





"""simple docstring"""




from math import sqrt

import numpy as np
from sympy import symbols

# Coefficient
# Speed of light (m/s)
UpperCamelCase_									=299_792_458

# Symbols
UpperCamelCase_				,     UpperCamelCase_				,     UpperCamelCase_				,     UpperCamelCase_									=symbols("""ct x y z""")





def 	a_    (							_lowercase       ):
						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 	a_    (							_lowercase       ):
						return 1 / sqrt(1 - beta(_lowercase       ) ** 2       )





def 	a_    (							_lowercase       ):
						return np.array(
						    [
						        [gamma(_lowercase       ), -gamma(_lowercase       ) * beta(_lowercase       ), 0, 0],
						        [-gamma(_lowercase       ) * beta(_lowercase       ), gamma(_lowercase       ), 0, 0],
						        [0, 0, 1, 0],
						        [0, 0, 0, 1],
						    ]       )





def 	a_    (							_lowercase	,						_lowercase = None       ):
						# Ensure event is not empty
						if event is None:
												_UpperCamelCase      : Dict         =   np.array([ct, x, y, z]       )  # Symbolic four vector
						else:
												event[0] *= c  # x0 is ct (speed of light * time)

						return transformation_matrix(_lowercase       ) @ event


if __name__ == "__main__":
						import doctest

						doctest.testmod()

						# Example of symbolic vector:
						UpperCamelCase_									=transform(29_979_245)
						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
						UpperCamelCase_									={ct: c, x: 1, y: 1, z: 1}
						UpperCamelCase_									=[four_vector[i].subs(sub_dict) for i in range(4)]

						print(F"\n{numerical_vector}")










"""simple docstring"""




from ..utils import is_flax_available, is_torch_available


if is_torch_available():
						from .autoencoder_kl import AutoencoderKL
						from .controlnet import ControlNetModel
						from .dual_transformer_ad import DualTransformeraDModel
						from .modeling_utils import ModelMixin
						from .prior_transformer import PriorTransformer
						from .ta_film_transformer import TaFilmDecoder
						from .transformer_ad import TransformeraDModel
						from .unet_ad import UNetaDModel
						from .unet_ad import UNetaDModel
						from .unet_ad_condition import UNetaDConditionModel
						from .unet_ad_condition import UNetaDConditionModel
						from .vq_model import VQModel

if is_flax_available():
						from .controlnet_flax import FlaxControlNetModel
						from .unet_ad_condition_flax import FlaxUNetaDConditionModel
						from .vae_flax import FlaxAutoencoderKL



