





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


UpperCamelCase__          =logging.getLogger(__name__)

require_version('pytorch_lightning>=1.0.4')

UpperCamelCase__          ={
    '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
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,
    # '': get_constant_schedule,             # not supported for now
    # '': get_constant_schedule_with_warmup, # not supported for now
}
UpperCamelCase__          =sorted(arg_to_scheduler.keys())
UpperCamelCase__          ='{' + ', '.join(arg_to_scheduler_choices) + '}'





class 	lowerCAmelCase__(       pl.LightningModule			):






       '''simple docstring'''


       def __init__(					self			,  __lowerCamelCase			,  __lowerCamelCase=None			,  __lowerCamelCase="base"			,  __lowerCamelCase=None			,  __lowerCamelCase=None			,  __lowerCamelCase=None			,  **__lowerCamelCase			,  )	->   List[str]:
            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							)
            _SCREAMING_SNAKE_CASE				:		int  			=							0
            _SCREAMING_SNAKE_CASE				:		List[str]  			=							Path(self.hparams.output_dir							)
            _SCREAMING_SNAKE_CASE				:		int  			=							self.hparams.cache_dir if self.hparams.cache_dir else None
            if config is None:
                 _SCREAMING_SNAKE_CASE				:		Union[str, Any]  			=							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:
                 _SCREAMING_SNAKE_CASE				:		PretrainedConfig  			=							config

            _SCREAMING_SNAKE_CASE				:		List[str]  			=							("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:
                 _SCREAMING_SNAKE_CASE				:		Tuple  			=							AutoTokenizer.from_pretrained(
                     self.hparams.tokenizer_name if self.hparams.tokenizer_name else self.hparams.model_name_or_path			,  cache_dir=__lowerCamelCase			,  )
            else:
                 _SCREAMING_SNAKE_CASE				:		PreTrainedTokenizer  			=							tokenizer
            _SCREAMING_SNAKE_CASE				:		int  			=							MODEL_MODES[mode]
            if model is None:
                 _SCREAMING_SNAKE_CASE				:		Any  			=							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:
                 _SCREAMING_SNAKE_CASE				:		Union[str, Any]  			=							model




       def 			UpperCamelCase_	(					self			,  *__lowerCamelCase			,  **__lowerCamelCase							)	->   List[str]:
            _SCREAMING_SNAKE_CASE				:		str  			=							self.model_type.from_pretrained(*__lowerCamelCase			,  **__lowerCamelCase							)




       def 			UpperCamelCase_	(					self							)	->   str:
            _SCREAMING_SNAKE_CASE				:		Union[str, Any]  			=							arg_to_scheduler[self.hparams.lr_scheduler]
            _SCREAMING_SNAKE_CASE				:		Dict  			=							get_schedule_func(
                self.opt			,  num_warmup_steps=self.hparams.warmup_steps			,  num_training_steps=self.total_steps()							)
            _SCREAMING_SNAKE_CASE				:		Optional[int]  			=							{"scheduler": scheduler, "interval": "step", "frequency": 1}
            return scheduler




       def 			UpperCamelCase_	(					self							)	->   Union[str, Any]:
            _SCREAMING_SNAKE_CASE				:		str  			=							self.model
            _SCREAMING_SNAKE_CASE				:		List[str]  			=							["bias", "LayerNorm.weight"]
            _SCREAMING_SNAKE_CASE				:		List[Any]  			=							[
                {
                    "params": [p for n, p in model.named_parameters() if not any(nd in n for nd in no_decay							)],
                    "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:
                 _SCREAMING_SNAKE_CASE				:		str  			=							Adafactor(
                     __lowerCamelCase			,  lr=self.hparams.learning_rate			,  scale_parameter=__lowerCamelCase			,  relative_step=__lowerCamelCase							)

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

            _SCREAMING_SNAKE_CASE				:		Optional[int]  			=							self.get_lr_scheduler()

            return [optimizer], [scheduler]




       def 			UpperCamelCase_	(					self			,  __lowerCamelCase			,  __lowerCamelCase							)	->   Tuple:
            return self.validation_step(__lowerCamelCase			,  __lowerCamelCase							)




       def 			UpperCamelCase_	(					self			,  __lowerCamelCase							)	->   Dict:
            return self.validation_end(__lowerCamelCase							)




       def 			UpperCamelCase_	(					self							)	->   int:
            _SCREAMING_SNAKE_CASE				:		Optional[int]  			=							max(1			,  self.hparams.gpus							)  # TODO: consider num_tpu_cores
            _SCREAMING_SNAKE_CASE				:		Union[str, Any]  			=							self.hparams.train_batch_size * self.hparams.accumulate_grad_batches * num_devices
            return (self.dataset_size / effective_batch_size) * self.hparams.max_epochs




