text: import itertools
  import math
  import numbers
  import tempfile
  from abc import ABCMeta, abstractmethod
  from collections import OrderedDict
  from copy import copy
  from pathlib import Path
  from typing import Any, Dict, List, Mapping, Optional, Sequence, Tuple, Type, Union, cast
  
  import torch
  from torch.optim.lr_scheduler import _LRScheduler
  from torch.optim.optimizer import Optimizer
  
  from ignite.engine import Engine
  
  
  class ParamScheduler(metaclass=ABCMeta):
      """An abstract class for updating an optimizer's parameter value during
      training.
  
      Args:
          optimizer (torch.optim.Optimizer or object): torch optimizer or any object with attribute ``param_groups``
              as a sequence.
          param_name (str): name of optimizer's parameter to update.
          save_history (bool, optional): whether to log the parameter values to
              `engine.state.param_history`, (default=False).
          param_group_index (int, optional): optimizer's parameters group to use
  
      Note:
          Parameter scheduler works independently of the internal state of the attached optimizer.
          More precisely, whatever the state of the optimizer (newly created or used by another scheduler) the scheduler
          sets defined absolute values.
  
      """
  
      def __init__(
          self,
          optimizer: Optimizer,
          param_name: str,
          save_history: bool = False,
          param_group_index: Optional[int] = None,
      ) -> None:
  
          if not (
              isinstance(optimizer, Optimizer)
              or (hasattr(optimizer, "param_groups") and isinstance(optimizer.param_groups, Sequence))
          ):
              raise TypeError(
                  "Argument optimizer should be torch.optim.Optimizer or has attribute 'param_groups' as list/tuple, "
                  f"but given {type(optimizer)}"
              )
  
          self.optimizer = optimizer
          self.param_group_index = param_group_index
          self.param_name = param_name
          self.event_index = 0
          self._save_history = save_history
          self._state_attrs = ["event_index", "param_name", "save_history", "param_group_index"]
  
      def __call__(self, engine: Optional[Engine], name: Optional[str] = None) -> None:
  
          value = self.get_param()
  
          if isinstance(value, list):
              if len(value) != len(self.optimizer_param_groups):
                  raise ValueError(
                      "size of value is different than optimizer_param_groups "
                      f"{len(value)} != {len(self.optimizer_param_groups)}"
                  )
  
              for i, param_group in enumerate(self.optimizer_param_groups):
                  param_group[self.param_name] = value[i]
          else:
              for i, param_group in enumerate(self.optimizer_param_groups):
                  param_group[self.param_name] = value
  
          if name is None:
              name = self.param_name
  
          if self.save_history and engine:
              if not hasattr(engine.state, "param_history") or engine.state.param_history is None:  # type: ignore
                  setattr(engine.state, "param_history", {})
              engine.state.param_history.setdefault(name, [])  # type: ignore[attr-defined]
              values = [pg[self.param_name] for pg in self.optimizer_param_groups]
              engine.state.param_history[name].append(values)  # type: ignore[attr-defined]
          self.event_index += 1
  
      @property
      def optimizer_param_groups(self) -> List[Dict[str, Any]]:
          if self.param_group_index is None:
              return self.optimizer.param_groups
          return [self.optimizer.param_groups[self.param_group_index]]
  
      @property
      def save_history(self) -> bool:
          return self._save_history
  
      @save_history.setter
      def save_history(self, value: bool) -> None:
          self._save_history = value
  
      def state_dict(self) -> Dict[str, Any]:
          """Returns a dictionary containing a whole state of ParamScheduler.
  
          Returns:
              dict:
                  a dictionary containing a whole state of ParamScheduler
          """
          destination = OrderedDict()
          for name in self._state_attrs:
              if hasattr(self, name):
                  val = getattr(self, name)
                  if hasattr(val, "state_dict"):
                      val = val.state_dict()
                  destination[name] = copy(val)
          return destination
  
      def load_state_dict(self, state_dict: Mapping) -> None:
          """Copies parameters from :attr:`state_dict` into this ParamScheduler.
  
          Args:
              state_dict (dict): a dict containing parameters.
          """
          if not isinstance(state_dict, Mapping):
              raise TypeError(f"Argument state_dict should be a dictionary, but given {type(state_dict)}")
  
          for name in self._state_attrs:
              if name not in state_dict:
                  raise ValueError(
                      f"Required state attribute '{name}' is absent in provided state_dict '{state_dict.keys()}'"
                  )
              val = state_dict[name]
              obj = getattr(self, name)
              if isinstance(val, Mapping) and hasattr(obj, "load_state_dict"):
                  obj.load_state_dict(val)
              else:
                  setattr(self, name, val)
  
      @abstractmethod
      def get_param(self) -> Union[List[float], float]:
          """Method to get current optimizer's parameter values
  
          Returns:
              list of params, or scalar param
          """
          pass
  
      @classmethod
      def simulate_values(cls, num_events: int, **scheduler_kwargs: Any) -> List[List[int]]:
          """Method to simulate scheduled values during `num_events` events.
  
          Args:
              num_events (int): number of events during the simulation.
              **scheduler_kwargs : parameter scheduler configuration kwargs.
  
