Flake: test_bidiagonalize_real_matrix_pair_with_symmetric_products

[balopat]

Description of the issue

https://github.com/quantumlib/Cirq/pull/3914/checks?check_run_id=2107089159

_____ test_bidiagonalize_real_matrix_pair_with_symmetric_products[a40-b40] _____

a = array([[ 0.3339604 , -0.64209018,  0.08013909, -0.48298666],
       [ 0.5876492 ,  0.06662798, -0.17019409,  0.5355366...    [ 0.40079316, -0.21360456,  0.12212223,  0.19078334],
       [ 0.13534768,  0.11948305, -0.81295149, -0.30458568]])
b = array([[-0.00938582, -0.02506192, -0.00410744, -0.04594066],
       [ 0.00838088,  0.02237856,  0.00366766,  0.0410218...    [ 0.00206892,  0.00552442,  0.00090541,  0.01012673],
       [-0.00352259, -0.00940599, -0.00154157, -0.01724199]])

    @pytest.mark.parametrize(
        'a,b',
        [
            (np.zeros((0, 0)), np.zeros((0, 0))),
            (np.eye(2), np.eye(2)),
            (np.eye(4), np.eye(4)),
            (np.eye(4), np.zeros((4, 4))),
            (H, H),
            (cirq.kron(np.eye(2), H), cirq.kron(H, np.eye(2))),
            (cirq.kron(np.eye(2), Z), cirq.kron(X, np.eye(2))),
        ]
        + [random_bi_diagonalizable_pair(2) for _ in range(10)]
        + [random_bi_diagonalizable_pair(4) for _ in range(10)]
        + [
            random_bi_diagonalizable_pair(4, d1, d2)
            for _ in range(10)
            for d1 in range(4)
            for d2 in range(4)
        ]
        + [random_bi_diagonalizable_pair(k) for k in range(1, 10)],
    )
    def test_bidiagonalize_real_matrix_pair_with_symmetric_products(a, b):
        a = np.array(a)
        b = np.array(b)
        p, q = cirq.bidiagonalize_real_matrix_pair_with_symmetric_products(a, b)
>       assert_bidiagonalized_by(a, p, q)

cirq/linalg/diagonalize_test.py:207: 
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 

m = array([[ 0.3339604 , -0.64209018,  0.08013909, -0.48298666],
       [ 0.5876492 ,  0.06662798, -0.17019409,  0.5355366...    [ 0.40079316, -0.21360456,  0.12212223,  0.19078334],
       [ 0.13534768,  0.11948305, -0.81295149, -0.30458568]])
p = array([[ 0.70945677, -0.63349569, -0.15638607,  0.2662662 ],
       [ 0.211501  , -0.20218289,  0.17925377, -0.9392856...    [ 0.60832511,  0.59973378,  0.50914112,  0.10504891],
       [-0.28614502, -0.44511199,  0.82715585,  0.18923411]])
q = array([[-0.17600994, -0.11475276,  0.85828799,  0.46818163],
       [-0.46998004, -0.33249548, -0.49558939,  0.6503511...    [-0.0770259 ,  0.92813344, -0.08489247,  0.354159  ],
       [-0.86151394,  0.12184777,  0.10259709, -0.48210029]])
rtol = 1e-05, atol = 1e-08

    def assert_bidiagonalized_by(m, p, q, rtol: float = 1e-5, atol: float = 1e-8):
        d = p.dot(m).dot(q)
    
>       assert (
            cirq.is_orthogonal(p) and cirq.is_orthogonal(q) and cirq.is_diagonal(d, atol=atol)
        ), _get_assert_bidiagonalized_by_str(m, p, q, d)
E       AssertionError: m.round(3) : [[ 0.334 -0.642  0.08  -0.483]
E          [ 0.588  0.067 -0.17   0.536]
E          [ 0.401 -0.214  0.122  0.191]
E          [ 0.135  0.119 -0.813 -0.305]], p.round(3) : [[ 0.709 -0.633 -0.156  0.266]
E          [ 0.212 -0.202  0.179 -0.939]
E          [ 0.608  0.6    0.509  0.105]
E          [-0.286 -0.445  0.827  0.189]], q.round(3): [[-0.176 -0.115  0.858  0.468]
E          [-0.47  -0.332 -0.496  0.65 ]
E          [-0.077  0.928 -0.085  0.354]
E          [-0.862  0.122  0.103 -0.482]], np.abs(p.T @ m @ p).round(2): [[0.92 0.   0.   0.  ]
E          [0.   0.9  0.   0.  ]
E          [0.   0.   0.9  0.  ]
E          [0.   0.   0.   0.  ]]
E       assert (True and True and False)
E        +  where True = <function is_orthogonal at 0x7fc49042b290>(array([[ 0.70945677, -0.63349569, -0.15638607,  0.2662662 ],\n       [ 0.211501  , -0.20218289,  0.17925377, -0.9392856...    [ 0.60832511,  0.59973378,  0.50914112,  0.10504891],\n       [-0.28614502, -0.44511199,  0.82715585,  0.18923411]]))
E        +    where <function is_orthogonal at 0x7fc49042b290> = cirq.is_orthogonal
E        +  and   True = <function is_orthogonal at 0x7fc49042b290>(array([[-0.17600994, -0.11475276,  0.85828799,  0.46818163],\n       [-0.46998004, -0.33249548, -0.49558939,  0.6503511...    [-0.0770259 ,  0.92813344, -0.08489247,  0.354159  ],\n       [-0.86151394,  0.12184777,  0.10259709, -0.48210029]]))
E        +    where <function is_orthogonal at 0x7fc49042b290> = cirq.is_orthogonal
E        +  and   False = <function is_diagonal at 0x7fc4904273b0>(array([[ 9.20304375e-01, -3.90039323e-17, -6.84034194e-17, -1.19018274e-16],\n       [-4.92727203e-17,  9.01642270e-01,...1e-07,  9.01641372e-01,  3.07323624e-17],\n       [-6.18416776e-17,  1.16821231e-16, -1.27458159e-17,  3.20614510e-17]]), atol=1e-08)
E        +    where <function is_diagonal at 0x7fc4904273b0> = cirq.is_diagonal

cirq/linalg/diagonalize_test.py:88: AssertionError

[dstrain115]

I wasn't able to reproduce this, so I am not sure if it is still an issue.