def ensemble_depth(
    depth: torch.Tensor,
    scale_invariant: bool = True,
    shift_invariant: bool = True,
    output_uncertainty: bool = False,
    reduction: str = "median",
    regularizer_strength: float = 0.02,
    max_iter: int = 50,
    tol: float = 1e-6,
    max_res: int = 1024,
) -> Tuple[torch.Tensor, Optional[torch.Tensor]]:
    """
    Ensembles depth maps represented by the `depth` tensor with expected shape `(B, 1, H, W)`, where B is the
    number of ensemble members for a given prediction of size `(H x W)`. Even though the function is designed for
    depth maps, it can also be used with disparity maps as long as the input tensor values are non-negative. The
    alignment happens when the predictions have one or more degrees of freedom, that is when they are either
    affine-invariant (`scale_invariant=True` and `shift_invariant=True`), or just scale-invariant (only
    `scale_invariant=True`). For absolute predictions (`scale_invariant=False` and `shift_invariant=False`)
    alignment is skipped and only ensembling is performed.

    Args:
        depth (`torch.Tensor`):
            Input ensemble depth maps.
        scale_invariant (`bool`, *optional*, defaults to `True`):
            Whether to treat predictions as scale-invariant.
        shift_invariant (`bool`, *optional*, defaults to `True`):
            Whether to treat predictions as shift-invariant.
        output_uncertainty (`bool`, *optional*, defaults to `False`):
            Whether to output uncertainty map.
        reduction (`str`, *optional*, defaults to `"median"`):
            Reduction method used to ensemble aligned predictions. The accepted values are: `"mean"` and
            `"median"`.
        regularizer_strength (`float`, *optional*, defaults to `0.02`):
            Strength of the regularizer that pulls the aligned predictions to the unit range from 0 to 1.
        max_iter (`int`, *optional*, defaults to `2`):
            Maximum number of the alignment solver steps. Refer to `scipy.optimize.minimize` function, `options`
            argument.
        tol (`float`, *optional*, defaults to `1e-3`):
            Alignment solver tolerance. The solver stops when the tolerance is reached.
        max_res (`int`, *optional*, defaults to `1024`):
            Resolution at which the alignment is performed; `None` matches the `processing_resolution`.
    Returns:
        A tensor of aligned and ensembled depth maps and optionally a tensor of uncertainties of the same shape:
        `(1, 1, H, W)`.
    """
    if depth.dim() != 4 or depth.shape[1] != 1:
        raise ValueError(f"Expecting 4D tensor of shape [B,1,H,W]; got {depth.shape}.")
    if reduction not in ("mean", "median"):
        raise ValueError(f"Unrecognized reduction method: {reduction}.")
    if not scale_invariant and shift_invariant:
        raise ValueError("Pure shift-invariant ensembling is not supported.")

    def init_param(depth: torch.Tensor):
        init_min = depth.reshape(ensemble_size, -1).min(dim=1).values
        init_max = depth.reshape(ensemble_size, -1).max(dim=1).values

        if scale_invariant and shift_invariant:
            init_s = 1.0 / (init_max - init_min).clamp(min=1e-6)
            init_t = -init_s * init_min
            param = torch.cat((init_s, init_t)).cpu().numpy()
        elif scale_invariant:
            init_s = 1.0 / init_max.clamp(min=1e-6)
            param = init_s.cpu().numpy()
        else:
            raise ValueError("Unrecognized alignment.")

        return param.astype(np.float64)

    def align(depth: torch.Tensor, param: np.ndarray) -> torch.Tensor:
        if scale_invariant and shift_invariant:
            s, t = np.split(param, 2)
            s = torch.from_numpy(s).to(depth).view(ensemble_size, 1, 1, 1)
            t = torch.from_numpy(t).to(depth).view(ensemble_size, 1, 1, 1)
            out = depth * s + t
        elif scale_invariant:
            s = torch.from_numpy(param).to(depth).view(ensemble_size, 1, 1, 1)
            out = depth * s
        else:
            raise ValueError("Unrecognized alignment.")
        return out

