


'''simple docstring'''


from typing import List, Optional, TypeVar

from .arrow_dataset import Dataset, _concatenate_map_style_datasets, _interleave_map_style_datasets
from .dataset_dict import DatasetDict, IterableDatasetDict
from .info import DatasetInfo
from .iterable_dataset import IterableDataset, _concatenate_iterable_datasets, _interleave_iterable_datasets
from .splits import NamedSplit
from .utils import logging
from .utils.py_utils import Literal


lowerCamelCase__    	=     logging.get_logger(__name__)


lowerCamelCase__    	=     TypeVar('DatasetType', Dataset, IterableDataset)






def  __lowerCAmelCase (__lowerCAmelCase      , __lowerCAmelCase = None      , __lowerCAmelCase = None      , __lowerCAmelCase = None      , __lowerCAmelCase = None      , __lowerCAmelCase = "first_exhausted"      , ):
		from .arrow_dataset import Dataset
		from .iterable_dataset import IterableDataset

		if not datasets:
				raise ValueError("Unable to interleave an empty list of datasets."   )
		for i, dataset in enumerate(_UpperCamelCase   ):
				if not isinstance(_UpperCamelCase      , (Dataset, IterableDataset)   ):
						if isinstance(_UpperCamelCase      , (DatasetDict, IterableDatasetDict)   ):
								if not dataset:
										raise ValueError(
										    F"""Expected a list of Dataset objects or a list of IterableDataset objects, but element at position {i} """
										    "is an empty dataset dictionary."   )
								raise ValueError(
								    F"""Dataset at position {i} has at least one split: {list(_UpperCamelCase   )}\n"""
								    F"""Please pick one to interleave with the other datasets, for example: dataset['{next(iter(_UpperCamelCase   )   )}']"""   )
						raise ValueError(
						    F"""Expected a list of Dataset objects or a list of IterableDataset objects, but element at position {i} is a {type(_UpperCamelCase   ).__name__}."""   )
				if i == 0:
						_UpperCAmelCase					,    _UpperCAmelCase		:       Any								=      (
						    (Dataset, IterableDataset) if isinstance(_UpperCamelCase      , _UpperCamelCase   ) else (IterableDataset, Dataset)
						)
				elif not isinstance(_UpperCamelCase      , _UpperCamelCase   ):
						raise ValueError(
						    F"""Unable to interleave a {dataset_type.__name__} (at position 0) with a {other_type.__name__} (at position {i}). Expected a list of Dataset objects or a list of IterableDataset objects."""   )
		if stopping_strategy not in ["first_exhausted", "all_exhausted"]:
				raise ValueError(F"""{stopping_strategy} is not supported. Please enter a valid stopping_strategy."""   )
		if dataset_type is Dataset:
				return _interleave_map_style_datasets(
				    _UpperCamelCase      , _UpperCamelCase      , _UpperCamelCase      , info=_UpperCamelCase      , split=_UpperCamelCase      , stopping_strategy=_UpperCamelCase   )
		else:
				return _interleave_iterable_datasets(
				    _UpperCamelCase      , _UpperCamelCase      , _UpperCamelCase      , info=_UpperCamelCase      , split=_UpperCamelCase      , stopping_strategy=_UpperCamelCase   )






def  __lowerCAmelCase (__lowerCAmelCase      , __lowerCAmelCase = None      , __lowerCAmelCase = None      , __lowerCAmelCase = 0      , ):






		if not dsets:
				raise ValueError("Unable to concatenate an empty list of datasets."   )
		for i, dataset in enumerate(_UpperCamelCase   ):
				if not isinstance(_UpperCamelCase      , (Dataset, IterableDataset)   ):
						if isinstance(_UpperCamelCase      , (DatasetDict, IterableDatasetDict)   ):
								if not dataset:
										raise ValueError(
										    F"""Expected a list of Dataset objects or a list of IterableDataset objects, but element at position {i} """
										    "is an empty dataset dictionary."   )
								raise ValueError(
								    F"""Dataset at position {i} has at least one split: {list(_UpperCamelCase   )}\n"""
								    F"""Please pick one to interleave with the other datasets, for example: dataset['{next(iter(_UpperCamelCase   )   )}']"""   )
						raise ValueError(
						    F"""Expected a list of Dataset objects or a list of IterableDataset objects, but element at position {i} is a {type(_UpperCamelCase   ).__name__}."""   )
				if i == 0:
						_UpperCAmelCase					,    _UpperCAmelCase		:       str								=      (
						    (Dataset, IterableDataset) if isinstance(_UpperCamelCase      , _UpperCamelCase   ) else (IterableDataset, Dataset)
						)
				elif not isinstance(_UpperCamelCase      , _UpperCamelCase   ):
						raise ValueError(
						    F"""Unable to interleave a {dataset_type.__name__} (at position 0) with a {other_type.__name__} (at position {i}). Expected a list of Dataset objects or a list of IterableDataset objects."""   )
		if dataset_type is Dataset:
				return _concatenate_map_style_datasets(_UpperCamelCase      , info=_UpperCamelCase      , split=_UpperCamelCase      , axis=_UpperCamelCase   )
		else:
				return _concatenate_iterable_datasets(_UpperCamelCase      , info=_UpperCamelCase      , split=_UpperCamelCase      , axis=_UpperCamelCase   )







'''simple docstring'''


from math import factorial






class 	lowerCAmelCase__			:




			def __init__(		self  :     int	,  lowerCamelCase__  :     Union[str, Any]	,  lowerCamelCase__  :     str )   ->Dict:



					'''simple docstring'''







