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non_quadraticities.py
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non_quadraticities.py
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import matplotlib.pyplot as plt
import numpy as np
import gvar as gv
import lsqfit
import EM, symmetry_energy, quadratic_symmetry_energy
def main():
# Import results from Effective Mass module
# EM = Effective Mass; par = Best fit parameter values
# SM = Symmetric matter; NM = Neutron matter
global EM_par_SM_1 , EM_par_NM_1
EM_par_SM_1, _ , EM_par_NM_1 , _ = EM.EM_results()
# Import results from symmetry energy module
# Refer to this module for explanation of variables
global te_SM_av,te_NM_av,f_SM,SM3_par,f_NM,NM3_par
te_SM_av,te_NM_av,f_SM,SM3_par,f_NM,NM3_par = symmetry_energy.e_sym_results()
# Import results from quadratic_symmetry energy module
# Refer to this module for explanation of variables
global d,e,td,te,e_sym2,esym2_eta,esym4_eta,e_sym2_av,e_sym2_eta_av,f_esym2_c,e_sym2_par,e_sym2_eta_par
d,e,td,te,e_sym2,esym2_eta,esym4_eta,e_sym2_av,e_sym2_eta_av,f_esym2_c,e_sym2_par,e_sym2_eta_par = quadratic_symmetry_energy.quadratic_results()
# Calculate and plot non-quadratic symmetry energies
plot_e_symnq()
# Calculate and plot Final residuals of the fit wrt the data
plot_residues()
# Print best fit value of parameters
print ('----------Delta----------')
print ("E_sym,nq = ", NM3_par['E_sat+E_sym'] - SM3_par['E_sat'] - e_sym2_par['E_sym2'] )
print ("L_sym,nq = ", NM3_par['L_sym'] - e_sym2_par['L_sym2'] )
print ("K_sym,nq = ", NM3_par['K_sat+K_sym'] - SM3_par['K_sat'] - e_sym2_par['K_sym2'] )
print ("Q_sym,nq = ", NM3_par['Q_sat+Q_sym'] - SM3_par['Q_sat'] - e_sym2_par['Q_sym2'] )
print ("Z_sym,nq = ", NM3_par['Z_sat+Z_sym'] - SM3_par['Z_sat'] - e_sym2_par['Z_sym2'] )
print ('----------Eta----------')
print ("E_sym,nq = ", NM3_par['E_sat+E_sym'] - SM3_par['E_sat'] - e_sym2_eta_par['E_sym2'] )
print ("L_sym,nq = ", NM3_par['L_sym'] - e_sym2_eta_par['L_sym2'] )
print ("K_sym,nq = ", NM3_par['K_sat+K_sym'] - SM3_par['K_sat'] - e_sym2_eta_par['K_sym2'] )
print ("Q_sym,nq = ", NM3_par['Q_sat+Q_sym'] - SM3_par['Q_sat'] - e_sym2_eta_par['Q_sym2'] )
print ("Z_sym,nq = ", NM3_par['Z_sat+Z_sym'] - SM3_par['Z_sat'] - e_sym2_eta_par['Z_sym2'] )
print ('----------Fit to E_sym4 without meta-model----------')
e_sym4_eta_par = Fit_e_sym4_eta()
print (e_sym4_eta_par)
print ('----------Fit to E_symnq without meta-model----------')
e_symnq_eta_par = Fit_e_symnq_eta()
print (e_symnq_eta_par)
############################## Sub-modules #################################
#Linear fit !!
def m_e_inv_SM(x):
k1 = gv.gvar ('3.33(18)')
return 1+ x*k1
#Linear fit !!
def m_e_inv_NM(x):
k1 = gv.gvar ('0.89 (19)')
return 1+ x*k1
def T(x,y):
m = 938.919
hbar = 197.3
e_F = ( hbar**2 / (2*m) ) * (1.5* np.pi**2 * x )**(2./3.)
f = (1+y)**(5/3) + (1-y)**(5/3)
ans = 3/5 * e_F * f/2
return ans
def T_eff(x,y):
m = 938.919
hbar = 197.3
e_F = ( hbar**2 / (2*m) ) * (1.5* np.pi**2 * x )**(2./3.)