       def 			UpperCamelCase_	(					self			,  __lowerCamelCase							)	->   Dict:
            if mode == "test":
                 _SCREAMING_SNAKE_CASE				:		str  			=							len(self.test_dataloader().dataset							)
            else:
                 _SCREAMING_SNAKE_CASE				:		Optional[Any]  			=							self.get_dataloader("train"			,  self.hparams.train_batch_size			,  shuffle=__lowerCamelCase							)
                 _SCREAMING_SNAKE_CASE				:		Optional[int]  			=							len(self.train_dataloader().dataset							)




       def 			UpperCamelCase_	(					self			,  __lowerCamelCase			,  __lowerCamelCase			,  __lowerCamelCase = False							)	->   Dict:
            raise NotImplementedError("You must implement this for your task"							)




       def 			UpperCamelCase_	(					self							)	->   int:
            return self.train_loader




       def 			UpperCamelCase_	(					self							)	->   Tuple:
            return self.get_dataloader("dev"			,  self.hparams.eval_batch_size			,  shuffle=__lowerCamelCase							)




       def 			UpperCamelCase_	(					self							)	->   List[Any]:
            return self.get_dataloader("test"			,  self.hparams.eval_batch_size			,  shuffle=__lowerCamelCase							)




       def 			UpperCamelCase_	(					self			,  __lowerCamelCase							)	->   int:
            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 			UpperCamelCase_	(					self			,  __lowerCamelCase							)	->   None:
            _SCREAMING_SNAKE_CASE				:		int  			=							self.output_dir.joinpath("best_tfmr"							)
            _SCREAMING_SNAKE_CASE				:		str  			=							self.step_count
            self.model.save_pretrained(__lowerCamelCase							)
            self.tokenizer.save_pretrained(__lowerCamelCase							)







       @staticmethod
       def 			UpperCamelCase_	(					__lowerCamelCase			,  __lowerCamelCase							)	->   str:
            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=""			,  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=3_2			,  type=__lowerCamelCase							)
            parser.add_argument("--eval_batch_size"			,  default=3_2			,  type=__lowerCamelCase							)
            parser.add_argument("--adafactor"			,  action="store_true"							)





class 	lowerCAmelCase__(       pl.Callback			):






       '''simple docstring'''


       def 			UpperCamelCase_	(					self			,  __lowerCamelCase			,  __lowerCamelCase							)	->   Tuple:
            _SCREAMING_SNAKE_CASE				:		Union[str, Any]  			=							trainer.lr_schedulers[0]["scheduler"]
            _SCREAMING_SNAKE_CASE				:		Union[str, Any]  			=							{F"""lr_group_{i}""": lr for i, lr in enumerate(lr_scheduler.get_lr()							)}
            pl_module.logger.log_metrics(__lowerCamelCase							)




       def 			UpperCamelCase_	(					self			,  __lowerCamelCase			,  __lowerCamelCase							)	->   Union[str, Any]:
            rank_zero_info("***** Validation results *****"							)
            _SCREAMING_SNAKE_CASE				:		Any  			=							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 			UpperCamelCase_	(					self			,  __lowerCamelCase			,  __lowerCamelCase							)	->   str:
            rank_zero_info("***** Test results *****"							)
            _SCREAMING_SNAKE_CASE				:		int  			=							trainer.callback_metrics
            # Log and save results to file
            _SCREAMING_SNAKE_CASE				:		str  			=							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 			lowerCamelCase__	(__lowerCamelCase,				__lowerCamelCase		):
     #  To allow all pl args uncomment the following line
     #  parser = pl.Trainer.add_argparse_args(parser)
     parser.add_argument(
         "--output_dir",				default=__lowerCamelCase,				type=__lowerCamelCase,				required=__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=__lowerCamelCase,				type=__lowerCamelCase,				required=__lowerCamelCase,				help="The input data dir. Should contain the training files for the CoNLL-2003 NER task.",				)






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

     # init model
     _SCREAMING_SNAKE_CASE				:		List[str]  			=							Path(model.hparams.output_dir		)
     odir.mkdir(exist_ok=__lowerCamelCase		)

     # add custom checkpoints
     if checkpoint_callback is None:
          _SCREAMING_SNAKE_CASE				:		List[str]  			=							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:
          _SCREAMING_SNAKE_CASE				:		Any  			=							LoggingCallback()

