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1.SM,NM.py
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1.SM,NM.py
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import matplotlib.pyplot as plt
import numpy as np
from scipy import interpolate
import gvar as gv
import lsqfit
from sklearn.metrics import r2_score
d=np.zeros([35,11])
e=np.zeros([35,11,6])
################ Read data ##############################
for i in range(0,10):
f = np.loadtxt("data/Jerome_EOS_Drischler/EOS_spec_4_beta_0."+str(i)+".txt")
d[:,i] = f[:,0]
for k in range(0,6):
if k == 5:
e[:,i,k] = f[:,k+2]
else:
e[:,i,k] = f[:,k+1]
f = np.loadtxt("data/Jerome_EOS_Drischler/EOS_spec_4_beta_1.0.txt")
d[:,10] = f[:,0]
for k in range(0,6):
if k == 5:
e[:,10,k] = f[:,k+2]
else:
e[:,10,k] = f[:,k+1]
e_SM = e[:,0,:]
e_NM = e[:,10,:]
d_SM = d[:,0]
d_NM = d[:,10]
def m_e_inv_SM_2(x):
k1,k2 = gv.gvar([6.247360336420315, -16.916984419115057], [[0.12573594,-0.49209029], [-0.49209029, 2.58439037]])
return 1+ x*k1 + x**2 *k2
def m_e_inv_NM_2(x):
k1,k2 = gv.gvar([2.630969540591772, -11.079806675726502], [[0.01866276, -0.23951577], [ -0.23951577, 3.58448543]])
return 1+ x*k1 + x**2 *k2
def m_e_inv_SM(x):
k1 = gv.gvar ('3.33 (18)')
return 1+ x*k1
def m_e_inv_NM(x):
k1 = gv.gvar ('0.89 (19)')
return 1+ x*k1
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_SM_eff_2 (x):
return T_SM(x)*m_e_inv_SM_2(x)
def T_NM_eff_2 (x):
return T_NM(x)*m_e_inv_NM_2(x)
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
e_SM_mod = np.zeros([35,6])
e_NM_mod = np.zeros([35,6])
for k in range(0,6):
e_SM_mod[:,k] = e_SM[:,k]/T_SM(d_SM)
e_NM_mod[:,k] = e_NM[:,k]/T_NM(d_NM)
e_SM_mod_av=[]
e_NM_mod_av=[]
for h in range(6):
e_SM_mod_av.append (e_SM_mod[:,h] )
e_NM_mod_av.append (e_NM_mod[:,h] )
s_SM_mod = gv.dataset.svd_diagnosis(e_SM_mod_av)
e_SM_mod_av = gv.dataset.avg_data(e_SM_mod_av,spread=True)
s_NM_mod = gv.dataset.svd_diagnosis(e_NM_mod_av)
e_NM_mod_av = gv.dataset.avg_data(e_NM_mod_av,spread=True)
###################### interpolation####################################
td = np.arange(0.02, 0.2, 0.01)
te_SM = np.zeros([td.size,6])
te_NM = np.zeros([td.size,6])
for k in range(0,6):
tck = interpolate.splrep(d_SM, e_SM[:,k])
te_SM[:,k] = interpolate.splev(td, tck, der=0)
for k in range(0,6):
tck = interpolate.splrep(d_NM, e_NM[:,k])
te_NM[:,k] = interpolate.splev(td, tck, der=0)
te_SM_mod = np.zeros([td.size,6])
te_NM_mod = np.zeros([td.size,6])
for k in range(0,6):
te_SM_mod[:,k] = te_SM[:,k]/T_SM(td)
te_NM_mod[:,k] = te_NM[:,k]/T_NM(td)
te_SM_av=[]
