






import warnings
from typing import List, Optional, Union

import numpy as np
import PIL
import torch
from PIL import Image

from .configuration_utils import ConfigMixin, register_to_config
from .utils import CONFIG_NAME, PIL_INTERPOLATION, deprecate







class       UpperCAmelCase_						( lowercase			):



      """simple docstring"""
      UpperCamelCase_    : Any									=CONFIG_NAME
      @register_to_config
      def __init__(    self   ,    SCREAMING_SNAKE_CASE_ = True   ,    SCREAMING_SNAKE_CASE_ = 8   ,    SCREAMING_SNAKE_CASE_ = "lanczos"   ,    SCREAMING_SNAKE_CASE_ = True   ,    SCREAMING_SNAKE_CASE_ = False   ,    )    ->				Any:
          super().__init__()
      @staticmethod
      def    UpperCAmelCase						(    SCREAMING_SNAKE_CASE_			)    ->				PIL.Image.Image:
          if images.ndim == 3:
              UpperCamelCase	:Optional[Any]     							=       images[None, ...]
          UpperCamelCase	:Optional[int]     							=       (images * 255).round().astype('''uint8'''			)
          if images.shape[-1] == 1:
              # special case for grayscale (single channel) images
              UpperCamelCase	:Optional[Any]     							=       [Image.fromarray(image.squeeze()   ,    mode='''L'''			) for image in images]
          else:
              UpperCamelCase	:Dict     							=       [Image.fromarray(SCREAMING_SNAKE_CASE_			) for image in images]

          return pil_images
      @staticmethod
      def    UpperCAmelCase						(    SCREAMING_SNAKE_CASE_			)    ->				np.ndarray:
          if not isinstance(SCREAMING_SNAKE_CASE_   ,    SCREAMING_SNAKE_CASE_			):
              UpperCamelCase	:Optional[int]     							=       [images]
          UpperCamelCase	:Any     							=       [np.array(SCREAMING_SNAKE_CASE_			).astype(np.floataa			) / 255.0 for image in images]
          UpperCamelCase	:Optional[int]     							=       np.stack(SCREAMING_SNAKE_CASE_   ,    axis=0			)

          return images
      @staticmethod
      def    UpperCAmelCase						(    SCREAMING_SNAKE_CASE_			)    ->				torch.FloatTensor:
          if images.ndim == 3:
              UpperCamelCase	:Tuple     							=       images[..., None]

          UpperCamelCase	:int     							=       torch.from_numpy(images.transpose(0   ,    3   ,    1   ,    2			)			)
          return images
      @staticmethod
      def    UpperCAmelCase						(    SCREAMING_SNAKE_CASE_			)    ->				np.ndarray:
          UpperCamelCase	:Optional[int]     							=       images.cpu().permute(0   ,    2   ,    3   ,    1			).float().numpy()
          return images
      @staticmethod
      def    UpperCAmelCase						(    SCREAMING_SNAKE_CASE_			)    ->				Tuple:
          return 2.0 * images - 1.0
      @staticmethod
      def    UpperCAmelCase						(    SCREAMING_SNAKE_CASE_			)    ->				Any:
          return (images / 2 + 0.5).clamp(0   ,    1			)
      @staticmethod
      def    UpperCAmelCase						(    SCREAMING_SNAKE_CASE_			)    ->				PIL.Image.Image:
          UpperCamelCase	:Dict     							=       image.convert('''RGB'''			)
          return image
      def    UpperCAmelCase						(    self   ,    SCREAMING_SNAKE_CASE_   ,    SCREAMING_SNAKE_CASE_ = None   ,    SCREAMING_SNAKE_CASE_ = None   ,    )    ->				PIL.Image.Image:
          if height is None:
              UpperCamelCase	:Optional[Any]     							=       image.height
          if width is None:
              UpperCamelCase	:int     							=       image.width

          UpperCamelCase							,       UpperCamelCase	:Tuple     							=       (
              x - x % self.config.vae_scale_factor for x in (width, height)
          )  # resize to integer multiple of vae_scale_factor
          UpperCamelCase	:str     							=       image.resize((width, height)   ,    resample=PIL_INTERPOLATION[self.config.resample]			)
          return image
      def    UpperCAmelCase						(    self   ,    SCREAMING_SNAKE_CASE_   ,    SCREAMING_SNAKE_CASE_ = None   ,    SCREAMING_SNAKE_CASE_ = None   ,    )    ->				torch.Tensor:
          UpperCamelCase	:str     							=       (PIL.Image.Image, np.ndarray, torch.Tensor)
          if isinstance(SCREAMING_SNAKE_CASE_   ,    SCREAMING_SNAKE_CASE_			):
              UpperCamelCase	:Any     							=       [image]
          elif not (isinstance(SCREAMING_SNAKE_CASE_   ,    SCREAMING_SNAKE_CASE_			) and all(isinstance(SCREAMING_SNAKE_CASE_   ,    SCREAMING_SNAKE_CASE_			) for i in image			)):
              raise ValueError(
                  F'''Input is in incorrect format: {[type(SCREAMING_SNAKE_CASE_			) for i in image]}. Currently, we only support {", ".join(SCREAMING_SNAKE_CASE_			)}'''			)

