

from math import factorial

class 				a  :


						def __init__(       self						,					A_						,					A_	):







										'''simple docstring'''


										_UpperCAmelCase       :		Union[str, Any] 		=    real
										if isinstance(A_						,					A_	):
														_UpperCAmelCase       :		Any 		=    [1] * rank
										else:
														_UpperCAmelCase       :		Optional[int] 		=    rank


						def __repr__(       self	):







										'''simple docstring'''


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


						def        _UpperCAmelCase				(       self	):







										'''simple docstring'''


										_UpperCAmelCase       :		List[str] 		=    self.duals.copy()
										while cur[-1] == 0:
														cur.pop(-1	)
										return Dual(self.real						,					A_	)


						def __add__(       self						,					A_	):







										'''simple docstring'''


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

						_lowercase    						=			__add__


						def __sub__(       self						,					A_	):







										'''simple docstring'''


										return self + other * -1


						def __mul__(       self						,					A_	):







										'''simple docstring'''


										if not isinstance(A_						,					A_	):
														_UpperCAmelCase       :		Dict 		=    []
														for i in self.duals:
																		new_duals.append(i * other	)
														return Dual(self.real * other						,					A_	)
										_UpperCAmelCase       :		Optional[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						,					A_	)

						_lowercase    						=			__mul__


						def __truediv__(       self						,					A_	):







										'''simple docstring'''


										if not isinstance(A_						,					A_	):
														_UpperCAmelCase       :		Optional[Any] 		=    []
														for i in self.duals:
																		new_duals.append(i / other	)
														return Dual(self.real / other						,					A_	)
										raise ValueError


						def __floordiv__(       self						,					A_	):







										'''simple docstring'''


										if not isinstance(A_						,					A_	):
														_UpperCAmelCase       :		Optional[int] 		=    []
														for i in self.duals:
																		new_duals.append(i // other	)
														return Dual(self.real // other						,					A_	)
										raise ValueError





						def __pow__(       self						,					A_	):







										'''simple docstring'''


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







def 							__SCREAMING_SNAKE_CASE							(				lowerCAmelCase:  Optional[int]  ,      lowerCAmelCase:  Any  ,      lowerCAmelCase:  Optional[int] )   ->       Dict:
				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       :		List[str] 		=    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[str] )   ->       List[Any]:
									return y**2 * y**4





					print(differentiate(f, 9, 2))





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


SCREAMING_SNAKE_CASE_        =      False

class 				a  (	unittest.TestCase				):


						def        _UpperCAmelCase				(       self	):







										'''simple docstring'''


										super().tearDown()
										gc.collect()
										torch.cuda.empty_cache()


						@property
						def        _UpperCAmelCase				(       self	):







										'''simple docstring'''


										return 12


						@property
						def        _UpperCAmelCase				(       self	):







										'''simple docstring'''


										return 12


						@property
						def        _UpperCAmelCase				(       self	):







										'''simple docstring'''


										return 32


						@property
						def        _UpperCAmelCase				(       self	):







										'''simple docstring'''


										torch.manual_seed(0	)
										_UpperCAmelCase       :		Optional[int] 		=    VQModel(
										    block_out_channels=[32, 64]						,					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        _UpperCAmelCase				(       self	):







										'''simple docstring'''


										_UpperCAmelCase       :		List[str] 		=    CLIPTokenizer.from_pretrained("hf-internal-testing/tiny-random-clip"	)
										return tokenizer


						@property
						def        _UpperCAmelCase				(       self	):







										'''simple docstring'''


										torch.manual_seed(0	)
										_UpperCAmelCase       :		int 		=    CLIPTextConfig(
										    bos_token_id=0						,					eos_token_id=2						,					hidden_size=self.text_embedder_hidden_size						,					intermediate_size=37						,					layer_norm_eps=1e-05						,					num_attention_heads=4						,					num_hidden_layers=5						,					pad_token_id=1						,					vocab_size=1000						,					)
										return CLIPTextModel(A_	)


						@property
						def        _UpperCAmelCase				(       self	):







										'''simple docstring'''


										torch.manual_seed(0	)

										_UpperCAmelCase       :		Optional[int] 		=    12
										_UpperCAmelCase       :		Union[str, Any] 		=    12

										_UpperCAmelCase       :		str 		=    {
										    "attention_bias": True,
										    "cross_attention_dim": 32,
										    "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": 32,
										    "sample_size": width,
										    "activation_fn": "geglu-approximate",
										}

										_UpperCAmelCase       :		Any 		=    TransformeraDModel(**A_	)
										return model


						def        _UpperCAmelCase				(       self	):







