Source code for pytorch_lightning.loops.epoch.training_epoch_loop
# Copyright The PyTorch Lightning team.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
import math
from collections import defaultdict, OrderedDict
from typing import Any, DefaultDict, Dict, Generator, List, Optional, overload, Tuple, Union
import numpy as np
import torch
import pytorch_lightning as pl
from pytorch_lightning import loops # import as loops to avoid circular imports
from pytorch_lightning.loops.batch import TrainingBatchLoop
from pytorch_lightning.loops.batch.training_batch_loop import _OUTPUTS_TYPE as _BATCH_OUTPUTS_TYPE
from pytorch_lightning.loops.utilities import _get_active_optimizers, _is_max_limit_reached, _v1_8_output_format
from pytorch_lightning.trainer.connectors.logger_connector.result import _ResultCollection
from pytorch_lightning.trainer.progress import BatchProgress, SchedulerProgress
from pytorch_lightning.trainer.supporters import CombinedLoader
from pytorch_lightning.utilities.apply_func import apply_to_collection
from pytorch_lightning.utilities.auto_restart import _collect_states_on_rank_zero_over_collection
from pytorch_lightning.utilities.exceptions import MisconfigurationException
from pytorch_lightning.utilities.fetching import AbstractDataFetcher, DataLoaderIterDataFetcher
from pytorch_lightning.utilities.model_helpers import is_overridden
from pytorch_lightning.utilities.rank_zero import rank_zero_deprecation, rank_zero_warn
from pytorch_lightning.utilities.signature_utils import is_param_in_hook_signature
from pytorch_lightning.utilities.warnings import WarningCache
_OUTPUTS_TYPE = List[_BATCH_OUTPUTS_TYPE]
[docs]class TrainingEpochLoop(loops.Loop[_OUTPUTS_TYPE]):
"""Runs over all batches in a dataloader (one epoch).
Args:
min_steps: The minimum number of steps (batches) to process
max_steps: The maximum number of steps (batches) to process
"""
def __init__(self, min_steps: Optional[int] = None, max_steps: int = -1) -> None:
super().__init__()
if max_steps < -1:
raise MisconfigurationException(
f"`max_steps` must be a non-negative integer or -1 (infinite steps). You passed in {max_steps}."
)
self.min_steps = min_steps
self.max_steps = max_steps
self.batch_progress = BatchProgress()
self.scheduler_progress = SchedulerProgress()
self.batch_loop = TrainingBatchLoop()
self.val_loop = loops.EvaluationLoop(verbose=False)
self._results = _ResultCollection(training=True)
self._outputs: _OUTPUTS_TYPE = []
self._warning_cache = WarningCache()
# caches the loaded dataloader state until dataloader objects are available
self._dataloader_state_dict: Dict[str, Any] = {}
self._batches_that_stepped: int = 0
@property
def total_batch_idx(self) -> int:
"""Returns the current batch index (across epochs)"""
# use `ready` instead of `completed` in case this is accessed after `completed` has been increased
# but before the next `ready` increase
return self.batch_progress.total.ready - 1
@property
def batch_idx(self) -> int:
"""Returns the current batch index (within this epoch)"""
# use `ready` instead of `completed` in case this is accessed after `completed` has been increased
# but before the next `ready` increase
return self.batch_progress.current.ready - 1
@property
def global_step(self) -> int:
lightning_module = self.trainer.lightning_module
if lightning_module is None or lightning_module.automatic_optimization:
return self.batch_loop.optimizer_loop.optim_progress.optimizer_steps
return self.batch_loop.manual_loop.optim_step_progress.total.completed
@property
def _is_training_done(self) -> bool:
max_steps_reached = _is_max_limit_reached(self.global_step, self.max_steps)
return max_steps_reached or self._num_ready_batches_reached()
@property
def _is_validation_done(self) -> bool:
# when we are restarting we want to check whether the val loop has finished
return not self.restarting or self.val_loop.done
@property
def done(self) -> bool:
"""Evaluates when to leave the loop."""
return (self._is_training_done and self._is_validation_done) or self.trainer.should_stop
[docs] def connect( # type: ignore[override]
self,
batch_loop: Optional[TrainingBatchLoop] = None,
val_loop: Optional["loops.EvaluationLoop"] = None,
) -> None:
"""Optionally connect a custom batch or validation loop to this training epoch loop."""
