def test_discreteuniform():
# Symbolic
a, b, c, t = symbols('a b c t')
X = DiscreteUniform('X', [a, b, c])
assert E(X) == (a + b + c) / 3
assert simplify(
variance(X) - ((a**2 + b**2 + c**2) / 3 -
(a / 3 + b / 3 + c / 3)**2)) == 0
assert P(Eq(X, a)) == P(Eq(X, b)) == P(Eq(X, c)) == S('1/3')
Y = DiscreteUniform('Y', range(-5, 5))
# Numeric
assert E(Y) == S('-1/2')
assert variance(Y) == S('33/4')
for x in range(-5, 5):
assert P(Eq(Y, x)) == S('1/10')
assert P(Y <= x) == S(x + 6) / 10
assert P(Y >= x) == S(5 - x) / 10
assert dict(density(Die('D', 6)).items()) == \
dict(density(DiscreteUniform('U', range(1, 7))).items())
assert characteristic_function(X)(
t) == exp(I * a * t) / 3 + exp(I * b * t) / 3 + exp(I * c * t) / 3
assert moment_generating_function(X)(
t) == exp(a * t) / 3 + exp(b * t) / 3 + exp(c * t) / 3
def test_discreteuniform():
# Symbolic
a, b, c, t = symbols("a b c t")
X = DiscreteUniform("X", [a, b, c])
assert E(X) == (a + b + c) / 3
assert (simplify(
variance(X) - ((a**2 + b**2 + c**2) / 3 -
(a / 3 + b / 3 + c / 3)**2)) == 0)
assert P(Eq(X, a)) == P(Eq(X, b)) == P(Eq(X, c)) == S("1/3")
Y = DiscreteUniform("Y", range(-5, 5))
# Numeric
assert E(Y) == S("-1/2")
assert variance(Y) == S("33/4")
for x in range(-5, 5):
assert P(Eq(Y, x)) == S("1/10")
assert P(Y <= x) == S(x + 6) / 10
assert P(Y >= x) == S(5 - x) / 10
assert dict(density(Die("D", 6)).items()) == dict(
density(DiscreteUniform("U", range(1, 7))).items())
assert (characteristic_function(X)(t) == exp(I * a * t) / 3 +
exp(I * b * t) / 3 + exp(I * c * t) / 3)
assert (moment_generating_function(X)(t) == exp(a * t) / 3 +
exp(b * t) / 3 + exp(c * t) / 3)
def test_sampling_methods():
distribs_random = [DiscreteUniform("D", list(range(5)))]
distribs_scipy = [Hypergeometric("H", 1, 1, 1)]
distribs_pymc3 = [BetaBinomial("B", 1, 1, 1)]
size = 5
for X in distribs_random:
sam = X.pspace.distribution._sample_random(size)
for i in range(size):
assert sam[i] in X.pspace.domain.set
scipy = import_module('scipy')
if not scipy:
skip('Scipy not installed. Abort tests for _sample_scipy.')
else:
for X in distribs_scipy:
sam = X.pspace.distribution._sample_scipy(size)
for i in range(size):
assert sam[i] in X.pspace.domain.set
pymc3 = import_module('pymc3')
if not pymc3:
skip('PyMC3 not installed. Abort tests for _sample_pymc3.')
else:
for X in distribs_pymc3:
sam = X.pspace.distribution._sample_pymc3(size)
for i in range(size):
assert sam[i] in X.pspace.domain.set
def test_sample_iter():
X = Normal('X', 0, 1)
Y = DiscreteUniform('Y', [1, 2, 7])
Z = Poisson('Z', 2)
scipy = import_module('scipy')
if not scipy:
skip('Scipy is not installed. Abort tests')
expr = X**2 + 3
iterator = sample_iter(expr)
expr2 = Y**2 + 5 * Y + 4
iterator2 = sample_iter(expr2)
expr3 = Z**3 + 4
iterator3 = sample_iter(expr3)
def is_iterator(obj):
if (hasattr(obj, '__iter__')
and (hasattr(obj, 'next') or hasattr(obj, '__next__'))
and callable(obj.__iter__) and obj.__iter__() is obj):
return True
else:
return False
assert is_iterator(iterator)
assert is_iterator(iterator2)
assert is_iterator(iterator3)
def test_sample_scipy():
distribs_scipy = [
FiniteRV('F', {
1: S.Half,
2: Rational(1, 4),
3: Rational(1, 4)
}),
DiscreteUniform("Y", list(range(5))),
Die("D"),
Bernoulli("Be", 0.3),
Binomial("Bi", 5, 0.4),
BetaBinomial("Bb", 2, 1, 1),
Hypergeometric("H", 1, 1, 1),
Rademacher("R")
]
size = 3
scipy = import_module('scipy')
if not scipy:
skip('Scipy not installed. Abort tests for _sample_scipy.')