f = (m_e_inv_SM(x) + y* (m_e_inv_NM(x) - m_e_inv_SM(x)) )*(1+y)**(5/3) + (m_e_inv_SM(x) - y* (m_e_inv_NM(x) - m_e_inv_SM(x)) )*(1-y)**(5/3)
ans = 3/5 * e_F * f/2
return ans
def T_SM (x):
m = 938.919
hbar = 197.3
ans = 3*hbar**2/(10*m) * (3*np.pi*np.pi*x/2)**(2/3)
return ans
def T_NM (x):
m = 938.919
hbar = 197.3
ans = 3*hbar**2/(10*m) * (3*np.pi*np.pi*x)**(2/3)
return ans
def T_SM_eff (x):
return T_SM(x)*m_e_inv_SM(x)
def T_NM_eff (x):
return T_NM(x)*m_e_inv_NM(x)
def T_2_eff(x):
return T_SM(x)* 5/9 * ( m_e_inv_SM(x) + 3*( m_e_inv_NM(x) - m_e_inv_SM (x) ) )
# calculates and plots e_sym,nq
def plot_e_symnq():
#### E_sym
e_sym_res = f_NM(td,NM3_par) - f_SM(td,SM3_par)
e_sym_pot_res = f_NM(td,NM3_par) - f_SM(td,SM3_par) - T_NM(td) + T_SM(td)
e_sym_pot_eff_res = f_NM(td,NM3_par) - f_SM(td,SM3_par) - T_NM_eff(td) + T_SM_eff(td)
######################## Non-Quadraticities ############################
### e_symnq
e_symnq_res = e_sym_res - f_esym2_c(td,e_sym2_par)
e_symnq_data = te_NM_av - te_SM_av - e_sym2_av
e_symnq_eta_res = e_sym_res - f_esym2_c(td,e_sym2_eta_par)
e_symnq_eta_data = te_NM_av - te_SM_av - e_sym2_eta_av
fig, axes = plt.subplots(1,3,figsize=(11,4), sharey='row')
for h in range(6):
if h==5:
axes[0].plot(td,te[:,10,h] - te[:,0,h] -e_sym2[:,h],color='C'+str(h) ,label='H'+str(h+2))
else:
axes[0].plot(td,te[:,10,h] - te[:,0,h] -e_sym2[:,h],color='C'+str(h) ,label='H'+str(h+1))
# axes[0].plot (td , gv.mean(e_symnq_data) , 'bs',label='Data (delta)') # without error-bars
# axes[0].plot (td , gv.mean(e_symnq_eta_data) , 'rs',label='Data (eta)')
axes[0].errorbar (td , gv.mean(e_symnq_data),gv.sdev(e_symnq_data) ,fmt='ob')
axes[0].errorbar (td , gv.mean(e_symnq_eta_data),gv.sdev(e_symnq_eta_data),fmt='or')
axes[0].fill_between (td,gv.mean(e_symnq_res)+gv.sdev(e_symnq_res),gv.mean(e_symnq_res)-gv.sdev(e_symnq_res),color='blue',alpha=0.1)
axes[0].fill_between (td,gv.mean(e_symnq_eta_res)+gv.sdev(e_symnq_eta_res),gv.mean(e_symnq_eta_res)-gv.sdev(e_symnq_eta_res),color='red',alpha=0.2)
axes[0].axhline(color='black')
axes[0].set_xlabel('$n$ (fm$^{-3}$)',fontsize='13')
axes[0].set_ylabel('$e_{\mathrm{sym,nq}}$ (MeV)',fontsize='13')
axes[0].tick_params(labelsize='13')
axes[0].tick_params(right=True)
axes[0].tick_params(top=True)
axes[0].tick_params(direction='in')
axes[0].legend(loc='upper left')
## e_symnq_pot
for h in range(6):
axes[1].plot(td,te[:,10,h] - T_NM(td) - te[:,0,h] + T_SM(td) -e_sym2[:,h]+ 5/9*T_SM(td),color='C'+str(h) )
e_symnq_pot_res = e_sym_pot_res - f_esym2_c(td,e_sym2_par) + 5/9*T_SM(td)
e_symnq_pot_data = te_NM_av- T_NM(td) - te_SM_av+ T_SM(td) - e_sym2_av+ 5/9*T_SM(td)
e_symnq_pot_eta_res = e_sym_pot_res - f_esym2_c(td,e_sym2_eta_par)+ 5/9*T_SM(td)
e_symnq_pot_eta_data = te_NM_av- T_NM(td) - te_SM_av+ T_SM(td) - e_sym2_eta_av+ 5/9*T_SM(td)
# axes[1].plot (td , gv.mean(e_symnq_pot_data) , 'bs',label='Data (delta)')
# axes[1].plot (td , gv.mean(e_symnq_pot_eta_data) , 'rs',label='Data (eta)')
axes[1].errorbar (td , gv.mean(e_symnq_pot_data),gv.sdev(e_symnq_pot_data) ,fmt='ob',label='Data (delta) (68% CL)')
