botorch/utils/multi_objective/box_decompositions/utils.py [223:252]:
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    pareto_Y_sorted: Tensor, ref_point: Tensor
) -> Tensor:
    r"""Compute an axis-aligned partitioning of the non-dominated space for 2 objectives.

    Args:
        pareto_Y_sorted: A `(batch_shape) x n_pareto x 2`-dim tensor of pareto outcomes
            that are sorted by the 0th dimension in increasing order. All points must be
            better than the reference point.
        ref_point: A `(batch_shape) x 2`-dim reference point.

    Returns:
        A `2 x (batch_shape) x n_pareto + 1 x m`-dim tensor of cell bounds.
    """
    # add boundary point to each front
    # the boundary point is the extreme value in each outcome
    # (a single coordinate of reference point)
    batch_shape = pareto_Y_sorted.shape[:-2]
    if ref_point.ndim == pareto_Y_sorted.ndim - 1:
        expanded_boundary_point = ref_point.unsqueeze(-2)
    else:
        view_shape = torch.Size([1] * len(batch_shape)) + torch.Size([1, 2])
        expanded_shape = batch_shape + torch.Size([1, 2])
        expanded_boundary_point = ref_point.view(view_shape).expand(expanded_shape)

    # add the points (ref, y) and (x, ref) to the corresponding ends
    pareto_Y_sorted0, pareto_Y_sorted1 = torch.split(pareto_Y_sorted, 1, dim=-1)
    expanded_boundary_point0, expanded_boundary_point1 = torch.split(
        expanded_boundary_point, 1, dim=-1
    )
    left_end = torch.cat(
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botorch/utils/multi_objective/box_decompositions/utils.py [291:319]:
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    pareto_Y_sorted: Tensor, ref_point: Tensor
) -> Tensor:
    r"""Compute an axis-aligned partitioning of the dominated space for 2-objectives.

    Args:
        pareto_Y_sorted: A `(batch_shape) x n_pareto x 2`-dim tensor of pareto outcomes
            that are sorted by the 0th dimension in increasing order.
        ref_point: A `2`-dim reference point.

    Returns:
        A `2 x (batch_shape) x n_pareto x m`-dim tensor of cell bounds.
    """
    # add boundary point to each front
    # the boundary point is the extreme value in each outcome
    # (a single coordinate of reference point)
    batch_shape = pareto_Y_sorted.shape[:-2]
    if ref_point.ndim == pareto_Y_sorted.ndim - 1:
        expanded_boundary_point = ref_point.unsqueeze(-2)
    else:
        view_shape = torch.Size([1] * len(batch_shape)) + torch.Size([1, 2])
        expanded_shape = batch_shape + torch.Size([1, 2])
        expanded_boundary_point = ref_point.view(view_shape).expand(expanded_shape)

    # add the points (ref, y) and (x, ref) to the corresponding ends
    pareto_Y_sorted0, pareto_Y_sorted1 = torch.split(pareto_Y_sorted, 1, dim=-1)
    expanded_boundary_point0, expanded_boundary_point1 = torch.split(
        expanded_boundary_point, 1, dim=-1
    )
    left_end = torch.cat(
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