else:
for X in distribs_scipy:
samps = sample(X, size=size)
samps2 = sample(X, size=(2, 2))
for sam in samps:
assert sam in X.pspace.domain.set
for i in range(2):
for j in range(2):
assert samps2[i][j] in X.pspace.domain.set
def test_sample_iter():
X = Normal("X", 0, 1)
Y = DiscreteUniform("Y", [1, 2, 7])
Z = Poisson("Z", 2)
expr = X ** 2 + 3
iterator = sample_iter(expr)
expr2 = Y ** 2 + 5 * Y + 4
iterator2 = sample_iter(expr2)
expr3 = Z ** 3 + 4
iterator3 = sample_iter(expr3)
def is_iterator(obj):
if (
hasattr(obj, "__iter__")
and (hasattr(obj, "next") or hasattr(obj, "__next__"))
and callable(obj.__iter__)
and obj.__iter__() is obj
):
return True
else:
return False
assert is_iterator(iterator)
assert is_iterator(iterator2)
assert is_iterator(iterator3)
def test_sample_scipy():
distribs_scipy = [
FiniteRV('F', {1: S.Half, 2: Rational(1, 4), 3: Rational(1, 4)}),
DiscreteUniform("Y", list(range(5))),
Die("D"),
Bernoulli("Be", 0.3),
Binomial("Bi", 5, 0.4),
BetaBinomial("Bb", 2, 1, 1),
Hypergeometric("H", 1, 1, 1),
Rademacher("R")
]
size = 3
numsamples = 5
scipy = import_module('scipy')
if not scipy:
skip('Scipy not installed. Abort tests for _sample_scipy.')
else:
with ignore_warnings(UserWarning): ### TODO: Restore tests once warnings are removed
h_sample = list(sample(Hypergeometric("H", 1, 1, 1), size=size, numsamples=numsamples))
assert len(h_sample) == numsamples
for X in distribs_scipy:
samps = next(sample(X, size=size))
samps2 = next(sample(X, size=(2, 2)))
for sam in samps:
assert sam in X.pspace.domain.set
for i in range(2):
for j in range(2):
assert samps2[i][j] in X.pspace.domain.set
def test_sample_iter():
X = Normal('X', 0, 1)
Y = DiscreteUniform('Y', [1, 2, 7])
Z = Poisson('Z', 2)
expr = X**2 + 3
iterator = sample_iter(expr)
expr2 = Y**2 + 5 * Y + 4
iterator2 = sample_iter(expr2)
expr3 = Z**3 + 4
iterator3 = sample_iter(expr3)
def is_iterator(obj):
if (hasattr(obj, '__iter__')
and (hasattr(obj, 'next') or hasattr(obj, '__next__'))
and callable(obj.__iter__) and obj.__iter__() is obj):
return True
else:
return False
assert is_iterator(iterator)
assert is_iterator(iterator2)
assert is_iterator(iterator3)
def test_discreteuniform():
# Symbolic
a, b, c = symbols('a b c')
X = DiscreteUniform('X', [a, b, c])
assert E(X) == (a + b + c) / 3
assert variance(X) == (a**2 + b**2 + c**2) / 3 - (a / 3 + b / 3 + c / 3)**2
assert P(Eq(X, a)) == P(Eq(X, b)) == P(Eq(X, c)) == S('1/3')
Y = DiscreteUniform('Y', range(-5, 5))
# Numeric
assert E(Y) == S('-1/2')
assert variance(Y) == S('33/4')
assert skewness(Y) == 0
for x in range(-5, 5):
assert P(Eq(Y, x)) == S('1/10')
assert P(Y <= x) == S(x + 6) / 10
assert P(Y >= x) == S(5 - x) / 10
assert density(Die('D', 6)) == density(DiscreteUniform('U', range(1, 7)))
def test_moment_generating_function():
X = Normal('X', 0, 1)
Y = DiscreteUniform('Y', [1, 2, 7])
Z = Poisson('Z', 2)
t = symbols('_t')
P = Lambda(t, exp(t**2 / 2))
Q = Lambda(t, (exp(7 * t) / 3 + exp(2 * t) / 3 + exp(t) / 3))
R = Lambda(t, exp(2 * exp(t) - 2))
assert moment_generating_function(X).dummy_eq(P)
assert moment_generating_function(Y).dummy_eq(Q)
assert moment_generating_function(Z).dummy_eq(R)
def test_moment_generating_function():
X = Normal("X", 0, 1)
Y = DiscreteUniform("Y", [1, 2, 7])
Z = Poisson("Z", 2)
t = symbols("_t")
P = Lambda(t, exp(t ** 2 / 2))
Q = Lambda(t, (exp(7 * t) / 3 + exp(2 * t) / 3 + exp(t) / 3))
R = Lambda(t, exp(2 * exp(t) - 2))
assert moment_generating_function(X) == P
assert moment_generating_function(Y) == Q
assert moment_generating_function(Z) == R
def test_characteristic_function():
# Imports I from sympy
from sympy.core.numbers import I
X = Normal('X', 0, 1)
Y = DiscreteUniform('Y', [1, 2, 7])
Z = Poisson('Z', 2)
t = symbols('_t')
P = Lambda(t, exp(-t**2 / 2))
Q = Lambda(t, exp(7 * t * I) / 3 + exp(2 * t * I) / 3 + exp(t * I) / 3)
R = Lambda(t, exp(2 * exp(t * I) - 2))
assert characteristic_function(X).dummy_eq(P)
assert characteristic_function(Y).dummy_eq(Q)
assert characteristic_function(Z).dummy_eq(R)
def test_characteristic_function():
# Imports I from sympy
from sympy import I
X = Normal("X", 0, 1)
Y = DiscreteUniform("Y", [1, 2, 7])
Z = Poisson("Z", 2)
t = symbols("_t")
P = Lambda(t, exp(-(t ** 2) / 2))
Q = Lambda(t, exp(7 * t * I) / 3 + exp(2 * t * I) / 3 + exp(t * I) / 3)
R = Lambda(t, exp(2 * exp(t * I) - 2))
assert characteristic_function(X) == P
assert characteristic_function(Y) == Q
assert characteristic_function(Z) == R
