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InTerSect_EL_level.py
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#
import numpy as np
from scipy.optimize import curve_fit
import matplotlib.pyplot as plt
from matplotlib.font_manager import FontProperties
import sys
from sympy import *
import sympy as sym
import os
from itertools import chain
import pickle as pl
# Intial candidates for fit, per FU: - thus, the E vs V input data has to be per FU
E0_init = -941.510817926696 # -1882.50963222/2.0
V0_init = 63.54960592453 #125.8532/2.0
B0_init = 76.3746233515232 #74.49
B0_prime_init = 4.05340727164527 #4.15
def BM(x, a, b, c, d):
return a + b*x + c*x**2 + d*x**3
def P(x, b, c, d):
return 4.3597482E+3 * (-b - 2*c*x - 3 *d*x**2)
def H(x, a, b, c, d):
return a + b*x + c*x**2 + d*x**3
filefolder_Calcite_I_SG_167 = '../Files_Outputs/Calcite_I'
filefolder_Calcite_II_SG_14 = '../Files_Outputs/Calcite_II'
filefolder_energetics = 'EL_vs_V'
# Calcite I (Red triangles):
V_C_I, E_C_I = np.loadtxt(os.path.join(filefolder_Calcite_I_SG_167, filefolder_energetics, 'EL_vs_V.dat'), skiprows = 1).T
# 14 (Empty grey triangles):
V_14, E_14 = np.loadtxt(os.path.join(filefolder_Calcite_II_SG_14, filefolder_energetics, 'EL_vs_V.dat'), skiprows = 1).T
init_vals = [E0_init, V0_init, B0_init, B0_prime_init]
popt_C_I, pcov_C_I = curve_fit(BM, V_C_I, E_C_I, p0=init_vals)
popt_14, pcov_14 = curve_fit(BM, V_14, E_14, p0=init_vals)
# Linspace for plotting the fitting curves:
V_C_I_lin = np.linspace(V_C_I[0], V_C_I[-1], 10000)
V_14_lin = np.linspace(V_14[0], V_14[-1], 10000)
fig_handle = plt.figure()
# Plotting the fitting curves:
p2, = plt.plot(V_C_I_lin, BM(V_C_I_lin, *popt_C_I), color='black', label='Cubic fit Calcite I' )
p6, = plt.plot(V_14_lin, BM(V_14_lin, *popt_14), 'b', label='Cubic fit Calcite II')
# Plotting the scattered points:
p1 = plt.scatter(V_C_I, E_C_I, color='red', marker="^", label='Calcite I', s=100)
p5 = plt.scatter(V_14, E_14, color='grey', marker="^", facecolors='none', label='Calcite II', s=100)
fontP = FontProperties()
fontP.set_size('15')
plt.legend((p1, p2, p5, p6), ("Calcite I", "Cubic fit Calcite I", "Calcite II", 'Cubic fit Calcite II'), prop=fontP)
global V0, B0, B0_prime
E0 = popt_C_I[0]
V0 = popt_C_I[1]
B0 = popt_C_I[2]
B0_prime = popt_C_I[3]
pressures_per_F_unit_C_I = P(V_C_I, V0, B0, B0_prime)
output_array_2 = np.vstack((E_C_I, V_C_I, pressures_per_F_unit_C_I)).T
np.savetxt('Volumes_and_pressures_C_I.dat', output_array_2, header="Energy / FU (a.u.) \t Volume / FU (A^3) \t Pressures (GPa)", fmt="%0.13f")
global V0_14, B0_14, B0_prime_14
E0_14 = popt_14[0]
V0_14 = popt_14[1]
B0_14 = popt_14[2]
B0_prime_14 = popt_14[3]
pressures_per_F_unit_14 = P(V_14, V0_14, B0_14, B0_prime_14)
output_array_2 = np.vstack((E_14, V_14, pressures_per_F_unit_14)).T
np.savetxt('Volumes_and_pressures_14.dat', output_array_2, header="Energy / FU (a.u.) \t Volume / FU (A^3) \t Pressures (GPa)", fmt="%0.13f")
plt.xlabel('$V$ / F.U. (Angstrom$^{3}$)', fontsize=20)
plt.ylabel(r'$E$ / F.U. (a.u.)', fontsize=20)
plt.suptitle("PBE-D3, pob-TZVP, SHRINK 8 8, Bipolar 18 18, TOLINTEG 8 18, XXLGRID, TOLDEE 8")
plt.title("(0.87 - 0.98)$V_{eq}$ and (0.98 - 1.08)$V_{eq}$", fontsize=10)