if batch_loop is not None:
self.batch_loop = batch_loop
if val_loop is not None:
self.val_loop = val_loop
[docs] def reset(self) -> None:
"""Resets the internal state of the loop for a new run."""
if self.restarting:
self.batch_progress.reset_on_restart()
self.scheduler_progress.reset_on_restart()
self.batch_loop.optimizer_loop.optim_progress.reset_on_restart()
trainer = self.trainer
if not trainer.state._fault_tolerant_mode.is_enabled and trainer.num_training_batches != float("inf"):
expected_steps = math.ceil(trainer.num_training_batches / trainer.accumulate_grad_batches)
if self.global_step % expected_steps != 0:
rank_zero_warn(
"You're resuming from a checkpoint that ended before the epoch ended. This can cause unreliable"
" results if further training is done. Consider using an end-of-epoch checkpoint or enabling"
" fault-tolerant training:"
" https://pytorch-lightning.readthedocs.io/en/stable/advanced/fault_tolerant_training.html"
)
else:
self.batch_progress.reset_on_run()
self.scheduler_progress.reset_on_run()
self.batch_loop.optimizer_loop.optim_progress.reset_on_run()
# when the epoch starts, the total val batch progress should be reset as it's supposed to count the batches
# seen per epoch, this is useful for tracking when validation is run multiple times per epoch
self.val_loop.epoch_loop.batch_progress.total.reset()
self._outputs = []
[docs] def on_run_start(self, data_fetcher: AbstractDataFetcher) -> None: # type: ignore[override]
self._reload_dataloader_state_dict(data_fetcher)
_ = iter(data_fetcher) # creates the iterator inside the fetcher
# add the previous `fetched` value to properly track `is_last_batch` with no prefetching
data_fetcher.fetched += self.batch_progress.current.ready
data_fetcher._start_profiler = self._on_before_fetch
data_fetcher._stop_profiler = self._on_after_fetch
def _on_before_fetch(self) -> None:
self.trainer.profiler.start(f"[{self.__class__.__name__}].train_dataloader_next")
def _on_after_fetch(self) -> None:
self.trainer.profiler.stop(f"[{self.__class__.__name__}].train_dataloader_next")
[docs] def advance(self, data_fetcher: AbstractDataFetcher) -> None: # type: ignore[override]
"""Runs a single training batch.
Raises:
StopIteration: When the epoch is canceled by the user returning -1
"""
if self.restarting and self._should_check_val_fx():
# skip training and run validation in `on_advance_end`
return
# we are going to train first so the val loop does not need to restart
self.val_loop.restarting = False
if not isinstance(data_fetcher, DataLoaderIterDataFetcher):
batch_idx = self.batch_idx + 1
batch = next(data_fetcher)
else:
batch_idx, batch = next(data_fetcher)
self.batch_progress.is_last_batch = data_fetcher.done
kwargs = self._build_kwargs(OrderedDict(), batch, batch_idx)
self.batch_progress.increment_ready()
self.trainer._logger_connector.on_batch_start(batch, batch_idx)
if batch is None:
self._warning_cache.warn("train_dataloader yielded None. If this was on purpose, ignore this warning...")
