code: 
  
  
  
  
  
  
  import types
  from typing import List, Optional, Tuple, Union
  
  import torch
  from transformers import CLIPTextModelWithProjection, CLIPTokenizer
  from transformers.models.clip.modeling_clip import CLIPTextModelOutput
  
  from diffusers.models import PriorTransformer
  from diffusers.pipelines import DiffusionPipeline, StableDiffusionImageVariationPipeline
  from diffusers.schedulers import UnCLIPScheduler
  from diffusers.utils import logging, randn_tensor
  
  
  lowerCamelCase			:							Optional[int]       =logging.get_logger(__name__)  # pylint: disable=invalid-name
  
  
  
  
  
  
  
  def 	SCREAMING_SNAKE_CASE							(      self      ,					__lowerCAmelCase      ,					__lowerCAmelCase      ,					__lowerCAmelCase      ,					__lowerCAmelCase    )				->			Tuple:
       UpperCamelCase__    :     Any        =						image.to(device=__lowerCAmelCase    )
       UpperCamelCase__    :     Optional[int]        =						image  # take image as image_embeddings
       UpperCamelCase__    :     str        =						image_embeddings.unsqueeze(1    )
  
       # duplicate image embeddings for each generation per prompt, using mps friendly method
       UpperCamelCase__       ,  UpperCamelCase__       ,  UpperCamelCase__    :     Any        =						image_embeddings.shape
       UpperCamelCase__    :     List[Any]        =						image_embeddings.repeat(1      ,					__lowerCAmelCase      ,					1    )
       UpperCamelCase__    :     Any        =						image_embeddings.view(bs_embed * num_images_per_prompt      ,					__lowerCAmelCase      ,					-1    )
  
       if do_classifier_free_guidance:
            UpperCamelCase__    :     Optional[int]        =						torch.zeros_like(__lowerCAmelCase    )
  
            # For classifier free guidance, we need to do two forward passes.
            # Here we concatenate the unconditional and text embeddings into a single batch
            # to avoid doing two forward passes
            UpperCamelCase__    :     Optional[Any]        =						torch.cat([uncond_embeddings, image_embeddings]    )
  
       return image_embeddings
  
  
  
  
  
  class     __a						(					lowerCAmelCase__ ):
  
  
  
  
  
  
  
   def __init__(	self      :     Optional[Any]							,     SCREAMING_SNAKE_CASE      :     PriorTransformer							,     SCREAMING_SNAKE_CASE      :     CLIPTokenizer							,     SCREAMING_SNAKE_CASE      :     CLIPTextModelWithProjection							,     SCREAMING_SNAKE_CASE      :     UnCLIPScheduler							,     SCREAMING_SNAKE_CASE      :     Optional[dict] = None							,     ):
  
  
        '''simple docstring'''
  
  
  
  
  
  
        super().__init__()
  
        UpperCamelCase__    :     Optional[int]        =						{"image_encoder": None} if decoder_pipe_kwargs is None else decoder_pipe_kwargs
  
        UpperCamelCase__    :     List[str]        =						decoder_pipe_kwargs.get("torch_dtype"							,     lowerCAmelCase_		) or prior.dtype
  
        UpperCamelCase__    :     Tuple        =						StableDiffusionImageVariationPipeline.from_pretrained(
            "lambdalabs/sd-image-variations-diffusers"							,     **lowerCAmelCase_		)
  
        # replace `_encode_image` method
        UpperCamelCase__    :     Dict        =						types.MethodType(_encode_image							,     self.decoder_pipe		)
  
        self.register_modules(
            prior=lowerCAmelCase_							,     tokenizer=lowerCAmelCase_							,     text_encoder=lowerCAmelCase_							,     prior_scheduler=lowerCAmelCase_							,     )
  
  
  
  
  
  
  
   def       __lowercase      (	self      :     List[Any]							,     SCREAMING_SNAKE_CASE      :     str							,     SCREAMING_SNAKE_CASE      :     List[Any]							,     SCREAMING_SNAKE_CASE      :     List[str]							,     SCREAMING_SNAKE_CASE      :     Union[str, Any]							,     SCREAMING_SNAKE_CASE      :     Optional[Union[CLIPTextModelOutput, Tuple]] = None							,     SCREAMING_SNAKE_CASE      :     Optional[torch.Tensor] = None							,     ):
  
  
        '''simple docstring'''
  
  
  