te_NM_av=[]
te_SM_mod_av=[]
te_NM_mod_av=[]
for h in range(6):
te_SM_av.append ( te_SM[:,h] )
te_NM_av.append ( te_NM[:,h] )
te_SM_mod_av.append ( te_SM_mod[:,h] )
te_NM_mod_av.append ( te_NM_mod[:,h] )
ts_SM = gv.dataset.svd_diagnosis(te_SM_av)
te_SM_av = gv.dataset.avg_data(te_SM_av,spread=True)
ts_NM = gv.dataset.svd_diagnosis(te_NM_av)
te_NM_av = gv.dataset.avg_data(te_NM_av,spread=True)
ts_SM_mod = gv.dataset.svd_diagnosis(te_SM_mod_av)
te_SM_mod_av = gv.dataset.avg_data(te_SM_mod_av,spread=True)
ts_NM_mod = gv.dataset.svd_diagnosis(te_NM_mod_av)
te_NM_mod_av = gv.dataset.avg_data(te_NM_mod_av,spread=True)
############################ Fit for SM ##################################
def f_pot_SM(x,p):
xt = (x-p['n_sat'])/(3*p['n_sat'])
v0 = p['E_sat'] - T_SM(p['n_sat'])
v1 = -2*T_SM(p['n_sat'])
v2 = p['K_sat'] + 2*T_SM(p['n_sat'])
v3 = p['Q_sat'] -8*T_SM(p['n_sat'])
v4 = p['Z_sat'] + 56*T_SM(p['n_sat'])
ans = v0 + v1*xt + (v2/2.)*xt**2 + (v3/6.)*xt**3 + (v4/24.)*(xt)**4
return ans
def f_pot_SM_c(x,p):
xt = (x-p['n_sat'])/(3*p['n_sat'])
lam = f_pot_SM(0,p) * 3.**5
beta=3
return f_pot_SM(x,p) + lam * xt**5 * np.exp( -p['b']* (x/0.16)**(beta/3) )
def f_SM(x,p):
return T_SM(x) + f_pot_SM_c(x,p)
def f_SM_mod(x,p):
return f_SM(x,p)/T_SM(x)
# prior_e_SM = {} # Drischler priors
# prior_e_SM['n_sat'] = gv.gvar(0.171, 0.016)
# prior_e_SM['E_sat'] = gv.gvar(-15.16, 1.24)
# prior_e_SM['K_sat'] = gv.gvar(214, 22)
# prior_e_SM['Q_sat'] = gv.gvar(-139, 104)
# prior_e_SM['Z_sat'] = gv.gvar(1306, 214)
# prior_e_SM['b'] = gv.gvar(0,50)
prior_e_SM = {} # Jerome priors
prior_e_SM['n_sat'] = gv.gvar(0.16, 0.01)
prior_e_SM['E_sat'] = gv.gvar(-15.5,1.0)
prior_e_SM['K_sat'] = gv.gvar(230, 20)
prior_e_SM['Q_sat'] = gv.gvar(-300, 400)
prior_e_SM['Z_sat'] = gv.gvar(1300, 500)
prior_e_SM['b'] = gv.gvar(0,50)
x = d_SM
y = e_SM_mod_av
fit = lsqfit.nonlinear_fit(data=(x, y), prior=prior_e_SM, fcn=f_SM_mod, debug=True ,svdcut=s_SM_mod.svdcut)
SM1_par = fit.p
x = td
y = te_SM_mod_av
fit = lsqfit.nonlinear_fit(data=(x, y), prior=prior_e_SM, fcn=f_SM_mod, debug=True,svdcut=ts_SM_mod.svdcut)
SM2_par = fit.p
x = td
y = te_SM_av
fit = lsqfit.nonlinear_fit(data=(x, y), prior=prior_e_SM, fcn=f_SM, debug=True,svdcut=ts_SM.svdcut)
SM3_par = fit.p
print ('---------Symmetric matter--------------')
print ('Scaling 1:')
print (SM1_par)
print ('\n')
print ('Scaling 2:')
print (SM2_par)
print ('\n')
print ('Scaling 3:')
print (SM3_par)
print ('\n')
e,ev = np.linalg.eig (gv.evalcorr (e_SM_mod_av) )
d2 = np.std( np.absolute(ev[0]) ) **2