          Returns:
              list of pairs: [event_index, value]
  
          Examples:
  
          .. code-block:: python
  
              lr_values = np.array(LinearCyclicalScheduler.simulate_values(num_events=50, param_name='lr',
                                                                           start_value=1e-1, end_value=1e-3,
                                                                           cycle_size=10))
  
              plt.plot(lr_values[:, 0], lr_values[:, 1], label="learning rate")
              plt.xlabel("events")
              plt.ylabel("values")
              plt.legend()
  
          """
          keys_to_remove = ["optimizer", "save_history"]
          for key in keys_to_remove:
              if key in scheduler_kwargs:
                  del scheduler_kwargs[key]
          values = []
          scheduler = cls(optimizer=_get_fake_optimizer(), save_history=False, **scheduler_kwargs)
          for i in range(num_events):
              scheduler(engine=None)
              values.append([i, scheduler.optimizer_param_groups[0][scheduler.param_name]])
          return values
  
      @classmethod
      def plot_values(cls, num_events: int, **scheduler_kwargs: Mapping) -> Any:
          """Method to plot simulated scheduled values during `num_events` events.
  
          This class requires `matplotlib package <https://matplotlib.org/>`_ to be installed:
  
          .. code-block:: bash
  
              pip install matplotlib
  
          Args:
              num_events (int): number of events during the simulation.
              **scheduler_kwargs : parameter scheduler configuration kwargs.
  
          Returns:
              matplotlib.lines.Line2D
  
          Examples:
  
              .. code-block:: python
  
                  import matplotlib.pylab as plt
  
                  plt.figure(figsize=(10, 7))
                  LinearCyclicalScheduler.plot_values(num_events=50, param_name='lr',
                                                      start_value=1e-1, end_value=1e-3, cycle_size=10))
          """
          try:
              import matplotlib.pylab as plt
          except ImportError:
              raise RuntimeError(
                  "This method requires matplotlib to be installed. "
                  "Please install it with command: \n pip install matplotlib"
              )
  
          values = cls.simulate_values(num_events=num_events, **scheduler_kwargs)
          label = scheduler_kwargs.get("param_name", "learning rate")
          ax = plt.plot([e for e, _ in values], [v for _, v in values], label=label)
          plt.legend()
          plt.grid(which="both")
          return ax
  
  
  class CyclicalScheduler(ParamScheduler):
      """An abstract class for updating an optimizer's parameter value over a
      cycle of some size.
  
      Args:
          optimizer (torch.optim.Optimizer or object): torch optimizer or any object with attribute ``param_groups``
              as a sequence.
          param_name (str): name of optimizer's parameter to update.
          start_value (float): value at start of cycle.
          end_value (float): value at the middle of the cycle.
          cycle_size (int): length of cycle, value should be larger than 1.
          cycle_mult (float, optional): ratio by which to change the cycle_size.
              at the end of each cycle (default=1.0).
          start_value_mult (float, optional): ratio by which to change the start value at the
              end of each cycle (default=1.0).
          end_value_mult (float, optional): ratio by which to change the end value at the
              end of each cycle (default=1.0).
          save_history (bool, optional): whether to log the parameter values to
              `engine.state.param_history`, (default=False).
          param_group_index (int, optional): optimizer's parameters group to use.
  
      Note:
          If the scheduler is bound to an 'ITERATION_*' event, 'cycle_size' should
          usually be the number of batches in an epoch.
      """
  
      def __init__(
          self,
          optimizer: Optimizer,
          param_name: str,
          start_value: float,
          end_value: float,
          cycle_size: int,
          cycle_mult: float = 1.0,
          start_value_mult: float = 1.0,
          end_value_mult: float = 1.0,
          save_history: bool = False,
          param_group_index: Optional[int] = None,
      ):
          super(CyclicalScheduler, self).__init__(
              optimizer, param_name, save_history=save_history, param_group_index=param_group_index
          )
          self.start_value = start_value
          self.end_value = end_value
          self.cycle_size = int(cycle_size)  # Ensure cycle_size is integer
          self.cycle_mult = cycle_mult
          self.cycle = 0
          self.start_value_mult = start_value_mult
          self.end_value_mult = end_value_mult
  
          if self.cycle_size < 2:
              raise ValueError(f"Argument cycle_size should be positive and larger than 1, but given {cycle_size}")
  
          self._state_attrs += [
              "start_value",
              "end_value",
              "cycle_size",
              "cycle_mult",
              "cycle",
              "start_value_mult",
              "end_value_mult",
          ]
  
      def __call__(self, engine: Optional[Engine], name: Optional[str] = None) -> None:
          if self.event_index != 0 and self.event_index % self.cycle_size == 0:
              self.event_index = 0
              self.cycle_size = int(self.cycle_size * self.cycle_mult)
              self.cycle += 1
              self.start_value *= self.start_value_mult
              self.end_value *= self.end_value_mult
  
          return super(CyclicalScheduler, self).__call__(engine, name)
  
  
  class LinearCyclicalScheduler(CyclicalScheduler):
      """Linearly adjusts param value to 'end_value' for a half-cycle, then linearly
      adjusts it back to 'start_value' for a half-cycle.
  
      Args:
          optimizer (torch.optim.Optimizer or object): torch optimizer or any object with attribute ``param_groups``
              as a sequence.
          param_name (str): name of optimizer's parameter to update.
          start_value (float): value at start of cycle.
          end_value (float): value at the middle of the cycle.
          cycle_size (int): length of cycle.
          cycle_mult (float, optional): ratio by which to change the cycle_size
              at the end of each cycle (default=1).
          start_value_mult (float, optional): ratio by which to change the start value at the
              end of each cycle (default=1.0).
          end_value_mult (float, optional): ratio by which to change the end value at the
              end of each cycle (default=1.0).
          save_history (bool, optional): whether to log the parameter values to
              `engine.state.param_history`, (default=False).
          param_group_index (int, optional): optimizer's parameters group to use.
  
