


'''simple docstring'''

from __future__ import annotations

import math

def _SCREAMING_SNAKE_CASE (A    ,					A			)			->			float:






       """simple docstring"""







       lowercase__      =					u
       for i in range(1    ,					A			):
              lowercase__      =					temp * (u - i)
       return temp

def _SCREAMING_SNAKE_CASE ()			->			None:






       """simple docstring"""







       lowercase__      =					int(input('''enter the numbers of values: '''			)			)
       lowercase__      =					[]
       for _ in range(A			):
              y.append([]			)
       for i in range(A			):
              for j in range(A			):
                     y[i].append(A			)
                     lowercase__      =					0

       print('''enter the values of parameters in a list: '''			)
       lowercase__      =					list(map(A    ,					input().split()			)			)

       print('''enter the values of corresponding parameters: '''			)
       for i in range(A			):
              lowercase__      =					float(input()			)

       lowercase__      =					int(input('''enter the value to interpolate: '''			)			)
       lowercase__      =					(value - x[0]) / (x[1] - x[0])

       # for calculating forward difference table

       for i in range(1    ,					A			):
              for j in range(n - i			):
                     lowercase__      =					y[j + 1][i - 1] - y[j][i - 1]

       lowercase__      =					y[0][0]
       for i in range(1    ,					A			):
              summ += (ucal(A    ,					A			) * y[0][i]) / math.factorial(A			)

       print(f"the value at {value} is {summ}"			)


if __name__ == "__main__":
 main()








'''simple docstring'''

# Lint as: python3
import sys
from collections.abc import Mapping
from typing import TYPE_CHECKING

import numpy as np
import pyarrow as pa

from .. import config
from ..utils.py_utils import map_nested
from .formatting import TensorFormatter


if TYPE_CHECKING:
 import torch
class     __lowerCAmelCase		(TensorFormatter[Mapping, """torch.Tensor""", Mapping]	):





      '''simple docstring'''






      def __init__(self       :       Optional[Any]  ,		UpperCamelCase       :       Tuple=None  ,		**UpperCamelCase       :       List[str]					):

             '''simple docstring'''







             super().__init__(features=UpperCamelCase					)
             lowercase__      =					torch_tensor_kwargs
             import torch  # noqa import torch at initialization



      def  UpperCamelCase__						(self       :       List[str]  ,		UpperCamelCase       :       Union[str, Any]					):

             '''simple docstring'''







             import torch

             if isinstance(UpperCamelCase  ,		UpperCamelCase					) and column:
                    if all(
                        isinstance(UpperCamelCase  ,		torch.Tensor					) and x.shape == column[0].shape and x.dtype == column[0].dtype
                        for x in column					):
                           return torch.stack(UpperCamelCase					)
             return column



      def  UpperCamelCase__						(self       :       List[Any]  ,		UpperCamelCase       :       Optional[Any]					):

             '''simple docstring'''







             import torch

             if isinstance(UpperCamelCase  ,		(str, bytes, type(UpperCamelCase					))					):
                    return value
             elif isinstance(UpperCamelCase  ,		(np.character, np.ndarray)					) and np.issubdtype(value.dtype  ,		np.character					):
                    return value.tolist()

             lowercase__      =					{}

             if isinstance(UpperCamelCase  ,		(np.number, np.ndarray)					) and np.issubdtype(value.dtype  ,		np.integer					):
                    lowercase__      =					{'''dtype''': torch.intaa}
             elif isinstance(UpperCamelCase  ,		(np.number, np.ndarray)					) and np.issubdtype(value.dtype  ,		np.floating					):
                    lowercase__      =					{'''dtype''': torch.floataa}
             elif config.PIL_AVAILABLE and "PIL" in sys.modules:
                    import PIL.Image

                    if isinstance(UpperCamelCase  ,		PIL.Image.Image					):
                           lowercase__      =					np.asarray(UpperCamelCase					)
             return torch.tensor(UpperCamelCase  ,		**{**default_dtype, **self.torch_tensor_kwargs}					)



      def  UpperCamelCase__						(self       :       Optional[int]  ,		UpperCamelCase       :       Dict					):

             '''simple docstring'''







             import torch

             # support for torch, tf, jax etc.
             if hasattr(UpperCamelCase  ,		'''__array__'''					) and not isinstance(UpperCamelCase  ,		torch.Tensor					):
                    lowercase__      =					data_struct.__array__()
             # support for nested types like struct of list of struct
             if isinstance(UpperCamelCase  ,		np.ndarray					):
                    if data_struct.dtype == object:  # torch tensors cannot be instantied from an array of objects
                           return self._consolidate([self.recursive_tensorize(UpperCamelCase					) for substruct in data_struct]					)
             elif isinstance(UpperCamelCase  ,		(list, tuple)					):
                    return self._consolidate([self.recursive_tensorize(UpperCamelCase					) for substruct in data_struct]					)
             return self._tensorize(UpperCamelCase					)



      def  UpperCamelCase__						(self       :       List[str]  ,		UpperCamelCase       :       dict					):

             '''simple docstring'''







             return map_nested(self._recursive_tensorize  ,		UpperCamelCase  ,		map_list=UpperCamelCase					)



      def  UpperCamelCase__						(self       :       Dict  ,		UpperCamelCase       :       pa.Table					):

             '''simple docstring'''







             lowercase__      =					self.numpy_arrow_extractor().extract_row(UpperCamelCase					)
             lowercase__      =					self.python_features_decoder.decode_row(UpperCamelCase					)
             return self.recursive_tensorize(UpperCamelCase					)



      def  UpperCamelCase__						(self       :       List[Any]  ,		UpperCamelCase       :       pa.Table					):

             '''simple docstring'''







             lowercase__      =					self.numpy_arrow_extractor().extract_column(UpperCamelCase					)
             lowercase__      =					self.python_features_decoder.decode_column(UpperCamelCase  ,		pa_table.column_names[0]					)
             lowercase__      =					self.recursive_tensorize(UpperCamelCase					)
             lowercase__      =					self._consolidate(UpperCamelCase					)
             return column






      def  UpperCamelCase__						(self       :       Tuple  ,		UpperCamelCase       :       pa.Table					):

             '''simple docstring'''







             lowercase__      =					self.numpy_arrow_extractor().extract_batch(UpperCamelCase					)
             lowercase__      =					self.python_features_decoder.decode_batch(UpperCamelCase					)
             lowercase__      =					self.recursive_tensorize(UpperCamelCase					)
             for column_name in batch:
                    lowercase__      =					self._consolidate(batch[column_name]					)
             return batch




