


"""simple docstring"""
from math import factorial




class 	lowercase__				:





   def __init__(							self      ,   SCREAMING_SNAKE_CASE      ,   SCREAMING_SNAKE_CASE)  ->  Optional[int]:
      _lowerCamelCase	:					List[Any]   =		real
      if isinstance(SCREAMING_SNAKE_CASE      ,   SCREAMING_SNAKE_CASE):
         _lowerCamelCase	:					Tuple   =		[1] * rank
      else:
         _lowerCamelCase	:					Any   =		rank





   def __repr__(							self)  ->  Optional[Any]:
      return (
          F'{self.real}+'
          F'{"+".join(str(SCREAMING_SNAKE_CASE)+"E"+str(n+1)for n,dual in enumerate(self.duals))}'
      )





   def 		UpperCamelCase_  (							self)  ->  Any:
      _lowerCamelCase	:					Optional[int]   =		self.duals.copy()
      while cur[-1] == 0:
         cur.pop(-1)
      return Dual(self.real      ,   SCREAMING_SNAKE_CASE)





   def __add__(							self      ,   SCREAMING_SNAKE_CASE)  ->  List[str]:
      if not isinstance(SCREAMING_SNAKE_CASE      ,   SCREAMING_SNAKE_CASE):
         return Dual(self.real + other      ,   self.duals)
      _lowerCamelCase	:					Optional[int]   =		self.duals.copy()
      _lowerCamelCase	:					List[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)))
      _lowerCamelCase	:					Any   =		[]
      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)

   __UpperCAmelCase							       =					__add__





   def __sub__(							self      ,   SCREAMING_SNAKE_CASE)  ->  Optional[int]:
      return self + other * -1





   def __mul__(							self      ,   SCREAMING_SNAKE_CASE)  ->  Optional[Any]:
      if not isinstance(SCREAMING_SNAKE_CASE      ,   SCREAMING_SNAKE_CASE):
         _lowerCamelCase	:					Union[str, Any]   =		[]
         for i in self.duals:
            new_duals.append(i * other)
         return Dual(self.real * other      ,   SCREAMING_SNAKE_CASE)
      _lowerCamelCase	:					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)

   __UpperCAmelCase							       =					__mul__





   def __truediv__(							self      ,   SCREAMING_SNAKE_CASE)  ->  Optional[int]:
      if not isinstance(SCREAMING_SNAKE_CASE      ,   SCREAMING_SNAKE_CASE):
         _lowerCamelCase	:					Union[str, Any]   =		[]
         for i in self.duals:
            new_duals.append(i / other)
         return Dual(self.real / other      ,   SCREAMING_SNAKE_CASE)
      raise ValueError





   def __floordiv__(							self      ,   SCREAMING_SNAKE_CASE)  ->  int:
      if not isinstance(SCREAMING_SNAKE_CASE      ,   SCREAMING_SNAKE_CASE):
         _lowerCamelCase	:					List[Any]   =		[]
         for i in self.duals:
            new_duals.append(i // other)
         return Dual(self.real // other      ,   SCREAMING_SNAKE_CASE)
      raise ValueError





   def __pow__(							self      ,   SCREAMING_SNAKE_CASE)  ->  Optional[Any]:
      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
      _lowerCamelCase	:					int   =		self
      for _ in range(n - 1):
         x *= self
      return x







def 				_snake_case      (   __snake_case							:      List[Any]						, __snake_case							:      Dict						, __snake_case							:      Dict   ):




   """simple docstring"""







   if not callable(__snake_case   ):
      raise ValueError("""differentiate() requires a function as input for func"""   )
   if not isinstance(__snake_case						, (float, int)   ):
      raise ValueError("""differentiate() requires a float as input for position"""   )
   if not isinstance(__snake_case						, __snake_case   ):
      raise ValueError("""differentiate() requires an int as input for order"""   )
   _lowerCamelCase	:					Any   =		Dual(__snake_case						, 1   )
   _lowerCamelCase	:					Tuple   =		func(__snake_case   )
   if order == 0:
      return result.real
   return result.duals[order - 1] * factorial(__snake_case   )


if __name__ == "__main__":
 import doctest

 doctest.testmod()

 def 				_snake_case      (   __snake_case							:      Tuple   ):




    """simple docstring"""







    return y**2 * y**4





 print(differentiate(f, 9, 2))





'''simple docstring'''





import gc
import unittest

import numpy as np
import torch
from transformers import CLIPTextConfig, CLIPTextModel, CLIPTokenizer

from diffusers import TransformeraDModel, VQDiffusionPipeline, VQDiffusionScheduler, VQModel
from diffusers.pipelines.vq_diffusion.pipeline_vq_diffusion import LearnedClassifierFreeSamplingEmbeddings
from diffusers.utils import load_numpy, slow, torch_device
from diffusers.utils.testing_utils import require_torch_gpu


