


from ..utils import (
    OptionalDependencyNotAvailable,
    is_flax_available,
    is_scipy_available,
    is_torch_available,
    is_torchsde_available,
)


try:
   if not is_torch_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   from ..utils.dummy_pt_objects import *  # noqa F403
else:
   from .scheduling_consistency_models import CMStochasticIterativeScheduler
   from .scheduling_ddim import DDIMScheduler
   from .scheduling_ddim_inverse import DDIMInverseScheduler
   from .scheduling_ddim_parallel import DDIMParallelScheduler
   from .scheduling_ddpm import DDPMScheduler
   from .scheduling_ddpm_parallel import DDPMParallelScheduler
   from .scheduling_deis_multistep import DEISMultistepScheduler
   from .scheduling_dpmsolver_multistep import DPMSolverMultistepScheduler
   from .scheduling_dpmsolver_multistep_inverse import DPMSolverMultistepInverseScheduler
   from .scheduling_dpmsolver_singlestep import DPMSolverSinglestepScheduler
   from .scheduling_euler_ancestral_discrete import EulerAncestralDiscreteScheduler
   from .scheduling_euler_discrete import EulerDiscreteScheduler
   from .scheduling_heun_discrete import HeunDiscreteScheduler
   from .scheduling_ipndm import IPNDMScheduler
   from .scheduling_k_dpm_2_ancestral_discrete import KDPMaAncestralDiscreteScheduler
   from .scheduling_k_dpm_2_discrete import KDPMaDiscreteScheduler
   from .scheduling_karras_ve import KarrasVeScheduler
   from .scheduling_pndm import PNDMScheduler
   from .scheduling_repaint import RePaintScheduler
   from .scheduling_sde_ve import ScoreSdeVeScheduler
   from .scheduling_sde_vp import ScoreSdeVpScheduler
   from .scheduling_unclip import UnCLIPScheduler
   from .scheduling_unipc_multistep import UniPCMultistepScheduler
   from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin
   from .scheduling_vq_diffusion import VQDiffusionScheduler

try:
   if not is_flax_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   from ..utils.dummy_flax_objects import *  # noqa F403
else:
   from .scheduling_ddim_flax import FlaxDDIMScheduler
   from .scheduling_ddpm_flax import FlaxDDPMScheduler
   from .scheduling_dpmsolver_multistep_flax import FlaxDPMSolverMultistepScheduler
   from .scheduling_karras_ve_flax import FlaxKarrasVeScheduler
   from .scheduling_lms_discrete_flax import FlaxLMSDiscreteScheduler
   from .scheduling_pndm_flax import FlaxPNDMScheduler
   from .scheduling_sde_ve_flax import FlaxScoreSdeVeScheduler
   from .scheduling_utils_flax import (
       FlaxKarrasDiffusionSchedulers,
       FlaxSchedulerMixin,
       FlaxSchedulerOutput,
       broadcast_to_shape_from_left,
   )


try:
   if not (is_torch_available() and is_scipy_available()):
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   from ..utils.dummy_torch_and_scipy_objects import *  # noqa F403
else:
   from .scheduling_lms_discrete import LMSDiscreteScheduler

try:
   if not (is_torch_available() and is_torchsde_available()):
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   from ..utils.dummy_torch_and_torchsde_objects import *  # noqa F403
else:
   from .scheduling_dpmsolver_sde import DPMSolverSDEScheduler







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}''')



