
from collections.abc import Callable

import numpy as np







def 							A__       (    lowerCamelCase  ,     lowerCamelCase  ,     lowerCamelCase  ,     lowerCamelCase  ,     lowerCamelCase    )	->						np.array:
				UpperCamelCase_:				Any						=    int(np.ceil((x_end - xa) / step_size    )    )
				UpperCamelCase_:				Union[str, Any]						=    np.zeros((n + 1,)    )
				UpperCamelCase_:				Any						=    ya
				UpperCamelCase_:				str						=    xa

				for k in range(__lowerCAmelCase    ):
								UpperCamelCase_:				Dict						=    y[k] + step_size * ode_func(__lowerCAmelCase  ,     y[k]    )
								UpperCamelCase_:				List[Any]						=    y[k] + (
								    (step_size / 2) * (ode_func(__lowerCAmelCase  ,     y[k]    ) + ode_func(x + step_size  ,     __lowerCAmelCase    ))
								)
								x += step_size

				return y


if __name__ == "__main__":
							import doctest

							doctest.testmod()













'''simple docstring'''




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

