






from typing import List, Optional, Union

import numpy as np
import PIL.Image

from ...image_processing_utils import BaseImageProcessor, BatchFeature
from ...image_transforms import rescale, resize, to_channel_dimension_format
from ...image_utils import (
    ChannelDimension,
    PILImageResampling,
    get_image_size,
    make_list_of_images,
    to_numpy_array,
    valid_images,
)
from ...utils import TensorType, logging


lowerCamelCase	:							str				=logging.get_logger(__name__)





class 			__a  (    A__       ):
 _lowerCAmelCase       :       Tuple        = ['''pixel_values''']







 def __init__(		self					:   Optional[int]							,   SCREAMING_SNAKE_CASE					:   bool = True							,   SCREAMING_SNAKE_CASE					:   int = 32							,   SCREAMING_SNAKE_CASE					:   int=PILImageResampling.BILINEAR							,   SCREAMING_SNAKE_CASE					:   bool = True							,   **SCREAMING_SNAKE_CASE					:   Dict							,   ):


      '''simple docstring'''






      UpperCamelCase__			:   List[Any]       				=  do_resize
      UpperCamelCase__			:   int       				=  do_rescale
      UpperCamelCase__			:   Dict       				=  size_divisor
      UpperCamelCase__			:   int       				=  resample
      super().__init__(**SCREAMING_SNAKE_CASE						)







 def 					__lowercase					(		self					:   str							,   SCREAMING_SNAKE_CASE					:   np.ndarray							,   SCREAMING_SNAKE_CASE					:   int							,   SCREAMING_SNAKE_CASE					:   Optional[Any]							,   SCREAMING_SNAKE_CASE					:   Optional[ChannelDimension] = None							,   **SCREAMING_SNAKE_CASE					:   Union[str, Any]						):


      '''simple docstring'''






      UpperCamelCase__				,     UpperCamelCase__			:   Any       				=  get_image_size(SCREAMING_SNAKE_CASE						)
      # Rounds the height and width down to the closest multiple of size_divisor
      UpperCamelCase__			:   Union[str, Any]       				=  height // size_divisor * size_divisor
      UpperCamelCase__			:   List[str]       				=  width // size_divisor * size_divisor
      UpperCamelCase__			:   Any       				=  resize(SCREAMING_SNAKE_CASE							,   (new_h, new_w)							,   resample=SCREAMING_SNAKE_CASE							,   data_format=SCREAMING_SNAKE_CASE							,   **SCREAMING_SNAKE_CASE						)
      return image







 def 					__lowercase					(		self					:   Optional[Any]							,   SCREAMING_SNAKE_CASE					:   np.ndarray							,   SCREAMING_SNAKE_CASE					:   float							,   SCREAMING_SNAKE_CASE					:   Optional[ChannelDimension] = None							,   **SCREAMING_SNAKE_CASE					:   str						):


      '''simple docstring'''






      return rescale(image=SCREAMING_SNAKE_CASE							,   scale=SCREAMING_SNAKE_CASE							,   data_format=SCREAMING_SNAKE_CASE							,   **SCREAMING_SNAKE_CASE						)







 def 					__lowercase					(		self					:   Optional[Any]							,   SCREAMING_SNAKE_CASE					:   Union["PIL.Image.Image", TensorType, List["PIL.Image.Image"], List[TensorType]]							,   SCREAMING_SNAKE_CASE					:   Optional[bool] = None							,   SCREAMING_SNAKE_CASE					:   Optional[int] = None							,   SCREAMING_SNAKE_CASE					:   int=None							,   SCREAMING_SNAKE_CASE					:   Optional[bool] = None							,   SCREAMING_SNAKE_CASE					:   Optional[Union[TensorType, str]] = None							,   SCREAMING_SNAKE_CASE					:   ChannelDimension = ChannelDimension.FIRST							,   **SCREAMING_SNAKE_CASE					:   int							,   ):


      '''simple docstring'''






