
from typing import Any

import numpy as np







def        __UpperCamelCase					(    lowerCAmelCase__							:    np.ndarray  ):
 return np.array_equal(lowerCAmelCase__  ,       matrix.conjugate().T  )







def        __UpperCamelCase					(    lowerCAmelCase__							:    np.ndarray  ,       lowerCAmelCase__							:    np.ndarray  ):
 __a			:  Optional[int]		    =  v.conjugate().T
 __a			:  List[Any]		    =  v_star.dot(lowerCAmelCase__  )
 assert isinstance(lowerCAmelCase__  ,       np.ndarray  )
 return (v_star_dot.dot(lowerCAmelCase__  )) / (v_star.dot(lowerCAmelCase__  ))







def        __UpperCamelCase					(    ):
 __a			:  List[str]		    =  np.array([[2, 2 + 1j, 4], [2 - 1j, 3, 1j], [4, -1j, 1]]  )
 __a			:  Any		    =  np.array([[1], [2], [3]]  )
 assert is_hermitian(lowerCAmelCase__  ), f"{a} is not hermitian."
 print(rayleigh_quotient(lowerCAmelCase__  ,       lowerCAmelCase__  )  )

 __a			:  Tuple		    =  np.array([[1, 2, 4], [2, 3, -1], [4, -1, 1]]  )
 assert is_hermitian(lowerCAmelCase__  ), f"{a} is not hermitian."
 assert rayleigh_quotient(lowerCAmelCase__  ,       lowerCAmelCase__  ) == float(3  )


if __name__ == "__main__":
      import doctest

      doctest.testmod()
      tests()


import unittest

from transformers import is_torch_available
from transformers.testing_utils import require_sentencepiece, require_tokenizers, require_torch, slow, torch_device


if is_torch_available():
      from transformers import AutoModelForSeqaSeqLM, AutoTokenizer



@require_torch
@require_sentencepiece
@require_tokenizers
class 		UpperCamelCase__  (	unittest.TestCase   ):
   @slow
   def 				lowerCAmelCase      (self			: Tuple       ):
    __a			:  List[str]		    =  AutoModelForSeqaSeqLM.from_pretrained('''google/mt5-small''' ,    return_dict=snake_case_       ).to(snake_case_       )
    __a			:  List[Any]		    =  AutoTokenizer.from_pretrained('''google/mt5-small'''       )

    __a			:  Optional[int]		    =  tokenizer('''Hello there''' ,    return_tensors='''pt'''       ).input_ids
    __a			:  Dict		    =  tokenizer('''Hi I am''' ,    return_tensors='''pt'''       ).input_ids

    __a			:  Optional[Any]		    =  model(input_ids.to(snake_case_       ) ,    labels=labels.to(snake_case_       )       ).loss
    __a			:  Tuple		    =  -(labels.shape[-1] * loss.item())

    __a			:  Dict		    =  -84.9127
    self.assertTrue(abs(mtf_score - EXPECTED_SCORE       ) < 1E-4       )
