def test_as_immutable():
X = Matrix([[1, 2], [3, 4]])
assert sympify(X) == X.as_immutable() == ImmutableMatrix([[1, 2], [3, 4]])
X = SparseMatrix(5, 5, {})
assert sympify(X) == X.as_immutable() == ImmutableSparseMatrix(
[[0 for i in range(5)] for i in range(5)])
def test_im():
x, y = symbols('x,y')
a, b = symbols('a,b', real=True)
r = Symbol('r', real=True)
i = Symbol('i', imaginary=True)
assert im(nan) == nan
assert im(oo * I) == oo
assert im(-oo * I) == -oo
assert im(0) == 0
assert im(1) == 0
assert im(-1) == 0
assert im(E * I) == E
assert im(-E * I) == -E
assert unchanged(im, x)
assert im(x * I) == re(x)
assert im(r * I) == r
assert im(r) == 0
assert im(i * I) == 0
assert im(i) == -I * i
assert im(x + y) == im(x + y)
assert im(x + r) == im(x)
assert im(x + r * I) == im(x) + r
assert im(im(x) * I) == im(x)
assert im(2 + I) == 1
assert im(x + I) == im(x) + 1
assert im(x + y * I) == im(x) + re(y)
assert im(x + r * I) == im(x) + r
assert im(log(2 * I)) == pi / 2
assert im((2 + I)**2).expand(complex=True) == 4
assert im(conjugate(x)) == -im(x)
assert conjugate(im(x)) == im(x)
assert im(x).as_real_imag() == (im(x), 0)
assert im(i * r * x).diff(r) == im(i * x)
assert im(i * r * x).diff(i) == -I * re(r * x)
assert im(
sqrt(a +
b * I)) == (a**2 + b**2)**Rational(1, 4) * sin(atan2(b, a) / 2)
assert im(a * (2 + b * I)) == a * b
assert im((1 + sqrt(a + b*I))/2) == \
(a**2 + b**2)**Rational(1, 4)*sin(atan2(b, a)/2)/2
assert im(x).rewrite(re) == -S.ImaginaryUnit * (x - re(x))
assert (x + im(y)).rewrite(im, re) == x - S.ImaginaryUnit * (y - re(y))
a = Symbol('a', algebraic=True)
t = Symbol('t', transcendental=True)
x = Symbol('x')
assert re(a).is_algebraic
assert re(x).is_algebraic is None
assert re(t).is_algebraic is False
assert im(S.ComplexInfinity) == S.NaN
n, m, l = symbols('n m l')
A = MatrixSymbol('A', n, m)
assert im(A) == (S(1) / (2 * I)) * (A - conjugate(A))
A = Matrix([[1 + 4 * I, 2], [0, -3 * I]])
assert im(A) == Matrix([[4, 0], [0, -3]])
A = ImmutableMatrix([[1 + 3 * I, 3 - 2 * I], [0, 2 * I]])
assert im(A) == ImmutableMatrix([[3, -2], [0, 2]])
X = ImmutableSparseMatrix([[i * I + i for i in range(5)]
for i in range(5)])
Y = SparseMatrix([[i for i in range(5)] for i in range(5)])
assert im(X).as_immutable() == Y
X = FunctionMatrix(3, 3, Lambda((n, m), n + m * I))
assert im(X) == Matrix([[0, 1, 2], [0, 1, 2], [0, 1, 2]])
def setup(self):
self.M1 = MutableDenseMatrix.zeros(5, 5)
self.M2 = ImmutableDenseMatrix.zeros(5, 5)
self.M3 = MutableSparseMatrix.zeros(5, 5)
self.M4 = ImmutableSparseMatrix.zeros(5, 5)