axes[1].errorbar (td , gv.mean(e_symnq_pot_eta_data),gv.sdev(e_symnq_pot_eta_data),fmt='or',label='Data (eta) (68% CL)')
axes[1].fill_between (td,gv.mean(e_symnq_pot_res)+gv.sdev(e_symnq_pot_res),gv.mean(e_symnq_pot_res)-gv.sdev(e_symnq_pot_res),color='blue',alpha=0.1)
axes[1].fill_between (td,gv.mean(e_symnq_pot_eta_res)+gv.sdev(e_symnq_pot_eta_res),gv.mean(e_symnq_pot_eta_res)-gv.sdev(e_symnq_pot_eta_res),color='red',alpha=0.2)
axes[1].axhline(color='black')
axes[1].set_xlabel('$n$ (fm$^{-3}$)',fontsize='13')
axes[1].set_ylabel('$e_{\mathrm{sym,nq}}^{\mathrm{pot}}$ (MeV)',fontsize='13')
axes[1].tick_params(labelsize='13')
axes[1].tick_params(right=True)
axes[1].tick_params(top=True)
axes[1].tick_params(direction='in')
axes[1].legend(loc='upper left')
### e_symnq_pot_eff
for h in range(6):
axes[2].plot(td,te[:,10,h] - gv.mean(T_NM_eff(td)) - te[:,0,h] + gv.mean(T_SM_eff(td)) -e_sym2[:,h]+ gv.mean(T_2_eff(td)),color='C'+str(h) )
e_symnq_pot_eff_res = e_sym_pot_eff_res - f_esym2_c(td,e_sym2_par) + T_2_eff(td)
e_symnq_pot_eff_data = te_NM_av- T_NM_eff(td) - te_SM_av+ T_SM_eff(td) - e_sym2_av+ T_2_eff(td)
e_symnq_pot_eff_eta_res = e_sym_pot_eff_res - f_esym2_c(td,e_sym2_eta_par)+ T_2_eff(td)
e_symnq_pot_eff_eta_data = te_NM_av- T_NM_eff(td) - te_SM_av+ T_SM_eff(td) - e_sym2_eta_av + T_2_eff(td)
# axes[2].plot (td , gv.mean(e_symnq_pot_eff_data) , 'bs',label='Data (delta)')
# axes[2].plot (td , gv.mean(e_symnq_pot_eff_eta_data) , 'rs',label='Data (eta)')
axes[2].errorbar (td , gv.mean(e_symnq_pot_eff_data),gv.sdev(e_symnq_pot_eff_data) ,fmt='ob')
axes[2].errorbar (td , gv.mean(e_symnq_pot_eff_eta_data),gv.sdev(e_symnq_pot_eff_eta_data),fmt='or')
axes[2].fill_between (td,gv.mean(e_symnq_pot_eff_res)+gv.sdev(e_symnq_pot_eff_res),gv.mean(e_symnq_pot_eff_res)-gv.sdev(e_symnq_pot_eff_res),label='Fit (delta) (68% CL)',color='blue',alpha=0.1)
axes[2].fill_between (td,gv.mean(e_symnq_pot_eff_eta_res)+gv.sdev(e_symnq_pot_eff_eta_res),gv.mean(e_symnq_pot_eff_eta_res)-gv.sdev(e_symnq_pot_eff_eta_res),label='Fit (eta) (68% CL)',color='red',alpha=0.2)
axes[2].axhline(color='black')
axes[2].set_ylim(bottom=-1.5)
axes[2].set_xlabel('$n$ (fm$^{-3}$)',fontsize='13')
axes[2].set_ylabel('$e_{\mathrm{sym,nq}}^{\mathrm{pot*}}$ (MeV)',fontsize='13')
axes[2].tick_params(labelsize='13')
axes[2].tick_params(right=True)
axes[2].tick_params(top=True)
axes[2].tick_params(direction='in')
axes[2].legend(loc='upper left')
plt.tight_layout()
fig.show()
# calculate and plot the residuals
def plot_residues():
delta = np.arange(0,11,1)
delta = 0.1 * delta
def fit(den,delta):
ans = f_SM(den,SM3_par) + f_esym2_c(den,e_sym2_par)* delta**2
ans = ans + ( f_NM(den,NM3_par) - f_SM(den,SM3_par) - f_esym2_c(den,e_sym2_par) )* delta**4
return ans
def fit_eta(den,delta):
ans = f_SM(den,SM3_par) + f_esym2_c(den,e_sym2_eta_par)* delta**2
ans = ans + ( f_NM(den,NM3_par) - f_SM(den,SM3_par) - f_esym2_c(den,e_sym2_eta_par) )* delta**4
return ans
def fit_pot(den,delta):
ans = f_SM(den,SM3_par) - T_SM(den) + (f_esym2_c(den,e_sym2_par) - 5/9*T_SM(den))* delta**2
