


def 			UpperCamelCase			(					_a						)    ->							str:
     '''simple docstring'''





     if len(lowerCAmelCase_						) == 0 or not all(len(lowerCAmelCase_						) == 2 for pair in coordinates						):
          raise ValueError('''The program cannot work out a fitting polynomial.'''						)

     if len({tuple(lowerCAmelCase_						) for pair in coordinates}						) != len(lowerCAmelCase_						):
          raise ValueError('''The program cannot work out a fitting polynomial.'''						)

     lowercase_				:Optional[Any]       			=				{x for x, _ in coordinates}
     if len(lowerCAmelCase_						) == 1:
          return f"x={coordinates[0][0]}"

     if len(lowerCAmelCase_						) != len(lowerCAmelCase_						):
          raise ValueError('''The program cannot work out a fitting polynomial.'''						)

     lowercase_				:List[Any]       			=				len(lowerCAmelCase_						)

     lowercase_				:Any       			=				0
     lowercase_				:Union[str, Any]       			=				[]
     # put the x and x to the power values in a matrix
     while count_of_line < x:
          lowercase_				:Any       			=				0
          lowercase_				:Dict       			=				coordinates[count_of_line][0]
          lowercase_				:Optional[Any]       			=				[]
          while count_in_line < x:
               count_line.append(a ** (x - (count_in_line + 1))						)
               count_in_line += 1
          matrix.append(lowerCAmelCase_						)
          count_of_line += 1

     lowercase_				:Dict       			=				0
     # put the y values into a vector
     lowercase_				:Union[str, Any]       			=				[]
     while count_of_line < x:
          vector.append(coordinates[count_of_line][1]						)
          count_of_line += 1

     lowercase_				:int       			=				0

     while count < x:
          lowercase_				:Any       			=				0
          while zahlen < x:
               if count == zahlen:
                    zahlen += 1
               if zahlen == x:
                    break
               lowercase_				:Tuple       			=				matrix[zahlen][count] / matrix[count][count]
               for counting_columns, item in enumerate(matrix[count]						):
                    # manipulating all the values in the matrix
                    matrix[zahlen][counting_columns] -= item * bruch
               # manipulating the values in the vector
               vector[zahlen] -= vector[count] * bruch
               zahlen += 1
          count += 1

     lowercase_				:Any       			=				0
     # make solutions
     lowercase_				:Any       			=				[]
     while count < x:
          solution.append(str(vector[count] / matrix[count][count]						)						)
          count += 1

     lowercase_				:Optional[int]       			=				0
     lowercase_				:Dict       			=				'''f(x)='''

     while count < x:
          lowercase_				:Union[str, Any]       			=				solution[count].split('''E'''						)
          if len(lowerCAmelCase_						) > 1:
               lowercase_				:str       			=				f"{remove_e[0]}*10^{remove_e[1]}"
          solved += f"x^{x - (count + 1)}*{solution[count]}"
          if count + 1 != x:
               solved += "+"
          count += 1

     return solved


if __name__ == "__main__":
   print(points_to_polynomial([]))
   print(points_to_polynomial([[]]))
   print(points_to_polynomial([[1, 0], [2, 0], [3, 0]]))
   print(points_to_polynomial([[1, 1], [2, 1], [3, 1]]))
   print(points_to_polynomial([[1, 3], [2, 3], [3, 3]]))
   print(points_to_polynomial([[1, 1], [2, 2], [3, 3]]))
   print(points_to_polynomial([[1, 1], [2, 4], [3, 9]]))
   print(points_to_polynomial([[1, 3], [2, 6], [3, 11]]))
   print(points_to_polynomial([[1, -3], [2, -6], [3, -11]]))
   print(points_to_polynomial([[1, 5], [2, 2], [3, 9]]))







import argparse

import torch
from flax.training.checkpoints import restore_checkpoint

from transformers import FNetConfig, FNetForPreTraining
from transformers.utils import logging


logging.set_verbosity_info()



def 							_A   (						lowerCAmelCase_     :					Dict   ,				lowerCAmelCase_     :					List[str]   ,				lowerCAmelCase_     :					int			):
     """simple docstring"""

     lowerCAmelCase__		= FNetConfig.from_json_file(lowerCAmelCase_			)
     print(F'Building PyTorch model from configuration: {config}'			)
     lowerCAmelCase__		= FNetForPreTraining(lowerCAmelCase_			)

     lowerCAmelCase__		= restore_checkpoint(lowerCAmelCase_   ,				lowerCAmelCase_			)
     lowerCAmelCase__		= checkpoint_dict["target"]

