





import argparse
import os

# New Code #
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
from accelerate.utils import find_executable_batch_size


########################################################################
# This is a fully working simple example to use Accelerate,
# specifically showcasing how to combine both the gradient accumulation
# and automatic batch size finder utilities of Accelerate to perfrom
# automatic gradient accumulation
#
# 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)
#
# New additions from the base script can be found quickly by
# looking for the # New Code # tags
#
# 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
#
########################################################################

A_        =  3_2





def  __UpperCamelCase   (     a,  a = 16)			->Optional[int]:
					lowerCamelCase__      =							AutoTokenizer.from_pretrained("bert-base-cased")
					lowerCamelCase__      =							load_dataset("glue",  "mrpc")

					def tokenize_function(a):
										# max_length=None => use the model max length (it's actually the default)
										lowerCamelCase__      =							tokenizer(examples["sentence1"],  examples["sentence2"],  truncation=a,  max_length=a)
										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():
										lowerCamelCase__      =							datasets.map(
										    a,  batched=a,  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
					lowerCamelCase__      =							tokenized_datasets.rename_column("label",  "labels")

					def collate_fn(a):
										# When using mixed precision we want round multiples of 8/16
										if accelerator.mixed_precision == "fp8":
															lowerCamelCase__      =							16
										elif accelerator.mixed_precision != "no":
															lowerCamelCase__      =							8
										else:
															lowerCamelCase__      =							None

										return tokenizer.pad(
										    a,  padding="longest",  pad_to_multiple_of=a,  return_tensors="pt",  )

					# Instantiate dataloaders.
					lowerCamelCase__      =							DataLoader(
					    tokenized_datasets["train"],  shuffle=a,  collate_fn=a,  batch_size=a)
					lowerCamelCase__      =							DataLoader(
					    tokenized_datasets["validation"],  shuffle=a,  collate_fn=a,  batch_size=a)

					return train_dataloader, eval_dataloader


# For testing only
if os.environ.get("TESTING_MOCKED_DATALOADERS", None) == "1":
						from accelerate.test_utils.training import mocked_dataloaders

						A_        =  mocked_dataloaders  # noqa: F811





def  __UpperCamelCase   (     a,  a)			->Dict:
					# For testing only
					if os.environ.get("TESTING_MOCKED_DATALOADERS",  a) == "1":
										lowerCamelCase__      =							2
					# Initialize accelerator
					lowerCamelCase__      =							Accelerator(cpu=args.cpu,  mixed_precision=args.mixed_precision)
					# Sample hyper-parameters for learning rate, batch size, seed and a few other HPs
					lowerCamelCase__      =							config["lr"]
					lowerCamelCase__      =							int(config["num_epochs"])
					lowerCamelCase__      =							int(config["seed"])
					lowerCamelCase__      =							int(config["batch_size"])

					lowerCamelCase__      =							evaluate.load("glue",  "mrpc")

					# New Code #
					# We use the `find_executable_batch_size` decorator, passing in the desired observed batch size
					# to train on. If a CUDA OOM error occurs, it will retry this loop cutting the batch size in
					# half each time. From this, we can calculate the number of gradient accumulation steps needed
					# and modify the Accelerator object as a result
					@find_executable_batch_size(starting_batch_size=int(a))
					def inner_training_loop(a):
										# Since we need to modify the outside accelerator object, we need to bring it
										# to the local scope
										nonlocal accelerator

										# We can calculate the number of gradient accumulation steps based on the current
										# batch size vs the starting batch size
										lowerCamelCase__      =							observed_batch_size // batch_size

										# And then set it in the Accelerator directly:
										lowerCamelCase__      =							num_gradient_accumulation_steps

										# Next we need to free all of the stored model references in the Accelerator each time
										accelerator.free_memory()

										# And set the seed so our results are reproducable each reset
										set_seed(a)

										# Instantiate the model (we build the model here so that the seed also control new weights initialization)
										lowerCamelCase__      =							AutoModelForSequenceClassification.from_pretrained("bert-base-cased",  return_dict=a)

										# 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).
										lowerCamelCase__      =							model.to(accelerator.device)

										# Instantiate optimizer
										lowerCamelCase__      =							AdamW(params=model.parameters(),  lr=a)
										lowerCamelCase__     ,		lowerCamelCase__      =							get_dataloaders(a,  a)

										# Instantiate scheduler
										lowerCamelCase__      =							get_linear_schedule_with_warmup(
										    optimizer=a,  num_warmup_steps=100,  num_training_steps=(len(a) * num_epochs),  )

										# 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.
										lowerCamelCase__     ,		lowerCamelCase__     ,		lowerCamelCase__     ,		lowerCamelCase__     ,		lowerCamelCase__      =							accelerator.prepare(
										    a,  a,  a,  a,  a)

										# Now we train the model
										for epoch in range(a):
															model.train()
															for step, batch in enumerate(a):
																				# And perform gradient accumulation
																				with accelerator.accumulate(a):
																									# We could avoid this line since we set the accelerator with `device_placement=True`.
																									batch.to(accelerator.device)
																									lowerCamelCase__      =							model(**a)
																									lowerCamelCase__      =							outputs.loss
																									accelerator.backward(a)
																									optimizer.step()
																									lr_scheduler.step()
																									optimizer.zero_grad()

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

															lowerCamelCase__      =							metric.compute()
															# Use accelerator.print to print only on the main process.
															accelerator.print(f"epoch {epoch}:",  a)

    # New Code #
    # And call it at the end with no arguments
    # Note: You could also refactor this outside of your training loop function
					inner_training_loop()





def  __UpperCamelCase   (     )			->Optional[int]:
					lowerCamelCase__      =							argparse.ArgumentParser(description="Simple example of training script.")
					parser.add_argument(
					    "--mixed_precision",  type=a,  default=a,  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.")
					lowerCamelCase__      =							parser.parse_args()
					# New Code #
					# We modify the starting batch size to be an observed batch size of 256, to guarentee an initial CUDA OOM
					lowerCamelCase__      =							{"lr": 2E-5, "num_epochs": 3, "seed": 42, "batch_size": 256}
					training_function(a,  a)


if __name__ == "__main__":
						main()








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

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

					lowerCamelCase__      =							{x for x, _ in coordinates}
					if len(a) == 1:
										return f"x={coordinates[0][0]}"

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

					lowerCamelCase__      =							len(a)

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

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

					lowerCamelCase__      =							0

					while count < x:
										lowerCamelCase__      =							0
										while zahlen < x:
															if count == zahlen:
																				zahlen += 1
															if zahlen == x:
																				break
															lowerCamelCase__      =							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

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

					lowerCamelCase__      =							0
					lowerCamelCase__      =							"f(x)="

					while count < x:
										lowerCamelCase__      =							solution[count].split("E")
										if len(a) > 1:
															lowerCamelCase__      =							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, 1_1]]))
						print(points_to_polynomial([[1, -3], [2, -6], [3, -1_1]]))
						print(points_to_polynomial([[1, 5], [2, 2], [3, 9]]))