__lowerCamelCase												=						False




class 				UpperCAmelCase			(			unittest.TestCase						):


 def        __SCREAMING_SNAKE_CASE					(      self							:	Optional[Any] ):
    # clean up the VRAM after each test
    super().tearDown()
    gc.collect()
    torch.cuda.empty_cache()


 @property
 def        __SCREAMING_SNAKE_CASE					(      self							:	str ):
    return 1_2


 @property
 def        __SCREAMING_SNAKE_CASE					(      self							:	List[Any] ):
    return 1_2


 @property
 def        __SCREAMING_SNAKE_CASE					(      self							:	Optional[int] ):
    return 3_2


 @property
 def        __SCREAMING_SNAKE_CASE					(      self							:	List[str] ):
    torch.manual_seed(0 )
    UpperCAmelCase__	:List[str]      =      VQModel(
        block_out_channels=[3_2, 6_4]			,       in_channels=3			,       out_channels=3			,       down_block_types=['''DownEncoderBlock2D''', '''DownEncoderBlock2D''']			,       up_block_types=['''UpDecoderBlock2D''', '''UpDecoderBlock2D''']			,       latent_channels=3			,       num_vq_embeddings=self.num_embed			,       vq_embed_dim=3			,       )
    return model


 @property
 def        __SCREAMING_SNAKE_CASE					(      self							:	int ):
    UpperCAmelCase__	:Tuple      =      CLIPTokenizer.from_pretrained('''hf-internal-testing/tiny-random-clip''' )
    return tokenizer


 @property
 def        __SCREAMING_SNAKE_CASE					(      self							:	Tuple ):
    torch.manual_seed(0 )
    UpperCAmelCase__	:Optional[Any]      =      CLIPTextConfig(
        bos_token_id=0			,       eos_token_id=2			,       hidden_size=self.text_embedder_hidden_size			,       intermediate_size=3_7			,       layer_norm_eps=1e-05			,       num_attention_heads=4			,       num_hidden_layers=5			,       pad_token_id=1			,       vocab_size=1_0_0_0			,       )
    return CLIPTextModel(__lowerCamelCase )


 @property
 def        __SCREAMING_SNAKE_CASE					(      self							:	List[str] ):
    torch.manual_seed(0 )

    UpperCAmelCase__	:List[str]      =      1_2
    UpperCAmelCase__	:Optional[int]      =      1_2

    UpperCAmelCase__	:Optional[int]      =      {
        '''attention_bias''': True,
        '''cross_attention_dim''': 3_2,
        '''attention_head_dim''': height * width,
        '''num_attention_heads''': 1,
        '''num_vector_embeds''': self.num_embed,
        '''num_embeds_ada_norm''': self.num_embeds_ada_norm,
        '''norm_num_groups''': 3_2,
        '''sample_size''': width,
        '''activation_fn''': '''geglu-approximate''',
    }

    UpperCAmelCase__	:List[str]      =      TransformeraDModel(**__lowerCamelCase )
    return model


 def        __SCREAMING_SNAKE_CASE					(      self							:	List[Any] ):
    UpperCAmelCase__	:Union[str, Any]      =      '''cpu'''

    UpperCAmelCase__	:Optional[Any]      =      self.dummy_vqvae
    UpperCAmelCase__	:Optional[int]      =      self.dummy_text_encoder
    UpperCAmelCase__	:Union[str, Any]      =      self.dummy_tokenizer
    UpperCAmelCase__	:List[Any]      =      self.dummy_transformer
    UpperCAmelCase__	:str      =      VQDiffusionScheduler(self.num_embed )
    UpperCAmelCase__	:Optional[Any]      =      LearnedClassifierFreeSamplingEmbeddings(learnable=__lowerCamelCase )

    UpperCAmelCase__	:Any      =      VQDiffusionPipeline(
        vqvae=__lowerCamelCase			,       text_encoder=__lowerCamelCase			,       tokenizer=__lowerCamelCase			,       transformer=__lowerCamelCase			,       scheduler=__lowerCamelCase			,       learned_classifier_free_sampling_embeddings=__lowerCamelCase			,       )
    UpperCAmelCase__	:Any      =      pipe.to(__lowerCamelCase )
    pipe.set_progress_bar_config(disable=__lowerCamelCase )

    UpperCAmelCase__	:str      =      '''teddy bear playing in the pool'''

    UpperCAmelCase__	:Optional[int]      =      torch.Generator(device=__lowerCamelCase ).manual_seed(0 )
    UpperCAmelCase__	:Any      =      pipe([prompt]			,       generator=__lowerCamelCase			,       num_inference_steps=2			,       output_type='''np''' )
    UpperCAmelCase__	:str      =      output.images

    UpperCAmelCase__	:List[Any]      =      torch.Generator(device=__lowerCamelCase ).manual_seed(0 )
    UpperCAmelCase__	:Dict      =      pipe(
        [prompt]			,       generator=__lowerCamelCase			,       output_type='''np'''			,       return_dict=__lowerCamelCase			,       num_inference_steps=2 )[0]

