





def 	lowerCamelCase_		(							_UpperCamelCase					,							_UpperCamelCase					,							_UpperCamelCase					)						->		list:






				"""simple docstring"""


				snake_case_		:       Tuple           =    len(_UpperCamelCase					)
				snake_case_		:       Union[str, Any]           =    [[0] * n for i in range(_UpperCamelCase					)]
				for i in range(_UpperCamelCase					):
								snake_case_		:       Any           =    y_points[i]

				for i in range(2					,							_UpperCamelCase					):
								for j in range(_UpperCamelCase					,							_UpperCamelCase					):
												snake_case_		:       Optional[int]           =    (
												    (xa - x_points[j - i + 1]) * q[j][i - 1]
												    - (xa - x_points[j]) * q[j - 1][i - 1]
												) / (x_points[j] - x_points[j - i + 1])

				return [q[n - 1][n - 1], q]


if __name__ == "__main__":
	import doctest

	doctest.testmod()






import argparse
import logging
import os
from pathlib import Path
from typing import Any, Dict

import pytorch_lightning as pl
from pytorch_lightning.utilities import rank_zero_info

from transformers import (
    AdamW,
    AutoConfig,
    AutoModel,
    AutoModelForPreTraining,
    AutoModelForQuestionAnswering,
    AutoModelForSeqaSeqLM,
    AutoModelForSequenceClassification,
    AutoModelForTokenClassification,
    AutoModelWithLMHead,
    AutoTokenizer,
    PretrainedConfig,
    PreTrainedTokenizer,
)
from transformers.optimization import (
    Adafactor,
    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.utils.versions import require_version


__magic_name__  :  Any					=       logging.getLogger(__name__)

require_version("""pytorch_lightning>=1.0.4""")

__magic_name__  :  List[Any]					=       {
    """base""": AutoModel,
    """sequence-classification""": AutoModelForSequenceClassification,
    """question-answering""": AutoModelForQuestionAnswering,
    """pretraining""": AutoModelForPreTraining,
    """token-classification""": AutoModelForTokenClassification,
    """language-modeling""": AutoModelWithLMHead,
    """summarization""": AutoModelForSeqaSeqLM,
    """translation""": AutoModelForSeqaSeqLM,
}


# update this and the import above to support new schedulers from transformers.optimization
__magic_name__  :  Union[str, Any]					=       {
    """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,
    # '': get_constant_schedule,             # not supported for now
    # '': get_constant_schedule_with_warmup, # not supported for now
}
__magic_name__  :  Union[str, Any]					=       sorted(arg_to_scheduler.keys())
__magic_name__  :  Tuple					=       """{""" + """, """.join(arg_to_scheduler_choices) + """}"""





class     SCREAMING_SNAKE_CASE__		(pl.LightningModule			):
     def __init__(						self	:		Optional[int]       ,						__lowerCamelCase	:		argparse.Namespace       ,						__lowerCamelCase	:		Any=None       ,						__lowerCamelCase	:		Dict="base"       ,						__lowerCamelCase	:		List[Any]=None       ,						__lowerCamelCase	:		Optional[Any]=None       ,						__lowerCamelCase	:		Any=None       ,						**__lowerCamelCase	:		int       ,						):



       """simple docstring"""
       super().__init__()
       # TODO: move to self.save_hyperparameters()
       # self.save_hyperparameters()
       # can also expand arguments into trainer signature for easier reading

       self.save_hyperparameters(__lowerCamelCase						)
       lowerCAmelCase__										=      0
       lowerCAmelCase__										=      Path(self.hparams.output_dir						)
       lowerCAmelCase__										=      self.hparams.cache_dir if self.hparams.cache_dir else None
       if config is None:
         lowerCAmelCase__										=      AutoConfig.from_pretrained(
             self.hparams.config_name if self.hparams.config_name else self.hparams.model_name_or_path       ,						**({'''num_labels''': num_labels} if num_labels is not None else {})       ,						cache_dir=__lowerCamelCase       ,						**__lowerCamelCase       ,						)
       else:
         lowerCAmelCase__										=      config

