


from __future__ import annotations

import math
import random
from collections.abc import Collection
from typing import overload


class      __lowerCAmelCase  :






  """simple docstring"""





  def __init__(  self							:							str     ,					_lowerCAmelCase							:							Collection[float] | None = None	) ->			None:




     """simple docstring"""
     if components is None:
        snake_case_            =       []
     snake_case_            =       list(_lowerCAmelCase	)



  def __len__(  self							:							Dict	) ->			int:




     """simple docstring"""
     return len(self.__components	)



  def __str__(  self							:							Union[str, Any]	) ->			str:




     """simple docstring"""
     return "(" + ",".join(map(_lowerCAmelCase     ,					self.__components	)	) + ")"



  def __add__(  self							:							List[str]     ,					_lowerCAmelCase							:							Vector	) ->			Vector:




     """simple docstring"""
     snake_case_            =       len(self	)
     if size == len(_lowerCAmelCase	):
        snake_case_            =       [self.__components[i] + other.component(_lowerCAmelCase	) for i in range(_lowerCAmelCase	)]
        return Vector(_lowerCAmelCase	)
     else:
        raise Exception("must have the same size"	)



  def __sub__(  self							:							int     ,					_lowerCAmelCase							:							Vector	) ->			Vector:




     """simple docstring"""
     snake_case_            =       len(self	)
     if size == len(_lowerCAmelCase	):
        snake_case_            =       [self.__components[i] - other.component(_lowerCAmelCase	) for i in range(_lowerCAmelCase	)]
        return Vector(_lowerCAmelCase	)
     else:  # error case
        raise Exception("must have the same size"	)



  @overload
  def __mul__(  self							:							List[Any]     ,					_lowerCAmelCase							:							float	) ->			Vector:




     """simple docstring"""
     ...



  @overload
  def __mul__(  self							:							Any     ,					_lowerCAmelCase							:							Vector	) ->			float:




     """simple docstring"""
     ...



  def __mul__(  self							:							Any     ,					_lowerCAmelCase							:							float | Vector	) ->			float | Vector:




     """simple docstring"""
     if isinstance(_lowerCAmelCase     ,					(float, int)	):
        snake_case_            =       [c * other for c in self.__components]
        return Vector(_lowerCAmelCase	)
     elif isinstance(_lowerCAmelCase     ,					_lowerCAmelCase	) and len(self	) == len(_lowerCAmelCase	):
        snake_case_            =       len(self	)
        snake_case_            =       [self.__components[i] * other.component(_lowerCAmelCase	) for i in range(_lowerCAmelCase	)]
        return sum(_lowerCAmelCase	)
     else:  # error case
        raise Exception("invalid operand!"	)



  def        lowerCAmelCase__	(  self							:							Optional[Any]	) ->			Vector:




     """simple docstring"""
     return Vector(self.__components	)



  def        lowerCAmelCase__	(  self							:							Optional[int]     ,					_lowerCAmelCase							:							int	) ->			float:




     """simple docstring"""
     if isinstance(_lowerCAmelCase     ,					_lowerCAmelCase	) and -len(self.__components	) <= i < len(self.__components	):
        return self.__components[i]
     else:
        raise Exception("index out of range"	)



  def        lowerCAmelCase__	(  self							:							Any     ,					_lowerCAmelCase							:							int     ,					_lowerCAmelCase							:							float	) ->			None:




     """simple docstring"""
     assert -len(self.__components	) <= pos < len(self.__components	)
     snake_case_            =       value



  def        lowerCAmelCase__	(  self							:							Tuple	) ->			float:




     """simple docstring"""
     if len(self.__components	) == 0:
        raise Exception("Vector is empty"	)
     snake_case_            =       [c**2 for c in self.__components]
     return math.sqrt(sum(_lowerCAmelCase	)	)



  def        lowerCAmelCase__	(  self							:							Union[str, Any]     ,					_lowerCAmelCase							:							Vector     ,					_lowerCAmelCase							:							bool = False	) ->			float:




