def test_Normal():
m = Normal('A', [1, 2], [[1, 0], [0, 1]])
assert density(m)(1, 2) == 1 / (2 * pi)
raises (ValueError,\
lambda: Normal('M',[1, 2], [[0, 0], [0, 1]]))
n = Normal('B', [1, 2, 3], [[1, 0, 0], [0, 1, 0], [0, 0, 1]])
p = Normal('C', Matrix([1, 2]), Matrix([[1, 0], [0, 1]]))
assert density(m)(x, y) == density(p)(x, y)
assert marginal_distribution(n, 0, 1)(1, 2) == 1 / (2 * pi)
assert integrate(density(m)(x, y), (x, -oo, oo), (y, -oo, oo)).evalf() == 1
raises(ValueError, lambda: Normal('M', [1, 2], [[1, 1], [1, -1]]))
def test_density():
x = Symbol('x')
l = Symbol('l', positive=True)
rate = Beta(l, 2, 3)
X = Poisson(x, rate)
assert isinstance(pspace(X), JointPSpace)
assert density(X, Eq(rate, rate.symbol)) == PoissonDistribution(l)
N1 = Normal('N1', 0, 1)
N2 = Normal('N2', N1, 2)
assert density(N2)(0).doit() == sqrt(10) / (10 * sqrt(pi))
assert simplify(density(N2, Eq(N1, 1))(x)) == \
sqrt(2)*exp(-(x - 1)**2/8)/(4*sqrt(pi))
def test_Normal():
m = Normal('A', [1, 2], [[1, 0], [0, 1]])
assert density(m)(1, 2) == 1 / (2 * pi)
raises (ValueError,\
lambda: Normal('M',[1, 2], [[0, 0], [0, 1]]))
n = Normal('B', [1, 2, 3], [[1, 0, 0], [0, 1, 0], [0, 0, 1]])
p = Normal('C', Matrix([1, 2]), Matrix([[1, 0], [0, 1]]))
assert density(m)(x, y) == density(p)(x, y)
assert marginal_distribution(n, 0, 1)(1, 2) == 1 / (2 * pi)
assert integrate(density(m)(x, y), (x, -oo, oo), (y, -oo, oo)).evalf() == 1
N1 = Normal('N1', [1, 2], [[x, 0], [0, y]])
assert str(density(N1)(0, 0)) == "exp(-(4*x + y)/(2*x*y))/(2*pi*sqrt(x*y))"
raises(ValueError, lambda: Normal('M', [1, 2], [[1, 1], [1, -1]]))
def test_Normal():
m = Normal('A', [1, 2], [[1, 0], [0, 1]])
assert density(m)(1, 2) == 1/(2*pi)
raises (ValueError, lambda:m[2])
raises (ValueError,\
lambda: Normal('M',[1, 2], [[0, 0], [0, 1]]))
n = Normal('B', [1, 2, 3], [[1, 0, 0], [0, 1, 0], [0, 0, 1]])
p = Normal('C', Matrix([1, 2]), Matrix([[1, 0], [0, 1]]))
assert density(m)(x, y) == density(p)(x, y)
assert marginal_distribution(n, 0, 1)(1, 2) == 1/(2*pi)
assert integrate(density(m)(x, y), (x, -oo, oo), (y, -oo, oo)).evalf() == 1
N = Normal('N', [1, 2], [[x, 0], [0, y]])
assert density(N)(0, 0) == exp(-2/y - 1/(2*x))/(2*pi*sqrt(x*y))
raises (ValueError, lambda: Normal('M', [1, 2], [[1, 1], [1, -1]]))
# symbolic
n = symbols('n', natural=True)
mu = MatrixSymbol('mu', n, 1)
sigma = MatrixSymbol('sigma', n, n)
X = Normal('X', mu, sigma)
assert density(X) == MultivariateNormalDistribution(mu, sigma)
def test_joint_vector_expectation():
from sympy.stats import E
m = Normal('A', [x, y], [[1, 0], [0, 1]])
assert E(m) == (x, y)
def test_expectation():
from sympy import simplify
from sympy.stats import E
m = Normal('A', [x, y], [[1, 0], [0, 1]])
assert simplify(E(m[1])) == y