ans = ans + ( f_NM(den,NM3_par) - T_NM(den) - f_SM(den,SM3_par) + T_SM(den) - f_esym2_c(den,e_sym2_par) + 5/9*T_SM(den) )* delta**4
return ans
def fit_eta_pot(den,delta):
ans = f_SM(den,SM3_par) - T_SM(den) + ( f_esym2_c(den,e_sym2_eta_par) - 5/9*T_SM(den))* delta**2
ans = ans + ( f_NM(den,NM3_par) - T_NM(den)- f_SM(den,SM3_par) + T_SM(den)- f_esym2_c(den,e_sym2_eta_par)+ 5/9*T_SM(den) )* delta**4
return ans
def fit_pot_eff(den,delta):
ans = f_SM(den,SM3_par) - T_SM_eff(den) + (f_esym2_c(den,e_sym2_par) - T_2_eff(den))* delta**2
ans = ans + ( f_NM(den,NM3_par) - T_NM_eff(den) - f_SM(den,SM3_par) + T_SM_eff(den) - f_esym2_c(den,e_sym2_par) + T_2_eff(den) )* delta**4
return ans
def fit_pot_eff_meanmass(den,delta):
ans = f_SM(den,SM3_par) - gv.mean(T_SM_eff(den)) + (f_esym2_c(den,e_sym2_par) - gv.mean(T_2_eff(den)))* delta**2
ans = ans + ( f_NM(den,NM3_par) - gv.mean(T_NM_eff(den)) - f_SM(den,SM3_par) + gv.mean(T_SM_eff(den)) - f_esym2_c(den,e_sym2_par) + gv.mean(T_2_eff(den)) )* delta**4
return ans
def fit_eta_pot_eff(den,delta):
ans = f_SM(den,SM3_par) - T_SM_eff(den) + ( f_esym2_c(den,e_sym2_eta_par) - T_2_eff(den))* delta**2
ans = ans + ( f_NM(den,NM3_par) - T_NM_eff(den)- f_SM(den,SM3_par) + T_SM_eff(den)- f_esym2_c(den,e_sym2_eta_par)+ T_2_eff(den) )* delta**4
return ans
fig, axes = plt.subplots(3, 3, sharex='col', sharey = 'row',figsize=(15,8))
## First row (den=0.06)
data = []
data_pot=[]
data_pot_eff = []
data_pot_eff_meanmass = []
for h in range(6):
data.append (te[4,:,h])
data_pot.append ( te[4,:,h] )
data_pot_eff.append ( te[4,:,h] )
data_pot_eff_meanmass.append ( te[4,:,h] )
data = gv.dataset.avg_data(data,spread=True)
data_pot = gv.dataset.avg_data(data_pot,spread=True) - T(0.06,delta)
data_pot_eff = gv.dataset.avg_data(data_pot_eff,spread=True)- T_eff(0.06,delta)
data_pot_eff_meanmass = gv.dataset.avg_data(data_pot_eff_meanmass,spread=True)- gv.mean(T_eff(0.06,delta))
res = fit(0.06,delta) - data
res_eta = fit_eta(0.06,delta) - data
res_pot = fit_pot(0.06,delta) - data_pot
res_eta_pot = fit_eta_pot(0.06,delta) - data_pot
res_pot_eff = fit_pot_eff(0.06,delta) - data_pot_eff
res_eta_pot_eff = fit_eta_pot_eff(0.06,delta) - data_pot_eff
res_pot_eff_meanmass = fit_pot_eff_meanmass(0.06,delta) - data_pot_eff_meanmass
for h in range(6):
axes[0,0].plot (delta, gv.mean ( fit(0.06,delta) - te[4,:,h] ) ,color='C'+str(h)+'')
axes[0,1].plot (delta, gv.mean ( fit_pot(0.06,delta) - te[4,:,h] + T(0.06,delta) ) ,color='C'+str(h)+'' )
axes[0,2].plot (delta, gv.mean ( fit_pot_eff(0.06,delta) - te[4,:,h] + T_eff(0.06,delta) ) ,color='C'+str(h)+'' )
axes[0,0].plot (delta, gv.mean(res) ,'bs' ,label='Mean R (Delta)')
axes[0,0].plot (delta, gv.mean(res_eta) ,'rs',label='Mean R (Eta)')
axes[0,0].fill_between (delta,gv.mean(res)+gv.sdev(res),gv.mean(res)-gv.sdev(res),color='blue',alpha=0.1,label='$\pm \sigma$(R) (Delta)')
axes[0,0].fill_between (delta,gv.mean(res_eta)+gv.sdev(res_eta),gv.mean(res_eta)-gv.sdev(res_eta),color='red',alpha=0.2,label='$\pm \sigma$(R) (Eta)')
axes[0,0].set_ylabel('R = Fit - Data (MeV)',fontsize='14')
