






import argparse
import os

import evaluate
import torch
from datasets import load_dataset
from torch.optim import AdamW
from torch.utils.data import DataLoader
from transformers import AutoModelForSequenceClassification, AutoTokenizer, get_linear_schedule_with_warmup, set_seed

from accelerate import Accelerator, DistributedType


########################################################################
# This is a fully working simple example to use Accelerate
#
# This example trains a Bert base model on GLUE MRPC
# in any of the following settings (with the same script):
#   - single CPU or single GPU
#   - multi GPUS (using PyTorch distributed mode)
#   - (multi) TPUs
#   - fp16 (mixed-precision) or fp32 (normal precision)
#
# This example also demonstrates the checkpointing and sharding capabilities
#
# To run it in each of these various modes, follow the instructions
# in the readme for examples:
# https://github.com/huggingface/accelerate/tree/main/examples
#
########################################################################


__snake_case							 =  16
__snake_case							 =  32


def   _A       (    SCREAMING_SNAKE_CASE__  :     Optional[Any]					,  SCREAMING_SNAKE_CASE__  :     Optional[Any]	):
    # Initialize accelerator
    if args.with_tracking:
        UpperCamelCase	:Optional[Any]     							=       Accelerator(
            cpu=args.cpu					,  mixed_precision=args.mixed_precision					,  log_with='''all'''					,  project_dir=args.project_dir	)
    else:
        UpperCamelCase	:Any     							=       Accelerator(cpu=args.cpu					,  mixed_precision=args.mixed_precision	)

    if hasattr(args.checkpointing_steps					,  '''isdigit'''	):
        if args.checkpointing_steps == "epoch":
            UpperCamelCase	:int     							=       args.checkpointing_steps
        elif args.checkpointing_steps.isdigit():
            UpperCamelCase	:List[str]     							=       int(args.checkpointing_steps	)
        else:
            raise ValueError(
                F'''Argument `checkpointing_steps` must be either a number or `epoch`. `{args.checkpointing_steps}` passed.'''	)
    else:
        UpperCamelCase	:Any     							=       None
    # Sample hyper-parameters for learning rate, batch size, seed and a few other HPs
    UpperCamelCase	:List[Any]     							=       config['''lr''']
    UpperCamelCase	:Dict     							=       int(config['''num_epochs''']	)
    UpperCamelCase	:Dict     							=       int(config['''seed''']	)
    UpperCamelCase	:str     							=       int(config['''batch_size''']	)

    # We need to initialize the trackers we use, and also store our configuration
    if args.with_tracking:
        UpperCamelCase	:int     							=       os.path.split(SCREAMING_SNAKE_CASE__	)[-1].split('''.'''	)[0]
        accelerator.init_trackers(SCREAMING_SNAKE_CASE__					,  SCREAMING_SNAKE_CASE__	)

    UpperCamelCase	:List[Any]     							=       AutoTokenizer.from_pretrained('''bert-base-cased'''	)
    UpperCamelCase	:int     							=       load_dataset('''glue'''					,  '''mrpc'''	)
    UpperCamelCase	:Tuple     							=       evaluate.load('''glue'''					,  '''mrpc'''	)

    def tokenize_function(SCREAMING_SNAKE_CASE__  :     Optional[int]	):
        # max_length=None => use the model max length (it's actually the default)
        UpperCamelCase	:Optional[int]     							=       tokenizer(examples['''sentence1''']					,  examples['''sentence2''']					,  truncation=SCREAMING_SNAKE_CASE__					,  max_length=SCREAMING_SNAKE_CASE__	)
        return outputs

    # Apply the method we just defined to all the examples in all the splits of the dataset
    # starting with the main process first:
    with accelerator.main_process_first():
        UpperCamelCase	:Any     							=       datasets.map(
            SCREAMING_SNAKE_CASE__					,  batched=SCREAMING_SNAKE_CASE__					,  remove_columns=['''idx''', '''sentence1''', '''sentence2''']					,  )

    # We also rename the 'label' column to 'labels' which is the expected name for labels by the models of the
    # transformers library
    UpperCamelCase	:Any     							=       tokenized_datasets.rename_column('''label'''					,  '''labels'''	)