          if isinstance(image[0]   ,    PIL.Image.Image			):
              if self.config.do_convert_rgb:
                  UpperCamelCase	:Any     							=       [self.convert_to_rgb(SCREAMING_SNAKE_CASE_			) for i in image]
              if self.config.do_resize:
                  UpperCamelCase	:int     							=       [self.resize(SCREAMING_SNAKE_CASE_   ,    SCREAMING_SNAKE_CASE_   ,    SCREAMING_SNAKE_CASE_			) for i in image]
              UpperCamelCase	:Union[str, Any]     							=       self.pil_to_numpy(SCREAMING_SNAKE_CASE_			)  # to np
              UpperCamelCase	:Optional[Any]     							=       self.numpy_to_pt(SCREAMING_SNAKE_CASE_			)  # to pt

          elif isinstance(image[0]   ,    np.ndarray			):
              UpperCamelCase	:Optional[int]     							=       np.concatenate(SCREAMING_SNAKE_CASE_   ,    axis=0			) if image[0].ndim == 4 else np.stack(SCREAMING_SNAKE_CASE_   ,    axis=0			)
              UpperCamelCase	:Optional[Any]     							=       self.numpy_to_pt(SCREAMING_SNAKE_CASE_			)
              UpperCamelCase							,       UpperCamelCase							,       UpperCamelCase							,       UpperCamelCase	:Optional[int]     							=       image.shape
              if self.config.do_resize and (
                  height % self.config.vae_scale_factor != 0 or width % self.config.vae_scale_factor != 0
              ):
                  raise ValueError(
                      F'''Currently we only support resizing for PIL image - please resize your numpy array to be divisible by {self.config.vae_scale_factor}'''
                      F'''currently the sizes are {height} and {width}. You can also pass a PIL image instead to use resize option in VAEImageProcessor'''			)

          elif isinstance(image[0]   ,    torch.Tensor			):
              UpperCamelCase	:int     							=       torch.cat(SCREAMING_SNAKE_CASE_   ,    axis=0			) if image[0].ndim == 4 else torch.stack(SCREAMING_SNAKE_CASE_   ,    axis=0			)
              UpperCamelCase							,       UpperCamelCase							,       UpperCamelCase							,       UpperCamelCase	:int     							=       image.shape

              # don't need any preprocess if the image is latents
              if channel == 4:
                  return image

              if self.config.do_resize and (
                  height % self.config.vae_scale_factor != 0 or width % self.config.vae_scale_factor != 0
              ):
                  raise ValueError(
                      F'''Currently we only support resizing for PIL image - please resize your pytorch tensor to be divisible by {self.config.vae_scale_factor}'''
                      F'''currently the sizes are {height} and {width}. You can also pass a PIL image instead to use resize option in VAEImageProcessor'''			)

        # expected range [0,1], normalize to [-1,1]
          UpperCamelCase	:int     							=       self.config.do_normalize
          if image.min() < 0:
              warnings.warn(
                  '''Passing `image` as torch tensor with value range in [-1,1] is deprecated. The expected value range for image tensor is [0,1] '''
                  F'''when passing as pytorch tensor or numpy Array. You passed `image` with value range [{image.min()},{image.max()}]'''   ,    SCREAMING_SNAKE_CASE_   ,    )
              UpperCamelCase	:int     							=       False

          if do_normalize:
              UpperCamelCase	:Optional[int]     							=       self.normalize(SCREAMING_SNAKE_CASE_			)

          return image




      def    UpperCAmelCase						(    self   ,    SCREAMING_SNAKE_CASE_   ,    SCREAMING_SNAKE_CASE_ = "pil"   ,    SCREAMING_SNAKE_CASE_ = None   ,    )    ->				Tuple:
          if not isinstance(SCREAMING_SNAKE_CASE_   ,    torch.Tensor			):
              raise ValueError(
                  F'''Input for postprocessing is in incorrect format: {type(SCREAMING_SNAKE_CASE_			)}. We only support pytorch tensor'''			)
          if output_type not in ["latent", "pt", "np", "pil"]:
              UpperCamelCase	:Any     							=       (
                  F'''the output_type {output_type} is outdated and has been set to `np`. Please make sure to set it to one of these instead: '''
                  '''`pil`, `np`, `pt`, `latent`'''
              )
              deprecate('''Unsupported output_type'''   ,    '''1.0.0'''   ,    SCREAMING_SNAKE_CASE_   ,    standard_warn=SCREAMING_SNAKE_CASE_			)
              UpperCamelCase	:List[Any]     							=       '''np'''

          if output_type == "latent":
              return image

          if do_denormalize is None:
              UpperCamelCase	:int     							=       [self.config.do_normalize] * image.shape[0]