plt.ticklabel_format(useOffset=False)
plt.savefig('calcite_I_and_II_all_2_summary_better_plot.pdf', bbox_inches='tight')
pl.dump(fig_handle,file('sinus.pickle_calcite_I_and_II_all_2_summary_better_plot','w'))
# Plotting P vs V:
fig_handle = plt.figure()
p2, = plt.plot(V_C_I_lin, P(V_C_I_lin, V0, B0, B0_prime), color='black', label='Cubic fit Calcite I' )
p6, = plt.plot(V_14_lin, P(V_14_lin, V0_14, B0_14, B0_prime_14), 'b', label='Cubic fit Calcite II')
# Plotting the scattered points:
p1 = plt.scatter(V_C_I, pressures_per_F_unit_C_I, color='red', marker="^", label='Calcite I', s=100)
p5 = plt.scatter(V_14, pressures_per_F_unit_14, color='grey', marker="^", facecolors='none', label='Calcite II', s=100)
fontP = FontProperties()
fontP.set_size('13')
plt.legend((p1, p5), ("Calcite I", "Calcite II"), prop=fontP)
plt.xlabel('$V$ / F.U. (Angstrom$^{3}$)', fontsize=20)
plt.ylabel(r'$P = -\frac{\partial E }{\partial V}$ (GPa)', fontsize=20)
plt.suptitle("PBE-D3, pob-TZVP, SHRINK 8 8, Bipolar 18 18, TOLINTEG 8 18, XXLGRID, TOLDEE 8")
plt.title("(0.87 - 0.98)$V_{eq}$ and (0.98 - 1.08)$V_{eq}$", fontsize=10)
plt.ticklabel_format(useOffset=False)
plt.savefig('calcite_I_and_II_all_2_summary_better_plot_P_vs_V.pdf', bbox_inches='tight')
pl.dump(fig_handle,file('sinus.pickle_calcite_I_and_II_all_2_summary_better_plot_P_vs_V','w'))
H_C_I = E_C_I + pressures_per_F_unit_C_I * V_C_I * (2.293710449E+17)*(1E-21)
H_14 = E_14 + pressures_per_F_unit_14 * V_14 * (2.293710449E+17)*(1E-21)
output_array_3 = np.vstack((E_C_I, V_C_I, pressures_per_F_unit_C_I, H_C_I)).T
np.savetxt('E_V_P_H__C_I.dat', output_array_3, header="Energy / FU (a.u.) \t Volume / FU (A^3) \t Pressure / F.U. (GPa) \t Enthalpy (a.u.)", fmt="%0.13f")
output_array_4 = np.vstack((E_14, V_14, pressures_per_F_unit_14, H_14)).T
np.savetxt('E_V_P_H__14.dat', output_array_4, header="Energy / FU (a.u.) \t Volume / FU (A^3) \t Pressure / F.U. (GPa) \t Enthalpy (a.u.)", fmt="%0.13f")
# Saving into variables:
P_lin_C_I = P(V_C_I_lin, V0, B0, B0_prime)
H_lin_C_I = BM(V_C_I_lin, *popt_C_I) + P(V_C_I_lin, V0, B0, B0_prime) * V_C_I_lin * (2.293710449E+17)*(1E-21)
P_lin_14 = P(V_14_lin, V0_14, B0_14, B0_prime_14)
H_lin_14 = BM(V_14_lin, *popt_14) + P(V_14_lin, V0_14, B0_14, B0_prime_14) * V_14_lin * (2.293710449E+17)*(1E-21)
output_array_1 = np.vstack((P_lin_C_I, H_lin_C_I)).T
np.savetxt('P_lin_C_I__H_lin_C_I.dat', output_array_1, header="P(GPa) \t H per F unit (a.u)", fmt="%0.13f")
output_array_2 = np.vstack((P_lin_14, H_lin_14)).T
np.savetxt('P_lin_14__H_lin_14.dat', output_array_2, header="P(GPa) \t H per F unit (a.u)", fmt="%0.13f")
init_vals = [E0_init, V0_init, B0_init, B0_prime_init]
popt_HofP_C_I, pcov_HofP_C_I = curve_fit(H, pressures_per_F_unit_C_I, H_C_I, p0=init_vals)
popt_HofP_14, pcov_HofP_14 = curve_fit(H, pressures_per_F_unit_14, H_14, p0=init_vals)
pressures_per_F_unit_14_sorted = np.sort(pressures_per_F_unit_14)
pressures_per_F_unit_14_lin = pressures_per_F_unit_14_sorted
pressures_per_F_unit_C_I_sorted = np.sort(pressures_per_F_unit_C_I)
pressures_per_F_unit_C_I_lin = pressures_per_F_unit_C_I_sorted
P_lin_for_coll = np.linspace(0.5, 16, 10000)# 100000)
print 'P_lin_for_coll = ', P_lin_for_coll