      Note:
          If the scheduler is bound to an 'ITERATION_*' event, 'cycle_size' should
          usually be the number of batches in an epoch.
  
      Examples:
  
      .. code-block:: python
  
          from ignite.contrib.handlers.param_scheduler import LinearCyclicalScheduler
  
          scheduler = LinearCyclicalScheduler(optimizer, 'lr', 1e-3, 1e-1, len(train_loader))
          trainer.add_event_handler(Events.ITERATION_STARTED, scheduler)
          #
          # Linearly increases the learning rate from 1e-3 to 1e-1 and back to 1e-3
          # over the course of 1 epoch
          #
      """
  
      def get_param(self) -> float:
          cycle_progress = self.event_index / self.cycle_size
          return self.end_value + (self.start_value - self.end_value) * abs(cycle_progress - 0.5) * 2
  
  
  class CosineAnnealingScheduler(CyclicalScheduler):
      """Anneals 'start_value' to 'end_value' over each cycle.
  
      The annealing takes the form of the first half of a cosine
      wave (as suggested in [Smith17]_).
  
      Args:
          optimizer (torch.optim.Optimizer or object): torch optimizer or any object with attribute ``param_groups``
              as a sequence.
          param_name (str): name of optimizer's parameter to update.
          start_value (float): value at start of cycle.
          end_value (float): value at the end of the cycle.
          cycle_size (int): length of cycle.
          cycle_mult (float, optional): ratio by which to change the cycle_size
              at the end of each cycle (default=1).
          start_value_mult (float, optional): ratio by which to change the start value at the
              end of each cycle (default=1.0).
          end_value_mult (float, optional): ratio by which to change the end value at the
              end of each cycle (default=1.0).
          save_history (bool, optional): whether to log the parameter values to
              `engine.state.param_history`, (default=False).
          param_group_index (int, optional): optimizer's parameters group to use.
  
      Note:
          If the scheduler is bound to an 'ITERATION_*' event, 'cycle_size' should
          usually be the number of batches in an epoch.
  
      Examples:
  
      .. code-block:: python
  
          from ignite.contrib.handlers.param_scheduler import CosineAnnealingScheduler
  
          scheduler = CosineAnnealingScheduler(optimizer, 'lr', 1e-1, 1e-3, len(train_loader))
          trainer.add_event_handler(Events.ITERATION_STARTED, scheduler)
          #
          # Anneals the learning rate from 1e-1 to 1e-3 over the course of 1 epoch.
          #
  
      .. code-block:: python
  
          from ignite.contrib.handlers.param_scheduler import CosineAnnealingScheduler
          from ignite.contrib.handlers.param_scheduler import LinearCyclicalScheduler
  
          optimizer = SGD(
              [
                  {"params": model.base.parameters(), 'lr': 0.001},
                  {"params": model.fc.parameters(), 'lr': 0.01},
              ]
          )
  
          scheduler1 = LinearCyclicalScheduler(optimizer, 'lr', 1e-7, 1e-5, len(train_loader), param_group_index=0)
          trainer.add_event_handler(Events.ITERATION_STARTED, scheduler1, "lr (base)")
  
          scheduler2 = CosineAnnealingScheduler(optimizer, 'lr', 1e-5, 1e-3, len(train_loader), param_group_index=1)
          trainer.add_event_handler(Events.ITERATION_STARTED, scheduler2, "lr (fc)")
  
      .. [Smith17] Smith, Leslie N. "Cyclical learning rates for training neural networks."
                   Applications of Computer Vision (WACV), 2017 IEEE Winter Conference on. IEEE, 2017
      """
  
      def get_param(self) -> float:
          """Method to get current optimizer's parameter value
          """
          cycle_progress = self.event_index / self.cycle_size
          return self.start_value + ((self.end_value - self.start_value) / 2) * (1 - math.cos(math.pi * cycle_progress))
  
  
  class ConcatScheduler(ParamScheduler):
      """Concat a list of parameter schedulers.
  
      The `ConcatScheduler` goes through a list of schedulers given by `schedulers`. Duration of each
      scheduler is defined by `durations` list of integers.
  
      Args:
          schedulers (list of ParamScheduler): list of parameter schedulers.
          durations (list of int): list of number of events that lasts a parameter scheduler from schedulers.
          save_history (bool, optional): whether to log the parameter values to
              `engine.state.param_history`, (default=False).
  
      Examples:
  
      .. code-block:: python
  
          from ignite.contrib.handlers.param_scheduler import ConcatScheduler
          from ignite.contrib.handlers.param_scheduler import LinearCyclicalScheduler
          from ignite.contrib.handlers.param_scheduler import CosineAnnealingScheduler
  
          scheduler_1 = LinearCyclicalScheduler(optimizer, "lr", start_value=0.1, end_value=0.5, cycle_size=60)
          scheduler_2 = CosineAnnealingScheduler(optimizer, "lr", start_value=0.5, end_value=0.01, cycle_size=60)
  
          combined_scheduler = ConcatScheduler(schedulers=[scheduler_1, scheduler_2], durations=[30, ])
          trainer.add_event_handler(Events.ITERATION_STARTED, combined_scheduler)
          #
          # Sets the Learning rate linearly from 0.1 to 0.5 over 30 iterations. Then
          # starts an annealing schedule from 0.5 to 0.01 over 60 iterations.
          # The annealing cycles are repeated indefinitely.
          #
  