print ("N (Scale 1,SM) = ",np.size(d_SM))
print ("l_corr (Scale 1,SM) = ", 1 - np.size(d_SM)*d2 )
print ('\n')
e,ev = np.linalg.eig (gv.evalcorr (te_SM_mod_av) )
d2 = np.std( np.absolute(ev[0]) ) **2
print ("N (Scale 2,SM) = ",np.size(td))
print ("l_corr (Scale 2,SM) = ", 1 - np.size(td)*d2 )
print ('\n')
e,ev = np.linalg.eig (gv.evalcorr (te_SM_av) )
d2 = np.std( np.absolute(ev[0]) ) **2
print ("N (Scale 3,SM) = ",np.size(td))
print ("l_corr (Scale 3,SM) = ", 1 - np.size(td)*d2 )
############################ Fit for NM ##################################
def f_pot_NM(x,p):
xt = (x-p['n_sat'])/(3*p['n_sat'])
v0 = p['E_sat+E_sym'] - T_SM(p['n_sat']) - T_SM(p['n_sat']) *(2**(2/3)-1)
v1 = p['L_sym'] -2*T_SM(p['n_sat']) -2*T_SM(p['n_sat'])*(2**(2/3)-1)
v2 = p['K_sat+K_sym'] + 2*T_SM(p['n_sat'])-2*T_SM(p['n_sat'])*(-1*2**(2/3)+1)
v3 = p['Q_sat+Q_sym'] -8*T_SM(p['n_sat'])-2*T_SM(p['n_sat'])*(4*2**(2/3)-4)
v4 = p['Z_sat+Z_sym'] + 56*T_SM(p['n_sat']) -8*T_SM(p['n_sat'])*(-7*2**(2/3)+7)
ans = v0 + v1*xt + (v2/2.)*xt**2 + (v3/6.)*xt**3 + (v4/24.)*(xt)**4
return ans
def f_pot_NM_c(x,p):
xt = (x-p['n_sat'])/(3*p['n_sat'])
lam = f_pot_NM(0,p) * 3.**5
beta=3
return f_pot_NM(x,p) + lam * xt**5 * np.exp( -p['b']* (x/0.16)**(beta/3) )
def f_NM(x,p):
return T_NM(x) + f_pot_NM_c(x,p)
def f_NM_mod(x,p):
return f_NM(x,p)/T_NM(x)
# prior_eNM = {} # Drischler priors
# prior_eNM['n_sat'] = SM1_par['n_sat']
# prior_eNM['E_sat+E_sym'] = gv.gvar(16.85, 3.33)
# prior_eNM['L_sym'] = gv.gvar(48.1, 3.6)
# prior_eNM['K_sat+K_sym'] = gv.gvar(42,62)
# prior_eNM['Q_sat+Q_sym'] = gv.gvar(-303, 338)
# prior_eNM['Z_sat+Z_sym'] = gv.gvar(-1011, 593)
# prior_eNM['b'] = gv.gvar(0,50)
prior_eNM = {} # Jerome priors
prior_eNM['n_sat'] = SM1_par['n_sat']
prior_eNM['E_sat+E_sym'] = gv.gvar(16.0, 3.0)
prior_eNM['L_sym'] = gv.gvar(50, 10)
prior_eNM['K_sat+K_sym'] = gv.gvar(100,100)
prior_eNM['Q_sat+Q_sym'] = gv.gvar(0, 400)
prior_eNM['Z_sat+Z_sym'] = gv.gvar(-500, 500)
prior_eNM['b'] = gv.gvar(0,50)
x = d_NM
y = e_NM_mod_av
fit = lsqfit.nonlinear_fit(data=(x, y), prior=prior_eNM, fcn=f_NM_mod, debug=True,svdcut=s_NM_mod.svdcut)
NM1_par = fit.p
prior_eNM['n_sat'] = SM2_par['n_sat']
x = td
y = te_NM_mod_av
fit = lsqfit.nonlinear_fit(data=(x, y), prior=prior_eNM, fcn=f_NM_mod, debug=True,svdcut=ts_NM_mod.svdcut)
NM2_par = fit.p
prior_eNM['n_sat'] = SM3_par['n_sat']
x = td
y = te_NM_av
fit = lsqfit.nonlinear_fit(data=(x, y), prior=prior_eNM, fcn=f_NM, debug=True,svdcut=ts_NM.svdcut,add_svdnoise=False)
NM3_par = fit.p
######### QQ plot