     """simple docstring"""
     snake_case_            =       self * other
     snake_case_            =       self.euclidean_length() * other.euclidean_length()
     if deg:
        return math.degrees(math.acos(num / den	)	)
     else:
        return math.acos(num / den	)






def       _lowerCAmelCase    (				lowerCAmelCase_				:int				)->Vector:
   '''simple docstring'''






   assert isinstance(lowerCAmelCase_		,    lowerCAmelCase_				)
   return Vector([0] * dimension				)



def       _lowerCAmelCase    (				lowerCAmelCase_				:int		,    lowerCAmelCase_				:int				)->Vector:
   '''simple docstring'''






   assert isinstance(lowerCAmelCase_		,    lowerCAmelCase_				) and (isinstance(lowerCAmelCase_		,    lowerCAmelCase_				))
   snake_case_            =       [0] * dimension
   snake_case_            =       1
   return Vector(lowerCAmelCase_				)



def       _lowerCAmelCase    (				lowerCAmelCase_				:float		,    lowerCAmelCase_				:Vector		,    lowerCAmelCase_				:Vector				)->Vector:
   '''simple docstring'''






   assert (
       isinstance(lowerCAmelCase_		,    lowerCAmelCase_				)
       and isinstance(lowerCAmelCase_		,    lowerCAmelCase_				)
       and (isinstance(lowerCAmelCase_		,    (int, float)				))
   )
   return x * scalar + y



def       _lowerCAmelCase    (				lowerCAmelCase_				:int		,    lowerCAmelCase_				:int		,    lowerCAmelCase_				:int				)->Vector:
   '''simple docstring'''






   random.seed(lowerCAmelCase_				)
   snake_case_            =       [random.randint(lowerCAmelCase_		,    lowerCAmelCase_				) for _ in range(lowerCAmelCase_				)]
   return Vector(lowerCAmelCase_				)


class      __lowerCAmelCase  :






  """simple docstring"""





  def __init__(  self							:							Any     ,					_lowerCAmelCase							:							list[list[float]]     ,					_lowerCAmelCase							:							int     ,					_lowerCAmelCase							:							int	) ->			None:




     """simple docstring"""
     snake_case_            =       matrix
     snake_case_            =       w
     snake_case_            =       h



  def __str__(  self							:							Optional[Any]	) ->			str:




     """simple docstring"""
     snake_case_            =       ""
     for i in range(self.__height	):
        ans += "|"
        for j in range(self.__width	):
           if j < self.__width - 1:
              ans += str(self.__matrix[i][j]	) + ","
           else:
              ans += str(self.__matrix[i][j]	) + "|\n"
     return ans



  def __add__(  self							:							Optional[Any]     ,					_lowerCAmelCase							:							Matrix	) ->			Matrix:




     """simple docstring"""
     if self.__width == other.width() and self.__height == other.height():
        snake_case_            =       []
        for i in range(self.__height	):
           snake_case_            =       [
               self.__matrix[i][j] + other.component(_lowerCAmelCase     ,					_lowerCAmelCase	)
               for j in range(self.__width	)
           ]
           matrix.append(_lowerCAmelCase	)
        return Matrix(_lowerCAmelCase     ,					self.__width     ,					self.__height	)
     else:
        raise Exception("matrix must have the same dimension!"	)



  def __sub__(  self							:							Any     ,					_lowerCAmelCase							:							Matrix	) ->			Matrix:




     """simple docstring"""
     if self.__width == other.width() and self.__height == other.height():
        snake_case_            =       []
        for i in range(self.__height	):
           snake_case_            =       [
               self.__matrix[i][j] - other.component(_lowerCAmelCase     ,					_lowerCAmelCase	)
               for j in range(self.__width	)
           ]
           matrix.append(_lowerCAmelCase	)
        return Matrix(_lowerCAmelCase     ,					self.__width     ,					self.__height	)
     else:
        raise Exception("matrices must have the same dimension!"	)



  @overload
  def __mul__(  self							:							Optional[Any]     ,					_lowerCAmelCase							:							float	) ->			Matrix:




     """simple docstring"""
     ...