  
  
  
        if text_model_output is None:
             UpperCamelCase__    :     Tuple        =						len(lowerCAmelCase_		) if isinstance(lowerCAmelCase_							,     lowerCAmelCase_		) else 1
             # get prompt text embeddings
             UpperCamelCase__    :     Optional[Any]        =						self.tokenizer(
                 lowerCAmelCase_							,     padding="max_length"							,     max_length=self.tokenizer.model_max_length							,     return_tensors="pt"							,     )
             UpperCamelCase__    :     List[Any]        =						text_inputs.input_ids
             UpperCamelCase__    :     Optional[Any]        =						text_inputs.attention_mask.bool().to(lowerCAmelCase_		)
  
             if text_input_ids.shape[-1] > self.tokenizer.model_max_length:
                  UpperCamelCase__    :     Tuple        =						self.tokenizer.batch_decode(text_input_ids[:, self.tokenizer.model_max_length :]		)
                  logger.warning(
                      "The following part of your input was truncated because CLIP can only handle sequences up to"
                      F' {self.tokenizer.model_max_length} tokens: {removed_text}'		)
                  UpperCamelCase__    :     Optional[Any]        =						text_input_ids[:, : self.tokenizer.model_max_length]
  
             UpperCamelCase__    :     Any        =						self.text_encoder(text_input_ids.to(lowerCAmelCase_		)		)
  
             UpperCamelCase__    :     Union[str, Any]        =						text_encoder_output.text_embeds
             UpperCamelCase__    :     Optional[int]        =						text_encoder_output.last_hidden_state
  
        else:
             UpperCamelCase__    :     List[Any]        =						text_model_output[0].shape[0]
             UpperCamelCase__       ,  UpperCamelCase__    :     Dict        =						text_model_output[0], text_model_output[1]
             UpperCamelCase__    :     str        =						text_attention_mask
  
        UpperCamelCase__    :     Any        =						text_embeddings.repeat_interleave(lowerCAmelCase_							,     dim=0		)
        UpperCamelCase__    :     List[str]        =						text_encoder_hidden_states.repeat_interleave(lowerCAmelCase_							,     dim=0		)
        UpperCamelCase__    :     Union[str, Any]        =						text_mask.repeat_interleave(lowerCAmelCase_							,     dim=0		)
  
        if do_classifier_free_guidance:
             UpperCamelCase__    :     Optional[int]        =						[""] * batch_size
  
             UpperCamelCase__    :     List[Any]        =						self.tokenizer(
                 lowerCAmelCase_							,     padding="max_length"							,     max_length=self.tokenizer.model_max_length							,     truncation=lowerCAmelCase_							,     return_tensors="pt"							,     )
             UpperCamelCase__    :     int        =						uncond_input.attention_mask.bool().to(lowerCAmelCase_		)
             UpperCamelCase__    :     List[str]        =						self.text_encoder(uncond_input.input_ids.to(lowerCAmelCase_		)		)
  
             UpperCamelCase__    :     str        =						uncond_embeddings_text_encoder_output.text_embeds
             UpperCamelCase__    :     Union[str, Any]        =						uncond_embeddings_text_encoder_output.last_hidden_state
  
             # duplicate unconditional embeddings for each generation per prompt, using mps friendly method
  
             UpperCamelCase__    :     Optional[Any]        =						uncond_embeddings.shape[1]
             UpperCamelCase__    :     str        =						uncond_embeddings.repeat(1							,     lowerCAmelCase_		)
             UpperCamelCase__    :     Any        =						uncond_embeddings.view(batch_size * num_images_per_prompt							,     lowerCAmelCase_		)
  
             UpperCamelCase__    :     str        =						uncond_text_encoder_hidden_states.shape[1]
             UpperCamelCase__    :     Tuple        =						uncond_text_encoder_hidden_states.repeat(1							,     lowerCAmelCase_							,     1		)
             UpperCamelCase__    :     Tuple        =						uncond_text_encoder_hidden_states.view(
                 batch_size * num_images_per_prompt							,     lowerCAmelCase_							,     -1		)
             UpperCamelCase__    :     Dict        =						uncond_text_mask.repeat_interleave(lowerCAmelCase_							,     dim=0		)
  
             # done duplicates
  
             # For classifier free guidance, we need to do two forward passes.
             # Here we concatenate the unconditional and text embeddings into a single batch
             # to avoid doing two forward passes
             UpperCamelCase__    :     Dict        =						torch.cat([uncond_embeddings, text_embeddings]		)
             UpperCamelCase__    :     List[Any]        =						torch.cat([uncond_text_encoder_hidden_states, text_encoder_hidden_states]		)
  
             UpperCamelCase__    :     int        =						torch.cat([uncond_text_mask, text_mask]		)
  
        return text_embeddings, text_encoder_hidden_states, text_mask
  
  
  
  
  
  
  
   @property
   def       __lowercase      (	self      :     Dict		):
  
  
        '''simple docstring'''
  
  
  
