

from collections.abc import Callable

import numpy as np
def        UpperCAmelCase_     (		_A   ,	_A   ,	_A   ,	_A   ,	_A       ):





     '''simple docstring'''




     SCREAMING_SNAKE_CASE__					=					int(np.ceil((x_end - xa) / step_size       )       )
     SCREAMING_SNAKE_CASE__					=					np.zeros((n + 1,)       )
     SCREAMING_SNAKE_CASE__					=					ya
     SCREAMING_SNAKE_CASE__					=					xa

     for k in range(_A       ):
          SCREAMING_SNAKE_CASE__					=					y[k] + step_size * ode_func(_A   ,	y[k]       )
          SCREAMING_SNAKE_CASE__					=					y[k] + (
              (step_size / 2) * (ode_func(_A   ,	y[k]       ) + ode_func(x + step_size   ,	_A       ))
          )
          x += step_size

     return y


if __name__ == "__main__":
       import doctest

       doctest.testmod()





import doctest
from collections import deque

import numpy as np






class  UpperCAmelCase__	:






  """simple docstring"""


  def __init__(							self		:	Optional[Any]      )	->							None:
       SCREAMING_SNAKE_CASE__					=					[2, 1, 2, -1]
       SCREAMING_SNAKE_CASE__					=					[1, 2, 3, 4]







  def    lowercase_	(							self		:	List[str]      )	->							list[float]:
       SCREAMING_SNAKE_CASE__					=					len(self.first_signal      )
       SCREAMING_SNAKE_CASE__					=					len(self.second_signal      )

       SCREAMING_SNAKE_CASE__					=					max(__lowerCamelCase			,     __lowerCamelCase      )

       # create a zero matrix of max_length x max_length
       SCREAMING_SNAKE_CASE__					=					[[0] * max_length for i in range(__lowerCamelCase      )]

       # fills the smaller signal with zeros to make both signals of same length
       if length_first_signal < length_second_signal:
            self.first_signal += [0] * (max_length - length_first_signal)
       elif length_first_signal > length_second_signal:
            self.second_signal += [0] * (max_length - length_second_signal)
       for i in range(__lowerCamelCase      ):
            SCREAMING_SNAKE_CASE__					=					deque(self.second_signal      )
            rotated_signal.rotate(__lowerCamelCase      )
            for j, item in enumerate(__lowerCamelCase      ):
                 matrix[i][j] += item

        # multiply the matrix with the first signal
       SCREAMING_SNAKE_CASE__					=					np.matmul(np.transpose(__lowerCamelCase      )			,     np.transpose(self.first_signal      )      )

       # rounding-off to two decimal places
       return [round(__lowerCamelCase			,     2      ) for i in final_signal]


if __name__ == "__main__":
       doctest.testmod()