       lowerCAmelCase__										=      ('''encoder_layerdrop''', '''decoder_layerdrop''', '''dropout''', '''attention_dropout''')
       for p in extra_model_params:
         if getattr(self.hparams       ,						__lowerCamelCase       ,						__lowerCamelCase						):
           assert hasattr(self.config       ,						__lowerCamelCase						), F"""model config doesn't have a `{p}` attribute"""
           setattr(self.config       ,						__lowerCamelCase       ,						getattr(self.hparams       ,						__lowerCamelCase						)						)

       if tokenizer is None:
         lowerCAmelCase__										=      AutoTokenizer.from_pretrained(
             self.hparams.tokenizer_name if self.hparams.tokenizer_name else self.hparams.model_name_or_path       ,						cache_dir=__lowerCamelCase       ,						)
       else:
         lowerCAmelCase__										=      tokenizer
       lowerCAmelCase__										=      MODEL_MODES[mode]
       if model is None:
         lowerCAmelCase__										=      self.model_type.from_pretrained(
             self.hparams.model_name_or_path       ,						from_tf=bool('''.ckpt''' in self.hparams.model_name_or_path						)       ,						config=self.config       ,						cache_dir=__lowerCamelCase       ,						)
       else:
         lowerCAmelCase__										=      model
     def        A__      (						self	:		Tuple       ,						*__lowerCamelCase	:		List[str]       ,						**__lowerCamelCase	:		List[str]						):



       """simple docstring"""
       lowerCAmelCase__										=      self.model_type.from_pretrained(*__lowerCamelCase       ,						**__lowerCamelCase						)
     def        A__      (						self	:		Dict						):



       """simple docstring"""
       lowerCAmelCase__										=      arg_to_scheduler[self.hparams.lr_scheduler]
       lowerCAmelCase__										=      get_schedule_func(
           self.opt       ,						num_warmup_steps=self.hparams.warmup_steps       ,						num_training_steps=self.total_steps()						)
       lowerCAmelCase__										=      {'''scheduler''': scheduler, '''interval''': '''step''', '''frequency''': 1}
       return scheduler
     def        A__      (						self	:		Dict						):



       """simple docstring"""
       lowerCAmelCase__										=      self.model
       lowerCAmelCase__										=      ['''bias''', '''LayerNorm.weight''']
       lowerCAmelCase__										=      [
           {
               '''params''': [
                   p for n, p in model.named_parameters() if not any(nd in n for nd in no_decay						)
               ],  # check this named paramters
               '''weight_decay''': self.hparams.weight_decay,
           },
           {
               '''params''': [p for n, p in model.named_parameters() if any(nd in n for nd in no_decay						)],
               '''weight_decay''': 0.0,
           },
       ]
       if self.hparams.adafactor:
         lowerCAmelCase__										=      Adafactor(
             __lowerCamelCase       ,						lr=self.hparams.learning_rate       ,						scale_parameter=__lowerCamelCase       ,						relative_step=__lowerCamelCase						)

       else:
         lowerCAmelCase__										=      AdamW(
             __lowerCamelCase       ,						lr=self.hparams.learning_rate       ,						eps=self.hparams.adam_epsilon						)
       lowerCAmelCase__										=      optimizer

       lowerCAmelCase__										=      self.get_lr_scheduler()

       return [optimizer], [scheduler]
     def        A__      (						self	:		Optional[int]       ,						__lowerCamelCase	:		Optional[Any]       ,						__lowerCamelCase	:		Optional[Any]						):



       """simple docstring"""
       return self.validation_step(__lowerCamelCase       ,						__lowerCamelCase						)
     def        A__      (						self	:		Dict       ,						__lowerCamelCase	:		Dict						):



       """simple docstring"""
       return self.validation_end(__lowerCamelCase						)
     def        A__      (						self	:		List[Any]						):



       """simple docstring"""
       lowerCAmelCase__										=      max(1       ,						self.hparams.gpus						)  # TODO: consider num_tpu_cores
       lowerCAmelCase__										=      self.hparams.train_batch_size * self.hparams.accumulate_grad_batches * num_devices
       return (self.dataset_size / effective_batch_size) * self.hparams.max_epochs
     def        A__      (						self	:		Union[str, Any]       ,						__lowerCamelCase	:		Union[str, Any]						):



