def test_solver_23_reciprocal_lte():
for c in [1, 3]:
# Positive
# 1 / X < 10
solution = Interval.Ropen(-oo, 0) | Interval.Lopen(Rat(c, 10), oo)
event = (c / Y) < 10
assert event.solve() == solution
# 1 / X <= 10
solution = Interval.Ropen(-oo, 0) | Interval(Rat(c, 10), oo)
event = (c / Y) <= 10
assert event.solve() == solution
# 1 / X <= sqrt(2)
solution = Interval.Ropen(-oo, 0) | Interval(c / sympy.sqrt(2), oo)
event = (c / Y) <= sympy.sqrt(2)
assert event.solve() == solution
# Negative.
# 1 / X < -10
solution = Interval.open(-Rat(c, 10), 0)
event = (c / Y) < -10
assert event.solve() == solution
# 1 / X <= -10
solution = Interval.Ropen(-Rat(c, 10), 0)
event = (c / Y) <= -10
assert event.solve() == solution
# 1 / X <= -sqrt(2)
solution = Interval.Ropen(-c / sympy.sqrt(2), 0)
event = (c / Y) <= -sympy.sqrt(2)
assert event.solve() == solution
def test_solver_22():
# 2 < abs(X) < 5
event = (2 < abs(Y)) < 5
solution = Interval.open(2, 5) | Interval.open(-5, -2)
assert event.solve() == solution
# 2 <= abs(X) < 5
event = (2 <= abs(Y)) < 5
solution = Interval.Ropen(2, 5) | Interval.Lopen(-5, -2)
assert event.solve() == solution
# 2 < abs(X) <= 5
event = (2 < abs(Y)) <= 5
solution = Interval.Lopen(2, 5) | Interval.Ropen(-5, -2)
assert event.solve() == solution
# 2 <= abs(X) <= 5
event = (2 <= abs(Y)) <= 5
solution = Interval(2, 5) | Interval(-5, -2)
assert event.solve() == solution
# -2 < abs(X) < 5
event = (-2 < abs(Y)) < 5
solution = Interval.open(-5, 5)
assert event.solve() == solution
# # -2 <= abs(X) < 5
event = (-2 <= abs(Y)) < 5
solution = Interval.open(-5, 5)
assert event.solve() == solution
# -2 < abs(X) <= 5
event = (-2 < abs(Y)) <= 5
solution = Interval(-5, 5)
assert event.solve() == solution
# 2 <= abs(X) <= 5
event = (-2 <= abs(Y)) <= 5
solution = Interval(-5, 5)
assert event.solve() == solution
def test_Interval_in():
with pytest.raises(Exception):
Interval(3, 1)
assert 1 in Interval(0, 1)
assert 1 not in Interval.Ropen(0, 1)
assert 1 in Interval.Lopen(0, 1)
assert 0 in Interval(0, 1)
assert 0 not in Interval.Lopen(0, 1)
assert 0 in Interval.Ropen(0, 1)
assert inf not in Interval(-inf, inf)
assert -inf not in Interval(-inf, 0)
assert 10 in Interval(-inf, inf)
def test_event_inequality_parse():
assert (5 < (X < 10)) \
== ((5 < X) < 10) \
== EventInterval(X, Interval.open(5, 10))
assert (5 <= (X < 10)) \
== ((5 <= X) < 10) \
== EventInterval(X, Interval.Ropen(5, 10))
assert (5 < (X <= 10)) \
== ((5 < X) <= 10) \
== EventInterval(X, Interval.Lopen(5, 10))
assert (5 <= (X <= 10)) \
== ((5 <= X) <= 10) \
== EventInterval(X, Interval(5, 10))
# GOTCHA: This expression is syntactically equivalent to
# (5 < X) and (X < 10)
# Since and short circuits and 5 < X is not False,
# return value of expression is X < 10
assert (5 < X < 10) == (X < 10)
# Yields a finite set .
assert ((5 < X) < 5) == EventFiniteReal(X, EmptySet)
assert ((5 < X) <= 5) == EventFiniteReal(X, EmptySet)
assert ((5 <= X) < 5) == EventFiniteReal(X, EmptySet)
assert ((5 <= X) <= 5) == EventFiniteReal(X, FiniteReal(5))
