



'''simple docstring'''






import mpmath  # for roots of unity
import numpy as np

class 							a__:







    def __init__(   self				:						List[Any]		,    __snake_case				:						Dict=None		,    __snake_case				:						Optional[int]=None			):
      a		:      Any       =  list(poly_a or [0]			)[:]
      a		:      Dict       =  list(poly_b or [0]			)[:]

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

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

      # Add 0 to make lengths equal a power of 2
      a		:      Tuple       =  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		:      Optional[int]       =  complex(mpmath.root(x=1		,    n=self.c_max_length		,    k=1			)			)

      # The product
      a		:      str       =  self.__multiply()







    def     lowercase_ (   self				:						Optional[Any]		,    __snake_case				:						Union[str, Any]			):
      a		:      Tuple       =  [[x] for x in self.polyA] if which == '''A''' else [[x] for x in self.polyB]
      # Corner case
      if len(__snake_case			) <= 1:
        return dft[0]
      #
      a		:      List[Any]       =  self.c_max_length // 2
      while next_ncol > 0:
        a		:      str       =  [[] for i in range(__snake_case			)]
        a		:      List[str]       =  self.root**next_ncol

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







    def     lowercase_ (   self				:						int			):
      a		:      List[Any]       =  self.__dft('A'			)
      a		:      Union[str, Any]       =  self.__dft('B'			)
      a		:      Any       =  [[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		:      Tuple       =  2
      while next_ncol <= self.c_max_length:
        a		:      Tuple       =  [[] for i in range(__snake_case			)]
        a		:      Tuple       =  self.root ** (next_ncol // 2)
        a		:      Optional[int]       =  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		:      List[Any]       =  new_inverse_c
        next_ncol *= 2
      # Unpack
      a		:      List[str]       =  [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				:						Dict			):
      a		:      Optional[Any]       =  '''A = ''' + ''' + '''.join(
          F"""{coef}*x^{i}""" for coef, i in enumerate(self.polyA[: self.len_A]			)			)
      a		:      List[str]       =  '''B = ''' + ''' + '''.join(
          F"""{coef}*x^{i}""" for coef, i in enumerate(self.polyB[: self.len_B]			)			)
      a		:      Optional[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()




'''simple docstring'''






from typing import Dict, List, Optional, Tuple, Union

import numpy as np

from ...image_processing_utils import BaseImageProcessor, BatchFeature, get_size_dict
from ...image_transforms import (
    center_crop,
    get_resize_output_image_size,
    normalize,
    rescale,
    resize,
    to_channel_dimension_format,
)
from ...image_utils import (
    IMAGENET_STANDARD_MEAN,
    IMAGENET_STANDARD_STD,
    ChannelDimension,
    ImageInput,
    PILImageResampling,
    make_list_of_images,
    to_numpy_array,
    valid_images,
)
from ...utils import TensorType, is_torch_available, is_torch_tensor, logging


if is_torch_available():
     import torch


lowerCAmelCase:      Union[str, Any]		 =		logging.get_logger(__name__)

class 							a__(      lowerCamelCase__			):
    lowercase__				=					["""pixel_values"""]







    def __init__(   self				:						int		,    __snake_case				:						bool = True		,    __snake_case				:						Optional[Dict[str, int]] = None		,    __snake_case				:						PILImageResampling = PILImageResampling.BILINEAR		,    __snake_case				:						bool = True		,    __snake_case				:						Dict[str, int] = None		,    __snake_case				:						bool = True		,    __snake_case				:						Union[int, float] = 1 / 2_55		,    __snake_case				:						bool = True		,    __snake_case				:						Optional[Union[float, List[float]]] = None		,    __snake_case				:						Optional[Union[float, List[float]]] = None		,    **__snake_case				:						List[str]		,    ):
      super().__init__(**__snake_case			)
      a		:      Dict       =  size if size is not None else {'shortest_edge': 2_56}
      a		:      Optional[int]       =  get_size_dict(__snake_case		,    default_to_square=__snake_case			)
      a		:      List[str]       =  crop_size if crop_size is not None else {'height': 2_24, 'width': 2_24}
      a		:      Dict       =  get_size_dict(__snake_case		,    param_name='crop_size'			)
      a		:      Optional[int]       =  do_resize
      a		:      Union[str, Any]       =  size
      a		:      Optional[Any]       =  resample
      a		:      int       =  do_center_crop
      a		:      List[str]       =  crop_size
      a		:      Tuple       =  do_rescale
      a		:      Any       =  rescale_factor
      a		:      str       =  do_normalize
      a		:      int       =  image_mean if image_mean is not None else IMAGENET_STANDARD_MEAN
      a		:      List[str]       =  image_std if image_std is not None else IMAGENET_STANDARD_STD







