414 lines
17 KiB
Python
414 lines
17 KiB
Python
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# Copyright 2019 The JAX Authors.
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#
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# Licensed under the Apache License, Version 2.0 (the "License");
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# you may not use this file except in compliance with the License.
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# You may obtain a copy of the License at
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#
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# https://www.apache.org/licenses/LICENSE-2.0
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#
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# Unless required by applicable law or agreed to in writing, software
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# distributed under the License is distributed on an "AS IS" BASIS,
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# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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# See the License for the specific language governing permissions and
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# limitations under the License.
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# Helpers for indexed updates.
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import sys
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from typing import Any, Callable, Optional, Sequence, Tuple, Union
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import warnings
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import numpy as np
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from jax import lax
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from jax._src import core
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from jax._src import dtypes
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from jax._src import util
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from jax._src.lax import lax as lax_internal
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from jax._src.numpy import lax_numpy as jnp
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from jax._src.numpy import reductions
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from jax._src.numpy.util import check_arraylike, promote_dtypes
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Array = Any
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if sys.version_info >= (3, 10):
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from types import EllipsisType
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SingleIndex = Union[None, int, slice, Sequence[int], Array, EllipsisType]
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else:
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SingleIndex = Union[None, int, slice, Sequence[int], Array]
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Index = Union[SingleIndex, Tuple[SingleIndex, ...]]
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Scalar = Union[complex, float, int, np.number]
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def _scatter_update(x, idx, y, scatter_op, indices_are_sorted,
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unique_indices, mode=None, normalize_indices=True):
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"""Helper for indexed updates.
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Computes the value of x that would result from computing::
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x[idx] op= y
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except in a pure functional way, with no in-place updating.
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Args:
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x: ndarray to be updated.
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idx: None, an integer, a slice, an ellipsis, an ndarray with integer dtype,
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or a tuple of those indicating the locations of `x` into which to scatter-
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update the values in `y`.
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y: values to be scattered.
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scatter_op: callable, one of lax.scatter, lax.scatter_add, lax.scatter_min,
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or lax_scatter_max.
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indices_are_sorted: whether `idx` is known to be sorted
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unique_indices: whether `idx` is known to be free of duplicates
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Returns:
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An ndarray representing an updated `x` after performing the scatter-update.
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"""
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x = jnp.asarray(x)
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if (isinstance(y, int) and np.issubdtype(x.dtype, np.integer) and
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np.iinfo(x.dtype).min <= y <= np.iinfo(x.dtype).max):
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y = jnp.asarray(y, dtype=x.dtype)
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else:
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y = jnp.asarray(y)
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# XLA gathers and scatters are very similar in structure; the scatter logic
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# is more or less a transpose of the gather equivalent.
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treedef, static_idx, dynamic_idx = jnp._split_index_for_jit(idx, x.shape)
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return _scatter_impl(x, y, scatter_op, treedef, static_idx, dynamic_idx,
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indices_are_sorted, unique_indices, mode,
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normalize_indices)
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# TODO(phawkins): re-enable jit after fixing excessive recompilation for
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# slice indexes (e.g., slice(0, 5, None), slice(10, 15, None), etc.).
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# @partial(jit, static_argnums=(2, 3, 4))
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def _scatter_impl(x, y, scatter_op, treedef, static_idx, dynamic_idx,
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indices_are_sorted, unique_indices, mode,
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normalize_indices):
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dtype = lax.dtype(x)
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weak_type = dtypes.is_weakly_typed(x)
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if dtype != lax.dtype(y) and dtype != dtypes.result_type(x, y):
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# TODO(jakevdp): change this to an error after the deprecation period.
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warnings.warn("scatter inputs have incompatible types: cannot safely cast "
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f"value from dtype={lax.dtype(y)} to dtype={lax.dtype(x)}. "
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"In future JAX releases this will result in an error.",
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FutureWarning)
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idx = jnp._merge_static_and_dynamic_indices(treedef, static_idx, dynamic_idx)
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indexer = jnp._index_to_gather(jnp.shape(x), idx,
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normalize_indices=normalize_indices)
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# Avoid calling scatter if the slice shape is empty, both as a fast path and
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# to handle cases like zeros(0)[array([], int32)].
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if core.is_empty_shape(indexer.slice_shape):
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return x
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x, y = promote_dtypes(x, y)
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# Broadcast `y` to the slice output shape.
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y = jnp.broadcast_to(y, tuple(indexer.slice_shape))
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# Collapse any `None`/`jnp.newaxis` dimensions.
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y = jnp.squeeze(y, axis=indexer.newaxis_dims)
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if indexer.reversed_y_dims:
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y = lax.rev(y, indexer.reversed_y_dims)
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# Transpose the gather dimensions into scatter dimensions (cf.