       """simple docstring"""
       if stage == "test":
         lowerCAmelCase__										=      len(self.test_dataloader().dataset						)
       else:
         lowerCAmelCase__										=      self.get_dataloader('''train'''       ,						self.hparams.train_batch_size       ,						shuffle=__lowerCamelCase						)
         lowerCAmelCase__										=      len(self.train_dataloader().dataset						)
     def        A__      (						self	:		List[Any]       ,						__lowerCamelCase	:		str       ,						__lowerCamelCase	:		int       ,						__lowerCamelCase	:		bool = False						):



       """simple docstring"""
       raise NotImplementedError('''You must implement this for your task'''						)
     def        A__      (						self	:		Tuple						):



       """simple docstring"""
       return self.train_loader
     def        A__      (						self	:		List[Any]						):



       """simple docstring"""
       return self.get_dataloader('''dev'''       ,						self.hparams.eval_batch_size       ,						shuffle=__lowerCamelCase						)
     def        A__      (						self	:		str						):



       """simple docstring"""
       return self.get_dataloader('''test'''       ,						self.hparams.eval_batch_size       ,						shuffle=__lowerCamelCase						)
     def        A__      (						self	:		Dict       ,						__lowerCamelCase	:		Union[str, Any]						):



       """simple docstring"""
       return os.path.join(
           self.hparams.data_dir       ,						'''cached_{}_{}_{}'''.format(
               __lowerCamelCase       ,						list(filter(__lowerCamelCase       ,						self.hparams.model_name_or_path.split('''/'''						)						)						).pop()       ,						str(self.hparams.max_seq_length						)       ,						)       ,						)
     @pl.utilities.rank_zero_only
     def        A__      (						self	:		List[Any]       ,						__lowerCamelCase	:		Dict[str, Any]						):



       """simple docstring"""
       lowerCAmelCase__										=      self.output_dir.joinpath('''best_tfmr'''						)
       lowerCAmelCase__										=      self.step_count
       self.model.save_pretrained(__lowerCamelCase						)
       self.tokenizer.save_pretrained(__lowerCamelCase						)



     @staticmethod
     def        A__      (						__lowerCamelCase	:		Optional[int]       ,						__lowerCamelCase	:		Union[str, Any]						):



       """simple docstring"""
       parser.add_argument(
           '''--model_name_or_path'''       ,						default=__lowerCamelCase       ,						type=__lowerCamelCase       ,						required=__lowerCamelCase       ,						help='''Path to pretrained model or model identifier from huggingface.co/models'''       ,						)
       parser.add_argument(
           '''--config_name'''       ,						default=''''''       ,						type=__lowerCamelCase       ,						help='''Pretrained config name or path if not the same as model_name'''						)
       parser.add_argument(
           '''--tokenizer_name'''       ,						default=__lowerCamelCase       ,						type=__lowerCamelCase       ,						help='''Pretrained tokenizer name or path if not the same as model_name'''       ,						)
       parser.add_argument(
           '''--cache_dir'''       ,						default=str(Path(__lowerCamelCase						).parent / '''test_run''' / '''cache'''						)       ,						type=__lowerCamelCase       ,						help='''Where do you want to store the pre-trained models downloaded from huggingface.co'''       ,						)
       parser.add_argument(
           '''--encoder_layerdrop'''       ,						type=__lowerCamelCase       ,						help='''Encoder layer dropout probability (Optional). Goes into model.config'''       ,						)
       parser.add_argument(
           '''--decoder_layerdrop'''       ,						type=__lowerCamelCase       ,						help='''Decoder layer dropout probability (Optional). Goes into model.config'''       ,						)
       parser.add_argument(
           '''--dropout'''       ,						type=__lowerCamelCase       ,						help='''Dropout probability (Optional). Goes into model.config'''       ,						)
       parser.add_argument(
           '''--attention_dropout'''       ,						type=__lowerCamelCase       ,						help='''Attention dropout probability (Optional). Goes into model.config'''       ,						)
       parser.add_argument('''--learning_rate'''       ,						default=5e-5       ,						type=__lowerCamelCase       ,						help='''The initial learning rate for Adam.'''						)
       parser.add_argument(
           '''--lr_scheduler'''       ,						default='''linear'''       ,						choices=__lowerCamelCase       ,						metavar=__lowerCamelCase       ,						type=__lowerCamelCase       ,						help='''Learning rate scheduler'''       ,						)
       parser.add_argument('''--weight_decay'''       ,						default=0.0       ,						type=__lowerCamelCase       ,						help='''Weight decay if we apply some.'''						)
       parser.add_argument('''--adam_epsilon'''       ,						default=1e-8       ,						type=__lowerCamelCase       ,						help='''Epsilon for Adam optimizer.'''						)
       parser.add_argument('''--warmup_steps'''       ,						default=0       ,						type=__lowerCamelCase       ,						help='''Linear warmup over warmup_steps.'''						)
       parser.add_argument('''--num_workers'''       ,						default=4       ,						type=__lowerCamelCase       ,						help='''kwarg passed to DataLoader'''						)
       parser.add_argument('''--num_train_epochs'''       ,						dest='''max_epochs'''       ,						default=3       ,						type=__lowerCamelCase						)
       parser.add_argument('''--train_batch_size'''       ,						default=32       ,						type=__lowerCamelCase						)
       parser.add_argument('''--eval_batch_size'''       ,						default=32       ,						type=__lowerCamelCase						)
       parser.add_argument('''--adafactor'''       ,						action='''store_true'''						)