axes[0,0].text(0.3, 0.05, '$n = 0.06$ fm$^{-3}$ ' ,fontsize='14' , transform = axes[0,0].transAxes)
axes[0,0].text(0.5, 0.5, '$y = e$',fontsize='14' )
axes[0,0].tick_params(right=True)
axes[0,0].tick_params(top=True)
axes[0,0].tick_params(direction='in')
axes[0,0].axhline(color='black',alpha=1)
axes[0,0].tick_params(labelsize='14')
axes[0,1].plot (delta, gv.mean(res_pot) ,'bs' ,label='Mean R (Delta)')
axes[0,1].plot (delta, gv.mean(res_eta_pot) ,'rs',label='Mean R (Eta)')
axes[0,1].fill_between (delta,gv.mean(res_pot)+gv.sdev(res_pot),gv.mean(res_pot)-gv.sdev(res_pot),color='blue',alpha=0.1,label='$\pm \sigma$(R) (Delta)')
axes[0,1].fill_between (delta,gv.mean(res_eta_pot)+gv.sdev(res_eta_pot),gv.mean(res_eta_pot)-gv.sdev(res_eta_pot),color='red',alpha=0.2,label='$\pm \sigma$(R) (Eta)')
axes[0,1].text(0.3, 0.05, '$n = 0.06$ fm$^{-3}$ ',fontsize='14' , transform = axes[0,1].transAxes)
axes[0,1].axhline(color='black',alpha=1)
axes[0,1].tick_params(right=True)
axes[0,1].tick_params(top=True)
axes[0,1].tick_params(direction='in')
axes[0,1].text(0.5, 0.5, '$y = e^{\mathrm{pot}}$',fontsize='14' )
axes[0,2].plot (delta, gv.mean(res_pot_eff) ,'bs' ,label='Mean R (Delta)')
axes[0,2].plot (delta, gv.mean(res_eta_pot_eff) ,'rs',label='Mean R (Eta)')
axes[0,2].fill_between (delta,gv.mean(res_pot_eff)+gv.sdev(res_pot_eff),gv.mean(res_pot_eff)-gv.sdev(res_pot_eff),color='blue',alpha=0.1,label='$\pm \sigma$(R) (Delta)')
axes[0,2].fill_between (delta,gv.mean(res_eta_pot_eff)+gv.sdev(res_eta_pot_eff),gv.mean(res_eta_pot_eff)-gv.sdev(res_eta_pot_eff),color='red',alpha=0.2,label='$\pm \sigma$(R) (Eta)')
axes[0,2].plot (delta,gv.mean(res_pot_eff_meanmass)+gv.sdev(res_pot_eff_meanmass),'k--')
axes[0,2].plot (delta,gv.mean(res_pot_eff_meanmass)-gv.sdev(res_pot_eff_meanmass),'k--')
axes[0,2].text(0.3, 0.05, '$n = 0.06$ fm$^{-3}$ ' ,fontsize='14' , transform = axes[0,2].transAxes)
axes[0,2].axhline(color='black',alpha=1)
axes[0,2].tick_params(right=True)
axes[0,2].tick_params(top=True)
axes[0,2].tick_params(direction='in')
axes[0,2].text(0.5, 0.5, '$y = e^{\mathrm{pot*}}$' ,fontsize='14' )
## Second row (den=0.12)
data = []
data_pot=[]
data_pot_eff = []
data_pot_eff_meanmass = []
for h in range(6):
data.append (te[10,:,h])
data_pot.append ( te[10,:,h] )
data_pot_eff.append ( te[10,:,h] )
data_pot_eff_meanmass.append ( te[10,:,h] )
data = gv.dataset.avg_data(data,spread=True)
data_pot = gv.dataset.avg_data(data_pot,spread=True) - T(0.12,delta)
data_pot_eff = gv.dataset.avg_data(data_pot_eff,spread=True)- T_eff(0.12,delta)
data_pot_eff_meanmass = gv.dataset.avg_data(data_pot_eff_meanmass,spread=True)- gv.mean(T_eff(0.12,delta))
res = fit(0.12,delta) - data
res_eta = fit_eta(0.12,delta) - data
res_pot = fit_pot(0.12,delta) - data_pot
res_eta_pot = fit_eta_pot(0.12,delta) - data_pot
res_pot_eff = fit_pot_eff(0.12,delta) - data_pot_eff
res_eta_pot_eff = fit_eta_pot_eff(0.12,delta) - data_pot_eff
res_pot_eff_meanmass = fit_pot_eff_meanmass(0.12,delta) - data_pot_eff_meanmass
for h in range(6):
