import numpy as np
import matplotlib.pyplot as plt
def set_y0(x,k,L):
    y = np.zeros_like(x)
    y[x<L] = np.sin(k*x[x<L])*np.sin(np.abs(x[x<L]*np.pi/L))
    return y

if __name__ == "__main__":
    x = np.linspace(0,10,1000)
    k = np.pi*2/1.064
    L = 5
    y = set_y0(x,k,L)

    plt.plot(x,y)
    plt.show()

def wave1d(x,t,k,L):
    dx = x[1]-x[0]
    dt = t[1]-t[0]
    d2 = (dt/dx)**2
    y = np.zeros([len(t),len(x)])
    y[0,:] = set_y0(x,k,L)
    y[1,:] = set_y0(x-dt,k,L)
    for n in range(2,len(t)):
        y[n] = 2*y[n-1] - y[n-2] - d2*2*y[n-1]
        y[n,1:] += d2*y[n-1,:-1]
        y[n,:-1] += d2*y[n-1,1:]
        #邊界條件
        y[n,0] = 0
        y[n,-1] = 0   
    return y

import matplotlib.animation as animation
#輸入時間，自變量，因變量，圖題標(biāo)記
def drawGif(t,x,ys,mark="time="):
    tAxis = np.linspace(0,len(t)-1,100).astype(int)
    fig = plt.figure()
    ax = fig.add_subplot(111,xlim=(0,10),ylim=(-1.5,1.5))
    ax.grid()
    line, = ax.plot([],[],lw=0.2)
    time_text = ax.text(0.1,0.9,'',transform=ax.transAxes)
    def init():
        line.set_data([],[])
        time_text.set_text("")
        return line, time_text   
    def animate(i):
        y = ys[i]
        line.set_data(x,y)
        time_text.set_text(mark+str(t[i]))
        return line, time_text
    # 動態(tài)圖繪制命令
    # 輸入分別為畫圖窗口，動畫函數(shù)，動畫函數(shù)輸入變量，延時，初始函數(shù)
    ani = animation.FuncAnimation(fig, animate, tAxis,
        interval=200, init_func=init)
    #通過imagemagick引擎來保存gif
    ani.save('wave.gif',writer='imagemagick')
    plt.show()
if __name__ == "__main__":
    x = np.linspace(0,10,1000)
    t = np.linspace(0,12,2041)
    k = np.pi*2/1.064
    L = 5
    y = wave1d(x,t,k,L)
    drawGif(t,x,y)

def set_y0(x,k,L):
    y = np.zeros_like(x)
    y[x<L] = np.sin(np.abs(x[x<L]*np.pi/L))
    return y