# Source code for pyro.ops.indexing

```
# Copyright (c) 2017-2019 Uber Technologies, Inc.
# SPDX-License-Identifier: Apache-2.0
import torch
def _is_batched(arg):
return isinstance(arg, torch.Tensor) and arg.dim()
def _flatten(args, out):
if isinstance(args, tuple):
for arg in args:
_flatten(arg, out)
else:
# Combine consecutive Ellipsis.
if args is Ellipsis and out and out[-1] is Ellipsis:
return
out.append(args)
[docs]def index(tensor, args):
"""
Indexing with nested tuples.
See also the convenience wrapper :class:`Index`.
This is useful for writing indexing code that is compatible with multiple
interpretations, e.g. scalar evaluation, vectorized evaluation, or
reshaping.
For example suppose ``x`` is a parameter with ``x.dim() == 2`` and we wish
to generalize the expression ``x[..., t]`` where ``t`` can be any of:
- a scalar ``t=1`` as in ``x[..., 1]``;
- a slice ``t=slice(None)`` equivalent to ``x[..., :]``; or
- a reshaping operation ``t=(Ellipsis, None)`` equivalent to
``x.unsqueeze(-1)``.
While naive indexing would work for the first two , the third example would
result in a nested tuple ``(Ellipsis, (Ellipsis, None))``. This helper
flattens that nested tuple and combines consecutive ``Ellipsis``.
:param torch.Tensor tensor: A tensor to be indexed.
:param tuple args: An index, as args to ``__getitem__``.
:returns: A flattened interpetation of ``tensor[args]``.
:rtype: torch.Tensor
"""
if not isinstance(args, tuple):
return tensor[args]
if not args:
return tensor
# Flatten.
flat = []
_flatten(args, flat)
args = tuple(flat)
return tensor[args]
[docs]class Index:
"""
Convenience wrapper around :func:`index`.
The following are equivalent::
Index(x)[..., i, j, :]
index(x, (Ellipsis, i, j, slice(None)))
:param torch.Tensor tensor: A tensor to be indexed.
:return: An object with a special :meth:`__getitem__` method.
"""
def __init__(self, tensor):
self._tensor = tensor
def __getitem__(self, args):
return index(self._tensor, args)
[docs]def vindex(tensor, args):
"""
Vectorized advanced indexing with broadcasting semantics.
See also the convenience wrapper :class:`Vindex`.
This is useful for writing indexing code that is compatible with batching
and enumeration, especially for selecting mixture components with discrete
random variables.
For example suppose ``x`` is a parameter with ``x.dim() == 3`` and we wish
to generalize the expression ``x[i, :, j]`` from integer ``i,j`` to tensors
``i,j`` with batch dims and enum dims (but no event dims). Then we can
write the generalize version using :class:`Vindex` ::
xij = Vindex(x)[i, :, j]
batch_shape = broadcast_shape(i.shape, j.shape)
event_shape = (x.size(1),)
assert xij.shape == batch_shape + event_shape
To handle the case when ``x`` may also contain batch dimensions (e.g. if
``x`` was sampled in a plated context as when using vectorized particles),
:func:`vindex` uses the special convention that ``Ellipsis`` denotes batch
dimensions (hence ``...`` can appear only on the left, never in the middle
or in the right). Suppose ``x`` has event dim 3. Then we can write::
old_batch_shape = x.shape[:-3]
old_event_shape = x.shape[-3:]
xij = Vindex(x)[..., i, :, j] # The ... denotes unknown batch shape.
new_batch_shape = broadcast_shape(old_batch_shape, i.shape, j.shape)
new_event_shape = (x.size(1),)
assert xij.shape = new_batch_shape + new_event_shape
Note that this special handling of ``Ellipsis`` differs from the NEP [1].
Formally, this function assumes:
1. Each arg is either ``Ellipsis``, ``slice(None)``, an integer, or a
batched ``torch.LongTensor`` (i.e. with empty event shape). This
function does not support Nontrivial slices or ``torch.BoolTensor``
masks. ``Ellipsis`` can only appear on the left as ``args[0]``.
2. If ``args[0] is not Ellipsis`` then ``tensor`` is not
batched, and its event dim is equal to ``len(args)``.
3. If ``args[0] is Ellipsis`` then ``tensor`` is batched and
its event dim is equal to ``len(args[1:])``. Dims of ``tensor``
to the left of the event dims are considered batch dims and will be
broadcasted with dims of tensor args.
Note that if none of the args is a tensor with ``.dim() > 0``, then this
function behaves like standard indexing::
if not any(isinstance(a, torch.Tensor) and a.dim() for a in args):
assert Vindex(x)[args] == x[args]
**References**
[1] https://www.numpy.org/neps/nep-0021-advanced-indexing.html
introduces ``vindex`` as a helper for vectorized indexing.
The Pyro implementation is similar to the proposed notation
``x.vindex[]`` except for slightly different handling of ``Ellipsis``.
:param torch.Tensor tensor: A tensor to be indexed.
:param tuple args: An index, as args to ``__getitem__``.
:returns: A nonstandard interpetation of ``tensor[args]``.
:rtype: torch.Tensor
"""
if not isinstance(args, tuple):
return tensor[args]
if not args:
return tensor
# Compute event dim before and after indexing.
if args[0] is Ellipsis:
args = args[1:]
if not args:
return tensor
old_event_dim = len(args)
args = (slice(None),) * (tensor.dim() - len(args)) + args
else:
args = args + (slice(None),) * (tensor.dim() - len(args))
old_event_dim = len(args)
assert len(args) == tensor.dim()
if any(a is Ellipsis for a in args):
raise NotImplementedError("Non-leading Ellipsis is not supported")
# In simple cases, standard advanced indexing broadcasts correctly.
is_standard = True
if tensor.dim() > old_event_dim and _is_batched(args[0]):
is_standard = False
elif any(_is_batched(a) for a in args[1:]):
is_standard = False
if is_standard:
return tensor[args]
# Convert args to use broadcasting semantics.
new_event_dim = sum(isinstance(a, slice) for a in args[-old_event_dim:])
new_dim = 0
args = list(args)
for i, arg in reversed(list(enumerate(args))):
if isinstance(arg, slice):
# Convert slices to torch.arange()s.
if arg != slice(None):
raise NotImplementedError("Nontrivial slices are not supported")
arg = torch.arange(tensor.size(i), dtype=torch.long, device=tensor.device)
arg = arg.reshape((-1,) + (1,) * new_dim)
new_dim += 1
elif _is_batched(arg):
# Reshape nontrivial tensors.
arg = arg.reshape(arg.shape + (1,) * new_event_dim)
args[i] = arg
args = tuple(args)
return tensor[args]
[docs]class Vindex:
"""
Convenience wrapper around :func:`vindex`.
The following are equivalent::
Vindex(x)[..., i, j, :]
vindex(x, (Ellipsis, i, j, slice(None)))
:param torch.Tensor tensor: A tensor to be indexed.
:return: An object with a special :meth:`__getitem__` method.
"""
def __init__(self, tensor):
self._tensor = tensor
def __getitem__(self, args):
return vindex(self._tensor, args)
```