axes[1,0].plot (delta, gv.mean ( fit(0.12,delta) - te[10,:,h] ) ,color='C'+str(h)+'' )
axes[1,1].plot (delta, gv.mean ( fit_pot(0.12,delta) - te[10,:,h] + T(0.12,delta) ) ,color='C'+str(h)+'' )
axes[1,2].plot (delta, gv.mean ( fit_pot_eff(0.12,delta) - te[10,:,h] + T_eff(0.12,delta) ) ,color='C'+str(h)+'' )
axes[1,0].plot (delta, gv.mean(res) ,'bs' ,label='Mean R (Delta)')
axes[1,0].plot (delta, gv.mean(res_eta) ,'rs',label='Mean R (Eta)')
axes[1,0].fill_between (delta,gv.mean(res)+gv.sdev(res),gv.mean(res)-gv.sdev(res),color='blue',alpha=0.1,label='$\pm \sigma$(R) (Delta)')
axes[1,0].fill_between (delta,gv.mean(res_eta)+gv.sdev(res_eta),gv.mean(res_eta)-gv.sdev(res_eta),color='red',alpha=0.2,label='$\pm \sigma$(R) (Eta)')
axes[1,0].set_ylabel('R = Fit - Data (MeV)',fontsize='14')
axes[1,0].text(0.3, 0.05, '$n = 0.12$ fm$^{-3}$ ',fontsize='14' , transform = axes[1,0].transAxes)
axes[1,0].axhline(color='black',alpha=1)
axes[1,0].tick_params(right=True)
axes[1,0].tick_params(top=True)
axes[1,0].tick_params(direction='in')
axes[1,0].text(0.5, 1.75, '$y = e$' ,fontsize='14' )
axes[1,0].tick_params(labelsize='14')
axes[1,1].plot (delta, gv.mean(res_pot) ,'bs' ,label='Mean R (Delta)')
axes[1,1].plot (delta, gv.mean(res_eta_pot) ,'rs',label='Mean R (Eta)')
axes[1,1].fill_between (delta,gv.mean(res_pot)+gv.sdev(res_pot),gv.mean(res_pot)-gv.sdev(res_pot),color='blue',alpha=0.1)
axes[1,1].fill_between (delta,gv.mean(res_eta_pot)+gv.sdev(res_eta_pot),gv.mean(res_eta_pot)-gv.sdev(res_eta_pot),color='red',alpha=0.2)
axes[1,1].legend(loc='upper center',fontsize='12' )
axes[1,1].text(0.3, 0.05, '$n = 0.12$ fm$^{-3}$ ' ,fontsize='14' , transform = axes[1,1].transAxes)
axes[1,1].axhline(color='black',alpha=1)
axes[1,1].tick_params(right=True)
axes[1,1].tick_params(top=True)
axes[1,1].tick_params(direction='in')
axes[1,1].text(0.85, 1.75, '$y = e^{\mathrm{pot}}$',fontsize='14' )
axes[1,2].plot (delta, gv.mean(res_pot_eff) ,'bs' )
axes[1,2].plot (delta, gv.mean(res_eta_pot_eff) ,'rs')
axes[1,2].fill_between (delta,gv.mean(res_pot_eff)+gv.sdev(res_pot_eff),gv.mean(res_pot_eff)-gv.sdev(res_pot_eff),color='blue',alpha=0.1,label='$\pm \sigma$(R) (Delta)')
axes[1,2].fill_between (delta,gv.mean(res_eta_pot_eff)+gv.sdev(res_eta_pot_eff),gv.mean(res_eta_pot_eff)-gv.sdev(res_eta_pot_eff),color='red',alpha=0.2,label='$\pm \sigma$(R) (Eta)')
axes[1,2].plot (delta,gv.mean(res_pot_eff_meanmass)+gv.sdev(res_pot_eff_meanmass),'k--')
axes[1,2].plot (delta,gv.mean(res_pot_eff_meanmass)-gv.sdev(res_pot_eff_meanmass),'k--')
axes[1,2].text(0.3, 0.05, '$n = 0.12$ fm$^{-3}$ ',fontsize='14' , transform = axes[1,2].transAxes)
axes[1,2].axhline(color='black',alpha=1)
axes[1,2].tick_params(right=True)
axes[1,2].tick_params(top=True)
axes[1,2].tick_params(direction='in')
axes[1,2].text(0.75, 1.75, '$y = e^{\mathrm{pot*}}$' ,fontsize='14' )
axes[1,2].legend(loc='upper center',fontsize='12' )
## Third row (den=0.16)
data = []
data_pot=[]
data_pot_eff = []
data_pot_eff_meanmass = []
for h in range(6):
data.append (te[14,:,h])
data_pot.append ( te[14,:,h] )