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# lax._gather_transpose_rule)
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dnums = lax.ScatterDimensionNumbers(
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update_window_dims=indexer.dnums.offset_dims,
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inserted_window_dims=indexer.dnums.collapsed_slice_dims,
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scatter_dims_to_operand_dims=indexer.dnums.start_index_map
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)
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out = scatter_op(
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x, indexer.gather_indices, y, dnums,
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indices_are_sorted=indexer.indices_are_sorted or indices_are_sorted,
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unique_indices=indexer.unique_indices or unique_indices,
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mode=mode)
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return lax_internal._convert_element_type(out, dtype, weak_type)
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def _get_identity(op, dtype):
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"""Get an appropriate identity for a given operation in a given dtype."""
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if op is lax.scatter_add:
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return 0
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elif op is lax.scatter_mul:
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return 1
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elif op is lax.scatter_min:
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if dtype == dtypes.bool_:
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return True
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elif jnp.issubdtype(dtype, jnp.integer):
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return jnp.iinfo(dtype).max
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return float('inf')
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elif op is lax.scatter_max:
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if dtype == dtypes.bool_:
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return False
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elif jnp.issubdtype(dtype, jnp.integer):
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return jnp.iinfo(dtype).min
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return -float('inf')
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else:
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raise ValueError(f"Unrecognized op: {op}")
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def _segment_update(name: str,
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data: Array,
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segment_ids: Array,
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scatter_op: Callable,
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num_segments: Optional[int] = None,
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indices_are_sorted: bool = False,
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unique_indices: bool = False,
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bucket_size: Optional[int] = None,
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reducer: Optional[Callable] = None,
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mode: Optional[lax.GatherScatterMode] = None) -> Array:
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check_arraylike(name, data, segment_ids)
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mode = lax.GatherScatterMode.FILL_OR_DROP if mode is None else mode
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data = jnp.asarray(data)
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segment_ids = jnp.asarray(segment_ids)
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dtype = data.dtype
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if num_segments is None:
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num_segments = np.max(segment_ids) + 1
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num_segments = core.concrete_or_error(int, num_segments, "segment_sum() `num_segments` argument.")
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if num_segments is not None and num_segments < 0:
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raise ValueError("num_segments must be non-negative.")
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if bucket_size is None:
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out = jnp.full((num_segments,) + data.shape[1:],
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_get_identity(scatter_op, dtype), dtype=dtype)
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return _scatter_update(
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out, segment_ids, data, scatter_op, indices_are_sorted,
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unique_indices, normalize_indices=False, mode=mode)
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# Bucketize indices and perform segment_update on each bucket to improve
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# numerical stability for operations like product and sum.
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assert reducer is not None
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num_buckets = util.ceil_of_ratio(segment_ids.size, bucket_size)
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out = jnp.full((num_buckets, num_segments) + data.shape[1:],
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_get_identity(scatter_op, dtype), dtype=dtype)
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out = _scatter_update(
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out, np.index_exp[jnp.arange(segment_ids.shape[0]) // bucket_size,
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segment_ids[None, :]],
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data, scatter_op, indices_are_sorted,
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unique_indices, normalize_indices=False, mode=mode)
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return reducer(out, axis=0).astype(dtype)
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def segment_sum(data: Array,
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segment_ids: Array,
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num_segments: Optional[int] = None,
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indices_are_sorted: bool = False,
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unique_indices: bool = False,
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bucket_size: Optional[int] = None,
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mode: Optional[lax.GatherScatterMode] = None) -> Array:
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"""Computes the sum within segments of an array.
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Similar to TensorFlow's `segment_sum
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<https://www.tensorflow.org/api_docs/python/tf/math/segment_sum>`_
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Args:
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data: an array with the values to be summed.
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segment_ids: an array with integer dtype that indicates the segments of
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`data` (along its leading axis) to be summed. Values can be repeated and
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need not be sorted.
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num_segments: optional, an int with nonnegative value indicating the number
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of segments. The default is set to be the minimum number of segments that
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would support all indices in ``segment_ids``, calculated as
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``max(segment_ids) + 1``.
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Since `num_segments` determines the size of the output, a static value
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must be provided to use ``segment_sum`` in a JIT-compiled function.
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indices_are_sorted: whether ``segment_ids`` is known to be sorted.
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unique_indices: whether `segment_ids` is known to be free of duplicates.
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bucket_size: size of bucket to group indices into. ``segment_sum`` is
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performed on each bucket separately to improve numerical stability of
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addition. Default ``None`` means no bucketing.
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mode: a :class:`jax.lax.GatherScatterMode` value describing how
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out-of-bounds indices should be handled. By default, values outside of the
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range [0, num_segments) are dropped and do not contribute to the sum.
