How to use the gpytorch.distributions.MultitaskMultivariateNormal function in gpytorch

def _get_test_posterior(batch_shape, q=1, m=1, **tkwargs):
    mean = torch.rand(*batch_shape, q, m, **tkwargs)
    a = torch.rand(*batch_shape, q * m, q * m, **tkwargs)
    covar = a @ a.transpose(-1, -2)
    diag = torch.diagonal(covar, dim1=-2, dim2=-1)
    diag += torch.rand(*batch_shape, q * m, **tkwargs)  # in-place
    mvn = MultitaskMultivariateNormal(mean, covar)
    return GPyTorchPosterior(mvn)

logprob = mtmvn.log_prob(torch.zeros(2, 3, 2, device=device, dtype=dtype))
            logprob_expected = -14.52826 * torch.ones(2, device=device, dtype=dtype)
            self.assertTrue(torch.allclose(logprob, logprob_expected))
            logprob = mtmvn.log_prob(torch.zeros(3, 2, 3, 2, device=device, dtype=dtype))
            logprob_expected = -14.52826 * torch.ones(3, 2, device=device, dtype=dtype)
            self.assertTrue(torch.allclose(logprob, logprob_expected))
            conf_lower, conf_upper = mtmvn.confidence_region()
            self.assertTrue(torch.allclose(conf_lower, mtmvn.mean - 2 * mtmvn.stddev))
            self.assertTrue(torch.allclose(conf_upper, mtmvn.mean + 2 * mtmvn.stddev))
            self.assertTrue(mtmvn.sample().shape == torch.Size([2, 3, 2]))
            self.assertTrue(mtmvn.sample(torch.Size([3])).shape == torch.Size([3, 2, 3, 2]))
            self.assertTrue(mtmvn.sample(torch.Size([3, 4])).shape == torch.Size([3, 4, 2, 3, 2]))

            # non-interleaved
            covmat = variance.transpose(-1, -2).reshape(2, 1, -1) * torch.eye(6, device=device, dtype=dtype)
            mtmvn = MultitaskMultivariateNormal(mean=mean, covariance_matrix=covmat, interleaved=False)
            self.assertTrue(torch.equal(mtmvn.mean, mean))
            self.assertTrue(torch.allclose(mtmvn.variance, variance))
            self.assertTrue(torch.allclose(mtmvn.scale_tril, covmat.sqrt()))
            self.assertTrue(mtmvn.event_shape == torch.Size([3, 2]))
            self.assertTrue(mtmvn.batch_shape == torch.Size([2]))

mvn = MultivariateNormal(mean, covar)
            p = GPyTorchPosterior(mvn)
            mm = MockModel(p)
            weights = torch.tensor([0.5], device=self.device, dtype=dtype)
            obj = ScalarizedObjective(weights)
            ei = ExpectedImprovement(model=mm, best_f=0.0, objective=obj)
            X = torch.rand(1, 2, device=self.device, dtype=dtype)
            ei_expected = torch.tensor(0.2601, device=self.device, dtype=dtype)
            torch.allclose(ei(X), ei_expected, atol=1e-4)

            # test objective (multi-output)
            mean = torch.tensor([[-0.25, 0.5]], device=self.device, dtype=dtype)
            covar = torch.tensor(
                [[[0.5, 0.125], [0.125, 0.5]]], device=self.device, dtype=dtype
            )
            mvn = MultitaskMultivariateNormal(mean, covar)
            p = GPyTorchPosterior(mvn)
            mm = MockModel(p)
            weights = torch.tensor([2.0, 1.0], device=self.device, dtype=dtype)
            obj = ScalarizedObjective(weights)
            ei = ExpectedImprovement(model=mm, best_f=0.0, objective=obj)
            X = torch.rand(1, 2, device=self.device, dtype=dtype)
            ei_expected = torch.tensor(0.6910, device=self.device, dtype=dtype)
            torch.allclose(ei(X), ei_expected, atol=1e-4)

self.assertAlmostEqual(
                mtmvn.log_prob(torch.zeros(3, 2, device=device, dtype=dtype)).item(), -14.52826, places=4
            )
            logprob = mtmvn.log_prob(torch.zeros(2, 3, 2, device=device, dtype=dtype))
            logprob_expected = -14.52826 * torch.ones(2, device=device, dtype=dtype)
            self.assertTrue(torch.allclose(logprob, logprob_expected))
            conf_lower, conf_upper = mtmvn.confidence_region()
            self.assertTrue(torch.allclose(conf_lower, mtmvn.mean - 2 * mtmvn.stddev))
            self.assertTrue(torch.allclose(conf_upper, mtmvn.mean + 2 * mtmvn.stddev))
            self.assertTrue(mtmvn.sample().shape == torch.Size([3, 2]))
            self.assertTrue(mtmvn.sample(torch.Size([3])).shape == torch.Size([3, 3, 2]))
            self.assertTrue(mtmvn.sample(torch.Size([3, 4])).shape == torch.Size([3, 4, 3, 2]))

