

from __future__ import annotations

import matplotlib.pyplot as plt  # type: ignore
import numpy

# initial triangle of Koch snowflake
_A		:				Optional[int]									=       numpy.array([0, 0])
_A		:				Union[str, Any]									=       numpy.array([0.5, 0.8_66_02_54])
_A		:				List[Any]									=       numpy.array([1, 0])
_A		:				List[Any]									=       [VECTOR_1, VECTOR_2, VECTOR_3, VECTOR_1]



def     __lowerCAmelCase						(							snake_case	:    list[numpy.ndarray]						,      snake_case	:    int )       ->							list[numpy.ndarray]:
   __lowerCamelCase:				Optional[int]     =	initial_vectors
   for _ in range(snake_case ):
      __lowerCamelCase:				int     =	iteration_step(snake_case )
   return vectors



def     __lowerCAmelCase						(							snake_case	:    list[numpy.ndarray] )       ->							list[numpy.ndarray]:
   __lowerCamelCase:				Optional[int]     =	[]
   for i, start_vector in enumerate(vectors[:-1] ):
      __lowerCamelCase:				Union[str, Any]     =	vectors[i + 1]
      new_vectors.append(snake_case )
      __lowerCamelCase:				List[str]     =	end_vector - start_vector
      new_vectors.append(start_vector + difference_vector / 3 )
      new_vectors.append(
          start_vector + difference_vector / 3 + rotate(difference_vector / 3						,      60 ) )
      new_vectors.append(start_vector + difference_vector * 2 / 3 )
   new_vectors.append(vectors[-1] )
   return new_vectors



def     __lowerCAmelCase						(							snake_case	:    numpy.ndarray						,      snake_case	:    float )       ->							numpy.ndarray:
   __lowerCamelCase:				List[Any]     =	numpy.radians(snake_case )
   __lowerCamelCase:				Dict     =	numpy.cos(snake_case ), numpy.sin(snake_case )
   __lowerCamelCase:				Optional[int]     =	numpy.array(((c, -s), (s, c)) )
   return numpy.dot(snake_case						,      snake_case )



def     __lowerCAmelCase						(							snake_case	:    list[numpy.ndarray] )       ->							None:
   __lowerCamelCase:				Optional[Any]     =	plt.gca()
   axes.set_aspect("""equal""" )

   # matplotlib.pyplot.plot takes a list of all x-coordinates and a list of all
   # y-coordinates as inputs, which are constructed from the vector-list using
   # zip()
   __lowerCamelCase:				Optional[int]     =	zip(*snake_case )
   plt.plot(snake_case						,      snake_case )
   plt.show()


if __name__ == "__main__":
   import doctest

   doctest.testmod()

   _A		:				Dict									=       iterate(INITIAL_VECTORS, 5)
   plot(processed_vectors)






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


