
"""simple docstring"""



import os

from huggingface_hub.constants import HUGGINGFACE_HUB_CACHE, hf_cache_home


a					:	List[Any]							=		HUGGINGFACE_HUB_CACHE


a					:	Optional[int]							=		'''config.json'''
a					:	List[Any]							=		'''diffusion_pytorch_model.bin'''
a					:	Union[str, Any]							=		'''diffusion_flax_model.msgpack'''
a					:	Union[str, Any]							=		'''model.onnx'''
a					:	Optional[int]							=		'''diffusion_pytorch_model.safetensors'''
a					:	str							=		'''weights.pb'''
a					:	Dict							=		'''https://huggingface.co'''
a					:	Optional[Any]							=		default_cache_path
a					:	Dict							=		'''diffusers_modules'''
a					:	Optional[Any]							=		os.getenv('''HF_MODULES_CACHE''', os.path.join(hf_cache_home, '''modules'''))
a					:	str							=		['''fp16''', '''non-ema''']
a					:	Optional[Any]							=		'''.self_attn'''

"""simple docstring"""



from collections.abc import Callable

import numpy as np


def  _UpperCamelCase	(						_A					,      _A					,      _A					,      _A					,      _A      )    ->  np.array:





    """simple docstring"""

    _UpperCAmelCase          =   int(np.ceil((x_end - xa) / step_size      )      )
    _UpperCAmelCase          =   np.zeros((n + 1,)      )
    _UpperCAmelCase          =   ya
    _UpperCAmelCase          =   xa

    for k in range(_A      ):
        _UpperCAmelCase          =   y[k] + step_size * ode_func(_A					,      y[k]      )
        _UpperCAmelCase          =   y[k] + (
            (step_size / 2) * (ode_func(_A					,      y[k]      ) + ode_func(x + step_size					,      _A      ))
        )
        x += step_size

    return y


if __name__ == "__main__":
 import doctest

 doctest.testmod()