data_pot_eff.append ( te[14,:,h] )
data_pot_eff_meanmass.append ( te[14,:,h] )
data = gv.dataset.avg_data(data,spread=True)
data_pot = gv.dataset.avg_data(data_pot,spread=True) - T(0.16,delta)
data_pot_eff = gv.dataset.avg_data(data_pot_eff,spread=True)- T_eff(0.16,delta)
data_pot_eff_meanmass = gv.dataset.avg_data(data_pot_eff_meanmass,spread=True)- gv.mean( T_eff(0.16,delta))
res = fit(0.16,delta) - data
res_eta = fit_eta(0.16,delta) - data
res_pot = fit_pot(0.16,delta) - data_pot
res_eta_pot = fit_eta_pot(0.16,delta) - data_pot
res_pot_eff = fit_pot_eff(0.16,delta) - data_pot_eff
res_eta_pot_eff = fit_eta_pot_eff(0.16,delta) - data_pot_eff
res_pot_eff_meanmass = fit_pot_eff_meanmass(0.16,delta) - data_pot_eff_meanmass
for h in range(6):
if h<=2:
axes[2,0].plot (delta, gv.mean ( fit(0.16,delta) - te[14,:,h] ) ,color='C'+str(h)+'' ,label='H'+str(h+1)+'')
else:
axes[2,0].plot (delta, gv.mean ( fit(0.16,delta) - te[14,:,h] ) ,color='C'+str(h)+'' )
if h >2:
if h==5:
axes[2,1].plot (delta, gv.mean ( fit_pot(0.16,delta) - te[14,:,h] + T(0.16,delta) ) ,color='C'+str(h)+'' ,label='H'+str(h+2)+'')
else:
axes[2,1].plot (delta, gv.mean ( fit_pot(0.16,delta) - te[14,:,h] + T(0.16,delta) ) ,color='C'+str(h)+'' ,label='H'+str(h+1)+'')
else:
axes[2,1].plot (delta, gv.mean ( fit_pot(0.16,delta) - te[14,:,h] + T(0.16,delta) ) ,color='C'+str(h)+'' )
axes[2,2].plot (delta, gv.mean ( fit_pot_eff(0.16,delta) - te[14,:,h] + T_eff(0.16,delta) ) ,color='C'+str(h)+'' )
axes[2,0].plot (delta, gv.mean(res) ,'bs' )
axes[2,0].plot (delta, gv.mean(res_eta) ,'rs')
axes[2,0].fill_between (delta,gv.mean(res)+gv.sdev(res),gv.mean(res)-gv.sdev(res),color='blue',alpha=0.1)
axes[2,0].fill_between (delta,gv.mean(res_eta)+gv.sdev(res_eta),gv.mean(res_eta)-gv.sdev(res_eta),color='red',alpha=0.2)
axes[2,0].set_ylabel('R = Fit - Data (MeV)',fontsize='14')
axes[2,0].set_xlabel('$\delta$',fontsize='14')
axes[2,0].text(0.3, 0.05, '$n = 0.16$ fm$^{-3}$ ',fontsize='14' , transform = axes[2,0].transAxes)
axes[2,0].axhline(color='black',alpha=1)
axes[2,0].text(0.5, 3, '$y = e$',fontsize='14' )
axes[2,0].tick_params(right=True)
axes[2,0].tick_params(top=True)
axes[2,0].tick_params(direction='in')
axes[2,0].tick_params(labelsize='14')
axes[2,0].legend()
axes[2,1].plot (delta, gv.mean(res_pot) ,'bs' )
axes[2,1].plot (delta, gv.mean(res_eta_pot) ,'rs')
axes[2,1].fill_between (delta,gv.mean(res_pot)+gv.sdev(res_pot),gv.mean(res_pot)-gv.sdev(res_pot),color='blue',alpha=0.1)
axes[2,1].fill_between (delta,gv.mean(res_eta_pot)+gv.sdev(res_eta_pot),gv.mean(res_eta_pot)-gv.sdev(res_eta_pot),color='red',alpha=0.2)
axes[2,1].set_xlabel('$\delta$',fontsize='14')
axes[2,1].text(0.3, 0.05, '$n = 0.16$ fm$^{-3}$ ',fontsize='14' , transform = axes[2,1].transAxes)
axes[2,1].axhline(color='black',alpha=1)
axes[2,1].text(0.5, 3, '$y = e^{\mathrm{pot}}$',fontsize='14' )
axes[2,1].tick_params(right=True)
axes[2,1].tick_params(top=True)
axes[2,1].tick_params(direction='in')
axes[2,1].tick_params(labelsize='14')
axes[2,1].legend()
axes[2,2].plot (delta, gv.mean(res_pot_eff) ,'bs' )
