def test_markovchain_pmatrices():
"""
Test the methods of MarkovChain, as well as mc_compute_stationary,
with P matrix and known solutions
"""
# Matrix with two recurrent classes [0, 1] and [3, 4, 5],
# which have periods 2 and 3, respectively
Q = np.zeros((6, 6))
Q[0, 1], Q[1, 0] = 1, 1
Q[2, [0, 3]] = 1 / 2
Q[3, 4], Q[4, 5], Q[5, 3] = 1, 1, 1
Q_stationary_dists = \
np.array([[1/2, 1/2, 0, 0, 0, 0], [0, 0, 0, 1/3, 1/3, 1/3]])
testset = [
{
'P': np.array([[0.4, 0.6], [0.2, 0.8]]), # P matrix
'stationary_dists': np.array([[0.25, 0.75]]), # Known solution
'comm_classes': [np.arange(2)],
'rec_classes': [np.arange(2)],
'is_irreducible': True,
'period': 1,
'is_aperiodic': True,
'cyclic_classes': [np.arange(2)],
},
{
'P': sparse.csr_matrix([[0.4, 0.6], [0.2, 0.8]]),
'stationary_dists': np.array([[0.25, 0.75]]),
'comm_classes': [np.arange(2)],
'rec_classes': [np.arange(2)],
'is_irreducible': True,
'period': 1,
'is_aperiodic': True,
'cyclic_classes': [np.arange(2)],
},
{
'P': np.array([[0, 1], [1, 0]]),
'stationary_dists': np.array([[0.5, 0.5]]),
'comm_classes': [np.arange(2)],
'rec_classes': [np.arange(2)],
'is_irreducible': True,
'period': 2,
'is_aperiodic': False,
'cyclic_classes': [np.array([0]), np.array([1])],
},
{
'P': np.eye(2),
'stationary_dists': np.array([[1, 0], [0, 1]]),
'comm_classes': [np.array([0]), np.array([1])],
'rec_classes': [np.array([0]), np.array([1])],
'is_irreducible': False,
'period': 1,
'is_aperiodic': True,
},
# Reducible mc with a unique recurrent class,
# where n-1 is a transient state
{
'P': np.array([[1, 0], [1, 0]]),
'stationary_dists': np.array([[1, 0]]),
'comm_classes': [np.array([0]), np.array([1])],
'rec_classes': [np.array([0])],
'is_irreducible': False,
'period': 1,
'is_aperiodic': True,
},
{
'P': Q,
'stationary_dists': Q_stationary_dists,
'comm_classes':
[np.array([0, 1]),
np.array([2]),
np.array([3, 4, 5])],
'rec_classes': [np.array([0, 1]),
np.array([3, 4, 5])],
'is_irreducible': False,
'period': 6,
'is_aperiodic': False,
},
{
'P': sparse.csr_matrix(Q),
'stationary_dists': Q_stationary_dists,
'comm_classes':
[np.array([0, 1]),
np.array([2]),
np.array([3, 4, 5])],
'rec_classes': [np.array([0, 1]),
np.array([3, 4, 5])],
'is_irreducible': False,
'period': 6,
'is_aperiodic': False,
}
]
# Loop Through TestSet #
for test_dict in testset:
mc = MarkovChain(test_dict['P'])
computed = mc.stationary_distributions
assert_allclose(computed, test_dict['stationary_dists'])
assert (mc.num_communication_classes == len(test_dict['comm_classes']))
assert (mc.is_irreducible == test_dict['is_irreducible'])
assert (mc.num_recurrent_classes == len(test_dict['rec_classes']))
list_of_array_equal(
sorted(mc.communication_classes, key=lambda x: x[0]),
sorted(test_dict['comm_classes'], key=lambda x: x[0]))
list_of_array_equal(
sorted(mc.recurrent_classes, key=lambda x: x[0]),
sorted(test_dict['rec_classes'], key=lambda x: x[0]))
assert (mc.period == test_dict['period'])
assert (mc.is_aperiodic == test_dict['is_aperiodic'])
try:
list_of_array_equal(
sorted(mc.cyclic_classes, key=lambda x: x[0]),
