def test_Wishart():
W = Wishart('W', 5, [[1, 0], [0, 1]])
assert W.pspace.distribution.set == MatrixSet(2, 2, S.Reals)
X = MatrixSymbol('X', 2, 2)
term1 = exp(Trace(Matrix([[-S(1)/2, 0], [0, -S(1)/2]])*X))
assert density(W)(X).doit() == term1 * Determinant(X)/(24*pi)
assert density(W)([[2, 1], [1, 2]]).doit() == exp(-2)/(8*pi)
n = symbols('n', positive=True)
d = symbols('d', positive=True, integer=True)
Y = MatrixSymbol('Y', d, d)
SM = MatrixSymbol('SM', d, d)
W = Wishart('W', n, SM)
k = Dummy('k')
exprd = 2**(-d*n/2)*pi**(-d*(d - 1)/4)*exp(Trace(-(S(1)/2)*SM**(-1)*Y)
)*Determinant(SM)**(-n/2)*Determinant(Y)**(
-d/2 + n/2 - S(1)/2)/Product(gamma(-k/2 + n/2 + S(1)/2), (k, 1, d))
assert density(W)(Y).dummy_eq(exprd)
raises(ValueError, lambda: density(W)(1))
raises(ValueError, lambda: Wishart('W', -1, [[1, 0], [0, 1]]))
raises(ValueError, lambda: Wishart('W', -1, [[1, 0], [2, 1]]))
raises(ValueError, lambda: Wishart('W', 2, [[1, 0], [0]]))