


from typing import Any, Dict, List, Optional, Tuple, Union

import torch
from torch import nn
from torch.utils.data import DistributedSampler, RandomSampler

from transformers import PreTrainedModel, Trainer, logging
from transformers.integrations import is_fairscale_available
from transformers.models.fsmt.configuration_fsmt import FSMTConfig
from transformers.optimization import (
    Adafactor,
    AdamW,
    get_constant_schedule,
    get_constant_schedule_with_warmup,
    get_cosine_schedule_with_warmup,
    get_cosine_with_hard_restarts_schedule_with_warmup,
    get_linear_schedule_with_warmup,
    get_polynomial_decay_schedule_with_warmup,
)
from transformers.trainer_pt_utils import get_tpu_sampler
from transformers.training_args import ParallelMode
from transformers.utils import is_torch_tpu_available


if is_fairscale_available():
  from fairscale.optim import OSS


UpperCAmelCase__   	=							logging.get_logger(__name__)

UpperCAmelCase__   	=							{
    '''linear''': get_linear_schedule_with_warmup,
    '''cosine''': get_cosine_schedule_with_warmup,
    '''cosine_w_restarts''': get_cosine_with_hard_restarts_schedule_with_warmup,
    '''polynomial''': get_polynomial_decay_schedule_with_warmup,
    '''constant''': get_constant_schedule,
    '''constant_w_warmup''': get_constant_schedule_with_warmup,
}







class       lowerCamelCase__   (       lowerCAmelCase):





     def __init__(self		,     UpperCAmelCase=None		,     UpperCAmelCase=None		,     *UpperCAmelCase		,     **UpperCAmelCase       )     ->   Union[str, Any]:
      super().__init__(*UpperCAmelCase		,     **UpperCAmelCase       )

      if config is None:
       assert isinstance(self.model		,     UpperCAmelCase       ), (
           "If no `config` is passed the model to be trained has to be of type `PreTrainedModel`, but is"
           f" {self.model.__class__}"
       )
       _lowercase							      =self.model.config
      else:
       _lowercase							      =config

      _lowercase							      =data_args
      _lowercase							      =self.config.tgt_vocab_size if isinstance(self.config		,     UpperCAmelCase       ) else self.config.vocab_size

      if self.args.label_smoothing != 0 or (self.data_args is not None and self.data_args.ignore_pad_token_for_loss):
       assert self.config.pad_token_id is not None, (
           "Make sure that `config.pad_token_id` is correcly defined when ignoring `pad_token` for loss"
           " calculation or doing label smoothing."
       )

      if self.config.pad_token_id is None and self.config.eos_token_id is not None:
       logger.warning(
           f"The `config.pad_token_id` is `None`. Using `config.eos_token_id` = {self.config.eos_token_id} for"
           ''' padding..'''       )

      if self.args.label_smoothing == 0:
       _lowercase							      =torch.nn.CrossEntropyLoss(ignore_index=self.config.pad_token_id       )
      else:
       # dynamically import label_smoothed_nll_loss
       from utils import label_smoothed_nll_loss

       _lowercase							      =label_smoothed_nll_loss





     def      __A					(self		,     UpperCAmelCase       )     ->   int:
      if self.optimizer is None:
       _lowercase							      =['''bias''', '''LayerNorm.weight''']
       _lowercase							      =[
           {
               '''params''': [p for n, p in self.model.named_parameters() if not any(nd in n for nd in no_decay       )],
               '''weight_decay''': self.args.weight_decay,
           },
           {
               '''params''': [p for n, p in self.model.named_parameters() if any(nd in n for nd in no_decay       )],
               '''weight_decay''': 0.0,
           },
       ]
       _lowercase							      =Adafactor if self.args.adafactor else AdamW
       if self.args.adafactor:
        _lowercase							      =Adafactor
        _lowercase							      ={'''scale_parameter''': False, '''relative_step''': False}
       else:
        _lowercase							      =AdamW
        _lowercase							      ={
            '''betas''': (self.args.adam_betaa, self.args.adam_betaa),
            '''eps''': self.args.adam_epsilon,
        }
       _lowercase							      =self.args.learning_rate
       if self.sharded_ddp:
        _lowercase							      =OSS(
            params=UpperCAmelCase		,     optim=UpperCAmelCase		,     **UpperCAmelCase		,     )
       else:
        _lowercase							      =optimizer_cls(UpperCAmelCase		,     **UpperCAmelCase       )

      if self.lr_scheduler is None:
       _lowercase							      =self._get_lr_scheduler(UpperCAmelCase       )
      else:  # ignoring --lr_scheduler
       logger.warning('''scheduler is passed to `Seq2SeqTrainer`, `--lr_scheduler` arg is ignored.'''       )