batch_output = []
else:
# hook
self.trainer._call_callback_hooks("on_batch_start")
# hook
self.trainer._call_callback_hooks("on_train_batch_start", batch, batch_idx)
response = self.trainer._call_lightning_module_hook("on_train_batch_start", batch, batch_idx)
self.trainer._call_strategy_hook("on_train_batch_start", batch, batch_idx)
if response == -1:
self.batch_progress.increment_processed()
raise StopIteration
self.batch_progress.increment_started()
with self.trainer.profiler.profile("run_training_batch"):
batch_output = self.batch_loop.run(kwargs)
self.batch_progress.increment_processed()
# update non-plateau LR schedulers
# update epoch-interval ones only when we are at the end of training epoch
self.update_lr_schedulers("step", update_plateau_schedulers=False)
if self._num_ready_batches_reached():
self.update_lr_schedulers("epoch", update_plateau_schedulers=False)
batch_end_outputs = self._prepare_outputs_training_batch_end(
batch_output,
lightning_module=self.trainer.lightning_module,
num_optimizers=len(self.trainer.optimizers),
)
self.trainer._call_callback_hooks("on_train_batch_end", batch_end_outputs, batch, batch_idx)
self.trainer._call_lightning_module_hook("on_train_batch_end", batch_end_outputs, batch, batch_idx)
self.trainer._call_callback_hooks("on_batch_end")
self.trainer._logger_connector.on_batch_end()
self.batch_progress.increment_completed()
if is_overridden("training_epoch_end", self.trainer.lightning_module):
self._outputs.append(batch_output)
# -----------------------------------------
# SAVE METRICS TO LOGGERS AND PROGRESS_BAR
# -----------------------------------------
self.trainer._logger_connector.update_train_step_metrics()
[docs] def on_advance_end(self) -> None:
# -----------------------------------------
# VALIDATE IF NEEDED
# -----------------------------------------
should_check_val = self._should_check_val_fx()
if should_check_val:
self.trainer.validating = True
self._run_validation()
self.trainer.training = True
# update plateau LR scheduler after metrics are logged
self.update_lr_schedulers("step", update_plateau_schedulers=True)
if not self._should_accumulate():
# this is increased once per batch disregarding multiple optimizers or tbptt on purpose for loggers
self._batches_that_stepped += 1
# this will save based on the `batches_that_stepped` value
self._save_loggers_on_train_batch_end()
# if training finished, defer exit to the parent. this assumes there will be enough time in between
# which might not be the case depending on what's in the `*_epoch_end` hooks
if not self._is_training_done:
# if fault tolerant is enabled and process has been notified, exit.
self.trainer._exit_gracefully_on_signal()
[docs] def on_run_end(self) -> _OUTPUTS_TYPE:
outputs, self._outputs = self._outputs, []
return outputs
[docs] def teardown(self) -> None:
self._results.cpu()
self.batch_loop.teardown()
self.val_loop.teardown()
[docs] def on_save_checkpoint(self) -> Dict:
state_dict = super().on_save_checkpoint()
state_dict["_batches_that_stepped"] = self._batches_that_stepped
trainer = self._trainer
if (
trainer is not None
and trainer.state._fault_tolerant_mode.is_enabled
and trainer.train_dataloader is not None
and not self._num_completed_batches_reached() # did not finish
# TODO: fault-tolerance requires a minimum number of batches so probably should be > 0
and self.batch_progress.current.ready # did start
):
loader: CombinedLoader = trainer.train_dataloader
state = loader.state_dict(has_completed=self._has_completed())
if state:
state_dict["dataloader_state_dict"] = _collect_states_on_rank_zero_over_collection(state)
return state_dict
[docs] def on_load_checkpoint(self, state_dict: Dict) -> None:
# cache the dataloader state dict until the dataloader objects are available
self._dataloader_state_dict = state_dict.get("dataloader_state_dict", {})
# restore global step instead to make sure logging works correctly if checkpoints <v1.6.5 used to resume
self._batches_that_stepped = state_dict.get("_batches_that_stepped", self.global_step)
def _run_validation(self) -> None:
# reload dataloaders
self.val_loop._reload_evaluation_dataloaders()
with torch.no_grad():
self.val_loop.run()
def _accumulated_batches_reached(self) -> bool:
"""Determine if accumulation will be finished by the end of the current batch."""
return self.batch_progress.current.ready % self.trainer.accumulate_grad_batches == 0
def _num_ready_batches_reached(self) -> bool:
"""Checks if we are in the last batch or if there are more batches to follow."""
epoch_finished_on_ready = self.batch_progress.current.ready == self.trainer.num_training_batches
return epoch_finished_on_ready or self.batch_progress.is_last_batch
def _num_completed_batches_reached(self) -> bool:
epoch_finished_on_completed = self.batch_progress.current.completed == self.trainer.num_training_batches
dataloader_consumed_successfully = self.batch_progress.is_last_batch and self._has_completed()
return epoch_finished_on_completed or dataloader_consumed_successfully
def _has_completed(self) -> bool:
return self.batch_progress.current.ready == self.batch_progress.current.completed
def _should_accumulate(self) -> bool:
"""Checks if the optimizer step should be performed or gradients should be accumulated for the current
step."""
