


"""simple docstring"""



def     __lowerCAmelCase		(		lowercase    :    list[list]					)      ->		list[list]:


    """simple docstring"""





    snake_case       : str    =       current_set.copy()
    for row_index, row in enumerate(lowercase					):
        snake_case       : List[str]    =       row[0]
        for column_index, column in enumerate(lowercase					):
            if magnitude == 0:
                snake_case       : int    =       column
                continue
            snake_case       : Union[str, Any]    =       column / magnitude
    # Subtract to cancel term
    snake_case       : int    =       current_set[0]
    snake_case       : Dict    =       [first_row]
    snake_case       : Optional[int]    =       current_set[1::]
    for row in current_set:
        snake_case       : int    =       []
        # If first term is 0, it is already in form we want, so we preserve it
        if row[0] == 0:
            final_set.append(lowercase					)
            continue
        for column_index in range(len(lowercase					)					):
            temp_row.append(first_row[column_index] - row[column_index]					)
        final_set.append(lowercase					)
    # Create next recursion iteration set
    if len(final_set[0]					) != 3:
        snake_case       : Union[str, Any]    =       final_set[0]
        snake_case       : Dict    =       []
        snake_case       : Union[str, Any]    =       []
        for row in final_set[1::]:
            current_first_column.append(row[0]					)
            next_iteration.append(row[1::]					)
        snake_case       : Tuple    =       simplify(lowercase					)
        for i in range(len(lowercase					)					):
            resultant[i].insert(0		,				current_first_column[i]					)
        resultant.insert(0		,				lowercase					)
        snake_case       : Tuple    =       resultant
    return final_set







def     __lowerCAmelCase		(		lowercase    :    list[list]					)      ->		list:


    """simple docstring"""





    if len(lowercase					) == 0:
        raise IndexError("solve_simultaneous() requires n lists of length n+1"					)
    snake_case       : List[str]    =       len(lowercase					) + 1
    if any(len(lowercase					) != _length for item in equations					):
        raise IndexError("solve_simultaneous() requires n lists of length n+1"					)
    for row in equations:
        if any(not isinstance(lowercase		,				(int, float)					) for column in row					):
            raise ValueError("solve_simultaneous() requires lists of integers"					)
    if len(lowercase					) == 1:
        return [equations[0][-1] / equations[0][0]]
    snake_case       : Any    =       equations.copy()
    if any(0 in row for row in data_set					):
        snake_case       : int    =       data_set.copy()
        snake_case       : Union[str, Any]    =       []
        for row_index, row in enumerate(lowercase					):
            if 0 not in row:
                snake_case       : List[Any]    =       data_set.pop(lowercase					)
                break
        if not full_row:
            raise ValueError("solve_simultaneous() requires at least 1 full equation"					)
        data_set.insert(0		,				lowercase					)
    snake_case       : Union[str, Any]    =       data_set.copy()
    snake_case       : Optional[Any]    =       simplify(lowercase					)
    snake_case       : str    =       simplified[::-1]
    snake_case       : list    =       []
    for row in simplified:
        snake_case       : List[str]    =       row[-1]
        if not solutions:
            if row[-2] == 0:
                solutions.append(0					)
                continue
            solutions.append(current_solution / row[-2]					)
            continue
        snake_case       : Any    =       row.copy()[: len(lowercase					) - 1 :]
        while temp_row[0] == 0:
            temp_row.pop(0					)
        if len(lowercase					) == 0:
            solutions.append(0					)
            continue
        snake_case       : List[str]    =       temp_row[1::]
        snake_case       : List[Any]    =       temp_row[::-1]
        for column_index, column in enumerate(lowercase					):
            current_solution -= column * solutions[column_index]
        solutions.append(lowercase					)
    snake_case       : Optional[int]    =       []
    for item in solutions:
        final.append(float(round(lowercase		,				5					)					)					)
    return final[::-1]


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  __snake_case       =       [
      [2, 1, 1, 1, 1, 4],
      [1, 2, 1, 1, 1, 5],
      [1, 1, 2, 1, 1, 6],
      [1, 1, 1, 2, 1, 7],
      [1, 1, 1, 1, 2, 8],
  ]
  print(solve_simultaneous(eq))
  print(solve_simultaneous([[4, 2]]))









"""simple docstring"""



from .imports import is_tqdm_available


if is_tqdm_available():
  from tqdm.auto import tqdm as _tqdm

from ..state import PartialState







def     __lowerCAmelCase		(		lowercase    :    bool = True		,				*lowercase    :    str		,				**lowercase    :    List[Any]					)      ->		List[Any]:


    """simple docstring"""





    if not is_tqdm_available():
        raise ImportError("Accelerate's `tqdm` module requires `tqdm` to be installed. Please run `pip install tqdm`."					)
    snake_case       : Dict    =       False
    if main_process_only:
        snake_case       : int    =       PartialState().local_process_index == 0
    return _tqdm(*lowercase		,				**lowercase		,				disable=lowercase					)





