from math import factorial


class 			UpperCAmelCase__    :



  """simple docstring"""






  def __init__(				self:			Tuple				,				__lowerCAmelCase:			str				,				__lowerCAmelCase:			int   ) -> Tuple:




    '''simple docstring'''




    __UpperCAmelCase						    =       real
    if isinstance(__lowerCAmelCase				,				__lowerCAmelCase   ):
      __UpperCAmelCase						    =       [1] * rank
    else:
      __UpperCAmelCase						    =       rank






  def __repr__(				self:			List[Any]   ) -> int:




    '''simple docstring'''




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






  def 	_UpperCAmelCase				(				self:			int   ) -> List[str]:




    '''simple docstring'''




    __UpperCAmelCase						    =       self.duals.copy()
    while cur[-1] == 0:
      cur.pop(-1   )
    return Dual(self.real				,				__lowerCAmelCase   )






  def __add__(				self:			int				,				__lowerCAmelCase:			Dict   ) -> Union[str, Any]:




    '''simple docstring'''




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

  lowerCAmelCase__		:	Any    		= __add__






  def __sub__(				self:			Any				,				__lowerCAmelCase:			Union[str, Any]   ) -> List[Any]:




    '''simple docstring'''




    return self + other * -1






  def __mul__(				self:			List[Any]				,				__lowerCAmelCase:			Optional[int]   ) -> Dict:




    '''simple docstring'''




    if not isinstance(__lowerCAmelCase				,				__lowerCAmelCase   ):
      __UpperCAmelCase						    =       []
      for i in self.duals:
        new_duals.append(i * other   )
      return Dual(self.real * other				,				__lowerCAmelCase   )
    __UpperCAmelCase						    =       [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				,				__lowerCAmelCase   )

  lowerCAmelCase__		:	List[Any]    		= __mul__






  def __truediv__(				self:			Optional[int]				,				__lowerCAmelCase:			int   ) -> str:




    '''simple docstring'''




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






  def __floordiv__(				self:			Optional[int]				,				__lowerCAmelCase:			Optional[Any]   ) -> Tuple:




    '''simple docstring'''




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






  def __pow__(				self:			Optional[int]				,				__lowerCAmelCase:			Union[str, Any]   ) -> int:




    '''simple docstring'''




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






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


if __name__ == "__main__":
       import doctest

       doctest.testmod()




       def       __lowerCAmelCase      (						A_   : Optional[Any]					)    ->  Dict:
         return y**2 * y**4





       print(differentiate(f, 9, 2))




import gc
import unittest

import numpy as np
import torch

from diffusers import AutoencoderKL, DDIMScheduler, DiTPipeline, DPMSolverMultistepScheduler, TransformeraDModel
from diffusers.utils import is_xformers_available, load_numpy, slow, torch_device
from diffusers.utils.testing_utils import enable_full_determinism, require_torch_gpu

from ..pipeline_params import (
    CLASS_CONDITIONED_IMAGE_GENERATION_BATCH_PARAMS,
    CLASS_CONDITIONED_IMAGE_GENERATION_PARAMS,
)
from ..test_pipelines_common import PipelineTesterMixin


enable_full_determinism()


class 			UpperCAmelCase__    (		snake_case		,	unittest.TestCase					):



  """simple docstring"""






  lowerCAmelCase__		:	int    		= DiTPipeline
  lowerCAmelCase__		:	Any    		= CLASS_CONDITIONED_IMAGE_GENERATION_PARAMS
  lowerCAmelCase__		:	Optional[Any]    		= PipelineTesterMixin.required_optional_params - {
      'latents',
      'num_images_per_prompt',
      'callback',
      'callback_steps',
  }
  lowerCAmelCase__		:	List[Any]    		= CLASS_CONDITIONED_IMAGE_GENERATION_BATCH_PARAMS
  lowerCAmelCase__		:	Optional[int]    		= False






  def 	_UpperCAmelCase				(				self:			str   ) -> List[Any]:




    '''simple docstring'''




    torch.manual_seed(0   )
    __UpperCAmelCase						    =       TransformeraDModel(
        sample_size=16				,				num_layers=2				,				patch_size=4				,				attention_head_dim=8				,				num_attention_heads=2				,				in_channels=4				,				out_channels=8				,				attention_bias=__lowerCAmelCase				,				activation_fn="gelu-approximate"				,				num_embeds_ada_norm=1_000				,				norm_type="ada_norm_zero"				,				norm_elementwise_affine=__lowerCAmelCase				,				)
    __UpperCAmelCase						    =       AutoencoderKL()
    __UpperCAmelCase						    =       DDIMScheduler()
    __UpperCAmelCase						    =       {"transformer": transformer.eval(), "vae": vae.eval(), "scheduler": scheduler}
    return components






  def 	_UpperCAmelCase				(				self:			str				,				__lowerCAmelCase:			str				,				__lowerCAmelCase:			Optional[int]=0   ) -> int:




