





"""simple docstring"""




import mpmath  # for roots of unity
import numpy as np

class  _UpperCAmelCase  :



      '''simple docstring'''

      def __init__(     self					,      snake_case_=None					,      snake_case_=None  ):

        """simple docstring"""

        A_  :       Any										=  list(poly_a or [0]  )[:]
        A_  :       str										=  list(poly_b or [0]  )[:]

        # Remove leading zero coefficients
        while self.polyA[-1] == 0:
          self.polyA.pop()
        A_  :       Optional[Any]										=  len(self.polyA  )

        while self.polyB[-1] == 0:
          self.polyB.pop()
        A_  :       List[Any]										=  len(self.polyB  )

        # Add 0 to make lengths equal a power of 2
        A_  :       List[Any]										=  int(
            2 ** np.ceil(np.loga(len(self.polyA  ) + len(self.polyB  ) - 1  )  )  )

        while len(self.polyA  ) < self.c_max_length:
          self.polyA.append(0  )
        while len(self.polyB  ) < self.c_max_length:
          self.polyB.append(0  )
        # A complex root used for the fourier transform
        A_  :       Union[str, Any]										=  complex(mpmath.root(x=1					,      n=self.c_max_length					,      k=1  )  )

        # The product
        A_  :       int										=  self.__multiply()

      def 					lowerCamelCase_			(     self					,      snake_case_  ):

        """simple docstring"""

        A_  :       Optional[int]										=  [[x] for x in self.polyA] if which == 'A' else [[x] for x in self.polyB]
        # Corner case
        if len(_lowercase  ) <= 1:
          return dft[0]
        #
        A_  :       Tuple										=  self.c_max_length // 2
        while next_ncol > 0:
          A_  :       Tuple										=  [[] for i in range(_lowercase  )]
          A_  :       Optional[int]										=  self.root**next_ncol

          # First half of next step
          A_  :       List[str]										=  1
          for j in range(self.c_max_length // (next_ncol * 2)  ):
            for i in range(_lowercase  ):
              new_dft[i].append(dft[i][j] + current_root * dft[i + next_ncol][j]  )
            current_root *= root
          # Second half of next step
          A_  :       Optional[int]										=  1
          for j in range(self.c_max_length // (next_ncol * 2)  ):
            for i in range(_lowercase  ):
              new_dft[i].append(dft[i][j] - current_root * dft[i + next_ncol][j]  )
            current_root *= root
          # Update
          A_  :       Optional[int]										=  new_dft
          A_  :       Tuple										=  next_ncol // 2
        return dft[0]

      def 					lowerCamelCase_			(     self  ):

        """simple docstring"""

        A_  :       Tuple										=  self.__dft('A'  )
        A_  :       Optional[int]										=  self.__dft('B'  )
        A_  :       Dict										=  [[dft_a[i] * dft_b[i] for i in range(self.c_max_length  )]]
        del dft_a
        del dft_b

        # Corner Case
        if len(inverce_c[0]  ) <= 1:
          return inverce_c[0]
        # Inverse DFT
        A_  :       Optional[int]										=  2
        while next_ncol <= self.c_max_length:
          A_  :       List[Any]										=  [[] for i in range(_lowercase  )]
          A_  :       Optional[int]										=  self.root ** (next_ncol // 2)
          A_  :       List[str]										=  1
          # First half of next step
          for j in range(self.c_max_length // next_ncol  ):
            for i in range(next_ncol // 2  ):
              # Even positions
              new_inverse_c[i].append(
                  (
                      inverce_c[i][j]
                      + inverce_c[i][j + self.c_max_length // next_ncol]
                  )
                  / 2  )
              # Odd positions
              new_inverse_c[i + next_ncol // 2].append(
                  (
                      inverce_c[i][j]
                      - inverce_c[i][j + self.c_max_length // next_ncol]
                  )
                  / (2 * current_root)  )
            current_root *= root
          # Update
          A_  :       Tuple										=  new_inverse_c
          next_ncol *= 2
        # Unpack
        A_  :       Dict										=  [round(x[0].real					,      8  ) + round(x[0].imag					,      8  ) * 1J for x in inverce_c]

        # Remove leading 0's
        while inverce_c[-1] == 0:
          inverce_c.pop()
        return inverce_c

      def __str__(     self  ):

        """simple docstring"""

