def test_cdf():
X = Normal('x', 0, 1)
d = cdf(X)
assert P(X < 1) == d(1)
assert d(0) == Rational(1, 2)
d = cdf(X, X > 0) # given X>0
assert d(0) == 0
Y = Exponential('y', 10)
d = cdf(Y)
assert d(-5) == 0
assert P(Y > 3) == 1 - d(3)
pytest.raises(ValueError, lambda: cdf(X + Y))
Z = Exponential('z', 1)
f = cdf(Z)
z = Symbol('z')
assert f(z) == Piecewise((1 - exp(-z), z >= 0), (0, True))
U = Uniform('x', 3, 5)
u = cdf(U)
assert u(z) == z/2 - Rational(3, 2)
def test_RandomDomain():
X = Normal('x1', 0, 1)
assert str(where(X > 0)) == "Domain: (0 < x1) & (x1 < oo)"
D = Die('d1', 6)
assert str(where(D > 4)) == "Domain: (Eq(d1, 5)) | (Eq(d1, 6))"
A = Exponential('a', 1)
B = Exponential('b', 1)
assert str(pspace(Tuple(A, B)).domain) == "Domain: (0 <= a) & (0 <= b) & (a < oo) & (b < oo)"
def test_RandomDomain():
X = Normal('x1', 0, 1)
assert str(where(X > 0)) == "Domain: And(0 < x1, x1 < oo)"
D = Die('d1', 6)
assert str(where(D > 4)) == "Domain: Or(Eq(d1, 5), Eq(d1, 6))"
A = Exponential('a', 1)
B = Exponential('b', 1)
assert str(pspace(Tuple(
A, B)).domain) == "Domain: And(0 <= a, 0 <= b, a < oo, b < oo)"
def test_input_value_assertions():
a, b = symbols('a b')
p, q = symbols('p q', positive=True)
pytest.raises(ValueError, lambda: Normal('x', 3, 0))
pytest.raises(ValueError, lambda: Normal('x', a, b))
Normal('X', a, p) # No error raised
pytest.raises(ValueError, lambda: Exponential('x', a))
Exponential('Ex', p) # No error raised
for fn in [Pareto, Weibull, Beta, Gamma]:
pytest.raises(ValueError, lambda: fn('x', a, p))
pytest.raises(ValueError, lambda: fn('x', p, a))
fn('x', p, q) # No error raised
def test_rs_swap():
X = Normal('x', 0, 1)
Y = Exponential('y', 1)
XX = Normal('x', 0, 2)
YY = Normal('y', 0, 3)
expr = 2*X + Y
assert expr.subs(rs_swap((X, Y), (YY, XX))) == 2*XX + YY
def test_sympyissue_10052():
X = Exponential('X', 3)
assert P(X < oo) == 1
assert P(X > oo) == 0
assert P(X < 2, X > oo) == 0
assert P(X < oo, X > oo) == 0
assert P(X < oo, X > 2) == 1
assert P(X < 3, X == 2) == 0
pytest.raises(ValueError, lambda: P(1))
pytest.raises(ValueError, lambda: P(X < 1, 2))
def test_exponential():
rate = Symbol('lambda', positive=True, real=True)
X = Exponential('x', rate)
assert E(X) == 1 / rate
assert variance(X) == 1 / rate**2
assert skewness(X) == 2
assert skewness(X) == smoment(X, 3)
assert smoment(2 * X, 4) == smoment(X, 4)
assert moment(X, 3) == 3 * 2 * 1 / rate**3
assert P(X > 0) == Integer(1)
assert P(X > 1) == exp(-rate)
assert P(X > 10) == exp(-10 * rate)
assert where(X <= 1).set == Interval(0, 1)
# issue sympy/sympy#10003
X = Exponential('x', 3)
G = Gamma('g', 1, 2)
assert P(X < -1) == 0
assert P(G < -1) == 0
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 range(niter):
assert sample(var) in var.pspace.domain.set
def test_exponential():
rate = Symbol('lambda', positive=True, extended_real=True, finite=True)
X = Exponential('x', rate)
assert E(X) == 1 / rate
assert variance(X) == 1 / rate**2
assert skewness(X) == 2
assert skewness(X) == smoment(X, 3)
assert smoment(2 * X, 4) == smoment(X, 4)
assert moment(X, 3) == 3 * 2 * 1 / rate**3
assert P(X > 0) == Integer(1)
assert P(X > 1) == exp(-rate)
assert P(X > 10) == exp(-10 * rate)
assert where(X <= 1).set == Interval(0, 1)
def test_symbolic():
mu1, mu2 = symbols('mu1 mu2', real=True)
s1, s2 = symbols('sigma1 sigma2', real=True, positive=True)
rate = Symbol('lambda', real=True, positive=True)
X = Normal('x', mu1, s1)
Y = Normal('y', mu2, s2)
Z = Exponential('z', rate)
a, b, c = symbols('a b c', real=True)
assert E(X) == mu1
assert E(X + Y) == mu1 + mu2
assert E(a*X + b) == a*E(X) + b
assert variance(X) == s1**2
assert simplify(variance(X + a*Y + b)) == variance(X) + a**2*variance(Y)
assert E(Z) == 1/rate
assert E(a*Z + b) == a*E(Z) + b
assert E(X + a*Z + b) == mu1 + a/rate + b
def test_sympyissue_8129():
X = Exponential('X', 4)
assert P(X >= X) == 1
assert P(X > X) == 0
assert P(X > X+1) == 0
def test_sympyissue_8129():
# pylint: disable=comparison-with-itself
X = Exponential('X', 4)
assert P(X >= X) == 1
assert P(X > X) == 0
assert P(X > X + 1) == 0
def test_sympyissue_10003():
X = Exponential('x', 3)
G = Gamma('g', 1, 2)
assert P(X < -1) == 0
assert P(G < -1) == 0
def test_issue_10003():
X = Exponential('x', 3)
G = Gamma('g', 1, 2)
assert P(X < -1) == S.Zero
assert P(G < -1) == S.Zero