										'''simple docstring'''


										_UpperCAmelCase       :		Dict 		=    "cpu"

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

										_UpperCAmelCase       :		Optional[Any] 		=    VQDiffusionPipeline(
										    vqvae=A_						,					text_encoder=A_						,					tokenizer=A_						,					transformer=A_						,					scheduler=A_						,					learned_classifier_free_sampling_embeddings=A_						,					)
										_UpperCAmelCase       :		Optional[int] 		=    pipe.to(A_	)
										pipe.set_progress_bar_config(disable=A_	)

										_UpperCAmelCase       :		Union[str, Any] 		=    "teddy bear playing in the pool"

										_UpperCAmelCase       :		Union[str, Any] 		=    torch.Generator(device=A_	).manual_seed(0	)
										_UpperCAmelCase       :		List[Any] 		=    pipe([prompt]						,					generator=A_						,					num_inference_steps=2						,					output_type="np"	)
										_UpperCAmelCase       :		List[Any] 		=    output.images

										_UpperCAmelCase       :		Dict 		=    torch.Generator(device=A_	).manual_seed(0	)
										_UpperCAmelCase       :		Union[str, Any] 		=    pipe(
										    [prompt]						,					generator=A_						,					output_type="np"						,					return_dict=A_						,					num_inference_steps=2	)[0]

										_UpperCAmelCase       :		Optional[Any] 		=    image[0, -3:, -3:, -1]
										_UpperCAmelCase       :		int 		=    image_from_tuple[0, -3:, -3:, -1]

										assert image.shape == (1, 24, 24, 3)

										_UpperCAmelCase       :		List[str] 		=    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        _UpperCAmelCase				(       self	):







										'''simple docstring'''


										_UpperCAmelCase       :		Optional[int] 		=    "cpu"

										_UpperCAmelCase       :		Tuple 		=    self.dummy_vqvae
										_UpperCAmelCase       :		Optional[Any] 		=    self.dummy_text_encoder
										_UpperCAmelCase       :		List[str] 		=    self.dummy_tokenizer
										_UpperCAmelCase       :		List[Any] 		=    self.dummy_transformer
										_UpperCAmelCase       :		Dict 		=    VQDiffusionScheduler(self.num_embed	)
										_UpperCAmelCase       :		Dict 		=    LearnedClassifierFreeSamplingEmbeddings(
										    learnable=A_						,					hidden_size=self.text_embedder_hidden_size						,					length=tokenizer.model_max_length	)

										_UpperCAmelCase       :		Optional[int] 		=    VQDiffusionPipeline(
										    vqvae=A_						,					text_encoder=A_						,					tokenizer=A_						,					transformer=A_						,					scheduler=A_						,					learned_classifier_free_sampling_embeddings=A_						,					)
										_UpperCAmelCase       :		Union[str, Any] 		=    pipe.to(A_	)
										pipe.set_progress_bar_config(disable=A_	)

										_UpperCAmelCase       :		int 		=    "teddy bear playing in the pool"

										_UpperCAmelCase       :		Dict 		=    torch.Generator(device=A_	).manual_seed(0	)
										_UpperCAmelCase       :		int 		=    pipe([prompt]						,					generator=A_						,					num_inference_steps=2						,					output_type="np"	)
										_UpperCAmelCase       :		Union[str, Any] 		=    output.images

										_UpperCAmelCase       :		Optional[Any] 		=    torch.Generator(device=A_	).manual_seed(0	)
										_UpperCAmelCase       :		int 		=    pipe(
										    [prompt]						,					generator=A_						,					output_type="np"						,					return_dict=A_						,					num_inference_steps=2	)[0]

										_UpperCAmelCase       :		Any 		=    image[0, -3:, -3:, -1]
										_UpperCAmelCase       :		Optional[int] 		=    image_from_tuple[0, -3:, -3:, -1]

										assert image.shape == (1, 24, 24, 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 				a  (	unittest.TestCase				):


						def        _UpperCAmelCase				(       self	):







										'''simple docstring'''


										super().tearDown()
										gc.collect()
										torch.cuda.empty_cache()





						def        _UpperCAmelCase				(       self	):







										'''simple docstring'''


										_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       :		Dict 		=    VQDiffusionPipeline.from_pretrained("microsoft/vq-diffusion-ithq"	)
										_UpperCAmelCase       :		Optional[int] 		=    pipeline.to(A_	)
										pipeline.set_progress_bar_config(disable=A_	)

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

										_UpperCAmelCase       :		str 		=    output.images[0]

										assert image.shape == (256, 256, 3)
										assert np.abs(expected_image - image	).max() < 2.0