class     SCREAMING_SNAKE_CASE__		(pl.Callback			):
     def        A__      (						self	:		Any       ,						__lowerCamelCase	:		Dict       ,						__lowerCamelCase	:		List[Any]						):



       """simple docstring"""
       if (
           trainer.is_global_zero and trainer.global_rank == 0
       ):  # we initialize the retriever only on master worker with RAY. In new pytorch-lightning accelorators are removed.
         pl_module.model.rag.retriever.init_retrieval()  # better to use hook functions.





class     SCREAMING_SNAKE_CASE__		(pl.Callback			):
     def        A__      (						self	:		int       ,						__lowerCamelCase	:		List[str]       ,						__lowerCamelCase	:		Optional[int]						):



       """simple docstring"""
       # print(pl_module.model.rag)
       for name, param in pl_module.model.rag.named_parameters():
         if param.grad is None:
           print(__lowerCamelCase						)





class     SCREAMING_SNAKE_CASE__		(pl.Callback			):
     def        A__      (						self	:		Optional[int]       ,						__lowerCamelCase	:		Tuple       ,						__lowerCamelCase	:		Optional[Any]						):



       """simple docstring"""
       lowerCAmelCase__										=      trainer.lr_schedulers[0]['''scheduler''']
       lowerCAmelCase__										=      {F"""lr_group_{i}""": lr for i, lr in enumerate(lr_scheduler.get_lr()						)}
       pl_module.logger.log_metrics(__lowerCamelCase						)
     def        A__      (						self	:		Dict       ,						__lowerCamelCase	:		pl.Trainer       ,						__lowerCamelCase	:		pl.LightningModule						):



       """simple docstring"""
       rank_zero_info('''***** Validation results *****'''						)
       lowerCAmelCase__										=      trainer.callback_metrics
       # Log results
       for key in sorted(__lowerCamelCase						):
         if key not in ["log", "progress_bar"]:
           rank_zero_info('''{} = {}\n'''.format(__lowerCamelCase       ,						str(metrics[key]						)						)						)



     def        A__      (						self	:		str       ,						__lowerCamelCase	:		pl.Trainer       ,						__lowerCamelCase	:		pl.LightningModule						):



       """simple docstring"""
       rank_zero_info('''***** Test results *****'''						)
       lowerCAmelCase__										=      trainer.callback_metrics
       # Log and save results to file
       lowerCAmelCase__										=      os.path.join(pl_module.hparams.output_dir       ,						'''test_results.txt'''						)
       with open(__lowerCamelCase       ,						'''w'''						) as writer:
         for key in sorted(__lowerCamelCase						):
           if key not in ["log", "progress_bar"]:
             rank_zero_info('''{} = {}\n'''.format(__lowerCamelCase       ,						str(metrics[key]						)						)						)
             writer.write('''{} = {}\n'''.format(__lowerCamelCase       ,						str(metrics[key]						)						)						)