# Negated single interval.
assert ~(5 < X) == (X <= 5)
assert ~(5 <= X) == (X < 5)
assert ~(X < 5) == (5 <= X)
assert ~(X <= 5) == (5 < X)
# Negated union of two intervals.
assert ~(5 < (X < 10)) \
== ~((5 < X) < 10) \
== (X <= 5) | (10 <= X)
assert ~(5 <= (X < 10)) \
== ~((5 <= X) < 10) \
== (X < 5) | (10 <= X)
assert ~(5 < (X <= 10)) \
== ~((5 < X) <= 10) \
== (X <= 5) | (10 < X)
assert ~(5 <= (X <= 10)) \
== ~((5 <= X) <= 10) \
== (X < 5) | (10 < X)
assert ~((10 < X) < 5) \
== ~(10 < (X < 5)) \
== EventInterval(X, Interval(-oo, oo))
# A complicated negated union.
assert ((~(X < 5)) < 10) \
== ((5 <= X) < 10) \
== EventInterval(X, Interval.Ropen(5, 10))
def test_solver_26_piecewise_one_expr_basic_event():
event = (Y**2)*(0 <= Y) < 2
assert event.solve() == Interval.Ropen(0, sympy.sqrt(2))
event = (0 <= Y)*(Y**2) < 2
assert event.solve() == Interval.Ropen(0, sympy.sqrt(2))
event = ((0 <= Y) < 5)*(Y < 1) << {1}
assert event.solve() == Interval.Ropen(0, 1)
event = ((0 <= Y) < 5)*(~(Y < 1)) << {1}
assert event.solve() == Interval.Ropen(1, 5)
event = 10*(0 <= Y) << {10}
assert event.solve() == Interval(0, oo)
event = 10*(0 <= Y) << {0}
assert event.solve() == Interval.Ropen(-oo, 0)
def test_condition():
model = model_no_latents()
GPA = Id('GPA')
model_condition = model.condition(GPA << {4} | GPA << {10})
assert len(model_condition.children) == 2
assert model_condition.children[0].support == Interval.Ropen(4, 5)
assert model_condition.children[1].support == Interval.Ropen(10, 11)
model_condition = model.condition((0 < GPA < 4))
assert len(model_condition.children) == 2
assert model_condition.children[0].support \
== model_condition.children[1].support
assert allclose(model_condition.children[0].logprob(GPA < 1),
model_condition.children[1].logprob(GPA < 1))
def test_product_condition_or_probabilithy_zero():
X = Id('X')
Y = Id('Y')
spe = ProductSPE([X >> norm(loc=0, scale=1), Y >> gamma(a=1)])
# Condition on event which has probability zero.
event = (X > 2) & (X < 2)
with pytest.raises(ValueError):
spe.condition(event)
assert spe.logprob(event) == -float('inf')
# Condition on event which has probability zero.
event = (Y < 0) | (Y < -1)
with pytest.raises(ValueError):
spe.condition(event)
assert spe.logprob(event) == -float('inf')
# Condition on an event where one clause has probability
# zero, yielding a single product.
spe_condition = spe.condition((Y < 0) | ((Log(X) >= 0) & (1 <= Y)))
assert isinstance(spe_condition, ProductSPE)
assert spe_condition.children[0].symbol == X
assert spe_condition.children[0].conditioned
assert spe_condition.children[0].support == Interval(1, oo)
assert spe_condition.children[1].symbol == Y
assert spe_condition.children[1].conditioned
assert spe_condition.children[0].support == Interval(1, oo)
# We have (X < 2) & ~(1 < exp(|3X**2|) is empty.
# Thus Y remains unconditioned,
# and X is partitioned into (-oo, 0) U (0, oo) with equal weight.
event = (Exp(abs(3 * X**2)) > 1) | ((Log(Y) < 0.5) & (X < 2))
spe_condition = spe.condition(event)
#
# The most concise representation of spe_condition is:
# (Product (Sum [.5 .5] X|X<0 X|X>0) Y)
assert isinstance(spe_condition, ProductSPE)
assert isinstance(spe_condition.children[0], SumSPE)
assert spe_condition.children[0].weights == (-log(2), -log(2))
assert spe_condition.children[0].children[0].conditioned
assert spe_condition.children[0].children[1].conditioned
assert spe_condition.children[0].children[0].support \
in [Interval.Ropen(-oo, 0), Interval.Lopen(0, oo)]
assert spe_condition.children[0].children[1].support \
in [Interval.Ropen(-oo, 0), Interval.Lopen(0, oo)]
assert spe_condition.children[0].children[0].support \
!= spe_condition.children[0].children[1].support
assert spe_condition.children[1].symbol == Y
assert not spe_condition.children[1].conditioned
def test_solver_21__ci_():