  
  
  
        if self.device != torch.device("meta"		) or not hasattr(self.prior							,     "_hf_hook"		):
             return self.device
        for module in self.prior.modules():
             if (
                 hasattr(lowerCAmelCase_							,     "_hf_hook"		)
                 and hasattr(module._hf_hook							,     "execution_device"		)
                 and module._hf_hook.execution_device is not None
             ):
                  return torch.device(module._hf_hook.execution_device		)
        return self.device
  
  
  
  
  
  
  
   def       __lowercase      (	self      :     Optional[int]							,     SCREAMING_SNAKE_CASE      :     Tuple							,     SCREAMING_SNAKE_CASE      :     str							,     SCREAMING_SNAKE_CASE      :     Tuple							,     SCREAMING_SNAKE_CASE      :     Dict							,     SCREAMING_SNAKE_CASE      :     Tuple							,     SCREAMING_SNAKE_CASE      :     Any		):
  
  
        '''simple docstring'''
  
  
  
  
  
  
        if latents is None:
             UpperCamelCase__    :     str        =						randn_tensor(lowerCAmelCase_							,     generator=lowerCAmelCase_							,     device=lowerCAmelCase_							,     dtype=lowerCAmelCase_		)
        else:
             if latents.shape != shape:
                  raise ValueError(F'Unexpected latents shape, got {latents.shape}, expected {shape}'		)
             UpperCamelCase__    :     int        =						latents.to(lowerCAmelCase_		)
  
        UpperCamelCase__    :     int        =						latents * scheduler.init_noise_sigma
        return latents
  
  
  
  
  
  
  
   def       __lowercase      (	self      :     List[str]							,     SCREAMING_SNAKE_CASE      :     Optional[Union[str, torch.device]] = None		):
  
  
        '''simple docstring'''
  
  
  
  
  
  
        self.decoder_pipe.to(lowerCAmelCase_		)
        super().to(lowerCAmelCase_		)
  
  
  
  
  
  
  
   @torch.no_grad()
   def __call__(	self      :     int							,     SCREAMING_SNAKE_CASE      :     Optional[Union[str, List[str]]] = None							,     SCREAMING_SNAKE_CASE      :     Optional[int] = None							,     SCREAMING_SNAKE_CASE      :     Optional[int] = None							,     SCREAMING_SNAKE_CASE      :     int = 1							,     SCREAMING_SNAKE_CASE      :     int = 25							,     SCREAMING_SNAKE_CASE      :     Optional[torch.Generator] = None							,     SCREAMING_SNAKE_CASE      :     Optional[torch.FloatTensor] = None							,     SCREAMING_SNAKE_CASE      :     Optional[Union[CLIPTextModelOutput, Tuple]] = None							,     SCREAMING_SNAKE_CASE      :     Optional[torch.Tensor] = None							,     SCREAMING_SNAKE_CASE      :     float = 4.0							,     SCREAMING_SNAKE_CASE      :     float = 8.0							,     SCREAMING_SNAKE_CASE      :     int = 50							,     SCREAMING_SNAKE_CASE      :     Optional[int] = 1							,     SCREAMING_SNAKE_CASE      :     float = 0.0							,     SCREAMING_SNAKE_CASE      :     Optional[str] = "pil"							,     SCREAMING_SNAKE_CASE      :     bool = True							,     ):
  
  
        '''simple docstring'''
  
  
  
  
  
  
        if prompt is not None:
             if isinstance(lowerCAmelCase_							,     lowerCAmelCase_		):
                  UpperCamelCase__    :     int        =						1
             elif isinstance(lowerCAmelCase_							,     lowerCAmelCase_		):
                  UpperCamelCase__    :     List[Any]        =						len(lowerCAmelCase_		)
             else:
                  raise ValueError(F'`prompt` has to be of type `str` or `list` but is {type(lowerCAmelCase_		)}'		)
        else:
             UpperCamelCase__    :     Union[str, Any]        =						text_model_output[0].shape[0]
  
        UpperCamelCase__    :     Dict        =						self._execution_device
  
        UpperCamelCase__    :     Tuple        =						batch_size * num_images_per_prompt
  
        UpperCamelCase__    :     Union[str, Any]        =						prior_guidance_scale > 1.0 or decoder_guidance_scale > 1.0
  
        UpperCamelCase__       ,  UpperCamelCase__       ,  UpperCamelCase__    :     List[Any]        =						self._encode_prompt(
            lowerCAmelCase_							,     lowerCAmelCase_							,     lowerCAmelCase_							,     lowerCAmelCase_							,     lowerCAmelCase_							,     lowerCAmelCase_		)
  
        # prior
  
        self.prior_scheduler.set_timesteps(lowerCAmelCase_							,     device=lowerCAmelCase_		)
        UpperCamelCase__    :     List[str]        =						self.prior_scheduler.timesteps
  
        UpperCamelCase__    :     Union[str, Any]        =						self.prior.config.embedding_dim
  