      """
  
      def __init__(self, schedulers: List[ParamScheduler], durations: List[int], save_history: bool = False) -> None:
  
          if not isinstance(schedulers, Sequence):
              raise TypeError(f"Argument schedulers should be a sequence, but given {schedulers}")
  
          if len(schedulers) < 2:
              raise ValueError(
                  f"Argument schedulers should be of more than one parameter schedulers, but given {schedulers}"
              )
  
          if not isinstance(durations, (list, tuple)):
              raise TypeError(f"Argument durations should be list/tuple, but given {durations}")
  
          if not all([isinstance(t, numbers.Integral) for t in durations]):
              raise ValueError(f"Argument durations should be list/tuple of integers, but given {durations}")
  
          if len(schedulers) != len(durations) + 1:
              raise ValueError(
                  "Incorrect number schedulers or duration values, " f"given {len(schedulers)} and {len(durations)}"
              )
  
          for i, scheduler in enumerate(schedulers):
              if not isinstance(scheduler, ParamScheduler) and not isinstance(scheduler, ParamGroupScheduler):
                  raise TypeError(
                      f"Value at index {i} of schedulers should be a parameter scheduler, but given {type(scheduler)}"
                  )
  
          self.schedulers = schedulers
          self.durations = durations
  
          tmp_optimizers = [s.optimizer for s in self.schedulers]
          tmp_list_optimizers = [s if isinstance(s, list) else [s] for s in tmp_optimizers]
          param_optimizers = list(itertools.chain(*tmp_list_optimizers))
  
          optimizer = list(set(param_optimizers))
          if len(optimizer) != 1:
              raise ValueError("schedulers should be related to same optimizer")
  
          tmp_param_names = [s.param_name for s in self.schedulers]
          tmp_list_param_names = [s if isinstance(s, list) else [s] for s in tmp_param_names]
          param_names = list(itertools.chain(*tmp_list_param_names))
  
          param_name = list(set(param_names))
          if len(param_name) != 1:
              raise ValueError("schedulers should be related to same param_name")
  
          # schedulers should have save_history sync with ParamGroupScheduler
          for s in schedulers:
              s.save_history = save_history
  
          super(ConcatScheduler, self).__init__(
              optimizer=optimizer[0], param_name=param_name[0], save_history=save_history
          )
  
          self._scheduler_index = 0
          self._setup_scheduler()
          self._state_attrs += ["_current_duration", "durations", "_scheduler_index"]
  
      def state_dict(self) -> Dict[str, Any]:
          """Returns a dictionary containing a whole state of ConcatScheduler.
  
          Returns:
              dict:
                  a dictionary containing a whole state of ConcatScheduler
          """
  
          state_dict = super(ConcatScheduler, self).state_dict()
          state_dict["schedulers"] = []
          for s in self.schedulers:
              state_dict["schedulers"].append(s.state_dict())
          return state_dict
  
      def load_state_dict(self, state_dict: Mapping) -> None:
          """Copies parameters from :attr:`state_dict` into this ConcatScheduler.
  
          Args:
              state_dict (dict): a dict containing parameters.
          """
          if not isinstance(state_dict, Mapping):
              raise TypeError(f"Argument state_dict should be a dictionary, but given {type(state_dict)}")
  
          if "schedulers" not in state_dict:
              raise ValueError(
                  f"Required state attribute 'schedulers' is absent in provided state_dict '{state_dict.keys()}'"
              )
          sds = state_dict["schedulers"]
          if len(sds) != len(self.schedulers):
              raise ValueError(
                  f"Input state_dict contains {len(sds)} state_dicts of concatenated schedulers, "
                  f"but {len(self.schedulers)} needed"
              )
  
          for s, sd in zip(self.schedulers, sds):
              s.load_state_dict(sd)
          super(ConcatScheduler, self).load_state_dict(state_dict)
          self._setup_scheduler()
  
      def _setup_scheduler(self) -> None:
          self._current_scheduler = self.schedulers[self._scheduler_index]
          self._current_duration = (
              self.durations[self._scheduler_index] if self._scheduler_index < len(self.durations) else -1
          )
  
      def __call__(self, engine: Optional[Engine], name: Optional[str] = None) -> None:
          if self._current_duration == 0:
              self._scheduler_index += 1
              self._setup_scheduler()
          self._current_scheduler(engine, name)
          self._current_duration -= 1
  
      @property
      def optimizer_param_groups(self) -> List[Dict[str, Any]]:
          # We need to setup optimizer_param_groups as property
          # to synchonize with the latest _current_scheduler and its internal optimizer_param_groups
          return self._current_scheduler.optimizer_param_groups
  
      @property
      def save_history(self) -> bool:
          return self._current_scheduler.save_history
  
      @save_history.setter
      def save_history(self, value: bool) -> None:
          for s in self.schedulers:
              s.save_history = value
  
      def get_param(self) -> Union[List[float], float]:
          return self._current_scheduler.get_param()
  
      @classmethod
      def simulate_values(  # type: ignore[override]
          cls,
          num_events: int,
          schedulers: List[ParamScheduler],
          durations: List[int],
          param_names: Optional[Union[List[str], Tuple[str]]] = None,
          **kwargs: Any
      ) -> List[List[int]]:
          """Method to simulate scheduled values during num_events events.
  
          Args:
              num_events (int): number of events during the simulation.
              schedulers (list of ParamScheduler): list of parameter schedulers.
              durations (list of int): list of number of events that lasts a parameter scheduler from schedulers.
              param_names (list or tuple of str, optional): parameter name or list of parameter names to simulate values.
                  By default, the first scheduler's parameter name is taken.
  
