def test_lognormal():
    mean = Symbol('mu', real=True, finite=True)
    std = Symbol('sigma', positive=True, real=True, finite=True)
    X = LogNormal('x', mean, std)
    # The sympy integrator can't do this too well
    #assert E(X) == exp(mean+std**2/2)
    #assert variance(X) == (exp(std**2)-1) * exp(2*mean + std**2)

    # Right now, only density function and sampling works
    # Test sampling: Only e^mean in sample std of 0
    for i in range(3):
        X = LogNormal('x', i, 0)
        assert S(sample(X)) == N(exp(i))
    # The sympy integrator can't do this too well
    #assert E(X) ==

    mu = Symbol("mu", real=True)
    sigma = Symbol("sigma", positive=True)

    X = LogNormal('x', mu, sigma)
    assert density(X)(x) == (sqrt(2)*exp(-(-mu + log(x))**2
                                    /(2*sigma**2))/(2*x*sqrt(pi)*sigma))

    X = LogNormal('x', 0, 1)  # Mean 0, standard deviation 1
    assert density(X)(x) == sqrt(2)*exp(-log(x)**2/2)/(2*x*sqrt(pi))

def test_Sample():
    X = Die(6)
    Y = Normal(0,1)
    z = Symbol('z')

    assert sample(X) in [1,2,3,4,5,6]
    assert sample(X+Y).is_Float

    P(X+Y>0, Y<0, numsamples=10).is_number
    assert E(X+Y, numsamples=10).is_number
    assert variance(X+Y, numsamples=10).is_number

    raises(ValueError, lambda: P(Y>z, numsamples=5))

    assert P(sin(Y)<=1, numsamples=10) == 1
    assert P(sin(Y)<=1, cos(Y)<1, numsamples=10) == 1

    # Make sure this doesn't raise an error
    E(Sum(1/z**Y, (z,1,oo)), Y>2, numsamples=3)

def test_prefab_sampling():
    N = Normal('X', 0, 1)
    L = LogNormal('L', 0, 1)
    E = Exponential('Ex', 1)
    P = Pareto('P', 1, 3)
    W = Weibull('W', 1, 1)
    U = Uniform('U', 0, 1)
    B = Beta('B', 2, 5)
    G = Gamma('G', 1, 3)

    variables = [N, L, E, P, W, U, B, G]
    niter = 10
    for var in variables:
        for i in xrange(niter):
            assert sample(var) in var.pspace.domain.set

def test_sample():
    z = Symbol('z')
    Z = ContinuousRV(z, exp(-z), set=Interval(0, oo))
    assert sample(Z) in Z.pspace.domain.set
    sym, val = Z.pspace.sample().items()[0]
    assert sym == Z and val in Interval(0, oo)

def test_given():
    X = Die('X', 6)
    assert density(X, X > 5) == {S(6): S(1)}
    assert where(X > 2, X > 5).as_boolean() == Eq(X.symbol, 6)
    assert sample(X, X > 5) == 6

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