


'''simple docstring'''
from typing import List, Optional, Tuple, Union

import PIL
import torch
from torchvision import transforms

from diffusers.pipeline_utils import DiffusionPipeline, ImagePipelineOutput
from diffusers.schedulers import DDIMScheduler
from diffusers.utils import randn_tensor


__snake_case							      =     transforms.Compose(
    [
        transforms.Resize((256, 256)),
        transforms.ToTensor(),
        transforms.Normalize([0.5], [0.5]),
    ]
)


def 			a      (			__a   )  ->	Optional[Any]:



					'''simple docstring'''






					if isinstance(__a ,					torch.Tensor   ):
										return image
					elif isinstance(__a ,					PIL.Image.Image   ):
										UpperCamelCase__   :Any												= [image]

					UpperCamelCase__   :Any												= [trans(img.convert('''RGB'''   )   ) for img in image]
					UpperCamelCase__   :List[str]												= torch.stack(__a   )
					return image







class    lowercase	(							A__					):

		"""simple docstring"""

		def __init__(		self    ,   UpperCamelCase_    ,   UpperCamelCase_							):

							'''simple docstring'''


							super().__init__()

							# make sure scheduler can always be converted to DDIM
							UpperCamelCase__   :str												= DDIMScheduler.from_config(scheduler.config							)

							self.register_modules(unet=UpperCamelCase_    ,   scheduler=UpperCamelCase_							)




		def     lowerCAmelCase__				(		self    ,   UpperCamelCase_							):

							'''simple docstring'''


							if strength < 0 or strength > 1:
												raise ValueError(F'''The value of strength should in [0.0, 1.0] but is {strength}'''							)




		def     lowerCAmelCase__				(		self    ,   UpperCamelCase_    ,   UpperCamelCase_    ,   UpperCamelCase_							):

							'''simple docstring'''


							UpperCamelCase__   :List[str]												= min(int(num_inference_steps * strength							)    ,   UpperCamelCase_							)

							UpperCamelCase__   :List[str]												= max(num_inference_steps - init_timestep    ,   0							)
							UpperCamelCase__   :Dict												= self.scheduler.timesteps[t_start:]

							return timesteps, num_inference_steps - t_start




		def     lowerCAmelCase__				(		self    ,   UpperCamelCase_    ,   UpperCamelCase_    ,   UpperCamelCase_    ,   UpperCamelCase_    ,   UpperCamelCase_    ,   UpperCamelCase_=None							):

							'''simple docstring'''


							if not isinstance(UpperCamelCase_    ,   (torch.Tensor, PIL.Image.Image, list)							):
												raise ValueError(
												    F'''`image` has to be of type `torch.Tensor`, `PIL.Image.Image` or list but is {type(UpperCamelCase_							)}'''							)

							UpperCamelCase__   :List[str]												= image.to(device=UpperCamelCase_    ,   dtype=UpperCamelCase_							)

							if isinstance(UpperCamelCase_    ,   UpperCamelCase_							) and len(UpperCamelCase_							) != batch_size:
												raise ValueError(
												    F'''You have passed a list of generators of length {len(UpperCamelCase_							)}, but requested an effective batch'''
												    F''' size of {batch_size}. Make sure the batch size matches the length of the generators.'''							)

							UpperCamelCase__   :List[Any]												= init_latents.shape
							UpperCamelCase__   :int												= randn_tensor(UpperCamelCase_    ,   generator=UpperCamelCase_    ,   device=UpperCamelCase_    ,   dtype=UpperCamelCase_							)

							# get latents
							print('''add noise to latents at timestep'''    ,   UpperCamelCase_							)
							UpperCamelCase__   :Union[str, Any]												= self.scheduler.add_noise(UpperCamelCase_    ,   UpperCamelCase_    ,   UpperCamelCase_							)
							UpperCamelCase__   :Any												= init_latents

							return latents




		@torch.no_grad()
		def __call__(		self    ,   UpperCamelCase_ = None    ,   UpperCamelCase_ = 0.8    ,   UpperCamelCase_ = 1    ,   UpperCamelCase_ = None    ,   UpperCamelCase_ = 0.0    ,   UpperCamelCase_ = 50    ,   UpperCamelCase_ = None    ,   UpperCamelCase_ = "pil"    ,   UpperCamelCase_ = True    ,   ):

							'''simple docstring'''


							self.check_inputs(UpperCamelCase_							)

							# 2. Preprocess image
							UpperCamelCase__   :Tuple												= preprocess(UpperCamelCase_							)

							# 3. set timesteps
							self.scheduler.set_timesteps(UpperCamelCase_    ,   device=self.device							)
							UpperCamelCase__					,				UpperCamelCase__   :Tuple												= self.get_timesteps(UpperCamelCase_    ,   UpperCamelCase_    ,   self.device							)
							UpperCamelCase__   :Tuple												= timesteps[:1].repeat(UpperCamelCase_							)

							# 4. Prepare latent variables
							UpperCamelCase__   :int												= self.prepare_latents(UpperCamelCase_    ,   UpperCamelCase_    ,   UpperCamelCase_    ,   self.unet.dtype    ,   self.device    ,   UpperCamelCase_							)
							UpperCamelCase__   :int												= latents

							# 5. Denoising loop
							for t in self.progress_bar(UpperCamelCase_							):
												# 1. predict noise model_output
												UpperCamelCase__   :Optional[Any]												= self.unet(UpperCamelCase_    ,   UpperCamelCase_							).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
												UpperCamelCase__   :Dict												= self.scheduler.step(
												    UpperCamelCase_    ,   UpperCamelCase_    ,   UpperCamelCase_    ,   eta=UpperCamelCase_    ,   use_clipped_model_output=UpperCamelCase_    ,   generator=UpperCamelCase_    ,   ).prev_sample

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

							if not return_dict:
												return (image, latent_timestep.item())

							return ImagePipelineOutput(images=UpperCamelCase_							)
'''simple docstring'''

from math import sqrt

import numpy as np
from sympy import symbols

# Coefficient
# Speed of light (m/s)
_A			:      List[Any]					      =				299792458

# Symbols
_A      ,     _A      ,     _A      ,     _A			:      Union[str, Any]					      =				symbols('''ct x y z''')







def      UpperCamelCase_						(					snake_case_       :       float      )					->     float:






 '''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      UpperCamelCase_						(					snake_case_       :       float      )					->     float:






 '''simple docstring'''

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







def      UpperCamelCase_						(					snake_case_       :       float      )					->     np.ndarray:






 '''simple docstring'''

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







def      UpperCamelCase_						(					snake_case_       :       float						,		snake_case_       :       np.ndarray | None = None      )					->     np.ndarray:






 '''simple docstring'''

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

 return transformation_matrix(snake_case_      ) @ event


if __name__ == "__main__":
 import doctest

 doctest.testmod()

 # Example of symbolic vector:
 _A			:      str					      =				transform(29979245)
 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
 _A			:      int					      =				{ct: c, x: 1, y: 1, z: 1}
 _A			:      Any					      =				[four_vector[i].subs(sub_dict) for i in range(4)]

 print(f'\n{numerical_vector}')






