def test_OneMatrix():
A = MatrixSymbol('A', n, m)
a = MatrixSymbol('a', n, 1)
U = OneMatrix(n, m)
assert U.shape == (n, m)
assert isinstance(A + U, Add)
assert transpose(U) == OneMatrix(m, n)
assert U.conjugate() == U
assert OneMatrix(n, n) ** 0 == Identity(n)
with raises(NonSquareMatrixError):
U ** 0
with raises(NonSquareMatrixError):
U ** 1
with raises(NonSquareMatrixError):
U ** 2
with raises(ShapeError):
a + U
U = OneMatrix(n, n)
assert U[1, 2] == 1
U = OneMatrix(2, 3)
assert U.as_explicit() == ImmutableMatrix.ones(2, 3)
def test_Trace():
assert isinstance(Trace(A), Trace)
assert not isinstance(Trace(A), MatrixExpr)
raises(ShapeError, lambda: Trace(C))
assert trace(eye(3)) == 3
assert trace(Matrix(3, 3, [1, 2, 3, 4, 5, 6, 7, 8, 9])) == 15
assert adjoint(Trace(A)) == trace(Adjoint(A))
assert conjugate(Trace(A)) == trace(Adjoint(A))
assert transpose(Trace(A)) == Trace(A)
A / Trace(A) # Make sure this is possible
# Some easy simplifications
assert trace(Identity(5)) == 5
assert trace(ZeroMatrix(5, 5)) == 0
assert trace(OneMatrix(1, 1)) == 1
assert trace(OneMatrix(2, 2)) == 2
assert trace(OneMatrix(n, n)) == n
assert trace(2*A*B) == 2*Trace(A*B)
assert trace(A.T) == trace(A)
i, j = symbols('i j')
F = FunctionMatrix(3, 3, Lambda((i, j), i + j))
assert trace(F) == (0 + 0) + (1 + 1) + (2 + 2)
raises(TypeError, lambda: Trace(S.One))
assert Trace(A).arg is A
assert str(trace(A)) == str(Trace(A).doit())
assert Trace(A).is_commutative is True
def test_eval_determinant():
assert det(Identity(n)) == 1
assert det(ZeroMatrix(n, n)) == 0
assert det(OneMatrix(n, n)) == Determinant(OneMatrix(n, n))
assert det(OneMatrix(1, 1)) == 1
assert det(OneMatrix(2, 2)) == 0
assert det(Transpose(A)) == det(A)
def test_MatrixPermute_doit():
p = Permutation(0, 1, 2)
A = MatrixSymbol('A', 3, 3)
assert MatrixPermute(A, p).doit() == MatrixPermute(A, p)
p = Permutation(0, size=3)
A = MatrixSymbol('A', 3, 3)
assert MatrixPermute(A, p).doit().as_explicit() == \
MatrixPermute(A, p).as_explicit()
p = Permutation(0, 1, 2)
A = Identity(3)
assert MatrixPermute(A, p, 0).doit().as_explicit() == \
MatrixPermute(A, p, 0).as_explicit()
assert MatrixPermute(A, p, 1).doit().as_explicit() == \
MatrixPermute(A, p, 1).as_explicit()
A = ZeroMatrix(3, 3)
assert MatrixPermute(A, p).doit() == A
A = OneMatrix(3, 3)
assert MatrixPermute(A, p).doit() == A
A = MatrixSymbol('A', 4, 4)
p1 = Permutation(0, 1, 2, 3)
p2 = Permutation(0, 2, 3, 1)
expr = MatrixPermute(MatrixPermute(A, p1, 0), p2, 0)
assert expr.as_explicit() == expr.doit().as_explicit()
expr = MatrixPermute(MatrixPermute(A, p1, 1), p2, 1)
assert expr.as_explicit() == expr.doit().as_explicit()
def test_OneMatrix():
A = MatrixSymbol('A', n, m)
a = MatrixSymbol('a', n, 1)
U = OneMatrix(n, m)
assert U.shape == (n, m)
assert isinstance(A + U, Add)
assert transpose(U) == OneMatrix(m, n)
assert U.conjugate() == U
assert OneMatrix(n, n) ** 0 == Identity(n)
with raises(ShapeError):
U ** 0
with raises(ShapeError):
U ** 2
U = OneMatrix(n, n)
assert U[1, 2] == 1
U = OneMatrix(2, 3)
assert U.as_explicit() == ImmutableMatrix.ones(2, 3)
def test_one_matrix_creation():
assert OneMatrix(2, 2)
assert OneMatrix(0, 0)
assert Eq(OneMatrix(1, 1), Identity(1))
raises(ValueError, lambda: OneMatrix(-1, 2))
raises(ValueError, lambda: OneMatrix(2.0, 2))
raises(ValueError, lambda: OneMatrix(2j, 2))
raises(ValueError, lambda: OneMatrix(2, -1))
raises(ValueError, lambda: OneMatrix(2, 2.0))
raises(ValueError, lambda: OneMatrix(2, 2j))
n = symbols('n')
assert OneMatrix(n, n)
n = symbols('n', integer=False)
raises(ValueError, lambda: OneMatrix(n, n))
n = symbols('n', negative=True)
raises(ValueError, lambda: OneMatrix(n, n))
def test_OneMatrix_mul():
assert OneMatrix(n, m) * OneMatrix(m, k) == OneMatrix(n, k) * m
assert w * OneMatrix(1, 1) == w
assert OneMatrix(1, 1) * w.T == w.T
def test_OneMatrix_doit():
Unn = OneMatrix(Add(n, n, evaluate=False), n)
assert isinstance(Unn.rows, Add)
assert Unn.doit() == OneMatrix(2 * n, n)
assert isinstance(Unn.doit().rows, Mul)
def test_one_matrix_creation():
assert OneMatrix(2, 2)
assert OneMatrix(0, 0)
raises(ValueError, lambda: OneMatrix(-1, 2))
raises(ValueError, lambda: OneMatrix(2.0, 2))
raises(ValueError, lambda: OneMatrix(2j, 2))
raises(ValueError, lambda: OneMatrix(2, -1))
raises(ValueError, lambda: OneMatrix(2, 2.0))
raises(ValueError, lambda: OneMatrix(2, 2j))
n = symbols("n")
assert OneMatrix(n, n)
n = symbols("n", integer=False)
raises(ValueError, lambda: OneMatrix(n, n))
n = symbols("n", negative=True)
raises(ValueError, lambda: OneMatrix(n, n))
def test_OneMatrix_doit():
Unn = OneMatrix(Add(n, n, evaluate=False), n)
assert isinstance(Unn.rows, Add)
assert Unn.doit() == OneMatrix(2 * n, n)
assert isinstance(Unn.doit().rows, Mul)