     # Embeddings
     # Position IDs
     lowerCAmelCase__		= fnet_pretraining_model.state_dict()

     lowerCAmelCase__		= state_dict["fnet.embeddings.position_ids"]
     lowerCAmelCase__		= {"fnet.embeddings.position_ids": position_ids}
     # Embedding Layers
     lowerCAmelCase__		= torch.tensor(
         pretrained_model_params["encoder"]["embedder"]["word"]["embedding"]			)
     lowerCAmelCase__		= torch.tensor(
         pretrained_model_params["encoder"]["embedder"]["position"]["embedding"][0]			)
     lowerCAmelCase__		= torch.tensor(
         pretrained_model_params["encoder"]["embedder"]["type"]["embedding"]			)
     lowerCAmelCase__		= torch.tensor(
         pretrained_model_params["encoder"]["embedder"]["hidden_mapping_in"]["kernel"]			).T
     lowerCAmelCase__		= torch.tensor(
         pretrained_model_params["encoder"]["embedder"]["hidden_mapping_in"]["bias"]			)
     lowerCAmelCase__		= torch.tensor(
         pretrained_model_params["encoder"]["embedder"]["layer_norm"]["scale"]			)
     lowerCAmelCase__		= torch.tensor(
         pretrained_model_params["encoder"]["embedder"]["layer_norm"]["bias"]			)

     # Encoder Layers
     for layer in range(config.num_hidden_layers			):
          lowerCAmelCase__		= torch.tensor(
              pretrained_model_params["encoder"][F'encoder_{layer}']["mixing_layer_norm"]["scale"]			)
          lowerCAmelCase__		= torch.tensor(
              pretrained_model_params["encoder"][F'encoder_{layer}']["mixing_layer_norm"]["bias"]			)

          lowerCAmelCase__		= torch.tensor(
              pretrained_model_params["encoder"][F'feed_forward_{layer}']["intermediate"]["kernel"]			).T
          lowerCAmelCase__		= torch.tensor(
              pretrained_model_params["encoder"][F'feed_forward_{layer}']["intermediate"]["bias"]			)

          lowerCAmelCase__		= torch.tensor(
              pretrained_model_params["encoder"][F'feed_forward_{layer}']["output"]["kernel"]			).T
          lowerCAmelCase__		= torch.tensor(
              pretrained_model_params["encoder"][F'feed_forward_{layer}']["output"]["bias"]			)

          lowerCAmelCase__		= torch.tensor(
              pretrained_model_params["encoder"][F'encoder_{layer}']["output_layer_norm"]["scale"]			)
          lowerCAmelCase__		= torch.tensor(
              pretrained_model_params["encoder"][F'encoder_{layer}']["output_layer_norm"]["bias"]			)

     # Pooler Layers
     lowerCAmelCase__		= torch.tensor(pretrained_model_params["encoder"]["pooler"]["kernel"]			).T
     lowerCAmelCase__		= torch.tensor(pretrained_model_params["encoder"]["pooler"]["bias"]			)

     # Masked LM Layers
     lowerCAmelCase__		= torch.tensor(
         pretrained_model_params["predictions_dense"]["kernel"]			).T
     lowerCAmelCase__		= torch.tensor(
         pretrained_model_params["predictions_dense"]["bias"]			)
     lowerCAmelCase__		= torch.tensor(
         pretrained_model_params["predictions_layer_norm"]["scale"]			)
     lowerCAmelCase__		= torch.tensor(
         pretrained_model_params["predictions_layer_norm"]["bias"]			)
     lowerCAmelCase__		= torch.tensor(
         pretrained_model_params["encoder"]["embedder"]["word"]["embedding"]			)
     lowerCAmelCase__		= torch.tensor(
         pretrained_model_params["predictions_output"]["output_bias"]			)
     lowerCAmelCase__		= torch.tensor(pretrained_model_params["predictions_output"]["output_bias"]			)

     # Seq Relationship Layers
     lowerCAmelCase__		= torch.tensor(
         pretrained_model_params["classification"]["output_kernel"]			)
     lowerCAmelCase__		= torch.tensor(
         pretrained_model_params["classification"]["output_bias"]			)

     # Load State Dict
     fnet_pretraining_model.load_state_dict(lowerCAmelCase_			)

     # Save PreTrained
     print(F'Saving pretrained model to {save_path}'			)
     fnet_pretraining_model.save_pretrained(lowerCAmelCase_			)


if __name__ == "__main__":
     UpperCamelCase								=     argparse.ArgumentParser()
     # Required parameters
     parser.add_argument(
         '--flax_checkpoint_path', default=None, type=str, required=True, help='Path to the TensorFlow checkpoint path.'
     )
     parser.add_argument(
         '--fnet_config_file',
         default=None,
         type=str,
         required=True,
         help=(
             'The config json file corresponding to the pre-trained FNet model. \n'
             'This specifies the model architecture.'
         ),
     )
     parser.add_argument('--save_path', default=None, type=str, required=True, help='Path to the output model.')
     UpperCamelCase								=     parser.parse_args()
     convert_flax_checkpoint_to_pytorch(args.flax_checkpoint_path, args.fnet_config_file, args.save_path)