  @overload
  def __mul__(  self							:							Union[str, Any]     ,					_lowerCAmelCase							:							Vector	) ->			Vector:




     """simple docstring"""
     ...



  def __mul__(  self							:							Tuple     ,					_lowerCAmelCase							:							float | Vector	) ->			Vector | Matrix:




     """simple docstring"""
     if isinstance(_lowerCAmelCase     ,					_lowerCAmelCase	):  # matrix-vector
        if len(_lowerCAmelCase	) == self.__width:
           snake_case_            =       zero_vector(self.__height	)
           for i in range(self.__height	):
              snake_case_            =       [
                  self.__matrix[i][j] * other.component(_lowerCAmelCase	)
                  for j in range(self.__width	)
              ]
              ans.change_component(_lowerCAmelCase     ,					sum(_lowerCAmelCase	)	)
           return ans
        else:
           raise Exception(
               "vector must have the same size as the "
               "number of columns of the matrix!"	)
     elif isinstance(_lowerCAmelCase     ,					(int, float)	):  # matrix-scalar
        snake_case_            =       [
            [self.__matrix[i][j] * other for j in range(self.__width	)]
            for i in range(self.__height	)
        ]
        return Matrix(_lowerCAmelCase     ,					self.__width     ,					self.__height	)
     return None



  def        lowerCAmelCase__	(  self							:							Any	) ->			int:




     """simple docstring"""
     return self.__height



  def        lowerCAmelCase__	(  self							:							Any	) ->			int:




     """simple docstring"""
     return self.__width



  def        lowerCAmelCase__	(  self							:							Optional[Any]     ,					_lowerCAmelCase							:							int     ,					_lowerCAmelCase							:							int	) ->			float:




     """simple docstring"""
     if 0 <= x < self.__height and 0 <= y < self.__width:
        return self.__matrix[x][y]
     else:
        raise Exception("change_component: indices out of bounds"	)



  def        lowerCAmelCase__	(  self							:							Optional[int]     ,					_lowerCAmelCase							:							int     ,					_lowerCAmelCase							:							int     ,					_lowerCAmelCase							:							float	) ->			None:




     """simple docstring"""
     if 0 <= x < self.__height and 0 <= y < self.__width:
        snake_case_            =       value
     else:
        raise Exception("change_component: indices out of bounds"	)



  def        lowerCAmelCase__	(  self							:							Any     ,					_lowerCAmelCase							:							int     ,					_lowerCAmelCase							:							int	) ->			float:




     """simple docstring"""
     if self.__height != self.__width:
        raise Exception("Matrix is not square"	)
     snake_case_            =       self.__matrix[:x] + self.__matrix[x + 1 :]
     for i in range(len(_lowerCAmelCase	)	):
        snake_case_            =       minor[i][:y] + minor[i][y + 1 :]
     return Matrix(_lowerCAmelCase     ,					self.__width - 1     ,					self.__height - 1	).determinant()



  def        lowerCAmelCase__	(  self							:							List[str]     ,					_lowerCAmelCase							:							int     ,					_lowerCAmelCase							:							int	) ->			float:




     """simple docstring"""
     if self.__height != self.__width:
        raise Exception("Matrix is not square"	)
     if 0 <= x < self.__height and 0 <= y < self.__width:
        return (-1) ** (x + y) * self.minor(_lowerCAmelCase     ,					_lowerCAmelCase	)
     else:
        raise Exception("Indices out of bounds"	)



  def        lowerCAmelCase__	(  self							:							List[Any]	) ->			float:




