





from math import atan, cos, radians, sin, tan

from .haversine_distance import haversine_distance

_snake_case  :    Dict						    =  6_37_81_37.0
_snake_case  :    str						    =  6_35_67_52.31_42_45
_snake_case  :    Any						    =  6378137

def   a_    ( lowerCAmelCase_      :			float,	lowerCAmelCase_      :			float,	lowerCAmelCase_      :			float,	lowerCAmelCase_      :			float	):
   __lowerCAmelCase								=	(AXIS_A - AXIS_B) / AXIS_A
   # Parametric latitudes
   # https://en.wikipedia.org/wiki/Latitude#Parametric_(or_reduced)_latitude
   __lowerCAmelCase								=	atan((1 - flattening) * tan(radians(lowerCAmelCase_	)	)	)
   __lowerCAmelCase								=	atan((1 - flattening) * tan(radians(lowerCAmelCase_	)	)	)

   # Compute central angle between two points
   # using haversine theta. sigma =  haversine_distance / equatorial radius
   __lowerCAmelCase								=	haversine_distance(lowerCAmelCase_,	lowerCAmelCase_,	lowerCAmelCase_,	lowerCAmelCase_	) / EQUATORIAL_RADIUS

   # Intermediate P and Q values
   __lowerCAmelCase								=	(b_lata + b_lata) / 2
   __lowerCAmelCase								=	(b_lata - b_lata) / 2

   # Intermediate X value
   # X = (sigma - sin(sigma)) * sin^2Pcos^2Q / cos^2(sigma/2)
   __lowerCAmelCase								=	(sin(lowerCAmelCase_	) ** 2) * (cos(lowerCAmelCase_	) ** 2)
   __lowerCAmelCase								=	cos(sigma / 2	) ** 2
   __lowerCAmelCase								=	(sigma - sin(lowerCAmelCase_	)) * (x_numerator / x_demonimator)

   # Intermediate Y value
   # Y = (sigma + sin(sigma)) * cos^2Psin^2Q / sin^2(sigma/2)
   __lowerCAmelCase								=	(cos(lowerCAmelCase_	) ** 2) * (sin(lowerCAmelCase_	) ** 2)
   __lowerCAmelCase								=	sin(sigma / 2	) ** 2
   __lowerCAmelCase								=	(sigma + sin(lowerCAmelCase_	)) * (y_numerator / y_denominator)

   return EQUATORIAL_RADIUS * (sigma - ((flattening / 2) * (x_value + y_value)))


if __name__ == "__main__":
     import doctest

     doctest.testmod()








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