    def     lowercase_ (   self				:						str		,    __snake_case				:						np.ndarray		,    __snake_case				:						Dict[str, int]		,    __snake_case				:						PILImageResampling = PILImageResampling.BICUBIC		,    __snake_case				:						Optional[Union[str, ChannelDimension]] = None		,    **__snake_case				:						Any		,    ):
      a		:      str       =  get_size_dict(__snake_case		,    default_to_square=__snake_case			)
      if "shortest_edge" not in size:
        raise ValueError(F"""The `size` parameter must contain the key `shortest_edge`. Got {size.keys()}"""			)
      a		:      str       =  get_resize_output_image_size(__snake_case		,    size=size['shortest_edge']		,    default_to_square=__snake_case			)
      return resize(__snake_case		,    size=__snake_case		,    resample=__snake_case		,    data_format=__snake_case		,    **__snake_case			)







    def     lowercase_ (   self				:						Union[str, Any]		,    __snake_case				:						np.ndarray		,    __snake_case				:						Dict[str, int]		,    __snake_case				:						Optional[Union[str, ChannelDimension]] = None		,    **__snake_case				:						Any		,    ):
      a		:      Any       =  get_size_dict(__snake_case			)
      if "height" not in size or "width" not in size:
        raise ValueError(F"""The `size` parameter must contain the keys `height` and `width`. Got {size.keys()}"""			)
      return center_crop(__snake_case		,    size=(size['height'], size['width'])		,    data_format=__snake_case		,    **__snake_case			)







    def     lowercase_ (   self				:						str		,    __snake_case				:						np.ndarray		,    __snake_case				:						float		,    __snake_case				:						Optional[Union[str, ChannelDimension]] = None		,    **__snake_case				:						str			):
      return rescale(__snake_case		,    scale=__snake_case		,    data_format=__snake_case		,    **__snake_case			)







    def     lowercase_ (   self				:						Optional[int]		,    __snake_case				:						np.ndarray		,    __snake_case				:						Union[float, List[float]]		,    __snake_case				:						Union[float, List[float]]		,    __snake_case				:						Optional[Union[str, ChannelDimension]] = None		,    **__snake_case				:						List[str]		,    ):
      return normalize(__snake_case		,    mean=__snake_case		,    std=__snake_case		,    data_format=__snake_case		,    **__snake_case			)