# residuals = fit.residuals
# residuals = np.sort(residuals)
# np.random.seed(36725786)
# quantiles = np.random.normal(0, 1, np.size(residuals))
# quantiles = np.sort(quantiles)
#
# r2 = r2_score(residuals, quantiles)
# r2 = np.around(r2,2)
#
# z = np.polyfit(quantiles, residuals ,deg = 1 )
# p = np.poly1d(z)
# x = np.arange(np.min(quantiles),np.max(quantiles),0.001)
#
# fig,ax = plt.subplots(1)
# plt.plot (quantiles, residuals, 'ob')
# plt.plot (x,p(x), color='blue')
# plt.plot (x,x,'r--')
# ax.text(0.1, 0.9, 'R ='+str(r2)+'' , transform = ax.transAxes,fontsize='13')
# plt.xlabel ('Theoretical quantiles',fontsize='15')
# plt.ylabel ('Ordered fit residuals',fontsize='15')
# ax.tick_params(labelsize='14')
# plt.show()
############
print ('\n')
print ('---------Neutron matter--------------')
print ('Scaling 1:')
print (NM1_par)
print ('\n')
print ('Scaling 2:')
print (NM2_par)
print ('\n')
print ('Scaling 3:')
print (NM3_par)
print ('\n')
e,ev = np.linalg.eig (gv.evalcorr (e_SM_mod_av) )
d2 = np.std( np.absolute(ev[0]) ) **2
print ("N (Scale 1,NM) = ",np.size(d_NM))
print ("l_corr (Scale 1,NM) = ",1 - np.size(d_NM)*d2 )
print ('\n')
e,ev = np.linalg.eig (gv.evalcorr (te_NM_mod_av) )
d2 = np.std( np.absolute(ev[0]) ) **2
print ("N (Scale 2,NM) = ",np.size(td))
print ("l_corr (Scale 2,NM) = ",1 - np.size(td)*d2 )
print ('\n')
e,ev = np.linalg.eig (gv.evalcorr (te_NM_av) )
d2 = np.std( np.absolute(ev[0]) ) **2
print ("N (Scale 3,NM) = ",np.size(td))
print ("l_corr (Scale 3,NM) = ",1 - np.size(td)*d2 )
########## Plotting #############
fig, axes = plt.subplots(2, 3, sharex='col',figsize=(15,8))
#S1,SM
axes[0,0].errorbar ( (3*np.pi*np.pi*d_SM/2)**(1/3) ,gv.mean(e_SM_mod_av),gv.sdev(e_SM_mod_av) ,fmt='ob',label='data (68% CL)')
plot_Kf = np.arange(0.001, 2, 0.01)
plot_x = plot_Kf**3 * (2/3) * np.pi**(-2)
axes[0,0].fill_between ( plot_Kf ,gv.mean(f_SM_mod(plot_x,SM1_par)) +gv.sdev(f_SM_mod(plot_x,SM1_par)),gv.mean(f_SM_mod(plot_x,SM1_par)) -gv.sdev(f_SM_mod(plot_x,SM1_par)) ,label='fit (68% CL)',color='red',alpha=0.8)
axes[0,0].fill_between ( plot_Kf ,gv.mean(f_SM_mod(plot_x,SM1_par)) +2*gv.sdev(f_SM_mod(plot_x,SM1_par)),gv.mean(f_SM_mod(plot_x,SM1_par)) -2*gv.sdev(f_SM_mod(plot_x,SM1_par)) ,label='fit (95% CL)',color='red',alpha=0.2)
axes[0,0].set_ylabel('$e_{\mathrm{SNM}}/e^{\mathrm{FFG}}_{\mathrm{SNM}}$',fontsize='15')
axes[0,0].tick_params(right=True)
axes[0,0].text(0.1, 0.9, ' Scaling 1, SNM',fontsize='15' , transform = axes[0,0].transAxes)
axes[0,0].tick_params(labelsize=13)
axes[0,0].tick_params(right=True)
