




"""simple docstring"""
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 				__lowerCAmelCase					(					__lowerCAmelCase			:		Any=2  ,	__lowerCAmelCase			:		Optional[int]=True  ,	__lowerCAmelCase			:		Any=False						)    ->       str:
 _UpperCamelCase      :	Tuple					      =  Accelerator(step_scheduler_with_optimizer=__lowerCAmelCase  ,	split_batches=__lowerCAmelCase						)
 _UpperCamelCase      :	str					      =  torch.nn.Linear(2  ,	4						)
 _UpperCamelCase      :	Optional[Any]					      =  torch.optim.AdamW(model.parameters()  ,	lr=1.0						)
 _UpperCamelCase      :	Optional[Any]					      =  torch.optim.lr_scheduler.OneCycleLR(__lowerCAmelCase  ,	max_lr=0.01  ,	steps_per_epoch=2  ,	epochs=1						)
 _UpperCamelCase      ,	_UpperCamelCase      ,	_UpperCamelCase      :	List[str]					      =  accelerator.prepare(__lowerCAmelCase  ,	__lowerCAmelCase  ,	__lowerCAmelCase						)

 # 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 				__lowerCAmelCase					(					__lowerCAmelCase			:		Optional[int]=2  ,	__lowerCAmelCase			:		Union[str, Any]=True  ,	__lowerCAmelCase			:		int=False						)    ->       int:
 _UpperCamelCase      :	Optional[Any]					      =  Accelerator(step_scheduler_with_optimizer=__lowerCAmelCase  ,	split_batches=__lowerCAmelCase						)
 _UpperCamelCase      :	Tuple					      =  torch.nn.Linear(2  ,	4						)
 _UpperCamelCase      :	str					      =  torch.optim.AdamW(model.parameters()  ,	lr=1.0						)
 _UpperCamelCase      :	int					      =  torch.optim.lr_scheduler.LambdaLR(__lowerCAmelCase  ,	lr_lambda=lambda __lowerCAmelCase						: 1 - n / 10						)
 _UpperCamelCase      ,	_UpperCamelCase      ,	_UpperCamelCase      :	str					      =  accelerator.prepare(__lowerCAmelCase  ,	__lowerCAmelCase  ,	__lowerCAmelCase						)

 # Optimizer has stepped
 _UpperCamelCase      :	Optional[Any]					      =  False
 scheduler.step()
 _UpperCamelCase      :	Union[str, Any]					      =  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      :	Union[str, Any]					      =  True
 scheduler.step()
 if not step_scheduler_with_optimizer:
  _UpperCamelCase      :	Any					      =  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 				__lowerCAmelCase					(					__lowerCAmelCase			:		int = 2						)    ->       Any:
 from transformers import get_linear_schedule_with_warmup

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

  _UpperCamelCase      ,	_UpperCamelCase      ,	_UpperCamelCase      :	int					      =  accelerator.prepare(__lowerCAmelCase  ,	__lowerCAmelCase  ,	__lowerCAmelCase						)

  for i in range(10 * num_steps						):
   with accelerator.accumulate(__lowerCAmelCase						):
    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  _SCREAMING_SNAKE_CASE       (     unittest.TestCase				):



 '''simple docstring'''





 def lowercase_      (self   ):

  '''simple docstring'''







  debug_launcher(partial(lowerCAmelCase__					,     num_processes=1   )					,     num_processes=1   )
  debug_launcher(partial(lowerCAmelCase__					,     num_processes=1					,     split_batches=lowerCAmelCase__   )					,     num_processes=1   )






 def lowercase_      (self   ):

  '''simple docstring'''







  debug_launcher(partial(lowerCAmelCase__					,     num_processes=1   )					,     num_processes=1   )
  debug_launcher(partial(lowerCAmelCase__					,     num_processes=1					,     split_batches=lowerCAmelCase__   )					,     num_processes=1   )






 def lowercase_      (self   ):

  '''simple docstring'''







  debug_launcher(partial(lowerCAmelCase__					,     num_processes=1					,     step_scheduler_with_optimizer=lowerCAmelCase__   )					,     num_processes=1   )






 def lowercase_      (self   ):

