def multiple_inverse(p_final, n):
"""Returns p_initial for desired p_final with n multiple comparisons.
WARNING: multiple_inverse is not very reliable when p_final is very close
to 1 (say, within 1e-4) since we then take the ratio of two very similar
numbers.
"""
return one_minus_exp(log_one_minus(p_final)/n)
def test_log_one_minus_small(self):
"""log_one_minus_x should return -x if x is small"""
self.assertFloatEqualRel(log_one_minus(1e-30), 1e-30)
def test_log_one_minus_large(self):
"""log_one_minus_x should return math.log(1-x) if x is large"""
self.assertFloatEqual(log_one_minus(0.2), math.log(1-0.2))
def multiple_n(p_initial, p_final):
"""Returns number of comparisons such that p_initial maps to p_final.
WARNING: not very accurate when p_final is very close to 1.
"""
return log_one_minus(p_final)/log_one_minus(p_initial)
def test_log_one_minus_small(self):
"""log_one_minus_x should return -x if x is small"""
self.assertFloatEqualRel(log_one_minus(1e-30), 1e-30)
def test_log_one_minus_large(self):
"""log_one_minus_x should return math.log(1-x) if x is large"""
self.assertFloatEqual(log_one_minus(0.2), math.log(1 - 0.2))