human
Give me a the Python code you requested given the following:
I am working on the file "SC2/U3_ODE.ipynb".
The first task is:
Entonces, ¿cómo utilizamos la región de estabilidad?
Lo importante de este análisis es notar que no podemos definir $h$ a priori. Dados un método y $\lambda$ conocidos, debemos estudiar la región de estabilidad para determinar que valor de $h$ utilizar.
Can you write Python code for it?
assistant
#Here is the Python code you requested.

def plot_log_eq_stability_region(y0=1.2, h=0.5, T=10):
    # How did I get this? Why do I need it?
    def my_f_1D_prime(y):
        return np.array(1-2*y)

    # Choosing which solver to use
    solvers = ('euler','RK2','RK4')
    solver = solvers[2]

    t_times = np.arange(0, T+h, h)
    y_output = np.zeros(t_times.size)
    y_output[0] = y0

    for i in range(1,t_times.size):
        if solver=='euler':
            y_output[i]=euler_ode(y_output[i-1],t_times[i-1],my_f_1D,h)
            c1,c2,c3='b','k','k'
        elif solver=='RK2':
            y_output[i]=RK2_ode(y_output[i-1],t_times[i-1],my_f_1D,h)
            c1,c2,c3='k','b','k'
        else:
            y_output[i]=RK4_ode(y_output[i-1],t_times[i-1],my_f_1D,h)
            c1,c2,c3='k','k','b'

    fig = plt.figure(figsize=(L,L))
    ax1 = fig.add_subplot(221)
    ax2 = fig.add_subplot(222)
    ax3 = fig.add_subplot(223)

    ax1.axis("equal")
    ax1.grid(True)
    ax1.set_title("Numerical Approximation")
    ax1.axis([0, T, -0.5, 2])
    ax1.plot(t_times,y_output,'-')
    ax1.plot(t_times,y_output,'.k')

    # The next code is to plot in logscale unstable numerical simulations
    y_all=h*my_f_1D_prime(y_output)
    y_pos=y_all>0
    y_neg=np.logical_not(y_pos)
    ax2.semilogy(t_times[y_pos],y_all[y_pos],'.r',ms=20)
    ax2.semilogy(t_times[y_neg],-y_all[y_neg],'.b',ms=20)
    ax2.grid("on")
    ax2.set_title("Numerical Approximation in log scale")

    zplot2(W1,ax3,line_color=c1)
    zplot2(W2,ax3,line_color=c2)
    zplot2(W4,ax3,line_color=c3)
    k_lambdah=h*my_f_1D_prime(y_output)
    ax3.plot(np.real(k_lambdah),np.imag(k_lambdah),'.r',ms=20)
    ax3.axis("equal")
    ax3.axis([-5, 2, -3.5, 3.5])
    ax3.grid("on")
    ax3.set_title("Stability Region and $k=\lambda\,h$")

#y0=1.2 # 1.2, 2.0, 4.0
#h=0.5  # 0.5, 0.1
#T=10
interact(plot_log_eq_stability_region,y0=(-2,5,0.1),h=(0.01,1,0.1), T=(1,20,1))