Visualize simple state space model

gen.py

import pylab as plt
import numpy as np

def gen(x, evolve, project, n=1000, sigma=.1):
  y = []
  for i in xrange(int(n)):
    y.append(np.dot(project, x))
    x = np.dot(evolve, x)
    x = np.clip(x, -100, 100)
    x += np.random.randn(*x.shape) * sigma

  return np.asarray(y)


if __name__ == '__main__':
  r = 2
  E = np.eye(r) + .01 * (np.random.rand(r, r) - .5)
  P = (np.eye(r) + .01 * np.random.randn(r, r))[:2]

  print E, P, E.shape, P.shape
  for i in range(50):
    Y = gen(10 * np.random.randn(r), E, P, sigma=0.1, n=1e4)

    plt.ion()
    Y = Y[::20]
    plt.plot(Y[:,0], Y[:,1], c='k')