      UpperCamelCase__			:   Tuple       				=  do_resize if do_resize is not None else self.do_resize
      UpperCamelCase__			:   Dict       				=  do_rescale if do_rescale is not None else self.do_rescale
      UpperCamelCase__			:   int       				=  size_divisor if size_divisor is not None else self.size_divisor
      UpperCamelCase__			:   Union[str, Any]       				=  resample if resample is not None else self.resample

      if do_resize and size_divisor is None:
           raise ValueError("size_divisor is required for resizing"						)

      UpperCamelCase__			:   Union[str, Any]       				=  make_list_of_images(SCREAMING_SNAKE_CASE						)

      if not valid_images(SCREAMING_SNAKE_CASE						):
           raise ValueError("Invalid image(s)"						)

      # All transformations expect numpy arrays.
      UpperCamelCase__			:   str       				=  [to_numpy_array(SCREAMING_SNAKE_CASE						) for img in images]

      if do_resize:
           UpperCamelCase__			:   Union[str, Any]       				=  [self.resize(SCREAMING_SNAKE_CASE							,   size_divisor=SCREAMING_SNAKE_CASE							,   resample=SCREAMING_SNAKE_CASE						) for image in images]

      if do_rescale:
           UpperCamelCase__			:   str       				=  [self.rescale(SCREAMING_SNAKE_CASE							,   scale=1 / 2_55						) for image in images]

      UpperCamelCase__			:   int       				=  [to_channel_dimension_format(SCREAMING_SNAKE_CASE							,   SCREAMING_SNAKE_CASE						) for image in images]

      UpperCamelCase__			:   Dict       				=  {"pixel_values": images}
      return BatchFeature(data=SCREAMING_SNAKE_CASE							,   tensor_type=SCREAMING_SNAKE_CASE						)







from math import factorial





class 			__a  :







 def __init__(		self					:   Union[str, Any]							,   SCREAMING_SNAKE_CASE					:   Tuple							,   SCREAMING_SNAKE_CASE					:   Optional[int]						):


      '''simple docstring'''






      UpperCamelCase__			:   Tuple       				=  real
      if isinstance(SCREAMING_SNAKE_CASE							,   SCREAMING_SNAKE_CASE						):
           UpperCamelCase__			:   Union[str, Any]       				=  [1] * rank
      else:
           UpperCamelCase__			:   int       				=  rank







 def __repr__(		self					:   Tuple						):


      '''simple docstring'''






      return (
          F'{self.real}+'
          F'{"+".join(str(SCREAMING_SNAKE_CASE						)+"E"+str(n+1						)for n,dual in enumerate(self.duals						)						)}'
      )







 def 					__lowercase					(		self					:   Tuple						):


      '''simple docstring'''






      UpperCamelCase__			:   Optional[Any]       				=  self.duals.copy()
      while cur[-1] == 0:
           cur.pop(-1						)
      return Dual(self.real							,   SCREAMING_SNAKE_CASE						)







 def __add__(		self					:   Union[str, Any]							,   SCREAMING_SNAKE_CASE					:   Dict						):


      '''simple docstring'''






      if not isinstance(SCREAMING_SNAKE_CASE							,   SCREAMING_SNAKE_CASE						):
           return Dual(self.real + other							,   self.duals						)
      UpperCamelCase__			:   Optional[int]       				=  self.duals.copy()
      UpperCamelCase__			:   Any       				=  other.duals.copy()
      if len(SCREAMING_SNAKE_CASE						) > len(SCREAMING_SNAKE_CASE						):
           o_dual.extend([1] * (len(SCREAMING_SNAKE_CASE						) - len(SCREAMING_SNAKE_CASE						))						)
      elif len(SCREAMING_SNAKE_CASE						) < len(SCREAMING_SNAKE_CASE						):
           s_dual.extend([1] * (len(SCREAMING_SNAKE_CASE						) - len(SCREAMING_SNAKE_CASE						))						)
      UpperCamelCase__			:   Optional[int]       				=  []
      for i in range(len(SCREAMING_SNAKE_CASE						)						):
           new_duals.append(s_dual[i] + o_dual[i]						)
      return Dual(self.real + other.real							,   SCREAMING_SNAKE_CASE						)

