Source code for numpyro.ops.indexing

# Copyright Contributors to the Pyro project.
# SPDX-License-Identifier: Apache-2.0

import jax.numpy as jnp

def _is_batched(arg):
    return jnp.ndim(arg) > 0

[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 ``len(x.shape) == 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 integer tensor (i.e. with empty event shape). This function does not support Nontrivial slices or boolean tensor 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 ``len(shape) > 0``, then this function behaves like standard indexing:: if not any(isinstance(a, jnp.ndarray) and len(a.shape) > 0 for a in args): assert Vindex(x)[args] == x[args] **References** [1] introduces ``vindex`` as a helper for vectorized indexing. This implementation is similar to the proposed notation ``x.vindex[]`` except for slightly different handling of ``Ellipsis``. :param jnp.ndarray tensor: A tensor to be indexed. :param tuple args: An index, as args to ``__getitem__``. :returns: A nonstandard interpretation of ``tensor[args]``. :rtype: jnp.ndarray """ if not isinstance(args, tuple): return tensor[args] if not args: return tensor assert jnp.ndim(tensor) > 0 # 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),) * (jnp.ndim(tensor) - len(args)) + args else: args = args + (slice(None),) * (jnp.ndim(tensor) - len(args)) old_event_dim = len(args) assert len(args) == jnp.ndim(tensor) 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 jnp.ndim(tensor) > 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 arange()s. if arg != slice(None): raise NotImplementedError("Nontrivial slices are not supported") arg = jnp.arange(tensor.shape[i], dtype=jnp.int32) 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 jnp.ndarray 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)