# 1 <= log(x**3 - 3*x + 3) < 5
# Can only be solved by numerical approximation of roots.
# https://www.wolframalpha.com/input/?i=1+%3C%3D+log%28x**3+-+3x+%2B+3%29+%3C+5
solution = Union(
Interval(
-1.777221448430427630375448631016427343692,
0.09418455242255462832154474245589911789464),
Interval.Ropen(
1.683036896007873002053903888560528225797,
5.448658707897512189124586716091172798465))
expr = Log(Y**3 - 3*Y + 3)
event = ((1 <= expr) & (expr < 5))
answer = event.solve()
assert isinstance(answer, Union)
assert len(answer.args) == 2
first = answer.args[0] if answer.args[0].a < 0 else answer.args[1]
second = answer.args[0] if answer.args[0].a > 0 else answer.args[1]
# Check first interval.
assert not first.left_open
assert not first.right_open
assert allclose(float(first.a), float(solution.args[0].a))
assert allclose(float(first.b), float(solution.args[0].b))
# Check second interval.
assert not second.left_open
assert second.right_open
assert allclose(float(second.a), float(solution.args[1].a))
assert allclose(float(second.b), float(solution.args[1].b))
def test_parse_21__ci_():
# 1 <= log(x**3 - 3*x + 3) < 5
# Can only be solved by numerical approximation of roots.
# https://www.wolframalpha.com/input/?i=1+%3C%3D+log%28x**3+-+3x+%2B+3%29+%3C+5
expr = Log(X**3 - 3*X + 3)
expr_prime = Log(Poly(Y, [3, -3, 0, 1]))
assert expr == expr_prime
assert ((1 <= expr) & (expr < 5)) \
== EventInterval(expr, Interval.Ropen(1, 5))
def test_Union_and():
x = (Interval(0, 1) | FR(1)) & (FN('a'))
assert x is EmptySet
x = (FN('x', b=True) | Interval(0, 1) | FR(1)) & (FN('a'))
assert x == FN('a')
x = (FN('x') | Interval(0, 1) | FR(1)) & (FN('a'))
assert x is EmptySet
x = (FN('x') | Interval.open(0, 1) | FR(7)) & (
(FN('x')) | FR(.5) | Interval(.75, 1.2))
assert x == Union(FR(.5), FN('x'), Interval.Ropen(.75, 1))
x = (FN('x') | Interval.open(0, 1) | FR(7)) & (FR(3))
assert x is EmptySet
x = (Interval.Lopen(-5, inf)) & (Interval(0, inf) | FR(inf))
assert x == Interval(0, inf)
x = (FR(1, 2) | Interval.Ropen(-inf, 0)) & Interval(0, inf)
assert x == FR(1, 2)
x = (FR(1, 12) | Interval(0, 5) | Interval(7, 10)) & Interval(4, 12)
assert x == Union(Interval(4, 5), Interval(7, 10), FR(12))
def test_parse_26_piecewise_one_expr_basic_event():
assert (Y**2)*(0 <= Y) == Piecewise(
[Poly(Y, [0, 0, 1])],
[EventInterval(Y, Interval(0, oo))])
assert (0 <= Y)*(Y**2) == Piecewise(
[Poly(Y, [0, 0, 1])],
[EventInterval(Y, Interval(0, oo))])
assert ((0 <= Y) < 5)*(Y < 1) == Piecewise(
[EventInterval(Y, Interval.Ropen(-oo, 1))],
[EventInterval(Y, Interval.Ropen(0, 5))],
)
assert ((0 <= Y) < 5)*(~(Y < 1)) == Piecewise(
[EventInterval(Y, Interval(1, oo))],
[EventInterval(Y, Interval.Ropen(0, 5))],
)
assert 10*(0 <= Y) == Poly(
EventInterval(Y, Interval(0, oo)),
[0, 10])
def test_FiniteReal_and():
assert FR(1) & FR(2) is EmptySet
assert FR(1, 2) & FR(2) == FR(2)
assert FR(1, 2) & FN('2') is EmptySet
