






import unittest
from functools import partial

import torch

from accelerate import Accelerator, debug_launcher
from accelerate.state import AcceleratorState, GradientState
from accelerate.test_utils import require_cpu, require_huggingface_suite
from accelerate.utils import GradientAccumulationPlugin


def   _A       (    SCREAMING_SNAKE_CASE__  :     Tuple=2					,  SCREAMING_SNAKE_CASE__  :     Optional[Any]=True					,  SCREAMING_SNAKE_CASE__  :     Optional[Any]=False	):
    UpperCamelCase	:int     							=       Accelerator(step_scheduler_with_optimizer=SCREAMING_SNAKE_CASE__					,  split_batches=SCREAMING_SNAKE_CASE__	)
    UpperCamelCase	:Dict     							=       torch.nn.Linear(2					,  4	)
    UpperCamelCase	:Optional[Any]     							=       torch.optim.AdamW(model.parameters()					,  lr=1.0	)
    UpperCamelCase	:Union[str, Any]     							=       torch.optim.lr_scheduler.OneCycleLR(SCREAMING_SNAKE_CASE__					,  max_lr=0.01					,  steps_per_epoch=2					,  epochs=1	)
    UpperCamelCase							,       UpperCamelCase							,       UpperCamelCase	:int     							=       accelerator.prepare(SCREAMING_SNAKE_CASE__					,  SCREAMING_SNAKE_CASE__					,  SCREAMING_SNAKE_CASE__	)

    # Optimizer has stepped
    scheduler.step()
    if step_scheduler_with_optimizer or (num_processes == 1):
        assert (
            scheduler.scheduler.last_epoch == num_processes
        ), F'''Last Epoch ({scheduler.scheduler.last_epoch}) != Num Processes ({num_processes})'''
    else:
        assert (
            scheduler.scheduler.last_epoch != num_processes
        ), F'''Last Epoch ({scheduler.scheduler.last_epoch}) == Num Processes ({num_processes})'''


def   _A       (    SCREAMING_SNAKE_CASE__  :     Dict=2					,  SCREAMING_SNAKE_CASE__  :     int=True					,  SCREAMING_SNAKE_CASE__  :     Any=False	):
    UpperCamelCase	:Any     							=       Accelerator(step_scheduler_with_optimizer=SCREAMING_SNAKE_CASE__					,  split_batches=SCREAMING_SNAKE_CASE__	)
    UpperCamelCase	:Any     							=       torch.nn.Linear(2					,  4	)
    UpperCamelCase	:int     							=       torch.optim.AdamW(model.parameters()					,  lr=1.0	)
    UpperCamelCase	:str     							=       torch.optim.lr_scheduler.LambdaLR(SCREAMING_SNAKE_CASE__					,  lr_lambda=lambda SCREAMING_SNAKE_CASE__	: 1 - n / 10	)
    UpperCamelCase							,       UpperCamelCase							,       UpperCamelCase	:Tuple     							=       accelerator.prepare(SCREAMING_SNAKE_CASE__					,  SCREAMING_SNAKE_CASE__					,  SCREAMING_SNAKE_CASE__	)

    # Optimizer has stepped
    UpperCamelCase	:Optional[int]     							=       False
    scheduler.step()
    UpperCamelCase	:Optional[int]     							=       1 - (num_processes if (step_scheduler_with_optimizer and not split_batches) else 1) / 10
    assert (
        scheduler.get_last_lr()[0] == expected_lr
    ), F'''Wrong lr found at first step, expected {expected_lr}, got {scheduler.get_last_lr()[0]}'''

    # Optimizer has not stepped
    UpperCamelCase	:Optional[int]     							=       True
    scheduler.step()
    if not step_scheduler_with_optimizer:
        UpperCamelCase	:Optional[int]     							=       1 - 2 / 10
    assert (
        scheduler.get_last_lr()[0] == expected_lr
    ), F'''Wrong lr found at second step, expected {expected_lr}, got {scheduler.get_last_lr()[0]}'''


def   _A       (    SCREAMING_SNAKE_CASE__  :     int = 2	):
    from transformers import get_linear_schedule_with_warmup

    UpperCamelCase	:Optional[Any]     							=       [1, 2, 4]
    for num_steps in steps:
        UpperCamelCase	:Any     							=       GradientAccumulationPlugin(num_steps=SCREAMING_SNAKE_CASE__					,  adjust_scheduler=num_steps > 1	)
        UpperCamelCase	:str     							=       Accelerator(gradient_accumulation_plugin=SCREAMING_SNAKE_CASE__	)
        UpperCamelCase	:Optional[Any]     							=       torch.nn.Linear(2					,  4	)
        UpperCamelCase	:Any     							=       torch.optim.AdamW(model.parameters()					,  lr=10.0	)
        UpperCamelCase	:Union[str, Any]     							=       get_linear_schedule_with_warmup(optimizer=SCREAMING_SNAKE_CASE__					,  num_warmup_steps=0					,  num_training_steps=20	)