            # non-interleaved
            covmat = variance.transpose(-1, -2).reshape(-1).diag()
            mtmvn = MultitaskMultivariateNormal(mean=mean, covariance_matrix=covmat, interleaved=False)
            self.assertTrue(torch.equal(mtmvn.mean, mean))
            self.assertTrue(torch.allclose(mtmvn.variance, variance))
            self.assertTrue(torch.allclose(mtmvn.scale_tril, covmat.sqrt()))
            self.assertTrue(mtmvn.event_shape == torch.Size([3, 2]))
            self.assertTrue(mtmvn.batch_shape == torch.Size())

mtmvn = MultitaskMultivariateNormal(mean=mean, covariance_matrix=cov)
            posterior = GPyTorchPosterior(mvn=mtmvn)
            for sample_shape, qmc, seed in itertools.product(
                (torch.Size([5]), torch.Size([5, 3])), (False, True), (None, 1234)
            ):
                expected_shape = sample_shape + torch.Size([2, 2])
                samples = construct_base_samples_from_posterior(
                    posterior=posterior, sample_shape=sample_shape, qmc=qmc, seed=seed
                )
                self.assertEqual(samples.shape, expected_shape)
                self.assertEqual(samples.device.type, self.device.type)
                self.assertEqual(samples.dtype, dtype)
            # multi-output, batch mode
            mean = torch.zeros(2, 2, 2, device=self.device, dtype=dtype)
            cov = torch.eye(4, device=self.device, dtype=dtype).expand(2, 4, 4)
            mtmvn = MultitaskMultivariateNormal(mean=mean, covariance_matrix=cov)
            posterior = GPyTorchPosterior(mvn=mtmvn)
            for sample_shape, qmc, seed, collapse_batch_dims in itertools.product(
                (torch.Size([5]), torch.Size([5, 3])),
                (False, True),
                (None, 1234),
                (False, True),
            ):
                if collapse_batch_dims:
                    expected_shape = sample_shape + torch.Size([1, 2, 2])
                else:
                    expected_shape = sample_shape + torch.Size([2, 2, 2])
                samples = construct_base_samples_from_posterior(
                    posterior=posterior,
                    sample_shape=sample_shape,
                    qmc=qmc,
                    collapse_batch_dims=collapse_batch_dims,

def __call__(self, x, prior=False):
        function_dist = self.base_variational_strategy(x, prior=prior)
        if (
            self.task_dim > 0
            and self.task_dim > len(function_dist.batch_shape)
            or self.task_dim < 0
            and self.task_dim + len(function_dist.batch_shape) < 0
        ):
            return MultitaskMultivariateNormal.from_repeated_mvn(function_dist, num_tasks=self.num_tasks)
        else:
            function_dist = MultitaskMultivariateNormal.from_batch_mvn(function_dist, task_dim=self.task_dim)
            assert function_dist.event_shape[-1] == self.num_tasks
            return function_dist

def forward(self, x):
                mean_x = self.mean_module(x)
                covar_x = self.covar_module(x)
                return gpytorch.distributions.MultitaskMultivariateNormal(mean_x, covar_x)

raise RuntimeError(
                    f"Input shape did not match self.input_dims. Got total feature dims [{inputs.size(-1)}],"
                    f" expected [{self.input_dims}]"
                )

        # Repeat the input for all possible outputs
        if self.output_dims is not None:
            inputs = inputs.unsqueeze(-3)
            inputs = inputs.expand(*inputs.shape[:-3], self.output_dims, *inputs.shape[-2:])

        # Now run samples through the GP
        output = ApproximateGP.__call__(self, inputs)
        if self.output_dims is not None:
            mean = output.loc.transpose(-1, -2)
            covar = BlockDiagLazyTensor(output.lazy_covariance_matrix, block_dim=-3)
            output = MultitaskMultivariateNormal(mean, covar, interleaved=False)

        return output