accumulation_done = self._accumulated_batches_reached()
# Lightning steps on the final batch
is_final_batch = self._num_ready_batches_reached()
# but the strategy might not
strategy_accumulates_on_final_batch = self.trainer.strategy.handles_gradient_accumulation or not is_final_batch
return not accumulation_done and strategy_accumulates_on_final_batch
@staticmethod
def _prepare_outputs_training_batch_end(
batch_output: _BATCH_OUTPUTS_TYPE,
lightning_module: "pl.LightningModule",
num_optimizers: int,
) -> Union[List[List[Dict[str, Any]]], List[Dict[str, Any]]]:
"""Processes the outputs from the batch loop into the format passed to the ``on_train_batch_end`` hook."""
if not batch_output:
return [] # type: ignore[return-value]
# convert optimizer dicts to list
if lightning_module.automatic_optimization:
batch_output = apply_to_collection(
batch_output, dtype=dict, function=_convert_optim_dict, num_optimizers=num_optimizers
)
array = np.array(batch_output, dtype=object)
# TODO: remove in v1.8
if (
num_optimizers > 1
and lightning_module.truncated_bptt_steps > 0
and is_overridden("on_train_batch_end", lightning_module)
and not _v1_8_output_format(lightning_module.on_train_batch_end)
):
rank_zero_deprecation(
"You are training with multiple optimizers AND truncated backpropagation through time enabled."
" The current format of the `on_train_batch_end(outputs, ...)` is a 2d list with sizes"
" (n_optimizers, tbptt_steps), however, this has been deprecated and will change in version v1.8 to"
" (tbptt_steps, n_optimizers). You can update your code by adding the following parameter to your"
" hook signature: `on_train_batch_end(outputs, ..., new_format=True)`."
)
# (tbptt_steps, n_opt) -> (n_opt, tbptt_steps)
if array.ndim == 1:
array = np.expand_dims(array, 1)
array = array.transpose((1, 0))
# squeeze all single-element dimensions
array = array.squeeze()
array = array.tolist()
array = _recursive_unpad(array)
return array
@staticmethod
def _prepare_outputs_training_epoch_end(
batch_outputs: _OUTPUTS_TYPE,
lightning_module: "pl.LightningModule",
num_optimizers: int,
) -> Union[List[List[List[Dict[str, Any]]]], List[List[Dict[str, Any]]], List[Dict[str, Any]]]:
"""Processes the outputs from the batch loop into the format passed to the ``training_epoch_end`` hook."""
# `batch_outputs` (plural) is the same as `epoch_end_output` (singular)
if not batch_outputs:
return [] # type: ignore[return-value]
# convert optimizer dicts to list
if lightning_module.automatic_optimization:
batch_outputs = apply_to_collection(
batch_outputs, dtype=dict, function=_convert_optim_dict, num_optimizers=num_optimizers
)
array = _recursive_pad(batch_outputs)
# TODO: remove in v1.8
if (
num_optimizers > 1
and lightning_module.truncated_bptt_steps > 0
and not _v1_8_output_format(lightning_module.on_train_epoch_end)
):
rank_zero_deprecation(
"You are training with multiple optimizers AND truncated backpropagation through time enabled."
" The current format of the `training_epoch_end(outputs)` is a 3d list with sizes"
" (n_optimizers, n_batches, tbptt_steps), however, this has been deprecated and will change in version"
" v1.8 to (n_batches, tbptt_steps, n_optimizers). You can update your code by adding the following"
" parameter to your hook signature: `training_epoch_end(outputs, new_format=True)`."
)
# (n_batches, tbptt_steps, n_opt) -> (n_opt, n_batches, tbptt_steps)
if array.ndim == 2:
array = np.expand_dims(array, 2)
array = array.transpose((2, 0, 1))
# squeeze all single-element dimensions
array = array.squeeze()
array = array.tolist()
array = _recursive_unpad(array)
# in case we squeezed from 1-element array to a 0-dim array
array = array if isinstance(array, list) else [array]
# remove residual empty lists
array = [item for item in array if not isinstance(item, list) or len(item)]
return array
[docs] def update_lr_schedulers(self, interval: str, update_plateau_schedulers: bool) -> None:
"""updates the lr schedulers based on the given interval."""
if interval == "step" and self._should_accumulate():
return
active_optimizers = _get_active_optimizers(
self.trainer.optimizers, self.trainer.optimizer_frequencies, self.total_batch_idx
)
self._update_learning_rates(
interval=interval,
update_plateau_schedulers=update_plateau_schedulers,
opt_indices=[opt_idx for opt_idx, _ in active_optimizers],
)
def _update_learning_rates(
self, interval: str, update_plateau_schedulers: bool, opt_indices: Optional[List[int]] = None
) -> None:
"""Update learning rates.