assert FR(1, 2) & FN('2', b=True) is EmptySet
assert FR(1, 2) & Interval(0, 1) == FR(1)
assert FR(1, 2) & Interval.Ropen(0, 1) is EmptySet
assert FR(0, 2) & Interval(0, 1) == FR(0)
assert FR(0, 2) & Interval.Lopen(0, 1) is EmptySet
assert FR(-1, 1) & Interval(-10, 10) == FR(-1, 1)
assert FR(-1, 11) & Interval(-10, 10) == FR(-1)
def test_Union_or():
x = Interval(0, 1) | Interval(5, 6) | Interval(10, 11)
assert x == Union(Interval(0, 1), Interval(5, 6), Interval(10, 11))
x = Interval.Ropen(0, 1) | Interval.Lopen(1, 2) | Interval(10, 11)
assert x == Union(Interval.Ropen(0, 1), Interval.Lopen(1, 2),
Interval(10, 11))
x = Interval.Ropen(0, 1) | Interval.Lopen(1, 2) | Interval(10, 11) | FR(1)
assert x == Union(Interval(0, 2), Interval(10, 11))
x = (Interval.Ropen(0, 1) | Interval.Lopen(1, 2)) | (Interval(10, 11)
| FR(1))
assert x == Union(Interval(0, 2), Interval(10, 11))
x = FR(1) | ((Interval.Ropen(0,1) | Interval.Lopen(1,2) | FR(10,13)) \
| (Interval.Lopen(10,11) | FR(7)))
assert x == Union(Interval(0, 2), Interval(10, 11), FR(13, 7))
assert 2 in x
assert 13 in x
x = FN('f') | (FR(1) | FN('g', b=True))
assert x == Union(FR(1), FN('g', b=True))
assert 'w' in x
assert 'g' not in x
def test_FiniteReal_or():
assert FR(1) | FR(2) == FR(1, 2)
assert FR(1, 2) | FR(2) == FR(1, 2)
assert FR(1, 2) | FN('2') == Union(FR(1, 2), FN('2'))
assert FR(1, 2) | Interval(0, 1) == Union(Interval(0, 1), FR(2))
assert FR(1, 2) | Interval.Ropen(0, 1) == Union(Interval(0, 1), FR(2))
assert FR(0, 1, 2) | Interval.open(0, 1) == Union(Interval(0, 1), FR(2))
assert FR(0, 2) | Interval.Lopen(0, 1) == Union(Interval(0, 1), FR(2))
assert FR(0, 2) | Interval.Lopen(2.5, 10) == Union(Interval.Lopen(2.5, 10),
FR(0, 2))
assert FR(-1, 1) | Interval(-10, 10) == Interval(-10, 10)
assert FR(-1, 11) | Interval(-10, 10) == Union(Interval(-10, 10), FR(11))
def test_union_intervals():
assert union_intervals([Interval(0, 1),
Interval(2, 3),
Interval(1, 2)]) == [Interval(0, 3)]
assert union_intervals(
[Interval.open(0, 1),
Interval(2, 3), Interval(1, 2)]) == [Interval.Lopen(0, 3)]
assert union_intervals(
[Interval.open(0, 1),
Interval(2, 3),
Interval.Lopen(1, 2)]) == [Interval.open(0, 1),
Interval.Lopen(1, 3)]
assert union_intervals(
[Interval.open(0, 1),
Interval.Ropen(0, 3),
Interval.Lopen(1, 2)]) == [Interval.Ropen(0, 3)]
assert union_intervals(
[Interval.open(-2, -1),
Interval.Ropen(0, 3),
Interval.Lopen(1,
2)]) == [Interval.open(-2, -1),
Interval.Ropen(0, 3)]
def test_event_containment_real():
assert (X << Interval(0, 10)) == EventInterval(X, Interval(0, 10))
for values in [FiniteReal(0, 10), [0, 10], {0, 10}]:
assert (X << values) == EventFiniteReal(X, FiniteReal(0, 10))
# with pytest.raises(ValueError):
# X << {1, None}
assert X << {1, 2} == EventFiniteReal(X, {1, 2})
assert ~(X << {1, 2}) == EventOr([
EventInterval(X, Interval.Ropen(-oo, 1)),
EventInterval(X, Interval.open(1, 2)),
EventInterval(X, Interval.Lopen(2, oo)),
])