          UpperCamelCase	:Optional[Any]     							=       torch.stack(
              [self.denormalize(image[i]			) if do_denormalize[i] else image[i] for i in range(image.shape[0]			)]			)

          if output_type == "pt":
              return image

          UpperCamelCase	:List[str]     							=       self.pt_to_numpy(SCREAMING_SNAKE_CASE_			)

          if output_type == "np":
              return image

          if output_type == "pil":
              return self.numpy_to_pil(SCREAMING_SNAKE_CASE_			)







class       UpperCAmelCase_						( lowercase			):



      """simple docstring"""
      UpperCamelCase_    : str									=CONFIG_NAME
      @register_to_config
      def __init__(    self   ,    SCREAMING_SNAKE_CASE_ = True   ,    SCREAMING_SNAKE_CASE_ = 8   ,    SCREAMING_SNAKE_CASE_ = "lanczos"   ,    SCREAMING_SNAKE_CASE_ = True   ,    )    ->				List[str]:
          super().__init__()
      @staticmethod
      def    UpperCAmelCase						(    SCREAMING_SNAKE_CASE_			)    ->				int:
          if images.ndim == 3:
              UpperCamelCase	:List[Any]     							=       images[None, ...]
          UpperCamelCase	:Union[str, Any]     							=       (images * 255).round().astype('''uint8'''			)
          if images.shape[-1] == 1:
              # special case for grayscale (single channel) images
              UpperCamelCase	:int     							=       [Image.fromarray(image.squeeze()   ,    mode='''L'''			) for image in images]
          else:
              UpperCamelCase	:Optional[int]     							=       [Image.fromarray(image[:, :, :3]			) for image in images]

          return pil_images
      @staticmethod
      def    UpperCAmelCase						(    SCREAMING_SNAKE_CASE_			)    ->				Union[str, Any]:
          return image[:, :, 1] * 2**8 + image[:, :, 2]
      def    UpperCAmelCase						(    self   ,    SCREAMING_SNAKE_CASE_			)    ->				str:
          if images.ndim == 3:
              UpperCamelCase	:Optional[Any]     							=       images[None, ...]
          UpperCamelCase	:List[str]     							=       images[:, :, :, 3:]
          if images.shape[-1] == 6:
              UpperCamelCase	:Optional[int]     							=       (images_depth * 255).round().astype('''uint8'''			)
              UpperCamelCase	:str     							=       [
                  Image.fromarray(self.rgblike_to_depthmap(SCREAMING_SNAKE_CASE_			)   ,    mode='''I;16'''			) for image_depth in images_depth
              ]
          elif images.shape[-1] == 4:
              UpperCamelCase	:List[str]     							=       (images_depth * 6_5535.0).astype(np.uintaa			)
              UpperCamelCase	:str     							=       [Image.fromarray(SCREAMING_SNAKE_CASE_   ,    mode='''I;16'''			) for image_depth in images_depth]
          else:
              raise Exception('''Not supported'''			)

          return pil_images




      def    UpperCAmelCase						(    self   ,    SCREAMING_SNAKE_CASE_   ,    SCREAMING_SNAKE_CASE_ = "pil"   ,    SCREAMING_SNAKE_CASE_ = None   ,    )    ->				List[str]:
          if not isinstance(SCREAMING_SNAKE_CASE_   ,    torch.Tensor			):
              raise ValueError(
                  F'''Input for postprocessing is in incorrect format: {type(SCREAMING_SNAKE_CASE_			)}. We only support pytorch tensor'''			)
          if output_type not in ["latent", "pt", "np", "pil"]:
              UpperCamelCase	:Optional[Any]     							=       (
                  F'''the output_type {output_type} is outdated and has been set to `np`. Please make sure to set it to one of these instead: '''
                  '''`pil`, `np`, `pt`, `latent`'''
              )
              deprecate('''Unsupported output_type'''   ,    '''1.0.0'''   ,    SCREAMING_SNAKE_CASE_   ,    standard_warn=SCREAMING_SNAKE_CASE_			)
              UpperCamelCase	:Tuple     							=       '''np'''

          if do_denormalize is None:
              UpperCamelCase	:List[Any]     							=       [self.config.do_normalize] * image.shape[0]

          UpperCamelCase	:Optional[int]     							=       torch.stack(
              [self.denormalize(image[i]			) if do_denormalize[i] else image[i] for i in range(image.shape[0]			)]			)

