def test_backward():
initMatrix = np.matrix([[1.0], [0]])
transitionMatrix = np.matrix([[0.9, 0.1, 0], [0, 0.9, 0.1]])
x = np.matrix([-0.2, 2.6, 1.3])
c = np.matrix([1.0, 0.1625, 0.8266, 0.0581])
mc = MarkovChain(initMatrix, transitionMatrix)
g1 = GaussD(mean=np.matrix([0]), stdev=np.matrix([1]))
g2 = GaussD(mean=np.matrix([3]), stdev=np.matrix([2]))
pX, logS = g1.prob(np.matrix([[g1], [g2]]), x)
betaHat = mc.backward(mc, pX, c)
print 'betaHat:', betaHat
print 'expected: [1.0003 1.0393 0; 8.4182 9.3536 2.0822]'
initMatrix = np.matrix([[1.0], [0]])
transitionMatrix = np.matrix([[0.9, 0.1], [0.1, 0.9]])
x = np.matrix([-0.2, 2.6, 1.3])
mc = MarkovChain(initMatrix, transitionMatrix)
g1 = GaussD(mean=np.matrix([0]), stdev=np.matrix([1]))
g2 = GaussD(mean=np.matrix([3]), stdev=np.matrix([2]))
pX, logS = g1.prob(np.matrix([g1, g2]), x)
alphaHat, c = mc.forward(mc, pX)
betaHat = mc.backward(mc, pX, c)
print 'betaHat:', betaHat
print 'expected: [1.0 6.798238264 1.125986646; 5.223087455 5.75095566 1.125986646]'
