import numpy as np
from scipy.optimize import fsolve , newton_krylov
import matplotlib.pyplot as plt
 
class ImpRK4 :
 
    def __init__(self, fun , t0, tf, dt , y0):
        self.func = fun
        self.t0=t0
        self.tf=tf
        self.dt=dt
        self.u0=y0
        self.n = round((tf-t0)/dt)
        self.time  = np.linspace(self.t0, self.tf, self.n+1 )
        self.u     = np.array([self.u0  for i in range(self.n+1) ])
 
    def f(self,ti,ui):
         return  np.array([functions(ti,ui) for functions in self.func])     
 
    def solve(self): 
 
 
       for i in range(len(self.time)-1):
 
            def equations(variable):
                k1,k2 = variable
                f1 = -k1 + self.f(self.time[i]+ (0.5+np.sqrt(3)/6)* self.dt , self.u[i]+0.25*self.dt* k1+ (0.25+ np.sqrt(3)/6)*self.dt*k2) 
                f2 = -k2 + self.f(self.time[i]+ (0.5-np.sqrt(3)/6)* self.dt , self.u[i]+(0.25-np.sqrt(3)/6)*self.dt *k1 + 0.25*self.dt* k2)
                return np.array([f1,f2]).ravel() #.reshape(2,)  
 
 
            k1 , k2 = fsolve(equations,(2,2)) #(self.u[i],self.u[i]))
            self.u[i+1] = self.u[i] + self.dt/2* (k1 + k2)
 
 
       plt.plot(self.time,self.u)
       plt.show()    
def main():
 
 
 
func00 = lambda t,u : -10*(t-1)*u[0]
 
func01 = lambda t,u : u[1] 
func02 = lambda t,u : (1-u[0]**2)*u[1] - u[0]
 
func0x = np.array([func00])
func0 = np.array([func01,func02])
 
 
 
t0 = 0. 
tf = 2.      
u0 = y01   
dt = 0.008 
 
y01 = np.array([1.,1.])
diffeq = ImpRK4(func0,t0,tf,dt,y01)    
 
 
#y0  = np.array([np.exp(-5)])
#diffeq.solve()
#diffeq = ImpRK4(func0x,t0,tf,dt,y0) ## with single equations works
diffeq.solve()
 
 
 
if __name__ == '__main__': 
    main()