# https://github.com/probcomp/sum-product-dsl/issues/22
# and of EventBasic does not yet perform simplifications.
assert ~(~(X << {1, 2})) == \
((1 <= X) & ((X <= 1) | (2 <= X)) & (X <= 2))
def test_solver_23_reciprocal_range():
solution = Interval.Ropen(-1, -Rat(1, 3))
event = ((-3 < 1/Y) <= -1)
assert event.solve() == solution
solution = Interval.open(0, Rat(1, 3))
event = ((-3 < 1/(2*Y-1)) < -1)
assert event.solve() == solution
solution = Interval.open(-1 / sympy.sqrt(3), 1 / sympy.sqrt(3))
event = ((-3 < 1/(2*(abs(Y)**2)-1)) <= -1)
assert event.solve() == solution
solution = Union(
Interval.open(-1 / sympy.sqrt(3), 0),
Interval.open(0, 1 / sympy.sqrt(3)))
event = ((-3 < 1/(2*(abs(Y)**2)-1)) < -1)
assert event.solve() == solution
def test_Interval_invert():
assert ~(Interval(0, 1)) == Union(Interval.Ropen(-inf, 0),
Interval.Lopen(1, inf))
assert ~(Interval.open(0, 1)) == Union(Interval(-inf, 0), Interval(1, inf))
assert ~(Interval.Lopen(0, 1)) == Union(Interval(-inf, 0),
Interval.Lopen(1, inf))
assert ~(Interval.Ropen(0, 1)) == Union(Interval.Ropen(-inf, 0),
Interval(1, inf))
assert ~(Interval(-inf, inf)) is EmptySet
assert ~(Interval(3, inf)) == Interval.Ropen(-inf, 3)
assert ~(Interval.open(3, inf)) == Interval(-inf, 3)
assert ~(Interval.Lopen(3, inf)) == Interval(-inf, 3)
assert ~(Interval.Ropen(3, inf)) == Interval.Ropen(-inf, 3)
assert ~(Interval(-inf, 3)) == Interval.Lopen(3, inf)
assert ~(Interval.open(-inf, 3)) == Interval(3, inf)
assert ~(Interval.Lopen(-inf, 3)) == Interval.Lopen(3, inf)
assert ~(Interval.Ropen(-inf, 3)) == Interval(3, inf)
assert ~(Interval.open(-inf, inf)) is EmptySet
def test_product_condition_basic():
X = Id('X')
Y = Id('Y')
spe = ProductSPE([X >> norm(loc=0, scale=1), Y >> gamma(a=1)])
# Condition on (X > 0) and ((X > 0) | (Y < 0))
# where the second clause reduces to first as Y < 0
# has probability zero.
for event in [(X > 0), (X > 0) | (Y < 0)]:
dX = spe.condition(event)
assert isinstance(dX, ProductSPE)
assert dX.children[0].symbol == Id('X')
assert dX.children[0].conditioned
assert dX.children[0].support == Interval.open(0, oo)
assert dX.children[1].symbol == Id('Y')
assert not dX.children[1].conditioned
assert dX.children[1].Fl == 0
assert dX.children[1].Fu == 1
# Condition on (Y < 0.5)
dY = spe.condition(Y < 0.5)
assert isinstance(dY, ProductSPE)
assert dY.children[0].symbol == Id('X')
assert not dY.children[0].conditioned
assert dY.children[1].symbol == Id('Y')
assert dY.children[1].conditioned
assert dY.children[1].support == Interval.Ropen(0, 0.5)
# Condition on (X > 0) & (Y < 0.5)
dXY_and = spe.condition((X > 0) & (Y < 0.5))
assert isinstance(dXY_and, ProductSPE)
assert dXY_and.children[0].symbol == Id('X')
assert dXY_and.children[0].conditioned
assert dXY_and.children[0].support == Interval.open(0, oo)
assert dXY_and.children[1].symbol == Id('Y')
assert dXY_and.children[1].conditioned
assert dXY_and.children[1].support == Interval.Ropen(0, 0.5)
# Condition on (X > 0) | (Y < 0.5)
event = (X > 0) | (Y < 0.5)
dXY_or = spe.condition((X > 0) | (Y < 0.5))
assert isinstance(dXY_or, SumSPE)
assert all(isinstance(d, ProductSPE) for d in dXY_or.children)
assert allclose(dXY_or.logprob(X > 0), dXY_or.weights[0])
samples = dXY_or.sample(100, prng=numpy.random.RandomState(1))
assert all(event.evaluate(sample) for sample in samples)
