

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

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

  UpperCAmelCase          =	{x for x, _ in coordinates}
  if len(__A      ) == 1:
    return F"x={coordinates[0][0]}"

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

  UpperCAmelCase          =	len(__A      )

  UpperCAmelCase          =	0
  UpperCAmelCase          =	[]
  # put the x and x to the power values in a matrix
  while count_of_line < x:
    UpperCAmelCase          =	0
    UpperCAmelCase          =	coordinates[count_of_line][0]
    UpperCAmelCase          =	[]
    while count_in_line < x:
      count_line.append(a ** (x - (count_in_line + 1))      )
      count_in_line += 1
    matrix.append(__A      )
    count_of_line += 1

  UpperCAmelCase          =	0
  # put the y values into a vector
  UpperCAmelCase          =	[]
  while count_of_line < x:
    vector.append(coordinates[count_of_line][1]      )
    count_of_line += 1

  UpperCAmelCase          =	0

  while count < x:
    UpperCAmelCase          =	0
    while zahlen < x:
      if count == zahlen:
        zahlen += 1
      if zahlen == x:
        break
      UpperCAmelCase          =	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

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

  UpperCAmelCase          =	0
  UpperCAmelCase          =	"f(x)="

  while count < x:
    UpperCAmelCase          =	solution[count].split("E"      )
    if len(__A      ) > 1:
      UpperCAmelCase          =	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 shutil
import tempfile
import unittest

import pytest

from transformers import WhisperTokenizer, is_speech_available
from transformers.testing_utils import require_sentencepiece, require_torch, require_torchaudio

from .test_feature_extraction_whisper import floats_list


if is_speech_available():
		from transformers import WhisperFeatureExtractor, WhisperProcessor


__UpperCAmelCase    	=  5_03_58
__UpperCAmelCase    	=  5_03_62


@require_torch
@require_torchaudio
@require_sentencepiece
class 						lowerCamelCase__			(		unittest.TestCase ):


						def 	_lowerCamelCase      (			self    :	List[Any]      ):
													a__:							str									="openai/whisper-small.en"
													a__:							Union[str, Any]									=tempfile.mkdtemp()


						def 	_lowerCamelCase      (			self    :	Optional[Any]   ,							**_a    :	Optional[int]      ):
													return WhisperTokenizer.from_pretrained(self.checkpoint   ,							**_a      )


						def 	_lowerCamelCase      (			self    :	str   ,							**_a    :	Tuple      ):
													return WhisperFeatureExtractor.from_pretrained(self.checkpoint   ,							**_a      )


						def 	_lowerCamelCase      (			self    :	Union[str, Any]      ):
													shutil.rmtree(self.tmpdirname      )


						def 	_lowerCamelCase      (			self    :	int      ):
													a__:							str									=self.get_tokenizer()
													a__:							Union[str, Any]									=self.get_feature_extractor()

													a__:							int									=WhisperProcessor(tokenizer=_a   ,							feature_extractor=_a      )

													processor.save_pretrained(self.tmpdirname      )
													a__:							List[Any]									=WhisperProcessor.from_pretrained(self.tmpdirname      )

													self.assertEqual(processor.tokenizer.get_vocab()   ,							tokenizer.get_vocab()      )
													self.assertIsInstance(processor.tokenizer   ,							_a      )

													self.assertEqual(processor.feature_extractor.to_json_string()   ,							feature_extractor.to_json_string()      )
													self.assertIsInstance(processor.feature_extractor   ,							_a      )


						def 	_lowerCamelCase      (			self    :	Dict      ):
													a__:							str									=WhisperProcessor(tokenizer=self.get_tokenizer()   ,							feature_extractor=self.get_feature_extractor()      )
													processor.save_pretrained(self.tmpdirname      )

													a__:							Tuple									=self.get_tokenizer(bos_token="(BOS)"   ,							eos_token="(EOS)"      )
													a__:							Optional[int]									=self.get_feature_extractor(do_normalize=_a   ,							padding_value=1.0      )

													a__:							Any									=WhisperProcessor.from_pretrained(
													    self.tmpdirname   ,							bos_token="(BOS)"   ,							eos_token="(EOS)"   ,							do_normalize=_a   ,							padding_value=1.0      )

													self.assertEqual(processor.tokenizer.get_vocab()   ,							tokenizer_add_kwargs.get_vocab()      )
													self.assertIsInstance(processor.tokenizer   ,							_a      )

													self.assertEqual(processor.feature_extractor.to_json_string()   ,							feature_extractor_add_kwargs.to_json_string()      )
													self.assertIsInstance(processor.feature_extractor   ,							_a      )


						def 	_lowerCamelCase      (			self    :	Tuple      ):
													a__:							Optional[int]									=self.get_feature_extractor()
													a__:							str									=self.get_tokenizer()

													a__:							int									=WhisperProcessor(tokenizer=_a   ,							feature_extractor=_a      )

													a__:							List[str]									=floats_list((3, 1_0_0_0)      )

