



import numpy as np
from numpy import floataa
from numpy.typing import NDArray






def 						_lowerCAmelCase    (					__lowerCamelCase :  NDArray[floataa]		,						__lowerCamelCase :  NDArray[floataa]  ):



 """simple docstring"""





 __SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE							:     Optional[Any]							=						np.shape(__lowerCamelCase  )

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

  __SCREAMING_SNAKE_CASE							:     int							=						(vector[row] - total) / coefficients[row, row]

 return x






def 						_lowerCAmelCase    (					__lowerCamelCase :  NDArray[floataa]		,						__lowerCamelCase :  NDArray[floataa]  ):



 """simple docstring"""





 __SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE							:     List[Any]							=						np.shape(__lowerCamelCase  )
 if rows != columns:
  return np.array(()		,						dtype=__lowerCamelCase  )

 # augmented matrix
 __SCREAMING_SNAKE_CASE							:     NDArray[floataa]							=						np.concatenate((coefficients, vector)		,						axis=1  )
 __SCREAMING_SNAKE_CASE							:     Optional[Any]							=						augmented_mat.astype("float64"  )

 # scale the matrix leaving it triangular
 for row in range(rows - 1  ):
  __SCREAMING_SNAKE_CASE							:     Tuple							=						augmented_mat[row, row]
  for col in range(row + 1		,						__lowerCamelCase  ):
   __SCREAMING_SNAKE_CASE							:     Any							=						augmented_mat[col, row] / pivot
   augmented_mat[col, :] -= factor * augmented_mat[row, :]

 __SCREAMING_SNAKE_CASE							:     Union[str, Any]							=						retroactive_resolution(
     augmented_mat[:, 0:columns]		,						augmented_mat[:, columns : columns + 1]  )

 return x


if __name__ == "__main__":
      import doctest

      doctest.testmod()











import inspect
import warnings

import torch

from .state import AcceleratorState, GradientState
from .utils import DistributedType, honor_type, is_tpu_available


if is_tpu_available(check_device=False):
      import torch_xla.core.xla_model as xm






def 						_lowerCAmelCase    (					__lowerCamelCase :  Any		,						__lowerCamelCase :  str  ):



 """simple docstring"""





 if isinstance(__lowerCamelCase		,						(list, tuple)  ):
  return honor_type(__lowerCamelCase		,						(move_to_device(__lowerCamelCase		,						__lowerCamelCase  ) for t in state)  )
 elif isinstance(__lowerCamelCase		,						__lowerCamelCase  ):
  return type(__lowerCamelCase  )({k: move_to_device(__lowerCamelCase		,						__lowerCamelCase  ) for k, v in state.items()}  )
 elif isinstance(__lowerCamelCase		,						torch.Tensor  ):
  return state.to(__lowerCamelCase  )
 return state






class    _SCREAMING_SNAKE_CASE						(torch.optim.Optimizer			):





     def __init__(							self			:				int  ,	UpperCamelCase			:				Any  ,	UpperCamelCase			:				List[str]=True  ,	UpperCamelCase			:				List[Any]=None					)->Optional[int]:
      __SCREAMING_SNAKE_CASE							:     str							=						optimizer
      __SCREAMING_SNAKE_CASE							:     Optional[Any]							=						scaler
      __SCREAMING_SNAKE_CASE							:     Any							=						AcceleratorState()
      __SCREAMING_SNAKE_CASE							:     int							=						GradientState()
      __SCREAMING_SNAKE_CASE							:     str							=						device_placement
      __SCREAMING_SNAKE_CASE							:     int							=						False
      __SCREAMING_SNAKE_CASE							:     Dict							=						None

      # Handle device placement
      if device_placement:
       __SCREAMING_SNAKE_CASE							:     List[str]							=						self.optimizer.state_dict()
       if self.accelerator_state.distributed_type == DistributedType.TPU:
        xm.send_cpu_data_to_device(UpperCamelCase  ,	self.accelerator_state.device					)
       else:
        __SCREAMING_SNAKE_CASE							:     Union[str, Any]							=						move_to_device(UpperCamelCase  ,	self.accelerator_state.device					)
       self.optimizer.load_state_dict(UpperCamelCase					)





     @property
     def 						__snake_case     (							self			:				Optional[Any]					)->List[str]:
      return self.optimizer.state





     @state.setter
     def 						__snake_case     (							self			:				Optional[int]  ,	UpperCamelCase			:				List[str]					)->Dict:
      __SCREAMING_SNAKE_CASE							:     List[str]							=						state





