def add_approximators(N, C):
'''
This function will add all approximators with denominator less than N
and that are coprime with its numerator
'''
approximators = []
treshold = mp.log10(mp.mpf(124) / mp.mpf(123))
for i in range(10, N):
chute = mp.floor(i * C)
if mp.absmax(chute / i - C) >= mp.absmax((chute + 1) / i - C):
chute += 1
if mcd(chute, i) == 1:
val = mp.frac(i * C)
if val < treshold:
approximators.append((i, val))
elif val > 1 - treshold:
approximators.append((i, val - 1))
return approximators
def family_graphical_combination(t, c, angle_alpha_prime):
"""
Aberdeen family of graphical operators
"""
if not (isinstance(t, Opinion) and isinstance(c, Opinion) \
and t.check() and c.check()):
raise Exception("Two valid Opinions are required!")
if mpmath.almosteq(angle_alpha_prime, -mpmath.pi / 3, epsilon):
new_magnitude = c.get_magnitude_ratio() * (
mpmath.mpf("2") * t.getUncertainty() /
mpmath.sqrt(mpmath.mpf("3")))
#new_magnitude = 0
elif mpmath.almosteq(angle_alpha_prime,
mpmath.mpf("2/3") * mpmath.pi, epsilon):
new_magnitude = c.get_magnitude_ratio() * (
mpmath.mpf("2") * (mpmath.mpf("1") - t.getUncertainty()) /
mpmath.sqrt(mpmath.mpf("3")))
#new_magnitude = 0
elif mpmath.almosteq(angle_alpha_prime,
mpmath.mpf("1/2") * mpmath.pi, epsilon):
#new_magnitude = 1 - t.getUncertainty()
new_magnitude = 2 * t.getBelief()
else:
new_magnitude = c.get_magnitude_ratio() * (mpmath.mpf("2") * \
(mpmath.sqrt(mpmath.power(mpmath.tan(angle_alpha_prime), mpmath.mpf("2")) +1 ) /
( mpmath.absmax(mpmath.tan(angle_alpha_prime) + mpmath.sqrt(mpmath.mpf("3"))) ) ) * \
t.getBelief())
new_uncertainty = t.getUncertainty(
) + mpmath.sin(angle_alpha_prime) * new_magnitude
new_disbelief = t.getDisbelief() + (
t.getUncertainty() - new_uncertainty) * mpmath.cos(
mpmath.pi / 3) + mpmath.cos(angle_alpha_prime) * mpmath.sin(
mpmath.pi / 3) * new_magnitude
if mpmath.almosteq(new_uncertainty, 1, epsilon):
new_uncertainty = mpmath.mpf("1")
if mpmath.almosteq(new_uncertainty, 0, epsilon):
new_uncertainty = mpmath.mpf("0")
if mpmath.almosteq(new_disbelief, 1, epsilon):
new_disbelief = mpmath.mpf("1")
if mpmath.almosteq(new_disbelief, 0, epsilon):
new_disbelief = mpmath.mpf("0")
return Opinion(1 - new_disbelief - new_uncertainty, new_disbelief,
new_uncertainty, "1/2")
def distance_expected_value(self, another):
"""
This method computes the distance between the two expected values
"""
return mpmath.absmax(self.expected_value() - another.expected_value())