Exemplo n.º 1
0
def test_determinant():
    M = Matrix()

    assert M.det() == 1
    # Evaluating these directly because they are never reached via M.det()
    assert M._eval_det_bareiss() == 1
    assert M._eval_det_berkowitz() == 1
    assert M._eval_det_lu() == 1

    M = Matrix([[0]])

    assert M.det() == 0
    assert M._eval_det_bareiss() == 0
    assert M._eval_det_berkowitz() == 0
    assert M._eval_det_lu() == 0

    M = Matrix([[5]])

    assert M.det() == 5
    assert M._eval_det_bareiss() == 5
    assert M._eval_det_berkowitz() == 5
    assert M._eval_det_lu() == 5

    M = Matrix(((-3, 2), (8, -5)))

    assert M.det(method="domain-ge") == -1
    assert M.det(method="bareiss") == -1
    assert M.det(method="berkowitz") == -1
    assert M.det(method="lu") == -1

    M = Matrix(((x, 1), (y, 2 * y)))

    assert M.det(method="domain-ge") == 2 * x * y - y
    assert M.det(method="bareiss") == 2 * x * y - y
    assert M.det(method="berkowitz") == 2 * x * y - y
    assert M.det(method="lu") == 2 * x * y - y

    M = Matrix(((1, 1, 1), (1, 2, 3), (1, 3, 6)))

    assert M.det(method="domain-ge") == 1
    assert M.det(method="bareiss") == 1
    assert M.det(method="berkowitz") == 1
    assert M.det(method="lu") == 1

    M = Matrix(((3, -2, 0, 5), (-2, 1, -2, 2), (0, -2, 5, 0), (5, 0, 3, 4)))

    assert M.det(method="domain-ge") == -289
    assert M.det(method="bareiss") == -289
    assert M.det(method="berkowitz") == -289
    assert M.det(method="lu") == -289

    M = Matrix(((1, 2, 3, 4), (5, 6, 7, 8), (9, 10, 11, 12), (13, 14, 15, 16)))

    assert M.det(method="domain-ge") == 0
    assert M.det(method="bareiss") == 0
    assert M.det(method="berkowitz") == 0
    assert M.det(method="lu") == 0

    M = Matrix(((3, 2, 0, 0, 0), (0, 3, 2, 0, 0), (0, 0, 3, 2, 0),
                (0, 0, 0, 3, 2), (2, 0, 0, 0, 3)))

    assert M.det(method="domain-ge") == 275
    assert M.det(method="bareiss") == 275
    assert M.det(method="berkowitz") == 275
    assert M.det(method="lu") == 275

    M = Matrix(((3, 0, 0, 0), (-2, 1, 0, 0), (0, -2, 5, 0), (5, 0, 3, 4)))

    assert M.det(method="domain-ge") == 60
    assert M.det(method="bareiss") == 60
    assert M.det(method="berkowitz") == 60
    assert M.det(method="lu") == 60

    M = Matrix(((1, 0, 0, 0), (5, 0, 0, 0), (9, 10, 11, 0), (13, 14, 15, 16)))

    assert M.det(method="domain-ge") == 0
    assert M.det(method="bareiss") == 0
    assert M.det(method="berkowitz") == 0
    assert M.det(method="lu") == 0

    M = Matrix(((3, 2, 0, 0, 0), (0, 3, 2, 0, 0), (0, 0, 3, 2, 0),
                (0, 0, 0, 3, 2), (0, 0, 0, 0, 3)))

    assert M.det(method="domain-ge") == 243
    assert M.det(method="bareiss") == 243
    assert M.det(method="berkowitz") == 243
    assert M.det(method="lu") == 243

    M = Matrix(((1, 0, 1, 2, 12), (2, 0, 1, 1, 4), (2, 1, 1, -1, 3),
                (3, 2, -1, 1, 8), (1, 1, 1, 0, 6)))

    assert M.det(method="domain-ge") == -55
    assert M.det(method="bareiss") == -55
    assert M.det(method="berkowitz") == -55
    assert M.det(method="lu") == -55

    M = Matrix(((-5, 2, 3, 4, 5), (1, -4, 3, 4, 5), (1, 2, -3, 4, 5),
                (1, 2, 3, -2, 5), (1, 2, 3, 4, -1)))

    assert M.det(method="domain-ge") == 11664
    assert M.det(method="bareiss") == 11664
    assert M.det(method="berkowitz") == 11664
    assert M.det(method="lu") == 11664

    M = Matrix(((2, 7, -1, 3, 2), (0, 0, 1, 0, 1), (-2, 0, 7, 0, 2),
                (-3, -2, 4, 5, 3), (1, 0, 0, 0, 1)))

    assert M.det(method="domain-ge") == 123
    assert M.det(method="bareiss") == 123
    assert M.det(method="berkowitz") == 123
    assert M.det(method="lu") == 123

    M = Matrix(((x, y, z), (1, 0, 0), (y, z, x)))

    assert M.det(method="domain-ge") == z**2 - x * y
    assert M.det(method="bareiss") == z**2 - x * y
    assert M.det(method="berkowitz") == z**2 - x * y
    assert M.det(method="lu") == z**2 - x * y

    # issue 13835
    a = symbols('a')
    M = lambda n: Matrix([[i + a * j for i in range(n)] for j in range(n)])
    assert M(5).det() == 0
    assert M(6).det() == 0
    assert M(7).det() == 0