     @property
     def 						__snake_case     (							self			:				List[Any]					)->str:
      return self.optimizer.param_groups





     @param_groups.setter
     def 						__snake_case     (							self			:				List[str]  ,	UpperCamelCase			:				Any					)->Dict:
      __SCREAMING_SNAKE_CASE							:     Optional[int]							=						param_groups





     @property
     def 						__snake_case     (							self			:				str					)->str:
      return self.optimizer.defaults





     @defaults.setter
     def 						__snake_case     (							self			:				int  ,	UpperCamelCase			:				Tuple					)->List[str]:
      __SCREAMING_SNAKE_CASE							:     List[str]							=						defaults





     def 						__snake_case     (							self			:				Any  ,	UpperCamelCase			:				Tuple					)->Optional[int]:
      self.optimizer.add_param_group(UpperCamelCase					)





     def 						__snake_case     (							self			:				Union[str, Any]  ,	UpperCamelCase			:				Union[str, Any]					)->Dict:
      if self.accelerator_state.distributed_type == DistributedType.TPU and self.device_placement:
       xm.send_cpu_data_to_device(UpperCamelCase  ,	self.accelerator_state.device					)
      self.optimizer.load_state_dict(UpperCamelCase					)





     def 						__snake_case     (							self			:				List[str]					)->List[Any]:
      return self.optimizer.state_dict()





     def 						__snake_case     (							self			:				Optional[int]  ,	UpperCamelCase			:				Any=None					)->Any:
      if self.gradient_state.sync_gradients:
       __SCREAMING_SNAKE_CASE							:     Optional[int]							=						"set_to_none" in inspect.signature(self.optimizer.zero_grad					).parameters
       if accept_arg:
        if set_to_none is None:
         __SCREAMING_SNAKE_CASE							:     Optional[int]							=						False
        self.optimizer.zero_grad(set_to_none=UpperCamelCase					)
       else:
        if set_to_none is not None:
         raise ValueError("`set_to_none` for Optimizer.zero_grad` is not supported by this optimizer."					)
        self.optimizer.zero_grad()





     def 						__snake_case     (							self			:				Dict  ,	UpperCamelCase			:				Tuple=None					)->List[Any]:
      if self.gradient_state.sync_gradients:
       if self.accelerator_state.distributed_type == DistributedType.TPU:
        __SCREAMING_SNAKE_CASE							:     List[str]							=						{"closure": closure} if closure is not None else {}
        xm.optimizer_step(self.optimizer  ,	optimizer_args=UpperCamelCase					)
       elif self.scaler is not None:
        __SCREAMING_SNAKE_CASE							:     Optional[int]							=						False
        if self._last_scale is None:
         # `get_scale` is an async operation requiring full synchronization
         # on CPU and GPUs before finishing. As a result, we store away
         # the prior one to reduce the call overhead
         __SCREAMING_SNAKE_CASE							:     List[Any]							=						self.scaler.get_scale()
         __SCREAMING_SNAKE_CASE							:     List[Any]							=						True
        self.scaler.step(self.optimizer  ,	UpperCamelCase					)
        self.scaler.update()
        __SCREAMING_SNAKE_CASE							:     Dict							=						self.scaler.get_scale()
        if not new_scale:
         # If we reduced the loss scale, it means the optimizer step was skipped because of gradient overflow.
         __SCREAMING_SNAKE_CASE							:     Optional[Any]							=						scale_after < self._last_scale
        __SCREAMING_SNAKE_CASE							:     List[Any]							=						scale_after

       else:
        self.optimizer.step(UpperCamelCase					)





     def 						__snake_case     (							self			:				Optional[int]  ,	UpperCamelCase			:				Optional[Any]					)->Any:
      for param_group in self.optimizer.param_groups:
       __SCREAMING_SNAKE_CASE							:     Tuple							=						[parameters_map.get(UpperCamelCase  ,	UpperCamelCase					) for p in param_group["params"]]





     @property
     def 						__snake_case     (							self			:				List[Any]					)->int:
      warnings.warn(
          "The `is_overflow` property is deprecated and will be removed in version 1.0 of Accelerate use "
          "`optimizer.step_was_skipped` instead."  ,	UpperCamelCase  ,	)
      return self._is_overflow





     @property
     def 						__snake_case     (							self			:				Optional[int]					)->List[Any]:
      return self._is_overflow





     def __getstate__(							self			:				List[str]					)->List[str]:
      return self.__dict__.copy()






     def __setstate__(							self			:				Union[str, Any]  ,	UpperCamelCase			:				str					)->int:
      self.__dict__.update(UpperCamelCase					)






