def __init__(self, X, P, codomain = None, check = False):
r"""
Create the discrete probability space with probabilities on the
space X given by the dictionary P with values in the field
real_field.
EXAMPLES::
sage: S = [ i for i in range(16) ]
sage: P = {}
sage: for i in range(15): P[i] = 2^(-i-1)
sage: P[15] = 2^-16
sage: X = DiscreteProbabilitySpace(S,P)
sage: X.domain()
(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15)
sage: X.set()
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}
sage: X.entropy()
1.9997253418
A probability space can be defined on any list of elements.
EXAMPLES::
sage: AZ = 'ABCDEFGHIJKLMNOPQRSTUVWXYZ'
sage: S = [ AZ[i] for i in range(26) ]
sage: P = { 'A':1/2, 'B':1/4, 'C':1/4 }
sage: X = DiscreteProbabilitySpace(S,P)
sage: X
Discrete probability space defined by {'A': 1/2, 'C': 1/4, 'B': 1/4}
sage: X.entropy()
1.5
"""
if codomain is None:
codomain = RealField()
if not is_RealField(codomain) and not is_RationalField(codomain):
raise TypeError, "Argument codomain (= %s) must be the reals or rationals" % codomain
if check:
one = sum([ P[x] for x in P.keys() ])
if is_RationalField(codomain):
if not one == 1:
raise TypeError, "Argument P (= %s) does not define a probability function"
else:
if not Abs(one-1) < 2^(-codomain.precision()+1):
raise TypeError, "Argument P (= %s) does not define a probability function"
ProbabilitySpace_generic.__init__(self, X, codomain)
DiscreteRandomVariable.__init__(self, self, P, codomain, check)
def __init__(self, X, P, codomain=None, check=False):
r"""
Create the discrete probability space with probabilities on the
space X given by the dictionary P with values in the field
real_field.
EXAMPLES::
sage: S = [ i for i in range(16) ]
sage: P = {}
sage: for i in range(15): P[i] = 2^(-i-1)
sage: P[15] = 2^-16
sage: X = DiscreteProbabilitySpace(S,P)
sage: X.domain()
(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15)
sage: X.set()
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}
sage: X.entropy()
1.9997253418
A probability space can be defined on any list of elements.
EXAMPLES::
sage: AZ = 'ABCDEFGHIJKLMNOPQRSTUVWXYZ'
sage: S = [ AZ[i] for i in range(26) ]
sage: P = { 'A':1/2, 'B':1/4, 'C':1/4 }
sage: X = DiscreteProbabilitySpace(S,P)
sage: X
Discrete probability space defined by {'A': 1/2, 'C': 1/4, 'B': 1/4}
sage: X.entropy()
1.5
"""
if codomain is None:
codomain = RealField()
if not is_RealField(codomain) and not is_RationalField(codomain):
raise TypeError, "Argument codomain (= %s) must be the reals or rationals" % codomain
if check:
one = sum([P[x] for x in P.keys()])
if is_RationalField(codomain):
if not one == 1:
raise TypeError, "Argument P (= %s) does not define a probability function"
else:
if not Abs(one - 1) < 2 ^ (-codomain.precision() + 1):
raise TypeError, "Argument P (= %s) does not define a probability function"
ProbabilitySpace_generic.__init__(self, X, codomain)
DiscreteRandomVariable.__init__(self, self, P, codomain, check)