    def ensemble(
        depth_aligned: torch.Tensor, return_uncertainty: bool = False
    ) -> Tuple[torch.Tensor, Optional[torch.Tensor]]:
        uncertainty = None
        if reduction == "mean":
            prediction = torch.mean(depth_aligned, dim=0, keepdim=True)
            if return_uncertainty:
                uncertainty = torch.std(depth_aligned, dim=0, keepdim=True)
        elif reduction == "median":
            prediction = torch.median(depth_aligned, dim=0, keepdim=True).values
            if return_uncertainty:
                uncertainty = torch.median(
                    torch.abs(depth_aligned - prediction), dim=0, keepdim=True
                ).values
        else:
            raise ValueError(f"Unrecognized reduction method: {reduction}.")
        return prediction, uncertainty

    def cost_fn(param: np.ndarray, depth: torch.Tensor) -> float:
        cost = 0.0
        depth_aligned = align(depth, param)

        for i, j in torch.combinations(torch.arange(ensemble_size)):
            diff = depth_aligned[i] - depth_aligned[j]
            cost += (diff**2).mean().sqrt().item()

        if regularizer_strength > 0:
            prediction, _ = ensemble(depth_aligned, return_uncertainty=False)
            err_near = (0.0 - prediction.min()).abs().item()
            err_far = (1.0 - prediction.max()).abs().item()
            cost += (err_near + err_far) * regularizer_strength

        return cost

    def compute_param(depth: torch.Tensor):
        import scipy

        depth_to_align = depth.to(torch.float32)
        if max_res is not None and max(depth_to_align.shape[2:]) > max_res:
            depth_to_align = resize_max_res(
                depth_to_align, max_res, get_tv_resample_method("nearest-exact")
            )

        param = init_param(depth_to_align)

        res = scipy.optimize.minimize(
            partial(cost_fn, depth=depth_to_align),
            param,
            method="BFGS",
            tol=tol,
            options={"maxiter": max_iter, "disp": False},
        )

        return res.x

    requires_aligning = scale_invariant or shift_invariant
    ensemble_size = depth.shape[0]

    if requires_aligning:
        param = compute_param(depth)
        depth = align(depth, param)

    depth, uncertainty = ensemble(depth, return_uncertainty=output_uncertainty)

    depth_max = depth.max()
    if scale_invariant and shift_invariant:
        depth_min = depth.min()
    elif scale_invariant:
        depth_min = 0
    else:
        raise ValueError("Unrecognized alignment.")
    depth_range = (depth_max - depth_min).clamp(min=1e-6)
    depth = (depth - depth_min) / depth_range
    if output_uncertainty:
        uncertainty /= depth_range

    return depth, uncertainty  # [1,1,H,W], [1,1,H,W]

    Ensembles depth maps represented by the `depth` tensor with expected shape `(B, 1, H, W)`, where B is the
    number of ensemble members for a given prediction of size `(H x W)`. Even though the function is designed for
    depth maps, it can also be used with disparity maps as long as the input tensor values are non-negative. The
    alignment happens when the predictions have one or more degrees of freedom, that is when they are either
    affine-invariant (`scale_invariant=True` and `shift_invariant=True`), or just scale-invariant (only
    `scale_invariant=True`). For absolute predictions (`scale_invariant=False` and `shift_invariant=False`)
    alignment is skipped and only ensembling is performed.

    Args:
        depth (`torch.Tensor`):
            Input ensemble depth maps.
        scale_invariant (`bool`, *optional*, defaults to `True`):
            Whether to treat predictions as scale-invariant.
        shift_invariant (`bool`, *optional*, defaults to `True`):
            Whether to treat predictions as shift-invariant.
        output_uncertainty (`bool`, *optional*, defaults to `False`):
            Whether to output uncertainty map.
        reduction (`str`, *optional*, defaults to `"median"`):
            Reduction method used to ensemble aligned predictions. The accepted values are: `"mean"` and
            `"median"`.
        regularizer_strength (`float`, *optional*, defaults to `0.02`):
            Strength of the regularizer that pulls the aligned predictions to the unit range from 0 to 1.
        max_iter (`int`, *optional*, defaults to `2`):
            Maximum number of the alignment solver steps. Refer to `scipy.optimize.minimize` function, `options`
            argument.
        tol (`float`, *optional*, defaults to `1e-3`):
            Alignment solver tolerance. The solver stops when the tolerance is reached.
        max_res (`int`, *optional*, defaults to `1024`):
            Resolution at which the alignment is performed; `None` matches the `processing_resolution`.
    Returns:
        A tensor of aligned and ensembled depth maps and optionally a tensor of uncertainties of the same shape:
        `(1, 1, H, W)`.
    
marigold/util/ensemble.py