    # If the batch size is too big we use gradient accumulation
    UpperCamelCase	:Any     							=       1
    if batch_size > MAX_GPU_BATCH_SIZE and accelerator.distributed_type != DistributedType.TPU:
        UpperCamelCase	:Dict     							=       batch_size // MAX_GPU_BATCH_SIZE
        UpperCamelCase	:Dict     							=       MAX_GPU_BATCH_SIZE

    def collate_fn(SCREAMING_SNAKE_CASE__  :     Any	):
        # On TPU it's best to pad everything to the same length or training will be very slow.
        UpperCamelCase	:Dict     							=       128 if accelerator.distributed_type == DistributedType.TPU else None
        # When using mixed precision we want round multiples of 8/16
        if accelerator.mixed_precision == "fp8":
            UpperCamelCase	:List[Any]     							=       16
        elif accelerator.mixed_precision != "no":
            UpperCamelCase	:str     							=       8
        else:
            UpperCamelCase	:Union[str, Any]     							=       None

        return tokenizer.pad(
            SCREAMING_SNAKE_CASE__					,  padding='''longest'''					,  max_length=SCREAMING_SNAKE_CASE__					,  pad_to_multiple_of=SCREAMING_SNAKE_CASE__					,  return_tensors='''pt'''					,  )

    # Instantiate dataloaders.
    UpperCamelCase	:Optional[int]     							=       DataLoader(
        tokenized_datasets['''train''']					,  shuffle=SCREAMING_SNAKE_CASE__					,  collate_fn=SCREAMING_SNAKE_CASE__					,  batch_size=SCREAMING_SNAKE_CASE__	)
    UpperCamelCase	:Union[str, Any]     							=       DataLoader(
        tokenized_datasets['''validation''']					,  shuffle=SCREAMING_SNAKE_CASE__					,  collate_fn=SCREAMING_SNAKE_CASE__					,  batch_size=SCREAMING_SNAKE_CASE__	)

    set_seed(SCREAMING_SNAKE_CASE__	)

    # Instantiate the model (we build the model here so that the seed also control new weights initialization)
    UpperCamelCase	:Any     							=       AutoModelForSequenceClassification.from_pretrained('''bert-base-cased'''					,  return_dict=SCREAMING_SNAKE_CASE__	)

    # We could avoid this line since the accelerator is set with `device_placement=True` (default value).
    # Note that if you are placing tensors on devices manually, this line absolutely needs to be before the optimizer
    # creation otherwise training will not work on TPU (`accelerate` will kindly throw an error to make us aware of that).
    UpperCamelCase	:Union[str, Any]     							=       model.to(accelerator.device	)

    # Instantiate optimizer
    UpperCamelCase	:List[str]     							=       AdamW(params=model.parameters()					,  lr=SCREAMING_SNAKE_CASE__	)

    # Instantiate scheduler
    UpperCamelCase	:Dict     							=       get_linear_schedule_with_warmup(
        optimizer=SCREAMING_SNAKE_CASE__					,  num_warmup_steps=100					,  num_training_steps=(len(SCREAMING_SNAKE_CASE__	) * num_epochs) // gradient_accumulation_steps					,  )

    # Prepare everything
    # There is no specific order to remember, we just need to unpack the objects in the same order we gave them to the
    # prepare method.
    UpperCamelCase							,       UpperCamelCase							,       UpperCamelCase							,       UpperCamelCase							,       UpperCamelCase	:str     							=       accelerator.prepare(
        SCREAMING_SNAKE_CASE__					,  SCREAMING_SNAKE_CASE__					,  SCREAMING_SNAKE_CASE__					,  SCREAMING_SNAKE_CASE__					,  SCREAMING_SNAKE_CASE__	)

    # We need to keep track of how many total steps we have iterated over
    UpperCamelCase	:Optional[int]     							=       0
    # We also need to keep track of the stating epoch so files are named properly
    UpperCamelCase	:List[str]     							=       0

    # Potentially load in the weights and states from a previous save
    if args.resume_from_checkpoint:
        if args.resume_from_checkpoint is not None or args.resume_from_checkpoint != "":
            accelerator.print(F'''Resumed from checkpoint: {args.resume_from_checkpoint}'''	)
            accelerator.load_state(args.resume_from_checkpoint	)
            UpperCamelCase	:str     							=       os.path.basename(args.resume_from_checkpoint	)
        else:
            # Get the most recent checkpoint
            UpperCamelCase	:Optional[Any]     							=       [f.name for f in os.scandir(os.getcwd()	) if f.is_dir()]
            dirs.sort(key=os.path.getctime	)
            UpperCamelCase	:int     							=       dirs[-1]  # Sorts folders by date modified, most recent checkpoint is the last
        # Extract `epoch_{i}` or `step_{i}`
        UpperCamelCase	:Optional[int]     							=       os.path.splitext(SCREAMING_SNAKE_CASE__	)[0]