# Evaluating:
H_C_I_lin_for_coll = H(P_lin_for_coll, *popt_HofP_C_I)
H_14_lin_for_coll = H(P_lin_for_coll, *popt_HofP_14)
print 'H_C_I_lin_for_coll = ', H_C_I_lin_for_coll
print 'H_14_lin_for_coll = ', H_14_lin_for_coll
fig_handle = plt.figure()
p1, = plt.plot(P_lin_for_coll, H(P_lin_for_coll, *popt_HofP_C_I), color='black', label='Calcite I cubic fit' )
p2, = plt.plot(P_lin_for_coll, H(P_lin_for_coll, *popt_HofP_14), color='blue', label='Calcite II cubic fit' )
fontP = FontProperties()
#fontP.set_size('small')
fontP.set_size('15')
plt.legend((p1, p2), ("Calcite I cubic fit", "Calcite II cubic Fit"), prop=fontP)
plt.xlabel('P / F.U. (GPa)', fontsize=20)
plt.ylabel(r'$(H = E + PV)$ / F.U. (a.u.)', fontsize=20)
plt.suptitle("PBE-D3, pob-TZVP, SHRINK 8 8, Bipolar 18 18, TOLINTEG 8 18, XXLGRID, TOLDEE 8")
plt.title("(0.87 - 0.98)$V_{eq}$ and (0.98 - 1.08)$V_{eq}$", fontsize=10)
plt.ticklabel_format(useOffset=False)
plt.savefig('calcite_I_and_II_all_2_summary_better_plot_delta_H_exact_expression_ALL_H.pdf', bbox_inches='tight')
pl.dump(fig_handle,file('sinus.pickle_calcite_I_and_II_all_2_summary_better_plot_delta_H_exact_expression_ALL_H','w'))
T_folder = 0.0
T_folder_float = float(T_folder)
print 'Performing the Analytic intersection....'
fig = plt.figure()
# Obtaining a cubic expression for H(P):
# Reminder:
#H_C_I = E_C_I + pressures_per_F_unit_C_I * V_C_I * (2.293710449E+17)*(1E-21)
#H_14 = E_14 + pressures_per_F_unit_14 * V_14 * (2.293710449E+17)*(1E-21)
init_vals = [E0_init, V0_init, B0_init, B0_prime_init]
popt_HofP_C_I, pcov_HofP_C_I = curve_fit(H, pressures_per_F_unit_C_I, H_C_I, p0=init_vals)
popt_HofP_14, pcov_HofP_14 = curve_fit(H, pressures_per_F_unit_14, H_14, p0=init_vals)
pressures_per_F_unit_14_sorted = np.sort(pressures_per_F_unit_14)
pressures_per_F_unit_14_lin = pressures_per_F_unit_14_sorted
pressures_per_F_unit_C_I_sorted = np.sort(pressures_per_F_unit_C_I)
pressures_per_F_unit_C_I_lin = pressures_per_F_unit_C_I_sorted
# Linspace for plotting the fitting curves:
P_C_I_lin = np.linspace(pressures_per_F_unit_C_I_lin[0], pressures_per_F_unit_C_I_lin[-1], 10000)
P_14_lin = np.linspace(pressures_per_F_unit_14_lin[0], pressures_per_F_unit_14_lin[-1], 10000)
fig_handle = plt.figure()
# Plotting the fitting curves:
p2, = plt.plot(P_C_I_lin, H(P_C_I_lin, *popt_HofP_C_I), color='black', label='Cubic fit Calcite I' )
p6, = plt.plot(P_14_lin, H(P_14_lin, *popt_HofP_14), 'b', label='Cubic fit Calcite II')
# Plotting the scattered points:
p1 = plt.scatter(pressures_per_F_unit_C_I, H_C_I, color='red', marker="^", label='Calcite I', s=100)
p5 = plt.scatter(pressures_per_F_unit_14, H_14, color='grey', marker="^", facecolors='none', label='Calcite II', s=100)
fontP = FontProperties()
fontP.set_size('13')
plt.legend((p1, p2, p5, p6), ("Calcite I", "Cubic fit Calcite I", "Calcite II", 'Cubic fit Calcite II'), prop=fontP)
global a0, a1, a2, a3
a0 = popt_HofP_C_I[0]
a1 = popt_HofP_C_I[1]
a2 = popt_HofP_C_I[2]
a3 = popt_HofP_C_I[3]
global a0_s2, a1_s2, a2_s2, a3_s2
a0_s2 = popt_HofP_14[0]
a1_s2 = popt_HofP_14[1]
a2_s2 = popt_HofP_14[2]
a3_s2 = popt_HofP_14[3]
print 'a0 = ', a0
print 'a1 = ', a1
print 'a2 = ', a2
print 'a3 = ', a3
print 'a0_s2 = ', a0_s2
print 'a1_s2 = ', a1_s2
print 'a2_s2 = ', a2_s2