# Condition on a disjoint union with one term in second clause.
dXY_disjoint_one = spe.condition((X > 0) & (Y < 0.5) | (X <= 0))
assert isinstance(dXY_disjoint_one, SumSPE)
component_0 = dXY_disjoint_one.children[0]
assert component_0.children[0].symbol == Id('X')
assert component_0.children[0].conditioned
assert component_0.children[0].support == Interval.open(0, oo)
assert component_0.children[1].symbol == Id('Y')
assert component_0.children[1].conditioned
assert component_0.children[1].support == Interval.Ropen(0, 0.5)
component_1 = dXY_disjoint_one.children[1]
assert component_1.children[0].symbol == Id('X')
assert component_1.children[0].conditioned
assert component_1.children[0].support == Interval(-oo, 0)
assert component_1.children[1].symbol == Id('Y')
assert not component_1.children[1].conditioned
# Condition on a disjoint union with two terms in each clause
dXY_disjoint_two = spe.condition((X > 0) & (Y < 0.5)
| ((X <= 0) & ~(Y < 3)))
assert isinstance(dXY_disjoint_two, SumSPE)
component_0 = dXY_disjoint_two.children[0]
assert component_0.children[0].symbol == Id('X')
assert component_0.children[0].conditioned
assert component_0.children[0].support == Interval.open(0, oo)
assert component_0.children[1].symbol == Id('Y')
assert component_0.children[1].conditioned
assert component_0.children[1].support == Interval.Ropen(0, 0.5)
component_1 = dXY_disjoint_two.children[1]
assert component_1.children[0].symbol == Id('X')
assert component_1.children[0].conditioned
assert component_1.children[0].support == Interval(-oo, 0)
assert component_1.children[1].symbol == Id('Y')
assert component_1.children[1].conditioned
assert component_1.children[1].support == Interval(3, oo)
# Some various conditioning.
spe.condition((X > 0) & (Y < 0.5) | ((X <= 1) | ~(Y < 3)))
spe.condition((X > 0) & (Y < 0.5) | ((X <= 1) & (Y < 3)))
def test_poisson():
X = Id('X')
spe = X >> poisson(mu=5)
a = spe.logprob((1 <= X) <= 7)
b = spe.logprob(X << {1, 2, 3, 4, 5, 6, 7})
c = logsumexp([spe.logprob(X << {i}) for i in range(1, 8)])
assert allclose(a, b)
assert allclose(a, c)
assert allclose(b, c)
spe_condition = spe.condition(10 <= X)
assert spe_condition.conditioned
assert spe_condition.support == Range(10, oo)
assert spe_condition.logZ == logdiffexp(0, spe.logprob(X <= 9))
assert allclose(spe_condition.logprob(X <= 10),
spe_condition.logprob(X << {10}))
assert allclose(spe_condition.logprob(X <= 10),
spe_condition.logpdf({X: 10}))
samples = spe_condition.sample(100)
assert all(10 <= s[X] for s in samples)
# Unify X = 5 with left interval to make one distribution.
event = ((1 <= X) < 5) | ((3 * X + 1) << {16})
spe_condition = spe.condition(event)
assert isinstance(spe_condition, DiscreteLeaf)
assert spe_condition.conditioned
assert spe_condition.xl == 1
assert spe_condition.xu == 5
assert spe_condition.support == Range(1, 5)
samples = spe_condition.sample(100, prng=numpy.random.RandomState(1))
assert all(event.evaluate(s) for s in samples)
# Ignore X = 14/3 as a probability zero condition.
spe_condition = spe.condition(((1 <= X) < 5) | (3 * X + 1) << {15})
assert isinstance(spe_condition, DiscreteLeaf)
assert spe_condition.conditioned
assert spe_condition.xl == 1
assert spe_condition.xu == 4
assert spe_condition.support == Interval.Ropen(1, 5)