  '''simple docstring'''







  debug_launcher(partial(lowerCAmelCase__					,     num_processes=1					,     step_scheduler_with_optimizer=lowerCAmelCase__   )					,     num_processes=1   )






 def lowercase_      (self   ):

  '''simple docstring'''







  AcceleratorState._reset_state(lowerCAmelCase__   )
  debug_launcher(lowerCAmelCase__   )
  debug_launcher(partial(lowerCAmelCase__					,     num_processes=1					,     split_batches=lowerCAmelCase__   )					,     num_processes=1   )






 def lowercase_      (self   ):

  '''simple docstring'''







  AcceleratorState._reset_state(lowerCAmelCase__   )
  debug_launcher(lowerCAmelCase__   )
  debug_launcher(partial(lowerCAmelCase__					,     num_processes=1					,     split_batches=lowerCAmelCase__   )					,     num_processes=1   )






 def lowercase_      (self   ):

  '''simple docstring'''







  AcceleratorState._reset_state(lowerCAmelCase__   )
  debug_launcher(partial(lowerCAmelCase__					,     step_scheduler_with_optimizer=lowerCAmelCase__   )   )






 def lowercase_      (self   ):

  '''simple docstring'''







  AcceleratorState._reset_state(lowerCAmelCase__   )
  debug_launcher(partial(lowerCAmelCase__					,     step_scheduler_with_optimizer=lowerCAmelCase__   )   )






 @require_huggingface_suite
 def lowercase_      (self   ):

  '''simple docstring'''







  AcceleratorState._reset_state(lowerCAmelCase__   )
  debug_launcher(partial(lowerCAmelCase__					,     num_processes=1   )   )
  debug_launcher(lowerCAmelCase__   )









"""simple docstring"""
import numpy as np
from numpy import floataa
from numpy.typing import NDArray






def 				__lowerCAmelCase					(					__lowerCAmelCase			:		NDArray[floataa]  ,	__lowerCAmelCase			:		NDArray[floataa]						)    ->       NDArray[floataa]:
 _UpperCamelCase      ,	_UpperCamelCase      :	Optional[Any]					      =  np.shape(__lowerCAmelCase						)

 _UpperCamelCase      :	NDArray[floataa]					      =  np.zeros((rows, 1)  ,	dtype=__lowerCAmelCase						)
 for row in reversed(range(__lowerCAmelCase						)						):
  _UpperCamelCase      :	List[str]					      =  0
  for col in range(row + 1  ,	__lowerCAmelCase						):
   total += coefficients[row, col] * x[col]

  _UpperCamelCase      :	Dict					      =  (vector[row] - total) / coefficients[row, row]

 return x






def 				__lowerCAmelCase					(					__lowerCAmelCase			:		NDArray[floataa]  ,	__lowerCAmelCase			:		NDArray[floataa]						)    ->       NDArray[floataa]:
 _UpperCamelCase      ,	_UpperCamelCase      :	Optional[Any]					      =  np.shape(__lowerCAmelCase						)
 if rows != columns:
  return np.array(()  ,	dtype=__lowerCAmelCase						)

 # augmented matrix
 _UpperCamelCase      :	NDArray[floataa]					      =  np.concatenate((coefficients, vector)  ,	axis=1						)
 _UpperCamelCase      :	List[str]					      =  augmented_mat.astype("float64"						)

 # scale the matrix leaving it triangular
 for row in range(rows - 1						):
  _UpperCamelCase      :	Optional[Any]					      =  augmented_mat[row, row]
  for col in range(row + 1  ,	__lowerCAmelCase						):
   _UpperCamelCase      :	Union[str, Any]					      =  augmented_mat[col, row] / pivot
   augmented_mat[col, :] -= factor * augmented_mat[row, :]

 _UpperCamelCase      :	Any					      =  retroactive_resolution(
     augmented_mat[:, 0:columns]  ,	augmented_mat[:, columns : columns + 1]						)

 return x


if __name__ == "__main__":
    import doctest

    doctest.testmod()