axes[0,0].tick_params(top=True)
axes[0,0].tick_params(direction='in')
#S2,SM
axes[0,1].errorbar ( td ,gv.mean(te_SM_mod_av),gv.sdev(te_SM_mod_av) ,fmt='ob',label='data (68% CL)')
axes[0,1].fill_between ( td ,gv.mean(f_SM_mod(td,SM2_par)) +gv.sdev(f_SM_mod(td,SM2_par)),gv.mean(f_SM_mod(td,SM2_par)) -gv.sdev(f_SM_mod(td,SM2_par)) ,label='fit (68% CL)',color='red',alpha=0.8)
axes[0,1].fill_between ( td ,gv.mean(f_SM_mod(td,SM2_par)) +2*gv.sdev(f_SM_mod(td,SM2_par)),gv.mean(f_SM_mod(td,SM2_par)) -2*gv.sdev(f_SM_mod(td,SM2_par)) ,label='fit (95% CL)',color='red',alpha=0.2)
axes[0,1].set_ylabel('$e_{\mathrm{SNM}}/e^{\mathrm{FFG}}_{\mathrm{SNM}}$',fontsize='15')
axes[0,1].tick_params(right=True)
axes[0,1].text(0.1, 0.9, ' Scaling 2, SNM',fontsize='15' , transform = axes[0,1].transAxes)
axes[0,1].tick_params(labelsize=13)
axes[0,1].tick_params(right=True)
axes[0,1].tick_params(top=True)
axes[0,1].tick_params(direction='in')
#S3,SM
axes[0,2].errorbar ( td ,gv.mean(te_SM_av),gv.sdev(te_SM_av) ,fmt='ob',label='data (68% CL)')
axes[0,2].fill_between ( td ,gv.mean(f_SM(td,SM3_par)) +gv.sdev(f_SM(td,SM3_par)),gv.mean(f_SM(td,SM3_par)) -gv.sdev(f_SM(td,SM3_par)) ,label='fit (68% CL)',color='red',alpha=0.8)
axes[0,2].fill_between ( td ,gv.mean(f_SM(td,SM3_par)) +2*gv.sdev(f_SM(td,SM3_par)),gv.mean(f_SM(td,SM3_par)) -2*gv.sdev(f_SM(td,SM3_par)) ,label='fit (95% CL)',color='red',alpha=0.2)
axes[0,2].set_ylabel('$e_{\mathrm{SNM}}$ (MeV)',fontsize='15')
axes[0,2].tick_params(right=True)
axes[0,2].text(0.1, 0.9, ' Scaling 3, SNM' ,fontsize='15', transform = axes[0,2].transAxes)
axes[0,2].tick_params(labelsize=13)
axes[0,2].tick_params(right=True)
axes[0,2].tick_params(top=True)
axes[0,2].tick_params(direction='in')
#S1, NM
axes[1,0].errorbar ( (3*np.pi*np.pi*d_NM)**(1/3) ,gv.mean(e_NM_mod_av),gv.sdev(e_NM_mod_av) ,fmt='ob',label='data (68% CL)')
plot_Kf = np.arange(0.001, 2, 0.01)
plot_x = plot_Kf**3 * (1/3) * np.pi**(-2)
axes[1,0].fill_between ( plot_Kf ,gv.mean(f_NM_mod(plot_x,NM1_par)) +gv.sdev(f_NM_mod(plot_x,NM1_par)),gv.mean(f_NM_mod(plot_x,NM1_par)) -gv.sdev(f_NM_mod(plot_x,NM1_par)) ,label='fit (68% CL)',color='red',alpha=0.8)
axes[1,0].fill_between ( plot_Kf ,gv.mean(f_NM_mod(plot_x,NM1_par)) +2*gv.sdev(f_NM_mod(plot_x,NM1_par)),gv.mean(f_NM_mod(plot_x,NM1_par)) -2*gv.sdev(f_NM_mod(plot_x,NM1_par)) ,label='fit (95% CL)',color='red',alpha=0.2)
axes[1,0].set_xlabel('$k_F$ (fm$^{-1}$)',fontsize='15')
axes[1,0].set_ylabel('$e_{\mathrm{PNM}}/e^{\mathrm{FFG}}_{\mathrm{PNM}}$',fontsize='15')
axes[1,0].tick_params(right=True)