    '''simple docstring'''




    if str(__lowerCAmelCase   ).startswith("mps"   ):
      __UpperCAmelCase						    =       torch.manual_seed(__lowerCAmelCase   )
    else:
      __UpperCAmelCase						    =       torch.Generator(device=__lowerCAmelCase   ).manual_seed(__lowerCAmelCase   )
    __UpperCAmelCase						    =       {
        "class_labels": [1],
        "generator": generator,
        "num_inference_steps": 2,
        "output_type": "numpy",
    }
    return inputs






  def 	_UpperCAmelCase				(				self:			Tuple   ) -> Dict:




    '''simple docstring'''




    __UpperCAmelCase						    =       "cpu"

    __UpperCAmelCase						    =       self.get_dummy_components()
    __UpperCAmelCase						    =       self.pipeline_class(**__lowerCAmelCase   )
    pipe.to(__lowerCAmelCase   )
    pipe.set_progress_bar_config(disable=__lowerCAmelCase   )

    __UpperCAmelCase						    =       self.get_dummy_inputs(__lowerCAmelCase   )
    __UpperCAmelCase						    =       pipe(**__lowerCAmelCase   ).images
    __UpperCAmelCase						    =       image[0, -3:, -3:, -1]

    self.assertEqual(image.shape				,				(1, 16, 16, 3)   )
    __UpperCAmelCase						    =       np.array([0.2946, 0.6601, 0.4329, 0.3296, 0.4144, 0.5319, 0.7273, 0.5013, 0.4457]   )
    __UpperCAmelCase						    =       np.abs(image_slice.flatten() - expected_slice   ).max()
    self.assertLessEqual(__lowerCAmelCase				,				1E-3   )






  def 	_UpperCAmelCase				(				self:			int   ) -> str:




    '''simple docstring'''




    self._test_inference_batch_single_identical(relax_max_difference=__lowerCAmelCase				,				expected_max_diff=1E-3   )






  @unittest.skipIf(
      torch_device != "cuda" or not is_xformers_available()				,				reason="XFormers attention is only available with CUDA and `xformers` installed"				,				)
  def 	_UpperCAmelCase				(				self:			Optional[int]   ) -> str:




    '''simple docstring'''




    self._test_xformers_attention_forwardGenerator_pass(expected_max_diff=1E-3   )






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



  """simple docstring"""






  def 	_UpperCAmelCase				(				self:			Any   ) -> Optional[Any]:




    '''simple docstring'''




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






  def 	_UpperCAmelCase				(				self:			Dict   ) -> List[Any]:




    '''simple docstring'''




    __UpperCAmelCase						    =       torch.manual_seed(0   )

    __UpperCAmelCase						    =       DiTPipeline.from_pretrained("facebook/DiT-XL-2-256"   )
    pipe.to("cuda"   )

    __UpperCAmelCase						    =       ["vase", "umbrella", "white shark", "white wolf"]
    __UpperCAmelCase						    =       pipe.get_label_ids(__lowerCAmelCase   )

    __UpperCAmelCase						    =       pipe(__lowerCAmelCase				,				generator=__lowerCAmelCase				,				num_inference_steps=40				,				output_type="np"   ).images

    for word, image in zip(__lowerCAmelCase				,				__lowerCAmelCase   ):
      __UpperCAmelCase						    =       load_numpy(
          F'''https://huggingface.co/datasets/hf-internal-testing/diffusers-images/resolve/main/dit/{word}.npy'''   )
      assert np.abs((expected_image - image).max()   ) < 1E-2






  def 	_UpperCAmelCase				(				self:			Any   ) -> List[str]:




    '''simple docstring'''




    __UpperCAmelCase						    =       DiTPipeline.from_pretrained("facebook/DiT-XL-2-512"   )
    __UpperCAmelCase						    =       DPMSolverMultistepScheduler.from_config(pipe.scheduler.config   )
    pipe.to("cuda"   )

    __UpperCAmelCase						    =       ["vase", "umbrella"]
    __UpperCAmelCase						    =       pipe.get_label_ids(__lowerCAmelCase   )

    __UpperCAmelCase						    =       torch.manual_seed(0   )
    __UpperCAmelCase						    =       pipe(__lowerCAmelCase				,				generator=__lowerCAmelCase				,				num_inference_steps=25				,				output_type="np"   ).images

    for word, image in zip(__lowerCAmelCase				,				__lowerCAmelCase   ):
      __UpperCAmelCase						    =       load_numpy(
          "https://huggingface.co/datasets/hf-internal-testing/diffusers-images/resolve/main"
          F'''/dit/{word}_512.npy'''   )

      assert np.abs((expected_image - image).max()   ) < 1E-1



