def _compute_stationary(self):
"""
Store the stationary distributions in self._stationary_distributions.
"""
if self.is_irreducible:
stationary_dists = gth_solve(self.P).reshape(1, self.n)
else:
rec_classes = self.recurrent_classes
stationary_dists = np.zeros((len(rec_classes), self.n))
for i, rec_class in enumerate(rec_classes):
stationary_dists[i, rec_class] = \
gth_solve(self.P[rec_class, :][:, rec_class])
self._stationary_dists = stationary_dists
def test_stoch_matrix():
"""Test with stochastic matrices"""
print(__name__ + '.' + test_stoch_matrix.__name__)
matrices = Matrices()
for matrix_dict in matrices.stoch_matrix_dicts:
x = gth_solve(matrix_dict['A'])
yield StationaryDistSumOne(), x
yield StationaryDistNonnegative(), x
yield StationaryDistEqualToKnown(), matrix_dict['stationary_dist'], x
def test_kmr_matrix():
"""Test with KMR matrices"""
print(__name__ + '.' + test_kmr_matrix.__name__)
matrices = Matrices()
for matrix_dict in matrices.kmr_matrix_dicts:
x = gth_solve(matrix_dict['A'])
yield StationaryDistSumOne(), x
yield StationaryDistNonnegative(), x
yield StationaryDistLeftEigenVec(), matrix_dict['A'], x
def kmr_compute_stationary(n,
epsilon=0.01,
payoffs=[[6, 0, 0], [5, 7, 5], [0, 5, 8]]):
"""
This function calculates the stationary state of KMR in genetal cases.
n : int
The number of Players
epsilon : float
The probability of mutation
Payoffs : list
The payoff matrix(symmetric)
"""
num_action = len(payoffs)
states_cool_lex = cool_lex(n, num_action - 1)
states = []
num_zeros = n
num_ones = num_action - 1
num_states = int(
factorial(num_zeros + num_ones) /
(factorial(num_zeros) * factorial(num_ones)))
tran_matrix = np.zeros([num_states, num_states])
print states_cool_lex
for i in states_cool_lex:
profile = []
for m, n in enumerate(i.split("1")):
profile.append(len(n))
states.append(profile) # ex. [[0,2,0,1,0], ...]
for s, i in enumerate(states):
current_profile = np.array(i) / sum(i)
expected_payoff = np.dot(payoffs, current_profile)
best_reply = expected_payoff.argmax()
state_no_before = s
for x, y in enumerate(i):
if y != 0: # The player may be chosen
for k in range(num_action):
adjacent_state = list(i)
adjacent_state[x] = adjacent_state[x] - 1
adjacent_state[k] = adjacent_state[k] + 1
state_no_after = states.index(adjacent_state)
if k == best_reply:
tran_matrix[state_no_before][
state_no_after] = tran_matrix[state_no_before][
state_no_after] + (y / num_zeros) * (
1 - epsilon * (1 - 1 / float(num_action)))
else:
tran_matrix[state_no_before][
state_no_after] = tran_matrix[state_no_before][
state_no_after] + (y / num_zeros) * epsilon * (
1 / float(num_action))
print tran_matrix
return gth_solve(tran_matrix)
def kmr_compute_stationary(n, epsilon=0.01, payoffs=[[6, 0, 0], [5, 7, 5], [0, 5, 8]]):
"""
This function calculates the stationary state of KMR in genetal cases.
n : int
The number of Players
epsilon : float
The probability of mutation
Payoffs : list
The payoff matrix(symmetric)
"""
num_action = len(payoffs)
states_cool_lex = cool_lex(n, num_action - 1)
states = []
num_zeros = n
num_ones = num_action - 1
num_states = int(factorial(num_zeros + num_ones) / (factorial(num_zeros) * factorial(num_ones)))
tran_matrix = np.zeros([num_states, num_states])
print states_cool_lex
for i in states_cool_lex:
profile = []
for m, n in enumerate(i.split("1")):
profile.append(len(n))
states.append(profile) # ex. [[0,2,0,1,0], ...]
for s, i in enumerate(states):
current_profile = np.array(i) / sum(i)
expected_payoff = np.dot(payoffs, current_profile)
best_reply = expected_payoff.argmax()
state_no_before = s
for x, y in enumerate(i):
if y != 0: # The player may be chosen
for k in range(num_action):
adjacent_state = list(i)
adjacent_state[x] = adjacent_state[x] - 1
adjacent_state[k] = adjacent_state[k] + 1
state_no_after = states.index(adjacent_state)
if k == best_reply:
tran_matrix[state_no_before][state_no_after] = tran_matrix[state_no_before][state_no_after] + (
y / num_zeros
) * (1 - epsilon * (1 - 1 / float(num_action)))
else:
tran_matrix[state_no_before][state_no_after] = tran_matrix[state_no_before][state_no_after] + (
y / num_zeros
) * epsilon * (1 / float(num_action))
print tran_matrix
return gth_solve(tran_matrix)
def test_raises_value_error_non_sym():
"""Test with non symmetric input"""
gth_solve(np.array([[0.4, 0.6]]))
def test_raises_value_error_non_2dim():
"""Test with non 2dim input"""
gth_solve(np.array([0.4, 0.6]))