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Returns:
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An array with shape :code:`(num_segments,) + data.shape[1:]` representing the
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segment sums.
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Examples:
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Simple 1D segment sum:
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>>> data = jnp.arange(5)
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>>> segment_ids = jnp.array([0, 0, 1, 1, 2])
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>>> segment_sum(data, segment_ids)
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Array([1, 5, 4], dtype=int32)
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Using JIT requires static `num_segments`:
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>>> from jax import jit
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>>> jit(segment_sum, static_argnums=2)(data, segment_ids, 3)
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Array([1, 5, 4], dtype=int32)
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"""
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return _segment_update(
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"segment_sum", data, segment_ids, lax.scatter_add, num_segments,
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indices_are_sorted, unique_indices, bucket_size, reductions.sum, mode=mode)
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def segment_prod(data: Array,
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segment_ids: Array,
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num_segments: Optional[int] = None,
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indices_are_sorted: bool = False,
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unique_indices: bool = False,
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bucket_size: Optional[int] = None,
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mode: Optional[lax.GatherScatterMode] = None) -> Array:
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"""Computes the product within segments of an array.
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Similar to TensorFlow's `segment_prod
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<https://www.tensorflow.org/api_docs/python/tf/math/segment_prod>`_
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Args:
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data: an array with the values to be reduced.
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segment_ids: an array with integer dtype that indicates the segments of
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`data` (along its leading axis) to be reduced. Values can be repeated and
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need not be sorted. Values outside of the range [0, num_segments) are
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dropped and do not contribute to the result.
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num_segments: optional, an int with nonnegative value indicating the number
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of segments. The default is set to be the minimum number of segments that
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would support all indices in ``segment_ids``, calculated as
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``max(segment_ids) + 1``.
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Since `num_segments` determines the size of the output, a static value
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must be provided to use ``segment_prod`` in a JIT-compiled function.
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indices_are_sorted: whether ``segment_ids`` is known to be sorted.
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unique_indices: whether `segment_ids` is known to be free of duplicates.
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bucket_size: size of bucket to group indices into. ``segment_prod`` is
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performed on each bucket separately to improve numerical stability of
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addition. Default ``None`` means no bucketing.
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mode: a :class:`jax.lax.GatherScatterMode` value describing how
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out-of-bounds indices should be handled. By default, values outside of the
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range [0, num_segments) are dropped and do not contribute to the sum.
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Returns:
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An array with shape :code:`(num_segments,) + data.shape[1:]` representing the
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segment products.
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Examples:
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Simple 1D segment product:
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>>> data = jnp.arange(6)
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>>> segment_ids = jnp.array([0, 0, 1, 1, 2, 2])
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>>> segment_prod(data, segment_ids)
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Array([ 0, 6, 20], dtype=int32)
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Using JIT requires static `num_segments`:
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>>> from jax import jit
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>>> jit(segment_prod, static_argnums=2)(data, segment_ids, 3)
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Array([ 0, 6, 20], dtype=int32)
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"""
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return _segment_update(
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"segment_prod", data, segment_ids, lax.scatter_mul, num_segments,
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indices_are_sorted, unique_indices, bucket_size, reductions.prod, mode=mode)
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def segment_max(data: Array,
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segment_ids: Array,
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num_segments: Optional[int] = None,
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indices_are_sorted: bool = False,
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unique_indices: bool = False,
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bucket_size: Optional[int] = None,
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mode: Optional[lax.GatherScatterMode] = None) -> Array:
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"""Computes the maximum within segments of an array.
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Similar to TensorFlow's `segment_max
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<https://www.tensorflow.org/api_docs/python/tf/math/segment_max>`_
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Args:
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data: an array with the values to be reduced.
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segment_ids: an array with integer dtype that indicates the segments of
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`data` (along its leading axis) to be reduced. Values can be repeated and
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need not be sorted. Values outside of the range [0, num_segments) are
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dropped and do not contribute to the result.
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num_segments: optional, an int with nonnegative value indicating the number
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of segments. The default is set to be the minimum number of segments that
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would support all indices in ``segment_ids``, calculated as
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``max(segment_ids) + 1``.
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Since `num_segments` determines the size of the output, a static value
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must be provided to use ``segment_max`` in a JIT-compiled function.
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indices_are_sorted: whether ``segment_ids`` is known to be sorted.
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unique_indices: whether `segment_ids` is known to be free of duplicates.
