



"""simple docstring"""







import numpy as np

def     UpperCamelCase_   (   lowerCAmelCase__				:    Optional[int]   ,       lowerCAmelCase__				:    int   ,       lowerCAmelCase__				:    Optional[Any]   ,       lowerCAmelCase__				:    Optional[Any]   ,       lowerCAmelCase__				:    Dict						)						->       List[Any]:

  """simple docstring"""




  lowerCAmelCase_       :    str								=			int(np.ceil((x_end - xa) / h						)						)
  lowerCAmelCase_       :    Optional[Any]								=			np.zeros((n + 1,)						)
  lowerCAmelCase_       :    Dict								=			ya
  lowerCAmelCase_       :    Optional[int]								=			xa

  for k in range(lowerCAmelCase__						):
    lowerCAmelCase_       :    List[str]								=			f(lowerCAmelCase__   ,       y[k]						)
    lowerCAmelCase_       :    Optional[Any]								=			f(x + 0.5 * h   ,       y[k] + 0.5 * h * ka						)
    lowerCAmelCase_       :    List[Any]								=			f(x + 0.5 * h   ,       y[k] + 0.5 * h * ka						)
    lowerCAmelCase_       :    List[Any]								=			f(x + h   ,       y[k] + h * ka						)
    lowerCAmelCase_       :    List[str]								=			y[k] + (1 / 6) * h * (ka + 2 * ka + 2 * ka + ka)
    x += h

  return y


if __name__ == "__main__":
     import doctest

     doctest.testmod()










"""simple docstring"""







from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_sentencepiece_available,
    is_speech_available,
    is_torch_available,
)


lowercase__		:    Optional[int]				   =     {
    """configuration_trocr""": ["""TROCR_PRETRAINED_CONFIG_ARCHIVE_MAP""", """TrOCRConfig"""],
    """processing_trocr""": ["""TrOCRProcessor"""],
}


try:
     if not is_torch_available():
          raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
     pass
else:
     lowercase__		:    Dict				   =     [
         """TROCR_PRETRAINED_MODEL_ARCHIVE_LIST""",
         """TrOCRForCausalLM""",
         """TrOCRPreTrainedModel""",
     ]


if TYPE_CHECKING:
     from .configuration_trocr import TROCR_PRETRAINED_CONFIG_ARCHIVE_MAP, TrOCRConfig
     from .processing_trocr import TrOCRProcessor

     try:
          if not is_torch_available():
               raise OptionalDependencyNotAvailable()
     except OptionalDependencyNotAvailable:
          pass
     else:
          from .modeling_trocr import TROCR_PRETRAINED_MODEL_ARCHIVE_LIST, TrOCRForCausalLM, TrOCRPreTrainedModel

else:
     import sys

     lowercase__		:    int				   =     _LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)





