#%%
#Libraries
import numpy as np
from scipy.integrate import odeint
import matplotlib.pyplot as plt
import matplotlib
matplotlib.rcParams.update({'font.size': 13})
from matplotlib.widgets import Slider, Button
#%%
def ODEfun(Yfuncvec, t): 
#    Sigma2= Yfuncvec(1)
    # Explicit equations
    C1= 0.0038746 + 0.2739782*t + 1.574621*t**2 - 0.2550041*t**3
    C2= -33.43818 + 37.18972*t - 11.58838*t**2 + 1.695303*t**3 - 0.1298667*t**4 + 0.005028*t**5 - 7.743*10**-5*t**6
    C = np.where(t<=4, C1, C2)
    E=C/51
    tmf=5.1
    dSigma2dt=((t-tmf)**2)*E
    # Differential equations
    return dSigma2dt

tspan = np.linspace(0, 14)
y0 = 0

#%%
fig, ax = plt.subplots()
fig.suptitle("""LEP-16-2: Mean Residence Time and Variance Calculations (Part c)""", x = 0.3, y=0.98, fontweight='bold')
plt.subplots_adjust(left  = 0.4)
sigma2 = odeint(ODEfun, y0, tspan)

plt.plot(tspan, sigma2**0.5)

plt.legend([r"$\sigma$"], loc='best')
ax.set_xlabel('Time (mins)', fontsize='medium')
ax.set_ylabel(r'$\sigma \hspace{0.5} (mins)$', fontsize='medium')
#plt.ylim(0,55)
plt.xlim(0,14)
plt.ylim(0,6)
plt.grid()

ax.text(-8, 0.6,'Differential Equations'
         '\n\n'
         r'$\dfrac{d\sigma^2}{dt} = E(t - t_{mf})^2$'
         '\n\n'

         'Explicit Equations'
         '\n\n'
         r'$C_1= +0.0038746 + 0.2739782t$''\n\t'
         r'$+ 1.574621t^2 - 0.2550041t^3$''\n\n'
         r'$C2= -33.43818 + 37.18972t$''\n\t'
         r'$- 11.58838t^2 + 1.695303t^3$''\n\t'
         r'$- 0.1298667t^4 + 0.005028t^5$''\n\t'
         r'$- 7.743.10{^-5}t^6$'    
         '\n\n'
         r'$C = If\hspace{0.5} (t<=t1)\hspace{0.5} then\hspace{0.5} (C_1) \hspace{0.5}else\hspace{0.5} (C_2)$'
         '\n\n'
         r'$E = \dfrac{C}{51}$'
         '\n\n'
         r'$t_{mf}=5.1$'         
         , ha='left', wrap = True, fontsize=13,
        bbox=dict(facecolor='none', edgecolor='black', pad=10.0), fontweight='bold')