# Make a mixture of two components.
spe_condition = spe.condition(((1 <= X) < 5) | (3 * X + 1) << {22})
assert isinstance(spe_condition, SumSPE)
xl = spe_condition.children[0].xl
idx0 = 0 if xl == 7 else 1
idx1 = 1 if xl == 7 else 0
assert spe_condition.children[idx1].conditioned
assert spe_condition.children[idx1].xl == 1
assert spe_condition.children[idx1].xu == 4
assert spe_condition.children[idx0].conditioned
assert spe_condition.children[idx0].xl == 7
assert spe_condition.children[idx0].xu == 7
assert spe_condition.children[idx0].support == Range(7, 7)
# Condition on probability zero event.
with pytest.raises(ValueError):
spe.condition(((-3 <= X) < 0) | (3 * X + 1) << {20})
# Condition on FiniteReal contiguous.
spe_condition = spe.condition(X << {1, 2, 3})
assert spe_condition.xl == 1
assert spe_condition.xu == 3
assert allclose(spe_condition.logprob((1 <= X) <= 3), 0)
# Condition on single point.
assert allclose(0, spe.condition(X << {2}).logprob(X << {2}))
# Constrain.
with pytest.raises(Exception):
spe.constrain({X: -1})
with pytest.raises(Exception):
spe.constrain({X: .5})
spe_constrain = spe.constrain({X: 10})
assert allclose(spe_constrain.prob(X << {0, 10}), 1)
def test_FiniteReal_invert():
assert ~FR(1) == Union(Interval.Ropen(-inf, 1), Interval.Lopen(1, inf))
assert ~(FR(0, -1)) == Union(Interval.Ropen(-inf, -1),
Interval.open(-1, 0), Interval.Lopen(0, inf))
def test_Interval_or():
assert Interval(0, 1) | Interval(-1, 1) == Interval(-1, 1)
assert Interval(0, 2) | Interval.open(0, 1) == Interval(0, 2)
assert Interval.Lopen(0, 1) | Interval(-1, 1) == Interval(-1, 1)
assert Interval.Ropen(0, 1) | Interval(-1, 1) == Interval(-1, 1)
assert Interval(0, 1) | Interval(1, 2) == Interval(0, 2)
assert Interval.open(0, 1) | Interval(0, 1) == Interval(0, 1)
assert Interval(0, 1) | Interval(0, .5) == Interval(0, 1)
assert Interval.Lopen(0, 1) | Interval(1, 2) == Interval.Lopen(0, 2)
assert Interval.Ropen(-1, 0) | Interval.Ropen(0, 1) == Interval.Ropen(
-1, 1)
assert Interval.Ropen(0, 1) | Interval.Ropen(-1, 0) == Interval.Ropen(
-1, 1)
assert Interval.Lopen(0, 1) | Interval.Lopen(1, 2) == Interval.Lopen(0, 2)
assert Interval.Lopen(0, 1) | Interval.Ropen(1, 2) == Interval.open(0, 2)
assert Interval.open(0, 2) | Interval(0, 1) == Interval.Ropen(0, 2)
assert Interval.open(0, 1) | Interval.Ropen(-1, 0) == Union(
Interval.open(0, 1), Interval.Ropen(-1, 0))
assert Interval(1, 2) | Interval.Ropen(0, 1) == Interval(0, 2)
assert Interval.Ropen(0, 1) | Interval(1, 2) == Interval(0, 2)
assert Interval.open(0, 1) | Interval(1, 2) == Interval.Lopen(0, 2)
assert Interval.Ropen(0, 1) | Interval.Ropen(1, 2) == Interval.Ropen(0, 2)
assert Interval(1, 2) | Interval.open(0, 1) == Interval.Lopen(0, 2)
assert Interval(1, 2) | Interval.Lopen(0, 1) == Interval.Lopen(0, 2)
assert Interval(1, 2) | Interval.Ropen(0, 1) == Interval(0, 2)
assert Interval.open(0, 1) | Interval(1, 2) == Interval.Lopen(0, 2)
assert Interval.Lopen(0, 1) | Interval(1, 2) == Interval.Lopen(0, 2)