          Returns:
              list of [event_index, value_0, value_1, ...], where values correspond to `param_names`.
  
          """
          if param_names is not None:
              if not isinstance(param_names, (list, tuple)):
                  raise TypeError(f"Argument param_names should be list or tuple, but given {type(param_names)}")
              if not all(isinstance(item, str) for item in param_names):
                  raise ValueError(f"Argument param_names should be list or tuple of strings, but given {param_names}")
  
          tmp_param_optimizers = [s.optimizer for s in schedulers]
          tmp_list_param_optimizers = [s if isinstance(s, list) else [s] for s in tmp_param_optimizers]
          param_optimizers = list(itertools.chain(*tmp_list_param_optimizers))
  
          tmp_optimizer = list(set(param_optimizers))
          if len(tmp_optimizer) != 1:
              raise ValueError("schedulers should be related to same optimizer")
  
          optimizer = tmp_optimizer[0]
  
          # This scheduler uses `ParamScheduler` which
          # should be replicated in order to simulate LR values and
          # not perturb original scheduler.
          with tempfile.TemporaryDirectory() as tmpdirname:
              cache_filepath = Path(tmpdirname) / "ignite_lr_scheduler_cache.pt"
              objs = {f"lr_scheduler_{i}": s.state_dict() for i, s in enumerate(schedulers)}
              # all schedulers should be related to the same optimizer
              objs["optimizer"] = optimizer.state_dict()
  
              torch.save(objs, cache_filepath.as_posix())
  
              # do not save_history
              for s in schedulers:
                  s.save_history = False
  
              output = []
              scheduler = cls(  # type: ignore[call-arg]
                  schedulers=schedulers, save_history=False, durations=durations, **kwargs
              )
              if param_names is None:
                  param_names = [scheduler.param_name]
              for i in range(num_events):
                  scheduler(engine=None)
                  values = [i]
                  for param_name in param_names:
                      params = [p[param_name] for p in scheduler.optimizer_param_groups]
                      values = values + params
                  output.append(values)
  
              objs = torch.load(cache_filepath.as_posix())
              for i, s in enumerate(schedulers):
                  s.load_state_dict(objs[f"lr_scheduler_{i}"])
              optimizer.load_state_dict(objs["optimizer"])
  
              return output
  
  
  class LRScheduler(ParamScheduler):
      """A wrapper class to call `torch.optim.lr_scheduler` objects as `ignite` handlers.
  
      Args:
          lr_scheduler (subclass of `torch.optim.lr_scheduler._LRScheduler`): lr_scheduler object to wrap.
          save_history (bool, optional): whether to log the parameter values to
              `engine.state.param_history`, (default=False).
  
      .. code-block:: python
  
          from ignite.contrib.handlers.param_scheduler import LRScheduler
          from torch.optim.lr_scheduler import StepLR
  
          step_scheduler = StepLR(optimizer, step_size=3, gamma=0.1)
          scheduler = LRScheduler(step_scheduler)
  
          # In this example, we assume to have installed PyTorch>=1.1.0
          # (with new `torch.optim.lr_scheduler` behaviour) and
          # we attach scheduler to Events.ITERATION_COMPLETED
          # instead of Events.ITERATION_STARTED to make sure to use
          # the first lr value from the optimizer, otherwise it is will be skipped:
          trainer.add_event_handler(Events.ITERATION_COMPLETED, scheduler)
      """
  
      def __init__(self, lr_scheduler: _LRScheduler, save_history: bool = False) -> None:
  
          if not isinstance(lr_scheduler, _LRScheduler):
              raise TypeError(
                  "Argument lr_scheduler should be a subclass of torch.optim.lr_scheduler._LRScheduler, "
                  f"but given {type(lr_scheduler)}"
              )
  
          self.lr_scheduler = lr_scheduler
          super(LRScheduler, self).__init__(
              optimizer=self.lr_scheduler.optimizer,  # type: ignore[attr-defined]
              param_name="lr",
              save_history=save_history,
          )
          self._state_attrs += ["lr_scheduler"]
  
      def __call__(self, engine: Optional[Engine], name: Optional[str] = None) -> None:
          self.lr_scheduler.last_epoch += 1  # type: ignore[attr-defined]
          super(LRScheduler, self).__call__(engine, name)
  
      def get_param(self) -> Union[float, List[float]]:
          """Method to get current optimizer's parameter value
          """
          # Emulate context manager for pytorch>=1.4
          self.lr_scheduler._get_lr_called_within_step = True  # type: ignore[attr-defined]
          lr_list = cast(List[float], self.lr_scheduler.get_lr())
          self.lr_scheduler._get_lr_called_within_step = False  # type: ignore[attr-defined]
          if len(lr_list) == 1:
              return lr_list[0]
          else:
              return lr_list
  
      @classmethod
      def simulate_values(  # type: ignore[override]
          cls, num_events: int, lr_scheduler: _LRScheduler, **kwargs: Any
      ) -> List[List[int]]:
          """Method to simulate scheduled values during num_events events.
  
          Args:
              num_events (int): number of events during the simulation.
              lr_scheduler (subclass of `torch.optim.lr_scheduler._LRScheduler`): lr_scheduler object to wrap.
  
