





"""simple docstring"""


import numpy as np




def        lowercase__     (       lowercase_		,lowercase_		,lowercase_ = 1e-12		,lowercase_ = 100		,)       ->		tuple[float, np.ndarray]:




      """simple docstring"""

      assert np.shape(snake_case__      )[0] == np.shape(snake_case__      )[1]
      # Ensure proper dimensionality.
      assert np.shape(snake_case__      )[0] == np.shape(snake_case__      )[0]
      # Ensure inputs are either both complex or both real
      assert np.iscomplexobj(snake_case__      ) == np.iscomplexobj(snake_case__      )
      _UpperCamelCase   :						Optional[int]    =							np.iscomplexobj(snake_case__      )
      if is_complex:
            # Ensure complex input_matrix is Hermitian
            assert np.array_equal(snake_case__		,input_matrix.conj().T      )

      # Set convergence to False. Will define convergence when we exceed max_iterations
      # or when we have small changes from one iteration to next.

      _UpperCamelCase   :						Optional[Any]    =							False
      _UpperCamelCase   :						Union[str, Any]    =							0
      _UpperCamelCase   :						Union[str, Any]    =							0
      _UpperCamelCase   :						Optional[Any]    =							1e12

      while not convergence:
            # Multiple matrix by the vector.
            _UpperCamelCase   :						Dict    =							np.dot(snake_case__		,snake_case__      )
            # Normalize the resulting output vector.
            _UpperCamelCase   :						str    =							w / np.linalg.norm(snake_case__      )
            # Find rayleigh quotient
            # (faster than usual b/c we know vector is normalized already)
            _UpperCamelCase   :						int    =							vector.conj().T if is_complex else vector.T
            _UpperCamelCase   :						int    =							np.dot(snake_case__		,np.dot(snake_case__		,snake_case__      )      )

            # Check convergence.
            _UpperCamelCase   :						Optional[int]    =							np.abs(lambda_ - lambda_previous      ) / lambda_
            iterations += 1

            if error <= error_tol or iterations >= max_iterations:
                  _UpperCamelCase   :						Union[str, Any]    =							True

            _UpperCamelCase   :						Optional[Any]    =							lambda_

      if is_complex:
            _UpperCamelCase   :						Any    =							np.real(lambda_      )

      return lambda_, vector




def        lowercase__     (       )       ->		None:




      """simple docstring"""

      _UpperCamelCase   :						Optional[Any]    =							np.array([[41, 4, 20], [4, 26, 30], [20, 30, 50]]      )
      _UpperCamelCase   :						int    =							np.array([41, 4, 20]      )
      _UpperCamelCase   :						Tuple    =							real_input_matrix.astype(np.complexaaa      )
      _UpperCamelCase   :						Optional[int]    =							np.triu(1J * complex_input_matrix		,1      )
      complex_input_matrix += imag_matrix
      complex_input_matrix += -1 * imag_matrix.T
      _UpperCamelCase   :						List[str]    =							np.array([41, 4, 20]      ).astype(np.complexaaa      )

      for problem_type in ["real", "complex"]:
            if problem_type == "real":
                  _UpperCamelCase   :						Tuple    =							real_input_matrix
                  _UpperCamelCase   :						List[str]    =							real_vector
            elif problem_type == "complex":
                  _UpperCamelCase   :						Optional[int]    =							complex_input_matrix
                  _UpperCamelCase   :						int    =							complex_vector

            # Our implementation.
            _UpperCamelCase   :						Union[str, Any]    =							power_iteration(snake_case__		,snake_case__      )

            # Numpy implementation.

            # Get eigenvalues and eigenvectors using built-in numpy
            # eigh (eigh used for symmetric or hermetian matrices).
            _UpperCamelCase   :						Union[str, Any]    =							np.linalg.eigh(snake_case__      )
            # Last eigenvalue is the maximum one.
            _UpperCamelCase   :						str    =							eigen_values[-1]
            # Last column in this matrix is eigenvector corresponding to largest eigenvalue.
            _UpperCamelCase   :						Optional[Any]    =							eigen_vectors[:, -1]

            # Check our implementation and numpy gives close answers.
            assert np.abs(eigen_value - eigen_value_max      ) <= 1e-6
            # Take absolute values element wise of each eigenvector.
            # as they are only unique to a minus sign.
            assert np.linalg.norm(np.abs(snake_case__      ) - np.abs(snake_case__      )      ) <= 1e-6


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  test_power_iteration()




"""simple docstring"""






import os
import unittest

from transformers.models.cpmant.tokenization_cpmant import VOCAB_FILES_NAMES, CpmAntTokenizer
from transformers.testing_utils import require_jieba, tooslow

from ...test_tokenization_common import TokenizerTesterMixin






@require_jieba
class      A(  lowerCamelCase__				,							unittest.TestCase		):

		"""simple docstring"""





		A    =							CpmAntTokenizer
		A    =							False
		def   _UpperCamelCase( self   )      ->	Union[str, Any]:

					"""simple docstring"""



					super().setUp()

					_UpperCamelCase					:str					     =	[
					    '''<d>''',
					    '''</d>''',
					    '''<s>''',
					    '''</s>''',
					    '''</_>''',
					    '''<unk>''',
					    '''<pad>''',
					    '''</n>''',
					    '''我''',
					    '''是''',
					    '''C''',
					    '''P''',
					    '''M''',
					    '''A''',
					    '''n''',
					    '''t''',
					]
					_UpperCamelCase					:List[str]					     =	os.path.join(self.tmpdirname					,				VOCAB_FILES_NAMES['''vocab_file''']   )
					with open(self.vocab_file					,				'''w'''					,				encoding='''utf-8'''   ) as vocab_writer:
								vocab_writer.write(''''''.join([x + '''\n''' for x in vocab_tokens]   )   )





		@tooslow
		def   _UpperCamelCase( self   )      ->	Tuple:

					"""simple docstring"""



					_UpperCamelCase					:Any					     =	CpmAntTokenizer.from_pretrained('''openbmb/cpm-ant-10b'''   )
					_UpperCamelCase					:List[str]					     =	'''今天天气真好！'''
					_UpperCamelCase					:Tuple					     =	['''今天''', '''天气''', '''真''', '''好''', '''！''']
					_UpperCamelCase					:Tuple					     =	tokenizer.tokenize(SCREAMING_SNAKE_CASE__   )
					self.assertListEqual(SCREAMING_SNAKE_CASE__					,				SCREAMING_SNAKE_CASE__   )
					_UpperCamelCase					:Dict					     =	'''今天天气真好！'''
					_UpperCamelCase					:Optional[int]					     =	[tokenizer.bos_token] + tokens

					_UpperCamelCase					:List[str]					     =	[6, 98_02, 1_49_62, 20_82, 8_31, 2_44]
					self.assertListEqual(tokenizer.convert_tokens_to_ids(SCREAMING_SNAKE_CASE__   )					,				SCREAMING_SNAKE_CASE__   )

					_UpperCamelCase					:str					     =	tokenizer.decode(SCREAMING_SNAKE_CASE__   )
					self.assertEqual(SCREAMING_SNAKE_CASE__					,				SCREAMING_SNAKE_CASE__   )

