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]'
def test_forward():
initMatrix = np.matrix([[1.0], [0]])
transitionMatrix = np.matrix([[0.9, 0.1, 0], [0, 0.9, 0.1]])
mc = MarkovChain(initMatrix, transitionMatrix)
g1 = GaussD(mean=np.matrix([0]), stdev=np.matrix([1]))
g2 = GaussD(mean=np.matrix([3]), stdev=np.matrix([2]))
# output sequence
x = np.matrix([-0.2, 2.6, 1.3])
pX, logS = g1.prob(np.matrix([g1, g2]), x)
alphaHat, c = mc.forward(mc, pX)
print 'alphaHat:', alphaHat, 'expected: [1 0.3847 0.4189; 0 0.6153 0.5811]'
print 'c:', c, 'expected: [1 0.1625 0.8266 0.0581]'
h = HMM(mc, np.matrix([[g1], [g2]]))
# logP = P(X|h)
logP = h.logprob(h, x)
print 'logP: ', logP, 'expected: -9.1877'
initMatrix = np.matrix([[1.0], [0]])
transitionMatrix = np.matrix([[0.0, 1.0, 0.0], [0.0, 0.7, 0.3]])
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([1]))
h1 = HMM(mc, np.matrix([[g1], [g2]]))
transitionMatrix = np.matrix([[0.5, 0.5, 0.0], [0.0, 0.5, 0.5]])
mc2 = MarkovChain(initMatrix, transitionMatrix)
g3 = GaussD(mean=np.matrix([0]), stdev=np.matrix([1]))
g4 = GaussD(mean=np.matrix([3]), stdev=np.matrix([1]))
h2 = HMM(mc2, np.matrix([[g3], [g4]]))
logP = h1.logprob(np.matrix([h1, h2]), x)
print 'logP:', logP, 'expected: [-5.562463348 -6.345037882]'