          Returns:
              list of pairs: [event_index, value]
  
          """
  
          if not isinstance(lr_scheduler, _LRScheduler):
              raise TypeError(
                  "Argument lr_scheduler should be a subclass of torch.optim.lr_scheduler._LRScheduler, "
                  f"but given {type(lr_scheduler)}"
              )
  
          # This scheduler uses `torch.optim.lr_scheduler._LRScheduler` which
          # should be replicated in order to simulate LR values and
          # not perturb original scheduler.
          with tempfile.TemporaryDirectory() as tmpdirname:
              cache_filepath = Path(tmpdirname) / "ignite_lr_scheduler_cache.pt"
              obj = {
                  "lr_scheduler": lr_scheduler.state_dict(),
                  "optimizer": lr_scheduler.optimizer.state_dict(),  # type: ignore[attr-defined]
              }
              torch.save(obj, cache_filepath.as_posix())
  
              values = []
              scheduler = cls(save_history=False, lr_scheduler=lr_scheduler, **kwargs)  # type: ignore[call-arg]
              for i in range(num_events):
                  params = [p[scheduler.param_name] for p in scheduler.optimizer_param_groups]
                  values.append([i] + params)
                  scheduler(engine=None)
  
              obj = torch.load(cache_filepath.as_posix())
              lr_scheduler.load_state_dict(obj["lr_scheduler"])
              lr_scheduler.optimizer.load_state_dict(obj["optimizer"])  # type: ignore[attr-defined]
  
              return values
  
  
  def create_lr_scheduler_with_warmup(
      lr_scheduler: Union[ParamScheduler, _LRScheduler],
      warmup_start_value: float,
      warmup_duration: int,
      warmup_end_value: Optional[float] = None,
      save_history: bool = False,
      output_simulated_values: Optional[List] = None,
  ) -> "ConcatScheduler":
      """
      Helper method to create a learning rate scheduler with a linear warm-up.
  
      Args:
          lr_scheduler (ParamScheduler or subclass of `torch.optim.lr_scheduler._LRScheduler`): learning rate scheduler
              after the warm-up.
          warmup_start_value (float): learning rate start value of the warm-up phase.
          warmup_duration (int): warm-up phase duration, number of events.
          warmup_end_value (float, optional): learning rate end value of the warm-up phase, (default=None). If None,
               warmup_end_value is set to optimizer initial lr.
          save_history (bool, optional): whether to log the parameter values to
              `engine.state.param_history`, (default=False).
          output_simulated_values (list, optional): optional output of simulated learning rate values.
              If output_simulated_values is a list of None, e.g. `[None] * 100`, after the execution it will be filled
              by 100 simulated learning rate values.
  
      Returns:
          ConcatScheduler: learning rate scheduler with linear warm-up.
  
      Note:
          If the first learning rate value provided by `lr_scheduler` is different from `warmup_end_value`, an additional
          event is added after the warm-up phase such that the warm-up ends with `warmup_end_value` value and then
          `lr_scheduler` provides its learning rate values as normally.
  
      Examples:
  
          .. code-block:: python
  
              torch_lr_scheduler = ExponentialLR(optimizer=optimizer, gamma=0.98)
              lr_values = [None] * 100
              scheduler = create_lr_scheduler_with_warmup(torch_lr_scheduler,
                                                          warmup_start_value=0.0,
                                                          warmup_end_value=0.1,
                                                          warmup_duration=10,
                                                          output_simulated_values=lr_values)
              lr_values = np.array(lr_values)
              # Plot simulated values
              plt.plot(lr_values[:, 0], lr_values[:, 1], label="learning rate")
  
              # Attach to the trainer
              trainer.add_event_handler(Events.ITERATION_STARTED, scheduler)
  
      """
      if not isinstance(lr_scheduler, (ParamScheduler, _LRScheduler)):
          raise TypeError(
              "Argument lr_scheduler should be a subclass of torch.optim.lr_scheduler._LRScheduler or "
              f"ParamScheduler, but given {type(lr_scheduler)}"
          )
  
      if not isinstance(warmup_duration, numbers.Integral):
          raise TypeError(f"Argument warmup_duration should be integer, but given {warmup_duration}")
  
      if not (warmup_duration > 1):
          raise ValueError(f"Argument warmup_duration should be at least 2 events, but given {warmup_duration}")
  
      warmup_schedulers = []  # type: List[ParamScheduler]
  
      for param_group_index, param_group in enumerate(lr_scheduler.optimizer.param_groups):
  
          if warmup_end_value is None:
              param_group_warmup_end_value = param_group["lr"]
          else:
              param_group_warmup_end_value = warmup_end_value
  
          milestones_values = [(0, warmup_start_value), (warmup_duration - 1, param_group_warmup_end_value)]
  
          if isinstance(lr_scheduler, _LRScheduler):
              init_lr = param_group["lr"]
  
              if init_lr != param_group_warmup_end_value:
                  milestones_values.append((warmup_duration, init_lr))
  
              lr_scheduler = LRScheduler(lr_scheduler, save_history=save_history)
          else:
              init_lr = lr_scheduler.get_param()
              if init_lr == param_group_warmup_end_value:
                  if warmup_duration > 2:
                      d = (param_group_warmup_end_value - warmup_start_value) / (warmup_duration - 1)
                      milestones_values[-1] = (warmup_duration - 2, param_group_warmup_end_value - d)
                  else:
                      milestones_values.pop(-1)
  
          warmup_schedulers.append(
              PiecewiseLinear(
                  lr_scheduler.optimizer,
                  param_name="lr",
                  milestones_values=milestones_values,
                  param_group_index=param_group_index,
                  save_history=save_history,
              )
          )
  
      warmup_scheduler = ParamGroupScheduler(warmup_schedulers, save_history=save_history)
  
      schedulers = [
          warmup_scheduler,
          lr_scheduler,
      ]  # type: List[Union[ParamScheduler, ParamGroupScheduler, _LRScheduler]]
      durations = [milestones_values[-1][0] + 1]
      combined_scheduler = ConcatScheduler(schedulers, durations=durations, save_history=save_history)
  
      if output_simulated_values is not None:
          if not isinstance(output_simulated_values, list):
              raise TypeError(
                  "Argument output_simulated_values should be a list of None, e.g. `[None] * 100`, "
                  f"but given {type(output_simulated_values)}."
              )
          num_events = len(output_simulated_values)
          result = ConcatScheduler.simulate_values(num_events=num_events, schedulers=schedulers, durations=durations)
          for i in range(num_events):
              output_simulated_values[i] = result[i]
      return combined_scheduler
  
  
  class PiecewiseLinear(ParamScheduler):
      """
      Piecewise linear parameter scheduler
  