        UpperCamelCase__    :     Union[str, Any]        =						self.prepare_latents(
            (batch_size, embedding_dim)							,     text_embeddings.dtype							,     lowerCAmelCase_							,     lowerCAmelCase_							,     lowerCAmelCase_							,     self.prior_scheduler							,     )
  
        for i, t in enumerate(self.progress_bar(lowerCAmelCase_		)		):
             # expand the latents if we are doing classifier free guidance
             UpperCamelCase__    :     Union[str, Any]        =						torch.cat([prior_latents] * 2		) if do_classifier_free_guidance else prior_latents
  
             UpperCamelCase__    :     int        =						self.prior(
                 lowerCAmelCase_							,     timestep=lowerCAmelCase_							,     proj_embedding=lowerCAmelCase_							,     encoder_hidden_states=lowerCAmelCase_							,     attention_mask=lowerCAmelCase_							,     ).predicted_image_embedding
  
             if do_classifier_free_guidance:
                  UpperCamelCase__       ,  UpperCamelCase__    :     Optional[Any]        =						predicted_image_embedding.chunk(2		)
                  UpperCamelCase__    :     str        =						predicted_image_embedding_uncond + prior_guidance_scale * (
                      predicted_image_embedding_text - predicted_image_embedding_uncond
                  )
  
             if i + 1 == prior_timesteps_tensor.shape[0]:
                  UpperCamelCase__    :     List[str]        =						None
             else:
                  UpperCamelCase__    :     str        =						prior_timesteps_tensor[i + 1]
  
             UpperCamelCase__    :     str        =						self.prior_scheduler.step(
                 lowerCAmelCase_							,     timestep=lowerCAmelCase_							,     sample=lowerCAmelCase_							,     generator=lowerCAmelCase_							,     prev_timestep=lowerCAmelCase_							,     ).prev_sample
  
        UpperCamelCase__    :     Any        =						self.prior.post_process_latents(lowerCAmelCase_		)
  
        UpperCamelCase__    :     Tuple        =						prior_latents
  
        UpperCamelCase__    :     Dict        =						self.decoder_pipe(
            image=lowerCAmelCase_							,     height=lowerCAmelCase_							,     width=lowerCAmelCase_							,     num_inference_steps=lowerCAmelCase_							,     guidance_scale=lowerCAmelCase_							,     generator=lowerCAmelCase_							,     output_type=lowerCAmelCase_							,     return_dict=lowerCAmelCase_							,     num_images_per_prompt=lowerCAmelCase_							,     eta=lowerCAmelCase_							,     )
        return output
style_context: 
  
  
  
  
  
  
  def 	SCREAMING_SNAKE_CASE							(      __lowerCAmelCase    )				->			str:
       if len(__lowerCAmelCase    ) == 0 or not all(len(__lowerCAmelCase    ) == 2 for pair in coordinates    ):
            raise ValueError("The program cannot work out a fitting polynomial."    )
  
       if len({tuple(__lowerCAmelCase    ) for pair in coordinates}    ) != len(__lowerCAmelCase    ):
            raise ValueError("The program cannot work out a fitting polynomial."    )
  
       UpperCamelCase__    :     List[str]        =						{x for x, _ in coordinates}
       if len(__lowerCAmelCase    ) == 1:
            return f'x={coordinates[0][0]}'
  
       if len(__lowerCAmelCase    ) != len(__lowerCAmelCase    ):
            raise ValueError("The program cannot work out a fitting polynomial."    )
  
       UpperCamelCase__    :     Any        =						len(__lowerCAmelCase    )
  
       UpperCamelCase__    :     str        =						0
       UpperCamelCase__    :     list[list[float]]        =						[]
       # put the x and x to the power values in a matrix
       while count_of_line < x:
            UpperCamelCase__    :     int        =						0
            UpperCamelCase__    :     List[Any]        =						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(__lowerCAmelCase    )
            count_of_line += 1
  
       UpperCamelCase__    :     List[Any]        =						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__    :     Tuple        =						0
  
       while count < x:
            UpperCamelCase__    :     Dict        =						0
            while zahlen < x:
                 if count == zahlen:
                      zahlen += 1
                 if zahlen == x:
                      break
                 UpperCamelCase__    :     Optional[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__    :     Tuple        =						0
       # make solutions
       UpperCamelCase__    :     list[str]        =						[]
       while count < x:
            solution.append(str(vector[count] / matrix[count][count]    )    )
            count += 1
  
       UpperCamelCase__    :     int        =						0
       UpperCamelCase__    :     List[str]        =						"f(x)="
  
       while count < x:
            UpperCamelCase__    :     list[str]        =						solution[count].split("E"    )
            if len(__lowerCAmelCase    ) > 1:
                 UpperCamelCase__    :     Union[str, 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]]))