def test_given():
    X = Normal('X', 0, 1)
    Y = Normal('Y', 0, 1)
    A = given(X, True)
    B = given(X, Y > 2)

    assert X == A == B

def test_dependent_finite():
    X, Y = Die('X'), Die('Y')
    # Dependence testing requires symbolic conditions which currently break
    # finite random variables
    assert dependent(X, Y + X)

    XX, YY = given(Tuple(X, Y), X + Y > 5)  # Create a dependency
    assert dependent(XX, YY)

def test_ContinuousDomain():
    X = Normal('x', 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, lambda: where(sin(X) > 1))

    Y = given(X, X >= 0)

    assert Y.pspace.domain.set == Interval(0, oo)

def test_conditional_1d():
    X = Normal('x', 0, 1)
    Y = given(X, X >= 0)

    assert density(Y) == 2 * density(X)

    assert Y.pspace.domain.set == Interval(0, oo)
    assert E(Y) == sqrt(2) / sqrt(pi)

    assert E(X**2) == E(Y**2)

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)

    with raises(TypeError):
        XX = given(X, X+3)

def test_dependence():
    X, Y = Die('X'), Die('Y')
    assert independent(X, 2*Y)
    assert not dependent(X, 2*Y)

    X, Y = Normal('X', 0, 1), Normal('Y', 0, 1)
    assert independent(X, Y)
    assert dependent(X, 2*X)

    # Create a dependency
    XX, YY = given(Tuple(X, Y), Eq(X + Y, 3))
    assert dependent(XX, YY)

def test_random_parameters_given():
    mu = Normal('mu', 2, 3)
    meas = Normal('T', mu, 1)
    assert given(meas, Eq(mu, 5)) == Normal('T', 5, 1)