          UpperCamelCase	:Union[str, Any]     							=       self.pt_to_numpy(SCREAMING_SNAKE_CASE_			)

          if output_type == "np":
              if image.shape[-1] == 6:
                  UpperCamelCase	:Optional[Any]     							=       np.stack([self.rgblike_to_depthmap(im[:, :, 3:]			) for im in image]   ,    axis=0			)
              else:
                  UpperCamelCase	:List[Any]     							=       image[:, :, :, 3:]
              return image[:, :, :, :3], image_depth

          if output_type == "pil":
              return self.numpy_to_pil(SCREAMING_SNAKE_CASE_			), self.numpy_to_depth(SCREAMING_SNAKE_CASE_			)
          else:
              raise Exception(F'''This type {output_type} is not supported'''			)













def   _A       (    SCREAMING_SNAKE_CASE__  :     list[list[int]]	):
    if len(SCREAMING_SNAKE_CASE__	) == 0 or not all(len(SCREAMING_SNAKE_CASE__	) == 2 for pair in coordinates	):
        raise ValueError('''The program cannot work out a fitting polynomial.'''	)

    if len({tuple(SCREAMING_SNAKE_CASE__	) for pair in coordinates}	) != len(SCREAMING_SNAKE_CASE__	):
        raise ValueError('''The program cannot work out a fitting polynomial.'''	)

    UpperCamelCase	:str     							=       {x for x, _ in coordinates}
    if len(SCREAMING_SNAKE_CASE__	) == 1:
        return F'''x={coordinates[0][0]}'''

    if len(SCREAMING_SNAKE_CASE__	) != len(SCREAMING_SNAKE_CASE__	):
        raise ValueError('''The program cannot work out a fitting polynomial.'''	)

    UpperCamelCase	:List[Any]     							=       len(SCREAMING_SNAKE_CASE__	)

    UpperCamelCase	:Optional[int]     							=       0
    UpperCamelCase	:list[list[float]]     							=       []
    # put the x and x to the power values in a matrix
    while count_of_line < x:
        UpperCamelCase	:Tuple     							=       0
        UpperCamelCase	:Optional[int]     							=       coordinates[count_of_line][0]
        UpperCamelCase	:list[float]     							=       []
        while count_in_line < x:
            count_line.append(a ** (x - (count_in_line + 1))	)
            count_in_line += 1
        matrix.append(SCREAMING_SNAKE_CASE__	)
        count_of_line += 1

    UpperCamelCase	:Optional[int]     							=       0
    # put the y values into a vector
    UpperCamelCase	:list[float]     							=       []
    while count_of_line < x:
        vector.append(coordinates[count_of_line][1]	)
        count_of_line += 1

    UpperCamelCase	:str     							=       0

    while count < x:
        UpperCamelCase	:Optional[Any]     							=       0
        while zahlen < x:
            if count == zahlen:
                zahlen += 1
            if zahlen == x:
                break
            UpperCamelCase	:Union[str, Any]     							=       matrix[zahlen][count] / matrix[count][count]
            for counting_columns, item in enumerate(matrix[count]	):
                # manipulating all the values in the matrix
                matrix[zahlen][counting_columns] -= item * bruch
            # manipulating the values in the vector
            vector[zahlen] -= vector[count] * bruch
            zahlen += 1
        count += 1

    UpperCamelCase	:Optional[int]     							=       0
    # make solutions
    UpperCamelCase	:list[str]     							=       []
    while count < x:
        solution.append(str(vector[count] / matrix[count][count]	)	)
        count += 1

    UpperCamelCase	:Union[str, Any]     							=       0
    UpperCamelCase	:Any     							=       '''f(x)='''

    while count < x:
        UpperCamelCase	:list[str]     							=       solution[count].split('''E'''	)
        if len(SCREAMING_SNAKE_CASE__	) > 1:
            UpperCamelCase	:List[Any]     							=       F'''{remove_e[0]}*10^{remove_e[1]}'''
        solved += F'''x^{x - (count + 1)}*{solution[count]}'''
        if count + 1 != x:
            solved += "+"
        count += 1

    return solved


if __name__ == "__main__":
 print(points_to_polynomial([]))
 print(points_to_polynomial([[]]))
 print(points_to_polynomial([[1, 0], [2, 0], [3, 0]]))
 print(points_to_polynomial([[1, 1], [2, 1], [3, 1]]))
 print(points_to_polynomial([[1, 3], [2, 3], [3, 3]]))
 print(points_to_polynomial([[1, 1], [2, 2], [3, 3]]))
 print(points_to_polynomial([[1, 1], [2, 4], [3, 9]]))
 print(points_to_polynomial([[1, 3], [2, 6], [3, 11]]))
 print(points_to_polynomial([[1, -3], [2, -6], [3, -11]]))
 print(points_to_polynomial([[1, 5], [2, 2], [3, 9]]))





