(fnames) 

172 

173 for i, fname in enumerate(fnames): 

174 images = read(fname, ':') 

175 import matplotlib.pyplot as plt 

176 plt.subplot(nplots, 1, 1 + i) 

177 force_curve(images) 

178 plt.show() 

179 

180 

181if __name__ == '__main__': 

182 import sys 

183 fnames = sys.argv[1:] 

184 plotfromfile(*fnames)