        A_  :       Any										=  'A = ' + ' + '.join(
            F"""{coef}*x^{i}""" for coef, i in enumerate(self.polyA[: self.len_A]  )  )
        A_  :       Optional[int]										=  'B = ' + ' + '.join(
            F"""{coef}*x^{i}""" for coef, i in enumerate(self.polyB[: self.len_B]  )  )
        A_  :       Union[str, Any]										=  'A*B = ' + ' + '.join(
            F"""{coef}*x^{i}""" for coef, i in enumerate(self.product  )  )

        return F"""{a}\n{b}\n{c}"""


# Unit tests
if __name__ == "__main__":
   import doctest

   doctest.testmod()
import numpy as np
import skfuzzy as fuzz

if __name__ == "__main__":
   # Create universe of discourse in Python using linspace ()
   __lowerCamelCase			: List[Any]							   =		np.linspace(start=0, stop=75, num=75, endpoint=True, retstep=False)

   # Create two fuzzy sets by defining any membership function
   # (trapmf(), gbellmf(), gaussmf(), etc).
   __lowerCamelCase			: int							   =		[0, 25, 50]
   __lowerCamelCase			: Tuple							   =		[25, 50, 75]
   __lowerCamelCase			: List[str]							   =		fuzz.membership.trimf(X, abca)
   __lowerCamelCase			: Tuple							   =		fuzz.membership.trimf(X, abca)

   # Compute the different operations using inbuilt functions.
   __lowerCamelCase			: List[str]							   =		np.ones(75)
   __lowerCamelCase			: Tuple							   =		np.zeros((75,))
   # 1. Union = max(µA(x), µB(x))
   __lowerCamelCase			: str							   =		fuzz.fuzzy_or(X, young, X, middle_aged)[1]
   # 2. Intersection = min(µA(x), µB(x))
   __lowerCamelCase			: int							   =		fuzz.fuzzy_and(X, young, X, middle_aged)[1]
   # 3. Complement (A) = (1- min(µA(x))
   __lowerCamelCase			: Union[str, Any]							   =		fuzz.fuzzy_not(young)
   # 4. Difference (A/B) = min(µA(x),(1- µB(x)))
   __lowerCamelCase			: Union[str, Any]							   =		fuzz.fuzzy_and(X, young, X, fuzz.fuzzy_not(middle_aged)[1])[1]
   # 5. Algebraic Sum = [µA(x) + µB(x) – (µA(x) * µB(x))]
   __lowerCamelCase			: List[Any]							   =		young + middle_aged - (young * middle_aged)
   # 6. Algebraic Product = (µA(x) * µB(x))
   __lowerCamelCase			: int							   =		young * middle_aged
   # 7. Bounded Sum = min[1,(µA(x), µB(x))]
   __lowerCamelCase			: int							   =		fuzz.fuzzy_and(X, one, X, young + middle_aged)[1]
   # 8. Bounded difference = min[0,(µA(x), µB(x))]
   __lowerCamelCase			: str							   =		fuzz.fuzzy_or(X, zero, X, young - middle_aged)[1]

   # max-min composition
   # max-product composition

   # Plot each set A, set B and each operation result using plot() and subplot().
   from matplotlib import pyplot as plt

   plt.figure()

   plt.subplot(4, 3, 1)
   plt.plot(X, young)
   plt.title('''Young''')
   plt.grid(True)

   plt.subplot(4, 3, 2)
   plt.plot(X, middle_aged)
   plt.title('''Middle aged''')
   plt.grid(True)

   plt.subplot(4, 3, 3)
   plt.plot(X, union)
   plt.title('''union''')
   plt.grid(True)

   plt.subplot(4, 3, 4)
   plt.plot(X, intersection)
   plt.title('''intersection''')
   plt.grid(True)

   plt.subplot(4, 3, 5)
   plt.plot(X, complement_a)
   plt.title('''complement_a''')
   plt.grid(True)

   plt.subplot(4, 3, 6)
   plt.plot(X, difference)
   plt.title('''difference a/b''')
   plt.grid(True)

   plt.subplot(4, 3, 7)
   plt.plot(X, alg_sum)
   plt.title('''alg_sum''')
   plt.grid(True)

   plt.subplot(4, 3, 8)
   plt.plot(X, alg_product)
   plt.title('''alg_product''')
   plt.grid(True)

   plt.subplot(4, 3, 9)
   plt.plot(X, bdd_sum)
   plt.title('''bdd_sum''')
   plt.grid(True)

   plt.subplot(4, 3, 10)
   plt.plot(X, bdd_difference)
   plt.title('''bdd_difference''')
   plt.grid(True)

   plt.subplots_adjust(hspace=0.5)
   plt.show()
