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_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_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_solver_24_negative_power_Rat():
# Case 1.
event = Y**Rat(-1, 3) < 6
assert event.solve() == Interval.Lopen(Rat(1, 216), oo)
# Case 2.
event = (-1 < Y**Rat(-1, 3)) < 6
assert event.solve() == Interval.Lopen(Rat(1, 216), oo)
# Case 3.
event = 5 <= Y**Rat(-1, 3)
assert event.solve() == Interval.Lopen(0, Rat(1, 125))
# Case 4.
event = (5 <= Y**Rat(-1, 3)) < 6
assert event.solve() == Interval.Lopen(Rat(1, 216), Rat(1, 125))
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_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_24_negative_power_integer():
# Case 1.
event = Y**(-3) < 6
assert event.solve() == Union(
Interval.open(-oo, 0),
Interval.open(6**Rat(-1, 3), oo))
# Case 2.
event = (-1 < Y**(-3)) < 6
assert event.solve() == Union(
Interval.open(-oo, -1),
Interval.open(6**Rat(-1, 3), oo))
# Case 3.
event = 5 <= Y**(-3)
assert event.solve() == Interval.Lopen(0, 5**Rat(-1, 3))
# Case 4.
event = (5 <= Y**(-3)) < 6
assert event.solve() == Interval.Lopen(6**Rat(-1, 3), 5**Rat(-1, 3))
def test_union_intervals_finite():
assert union_intervals_finite([
Interval.open(0,1),
Interval(2,3),
Interval.Lopen(1,2)
], FR(1)) \
== [Interval.Lopen(0, 3)]
assert union_intervals_finite([
Interval.open(0,1),
Interval.open(2, 3),
Interval.open(1,2)
], FR(1, 3)) \
== [Interval.open(0, 2), Interval.Lopen(2, 3)]
assert union_intervals_finite([
Interval.open(0,1),
Interval.open(1, 3),
Interval.open(11,15)
], FR(1, -11, -19, 3)) \
== [Interval.Lopen(0, 3), Interval.open(11,15), FR(-11, -19)]
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_solver_23_reciprocal_gte():
for c in [1, 3]:
# Positive
# 10 < 1 / X
solution = Interval.open(0, Rat(c, 10))
event = 10 < (c / Y)
assert event.solve() == solution
# 10 <= 1 / X
solution = Interval.Lopen(0, Rat(c, 10))
event = 10 <= (c / Y)
assert event.solve() == solution
# Negative
# -10 < 1 / X
solution = Interval.Lopen(0, oo) | Interval.open(-oo, -Rat(c, 10))
event = -10 < (c / Y)
assert event.solve() == solution
# -10 <= 1 / X
solution = Interval.Lopen(0, oo) | Interval.Lopen(-oo, -Rat(c, 10))
event = -10 <= (c / Y)
assert event.solve() == solution
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_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_19():
# 3*(x**(1/7))**4 - 3*(x**(1/7))**2 <= 9
# or || 3*(x**(1/7))**4 - 3*(x**(1/7))**2 > 11
solution = Union(
Interval(0, (Rat(1, 2) + sympy.sqrt(13)/2)**(Rat(7, 2))),
Interval.open((Rat(1,2) + sympy.sqrt(141)/6)**(Rat(7, 2)), oo))
Z = Y**(Rat(1, 7))
expr = 3*Z**4 - 3*Z**2
event = (expr <= 9) | (expr > 11)
answer = event.solve()
assert answer == solution
interval = (~event).solve()
assert interval == Interval.Lopen(
solution.args[0].right,
solution.args[1].left)
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_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_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_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_lopen():
# (2*x + 10 < 4) & (x + 10 >= 3)
solution =Interval.Lopen(3-10, (4-10)/2)
event = ((2*Y + 10) <= 4) & (Y + 10 > 3)
answer = event.solve()
assert answer == solution