sorted(test_dict['cyclic_classes'], key=lambda x: x[0]))
except NotImplementedError:
assert (mc.is_irreducible is False)
# Test of mc_compute_stationary
computed = mc_compute_stationary(test_dict['P'])
assert_allclose(computed, test_dict['stationary_dists'])
def test_markovchain_pmatrices():
"""
Test the methods of MarkovChain, as well as mc_compute_stationary,
with P matrix and known solutions
"""
# Matrix with two recurrent classes [0, 1] and [3, 4, 5],
# which have periods 2 and 3, respectively
Q = np.zeros((6, 6))
Q[0, 1], Q[1, 0] = 1, 1
Q[2, [0, 3]] = 1/2
Q[3, 4], Q[4, 5], Q[5, 3] = 1, 1, 1
Q_stationary_dists = \
np.array([[1/2, 1/2, 0, 0, 0, 0], [0, 0, 0, 1/3, 1/3, 1/3]])
testset = [
{'P': np.array([[0.4, 0.6], [0.2, 0.8]]), # P matrix
'stationary_dists': np.array([[0.25, 0.75]]), # Known solution
'comm_classes': [np.arange(2)],
'rec_classes': [np.arange(2)],
'is_irreducible': True,
'period': 1,
'is_aperiodic': True,
'cyclic_classes': [np.arange(2)],
},
{'P': np.array([[0, 1], [1, 0]]),
'stationary_dists': np.array([[0.5, 0.5]]),
'comm_classes': [np.arange(2)],
'rec_classes': [np.arange(2)],
'is_irreducible': True,
'period': 2,
'is_aperiodic': False,
'cyclic_classes': [np.array([0]), np.array([1])],
},
{'P': np.eye(2),
'stationary_dists': np.array([[1, 0], [0, 1]]),
'comm_classes': [np.array([0]), np.array([1])],
'rec_classes': [np.array([0]), np.array([1])],
'is_irreducible': False,
'period': 1,
'is_aperiodic': True,
},
# Reducible mc with a unique recurrent class,
# where n-1 is a transient state
{'P': np.array([[1, 0], [1, 0]]),
'stationary_dists': np.array([[1, 0]]),
'comm_classes': [np.array([0]), np.array([1])],
'rec_classes': [np.array([0])],
'is_irreducible': False,
'period': 1,
'is_aperiodic': True,
},
{'P': Q,
'stationary_dists': Q_stationary_dists,
'comm_classes': [np.array([0, 1]), np.array([2]), np.array([3, 4, 5])],
'rec_classes': [np.array([0, 1]), np.array([3, 4, 5])],
'is_irreducible': False,
'period': 6,
'is_aperiodic': False,
}
]
# Loop Through TestSet #
for test_dict in testset:
mc = MarkovChain(test_dict['P'])
computed = mc.stationary_distributions
assert_allclose(computed, test_dict['stationary_dists'])
assert(mc.num_communication_classes == len(test_dict['comm_classes']))
assert(mc.is_irreducible == test_dict['is_irreducible'])
assert(mc.num_recurrent_classes == len(test_dict['rec_classes']))
list_of_array_equal(
sorted(mc.communication_classes, key=lambda x: x[0]),
sorted(test_dict['comm_classes'], key=lambda x: x[0])
)
list_of_array_equal(
sorted(mc.recurrent_classes, key=lambda x: x[0]),
sorted(test_dict['rec_classes'], key=lambda x: x[0])
)
assert(mc.period == test_dict['period'])
assert(mc.is_aperiodic == test_dict['is_aperiodic'])
try:
list_of_array_equal(
sorted(mc.cyclic_classes, key=lambda x: x[0]),
sorted(test_dict['cyclic_classes'], key=lambda x: x[0])
)
except NotImplementedError:
assert(mc.is_irreducible is False)
# Test of mc_compute_stationary
computed = mc_compute_stationary(test_dict['P'])
assert_allclose(computed, test_dict['stationary_dists'])