


from __future__ import annotations

from collections.abc import Callable

__snake_case   							=						list[list[float | int]]






def 		_A		(		_lowercase					,  _lowercase )					-> Matrix:


     """simple docstring"""


     __UpperCamelCase =			len(_lowercase )
     __UpperCamelCase =			[[0 for _ in range(size + 1 )] for _ in range(_lowercase )]
     __UpperCamelCase =			42
     __UpperCamelCase =			42
     __UpperCamelCase =			42
     __UpperCamelCase =			42
     __UpperCamelCase =			42
     __UpperCamelCase =			42

     for row in range(_lowercase ):
          for col in range(_lowercase ):
               __UpperCamelCase =			matrix[row][col]

          __UpperCamelCase =			vector[row][0]

     __UpperCamelCase =			0
     __UpperCamelCase =			0
     while row < size and col < size:
          # pivoting
          __UpperCamelCase =			max((abs(augmented[rowa][col] ), rowa) for rowa in range(_lowercase					,  _lowercase ) )[
              1
          ]
          if augmented[pivot_row][col] == 0:
               col += 1
               continue
          else:
               __UpperCamelCase,    __UpperCamelCase =			augmented[pivot_row], augmented[row]

          for rowa in range(row + 1					,  _lowercase ):
               __UpperCamelCase =			augmented[rowa][col] / augmented[row][col]
               __UpperCamelCase =			0
               for cola in range(col + 1					,  size + 1 ):
                    augmented[rowa][cola] -= augmented[row][cola] * ratio

          row += 1
          col += 1

     # back substitution
     for col in range(1					,  _lowercase ):
          for row in range(_lowercase ):
               __UpperCamelCase =			augmented[row][col] / augmented[col][col]
               for cola in range(_lowercase					,  size + 1 ):
                    augmented[row][cola] -= augmented[col][cola] * ratio

    # round to get rid of numbers like 2.000000000000004
     return [
         [round(augmented[row][size] / augmented[row][row]					,  10 )] for row in range(_lowercase )
     ]






def 		_A		(		_lowercase )					-> Callable[[int], int]:


     """simple docstring"""


     __UpperCamelCase =			len(_lowercase )
     __UpperCamelCase =			[[0 for _ in range(_lowercase )] for _ in range(_lowercase )]
     __UpperCamelCase =			[[0] for _ in range(_lowercase )]
     __UpperCamelCase =			42
     __UpperCamelCase =			42
     __UpperCamelCase =			42
     __UpperCamelCase =			42

     for x_val, y_val in enumerate(_lowercase ):
          for col in range(_lowercase ):
               __UpperCamelCase =			(x_val + 1) ** (size - col - 1)
          __UpperCamelCase =			y_val

     __UpperCamelCase =			solve(_lowercase					,  _lowercase )

     def interpolated_func(_lowercase ) -> int:
          return sum(
              round(coeffs[x_val][0] ) * (var ** (size - x_val - 1))
              for x_val in range(_lowercase ) )

     return interpolated_func






def 		_A		(		_lowercase )					-> int:


     """simple docstring"""


     return (
         1
         - variable
         + variable**2
         - variable**3
         + variable**4
         - variable**5
         + variable**6
         - variable**7
         + variable**8
         - variable**9
         + variable**10
     )






def 		_A		(		_lowercase = question_function					,  _lowercase = 10 )					-> int:


     """simple docstring"""


     __UpperCamelCase =			[func(_lowercase ) for x_val in range(1					,  order + 1 )]

     __UpperCamelCase =			[
         interpolate(data_points[:max_coeff] ) for max_coeff in range(1					,  order + 1 )
     ]

     __UpperCamelCase =			0
     __UpperCamelCase =			42
     __UpperCamelCase =			42

     for poly in polynomials:
          __UpperCamelCase =			1
          while func(_lowercase ) == poly(_lowercase ):
               x_val += 1

          ret += poly(_lowercase )

     return ret


if __name__ == "__main__":
    print(f"""{solution() = }""")






import math
class 		__magic_name__						:





     '''simple docstring'''



     def 	SCREAMING_SNAKE_CASE__						(					self:Optional[int]     ,		_a:list[list[float]]     ,		_a:list[int]   ):
       snake_case__						= 0.0
       snake_case__						= 0.0
       for i in range(len(_a   )   ):
         da += math.pow((sample[i] - weights[0][i])     ,		2   )
         da += math.pow((sample[i] - weights[1][i])     ,		2   )
         return 0 if da > da else 1
       return 0







     def 	SCREAMING_SNAKE_CASE__						(					self:Tuple     ,		_a:list[list[int | float]]     ,		_a:list[int]     ,		_a:int     ,		_a:float   ):
       for i in range(len(_a   )   ):
         weights[j][i] += alpha * (sample[i] - weights[j][i])
       return weights







def SCREAMING_SNAKE_CASE	(			)    ->				None:
  # Training Examples ( m, n )
  snake_case__						= [[1, 1, 0, 0], [0, 0, 0, 1], [1, 0, 0, 0], [0, 0, 1, 1]]

  # weight initialization ( n, C )
  snake_case__						= [[0.2, 0.6, 0.5, 0.9], [0.8, 0.4, 0.7, 0.3]]

  # training
  snake_case__						= SelfOrganizingMap()
  snake_case__						= 3
  snake_case__						= 0.5

  for _ in range(__lowerCAmelCase				):
    for j in range(len(__lowerCAmelCase				)				):
      # training sample
      snake_case__						= training_samples[j]

      # Compute the winning vector
      snake_case__						= self_organizing_map.get_winner(__lowerCAmelCase							,   __lowerCAmelCase				)

      # Update the winning vector
      snake_case__						= self_organizing_map.update(__lowerCAmelCase							,   __lowerCAmelCase							,   __lowerCAmelCase							,   __lowerCAmelCase				)

    # classify test sample
  snake_case__						= [0, 0, 0, 1]
  snake_case__						= self_organizing_map.get_winner(__lowerCAmelCase							,   __lowerCAmelCase				)

  # results
  print(F"""Clusters that the test sample belongs to : {winner}"""				)
  print(F"""Weights that have been trained : {weights}"""				)


# running the main() function
if __name__ == "__main__":
   main()