axes[1,0].text(0.1, 0.9, ' Scaling 1, PNM',fontsize='15' , transform = axes[1,0].transAxes)
#axes[1,0].legend(loc='center right',fontsize='15')
axes[1,0].legend(loc='center right', bbox_to_anchor=(1,0.6),fontsize='15')
axes[1,0].tick_params(labelsize=13)
axes[1,0].tick_params(right=True)
axes[1,0].tick_params(top=True)
axes[1,0].tick_params(direction='in')
#S2, NM
axes[1,1].errorbar ( td ,gv.mean(te_NM_mod_av),gv.sdev(te_NM_mod_av) ,fmt='ob',label='data (68% CL)')
axes[1,1].fill_between ( td ,gv.mean(f_NM_mod(td,NM2_par)) +gv.sdev(f_NM_mod(td,NM2_par)),gv.mean(f_NM_mod(td,NM2_par)) -gv.sdev(f_NM_mod(td,NM2_par)) ,label='fit (68% CL)',color='red',alpha=0.8)
axes[1,1].fill_between ( td ,gv.mean(f_NM_mod(td,NM2_par)) +2*gv.sdev(f_NM_mod(td,NM2_par)),gv.mean(f_NM_mod(td,NM2_par)) -2*gv.sdev(f_NM_mod(td,NM2_par)) ,label='fit (95% CL)',color='red',alpha=0.2)
axes[1,1].set_xlabel('$n$ (fm$^{-3}$)',fontsize='15')
axes[1,1].set_ylabel('$e_{\mathrm{PNM}}/e^{\mathrm{FFG}}_{\mathrm{PNM}}$',fontsize='15')
axes[1,1].tick_params(right=True)
axes[1,1].text(0.1, 0.9, ' Scaling 2, PNM' ,fontsize='15', transform = axes[1,1].transAxes)
axes[1,1].tick_params(labelsize=13)
axes[1,1].tick_params(right=True)
axes[1,1].tick_params(top=True)
axes[1,1].tick_params(direction='in')
#S3, NM
axes[1,2].errorbar ( td ,gv.mean(te_NM_av),gv.sdev(te_NM_av) ,fmt='ob',label='data (68% CL)')
axes[1,2].fill_between ( td ,gv.mean(f_NM(td,NM3_par)) +gv.sdev(f_NM(td,NM3_par)),gv.mean(f_NM(td,NM3_par)) -gv.sdev(f_NM(td,NM3_par)) ,label='fit (68% CL)',color='red',alpha=0.8)
axes[1,2].fill_between ( td ,gv.mean(f_NM(td,NM3_par)) +2*gv.sdev(f_NM(td,NM3_par)),gv.mean(f_NM(td,NM3_par)) -2*gv.sdev(f_NM(td,NM3_par)) ,label='fit (95% CL)',color='red',alpha=0.2)
axes[1,2].set_xlabel('$n$ (fm$^{-3}$)',fontsize='15')
axes[1,2].set_ylabel('$e_{\mathrm{PNM}}$ (MeV)',fontsize='15')
axes[1,2].tick_params(right=True)
axes[1,2].text(0.1, 0.9, ' Scaling 3, PNM' ,fontsize='15', transform = axes[1,2].transAxes)
axes[1,2].tick_params(labelsize=13)
axes[1,2].tick_params(right=True)
axes[1,2].tick_params(top=True)
axes[1,2].tick_params(direction='in')
plt.tight_layout()
fig.show()
### Plot with additional data (Ingo, Aurel, APR)
f = np.loadtxt("data/Jerome_EOS_Drischler/Aurel-QMC.dat")
A_den = f[:,0]
A_E = f[:,2]
f = np.loadtxt("data/Jerome_EOS_Drischler/Ingo-2016-QMC-band.dat")
I_den = f[:,0]
I_E = f[:,1]
I_E_err = f[:,2]
f = np.loadtxt("data/Jerome_EOS_Drischler/apr.dat")
apr_den = f[:,0]
apr_E = f[:,2]
fig,ax = plt.subplots(1,figsize=(7,5))