					_UpperCAmelCase		:       Optional[Any]								=      real
					if isinstance(lowerCamelCase__	,  lowerCamelCase__ ):
							_UpperCAmelCase		:       Any								=      [1] * rank
					else:
							_UpperCAmelCase		:       Dict								=      rank




			def __repr__(		self  :     str )   ->List[str]:



					'''simple docstring'''







					return (
					    F"""{self.real}+"""
					    F"""{'+'.join(str(lowerCamelCase__ )+'E'+str(n+1 )for n,dual in enumerate(self.duals ) )}"""
					)




			def 							lowerCAmelCase__    (		self  :     Dict )   ->Tuple:



					'''simple docstring'''







					_UpperCAmelCase		:       Union[str, Any]								=      self.duals.copy()
					while cur[-1] == 0:
							cur.pop(-1 )
					return Dual(self.real	,  lowerCamelCase__ )




			def __add__(		self  :     Dict	,  lowerCamelCase__  :     List[Any] )   ->Any:



					'''simple docstring'''







					if not isinstance(lowerCamelCase__	,  lowerCamelCase__ ):
							return Dual(self.real + other	,  self.duals )
					_UpperCAmelCase		:       Optional[int]								=      self.duals.copy()
					_UpperCAmelCase		:       Optional[int]								=      other.duals.copy()
					if len(lowerCamelCase__ ) > len(lowerCamelCase__ ):
							o_dual.extend([1] * (len(lowerCamelCase__ ) - len(lowerCamelCase__ )) )
					elif len(lowerCamelCase__ ) < len(lowerCamelCase__ ):
							s_dual.extend([1] * (len(lowerCamelCase__ ) - len(lowerCamelCase__ )) )
					_UpperCAmelCase		:       Union[str, Any]								=      []
					for i in range(len(lowerCamelCase__ ) ):
							new_duals.append(s_dual[i] + o_dual[i] )
					return Dual(self.real + other.real	,  lowerCamelCase__ )

			lowerCAmelCase :	Tuple          =     __add__




			def __sub__(		self  :     List[Any]	,  lowerCamelCase__  :     Union[str, Any] )   ->Dict:



					'''simple docstring'''







					return self + other * -1




			def __mul__(		self  :     List[str]	,  lowerCamelCase__  :     Optional[Any] )   ->Union[str, Any]:



					'''simple docstring'''







					if not isinstance(lowerCamelCase__	,  lowerCamelCase__ ):
							_UpperCAmelCase		:       Optional[int]								=      []
							for i in self.duals:
									new_duals.append(i * other )
							return Dual(self.real * other	,  lowerCamelCase__ )
					_UpperCAmelCase		:       Union[str, Any]								=      [0] * (len(self.duals ) + len(other.duals ) + 1)
					for i, item in enumerate(self.duals ):
							for j, jtem in enumerate(other.duals ):
									new_duals[i + j + 1] += item * jtem
					for k in range(len(self.duals ) ):
							new_duals[k] += self.duals[k] * other.real
					for index in range(len(other.duals ) ):
							new_duals[index] += other.duals[index] * self.real
					return Dual(self.real * other.real	,  lowerCamelCase__ )

			lowerCAmelCase :	Union[str, Any]          =     __mul__




			def __truediv__(		self  :     Optional[Any]	,  lowerCamelCase__  :     List[Any] )   ->Union[str, Any]:



					'''simple docstring'''







					if not isinstance(lowerCamelCase__	,  lowerCamelCase__ ):
							_UpperCAmelCase		:       Union[str, Any]								=      []
							for i in self.duals:
									new_duals.append(i / other )
							return Dual(self.real / other	,  lowerCamelCase__ )
					raise ValueError




			def __floordiv__(		self  :     str	,  lowerCamelCase__  :     str )   ->List[str]:



					'''simple docstring'''







					if not isinstance(lowerCamelCase__	,  lowerCamelCase__ ):
							_UpperCAmelCase		:       Tuple								=      []
							for i in self.duals:
									new_duals.append(i // other )
							return Dual(self.real // other	,  lowerCamelCase__ )
					raise ValueError






			def __pow__(		self  :     Tuple	,  lowerCamelCase__  :     Optional[Any] )   ->Optional[int]:



					'''simple docstring'''







					if n < 0 or isinstance(lowerCamelCase__	,  lowerCamelCase__ ):
							raise ValueError("power must be a positive integer" )
					if n == 0:
							return 1
					if n == 1:
							return self
					_UpperCAmelCase		:       str								=      self
					for _ in range(n - 1 ):
							x *= self
					return x






def  __lowerCAmelCase (__lowerCAmelCase      , __lowerCAmelCase      , __lowerCAmelCase   ):
		if not callable(__lowerCAmelCase   ):
				raise ValueError("differentiate() requires a function as input for func"   )
		if not isinstance(__lowerCAmelCase      , (float, int)   ):
				raise ValueError("differentiate() requires a float as input for position"   )
		if not isinstance(__lowerCAmelCase      , __lowerCAmelCase   ):
				raise ValueError("differentiate() requires an int as input for order"   )
		_UpperCAmelCase		:       int								=      Dual(__lowerCAmelCase      , 1   )
		_UpperCAmelCase		:       Optional[int]								=      func(__lowerCAmelCase   )
		if order == 0:
				return result.real
		return result.duals[order - 1] * factorial(__lowerCAmelCase   )


if __name__ == "__main__":
						import doctest

						doctest.testmod()






						def  __lowerCAmelCase (__lowerCAmelCase   ):
								return y**2 * y**4





						print(differentiate(f, 9, 2))