Args:
interval: either 'epoch' or 'step'.
update_plateau_schedulers: control whether ``ReduceLROnPlateau`` or non-plateau schedulers get updated.
This is used so non-plateau schedulers can be updated before running validation. Checkpoints are
commonly saved during validation, however, on-plateau schedulers might monitor a validation metric
so they have to be updated separately.
opt_indices: indices of the optimizers to update.
"""
if not self.trainer.lr_scheduler_configs or not self.trainer.lightning_module.automatic_optimization:
return
if opt_indices is None:
opt_indices = []
for config in self.trainer.lr_scheduler_configs:
if config.opt_idx not in opt_indices:
continue
if update_plateau_schedulers ^ config.reduce_on_plateau:
continue
current_idx = self.batch_idx if interval == "step" else self.trainer.current_epoch
current_idx += 1 # account for both batch and epoch starts from 0
# Take step if call to update_learning_rates matches the interval key and
# the current step modulo the schedulers frequency is zero
if config.interval == interval and current_idx % config.frequency == 0:
monitor_val = None
if config.reduce_on_plateau:
monitor_key = config.monitor
assert monitor_key is not None
monitor_val = self._get_monitor_value(monitor_key)
if monitor_val is None:
if config.strict:
avail_metrics = list(self.trainer.callback_metrics)
raise MisconfigurationException(
f"ReduceLROnPlateau conditioned on metric {monitor_key}"
f" which is not available. Available metrics are: {avail_metrics}."
" Condition can be set using `monitor` key in lr scheduler dict"
)
rank_zero_warn(
f"ReduceLROnPlateau conditioned on metric {monitor_key}"
" which is not available but strict is set to `False`."
" Skipping learning rate update.",
category=RuntimeWarning,
)
continue
self.scheduler_progress.increment_ready()
# update LR
self.trainer._call_lightning_module_hook(
"lr_scheduler_step",
config.scheduler,
config.opt_idx,
monitor_val,
)
self.scheduler_progress.increment_completed()
def _get_monitor_value(self, key: str) -> Optional[Any]:
# this is a separate method to aid in testing
return self.trainer.callback_metrics.get(key)
def _should_check_val_epoch(self) -> bool:
return self.trainer.enable_validation and (
self.trainer.check_val_every_n_epoch is None
or (self.trainer.current_epoch + 1) % self.trainer.check_val_every_n_epoch == 0
)
def _should_check_val_fx(self) -> bool:
"""Decide if we should run validation."""
if not self._should_check_val_epoch():
return False
# val_check_batch is inf for iterable datasets with no length defined
is_infinite_dataset = self.trainer.val_check_batch == float("inf")
is_last_batch = self.batch_progress.is_last_batch
if is_last_batch and is_infinite_dataset:
return True
if self.trainer.should_stop:
return True
# TODO(@awaelchli): let training/eval loop handle logic around limit_*_batches and val_check_batch
is_val_check_batch = is_last_batch
if isinstance(self.trainer.limit_train_batches, int) and is_infinite_dataset:
is_val_check_batch = (self.batch_idx + 1) % self.trainer.limit_train_batches == 0
elif self.trainer.val_check_batch != float("inf"):
# if `check_val_every_n_epoch is `None`, run a validation loop every n training batches
# else condition it based on the batch_idx of the current epoch
current_iteration = self.total_batch_idx if self.trainer.check_val_every_n_epoch is None else self.batch_idx
is_val_check_batch = (current_iteration + 1) % self.trainer.val_check_batch == 0
return is_val_check_batch
def _save_loggers_on_train_batch_end(self) -> None:
"""Flushes loggers to disk."""
if self.trainer.should_stop:
for logger in self.trainer.loggers:
logger.save()
def _reload_dataloader_state_dict(self, data_fetcher: AbstractDataFetcher) -> None:
if self._dataloader_state_dict:
data_fetcher.dataloader.load_state_dict(self._dataloader_state_dict)
self._dataloader_state_dict = {}
def _build_kwargs(self, kwargs: OrderedDict, batch: Any, batch_idx: int) -> OrderedDict:
"""Helper method to build the arguments for the current step.