axes[2,2].plot (delta, gv.mean(res_eta_pot_eff) ,'rs')
axes[2,2].fill_between (delta,gv.mean(res_pot_eff)+gv.sdev(res_pot_eff),gv.mean(res_pot_eff)-gv.sdev(res_pot_eff),color='blue',alpha=0.1)
axes[2,2].fill_between (delta,gv.mean(res_eta_pot_eff)+gv.sdev(res_eta_pot_eff),gv.mean(res_eta_pot_eff)-gv.sdev(res_eta_pot_eff),color='red',alpha=0.2)
axes[2,2].plot (delta,gv.mean(res_pot_eff_meanmass)+gv.sdev(res_pot_eff_meanmass),'k--')
axes[2,2].plot (delta,gv.mean(res_pot_eff_meanmass)-gv.sdev(res_pot_eff_meanmass),'k--')
axes[2,2].set_xlabel('$\delta$',fontsize='14')
axes[2,2].text(0.3, 0.05, '$n = 0.16$ fm$^{-3}$ ' ,fontsize='14', transform = axes[2,2].transAxes)
axes[2,2].axhline(color='black',alpha=1)
axes[2,2].tick_params(right=True)
axes[2,2].tick_params(top=True)
axes[2,2].tick_params(direction='in')
axes[2,2].text(0.5, 3, '$y = e^{\mathrm{pot*}}$' ,fontsize='14')
axes[2,2].tick_params(labelsize='14')
plt.tight_layout()
fig.show()
def Fit_e_sym4_eta():
e_sym4_eta_av =[]
for h in range(6):
e_sym4_eta_av.append ( esym4_eta[:,h] )
s4_eta = gv.dataset.svd_diagnosis(e_sym4_eta_av)
e_sym4_eta_av = gv.dataset.avg_data(e_sym4_eta_av,spread=True)
prior_esym4 = {} # comes from posterior of (e_sym - e_sym2) fit subtraction
prior_esym4['n_sat'] = gv.gvar ('0.1606(74)')
prior_esym4['E_sym4'] = gv.gvar ('1.3(1.5)')
prior_esym4['L_sym4'] = gv.gvar ('0.7(5.7)')
prior_esym4['K_sym4'] = gv.gvar ('-20(57)')
prior_esym4['Q_sym4'] = gv.gvar ('107(432)')
prior_esym4['Z_sym4'] = gv.gvar ('101(1058)')
def f_esym4(x,p):
xt = (x-p['n_sat'])/(3*p['n_sat'])
ans = p['E_sym4'] + (p['K_sym4']/2)*xt**2 \
+ (p['Q_sym4']/6)*xt**3 + (p['Z_sym4']/24)*(xt)**4 \
+ p['L_sym4']*xt
return ans
# def f_esym4_c(x,p):
# xt = (x-p['n_sat'])/(3*p['n_sat'])
# b = 6.93
# lam = f_esym4(0,p) * 3.**5
# return f_esym4(x,p) + lam * xt**5 * np.exp(-b*x/0.16)
x = td
y = e_sym4_eta_av
fit = lsqfit.nonlinear_fit(data=(x, y), prior=prior_esym4, fcn=f_esym4, debug=True,svdcut=0.1)
e_sym4_eta_par = fit.p
return e_sym4_eta_par
def Fit_e_symnq_eta():
prior_esymnq = {} # comes from posterior of (e_sym - e_sym2) fit subtraction
prior_esymnq['n_sat'] = gv.gvar ('0.1606(74)')
prior_esymnq['E_symnq'] = gv.gvar ('1.3(1.5)')
prior_esymnq['L_symnq'] = gv.gvar ('0.7(5.7)')
prior_esymnq['K_symnq'] = gv.gvar ('-20(57)')
prior_esymnq['Q_symnq'] = gv.gvar ('107(432)')
prior_esymnq['Z_symnq'] = gv.gvar ('101(1058)')
def f_esymnq(x,p):
xt = (x-p['n_sat'])/(3*p['n_sat'])
ans = p['E_symnq'] + (p['K_symnq']/2)*xt**2 \
+ (p['Q_symnq']/6)*xt**3 + (p['Z_symnq']/24)*(xt)**4 \
+ p['L_symnq']*xt
return ans
e_symnq_eta_av = []
for h in range(6):
e_symnq_eta_av.append ( te[:,10,h] - te[:,0,h] - esym2_eta[:,h] )
#snq_eta = gv.dataset.svd_diagnosis(e_symnq_eta_av)
e_symnq_eta_av = gv.dataset.avg_data(e_symnq_eta_av,spread=True)
x = td
y = e_symnq_eta_av
fit = lsqfit.nonlinear_fit(data=(x, y), prior=prior_esymnq, fcn=f_esymnq, debug=True,svdcut=0.2)
e_symnq_eta_par = fit.p
return e_symnq_eta_par
################# Launch main program #####################################
if __name__ == '__main__':
main()