 _lowerCAmelCase       :       Dict        = __add__







 def __sub__(		self					:   Tuple							,   SCREAMING_SNAKE_CASE					:   Tuple						):


      '''simple docstring'''






      return self + other * -1







 def __mul__(		self					:   int							,   SCREAMING_SNAKE_CASE					:   Dict						):


      '''simple docstring'''






      if not isinstance(SCREAMING_SNAKE_CASE							,   SCREAMING_SNAKE_CASE						):
           UpperCamelCase__			:   str       				=  []
           for i in self.duals:
                new_duals.append(i * other						)
           return Dual(self.real * other							,   SCREAMING_SNAKE_CASE						)
      UpperCamelCase__			:   List[Any]       				=  [0] * (len(self.duals						) + len(other.duals						) + 1)
      for i, item in enumerate(self.duals						):
           for j, jtem in enumerate(other.duals						):
                new_duals[i + j + 1] += item * jtem
      for k in range(len(self.duals						)						):
           new_duals[k] += self.duals[k] * other.real
      for index in range(len(other.duals						)						):
           new_duals[index] += other.duals[index] * self.real
      return Dual(self.real * other.real							,   SCREAMING_SNAKE_CASE						)

 _lowerCAmelCase       :       Union[str, Any]        = __mul__







 def __truediv__(		self					:   List[Any]							,   SCREAMING_SNAKE_CASE					:   Any						):


      '''simple docstring'''






      if not isinstance(SCREAMING_SNAKE_CASE							,   SCREAMING_SNAKE_CASE						):
           UpperCamelCase__			:   str       				=  []
           for i in self.duals:
                new_duals.append(i / other						)
           return Dual(self.real / other							,   SCREAMING_SNAKE_CASE						)
      raise ValueError







 def __floordiv__(		self					:   Union[str, Any]							,   SCREAMING_SNAKE_CASE					:   Tuple						):


      '''simple docstring'''






      if not isinstance(SCREAMING_SNAKE_CASE							,   SCREAMING_SNAKE_CASE						):
           UpperCamelCase__			:   Dict       				=  []
           for i in self.duals:
                new_duals.append(i // other						)
           return Dual(self.real // other							,   SCREAMING_SNAKE_CASE						)
      raise ValueError







 def __pow__(		self					:   str							,   SCREAMING_SNAKE_CASE					:   int						):


      '''simple docstring'''






      if n < 0 or isinstance(SCREAMING_SNAKE_CASE							,   SCREAMING_SNAKE_CASE						):
           raise ValueError("power must be a positive integer"						)
      if n == 0:
           return 1
      if n == 1:
           return self
      UpperCamelCase__			:   str       				=  self
      for _ in range(n - 1						):
           x *= self
      return x







def 		SCREAMING_SNAKE_CASE							(					__lowerCAmelCase					,    __lowerCAmelCase					,    __lowerCAmelCase			) ->	str:
     if not callable(__lowerCAmelCase			):
          raise ValueError("differentiate() requires a function as input for func"			)
     if not isinstance(__lowerCAmelCase					,    (float, int)			):
          raise ValueError("differentiate() requires a float as input for position"			)
     if not isinstance(__lowerCAmelCase					,    __lowerCAmelCase			):
          raise ValueError("differentiate() requires an int as input for order"			)
     UpperCamelCase__			:   Optional[Any]       				=  Dual(__lowerCAmelCase					,    1			)
     UpperCamelCase__			:   Any       				=  func(__lowerCAmelCase			)
     if order == 0:
          return result.real
     return result.duals[order - 1] * factorial(__lowerCAmelCase			)


if __name__ == "__main__":
 import doctest

 doctest.testmod()







 def 		SCREAMING_SNAKE_CASE							(					__lowerCAmelCase			) ->	List[Any]:
      return y**2 * y**4




 print(differentiate(f, 9, 2))