'''simple docstring'''




import pickle
import unittest

import torch

from accelerate import Accelerator
from accelerate.state import AcceleratorState
from accelerate.test_utils import require_cpu






@require_cpu
class 		__A       (unittest.TestCase   ):






       def 			_snake_case						(      self      ):
              __UpperCAmelCase  :				Optional[Any]       				=		torch.nn.Linear(10				,     10      )
              __UpperCAmelCase  :				Any       				=		torch.optim.SGD(model.parameters()				,     0.1      )
              __UpperCAmelCase  :				Optional[int]       				=		Accelerator()
              __UpperCAmelCase  :				List[str]       				=		accelerator.prepare(UpperCamelCase_      )
              try:
                     pickle.loads(pickle.dumps(UpperCamelCase_      )      )
              except Exception as e:
                     self.fail(f"""Accelerated optimizer pickling failed with {e}"""      )
              AcceleratorState._reset_state()







'''simple docstring'''




from __future__ import annotations

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

def _lowercase	(      lowerCamelCase__							,    lowerCamelCase__							,    lowerCamelCase__							,    lowerCamelCase__							,    )					->       list[float]:





       """simple docstring"""


       __UpperCAmelCase				, __UpperCAmelCase  :				Union[str, Any]       				=		coefficient_matrix.shape
       __UpperCAmelCase				, __UpperCAmelCase  :				Any       				=		constant_matrix.shape

       if rowsa != colsa:
              __UpperCAmelCase  :				str       				=		f"""Coefficient matrix dimensions must be nxn but received {rowsa}x{colsa}"""
              raise ValueError(lowerCamelCase__						)

       if colsa != 1:
              __UpperCAmelCase  :				Optional[Any]       				=		f"""Constant matrix must be nx1 but received {rowsa}x{colsa}"""
              raise ValueError(lowerCamelCase__						)

       if rowsa != rowsa:
              __UpperCAmelCase  :				Optional[int]       				=		(
                  "Coefficient and constant matrices dimensions must be nxn and nx1 but "
                  f"""received {rowsa}x{colsa} and {rowsa}x{colsa}"""
              )
              raise ValueError(lowerCamelCase__						)

       if len(lowerCamelCase__						) != rowsa:
              __UpperCAmelCase  :				List[str]       				=		(
                  "Number of initial values must be equal to number of rows in coefficient "
                  f"""matrix but received {len(lowerCamelCase__						)} and {rowsa}"""
              )
              raise ValueError(lowerCamelCase__						)

       if iterations <= 0:
              raise ValueError("Iterations must be at least 1"						)

       __UpperCAmelCase  :				NDArray[floataa]       				=		np.concatenate(
           (coefficient_matrix, constant_matrix)							,    axis=1						)

       __UpperCAmelCase				, __UpperCAmelCase  :				Tuple       				=		table.shape

       strictly_diagonally_dominant(lowerCamelCase__						)

       # Iterates the whole matrix for given number of times
       for _ in range(lowerCamelCase__						):
              __UpperCAmelCase  :				int       				=		[]
              for row in range(lowerCamelCase__						):
                     __UpperCAmelCase  :				List[str]       				=		0
                     for col in range(lowerCamelCase__						):
                            if col == row:
                                   __UpperCAmelCase  :				int       				=		table[row][col]
                            elif col == cols - 1:
                                   __UpperCAmelCase  :				Any       				=		table[row][col]
                            else:
                                   temp += (-1) * table[row][col] * init_val[col]
                     __UpperCAmelCase  :				List[Any]       				=		(temp + val) / denom
                     new_val.append(lowerCamelCase__						)
              __UpperCAmelCase  :				str       				=		new_val

       return [float(lowerCamelCase__						) for i in new_val]

def _lowercase	(      lowerCamelCase__						)					->       bool:





       """simple docstring"""


       __UpperCAmelCase				, __UpperCAmelCase  :				Optional[int]       				=		table.shape

       __UpperCAmelCase  :				str       				=		True

       for i in range(0							,    lowerCamelCase__						):
              __UpperCAmelCase  :				Union[str, Any]       				=		0
              for j in range(0							,    cols - 1						):
                     if i == j:
                            continue
                     else:
                            total += table[i][j]

              if table[i][i] <= total:
                     raise ValueError("Coefficient matrix is not strictly diagonally dominant"						)

       return is_diagonally_dominant


# Test Cases
if __name__ == "__main__":
   import doctest

   doctest.testmod()