     _SCREAMING_SNAKE_CASE				:		List[Any]  			=							{}

     # TODO: remove with PyTorch 1.6 since pl uses native amp
     if args.fpaa:
          _SCREAMING_SNAKE_CASE				:		Union[str, Any]  			=							16
          _SCREAMING_SNAKE_CASE				:		int  			=							args.fpaa_opt_level

     if args.gpus > 1:
          _SCREAMING_SNAKE_CASE				:		str  			=							"ddp"

     _SCREAMING_SNAKE_CASE				:		int  			=							args.accumulate_grad_batches
     _SCREAMING_SNAKE_CASE				:		Optional[int]  			=							extra_train_kwargs.get("accelerator",				__lowerCamelCase		)
     _SCREAMING_SNAKE_CASE				:		Optional[int]  			=							extra_train_kwargs.get("profiler",				__lowerCamelCase		)

     _SCREAMING_SNAKE_CASE				:		List[Any]  			=							pl.Trainer.from_argparse_args(
         __lowerCamelCase,				weights_summary=__lowerCamelCase,				callbacks=[logging_callback] + extra_callbacks,				logger=__lowerCamelCase,				checkpoint_callback=__lowerCamelCase,				**__lowerCamelCase,				)

     if args.do_train:
          trainer.fit(__lowerCamelCase		)

     return trainer


def    UpperCamelCase(					lowercase_							)	->				str:





  '''simple docstring'''





  if len(lowercase_							) == 0 or not all(len(lowercase_							) == 2 for pair in coordinates							):
    raise ValueError("""The program cannot work out a fitting polynomial."""							)

  if len({tuple(lowercase_							) for pair in coordinates}							) != len(lowercase_							):
    raise ValueError("""The program cannot work out a fitting polynomial."""							)

  snake_case_       						=      {x for x, _ in coordinates}
  if len(lowercase_							) == 1:
    return f'''x={coordinates[0][0]}'''

  if len(lowercase_							) != len(lowercase_							):
    raise ValueError("""The program cannot work out a fitting polynomial."""							)

  snake_case_       						=      len(lowercase_							)

  snake_case_       						=      0
  snake_case_       						=      []
  # put the x and x to the power values in a matrix
  while count_of_line < x:
    snake_case_       						=      0
    snake_case_       						=      coordinates[count_of_line][0]
    snake_case_       						=      []
    while count_in_line < x:
      count_line.append(a ** (x - (count_in_line + 1))							)
      count_in_line += 1
    matrix.append(lowercase_							)
    count_of_line += 1

  snake_case_       						=      0
  # put the y values into a vector
  snake_case_       						=      []
  while count_of_line < x:
    vector.append(coordinates[count_of_line][1]							)
    count_of_line += 1

  snake_case_       						=      0

  while count < x:
    snake_case_       						=      0
    while zahlen < x:
      if count == zahlen:
        zahlen += 1
      if zahlen == x:
        break
      snake_case_       						=      matrix[zahlen][count] / matrix[count][count]
      for counting_columns, item in enumerate(matrix[count]							):
        # manipulating all the values in the matrix
        matrix[zahlen][counting_columns] -= item * bruch
      # manipulating the values in the vector
      vector[zahlen] -= vector[count] * bruch
      zahlen += 1
    count += 1

  snake_case_       						=      0
  # make solutions
  snake_case_       						=      []
  while count < x:
    solution.append(str(vector[count] / matrix[count][count]							)							)
    count += 1

  snake_case_       						=      0
  snake_case_       						=      """f(x)="""

  while count < x:
    snake_case_       						=      solution[count].split("""E"""							)
    if len(lowercase_							) > 1:
      snake_case_       						=      f'''{remove_e[0]}*10^{remove_e[1]}'''
    solved += f'''x^{x - (count + 1)}*{solution[count]}'''
    if count + 1 != x:
      solved += "+"
    count += 1

  return solved


if __name__ == "__main__":
    print(points_to_polynomial([]))
    print(points_to_polynomial([[]]))
    print(points_to_polynomial([[1, 0], [2, 0], [3, 0]]))
    print(points_to_polynomial([[1, 1], [2, 1], [3, 1]]))
    print(points_to_polynomial([[1, 3], [2, 3], [3, 3]]))
    print(points_to_polynomial([[1, 1], [2, 2], [3, 3]]))
    print(points_to_polynomial([[1, 1], [2, 4], [3, 9]]))
    print(points_to_polynomial([[1, 3], [2, 6], [3, 11]]))
    print(points_to_polynomial([[1, -3], [2, -6], [3, -11]]))
    print(points_to_polynomial([[1, 5], [2, 2], [3, 9]]))