Args:
kwargs: The kwargs passed down to the hooks.
batch: The current batch to run through the step.
batch_idx: The current batch idx.
Returns:
The kwargs passed down to the hooks.
"""
kwargs["batch"] = batch
training_step_fx = getattr(self.trainer.lightning_module, "training_step")
# the `batch_idx` is optional, however, when there's more than 1 argument we cannot differentiate whether the
# user wants the `batch_idx` or another key like `optimizer_idx` as we are not strict about the argument names
if is_param_in_hook_signature(training_step_fx, "batch_idx", min_args=2):
kwargs["batch_idx"] = batch_idx
return kwargs
def _convert_optim_dict(outs: Dict[int, Dict[str, Any]], num_optimizers: int) -> List[Optional[Dict[str, Any]]]:
"""Converts an optimizer dict to a list in which the key of the dict determines the position of the element.
Example::
>>> _convert_optim_dict({0: {"loss": 0.0}, 2: {"loss": 0.2}}, num_optimizers=3)
[{'loss': 0.0}, None, {'loss': 0.2}]
"""
return [outs[opt_idx] if opt_idx in outs else None for opt_idx in range(num_optimizers)]
@overload
def _recursive_unpad(nested: List[Any], value: Optional[Any] = None) -> List[Any]:
...
@overload
def _recursive_unpad(nested: Any, value: Optional[Any] = None) -> Any:
...
def _recursive_unpad(nested: Union[Any, List[Any]], value: Optional[Any] = None) -> Union[Any, List[Any]]:
"""Removes the given pad value from the nested list. Not strictly the reverse operation of
:func:`_recursive_pad` because it removes the padding element everywhere, not just from the end of a list.
Example::
>>> _recursive_unpad([[[0, 1, 0]], [2], [0, 0]], value=0)
[[[1]], [2], []]
"""
if not isinstance(nested, list):
return nested
return [_recursive_unpad(item, value) for item in nested if item != value]
def _recursive_pad(nested: List[Any], fill_value: Optional[Any] = None) -> np.ndarray:
"""Pads a jagged nested list of lists with the given value such that a proper multi-dimensional array can be
formed with rectangular shape. The padding appends to the incomplete lists.
Example::
>>> _recursive_pad([[], [1], [2, 3], [4]], fill_value=0) # doctest: +NORMALIZE_WHITESPACE
array([[0, 0], [1, 0], [2, 3], [4, 0]], dtype=object)
"""
# code adapted from stackexchange:
# https://codereview.stackexchange.com/questions/222623/pad-a-ragged-multidimensional-array-to-rectangular-shape
dimensions = _get_max_shape(nested)
result = np.full(dimensions, fill_value, dtype=object)
for index, value in _iterate_nested_array(nested):
result[index] = value
return result
def _get_dimensions(array: List[Any], level: int = 0) -> Generator:
yield level, len(array)
if all(isinstance(row, list) for row in array):
for row in array:
yield from _get_dimensions(row, level + 1)
def _get_max_shape(array: List[Any]) -> List[int]:
"""Calculates the max size in each dimension of a jagged (non-rectangular) nested list of lists.
Example::
>>> _get_max_shape([[], [[1], [2]], []])
[3, 2, 1]
"""
dimensions: DefaultDict[int, int] = defaultdict(int)
for level, length in _get_dimensions(array):
dimensions[level] = max(dimensions[level], length)
return [value for _, value in sorted(dimensions.items())]
def _iterate_nested_array(array: List[Any], index: Tuple = ()) -> Generator:
if all(isinstance(item, list) for item in array):
for idx, row in enumerate(array):
yield from _iterate_nested_array(row, (*index, idx))
else: # final level
yield (*index, slice(len(array))), array