assert Interval.Ropen(0, 1) | Interval(1, 2) == Interval(0, 2)
assert Interval(0, 2) | Interval.open(0.5, 2.5) == Interval.Ropen(0, 2.5)
assert Interval.open(0, 2) | Interval.open(0, 2.5) == Interval.open(0, 2.5)
assert Interval.open(0, 2.5) | Interval.open(0, 2) == Interval.open(0, 2.5)
assert Interval.open(0, 1) | Interval.open(1, 2) == Union(
Interval.open(0, 1), Interval.open(1, 2))
assert Interval.Ropen(0, 2) | Interval.Lopen(0.5, 2.5) == Interval(0, 2.5)
assert Interval.open(0, 2) | Interval(0.5, 2.5) == Interval.Lopen(0, 2.5)
assert Interval.Lopen(0, 2) | Interval.Ropen(0, 2) == Interval(0, 2)
assert Interval(0, 1) | Interval(2, 3) == Union(Interval(0, 1),
Interval(2, 3))
assert Interval(2, 3) | Interval.Ropen(0, 1) == Union(
Interval(2, 3), Interval.Ropen(0, 1))
assert Interval.Lopen(0, 1) | Interval(1, 2) == Interval.Lopen(0, 2)
assert Interval(-10, 10) | FR(-1, 1) == Interval(-10, 10)
assert Interval(-10, 10) | FR(-1, 11) == Union(Interval(-10, 10), FR(11))
assert Interval(-inf, -3, right_open=True) | Interval(
-inf, inf) == Interval(-inf, inf)
def test_Interval_and():
assert Interval(0, 1) & Interval(-1, 1) == Interval(0, 1)
assert Interval(0, 2) & Interval.open(0, 1) == Interval.open(0, 1)
assert Interval.Lopen(0, 1) & Interval(-1, 1) == Interval.Lopen(0, 1)
assert Interval.Ropen(0, 1) & Interval(-1, 1) == Interval.Ropen(0, 1)
assert Interval(0, 1) & Interval(1, 2) == FR(1)
assert Interval.Lopen(0, 1) & Interval(1, 2) == FR(1)
assert Interval.Ropen(0, 1) & Interval(1, 2) is EmptySet
assert Interval.Lopen(0, 1) & Interval.Lopen(1, 2) is EmptySet
assert Interval(1, 2) & Interval.Lopen(0, 1) == FR(1)
assert Interval(1, 2) & Interval.open(0, 1) is EmptySet
assert Interval(0, 2) & Interval.Lopen(0.5, 2.5) == Interval.Lopen(0.5, 2)
assert Interval.Ropen(0, 2) & Interval.Lopen(0.5, 2.5) == Interval.open(
0.5, 2)
assert Interval.open(0, 2) & Interval(0.5, 2.5) == Interval.Ropen(0.5, 2)
assert Interval.Lopen(0, 2) & Interval.Ropen(0, 2) == Interval.open(0, 2)
assert Interval(0, 1) & Interval(2, 3) is EmptySet
assert Interval(2, 3) & Interval(0, 1) is EmptySet
assert Interval.open(0, 1) & Interval.open(0, 1) == Interval.open(0, 1)
assert Interval.Ropen(-inf, -3) & Interval(-inf, inf) == Interval.Ropen(
-inf, -3)
assert Interval(-inf, inf) & Interval.Ropen(-inf, -3) == Interval.Ropen(
-inf, -3)
assert Interval(0, inf) & (Interval.Lopen(-5, inf)) == Interval(0, inf)
assert Interval.Lopen(0, 1) & Interval.Ropen(0, 1) == Interval.open(0, 1)
assert Interval.Ropen(0, 1) & Interval.Lopen(0, 1) == Interval.open(0, 1)
assert Interval.Ropen(0, 5) & Interval.Ropen(-inf, 5) == Interval.Ropen(
0, 5)
def test_solver_5_ropen():
# (2*x+10 < 4) & (x + 10 >= 3)
solution = Interval.Ropen(3-10, (4-10)/2)
event = ((2*Y + 10) < 4) & (Y + 10 >= 3)
answer = event.solve()
assert answer == solution
def test_solver_16():
# (x**(1/7))**4 < 9
solution = Interval.Ropen(0, 27*sympy.sqrt(3))
event = ((Y**Rat(1,7)))**4 < 9
answer = event.solve()
assert answer == solution