



import numpy as np





def 							A			(  _UpperCAmelCase       :     List[str]							,     _UpperCAmelCase       :     int							,     _UpperCAmelCase       :     Optional[Any]							,     _UpperCAmelCase       :     Any							,     _UpperCAmelCase       :     int					)       ->				Dict:







			'''simple docstring'''
			_UpperCAmelCase	 =     int(np.ceil((x_end - xa) / h					)					)
			_UpperCAmelCase	 =     np.zeros((n + 1,)					)
			_UpperCAmelCase	 =     ya
			_UpperCAmelCase	 =     xa

			for k in range(_UpperCAmelCase					):
						_UpperCAmelCase	 =     f(_UpperCAmelCase							,     y[k]					)
						_UpperCAmelCase	 =     f(x + 0.5 * h							,     y[k] + 0.5 * h * ka					)
						_UpperCAmelCase	 =     f(x + 0.5 * h							,     y[k] + 0.5 * h * ka					)
						_UpperCAmelCase	 =     f(x + h							,     y[k] + h * ka					)
						_UpperCAmelCase	 =     y[k] + (1 / 6) * h * (ka + 2 * ka + 2 * ka + ka)
						x += h

			return y


if __name__ == "__main__":
							import doctest

							doctest.testmod()





from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available, is_vision_available


UpperCAmelCase__     = {"configuration_yolos": ["YOLOS_PRETRAINED_CONFIG_ARCHIVE_MAP", "YolosConfig", "YolosOnnxConfig"]}

try:
							if not is_vision_available():
														raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
							pass
else:
							UpperCAmelCase__     = ["YolosFeatureExtractor"]
							UpperCAmelCase__     = ["YolosImageProcessor"]

try:
							if not is_torch_available():
														raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
							pass
else:
							UpperCAmelCase__     = [
							    "YOLOS_PRETRAINED_MODEL_ARCHIVE_LIST",
							    "YolosForObjectDetection",
							    "YolosModel",
							    "YolosPreTrainedModel",
							]


if TYPE_CHECKING:
							from .configuration_yolos import YOLOS_PRETRAINED_CONFIG_ARCHIVE_MAP, YolosConfig, YolosOnnxConfig

							try:
														if not is_vision_available():
																					raise OptionalDependencyNotAvailable()
							except OptionalDependencyNotAvailable:
														pass
							else:
														from .feature_extraction_yolos import YolosFeatureExtractor
														from .image_processing_yolos import YolosImageProcessor

							try:
														if not is_torch_available():
																					raise OptionalDependencyNotAvailable()
							except OptionalDependencyNotAvailable:
														pass
							else:
														from .modeling_yolos import (
														    YOLOS_PRETRAINED_MODEL_ARCHIVE_LIST,
														    YolosForObjectDetection,
														    YolosModel,
														    YolosPreTrainedModel,
														)


else:
							import sys

							UpperCAmelCase__     = _LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)
