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# Init matplotlib

%matplotlib inline

import matplotlib


    

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FIG_SIZE = 4

def plot_linear_system(Ab, bounds=None, ax=None, color='r', alpha=1):
    """Plot the linear system defined by the extended matrix `Ab`."""
    
    # Check arguments #############
    
    assert Ab.ndim == 2
    assert Ab.shape[1] == 3
    
    if bounds is None:
        if ax is None:
            bounds = np.array([[-10, 10],
                               [-10, 10]])
        else:
            bounds = np.array(ax.axis()).reshape([2,2])
    
    assert bounds.ndim == 2
    assert bounds.shape == (2, 2)
    assert bounds[0,0] < bounds[0,1]
    assert bounds[1,0] < bounds[1,1]
    
    # Setup the plot ##############
    
    if ax is None:
        fig, ax = plt.subplots(figsize=(FIG_SIZE, FIG_SIZE))
        
    ax.axis('equal')

    ax.axis(bounds.flatten())
    ax.set_xticks(np.arange(*bounds[0], 1))
    ax.set_yticks(np.arange(*bounds[0], 1))

    ax.axhline(y=0, color='k')
    ax.axvline(x=0, color='k')

    # Compute points to plot ######

    x = bounds[0]            # horizontal axis limits
    
    Abnv = Ab[Ab[:,1] != 0]  # linear equations having a non-null x_2 coefficient (i.e. non-vertical line)
    Abv = Ab[Ab[:,1] == 0]   # linear equations having a null x_2 coefficient (i.e. vertical line)
    
    # Plot non-vertical lines #####
    
    yp1 = (Abnv[:,2] - Abnv[:,0] * x[0]) / Abnv[:,1]
    yp2 = (Abnv[:,2] - Abnv[:,0] * x[1]) / Abnv[:,1]
    plt.plot(x, np.array([yp1, yp2]), "-{}".format(color), alpha=alpha)
    
    # Plot vertical lines #########
    
    for ab in Abv:
        plt.axvline(ab[2] / ab[0], color=color, alpha=alpha)
    
    # TODO: add label (e.g. "2x + 3y = 1")

    plt.grid(True)
    
    return ax


    

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Ab = np.array([[0, 1, 1],
               [1, 0, 1],
               [1, 1, 2]])

plot_linear_system(Ab);


    

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Ab = np.array([[-3, 9, 9],
               [1, 1, 5]])

bounds = np.array([[-2, 6], [-2, 6]])

plot_linear_system(Ab, bounds=bounds);

Ab = np.array([[-1., 3., 3.],
               [-1., 7., 11.]])

Ab[0] = Ab[0] + -0.2 * Ab[1]

print(Ab)

plot_linear_system(Ab, bounds=bounds);

Ab = np.array([[1, 0, 3],
               [0, 1, 2]])

plot_linear_system(Ab, bounds=bounds);


    

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Ab = np.array([[-2, 4, -4],
               [ 6, 7, 11]])

ax = plot_linear_system(Ab, bounds=np.array([[-5, 5], [-5, 5]]), alpha=0.5);

Ab = np.array([[-2,  4, -4],
               [ 0, 19, -1]])

plot_linear_system(Ab, ax=ax, color='g', alpha=0.5);