



"""simple docstring"""
from typing import Any

import numpy as np



def        lowerCAmelCase_						(							SCREAMING_SNAKE_CASE__	)			->      Optional[int]:
  return np.array_equal(SCREAMING_SNAKE_CASE__, matrix.conjugate().T	)



def        lowerCAmelCase_						(							SCREAMING_SNAKE_CASE__, SCREAMING_SNAKE_CASE__	)			->      Any:
  a_     :      Any 						=     v.conjugate().T
  a_     :      Any 						=     v_star.dot(SCREAMING_SNAKE_CASE__	)
  assert isinstance(SCREAMING_SNAKE_CASE__, np.ndarray	)
  return (v_star_dot.dot(SCREAMING_SNAKE_CASE__	)) / (v_star.dot(SCREAMING_SNAKE_CASE__	))



def        lowerCAmelCase_						(							)			->      Union[str, Any]:
  a_     :      Tuple 						=     np.array([[2, 2 + 1J, 4], [2 - 1J, 3, 1J], [4, -1J, 1]]	)
  a_     :      Optional[int] 						=     np.array([[1], [2], [3]]	)
  assert is_hermitian(SCREAMING_SNAKE_CASE__	), F"""{a} is not hermitian."""
  print(rayleigh_quotient(SCREAMING_SNAKE_CASE__, SCREAMING_SNAKE_CASE__	)	)

  a_     :      List[str] 						=     np.array([[1, 2, 4], [2, 3, -1], [4, -1, 1]]	)
  assert is_hermitian(SCREAMING_SNAKE_CASE__	), F"""{a} is not hermitian."""
  assert rayleigh_quotient(SCREAMING_SNAKE_CASE__, SCREAMING_SNAKE_CASE__	) == float(3	)


if __name__ == "__main__":
     import doctest

     doctest.testmod()
     tests()




"""simple docstring"""
import unittest

import numpy as np
import torch

from diffusers import VersatileDiffusionImageVariationPipeline
from diffusers.utils.testing_utils import load_image, require_torch_gpu, slow, torch_device


SCREAMING_SNAKE_CASE_				= False




class 			snake_case_						(						unittest.TestCase				):
							pass




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






							def snake_case_  (   self      ):
									a_     :      Tuple 						=     VersatileDiffusionImageVariationPipeline.from_pretrained("shi-labs/versatile-diffusion"      )
									pipe.to(a_      )
									pipe.set_progress_bar_config(disable=a_      )

									a_     :      Optional[Any] 						=     load_image(
									    "https://huggingface.co/datasets/hf-internal-testing/diffusers-images/resolve/main/versatile_diffusion/benz.jpg"      )
									a_     :      Optional[Any] 						=     torch.manual_seed(0      )
									a_     :      Dict 						=     pipe(
									    image=a_			,     generator=a_			,     guidance_scale=7.5			,     num_inference_steps=5_0			,     output_type="numpy"			,     ).images

									a_     :      List[Any] 						=     image[0, 2_5_3:2_5_6, 2_5_3:2_5_6, -1]

									assert image.shape == (1, 5_1_2, 5_1_2, 3)
									a_     :      Any 						=     np.array([0.0_441, 0.0_469, 0.0_507, 0.0_575, 0.0_632, 0.0_650, 0.0_865, 0.0_909, 0.0_945]      )

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