        UpperCamelCase							,       UpperCamelCase							,       UpperCamelCase	:List[str]     							=       accelerator.prepare(SCREAMING_SNAKE_CASE__					,  SCREAMING_SNAKE_CASE__					,  SCREAMING_SNAKE_CASE__	)

        for i in range(10 * num_steps	):
            with accelerator.accumulate(SCREAMING_SNAKE_CASE__	):
                optimizer.step()
                scheduler.step()

            if i == (10 * num_steps - 2):
                assert (
                    scheduler.get_last_lr()[0] != 0
                ), F'''Wrong lr found at second-to-last step, expected non-zero, got {scheduler.get_last_lr()[0]}. num_steps: {num_steps}'''
        assert (
            scheduler.get_last_lr()[0] == 0
        ), F'''Wrong lr found at last step, expected 0, got {scheduler.get_last_lr()[0]}'''
        GradientState._reset_state()







@require_cpu
class       UpperCAmelCase_						( unittest.TestCase			):



      """simple docstring"""
      def    UpperCAmelCase						(    self			)    ->				Tuple:
          debug_launcher(partial(SCREAMING_SNAKE_CASE_   ,    num_processes=1			)   ,    num_processes=1			)
          debug_launcher(partial(SCREAMING_SNAKE_CASE_   ,    num_processes=1   ,    split_batches=SCREAMING_SNAKE_CASE_			)   ,    num_processes=1			)
      def    UpperCAmelCase						(    self			)    ->				Optional[Any]:
          debug_launcher(partial(SCREAMING_SNAKE_CASE_   ,    num_processes=1			)   ,    num_processes=1			)
          debug_launcher(partial(SCREAMING_SNAKE_CASE_   ,    num_processes=1   ,    split_batches=SCREAMING_SNAKE_CASE_			)   ,    num_processes=1			)
      def    UpperCAmelCase						(    self			)    ->				Optional[int]:
          debug_launcher(partial(SCREAMING_SNAKE_CASE_   ,    num_processes=1   ,    step_scheduler_with_optimizer=SCREAMING_SNAKE_CASE_			)   ,    num_processes=1			)
      def    UpperCAmelCase						(    self			)    ->				Tuple:
          debug_launcher(partial(SCREAMING_SNAKE_CASE_   ,    num_processes=1   ,    step_scheduler_with_optimizer=SCREAMING_SNAKE_CASE_			)   ,    num_processes=1			)
      def    UpperCAmelCase						(    self			)    ->				Union[str, Any]:
          AcceleratorState._reset_state(SCREAMING_SNAKE_CASE_			)
          debug_launcher(SCREAMING_SNAKE_CASE_			)
          debug_launcher(partial(SCREAMING_SNAKE_CASE_   ,    num_processes=1   ,    split_batches=SCREAMING_SNAKE_CASE_			)   ,    num_processes=1			)
      def    UpperCAmelCase						(    self			)    ->				List[Any]:
          AcceleratorState._reset_state(SCREAMING_SNAKE_CASE_			)
          debug_launcher(SCREAMING_SNAKE_CASE_			)
          debug_launcher(partial(SCREAMING_SNAKE_CASE_   ,    num_processes=1   ,    split_batches=SCREAMING_SNAKE_CASE_			)   ,    num_processes=1			)
      def    UpperCAmelCase						(    self			)    ->				Optional[Any]:
          AcceleratorState._reset_state(SCREAMING_SNAKE_CASE_			)
          debug_launcher(partial(SCREAMING_SNAKE_CASE_   ,    step_scheduler_with_optimizer=SCREAMING_SNAKE_CASE_			)			)
      def    UpperCAmelCase						(    self			)    ->				Dict:
          AcceleratorState._reset_state(SCREAMING_SNAKE_CASE_			)
          debug_launcher(partial(SCREAMING_SNAKE_CASE_   ,    step_scheduler_with_optimizer=SCREAMING_SNAKE_CASE_			)			)




      @require_huggingface_suite
      def    UpperCAmelCase						(    self			)    ->				str:
          AcceleratorState._reset_state(SCREAMING_SNAKE_CASE_			)
          debug_launcher(partial(SCREAMING_SNAKE_CASE_   ,    num_processes=1			)			)
          debug_launcher(SCREAMING_SNAKE_CASE_			)













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]]))





