def METHOD_NAME(self):
    seed = 4
    torch.random.manual_seed(seed)
    tensor = torch.randn(1000, 800)
    diag = torch.abs(torch.randn(1000))
    standard_lt = AddedDiagLinearOperator(RootLinearOperator(tensor), DiagLinearOperator(diag))
    evals, evecs = standard_lt.eigh()
    # this preconditioner is a simple example of near deflation
    def nonstandard_preconditioner(self):
        top_100_evecs = evecs[:, :100]
        top_100_evals = evals[:100] + 0.2 * torch.randn(100)
        precond_lt = RootLinearOperator(top_100_evecs @ torch.diag_embed(top_100_evals**0.5))
        logdet = top_100_evals.log().sum()
        def precond_closure(rhs):
            rhs2 = top_100_evecs.t() @ rhs
            return top_100_evecs @ torch.diag_embed(1.0 / top_100_evals) @ rhs2
        return precond_closure, precond_lt, logdet
    overrode_lt = AddedDiagLinearOperator(
        RootLinearOperator(tensor),
        DiagLinearOperator(diag),
        preconditioner_override=nonstandard_preconditioner,
    )
    # compute a solve - mostly to make sure that we can actually perform the solve
    rhs = torch.randn(1000, 1)
    standard_solve = standard_lt.solve(rhs)
    overrode_solve = overrode_lt.solve(rhs)
    # gut checking that our preconditioner is not breaking anything
    self.assertEqual(standard_solve.shape, overrode_solve.shape)
    self.assertLess(torch.norm(standard_solve - overrode_solve) / standard_solve.norm(), 1.0)