ax.errorbar ( I_den ,I_E,I_E_err ,fmt='.k',alpha=0.7,label='Tews $et$ $al.$ (2016)')
ax.plot(A_den, A_E,"vc",label='Wlazlowski $et$ $al.$ (2014)')
ax.plot(apr_den, apr_E,"sg",label='APR (1998)')
ax.errorbar ( td ,gv.mean(te_NM_av),gv.sdev(te_NM_av) ,fmt='ob',label='Drischler $et$ $al.$ (2016)')
ax.fill_between ( td ,gv.mean(f_NM(td,NM3_par)) +gv.sdev(f_NM(td,NM3_par)),gv.mean(f_NM(td,NM3_par)) -gv.sdev(f_NM(td,NM3_par)) ,label='fit (68% CL)',color='red',alpha=0.8)
ax.fill_between ( td ,gv.mean(f_NM(td,NM3_par)) +2*gv.sdev(f_NM(td,NM3_par)),gv.mean(f_NM(td,NM3_par)) -2*gv.sdev(f_NM(td,NM3_par)) ,label='fit (95% CL)',color='red',alpha=0.2)
ax.set_xlabel('$n$ (fm$^{-3}$)',fontsize='15')
ax.set_ylabel('$e_{\mathrm{PNM}}$ (MeV)',fontsize='15')
plt.tick_params(right=True)
plt.tick_params(top=True)
plt.tick_params(direction='in')
ax.set_xlim(right=0.21)
ax.set_xlim(left=0.001)
ax.set_ylim(top=21)
ax.set_ylim(bottom=0)
ax.tick_params(labelsize='14')
handles, labels = ax.get_legend_handles_labels()
handles = [handles[1], handles[0], handles[4], handles[5], handles[2], handles[3]]
labels = [labels[1], labels[0], labels[4], labels[5], labels[2], labels[3]]
ax.legend(handles,labels,loc='lower right',fontsize='13.5')
# Inset
left, bottom, width, height = [0.2, 0.63, 0.26, 0.32]
ax2 = fig.add_axes([left, bottom, width, height])
ax2.errorbar ( I_den ,I_E,I_E_err ,fmt='.k',alpha=0.7,label='Tews 2016(68% CL)')
ax2.plot(A_den, A_E,"vc",label='Wlazlowski 2014')
ax2.plot(apr_den, apr_E,"sg",label='APR')
ax2.errorbar ( td ,gv.mean(te_NM_av),gv.sdev(te_NM_av) ,fmt='ob',label='Drischler 2016 (68% CL)')
ax2.fill_between ( td ,gv.mean(f_NM(td,NM3_par)) +gv.sdev(f_NM(td,NM3_par)),gv.mean(f_NM(td,NM3_par)) -gv.sdev(f_NM(td,NM3_par)) ,label='fit (68% CL)',color='red',alpha=0.8)
ax2.fill_between ( td ,gv.mean(f_NM(td,NM3_par)) +2*gv.sdev(f_NM(td,NM3_par)),gv.mean(f_NM(td,NM3_par)) -2*gv.sdev(f_NM(td,NM3_par)) ,label='fit (95% CL)',color='red',alpha=0.2)
ax2.set_xlim(right=0.125)
ax2.set_xlim(left=0.075)
ax2.set_ylim(top=14)
ax2.set_ylim(bottom=8)
plt.tick_params(right=True)
plt.tick_params(top=True)
plt.tick_params(direction='in')
ax2.tick_params(labelsize='12')
plt.tight_layout()
plt.show()
### Plot with additional data, Scaling 1 (Ingo, Aurel, APR)
f = np.loadtxt("data/Jerome_EOS_Drischler/Aurel-QMC.dat")
A_den = f[:,0]
A_E = f[:,2]
f = np.loadtxt("data/Jerome_EOS_Drischler/Ingo-2016-QMC-band.dat")
I_den = f[:,0]
I_E = f[:,1]
I_E_err = f[:,2]
f = np.loadtxt("data/Jerome_EOS_Drischler/apr.dat")
apr_den = f[:,0]
apr_E = f[:,2]
fig,ax = plt.subplots(1,figsize=(7,5))
