
"""simple docstring"""







import torch

from accelerate import Accelerator, DistributedType






class      __a      :







       def __enter__(       self		):



          '''simple docstring'''

          if self.enabled:
             _UpperCAmelCase 						=       self.model.no_sync()
             self.model_sync_obj.__enter__()

          return self







       def __exit__(       self				,lowerCamelCase_				,lowerCamelCase_				,lowerCamelCase_		):



          '''simple docstring'''

          if self.enabled:
             # Average all models on exit
             self._sync_and_avg_model_params()
             self.model_sync_obj.__exit__(SCREAMING_SNAKE_CASE__				,SCREAMING_SNAKE_CASE__				,SCREAMING_SNAKE_CASE__		)







       def __init__(       self				,lowerCamelCase_				,lowerCamelCase_				,lowerCamelCase_				,lowerCamelCase_ = True		):



          '''simple docstring'''

          if accelerator.distributed_type not in [
              DistributedType.NO,
              DistributedType.MULTI_CPU,
              DistributedType.MULTI_GPU,
          ]:
             raise NotImplementedError("LocalSGD is supported only for CPUs and GPUs (no DeepSpeed or MegatronLM)"		)
          _UpperCAmelCase 						=       enabled and accelerator.distributed_type != DistributedType.NO
          _UpperCAmelCase 						=       0
          if self.enabled:
             _UpperCAmelCase 						=       accelerator
             _UpperCAmelCase 						=       model
             _UpperCAmelCase 						=       local_sgd_steps







       def  _snake_case      (       self		):



          '''simple docstring'''

          self.num_steps += 1
          if not self.enabled:
             return

          if self.num_steps % self.local_sgd_steps == 0:
             self._sync_and_avg_model_params()







       def  _snake_case      (       self		):



          '''simple docstring'''

          self.accelerator.wait_for_everyone()
          with self.accelerator.autocast():
             for param in self.model.parameters():
                _UpperCAmelCase 						=       self.accelerator.reduce(param.data				,reduction="mean"		)




"""simple docstring"""




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



def 						UpperCAmelCase__ (					A__						,     A__ )   ->   NDArray[floataa]:




   """simple docstring"""
   lowerCamelCase__       ,							lowerCamelCase__						       =      np.shape(A__ )

   lowerCamelCase__						       =      np.zeros((rows, 1)						,     dtype=A__ )
   for row in reversed(range(A__ ) ):
      lowerCamelCase__						       =      0
      for col in range(row + 1						,     A__ ):
         total += coefficients[row, col] * x[col]

      lowerCamelCase__						       =      (vector[row] - total) / coefficients[row, row]

   return x



def 						UpperCAmelCase__ (					A__						,     A__ )   ->   NDArray[floataa]:




   """simple docstring"""
   lowerCamelCase__       ,							lowerCamelCase__						       =      np.shape(A__ )
   if rows != columns:
      return np.array(()						,     dtype=A__ )

   # augmented matrix
   lowerCamelCase__						       =      np.concatenate((coefficients, vector)						,     axis=1 )
   lowerCamelCase__						       =      augmented_mat.astype("float64" )

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

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

   return x


if __name__ == "__main__":
     import doctest

     doctest.testmod()