													a__:							Optional[int]									=feature_extractor(_a   ,							return_tensors="np"      )
													a__:							Optional[int]									=processor(_a   ,							return_tensors="np"      )

													for key in input_feat_extract.keys():
																				self.assertAlmostEqual(input_feat_extract[key].sum()   ,							input_processor[key].sum()   ,							delta=1e-2      )


						def 	_lowerCamelCase      (			self    :	Optional[Any]      ):
													a__:							Dict									=self.get_feature_extractor()
													a__:							int									=self.get_tokenizer()

													a__:							List[Any]									=WhisperProcessor(tokenizer=_a   ,							feature_extractor=_a      )

													a__:							List[Any]									="This is a test string"

													a__:							Tuple									=processor(text=_a      )

													a__:							int									=tokenizer(_a      )

													for key in encoded_tok.keys():
																				self.assertListEqual(encoded_tok[key]   ,							encoded_processor[key]      )


						def 	_lowerCamelCase      (			self    :	Any      ):
													a__:							int									=self.get_feature_extractor()
													a__:							List[str]									=self.get_tokenizer()

													a__:							List[str]									=WhisperProcessor(tokenizer=_a   ,							feature_extractor=_a      )

													a__:							List[Any]									=[[1, 4, 5, 8, 1, 0, 8], [3, 4, 3, 1, 1, 8, 9]]

													a__:							List[Any]									=processor.batch_decode(_a      )
													a__:							int									=tokenizer.batch_decode(_a      )

													self.assertListEqual(_a   ,							_a      )


						def 	_lowerCamelCase      (			self    :	List[str]      ):
													a__:							List[Any]									=self.get_feature_extractor()
													a__:							Any									=self.get_tokenizer()

													a__:							Optional[int]									=WhisperProcessor(tokenizer=_a   ,							feature_extractor=_a      )

													self.assertListEqual(
													    processor.model_input_names   ,							feature_extractor.model_input_names   ,							msg="`processor` and `feature_extractor` model input names do not match"   ,							)


						def 	_lowerCamelCase      (			self    :	List[Any]      ):
													a__:							Any									=self.get_feature_extractor()
													a__:							str									=self.get_tokenizer()

													a__:							Dict									=WhisperProcessor(tokenizer=_a   ,							feature_extractor=_a      )
													a__:							List[Any]									=processor.get_decoder_prompt_ids(task="transcribe"   ,							no_timestamps=_a      )

													self.assertIsInstance(_a   ,							_a      )
													for ids in forced_decoder_ids:
																				self.assertIsInstance(_a   ,							(list, tuple)      )

													a__:							Any									=[TRANSCRIBE, NOTIMESTAMPS]
													self.assertListEqual([ids[-1] for ids in forced_decoder_ids]   ,							_a      )


						def 	_lowerCamelCase      (			self    :	str      ):
													a__:							Tuple									=WhisperProcessor(tokenizer=self.get_tokenizer()   ,							feature_extractor=self.get_feature_extractor()      )
													a__:							List[Any]									=processor.get_prompt_ids("Mr. Quilter"      )
													a__:							Optional[Any]									=processor.tokenizer.decode(_a      )

													self.assertListEqual(prompt_ids.tolist()   ,							[5_0_3_6_0, 1_7_7_0, 1_3, 2_2_6_4, 3_4_6, 3_5_3]      )
													self.assertEqual(_a   ,							"<|startofprev|> Mr. Quilter"      )


						def 	_lowerCamelCase      (			self    :	List[str]      ):
													a__:							int									=WhisperProcessor(tokenizer=self.get_tokenizer()   ,							feature_extractor=self.get_feature_extractor()      )
													a__:							List[str]									=processor.get_prompt_ids(""      )
													a__:							Any									=processor.tokenizer.decode(_a      )

													self.assertListEqual(prompt_ids.tolist()   ,							[5_0_3_6_0, 2_2_0]      )
													self.assertEqual(_a   ,							"<|startofprev|> "      )







						def 	_lowerCamelCase      (			self    :	Any      ):
													a__:							Tuple									=WhisperProcessor(tokenizer=self.get_tokenizer()   ,							feature_extractor=self.get_feature_extractor()      )

													def _test_prompt_error_raised_helper(_a    :	Union[str, Any]   ,							_a    :	List[str]      ):
																				with pytest.raises(_a      ) as excinfo:
																											processor.get_prompt_ids(_a      )
																				a__:							List[Any]									=F"Encountered text in the prompt corresponding to disallowed special token: {special_token}."
																				self.assertEqual(_a   ,							str(excinfo.value      )      )

													_test_prompt_error_raised_helper("<|startofprev|> test"   ,							"<|startofprev|>"      )
													_test_prompt_error_raised_helper("test <|notimestamps|>"   ,							"<|notimestamps|>"      )
													_test_prompt_error_raised_helper("test <|zh|> test <|transcribe|>"   ,							"<|zh|>"      )