     """simple docstring"""
     if self.__height != self.__width:
        raise Exception("Matrix is not square"	)
     if self.__height < 1:
        raise Exception("Matrix has no element"	)
     elif self.__height == 1:
        return self.__matrix[0][0]
     elif self.__height == 2:
        return (
            self.__matrix[0][0] * self.__matrix[1][1]
            - self.__matrix[0][1] * self.__matrix[1][0]
        )
     else:
        snake_case_            =       [
            self.__matrix[0][y] * self.cofactor(0     ,					_lowerCAmelCase	) for y in range(self.__width	)
        ]
        return sum(_lowerCAmelCase	)






def       _lowerCAmelCase    (				lowerCAmelCase_				:int				)->Matrix:
   '''simple docstring'''






   snake_case_            =       [[0] * n for _ in range(lowerCAmelCase_				)]
   return Matrix(lowerCAmelCase_		,    lowerCAmelCase_		,    lowerCAmelCase_				)



def       _lowerCAmelCase    (				lowerCAmelCase_				:int		,    lowerCAmelCase_				:int		,    lowerCAmelCase_				:int		,    lowerCAmelCase_				:int				)->Matrix:
   '''simple docstring'''






   random.seed(lowerCAmelCase_				)
   snake_case_            =       [
       [random.randint(lowerCAmelCase_		,    lowerCAmelCase_				) for _ in range(lowerCAmelCase_				)] for _ in range(lowerCAmelCase_				)
   ]
   return Matrix(lowerCAmelCase_		,    lowerCAmelCase_		,    lowerCAmelCase_				)








import logging
import os

from .state import PartialState


class      __lowerCAmelCase  (			logging.LoggerAdapter       ):






  """simple docstring"""





  @staticmethod
  def        lowerCAmelCase__	(  _lowerCAmelCase							:							int	) ->			Tuple:




     """simple docstring"""
     snake_case_            =       PartialState()
     return not main_process_only or (main_process_only and state.is_main_process)



  def        lowerCAmelCase__	(  self							:							Union[str, Any]     ,					_lowerCAmelCase							:							List[Any]     ,					_lowerCAmelCase							:							Tuple     ,					*_lowerCAmelCase							:							List[Any]     ,					**_lowerCAmelCase							:							Any	) ->			Optional[int]:




     """simple docstring"""
     if PartialState._shared_state == {}:
        raise RuntimeError(
            "You must initialize the accelerate state by calling either `PartialState()` or `Accelerator()` before using the logging utility."	)
     snake_case_            =       kwargs.pop("main_process_only"     ,					_lowerCAmelCase	)
     snake_case_            =       kwargs.pop("in_order"     ,					_lowerCAmelCase	)

     if self.isEnabledFor(_lowerCAmelCase	):
        if self._should_log(_lowerCAmelCase	):
           snake_case_     ,     snake_case_            =       self.process(_lowerCAmelCase     ,					_lowerCAmelCase	)
           self.logger.log(_lowerCAmelCase     ,					_lowerCAmelCase     ,					*_lowerCAmelCase     ,					**_lowerCAmelCase	)

        elif in_order:
           snake_case_            =       PartialState()
           for i in range(state.num_processes	):
              if i == state.process_index:
                 snake_case_     ,     snake_case_            =       self.process(_lowerCAmelCase     ,					_lowerCAmelCase	)
                 self.logger.log(_lowerCAmelCase     ,					_lowerCAmelCase     ,					*_lowerCAmelCase     ,					**_lowerCAmelCase	)
              state.wait_for_everyone()






def       _lowerCAmelCase    (				lowerCAmelCase_				:str		,    lowerCAmelCase_				:str = None				)->Any:
   '''simple docstring'''






   if log_level is None:
      snake_case_            =       os.environ.get("ACCELERATE_LOG_LEVEL"		,    lowerCAmelCase_				)
   snake_case_            =       logging.getLogger(lowerCAmelCase_				)
   if log_level is not None:
      logger.setLevel(log_level.upper()				)
      logger.root.setLevel(log_level.upper()				)
   return MultiProcessAdapter(lowerCAmelCase_		,    {}				)