    def     lowercase_ (   self				:						Union[str, Any]		,    __snake_case				:						ImageInput		,    __snake_case				:						Optional[bool] = None		,    __snake_case				:						Dict[str, int] = None		,    __snake_case				:						PILImageResampling = None		,    __snake_case				:						bool = None		,    __snake_case				:						Dict[str, int] = None		,    __snake_case				:						Optional[bool] = None		,    __snake_case				:						Optional[float] = None		,    __snake_case				:						Optional[bool] = None		,    __snake_case				:						Optional[Union[float, List[float]]] = None		,    __snake_case				:						Optional[Union[float, List[float]]] = None		,    __snake_case				:						Optional[Union[str, TensorType]] = None		,    __snake_case				:						Union[str, ChannelDimension] = ChannelDimension.FIRST		,    **__snake_case				:						Union[str, Any]		,    ):
      a		:      Dict       =  do_resize if do_resize is not None else self.do_resize
      a		:      str       =  size if size is not None else self.size
      a		:      Dict       =  get_size_dict(__snake_case		,    default_to_square=__snake_case			)
      a		:      Optional[int]       =  resample if resample is not None else self.resample
      a		:      List[str]       =  do_center_crop if do_center_crop is not None else self.do_center_crop
      a		:      int       =  crop_size if crop_size is not None else self.crop_size
      a		:      List[str]       =  get_size_dict(__snake_case		,    param_name='crop_size'			)
      a		:      Optional[Any]       =  do_rescale if do_rescale is not None else self.do_rescale
      a		:      List[str]       =  rescale_factor if rescale_factor is not None else self.rescale_factor
      a		:      List[Any]       =  do_normalize if do_normalize is not None else self.do_normalize
      a		:      Dict       =  image_mean if image_mean is not None else self.image_mean
      a		:      Dict       =  image_std if image_std is not None else self.image_std

      a		:      int       =  make_list_of_images(__snake_case			)

      if not valid_images(__snake_case			):
        raise ValueError(
            'Invalid image type. Must be of type PIL.Image.Image, numpy.ndarray, '
            'torch.Tensor, tf.Tensor or jax.ndarray.'			)

      if do_resize and size is None:
        raise ValueError('Size must be specified if do_resize is True.'			)

      if do_center_crop and crop_size is None:
        raise ValueError('Crop size must be specified if do_center_crop is True.'			)

      if do_rescale and rescale_factor is None:
        raise ValueError('Rescale factor must be specified if do_rescale is True.'			)

      if do_normalize and (image_mean is None or image_std is None):
        raise ValueError('Image mean and std must be specified if do_normalize is True.'			)

      # All transformations expect numpy arrays.
      a		:      int       =  [to_numpy_array(__snake_case			) for image in images]

      if do_resize:
        a		:      List[Any]       =  [self.resize(image=__snake_case		,    size=__snake_case		,    resample=__snake_case			) for image in images]

      if do_center_crop:
        a		:      Any       =  [self.center_crop(image=__snake_case		,    size=__snake_case			) for image in images]

      if do_rescale:
        a		:      Union[str, Any]       =  [self.rescale(image=__snake_case		,    scale=__snake_case			) for image in images]

      if do_normalize:
        a		:      List[str]       =  [self.normalize(image=__snake_case		,    mean=__snake_case		,    std=__snake_case			) for image in images]

      a		:      str       =  [to_channel_dimension_format(__snake_case		,    __snake_case			) for image in images]

      a		:      Tuple       =  {'pixel_values': images}
      return BatchFeature(data=__snake_case		,    tensor_type=__snake_case			)







    def     lowercase_ (   self				:						List[Any]		,    __snake_case				:						Tuple		,    __snake_case				:						List[Tuple] = None			):
      a		:      Union[str, Any]       =  outputs.logits

      # Resize logits and compute semantic segmentation maps
      if target_sizes is not None:
        if len(__snake_case			) != len(__snake_case			):
          raise ValueError(
              'Make sure that you pass in as many target sizes as the batch dimension of the logits'			)

        if is_torch_tensor(__snake_case			):
          a		:      Optional[int]       =  target_sizes.numpy()

        a		:      Union[str, Any]       =  []

        for idx in range(len(__snake_case			)			):
          a		:      Dict       =  torch.nn.functional.interpolate(
              logits[idx].unsqueeze(dim=0			)		,    size=target_sizes[idx]		,    mode='bilinear'		,    align_corners=__snake_case			)
          a		:      Optional[Any]       =  resized_logits[0].argmax(dim=0			)
          semantic_segmentation.append(__snake_case			)
      else:
        a		:      List[Any]       =  logits.argmax(dim=1			)
        a		:      List[str]       =  [semantic_segmentation[i] for i in range(semantic_segmentation.shape[0]			)]

      return semantic_segmentation