      Args:
          optimizer (torch.optim.Optimizer or object): torch optimizer or any object with attribute ``param_groups``
              as a sequence.
          param_name (str): name of optimizer's parameter to update.
          milestones_values (list of tuples (int, float)): list of tuples (event index, parameter value)
              represents milestones and parameter. Milestones should be increasing integers.
          save_history (bool, optional): whether to log the parameter values to
              `engine.state.param_history`, (default=False).
          param_group_index (int, optional): optimizer's parameters group to use.
  
      Returns:
          PiecewiseLinear: piecewise linear scheduler
  
  
      .. code-block:: python
  
          scheduler = PiecewiseLinear(optimizer, "lr",
                                      milestones_values=[(10, 0.5), (20, 0.45), (21, 0.3), (30, 0.1), (40, 0.1)])
          # Attach to the trainer
          trainer.add_event_handler(Events.ITERATION_STARTED, scheduler)
          #
          # Sets the learning rate to 0.5 over the first 10 iterations, then decreases linearly from 0.5 to 0.45 between
          # 10th and 20th iterations. Next there is a jump to 0.3 at the 21st iteration and LR decreases linearly
          # from 0.3 to 0.1 between 21st and 30th iterations and remains 0.1 until the end of the iterations.
          #
      """
  
      def __init__(
          self,
          optimizer: Optimizer,
          param_name: str,
          milestones_values: List[Tuple[int, float]],
          save_history: bool = False,
          param_group_index: Optional[int] = None,
      ):
          super(PiecewiseLinear, self).__init__(optimizer, param_name, save_history, param_group_index=param_group_index)
  
          if not isinstance(milestones_values, Sequence):
              raise TypeError(
                  f"Argument milestones_values should be a list or tuple, but given {type(milestones_values)}"
              )
          if len(milestones_values) < 1:
              raise ValueError(
                  f"Argument milestones_values should be with at least one value, but given {milestones_values}"
              )
  
          values = []  # type: List[float]
          milestones = []  # type: List[int]
          for pair in milestones_values:
              if not isinstance(pair, tuple) or len(pair) != 2:
                  raise ValueError("Argument milestones_values should be a list of pairs (milestone, param_value)")
              if not isinstance(pair[0], numbers.Integral):
                  raise TypeError(f"Value of a milestone should be integer, but given {type(pair[0])}")
              if len(milestones) > 0 and pair[0] < milestones[-1]:
                  raise ValueError(
                      f"Milestones should be increasing integers, but given {pair[0]} is smaller "
                      f"than the previous milestone {milestones[-1]}"
                  )
              milestones.append(pair[0])
              values.append(pair[1])
  
          self.values = values
          self.milestones = milestones
          self._index = 0
          self._state_attrs += ["values", "milestones", "_index"]
  
      def _get_start_end(self) -> Tuple[int, int, float, float]:
          if self.milestones[0] > self.event_index:
              return self.event_index - 1, self.event_index, self.values[0], self.values[0]
          elif self.milestones[-1] <= self.event_index:
              return (self.event_index, self.event_index + 1, self.values[-1], self.values[-1])
          elif self.milestones[self._index] <= self.event_index < self.milestones[self._index + 1]:
              return (
                  self.milestones[self._index],
                  self.milestones[self._index + 1],
                  self.values[self._index],
                  self.values[self._index + 1],
              )
          else:
              self._index += 1
              return self._get_start_end()
  
      def get_param(self) -> float:
          start_index, end_index, start_value, end_value = self._get_start_end()
          return start_value + (end_value - start_value) * (self.event_index - start_index) / (end_index - start_index)
  
  
  class ParamGroupScheduler:
      """
      Scheduler helper to group multiple schedulers into one.
  
      Args:
          schedulers (list/tuple of ParamScheduler): list/tuple of parameter schedulers.
          names (list of str): list of names of schedulers.
  
      .. code-block:: python
  
          optimizer = SGD(
              [
                  {"params": model.base.parameters(), 'lr': 0.001),
                  {"params": model.fc.parameters(), 'lr': 0.01),
              ]
          )
  
          scheduler1 = LinearCyclicalScheduler(optimizer, 'lr', 1e-7, 1e-5, len(train_loader), param_group_index=0)
          scheduler2 = CosineAnnealingScheduler(optimizer, 'lr', 1e-5, 1e-3, len(train_loader), param_group_index=1)
          lr_schedulers = [scheduler1, scheduler2]
          names = ["lr (base)", "lr (fc)"]
  
          scheduler = ParamGroupScheduler(schedulers=lr_schedulers, names=names)
          # Attach single scheduler to the trainer
          trainer.add_event_handler(Events.ITERATION_STARTED, scheduler)
  