        if "epoch" in training_difference:
            UpperCamelCase	:str     							=       int(training_difference.replace('''epoch_'''					,  ''''''	)	) + 1
            UpperCamelCase	:Dict     							=       None
        else:
            UpperCamelCase	:List[Any]     							=       int(training_difference.replace('''step_'''					,  ''''''	)	)
            UpperCamelCase	:str     							=       resume_step // len(SCREAMING_SNAKE_CASE__	)
            resume_step -= starting_epoch * len(SCREAMING_SNAKE_CASE__	)

    # Now we train the model
    for epoch in range(SCREAMING_SNAKE_CASE__					,  SCREAMING_SNAKE_CASE__	):
        model.train()
        if args.with_tracking:
            UpperCamelCase	:Any     							=       0
        if args.resume_from_checkpoint and epoch == starting_epoch and resume_step is not None:
            # We need to skip steps until we reach the resumed step
            UpperCamelCase	:List[str]     							=       accelerator.skip_first_batches(SCREAMING_SNAKE_CASE__					,  SCREAMING_SNAKE_CASE__	)
            overall_step += resume_step
        else:
            # After the first iteration though, we need to go back to the original dataloader
            UpperCamelCase	:Tuple     							=       train_dataloader
        for step, batch in enumerate(SCREAMING_SNAKE_CASE__	):
            # We could avoid this line since we set the accelerator with `device_placement=True`.
            batch.to(accelerator.device	)
            UpperCamelCase	:str     							=       model(**SCREAMING_SNAKE_CASE__	)
            UpperCamelCase	:Any     							=       outputs.loss
            UpperCamelCase	:List[Any]     							=       loss / gradient_accumulation_steps
            # We keep track of the loss at each epoch
            if args.with_tracking:
                total_loss += loss.detach().float()
            accelerator.backward(SCREAMING_SNAKE_CASE__	)
            if step % gradient_accumulation_steps == 0:
                optimizer.step()
                lr_scheduler.step()
                optimizer.zero_grad()

            overall_step += 1

            if isinstance(SCREAMING_SNAKE_CASE__					,  SCREAMING_SNAKE_CASE__	):
                UpperCamelCase	:List[str]     							=       F'''step_{overall_step}'''
                if overall_step % checkpointing_steps == 0:
                    if args.output_dir is not None:
                        UpperCamelCase	:Optional[int]     							=       os.path.join(args.output_dir					,  SCREAMING_SNAKE_CASE__	)
                    accelerator.save_state(SCREAMING_SNAKE_CASE__	)

        model.eval()
        for step, batch in enumerate(SCREAMING_SNAKE_CASE__	):
            # We could avoid this line since we set the accelerator with `device_placement=True`.
            batch.to(accelerator.device	)
            with torch.no_grad():
                UpperCamelCase	:Dict     							=       model(**SCREAMING_SNAKE_CASE__	)
            UpperCamelCase	:Tuple     							=       outputs.logits.argmax(dim=-1	)
            UpperCamelCase							,       UpperCamelCase	:Tuple     							=       accelerator.gather_for_metrics((predictions, batch['''labels'''])	)
            metric.add_batch(
                predictions=SCREAMING_SNAKE_CASE__					,  references=SCREAMING_SNAKE_CASE__					,  )

        UpperCamelCase	:Optional[int]     							=       metric.compute()
        # Use accelerator.print to print only on the main process.
        accelerator.print(F'''epoch {epoch}:'''					,  SCREAMING_SNAKE_CASE__	)
        if args.with_tracking:
            accelerator.log(
                {
                    '''accuracy''': eval_metric['''accuracy'''],
                    '''f1''': eval_metric['''f1'''],
                    '''train_loss''': total_loss.item() / len(SCREAMING_SNAKE_CASE__	),
                    '''epoch''': epoch,
                }					,  step=SCREAMING_SNAKE_CASE__					,  )

        if checkpointing_steps == "epoch":
            UpperCamelCase	:Any     							=       F'''epoch_{epoch}'''
            if args.output_dir is not None:
                UpperCamelCase	:Union[str, Any]     							=       os.path.join(args.output_dir					,  SCREAMING_SNAKE_CASE__	)
            accelerator.save_state(SCREAMING_SNAKE_CASE__	)