     def      __A					(self		,     UpperCAmelCase       )     ->   int:
      _lowercase							      =arg_to_scheduler[self.args.lr_scheduler]
      if self.args.lr_scheduler == "constant":
       _lowercase							      =schedule_func(self.optimizer       )
      elif self.args.lr_scheduler == "constant_w_warmup":
       _lowercase							      =schedule_func(self.optimizer		,     num_warmup_steps=self.args.warmup_steps       )
      else:
       _lowercase							      =schedule_func(
           self.optimizer		,     num_warmup_steps=self.args.warmup_steps		,     num_training_steps=UpperCAmelCase       )
      return scheduler





     def      __A					(self       )     ->   Optional[torch.utils.data.Sampler]:
      if isinstance(self.train_dataset		,     torch.utils.data.IterableDataset       ):
       return None
      elif is_torch_tpu_available():
       return get_tpu_sampler(self.train_dataset       )
      else:
       if self.args.sortish_sampler:
        self.train_dataset.make_sortish_sampler(
            self.args.per_device_train_batch_size		,     distributed=(self.args.parallel_mode == ParallelMode.DISTRIBUTED)		,     )

       return (
           RandomSampler(self.train_dataset       )
           if self.args.local_rank == -1
           else DistributedSampler(self.train_dataset       )
       )





     def      __A					(self		,     UpperCAmelCase		,     UpperCAmelCase		,     UpperCAmelCase       )     ->   List[str]:
      if self.args.label_smoothing == 0:
       if self.data_args is not None and self.data_args.ignore_pad_token_for_loss:
        # force training to ignore pad token
        _lowercase							      =model(**UpperCAmelCase		,     use_cache=UpperCAmelCase       )[0]
        _lowercase							      =self.loss_fn(logits.view(-1		,     logits.shape[-1]       )		,     labels.view(-1       )       )
       else:
        # compute usual loss via models
        _lowercase      ,    _lowercase							      =model(**UpperCAmelCase		,     labels=UpperCAmelCase		,     use_cache=UpperCAmelCase       )[:2]
      else:
       # compute label smoothed loss
       _lowercase							      =model(**UpperCAmelCase		,     use_cache=UpperCAmelCase       )[0]
       _lowercase							      =torch.nn.functional.log_softmax(UpperCAmelCase		,     dim=-1       )
       _lowercase      ,    _lowercase							      =self.loss_fn(UpperCAmelCase		,     UpperCAmelCase		,     self.args.label_smoothing		,     ignore_index=self.config.pad_token_id       )
      return loss, logits





     def      __A					(self		,     UpperCAmelCase		,     UpperCAmelCase       )     ->   str:
      _lowercase							      =inputs.pop('''labels'''       )
      _lowercase      ,    _lowercase							      =self._compute_loss(UpperCAmelCase		,     UpperCAmelCase		,     UpperCAmelCase       )
      return loss





     def      __A					(self		,     UpperCAmelCase		,     UpperCAmelCase		,     UpperCAmelCase		,     UpperCAmelCase = None		,     )     ->   Tuple[Optional[float], Optional[torch.Tensor], Optional[torch.Tensor]]:
      _lowercase							      =self._prepare_inputs(UpperCAmelCase       )

      _lowercase							      ={
          '''max_length''': self.data_args.val_max_target_length
          if self.data_args is not None
          else self.config.max_length,
          '''num_beams''': self.data_args.eval_beams if self.data_args is not None else self.config.num_beams,
      }

      if self.args.predict_with_generate and not self.args.prediction_loss_only:
       _lowercase							      =self.model.generate(
           inputs['''input_ids''']		,     attention_mask=inputs['''attention_mask''']		,     **UpperCAmelCase		,     )
       # in case the batch is shorter than max length, the output should be padded
       if generated_tokens.shape[-1] < gen_kwargs["max_length"]:
        _lowercase							      =self._pad_tensors_to_max_len(UpperCAmelCase		,     gen_kwargs['''max_length''']       )

      _lowercase							      =inputs.pop('''labels'''       )
      with torch.no_grad():
       # compute loss on predict data
       _lowercase      ,    _lowercase							      =self._compute_loss(UpperCAmelCase		,     UpperCAmelCase		,     UpperCAmelCase       )

      _lowercase							      =loss.mean().detach()
      if self.args.prediction_loss_only:
       return (loss, None, None)

