code: import timeit
  
  
  
  
  class    __lowerCAmelCase  :
  
  
  
   '''simple docstring'''
  
   def __init__(			self       :		Union[str, Any]       ,			lowerCamelCase       :		Union[str, Any]  ) ->							int:
          if isinstance(lowerCamelCase       ,			lowerCamelCase  ):  # Initializes a matrix identical to the one provided.
                 _UpperCamelCase     :       List[str]  						=  arg
                 _UpperCamelCase     :       List[str]  						=  len(lowerCamelCase  )
          else:  # Initializes a square matrix of the given size and set values to zero.
                 _UpperCamelCase     :       List[str]  						=  arg
                 _UpperCamelCase     :       Tuple  						=  [[0 for _ in range(self.n  )] for _ in range(self.n  )]
  
   def __mul__(			self       :		str       ,			lowerCamelCase       :		Union[str, Any]  ) ->							Any:
          _UpperCamelCase     :       str  						=  Matrix(self.n  )
          for i in range(self.n  ):
                 for j in range(self.n  ):
                        for k in range(self.n  ):
                               matrix.t[i][j] += self.t[i][k] * b.t[k][j]
          return matrix
  
  
  
  
  
  
  
  def SCREAMING_SNAKE_CASE				(     lowercase_:	Tuple		,						lowercase_:	Any				):
         _UpperCamelCase     :       Tuple  						=  Matrix([[1, 0], [0, 1]]				)
         while b > 0:
                if b & 1:
                       matrix *= a
                a *= a
                b >>= 1
         return matrix
  
  
  def SCREAMING_SNAKE_CASE				(     lowercase_:	int		,						lowercase_:	Optional[Any]		,						lowercase_:	List[Any]				):
         # Trivial Cases
         if n == 1:
                return fa
         elif n == 2:
                return fa
         _UpperCamelCase     :       int  						=  Matrix([[1, 1], [1, 0]]				)
         _UpperCamelCase     :       List[Any]  						=  modular_exponentiation(lowercase_		,						n - 2				)
         return fa * matrix.t[0][0] + fa * matrix.t[0][1]
  
  
  def SCREAMING_SNAKE_CASE				(     lowercase_:	Optional[int]		,						lowercase_:	Tuple		,						lowercase_:	str				):
         # Trivial Cases
         if n == 1:
                return fa
         elif n == 2:
                return fa
  
         _UpperCamelCase     :       List[Any]  						=  fa
         _UpperCamelCase     :       str  						=  fa
         n -= 2
  
         while n > 0:
                _UpperCamelCase     :       Tuple  						=  fn_a + fn_a, fn_a
                n -= 1
  
         return fn_a
  
  
  def SCREAMING_SNAKE_CASE				(     ):
         _UpperCamelCase     :       str  						=  '\nfrom random import randint\nfrom __main__ import fibonacci_with_matrix_exponentiation\n'
         _UpperCamelCase     :       Tuple  						=  'fibonacci_with_matrix_exponentiation(randint(1,70000), 1, 1)'
         _UpperCamelCase     :       Tuple  						=  timeit.timeit(setup=lowercase_		,						stmt=lowercase_		,						number=100				)
         print('With matrix exponentiation the average execution time is '		,						exec_time / 100				)
         return exec_time
  
  
  def SCREAMING_SNAKE_CASE				(     ):
         _UpperCamelCase     :       Tuple  						=  '\nfrom random import randint\nfrom __main__ import simple_fibonacci\n'
         _UpperCamelCase     :       Optional[Any]  						=  'simple_fibonacci(randint(1,70000), 1, 1)'
         _UpperCamelCase     :       str  						=  timeit.timeit(setup=lowercase_		,						stmt=lowercase_		,						number=100				)
         print(
             'Without matrix exponentiation the average execution time is '		,						exec_time / 100				)
         return exec_time
  
  
  def SCREAMING_SNAKE_CASE				(     ):
         matrix_exponentiation_time()
         simple_fibonacci_time()
  
  
  if __name__ == "__main__":
   main()
  
  
  
  
style_context: from .chunk_utils import chunk_layer
  from .data_transforms import make_atomaa_masks
  from .feats import atomaa_to_atomaa, frames_and_literature_positions_to_atomaa_pos, torsion_angles_to_frames
  from .loss import compute_predicted_aligned_error, compute_tm
  from .protein import Protein as OFProtein
  from .protein import to_pdb
  from .rigid_utils import Rigid, Rotation
  from .tensor_utils import dict_multimap, flatten_final_dims, permute_final_dims
  
  
  
  