def retrieval_fall_out(preds: Tensor, target: Tensor, k: Optional[int]=None) -> Tensor:
    'Computes the Fall-out (for information retrieval), as explained in `IR Fall-out`_ Fall-out is the fraction\n    of non-relevant documents retrieved among all the non-relevant documents.\n\n    ``preds`` and ``target`` should be of the same shape and live on the same device. If no ``target`` is ``True``,\n    ``0`` is returned. ``target`` must be either `bool` or `integers` and ``preds`` must be `float`,\n    otherwise an error is raised. If you want to measure Fall-out@K, ``k`` must be a positive integer.\n\n    Args:\n        preds: estimated probabilities of each document to be relevant.\n        target: ground truth about each document being relevant or not.\n        k: consider only the top k elements (default: `None`, which considers them all)\n\n    Returns:\n        a single-value tensor with the fall-out (at ``k``) of the predictions ``preds`` w.r.t. the labels ``target``.\n\n    Raises:\n        ValueError:\n            If ``k`` parameter is not `None` or an integer larger than 0\n\n    Example:\n        >>> from  torchmetrics.functional import retrieval_fall_out\n        >>> preds = tensor([0.2, 0.3, 0.5])\n        >>> target = tensor([True, False, True])\n        >>> retrieval_fall_out(preds, target, k=2)\n        tensor(1.)\n    '
    (preds, target) = _check_retrieval_functional_inputs(preds, target)
    k = (preds.shape[(- 1)] if (k is None) else k)
    if (not (isinstance(k, int) and (k > 0))):
        raise ValueError('`k` has to be a positive integer or None')
    target = (1 - target)
    if (not target.sum()):
        return tensor(0.0, device=preds.device)
    relevant = target[torch.argsort(preds, dim=(- 1), descending=True)][:k].sum().float()
    return (relevant / target.sum())
Computes the Fall-out (for information retrieval), as explained in `IR Fall-out`_ Fall-out is the fraction
of non-relevant documents retrieved among all the non-relevant documents.

``preds`` and ``target`` should be of the same shape and live on the same device. If no ``target`` is ``True``,
``0`` is returned. ``target`` must be either `bool` or `integers` and ``preds`` must be `float`,
otherwise an error is raised. If you want to measure Fall-out@K, ``k`` must be a positive integer.

Args:
    preds: estimated probabilities of each document to be relevant.
    target: ground truth about each document being relevant or not.
    k: consider only the top k elements (default: `None`, which considers them all)

Returns:
    a single-value tensor with the fall-out (at ``k``) of the predictions ``preds`` w.r.t. the labels ``target``.

Raises:
    ValueError:
        If ``k`` parameter is not `None` or an integer larger than 0

Example:
    >>> from  torchmetrics.functional import retrieval_fall_out
    >>> preds = tensor([0.2, 0.3, 0.5])
    >>> target = tensor([True, False, True])
    >>> retrieval_fall_out(preds, target, k=2)
    tensor(1.)
def retrieval_fall_out(preds: Tensor, target: Tensor, k: Optional[int]=None) -> Tensor:
    'Computes the Fall-out (for information retrieval), as explained in `IR Fall-out`_ Fall-out is the fraction\n    of non-relevant documents retrieved among all the non-relevant documents.\n\n    ``preds`` and ``target`` should be of the same shape and live on the same device. If no ``target`` is ``True``,\n    ``0`` is returned. ``target`` must be either `bool` or `integers` and ``preds`` must be `float`,\n    otherwise an error is raised. If you want to measure Fall-out@K, ``k`` must be a positive integer.\n\n    Args:\n        preds: estimated probabilities of each document to be relevant.\n        target: ground truth about each document being relevant or not.\n        k: consider only the top k elements (default: `None`, which considers them all)\n\n    Returns:\n        a single-value tensor with the fall-out (at ``k``) of the predictions ``preds`` w.r.t. the labels ``target``.\n\n    Raises:\n        ValueError:\n            If ``k`` parameter is not `None` or an integer larger than 0\n\n    Example:\n        >>> from  torchmetrics.functional import retrieval_fall_out\n        >>> preds = tensor([0.2, 0.3, 0.5])\n        >>> target = tensor([True, False, True])\n        >>> retrieval_fall_out(preds, target, k=2)\n        tensor(1.)\n    '
    (preds, target) = _check_retrieval_functional_inputs(preds, target)
    k = (preds.shape[(- 1)] if (k is None) else k)
    if (not (isinstance(k, int) and (k > 0))):
        raise ValueError('`k` has to be a positive integer or None')
    target = (1 - target)
    if (not target.sum()):
        return tensor(0.0, device=preds.device)
    relevant = target[torch.argsort(preds, dim=(- 1), descending=True)][:k].sum().float()
    return (relevant / target.sum())