#!/usr/bin/env python3

import numpy as np

def pdeHyperbolic(a, x, t, f, g = None, dtype=np.float64):
    """ Solve a Hyperbolic Partial Differential using finite differences. """
    
    m = len(x) # Amount of objects to track
    n = len(t) # Length of Time Vector

    # Determine stepsizes
    h = 1
    if m > 1:
        h = x[0] - x[1]

    k = 1
    if n > 1:
        k = t[0] - t[1]

    λ_sq = (a*k/h)**2


    # Create array to hold the solution
    w = np.zeros((n,m), dtype=dtype)

    # Create finite difference matrix 
    A = np.diag(m*[2*(1 - λ_sq)], k=0) + np.diag((m-1)*[λ_sq], k=-1) + np.diag((m-1)*[λ_sq], k=1)
    print(A)

    # Initialise first two timesteps
    w[0] = f(x, t[0])
    w[1] = A@w[0]/2 + k*g(x, t[0])
   
    # Calculate for following timesteps
    for j in range(2, n-1):
        w[j] = A@w[j-1] - w[j-2]

    return w





def test_pdeHyperbolic_case1(m=1e2, n=1e3,l=1, T=1):
    
    a = 1 # from the Schroedinger Equation

    # Setup spatial and time grids
    x = np.linspace(0, l, m)
    t = np.linspace(0, T, n)

    # Boundary conditions
    def f(x,t):
        return np.sin(2*np.pi*x)

    def g(x,t):
        return 2*np.pi*np.sin(2*np.pi*x)    

    # Solve it
    sol = pdeHyperbolic(a, x, t, f, g)

    # Plot it with the exact solution
    exact_sol = lambda x,t: np.sin(2*np.pi*x)*(np.cos(2*np.pi*t) + np.sin(2*np.pi*t))
    t_high_res = np.linspace(0, T, n * 1e4)

    from matplotlib import pyplot
    from matplotlib import animation as anim
    fig, _ = pyplot.subplots()

    if False:
        for _, x_i in enumerate(x):
            pyplot.plot(t_high_res, exact_sol(x_i, t_high_res), label="Exact")
        pyplot.plot(t, sol[:,1], label="iter")
    
        pyplot.grid()
        pyplot.xlabel("t")
        pyplot.ylabel("w")

    else:
        def animate(i):
            pyplot.clf()
            pyplot.ylim(-2, 2)
            pyplot.grid()
            pyplot.plot(x, exact_sol(x, t[i]), label="exact")
            pyplot.plot(x, sol[i,:], label="iter")
    
        frames = np.arange(1, n, dtype=np.int)
        myAnim = anim.FuncAnimation(fig, animate, frames, interval = 10 )

    pyplot.legend()
    pyplot.show()

def test_pdeHyperbolic_case2(m=200, n=400, l=1, T=1):
    
    a = 1 # from the Schroedinger Equation

    # Setup spatial and time grids
    x = np.linspace(0, l, m)
    t = np.linspace(0, T, n)

    # Boundary conditions
    def f(x,t):
            return 2*(x < 0.5) -1

    def g(x,t):
            return 0

    # Solve it
    sol = pdeHyperbolic(a, x, t, f, g)

    from matplotlib import pyplot
    from matplotlib import animation as anim
    fig, _ = pyplot.subplots()

    def animate(i):
        pyplot.clf()
        pyplot.grid()
        pyplot.ylim(-1.5,1.5)
        pyplot.plot(x, sol[i,:], label="iter")
 
    frames = np.arange(1, n)
    myAnim = anim.FuncAnimation(fig, animate, frames, interval = 5 )

    pyplot.legend()
    pyplot.show()



if __name__ == "__main__":
    #test_pdeHyperbolic_case1()
    test_pdeHyperbolic_case2()