      _lowercase							      =generated_tokens if self.args.predict_with_generate else logits

      if labels.shape[-1] < gen_kwargs["max_length"]:
       _lowercase							      =self._pad_tensors_to_max_len(UpperCAmelCase		,     gen_kwargs['''max_length''']       )

      return (loss, logits, labels)





     def      __A					(self		,     UpperCAmelCase		,     UpperCAmelCase       )     ->   Optional[Any]:
      # If PAD token is not defined at least EOS token has to be defined
      _lowercase							      =self.config.pad_token_id if self.config.pad_token_id is not None else self.config.eos_token_id

      if pad_token_id is None:
       raise ValueError(
           '''Make sure that either `config.pad_token_id` or `config.eos_token_id` is defined if tensor has to be'''
           f" padded to `max_length`={max_length}"       )

      _lowercase							      =pad_token_id * torch.ones(
          (tensor.shape[0], max_length)		,     dtype=tensor.dtype		,     device=tensor.device       )
      _lowercase							      =tensor
      return padded_tensor





from __future__ import annotations

from collections.abc import Callable

UpperCAmelCase__   	=							list[list[float | int]]
def 				UpperCAmelCase_					(							__snake_case     ,						__snake_case						)     ->			Matrix:







 """simple docstring"""


 _lowercase							      =len(__snake_case						)
 _lowercase							      =[[0 for _ in range(size + 1						)] for _ in range(__snake_case						)]
 _lowercase							      =42
 _lowercase							      =42
 _lowercase							      =42
 _lowercase							      =42
 _lowercase							      =42
 _lowercase							      =42

 for row in range(__snake_case						):
  for col in range(__snake_case						):
   _lowercase							      =matrix[row][col]

  _lowercase							      =vector[row][0]

 _lowercase							      =0
 _lowercase							      =0
 while row < size and col < size:
  # pivoting
  _lowercase							      =max((abs(augmented[rowa][col]						), rowa) for rowa in range(__snake_case     ,						__snake_case						)						)[
      1
  ]
  if augmented[pivot_row][col] == 0:
   col += 1
   continue
  else:
   _lowercase      ,    _lowercase							      =augmented[pivot_row], augmented[row]

  for rowa in range(row + 1     ,						__snake_case						):
   _lowercase							      =augmented[rowa][col] / augmented[row][col]
   _lowercase							      =0
   for cola in range(col + 1     ,						size + 1						):
    augmented[rowa][cola] -= augmented[row][cola] * ratio

  row += 1
  col += 1

 # back substitution
 for col in range(1     ,						__snake_case						):
  for row in range(__snake_case						):
   _lowercase							      =augmented[row][col] / augmented[col][col]
   for cola in range(__snake_case     ,						size + 1						):
    augmented[row][cola] -= augmented[col][cola] * ratio

    # round to get rid of numbers like 2.000000000000004
 return [
     [round(augmented[row][size] / augmented[row][row]     ,						10						)] for row in range(__snake_case						)
 ]
def 				UpperCAmelCase_					(							__snake_case						)     ->			Callable[[int], int]:







 """simple docstring"""


 _lowercase							      =len(__snake_case						)
 _lowercase							      =[[0 for _ in range(__snake_case						)] for _ in range(__snake_case						)]
 _lowercase							      =[[0] for _ in range(__snake_case						)]
 _lowercase							      =42
 _lowercase							      =42
 _lowercase							      =42
 _lowercase							      =42

 for x_val, y_val in enumerate(__snake_case						):
  for col in range(__snake_case						):
   _lowercase							      =(x_val + 1) ** (size - col - 1)
  _lowercase							      =y_val

 _lowercase							      =solve(__snake_case     ,						__snake_case						)

 def interpolated_func(__snake_case						) -> int:
  return sum(
      round(coeffs[x_val][0]						) * (var ** (size - x_val - 1))
      for x_val in range(__snake_case						)						)

 return interpolated_func
def 				UpperCAmelCase_					(							__snake_case						)     ->			int:







 """simple docstring"""


 return (
     1
     - variable
     + variable**2
     - variable**3
     + variable**4
     - variable**5
     + variable**6
     - variable**7
     + variable**8
     - variable**9
     + variable**10
 )
def 				UpperCAmelCase_					(							__snake_case = question_function     ,						__snake_case = 10						)     ->			int:







 """simple docstring"""


 _lowercase							      =[func(__snake_case						) for x_val in range(1     ,						order + 1						)]

 _lowercase							      =[
     interpolate(data_points[:max_coeff]						) for max_coeff in range(1     ,						order + 1						)
 ]

 _lowercase							      =0
 _lowercase							      =42
 _lowercase							      =42

 for poly in polynomials:
  _lowercase							      =1
  while func(__snake_case						) == poly(__snake_case						):
   x_val += 1

  ret += poly(__snake_case						)

 return ret


if __name__ == "__main__":
  print(f'''{solution() = }''')

