"""simple docstring"""


from math import exp

def 						UpperCamelCase				(	_lowerCAmelCase   :							str						):
    return 8 * x - 2 * exp(-x						)

def 						UpperCamelCase				(	_lowerCAmelCase   :							Tuple				, _lowerCAmelCase   :							List[Any]				, _lowerCAmelCase   :							Optional[int]						):
    __a			      =						lower_bound
    __a			      =						upper_bound
    for _ in range(0				, _lowerCAmelCase						):
        __a      ,  __a			      =						xa, xa - (f(_lowerCAmelCase						) * (xa - xa)) / (f(_lowerCAmelCase						) - f(_lowerCAmelCase						))
    return xa


if __name__ == "__main__":
 print(f'Example: {secant_method(1, 3, 2)}')





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


A__       =			logging.getLogger(__name__)

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

A__       =			{
    """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
A__       =			{
    """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
}
A__       =			sorted(arg_to_scheduler.keys())
A__       =			"""{""" + """, """.join(arg_to_scheduler_choices) + """}"""





class    __lowerCAmelCase					(	pl.LightningModule			):




				def __init__(				self		,							_snake_case		,							_snake_case=None		,							_snake_case="base"		,							_snake_case=None		,							_snake_case=None		,							_snake_case=None		,							**_snake_case		,							):



									"""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(_snake_case						)
									_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=_snake_case		,							**_snake_case		,							)
									else:
														_lowerCAmelCase         =       config

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

									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=_snake_case		,							)
									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=_snake_case		,							)
									else:
														_lowerCAmelCase         =       model




				def 				snake_case  (				self		,							*_snake_case		,							**_snake_case						):



									"""simple docstring"""





									_lowerCAmelCase         =       self.model_type.from_pretrained(*_snake_case		,							**_snake_case						)




				def 				snake_case  (				self						):



									"""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 				snake_case  (				self						):



									"""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						)],
									        """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(
														    _snake_case		,							lr=self.hparams.learning_rate		,							scale_parameter=_snake_case		,							relative_step=_snake_case						)

									else:
														_lowerCAmelCase         =       AdamW(
														    _snake_case		,							lr=self.hparams.learning_rate		,							eps=self.hparams.adam_epsilon						)
									_lowerCAmelCase         =       optimizer

									_lowerCAmelCase         =       self.get_lr_scheduler()

									return [optimizer], [scheduler]




				def 				snake_case  (				self		,							_snake_case		,							_snake_case						):



									"""simple docstring"""





									return self.validation_step(_snake_case		,							_snake_case						)




				def 				snake_case  (				self		,							_snake_case						):



									"""simple docstring"""





									return self.validation_end(_snake_case						)




				def 				snake_case  (				self						):



									"""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 				snake_case  (				self		,							_snake_case						):



									"""simple docstring"""





									if mode == "test":
														_lowerCAmelCase         =       len(self.test_dataloader().dataset						)
									else:
														_lowerCAmelCase         =       self.get_dataloader("""train"""		,							self.hparams.train_batch_size		,							shuffle=_snake_case						)
														_lowerCAmelCase         =       len(self.train_dataloader().dataset						)




				def 				snake_case  (				self		,							_snake_case		,							_snake_case		,							_snake_case = False						):



									"""simple docstring"""





									raise NotImplementedError("""You must implement this for your task"""						)




				def 				snake_case  (				self						):



									"""simple docstring"""





									return self.train_loader




				def 				snake_case  (				self						):



									"""simple docstring"""





									return self.get_dataloader("""dev"""		,							self.hparams.eval_batch_size		,							shuffle=_snake_case						)




				def 				snake_case  (				self						):



									"""simple docstring"""





									return self.get_dataloader("""test"""		,							self.hparams.eval_batch_size		,							shuffle=_snake_case						)




				def 				snake_case  (				self		,							_snake_case						):