    if args.with_tracking:
        accelerator.end_training()


def   _A       (    ):
    UpperCamelCase	:Optional[Any]     							=       argparse.ArgumentParser(description='''Simple example of training script.'''	)
    parser.add_argument(
        '''--mixed_precision'''					,  type=SCREAMING_SNAKE_CASE__					,  default=SCREAMING_SNAKE_CASE__					,  choices=['''no''', '''fp16''', '''bf16''', '''fp8''']					,  help='''Whether to use mixed precision. Choose'''
        '''between fp16 and bf16 (bfloat16). Bf16 requires PyTorch >= 1.10.'''
        '''and an Nvidia Ampere GPU.'''					,  )
    parser.add_argument('''--cpu'''					,  action='''store_true'''					,  help='''If passed, will train on the CPU.'''	)
    parser.add_argument(
        '''--checkpointing_steps'''					,  type=SCREAMING_SNAKE_CASE__					,  default=SCREAMING_SNAKE_CASE__					,  help='''Whether the various states should be saved at the end of every n steps, or \'epoch\' for each epoch.'''					,  )
    parser.add_argument(
        '''--resume_from_checkpoint'''					,  type=SCREAMING_SNAKE_CASE__					,  default=SCREAMING_SNAKE_CASE__					,  help='''If the training should continue from a checkpoint folder.'''					,  )
    parser.add_argument(
        '''--with_tracking'''					,  action='''store_true'''					,  help='''Whether to load in all available experiment trackers from the environment and use them for logging.'''					,  )
    parser.add_argument(
        '''--output_dir'''					,  type=SCREAMING_SNAKE_CASE__					,  default='''.'''					,  help='''Optional save directory where all checkpoint folders will be stored. Default is the current working directory.'''					,  )
    parser.add_argument(
        '''--project_dir'''					,  type=SCREAMING_SNAKE_CASE__					,  default='''logs'''					,  help='''Location on where to store experiment tracking logs` and relevent project information'''					,  )
    UpperCamelCase	:Union[str, Any]     							=       parser.parse_args()
    UpperCamelCase	:Union[str, Any]     							=       {'''lr''': 2e-5, '''num_epochs''': 3, '''seed''': 42, '''batch_size''': 16}
    training_function(SCREAMING_SNAKE_CASE__					,  SCREAMING_SNAKE_CASE__	)


if __name__ == "__main__":
 main()













def   _A       (    SCREAMING_SNAKE_CASE__  :     list[list[int]]	):
    if len(SCREAMING_SNAKE_CASE__	) == 0 or not all(len(SCREAMING_SNAKE_CASE__	) == 2 for pair in coordinates	):
        raise ValueError('''The program cannot work out a fitting polynomial.'''	)

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

    UpperCamelCase	:str     							=       {x for x, _ in coordinates}
    if len(SCREAMING_SNAKE_CASE__	) == 1:
        return F'''x={coordinates[0][0]}'''

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

    UpperCamelCase	:List[Any]     							=       len(SCREAMING_SNAKE_CASE__	)

    UpperCamelCase	:Optional[int]     							=       0
    UpperCamelCase	:list[list[float]]     							=       []
    # put the x and x to the power values in a matrix
    while count_of_line < x:
        UpperCamelCase	:Tuple     							=       0
        UpperCamelCase	:Optional[int]     							=       coordinates[count_of_line][0]
        UpperCamelCase	:list[float]     							=       []
        while count_in_line < x:
            count_line.append(a ** (x - (count_in_line + 1))	)
            count_in_line += 1
        matrix.append(SCREAMING_SNAKE_CASE__	)
        count_of_line += 1

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

    UpperCamelCase	:str     							=       0

    while count < x:
        UpperCamelCase	:Optional[Any]     							=       0
        while zahlen < x:
            if count == zahlen:
                zahlen += 1
            if zahlen == x:
                break
            UpperCamelCase	:Union[str, Any]     							=       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

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

    UpperCamelCase	:Union[str, Any]     							=       0
    UpperCamelCase	:Any     							=       '''f(x)='''

    while count < x:
        UpperCamelCase	:list[str]     							=       solution[count].split('''E'''	)
        if len(SCREAMING_SNAKE_CASE__	) > 1:
            UpperCamelCase	:List[Any]     							=       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]]))





