def test_immutablematrix():
A = ImmutableMatrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
assert A.shape == (3, 3)
assert A[1, 2] == 6
assert A[2, 2] == 9
assert A[1, :] == ImmutableMatrix([[4, 5, 6]])
assert A[:2, :2] == ImmutableMatrix([[1, 2], [4, 5]])
with raises(TypeError):
A[2, 2] = 5
X = DenseMatrix([[1, 2], [3, 4]])
assert X.as_immutable() == ImmutableMatrix([[1, 2], [3, 4]])
assert X.det() == -2
X = ImmutableMatrix(eye(3))
assert isinstance(X + A, ImmutableMatrix)
assert isinstance(X * A, ImmutableMatrix)
assert isinstance(X * 2, ImmutableMatrix)
assert isinstance(2 * X, ImmutableMatrix)
X = ImmutableMatrix([[1, 2], [3, 4]])
Y = ImmutableMatrix([[1], [0]])
assert type(X.LUsolve(Y)) == ImmutableMatrix
x = Symbol("x")
X = ImmutableMatrix([[1, 2], [3, 4]])
Y = ImmutableMatrix([[1, 2], [x, 4]])
assert Y.subs(x, 3) == X
assert Y.xreplace(x, 3) == X
X = ImmutableMatrix([[1, 2], [3, 4]])
Y = ImmutableMatrix([[5], [6]])
Z = X.row_join(Y)
assert isinstance(Z, ImmutableMatrix)
assert Z == ImmutableMatrix([[1, 2, 5], [3, 4, 6]])
X = ImmutableMatrix([[1, 2], [3, 4]])
Y = ImmutableMatrix([[5, 6]])
Z = X.col_join(Y)
assert isinstance(Z, ImmutableMatrix)
assert Z == ImmutableMatrix([[1, 2], [3, 4], [5, 6]])
# Operations of one immutable and one mutable matrix should give immutable result
X = ImmutableMatrix([1])
Y = DenseMatrix([1])
assert type(X + Y) == ImmutableMatrix
assert type(Y + X) == ImmutableMatrix
assert type(X * Y) == ImmutableMatrix
assert type(Y * X) == ImmutableMatrix
