1import numpy as np 

2from collections import namedtuple 

3from ase.geometry import find_mic 

4 

5 

6def fit_raw(energies, forces, positions, cell=None, pbc=None): 

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

8 a NEB plot.""" 

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

10 n_images = len(energies) 

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

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

13 

14 path = [0] 

15 for i in range(n_images - 1): 

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

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

18 dR, _ = find_mic(dR, cell, pbc) 

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

20 

21 lines = [] # tangent lines 

22 lastslope = None 

23 for i in range(n_images): 

24 if i == 0: 

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

26 dpath = 0.5 * path[1] 

27 elif i == n_images - 1: 

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

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

30 else: 

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

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

33 

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

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

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

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

38 lines.append((x, y)) 

39 

40 if i > 0: 

41 s0 = path[i - 1] 

42 s1 = path[i] 

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

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

45 (1, s1, s1**2, s1**3), 

46 (0, 1, 2 * s0, 3 * s0**2), 

47 (0, 1, 2 * s1, 3 * s1**2)]), 

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

49 lastslope, slope])) 

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

51 fit_path[(i - 1) * 20:i * 20] = x 

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

53 

54 lastslope = slope 

55 

56 fit_path[-1] = path[-1] 

57 fit_energies[-1] = energies[-1] 

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

59 

60 

61class ForceFit(namedtuple('ForceFit', ['path', 'energies', 'fit_path', 

62 'fit_energies', 'lines'])): 

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

64 

65 def plot(self, ax=None): 

66 import matplotlib.pyplot as plt 

67 if ax is None: 

68 ax = plt.gca() 

69 

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

71 for x, y in self.lines: 

72 ax.plot(x, y, '-g') 

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

74 ax.set_xlabel(r'path [Å]') 

75 ax.set_ylabel('energy [eV]') 

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

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

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

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

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

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

82 return ax 

83 

84 

85def fit_images(images): 

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

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

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

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

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

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

92 A = images[0].cell 

93 pbc = images[0].pbc 

94 return fit_raw(E, F, R, A, pbc) 

95 

96 

97def force_curve(images, ax=None): 

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

99 

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

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

102 available.""" 

103 

104 if ax is None: 

105 import matplotlib.pyplot as plt 

106 ax = plt.gca() 

107 

108 nim = len(images) 

109 

110 accumulated_distances = [] 

111 accumulated_distance = 0.0 

112 

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

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

115 energies = [atoms.get_potential_energy() 

116 for atoms in images] 

117 

118 for i in range(nim): 

119 atoms = images[i] 

120 f_ac = atoms.get_forces() 

121 

122 if i < nim - 1: 

123 rightpos = images[i + 1].positions 

124 else: 

125 rightpos = atoms.positions 

126 

127 if i > 0: 

128 leftpos = images[i - 1].positions 

129 else: 

130 leftpos = atoms.positions 

131 

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

133 pbc=atoms.pbc) 

134 

135 def total_displacement(disp): 

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

137 return sum(disp_a) 

138 

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

140 

141 linescale = 0.45 

142 

143 disp = 0.5 * total_displacement(disp_ac) 

144 

145 if i == 0 or i == nim - 1: 

146 disp *= 2 

147 dE_fdotr *= 2 

148 

149 x1 = accumulated_distance - disp * linescale 

150 x2 = accumulated_distance + disp * linescale 

151 y1 = energies[i] - dE_fdotr * linescale 

152 y2 = energies[i] + dE_fdotr * linescale 

153 

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

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

156 ax.set_ylabel('Energy [eV]') 

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

158 accumulated_distances.append(accumulated_distance) 

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

160 

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

162 return ax 

163 

164 

165def plotfromfile(*fnames): 

166 from ase.io import read 

167 nplots = len(fnames) 

168 

169 for i, fname in enumerate(fnames): 

170 images = read(fname, ':') 

171 import matplotlib.pyplot as plt 

172 plt.subplot(nplots, 1, 1 + i) 

173 force_curve(images) 

174 plt.show() 

175 

176 

177if __name__ == '__main__': 

178 import sys 

179 fnames = sys.argv[1:] 

180 plotfromfile(*fnames)