def modelbeta4(r0, vec0, vec1, vec2, vec3):
vec = np.array([vec0, vec1, vec2, vec3])
vec = traf(vec)
vec = gcc.map_betastar_sigmoid(vec, gp)
ba = phys.betastar(r0, vec, gp)
return ba
y = analytic_betastar(x)
popt3, pcov3 = curve_fit(modelbeta4, x, y, p0=npr.rand(4))
beta01opt = traf(popt3)
betaopt = gcc.map_betastar_sigmoid(beta01opt, gp)
print('beta01opt = ', beta01opt)
print('betaopt = ',betaopt)
fig = plt.figure(facecolor='white')
left, width = 0.25, 0.7
rect1 = [left, 0.4, width, 0.55]
rect2 = [left, 0.2, width, 0.2]
ax1 = fig.add_axes(rect1) #left, bottom, width, height
ax2 = fig.add_axes(rect2, sharex=ax1)
ax1.plot(x, y, 'b', lw=2, label='analytic')
ax1.plot(x, modelbeta4(x, *popt3), 'r--', lw=2, label='fit')
ax1.plot(x, phys.betastar(x, betaopt, gp), 'g--', lw=1, label='phys.betastar')
ax1.set_ylim([-0.2, 1.2])
ax1.set_xscale('log')
ax1.set_yticks(np.linspace(0.0, 1.0, 6,endpoint=True))
plt.setp(ax1.get_xticklabels(), visible=False)
ax1.set_ylabel('$\\beta*$')
legend = ax1.legend(loc='upper left', shadow=False, borderpad=0.2, labelspacing=0.1, handletextpad=0.1, borderaxespad=0.3)
frame = legend.get_frame()
frame.set_facecolor('1.0')
for label in legend.get_texts():
label.set_fontsize(8)
for label in legend.get_lines():
label.set_linewidth(2) # the legend line width
ax2.set_xscale('log')
ax2.plot(x, y-modelbeta4(x, *popt3), 'r.-', alpha=0.8)