									"""simple docstring"""





									return os.path.join(
									    self.hparams.data_dir		,							"""cached_{}_{}_{}""".format(
									        _snake_case		,							list(filter(_snake_case		,							self.hparams.model_name_or_path.split("""/"""						)						)						).pop()		,							str(self.hparams.max_seq_length						)		,							)		,							)




				@pl.utilities.rank_zero_only
				def 				snake_case  (				self		,							_snake_case						):



									"""simple docstring"""





									_lowerCAmelCase         =       self.output_dir.joinpath("""best_tfmr"""						)
									_lowerCAmelCase         =       self.step_count
									self.model.save_pretrained(_snake_case						)
									self.tokenizer.save_pretrained(_snake_case						)




				@staticmethod
				def 				snake_case  (				_snake_case		,							_snake_case						):



									"""simple docstring"""





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





class    __lowerCAmelCase					(	pl.Callback			):




				def 				snake_case  (				self		,							_snake_case		,							_snake_case						):



									"""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(_snake_case						)




				def 				snake_case  (				self		,							_snake_case		,							_snake_case						):



									"""simple docstring"""





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




				def 				snake_case  (				self		,							_snake_case		,							_snake_case						):



									"""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(_snake_case		,							"""w"""						) as writer:
														for key in sorted(_snake_case						):
																			if key not in ["log", "progress_bar"]:
																								rank_zero_info("""{} = {}\n""".format(_snake_case		,							str(metrics[key]						)						)						)
																								writer.write("""{} = {}\n""".format(_snake_case		,							str(metrics[key]						)						)						)


def 						_UpperCAmelCase							( snake_case      ,		snake_case     ):





					"""simple docstring"""

					parser.add_argument(
					    """--output_dir"""      ,		default=snake_case      ,		type=snake_case      ,		required=snake_case      ,		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=snake_case      ,		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=snake_case     )
					parser.add_argument("""--max_grad_norm"""      ,		dest="""gradient_clip_val"""      ,		default=1.0      ,		type=snake_case      ,		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=snake_case      ,		default=1      ,		help="""Number of updates steps to accumulate before performing a backward/update pass."""      ,		)
					parser.add_argument("""--seed"""      ,		type=snake_case      ,		default=42      ,		help="""random seed for initialization"""     )
					parser.add_argument(
					    """--data_dir"""      ,		default=snake_case      ,		type=snake_case      ,		required=snake_case      ,		help="""The input data dir. Should contain the training files for the CoNLL-2003 NER task."""      ,		)


def 						_UpperCAmelCase							( snake_case      ,		snake_case      ,		snake_case=None      ,		snake_case=True      ,		snake_case=[]      ,		snake_case=None      ,		snake_case=None      ,		**snake_case      ,		):





					"""simple docstring"""

					pl.seed_everything(args.seed     )

					# init model
					_lowerCAmelCase         =       Path(model.hparams.output_dir     )
					odir.mkdir(exist_ok=snake_case     )

					# 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(snake_case     )
					if logging_callback is None:
										_lowerCAmelCase         =       LoggingCallback()

					_lowerCAmelCase         =       {}

					# TODO: remove with PyTorch 1.6 since pl uses native amp
					if args.fpaa:
										_lowerCAmelCase         =       16
										_lowerCAmelCase         =       args.fpaa_opt_level

					if args.gpus > 1:
										_lowerCAmelCase         =       """ddp"""

					_lowerCAmelCase         =       args.accumulate_grad_batches
					_lowerCAmelCase         =       extra_train_kwargs.get("""accelerator"""      ,		snake_case     )
					_lowerCAmelCase         =       extra_train_kwargs.get("""profiler"""      ,		snake_case     )

					_lowerCAmelCase         =       pl.Trainer.from_argparse_args(
					    snake_case      ,		weights_summary=snake_case      ,		callbacks=[logging_callback] + extra_callbacks      ,		logger=snake_case      ,		checkpoint_callback=snake_case      ,		**snake_case      ,		)

					if args.do_train:
										trainer.fit(snake_case     )

					return trainer