ax.errorbar ( (3*np.pi*np.pi*I_den)**(1/3) ,I_E/T_NM (I_den),I_E_err/T_NM (I_den) ,fmt='.k',alpha=0.7,label='Tews 2016(68% CL)')
ax.plot((3*np.pi*np.pi*A_den)**(1/3), A_E/T_NM (A_den),"vc",label='Wlazlowski 2014')
ax.plot((3*np.pi*np.pi*apr_den)**(1/3), apr_E/T_NM (apr_den),"sg",label='APR')
ax.errorbar ( (3*np.pi*np.pi*d_NM)**(1/3) ,gv.mean(e_NM_mod_av),gv.sdev(e_NM_mod_av) ,fmt='ob',label='data (68% CL)')
plot_Kf = np.arange(0.001, 2, 0.01)
plot_x = plot_Kf**3 * (1/3) * np.pi**(-2)
ax.fill_between ( plot_Kf ,gv.mean(f_NM_mod(plot_x,NM1_par)) +gv.sdev(f_NM_mod(plot_x,NM1_par)),gv.mean(f_NM_mod(plot_x,NM1_par)) -gv.sdev(f_NM_mod(plot_x,NM1_par)) ,label='fit (68% CL)',color='red',alpha=0.8)
ax.fill_between ( plot_Kf ,gv.mean(f_NM_mod(plot_x,NM1_par)) +2*gv.sdev(f_NM_mod(plot_x,NM1_par)),gv.mean(f_NM_mod(plot_x,NM1_par)) -2*gv.sdev(f_NM_mod(plot_x,NM1_par)) ,label='fit (95% CL)',color='red',alpha=0.2)
ax.set_xlabel('$k_F$ (fm$^{-1}$)',fontsize='15')
ax.set_ylabel('$e_{\mathrm{PNM}}/e^{\mathrm{FFG}}_{\mathrm{PNM}}$',fontsize='15')
plt.tick_params(right=True)
plt.tick_params(top=True)
plt.tick_params(direction='in')
ax.set_xlim(right=2.1)
ax.set_xlim(left=0.)
ax.set_ylim(top=1)
ax.set_ylim(bottom=0.35)
ax.tick_params(labelsize='14')
# Inset
left, bottom, width, height = [0.4, 0.5, 0.4, 0.43]
ax2 = fig.add_axes([left, bottom, width, height])
ax2.errorbar ( (3*np.pi*np.pi*I_den)**(1/3) ,I_E/T_NM (I_den),I_E_err/T_NM (I_den) ,fmt='.k',alpha=0.7,label='Tews 2016(68% CL)')
ax2.plot((3*np.pi*np.pi*A_den)**(1/3), A_E/T_NM (A_den),"vc",label='Wlazlowski 2014')
ax2.plot((3*np.pi*np.pi*apr_den)**(1/3), apr_E/T_NM (apr_den),"sg",label='APR 1998')
ax2.errorbar ( (3*np.pi*np.pi*d_NM)**(1/3) ,gv.mean(e_NM_mod_av),gv.sdev(e_NM_mod_av) ,fmt='ob',label='data (68% CL)')
plot_Kf = np.arange(0.001, 2, 0.01)
plot_x = plot_Kf**3 * (1/3) * np.pi**(-2)
ax2.fill_between ( plot_Kf ,gv.mean(f_NM_mod(plot_x,NM1_par)) +gv.sdev(f_NM_mod(plot_x,NM1_par)),gv.mean(f_NM_mod(plot_x,NM1_par)) -gv.sdev(f_NM_mod(plot_x,NM1_par)) ,label='fit (68% CL)',color='red',alpha=0.8)
ax2.fill_between ( plot_Kf ,gv.mean(f_NM_mod(plot_x,NM1_par)) +2*gv.sdev(f_NM_mod(plot_x,NM1_par)),gv.mean(f_NM_mod(plot_x,NM1_par)) -2*gv.sdev(f_NM_mod(plot_x,NM1_par)) ,label='fit (95% CL)',color='red',alpha=0.2)
ax2.set_xlim(right=1.75)
ax2.set_xlim(left=1.)
ax2.set_ylim(top=0.6)
ax2.set_ylim(bottom=0.35)
plt.tick_params(right=True)
plt.tick_params(top=True)
plt.tick_params(direction='in')
ax2.tick_params(labelsize='12')
plt.tight_layout()
plt.show()