def fixation_probability(mutant_index,
resident_index,
intensity_of_selection,
population_size,
payoff_function=None,
game_matrix=None,
number_of_strategies=None,
mapping='EXP',
**kwargs):
suma = []
for k in range(1, population_size):
mult = []
for j in range(1, k + 1):
if payoff_function is not None and game_matrix is None:
if number_of_strategies is None:
raise ValueError(
'When using a custom payoff_function you must specify number_of_strategies.'
)
strategies = np.zeros(number_of_strategies, dtype=int)
strategies[mutant_index] = j
strategies[resident_index] = population_size - j
payoff_mutant = payoff_function(
mutant_index, population_composition=strategies, **kwargs)
payoff_resident = payoff_function(
resident_index,
population_composition=strategies,
**kwargs)
elif game_matrix is not None and payoff_function is None:
(payoff_mutant, payoff_resident) = payoff_from_matrix(
mutant_index, resident_index, game_matrix, j,
population_size)
else:
raise ValueError(
'No valid payoff structure given, please specify a game_matrix or a payoff_function.'
)
if mapping == 'EXP':
fitness_mutant = math.e**(intensity_of_selection *
payoff_mutant)
fitness_resident = math.e**(intensity_of_selection *
payoff_resident)
elif mapping == 'LIN':
fitness_mutant = 1.0 - intensity_of_selection + \
intensity_of_selection * payoff_mutant
fitness_resident = 1.0 - intensity_of_selection + intensity_of_selection * payoff_resident
else:
raise ValueError(
'No valid mapping given. Use EXP or LIN for exponential and linear respectively.'
)
mult.append(fitness_resident / fitness_mutant)
suma.append(utils.kahan_product(mult))
if any(np.isinf(suma)):
return 0.0
try:
complex_expression = utils.kahan_sum(suma)
except OverflowError:
return 0.0
if np.isinf(complex_expression):
return 0.0
return 1.0 / (1.0 + complex_expression)
def fixation_probability(mutant_index, resident_index, intensity_of_selection, population_size, payoff_function=None,
game_matrix=None, number_of_strategies=None, mapping='EXP', **kwargs):
suma = []
for k in range(1, population_size):
mult = []
for j in range(1, k + 1):
if payoff_function is not None and game_matrix is None:
if number_of_strategies is None:
raise ValueError(
'When using a custom payoff_function you must specify number_of_strategies.')
strategies = np.zeros(number_of_strategies, dtype=int)
strategies[mutant_index] = j
strategies[resident_index] = population_size - j
payoff_mutant = payoff_function(
mutant_index, population_composition=strategies, **kwargs)
payoff_resident = payoff_function(
resident_index, population_composition=strategies, **kwargs)
elif game_matrix is not None and payoff_function is None:
(payoff_mutant, payoff_resident) = payoff_from_matrix(
mutant_index, resident_index, game_matrix, j, population_size)
else:
raise ValueError(
'No valid payoff structure given, please specify a game_matrix or a payoff_function.')
if mapping == 'EXP':
fitness_mutant = math.e ** (intensity_of_selection * payoff_mutant)
fitness_resident = math.e ** (intensity_of_selection * payoff_resident)
elif mapping == 'LIN':
fitness_mutant = 1.0 - intensity_of_selection + \
intensity_of_selection * payoff_mutant
fitness_resident = 1.0 - intensity_of_selection + intensity_of_selection * payoff_resident
else:
raise ValueError(
'No valid mapping given. Use EXP or LIN for exponential and linear respectively.')
mult.append(fitness_resident / fitness_mutant)
suma.append(utils.kahan_product(mult))
if any(np.isinf(suma)):
return 0.0
try:
complex_expression = utils.kahan_sum(suma)
except OverflowError:
return 0.0
if np.isinf(complex_expression):
return 0.0
return 1.0 / (1.0 + complex_expression)
def test_kahan_product(self):
np.testing.assert_almost_equal(utils.kahan_product([2,3]), 2*3,decimal=10, err_msg="Kahan sum fails")
def test_kahan_product(self):
np.testing.assert_almost_equal(utils.kahan_product([2, 3]),
2 * 3,
decimal=10,
err_msg="Kahan sum fails")