def 		a_							( __lowerCAmelCase   , __lowerCAmelCase				):
  #  To allow all pl args uncomment the following line
  #  parser = pl.Trainer.add_argparse_args(parser)
  parser.add_argument(
      '''--output_dir'''   , default=str(Path(__lowerCAmelCase				).parent / '''test_run''' / '''model_checkpoints'''				)   , type=__lowerCAmelCase   , help='''The output directory where the model predictions and checkpoints will be written.'''   , )
  parser.add_argument(
      '''--fp16'''   , action='''store_true'''   , help='''Whether to use 16-bit (mixed) precision (through NVIDIA apex) instead of 32-bit'''   , )

  parser.add_argument(
      '''--fp16_opt_level'''   , type=__lowerCAmelCase   , default='''O2'''   , help=(
          '''For fp16: Apex AMP optimization level selected in [\'O0\', \'O1\', \'O2\', and \'O3\'].'''
          '''See details at https://nvidia.github.io/apex/amp.html'''
      )   , )
  parser.add_argument('''--n_tpu_cores'''   , dest='''tpu_cores'''   , type=__lowerCAmelCase				)
  parser.add_argument('''--max_grad_norm'''   , dest='''gradient_clip_val'''   , default=1.0   , type=__lowerCAmelCase   , help='''Max gradient norm'''				)
  parser.add_argument('''--do_train'''   , action='''store_true'''   , help='''Whether to run training.'''				)
  parser.add_argument('''--do_predict'''   , action='''store_true'''   , help='''Whether to run predictions on the test set.'''				)
  parser.add_argument(
      '''--gradient_accumulation_steps'''   , dest='''accumulate_grad_batches'''   , type=__lowerCAmelCase   , default=1   , help='''Number of updates steps to accumulate before performing a backward/update pass.'''   , )
  parser.add_argument('''--seed'''   , type=__lowerCAmelCase   , default=42   , help='''random seed for initialization'''				)
  parser.add_argument(
      '''--data_dir'''   , default=str(Path(__lowerCAmelCase				).parent / '''test_run''' / '''dummy-train-data'''				)   , type=__lowerCAmelCase   , help='''The input data dir. Should contain the training files for the CoNLL-2003 NER task.'''   , )




def 		a_							( __lowerCAmelCase   , __lowerCAmelCase   , __lowerCAmelCase=None   , __lowerCAmelCase=True   , __lowerCAmelCase=[]   , __lowerCAmelCase=None   , __lowerCAmelCase=None   , **__lowerCAmelCase   , ):
  pl.seed_everything(args.seed				)

  # init model
  lowerCAmelCase__										=      Path(model.hparams.output_dir				)
  odir.mkdir(exist_ok=__lowerCAmelCase				)

  # add custom checkpoints
  if checkpoint_callback is None:
    lowerCAmelCase__										=      pl.callbacks.ModelCheckpoint(
        filepath=args.output_dir   , prefix='''checkpoint'''   , monitor='''val_loss'''   , mode='''min'''   , save_top_k=1				)
  if early_stopping_callback:
    extra_callbacks.append(__lowerCAmelCase				)
  if logging_callback is None:
    lowerCAmelCase__										=      LoggingCallback()

  lowerCAmelCase__										=      {}

  if args.fpaa:
    lowerCAmelCase__										=      16

  if args.gpus > 1:
    lowerCAmelCase__										=      '''auto'''
    lowerCAmelCase__										=      '''ddp'''

  lowerCAmelCase__										=      args.accumulate_grad_batches
  lowerCAmelCase__										=      None
  lowerCAmelCase__										=      '''auto'''

  lowerCAmelCase__										=      pl.Trainer.from_argparse_args(
      __lowerCAmelCase   , weights_summary=__lowerCAmelCase   , callbacks=[logging_callback] + extra_callbacks + [InitCallback()] + [checkpoint_callback]   , logger=__lowerCAmelCase   , val_check_interval=1   , num_sanity_val_steps=2   , **__lowerCAmelCase   , )

  if args.do_train:
    trainer.fit(__lowerCAmelCase				)

  else:
    print('''RAG modeling tests with new set functions successfuly executed!'''				)
  return trainer