      """
  
      def __init__(self, schedulers: List[ParamScheduler], names: Optional[List[str]] = None, save_history: bool = False):
          if not isinstance(schedulers, Sequence):
              raise TypeError(f"Argument schedulers should be a list/tuple, but given {schedulers}")
  
          if not all(isinstance(scheduler, ParamScheduler) for scheduler in schedulers):
              raise ValueError(
                  f"Argument schedulers should be a list/tuple of parameter schedulers, but given {schedulers}"
              )
  
          if names is None:
              names = [s.param_name for s in schedulers]
  
          if not isinstance(names, (list, tuple)):
              raise TypeError(f"Argument names should be a list/tuple, but given {names}")
  
          if not all(isinstance(n, str) for n in names):
              raise ValueError(f"Argument names should be a list/tuple of parameter scheduler's names, but given {names}")
  
          if len(names) != len(schedulers):
              raise ValueError(f"{len(schedulers)} should be equal {len(names)}")
  
          self.schedulers = schedulers
          self.names = names
  
          # schedulers should have save_history sync with ParamGroupScheduler
          for s in schedulers:
              s.save_history = save_history
  
          self.optimizer = [s.optimizer for s in self.schedulers]
          self.param_name = [s.param_name for s in self.schedulers]
  
      def __call__(self, engine: Optional[Engine], name: Optional[str] = None) -> None:
          for scheduler, name in zip(self.schedulers, self.names):
              scheduler(engine, name)
  
      @property
      def optimizer_param_groups(self) -> List[Dict[str, Any]]:
          return [pg for scheduler in self.schedulers for pg in scheduler.optimizer_param_groups]
  
      @property
      def save_history(self) -> bool:
          return self.schedulers[0].save_history
  
      @save_history.setter
      def save_history(self, value: bool) -> None:
          for s in self.schedulers:
              s.save_history = value
  
      def state_dict(self) -> Dict[str, List[Any]]:
          """Returns a dictionary containing a whole state of ParamGroupScheduler.
  
          Returns:
              dict:
                  a dictionary containing a whole state of ParamGroupScheduler
          """
          state_dict = OrderedDict()  # type: Dict[str, List[Any]]
          state_dict["schedulers"] = []
          for n, s in zip(self.names, self.schedulers):
              state_dict["schedulers"].append((n, s.state_dict()))
          return state_dict
  
      def load_state_dict(self, state_dict: Mapping) -> None:
          """Copies parameters from :attr:`state_dict` into this ParamScheduler.
  
          Args:
              state_dict (dict): a dict containing parameters.
          """
          if not isinstance(state_dict, Mapping):
              raise TypeError(f"Argument state_dict should be a dictionary, but given {type(state_dict)}")
  
          if "schedulers" not in state_dict:
              raise ValueError(
                  f"Required state attribute '{'schedulers'}' is absent in provided state_dict '{state_dict.keys()}'"
              )
          sds = state_dict["schedulers"]
          if len(sds) != len(self.schedulers):
              raise ValueError(
                  f"Input state_dict contains {len(sds)} state_dicts of param group schedulers, "
                  f"but {len(self.schedulers)} needed"
              )
  
          for req_n, s, (n, sd) in zip(self.names, self.schedulers, sds):
              if req_n != n:
                  raise ValueError(
                      f"Name of scheduler from input state dict does not correspond to required one, {n} vs {req_n}"
                  )
              s.load_state_dict(sd)
  
      @classmethod
      def simulate_values(cls, num_events: int, schedulers: List[_LRScheduler], **kwargs: Any) -> List[List[int]]:
          """Method to simulate scheduled values during num_events events.
  
          Args:
              num_events (int): number of events during the simulation.
              schedulers (subclass of `torch.optim.lr_scheduler._LRScheduler`): lr_scheduler object to wrap.
  
          Returns:
              list of pairs: [event_index, value]
  
          """
  
          # This scheduler uses `torch.optim.lr_scheduler._LRScheduler` which
          # should be replicated in order to simulate LR values and
          # not perturb original scheduler.
          with tempfile.TemporaryDirectory() as tmpdirname:
              cache_filepath = Path(tmpdirname) / "ignite_lr_scheduler_cache.pt"
              objs = {f"lr_scheduler_{i}": s.state_dict() for i, s in enumerate(schedulers)}
              # all schedulers should be related to the same optimizer
              objs["optimizer"] = schedulers[0].optimizer.state_dict()  # type: ignore[attr-defined]
  
              torch.save(objs, cache_filepath.as_posix())
  
              values = []
              scheduler = cls(schedulers=schedulers, **kwargs)  # type: ignore[arg-type]
              for i in range(num_events):
                  params = [scheduler.get_param() for scheduler in schedulers]  # type: ignore[attr-defined]
                  values.append([i] + params)
                  scheduler(engine=None)
  
              objs = torch.load(cache_filepath.as_posix())
              for i, s in enumerate(schedulers):
                  s.load_state_dict(objs[f"lr_scheduler_{i}"])
                  s.optimizer.load_state_dict(objs["optimizer"])  # type: ignore[attr-defined]
  
              return values
  
  
  def _get_fake_optimizer(
      optimizer_cls: Optional[Union[Type[Optimizer], Type[torch.optim.SGD]]] = None, **kwargs: Any
  ) -> Union[Optimizer, torch.optim.SGD]:
      t = torch.zeros([1], requires_grad=True)
      if optimizer_cls is None:
          optimizer_cls = torch.optim.SGD
          kwargs["lr"] = 0.01
      return optimizer_cls([t], **kwargs)
  