print 'a3_s2 = ', a3_s2
print """
The equations are the following:
G_I (P) = a0 + a1*P + a2*P**2 + a3*P**3
G_II (P) = a0_s2 + a1_s2*P + a2_s2*P**2 + a3_s2*P**3
"""
print('G_I (P) = ({a0}) + ({a1})*P + ({a2})*P**2 + ({a3})*P**3 '.format(a0 = a0, a1 = a1, a2 = a2, a3 = a3, ))
print """
"""
print('G_II (P) = ({a0_s2}) + ({a1_s2})*P + ({a2_s2})*P**2 + ({a3_s2})*P**3 '.format(a0_s2 = a0_s2, a1_s2 = a1_s2, a2_s2 = a2_s2, a3_s2 = a3_s2))
print """
"""
print """
G_I (P) = G_II (P)
"""
# Setting "P" to be symbolic:
P = sym.symbols('P') #, real=True)
def z_I(P):
return a0 + a1*P + a2*P**2 + a3*P**3
def z_II(P):
return a0_s2 + a1_s2*P + a2_s2*P**2 + a3_s2*P**3
# Crude intersection:
sol = sym.solve(z_I(P) - z_II(P) , P)
print 'sol_ H_I(P) - H_II(P) =', sol
# Transform to complex notation, in order to
# better discard the complex root afterwards.
# Use of evalf to obtain better precision:
def is_close(a,b,tol):
if abs(a-b)<tol: return True
else: return False
P = sym.symbols('P')
sol = [complex(x.evalf()) for x in sol]
real_solutions = []
for x in sol:
print 'x = ', x
print 'x.real = ', x.real
print 'abs(x - x.real) = ', abs(x - x.real)
if is_close(x,x.real,10**(-10)): real_solutions.append(x.real)
print 'real_solutions = ', real_solutions
#real_roots = real_solutions
#print 'real_roots = ', real_roots
real_roots = [x for x in real_solutions if 0.1 <= x <= 4] or real_solutions
print 'real_roots = ', real_roots
# Transform each element of the list to a numpy array:
real_roots_zero_to_four = np.array(real_roots)
# Let's grab the root located between 0.1GPa and 4GPa (true for CI-CII phase trans.)
# If no element in the [real_roots] list is between 0.1 and 4.0, then the following line will also return the [real_roots] list.
#real_roots_zero_to_four = [x for x in real_roots if 0.1 <= x <= 4.0] or real_roots
#print 'real_roots_zero_to_four = ', real_roots_zero_to_four
P_real_intersection = real_roots_zero_to_four[0]
H_real_intersection = z_I(real_roots_zero_to_four[0])
T_folder = 0.0
T_folder_float = float(T_folder)
output_array_2 = np.vstack((T_folder, P_real_intersection, H_real_intersection)).T
np.savetxt('P_H_analytic_intersection_T_%sK.dat' %T_folder , output_array_2, header="Temperature (K) \t Pressure_Intersection (GPa) \t H_Intersection = E + PV (a.u.)", fmt="%0.13f")
plt.xlabel(r'$P$ (GPa)', fontsize=20)
plt.ylabel(r'$(H = E + PV)$ / F.U. (a.u.)', fontsize=15)
plt.suptitle("PBE-D3, pob-TZVP, SHRINK 8 8, Bipolar 18 18, TOLINTEG 8 18, XXLGRID, TOLDEE 8")
plt.title("(0.87 - 0.98)$V_{eq}$ and (0.98 - 1.08)$V_{eq}$", fontsize=10)
plt.ticklabel_format(useOffset=False)
ax = fig_handle.add_subplot(111)
ax.annotate('Analytic\nIntersection\nP= %g GPa\nG = %g a.u.' %(P_real_intersection, H_real_intersection), xy=(P_real_intersection, H_real_intersection), xytext=(P_real_intersection+2.5767, H_real_intersection-0.05), fontsize=15,
arrowprops=dict(arrowstyle="->", connectionstyle="arc3", color='purple'),
)
plt.savefig('calcite_I_and_II_all_2_summary_better_plot_delta_H_exact_expression_with_analytic_intersection.pdf', bbox_inches='tight')
pl.dump(fig_handle,file('sinus.pickle_calcite_I_and_II_all_2_summary_better_plot_delta_H_exact_expression_with_analytic_intersection','w'))
#
#plt.show()