import pysal as ps
import numpy as np
import matplotlib.pyplot as plt
from scipy.linalg import inv

%matplotlib inline

draw_map(0.95)

from IPython.html.widgets import interact
interact(draw_map, lamb=(-0.9, 0.9))

def draw_map(lamb):
    s = 20
    n = s**2
    w = ps.lat2W(s, s, rook=False)
    w.transform = 'R'
    e = np.random.random((n, 1))
    u = inv(np.eye(n) - lamb * w.full()[0])
    u = np.dot(u, e)
    ul = ps.lag_spatial(w, u)
    u = (u - u.mean()) / np.std(u)
    ul = (ul - ul.mean()) / np.std(ul)
    gu = u.reshape((s, s))
    # Figure
    f = plt.figure(figsize=(9, 4))
    ax1 = f.add_subplot(121)
    ax1.matshow(gu, cmap=plt.cm.YlGn)
    ax1.set_frame_on(False)
    ax1.axes.get_xaxis().set_visible(False)
    ax1.axes.get_yaxis().set_visible(False)
    #---
    ax2 = f.add_subplot(122)
    sc = ax2.scatter(u, ul, linewidth=0)
    ols = ps.spreg.OLS(ul, u)
    tag = "b = %.3f"%ols.betas[1][0]
    ax2.plot(u, ols.predy, c='red', label=tag)
    ax2.axvline(0, c='0.5')
    ax2.axhline(0, c='0.5')
    ax2.legend()
    plt.xlabel('u')
    plt.ylabel('Wu')
    plt.suptitle("$\lambda$ = %.2f"%lamb)
    plt.show()