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"""Collection of Ray Losses"""

import torch
from torchtyping import TensorType

from nerfactory.cameras.rays import RaySamples


def distortion_loss(
    ray_samples: RaySamples, densities: TensorType["bs":..., "num_samples", 1]
) -> TensorType["bs":..., 1]:
    """Ray baserd distortion loss proposed in MipNeRF-360.

    .. math::

        \\mathcal{L}(\\mathbf{s}, \\mathbf{w}) =\\iint\\limits_{-\\infty}^{\\,\\,\\,\\infty}
        \\mathbf{w}_\\mathbf{s}(u)\\mathbf{w}_\\mathbf{s}(v)|u - v|\\,d_{u}\\,d_{v}

    where :math:`\\mathbf{w}_\\mathbf{s}(u)=\\sum_i w_i \\mathbb{1}_{[\\mathbf{s}_i, \\mathbf{s}_{i+1})}(u)`
    is the weight at location :math:`u` between bin locations :math:`s_i` and :math:`s_{i+1}`.

    Args:
        ray_samples: Ray samples to compute loss over
        densities: Predicted sample densities

    Returns:
        Distortion Loss.
    """

    # Compute the weight at each sample location
    weights = ray_samples.get_weights(densities)

    midpoints = (ray_samples.frustums.starts + ray_samples.frustums.ends) / 2.0  # (..., num_samples, 1)

    loss = (
        weights * weights[..., None, :, 0] * torch.abs(midpoints - midpoints[..., None, :, 0])
    )  # (..., num_samples, num_samples)
    loss = torch.sum(loss, dim=(-1, -2))[..., None]  # (..., num_samples)
    loss = loss + 1 / 3.0 * torch.sum(weights**2 * (ray_samples.frustums.ends - ray_samples.frustums.starts), dim=-2)

    return loss