    UpperCAmelCase__	:int      =      image[0, -3:, -3:, -1]
    UpperCAmelCase__	:List[Any]      =      image_from_tuple[0, -3:, -3:, -1]

    assert image.shape == (1, 2_4, 2_4, 3)

    UpperCAmelCase__	:int      =      np.array([0.65_51, 0.61_68, 0.50_08, 0.56_76, 0.56_59, 0.42_95, 0.60_73, 0.55_99, 0.49_92] )

    assert np.abs(image_slice.flatten() - expected_slice ).max() < 1e-2
    assert np.abs(image_from_tuple_slice.flatten() - expected_slice ).max() < 1e-2





 def        __SCREAMING_SNAKE_CASE					(      self							:	Tuple ):
    UpperCAmelCase__	:List[Any]      =      '''cpu'''

    UpperCAmelCase__	:int      =      self.dummy_vqvae
    UpperCAmelCase__	:List[str]      =      self.dummy_text_encoder
    UpperCAmelCase__	:Union[str, Any]      =      self.dummy_tokenizer
    UpperCAmelCase__	:Optional[Any]      =      self.dummy_transformer
    UpperCAmelCase__	:List[str]      =      VQDiffusionScheduler(self.num_embed )
    UpperCAmelCase__	:List[str]      =      LearnedClassifierFreeSamplingEmbeddings(
        learnable=__lowerCamelCase			,       hidden_size=self.text_embedder_hidden_size			,       length=tokenizer.model_max_length )

    UpperCAmelCase__	:List[Any]      =      VQDiffusionPipeline(
        vqvae=__lowerCamelCase			,       text_encoder=__lowerCamelCase			,       tokenizer=__lowerCamelCase			,       transformer=__lowerCamelCase			,       scheduler=__lowerCamelCase			,       learned_classifier_free_sampling_embeddings=__lowerCamelCase			,       )
    UpperCAmelCase__	:str      =      pipe.to(__lowerCamelCase )
    pipe.set_progress_bar_config(disable=__lowerCamelCase )

    UpperCAmelCase__	:str      =      '''teddy bear playing in the pool'''

    UpperCAmelCase__	:str      =      torch.Generator(device=__lowerCamelCase ).manual_seed(0 )
    UpperCAmelCase__	:Union[str, Any]      =      pipe([prompt]			,       generator=__lowerCamelCase			,       num_inference_steps=2			,       output_type='''np''' )
    UpperCAmelCase__	:Any      =      output.images

    UpperCAmelCase__	:Optional[int]      =      torch.Generator(device=__lowerCamelCase ).manual_seed(0 )
    UpperCAmelCase__	:int      =      pipe(
        [prompt]			,       generator=__lowerCamelCase			,       output_type='''np'''			,       return_dict=__lowerCamelCase			,       num_inference_steps=2 )[0]

    UpperCAmelCase__	:List[Any]      =      image[0, -3:, -3:, -1]
    UpperCAmelCase__	:Optional[Any]      =      image_from_tuple[0, -3:, -3:, -1]

    assert image.shape == (1, 2_4, 2_4, 3)

    UpperCAmelCase__	:Union[str, Any]      =      np.array([0.66_93, 0.60_75, 0.49_59, 0.57_01, 0.55_83, 0.43_33, 0.61_71, 0.56_84, 0.49_88] )

    assert np.abs(image_slice.flatten() - expected_slice ).max() < 2.0
    assert np.abs(image_from_tuple_slice.flatten() - expected_slice ).max() < 1e-2




@slow
@require_torch_gpu
class 				UpperCAmelCase			(			unittest.TestCase						):


 def        __SCREAMING_SNAKE_CASE					(      self							:	Tuple ):
    # clean up the VRAM after each test
    super().tearDown()
    gc.collect()
    torch.cuda.empty_cache()





 def        __SCREAMING_SNAKE_CASE					(      self							:	Optional[int] ):
    UpperCAmelCase__	:Optional[Any]      =      load_numpy(
        '''https://huggingface.co/datasets/hf-internal-testing/diffusers-images/resolve/main'''
        '''/vq_diffusion/teddy_bear_pool_classifier_free_sampling.npy''' )

    UpperCAmelCase__	:Optional[Any]      =      VQDiffusionPipeline.from_pretrained('''microsoft/vq-diffusion-ithq''' )
    UpperCAmelCase__	:List[str]      =      pipeline.to(__lowerCamelCase )
    pipeline.set_progress_bar_config(disable=__lowerCamelCase )

    # requires GPU generator for gumbel softmax
    # don't use GPU generator in tests though
    UpperCAmelCase__	:int      =      torch.Generator(device=__lowerCamelCase ).manual_seed(0 )
    UpperCAmelCase__	:Union[str, Any]      =      pipeline(
        '''teddy bear playing in the pool'''			,       num_images_per_prompt=1			,       generator=__lowerCamelCase			,       output_type='''np'''			,       )

    UpperCAmelCase__	:List[str]      =      output.images[0]

    assert image.shape == (2_5_6, 2_5_6, 3)
    assert np.abs(expected_image - image ).max() < 2.0



