def test_domains():
x, y = symbols('x y')
X, Y= Die(6, symbol=x), Die(6, symbol=y)
# Domains
d = Where(X>Y)
assert d.condition == (x > y)
d = Where(And(X>Y, Y>3))
assert d.as_boolean() == Or(And(Eq(x,5), Eq(y,4)), And(Eq(x,6), Eq(y,5)),
And(Eq(x,6), Eq(y,4)))
assert len(d.elements) == 3
assert len(pspace(X+Y).domain.elements) == 36
Z = Die(4, symbol=x)
raises(ValueError, "P(X>Z)") # Two domains with same internal symbol
pspace(X+Y).domain.set == FiniteSet(1,2,3,4,5,6)**2
assert Where(X>3).set == FiniteSet(4,5,6)
assert X.pspace.domain.dict == FiniteSet(
Dict({X.symbol:i}) for i in range(1,7))
assert Where(X>Y).dict == FiniteSet(Dict({X.symbol:i, Y.symbol:j})
for i in range(1,7) for j in range(1,7) if i>j)
def test_ContinuousDomain():
X = Normal(0,1)
assert Where(X**2<=1).set == Interval(-1,1)
assert Where(X**2<=1).symbol == X.symbol
Where(And(X**2<=1, X>=0)).set == Interval(0,1)
raises(ValueError, "Where(sin(X)>1)")
Y = Given(X, X>=0)
assert Y.pspace.domain.set == Interval(0, oo)
def test_RandomDomain():
from sympy.stats import Normal, Die, Exponential, pspace, Where
X = Normal(0, 1, symbol=Symbol('x1'))
assert str(Where(X > 0)) == "Domain: 0 < x1"
D = Die(6, symbol=Symbol('d1'))
assert str(Where(D > 4)) == "Domain: Or(d1 == 5, d1 == 6)"
A = Exponential(1, symbol=Symbol('a'))
B = Exponential(1, symbol=Symbol('b'))
assert str(pspace(Tuple(A, B)).domain) == "Domain: And(0 <= a, 0 <= b)"
def test_latex_RandomDomain():
from sympy.stats import Normal, Die, Exponential, pspace, Where
X = Normal(0, 1, symbol=Symbol('x1'))
assert latex(Where(X > 0)) == "Domain: 0 < x_{1}"
D = Die(6, symbol=Symbol('d1'))
assert latex(Where(D > 4)) == r"Domain: d_{1} = 5 \vee d_{1} = 6"
A = Exponential(1, symbol=Symbol('a'))
B = Exponential(1, symbol=Symbol('b'))
assert latex(pspace(Tuple(A,
B)).domain) == "Domain: 0 \leq a \wedge 0 \leq b"
def test_domains():
x, y = symbols('x y')
X, Y = Die(6, symbol=x), Die(6, symbol=y)
# Domains
d = Where(X > Y)
assert d.condition == (x > y)
d = Where(And(X > Y, Y > 3))
assert d.as_boolean() == Or(And(Eq(x, 5), Eq(y,
4)), And(Eq(x, 6), Eq(y, 5)),
And(Eq(x, 6), Eq(y, 4)))
assert len(d.elements) == 3
assert len(pspace(X + Y).domain.elements) == 36
Z = Die(4, symbol=x)
raises(ValueError, "P(X>Z)") # Two domains with same internal symbol
pspace(X + Y).domain.set == FiniteSet(1, 2, 3, 4, 5, 6)**2
assert Where(X > 3).set == FiniteSet(4, 5, 6)
assert X.pspace.domain.dict == FiniteSet(
Dict({X.symbol: i}) for i in range(1, 7))
assert Where(X > Y).dict == FiniteSet(
Dict({
X.symbol: i,
Y.symbol: j
}) for i in range(1, 7) for j in range(1, 7) if i > j)
def test_exponential():
rate = Symbol('lambda', positive=True, real=True, bounded=True)
X = Exponential(rate)
assert E(X) == 1/rate
assert Var(X) == 1/rate**2
assert Skewness(X) == 2
assert P(X>0) == S(1)
assert P(X>1) == exp(-rate)
assert P(X>10) == exp(-10*rate)
assert Where(X<=1).set == Interval(0,1)
def test_dice():
X, Y, Z = Die(6), Die(6), Die(6)
a, b = symbols('a b')
assert E(X) == 3 + S.Half
assert Var(X) == S(35) / 12
assert E(X + Y) == 7
assert E(X + X) == 7
assert E(a * X + b) == a * E(X) + b
assert Var(X + Y) == Var(X) + Var(Y)
assert Var(X + X) == 4 * Var(X)
assert Covar(X, Y) == S.Zero
assert Covar(X, X + Y) == Var(X)
assert Density(Eq(cos(X * S.Pi), 1))[True] == S.Half
assert P(X > 3) == S.Half
assert P(2 * X > 6) == S.Half
assert P(X > Y) == S(5) / 12
assert P(Eq(X, Y)) == P(Eq(X, 1))
assert E(X, X > 3) == 5
assert E(X, Y > 3) == E(X)
assert E(X + Y, Eq(X, Y)) == E(2 * X)
assert E(X + Y - Z, 2 * X > Y + 1) == S(49) / 12
assert P(X > 3, X > 3) == S.One
assert P(X > Y, Eq(Y, 6)) == S.Zero
assert P(Eq(X + Y, 12)) == S.One / 36
assert P(Eq(X + Y, 12), Eq(X, 6)) == S.One / 6
assert Density(X + Y) == Density(Y + Z) != Density(X + X)
d = Density(2 * X + Y**Z)
assert d[S(22)] == S.One / 108 and d[S(4100)] == S.One / 216 and S(
3130) not in d
assert pspace(X).domain.as_boolean() == Or(
*[Eq(X.symbol, i) for i in [1, 2, 3, 4, 5, 6]])
assert Where(X > 3).set == FiniteSet(4, 5, 6)
def test_where():
X, Y = Die(), Die()
Z = Normal(0, 1)
assert Where(Z**2 <= 1).set == Interval(-1, 1)
assert Where(Z**2 <= 1).as_boolean() == Interval(-1,
1).as_relational(Z.symbol)
assert Where(And(X > Y,
Y > 4)).as_boolean() == And(Eq(X.symbol, 6),
Eq(Y.symbol, 5))
assert len(Where(X < 3).set) == 2
assert 1 in Where(X < 3).set
X, Y = Normal(0, 1), Normal(0, 1)
assert Where(And(X**2 <= 1, X >= 0)).set == Interval(0, 1)
XX = Given(X, And(X**2 <= 1, X >= 0))
assert XX.pspace.domain.set == Interval(0, 1)
assert XX.pspace.domain.as_boolean() == And(0 <= X.symbol,
X.symbol**2 <= 1)
raises(TypeError, "XX = Given(X, X+3)")
def test_given():
X = Die(6)
Density(X, X > 5) == {S(6): S(1)}
Where(X > 2, X > 5).as_boolean() == Eq(X.symbol, 6)
Sample(X, X > 5) == 6