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|
bucket_size: size of bucket to group indices into. ``segment_max`` is
|
||
|
|
performed on each bucket separately. Default ``None`` means no bucketing.
|
||
|
|
mode: a :class:`jax.lax.GatherScatterMode` value describing how
|
||
|
|
out-of-bounds indices should be handled. By default, values outside of the
|
||
|
|
range [0, num_segments) are dropped and do not contribute to the sum.
|
||
|
|
|
||
|
|
Returns:
|
||
|
|
An array with shape :code:`(num_segments,) + data.shape[1:]` representing the
|
||
|
|
segment maximums.
|
||
|
|
|
||
|
|
Examples:
|
||
|
|
Simple 1D segment max:
|
||
|
|
|
||
|
|
>>> data = jnp.arange(6)
|
||
|
|
>>> segment_ids = jnp.array([0, 0, 1, 1, 2, 2])
|
||
|
|
>>> segment_max(data, segment_ids)
|
||
|
|
Array([1, 3, 5], dtype=int32)
|
||
|
|
|
||
|
|
Using JIT requires static `num_segments`:
|
||
|
|
|
||
|
|
>>> from jax import jit
|
||
|
|
>>> jit(segment_max, static_argnums=2)(data, segment_ids, 3)
|
||
|
|
Array([1, 3, 5], dtype=int32)
|
||
|
|
"""
|
||
|
|
return _segment_update(
|
||
|
|
"segment_max", data, segment_ids, lax.scatter_max, num_segments,
|
||
|
|
indices_are_sorted, unique_indices, bucket_size, reductions.max, mode=mode)
|
||
|
|
|
||
|
|
|
||
|
|
def segment_min(data: Array,
|
||
|
|
segment_ids: Array,
|
||
|
|
num_segments: Optional[int] = None,
|
||
|
|
indices_are_sorted: bool = False,
|
||
|
|
unique_indices: bool = False,
|
||
|
|
bucket_size: Optional[int] = None,
|
||
|
|
mode: Optional[lax.GatherScatterMode] = None) -> Array:
|
||
|
|
"""Computes the minimum within segments of an array.
|
||
|
|
|
||
|
|
Similar to TensorFlow's `segment_min
|
||
|
|
<https://www.tensorflow.org/api_docs/python/tf/math/segment_min>`_
|
||
|
|
|
||
|
|
Args:
|
||
|
|
data: an array with the values to be reduced.
|
||
|
|
segment_ids: an array with integer dtype that indicates the segments of
|
||
|
|
`data` (along its leading axis) to be reduced. Values can be repeated and
|
||
|
|
need not be sorted. Values outside of the range [0, num_segments) are
|
||
|
|
dropped and do not contribute to the result.
|
||
|
|
num_segments: optional, an int with nonnegative value indicating the number
|
||
|
|
of segments. The default is set to be the minimum number of segments that
|
||
|
|
would support all indices in ``segment_ids``, calculated as
|
||
|
|
``max(segment_ids) + 1``.
|
||
|
|
Since `num_segments` determines the size of the output, a static value
|
||
|
|
must be provided to use ``segment_min`` in a JIT-compiled function.
|
||
|
|
indices_are_sorted: whether ``segment_ids`` is known to be sorted.
|
||
|
|
unique_indices: whether `segment_ids` is known to be free of duplicates.
|
||
|
|
bucket_size: size of bucket to group indices into. ``segment_min`` is
|
||
|
|
performed on each bucket separately. Default ``None`` means no bucketing.
|
||
|
|
mode: a :class:`jax.lax.GatherScatterMode` value describing how
|
||
|
|
out-of-bounds indices should be handled. By default, values outside of the
|
||
|
|
range [0, num_segments) are dropped and do not contribute to the sum.
|
||
|
|
|
||
|
|
Returns:
|
||
|
|
An array with shape :code:`(num_segments,) + data.shape[1:]` representing the
|
||
|
|
segment minimums.
|
||
|
|
|
||
|
|
Examples:
|
||
|
|
Simple 1D segment min:
|
||
|
|
|
||
|
|
>>> data = jnp.arange(6)
|
||
|
|
>>> segment_ids = jnp.array([0, 0, 1, 1, 2, 2])
|
||
|
|
>>> segment_min(data, segment_ids)
|
||
|
|
Array([0, 2, 4], dtype=int32)
|
||
|
|
|
||
|
|
Using JIT requires static `num_segments`:
|
||
|
|
|
||
|
|
>>> from jax import jit
|
||
|
|
>>> jit(segment_min, static_argnums=2)(data, segment_ids, 3)
|
||
|
|
Array([0, 2, 4], dtype=int32)
|
||
|
|
"""
|
||
|
|
return _segment_update(
|
||
|
|
"segment_min", data, segment_ids, lax.scatter_min, num_segments,
|
||
|
|
indices_are_sorted, unique_indices, bucket_size, reductions.min, mode=mode)
|