def METHOD_NAME():
    A11 = np.random.randn(2, 3)
    A12 = np.random.randn(2, 4)
    A21 = np.zeros((5, 3))
    A22 = np.random.randn(5, 4)
    A = np.vstack((np.hstack((A11, A12)),
                   np.hstack((A21, A22))))
    A11op = NumpyMatrixOperator(A11)
    A12op = NumpyMatrixOperator(A12)
    A22op = NumpyMatrixOperator(A22)
    Aop = BlockOperator(np.array([[A11op, A12op], [None, A22op]]))
    v1 = np.random.randn(2)
    v2 = np.random.randn(5)
    v = np.hstack((v1, v2))
    v1va = NumpyVectorSpace.from_numpy(v1)
    v2va = NumpyVectorSpace.from_numpy(v2)
    vva = BlockVectorSpace.make_array((v1va, v2va))
    wva = Aop.apply_adjoint(vva)
    w = np.hstack((wva.blocks[0].to_numpy(), wva.blocks[1].to_numpy()))
    assert np.allclose(A.T.dot(v), w)