def solve_VLE(self, Temp_VLE, show_plot=True):
'''
Determine optimal values of mu that result in equal pressures by
minimizing the square difference of the weights in the liquid and vapor
phases. Subsequentally, calls the function to compute the saturation
properties.
'''
self.Temp_VLE = Temp_VLE
self.build_MBAR_VLE_matrices()
mu_VLE_guess, mu_lower_bound, mu_upper_bound = self.mu_guess_bounds()
### Optimization of mu
mu_VLE_guess, mu_lower_bound, mu_upper_bound = self.mu_scan(Temp_VLE)
mu_opt = GOLDEN_multi(self.sqdeltaW,
mu_VLE_guess,
mu_lower_bound,
mu_upper_bound,
TOL=0.00001,
maxit=30)
sqdeltaW_opt = self.sqdeltaW(mu_opt)
self.f_k_opt = self.f_k_guess.copy()
self.mu_opt = mu_opt
self.calc_rhosat()
self.calc_Psat()
self.print_VLE()
if show_plot:
plt.plot(Temp_VLE, mu_opt, 'k-', label=r'$\mu_{\rm opt}$')
plt.plot(self.Temp_sim,
self.mu_sim,
'ro',
mfc='None',
label='Simulation')
plt.plot(Temp_VLE, mu_VLE_guess, 'b--', label=r'$\mu_{\rm guess}$')
plt.xlabel(r'$T$ (K)')
plt.ylabel(r'$\mu_{\rm opt}$ (K)')
plt.xlim([300, 550])
# plt.ylim([-4200,-3600])
plt.legend()
plt.show()
plt.plot(Temp_VLE, sqdeltaW_opt, 'ko')
plt.xlabel(r'$T$ (K)')
plt.ylabel(r'$(\Delta W^{\rm sat})^2$')
plt.show()
print("Effective number of samples")
print(self.mbar.computeEffectiveSampleNumber())
print('\nWhich is approximately ' +
str(self.mbar.computeEffectiveSampleNumber() / self.sumN_k *
100.) + '% of the total snapshots')
### Bounds for mu
mu_sim_low = np.ones(len(Temp_VLE))*mu_sim.min()
mu_sim_high = np.ones(len(Temp_VLE))*mu_sim.max()
Temp_sim_mu_low = Temp_sim[np.argmin(mu_sim)]
Temp_sim_mu_high = Temp_sim[np.argmax(mu_sim)]
### Guess for mu
mu_guess = lambda Temp: mu_sim_high + (mu_sim_low - mu_sim_high)/(Temp_sim_mu_low-Temp_sim_mu_high) * (Temp-Temp_sim_mu_high)
mu_VLE_guess = mu_guess(Temp_VLE)
print(r'$(\Delta W)^2$ for $\mu_{\rm guess}$ =')
print(sqdeltaW(mu_VLE_guess))
mu_opt = GOLDEN_multi(sqdeltaW,mu_VLE_guess,mu_sim_low,mu_sim_high,TOL=0.001,maxit=30)
sqdeltaW_opt = sqdeltaW(mu_opt)
plt.plot(Temp_VLE,mu_opt,'k-')
plt.plot(Temp_sim,mu_sim,'ro',mfc='None')
plt.xlabel(r'$T$ (K)')
plt.ylabel(r'$\mu_{\rm opt}$ (K)')
plt.xlim([300,550])
plt.ylim([-4200,-3600])
plt.show()
plt.plot(Temp_VLE,sqdeltaW_opt,'ko')
plt.xlabel(r'$T$ (K)')
plt.ylabel(r'$(\Delta W^{\rm sat})^2$')
plt.show()
mu_VLE_guess = mu_guess(Temp_VLE)
mu_VLE_guess[mu_VLE_guess < mu_sim.min()] = mu_sim.min()
mu_VLE_guess[mu_VLE_guess > mu_sim.max()] = mu_sim.max()
print(mu_VLE_guess)
mu_lower_bound = mu_sim_low * 1.005
mu_upper_bound = mu_sim_high * 0.995
print(r'$(\Delta W)^2$ for $\mu_{\rm guess}$ =')
print(sqdeltaW(mu_VLE_guess))
### Optimize mu
mu_opt = GOLDEN_multi(sqdeltaW,
mu_VLE_guess,
mu_lower_bound,
mu_upper_bound,
TOL=0.0001,
maxit=30)
sqdeltaW_opt = sqdeltaW(mu_opt)
plt.plot(Temp_VLE, mu_opt, 'k-', label=r'$\mu_{\rm opt}$')
plt.plot(Temp_sim, mu_sim, 'ro', mfc='None', label='Simulation')
plt.plot(Temp_VLE, mu_VLE_guess, 'b--', label=r'$\mu_{\rm guess}$')
plt.xlabel(r'$T$ (K)')
plt.ylabel(r'$\mu_{\rm opt}$ (K)')
plt.xlim([300, 550])
plt.ylim([-4200, -3600])
plt.legend()
plt.show()
plt.plot(Temp_VLE, sqdeltaW_opt, 'ko')