
"""simple docstring"""


# limitations under the License.


from typing import Optional, Tuple, Union

import torch

from diffusers import DiffusionPipeline, ImagePipelineOutput







class  lowerCAmelCase_ (					_lowercase			):



						'''simple docstring'''


						def __init__(       self   :					int     ,A_   :					Tuple     ,A_   :					List[str]					)   ->      Tuple:
							super().__init__()
							self.register_modules(unet=A_     ,scheduler=A_					)




						@torch.no_grad()
						def __call__(       self   :					Optional[Any]     ,A_   :					int = 1     ,A_   :					Optional[torch.Generator] = None     ,A_   :					int = 50     ,A_   :					Optional[str] = "pil"     ,A_   :					bool = True     ,**A_   :					Tuple     ,)   ->      Union[ImagePipelineOutput, Tuple]:
							A        =      torch.randn(
							    (batch_size, self.unet.config.in_channels, self.unet.config.sample_size, self.unet.config.sample_size)     ,generator=A_     ,)
							A        =      image.to(self.device					)

							# set step values
							self.scheduler.set_timesteps(A_					)

							for t in self.progress_bar(self.scheduler.timesteps					):
								# 1. predict noise model_output
								A        =      self.unet(A_     ,A_					).sample

								# 2. predict previous mean of image x_t-1 and add variance depending on eta
								# eta corresponds to η in paper and should be between [0, 1]
								# do x_t -> x_t-1
								A        =      self.scheduler.step(A_     ,A_     ,A_					).prev_sample

							A        =      (image / 2 + 0.5).clamp(0     ,1					)
							A        =      image.cpu().permute(0     ,2     ,3     ,1					).numpy()
							if output_type == "pil":
								A        =      self.numpy_to_pil(A_					)

							if not return_dict:
								return (image,), "This is a local test"

							return ImagePipelineOutput(images=A_					), "This is a local test"



from math import sqrt

import numpy as np
from sympy import symbols

# Coefficient
# Speed of light (m/s)
_snake_case             =     2_99_79_24_58

# Symbols
_snake_case      ,       _snake_case      ,       _snake_case      ,       _snake_case             =     symbols('''ct x y z''')






def 		lowercase_(  SCREAMING_SNAKE_CASE_	):


  '''simple docstring'''

  if velocity > c:
    raise ValueError("Speed must not exceed light speed 299,792,458 [m/s]!"	)
  elif velocity < 1:
    # Usually the speed should be much higher than 1 (c order of magnitude)
    raise ValueError("Speed must be greater than or equal to 1!"	)

  return velocity / c






def 		lowercase_(  SCREAMING_SNAKE_CASE_	):


  '''simple docstring'''

  return 1 / sqrt(1 - beta(SCREAMING_SNAKE_CASE_	) ** 2	)






def 		lowercase_(  SCREAMING_SNAKE_CASE_	):


  '''simple docstring'''

  return np.array(
      [
          [gamma(SCREAMING_SNAKE_CASE_	), -gamma(SCREAMING_SNAKE_CASE_	) * beta(SCREAMING_SNAKE_CASE_	), 0, 0],
          [-gamma(SCREAMING_SNAKE_CASE_	) * beta(SCREAMING_SNAKE_CASE_	), gamma(SCREAMING_SNAKE_CASE_	), 0, 0],
          [0, 0, 1, 0],
          [0, 0, 0, 1],
      ]	)






def 		lowercase_(  SCREAMING_SNAKE_CASE_      ,						SCREAMING_SNAKE_CASE_ = None	):


  '''simple docstring'''

  if event is None:
    lowerCamelCase :					Tuple    =				np.array([ct, x, y, z]	)  # Symbolic four vector
  else:
    event[0] *= c  # x0 is ct (speed of light * time)

  return transformation_matrix(SCREAMING_SNAKE_CASE_	) @ event


if __name__ == "__main__":
   import doctest

   doctest.testmod()

   # Example of symbolic vector:
   _snake_case             =     transform(29_97_92_45)
   print('''Example of four vector: ''')
   print(f'''ct\' = {four_vector[0]}''')
   print(f'''x\' = {four_vector[1]}''')
   print(f'''y\' = {four_vector[2]}''')
   print(f'''z\' = {four_vector[3]}''')

   # Substitute symbols with numerical values
   _snake_case             =     {ct: c, x: 1, y: 1, z: 1}
   _snake_case             =     [four_vector[i].subs(sub_dict) for i in range(4)]

   print(f'''\n{numerical_vector}''')



