import torch
from . import scatter_add, scatter_max
[docs]def scatter_logsumexp(src, index, dim=-1, out=None, dim_size=None,
fill_value=None, eps=1e-12):
r"""Fills :attr:`out` with the log of summed exponentials of all values
from the :attr:`src` tensor at the indices specified in the :attr:`index`
tensor along a given axis :attr:`dim`.
If multiple indices reference the same location, their
**exponential contributions add**
(`cf.` :meth:`~torch_scatter.scatter_add`).
For one-dimensional tensors, the operation computes
.. math::
\mathrm{out}_i = \log \, \left( \exp(\mathrm{out}_i) + \sum_j
\exp(\mathrm{src}_j) \right)
where :math:`\sum_j` is over :math:`j` such that
:math:`\mathrm{index}_j = i`.
Args:
src (Tensor): The source tensor.
index (LongTensor): The indices of elements to scatter.
dim (int, optional): The axis along which to index.
(default: :obj:`-1`)
out (Tensor, optional): The destination tensor. (default: :obj:`None`)
dim_size (int, optional): If :attr:`out` is not given, automatically
create output with size :attr:`dim_size` at dimension :attr:`dim`.
If :attr:`dim_size` is not given, a minimal sized output tensor is
returned. (default: :obj:`None`)
fill_value (int, optional): If :attr:`out` is not given, automatically
fill output tensor with :attr:`fill_value`. (default: :obj:`None`)
eps (float, optional): Small value to ensure numerical stability.
(default: :obj:`1e-12`)
:rtype: :class:`Tensor`
"""
if not torch.is_floating_point(src):
raise ValueError('`scatter_logsumexp` can only be computed over '
'tensors with floating point data types.')
max_value_per_index, _ = scatter_max(src, index, dim, out, dim_size,
fill_value)
max_per_src_element = max_value_per_index.gather(dim, index)
recentered_scores = src - max_per_src_element
out = (out - max_per_src_element).exp() if out is not None else None
sum_per_index = scatter_add(recentered_scores.exp(), index, dim, out,
dim_size, fill_value=0)
return torch.log(sum_per_index + eps) + max_value_per_index