from typing import Any

import numpy as np







def 	UpperCAmelCase       (		lowerCAmelCase_       )	->	bool:
     assert np.shape(lowerCAmelCase_       )[0] == np.shape(lowerCAmelCase_       )[1]

     # If matrix not symmetric, exit right away.
     if np.allclose(lowerCAmelCase_						,      matrix.T       ) is False:
          return False

     # Get eigenvalues and eignevectors for a symmetric matrix.
     a			,							a  :    int				=						np.linalg.eigh(lowerCAmelCase_       )

     # Check sign of all eigenvalues.
     # np.all returns a value of type np.bool_
     return bool(np.all(eigen_values > 0       )       )







def 	UpperCAmelCase       (		lowerCAmelCase_       )	->	Any:
     a  :    str				=						np.random.randn(lowerCAmelCase_						,      lowerCAmelCase_       )
     a  :    List[str]				=						np.dot(lowerCAmelCase_						,      random_matrix.T       )
     assert _is_matrix_spd(lowerCAmelCase_       )
     return spd_matrix







def 	UpperCAmelCase       (		lowerCAmelCase_						,      lowerCAmelCase_						,      lowerCAmelCase_ = 1_0_0_0						,      lowerCAmelCase_ = 1e-8						,      )	->	Any:
     assert np.shape(lowerCAmelCase_       )[0] == np.shape(lowerCAmelCase_       )[1]
     assert np.shape(lowerCAmelCase_       )[0] == np.shape(lowerCAmelCase_       )[0]
     assert _is_matrix_spd(lowerCAmelCase_       )

     # Initialize solution guess, residual, search direction.
     a  :    Dict				=						np.zeros((np.shape(lowerCAmelCase_       )[0], 1)       )
     a  :    Optional[int]				=						np.copy(lowerCAmelCase_       )
     a  :    Dict				=						np.copy(lowerCAmelCase_       )

     # Set initial errors in solution guess and residual.
     a  :    Optional[int]				=						1e9
     a  :    Optional[Any]				=						1e9
     a  :    Any				=						1e9

     # Set iteration counter to threshold number of iterations.
     a  :    Dict				=						0

     while error > tol:
          # Save this value so we only calculate the matrix-vector product once.
          a  :    int				=						np.dot(lowerCAmelCase_						,      lowerCAmelCase_       )

          # The main algorithm.

          # Update search direction magnitude.
          a  :    int				=						np.dot(ra.T						,      lowerCAmelCase_       ) / np.dot(pa.T						,      lowerCAmelCase_       )
          # Update solution guess.
          a  :    List[Any]				=						xa + alpha * pa
          # Calculate new residual.
          a  :    Optional[int]				=						ra - alpha * w
          # Calculate new Krylov subspace scale.
          a  :    List[Any]				=						np.dot(r.T						,      lowerCAmelCase_       ) / np.dot(ra.T						,      lowerCAmelCase_       )
          # Calculate new A conjuage search direction.
          a  :    Any				=						r + beta * pa

          # Calculate errors.
          a  :    int				=						np.linalg.norm(r - ra       )
          a  :    Optional[int]				=						np.linalg.norm(x - xa       )
          a  :    int				=						np.maximum(lowerCAmelCase_						,      lowerCAmelCase_       )

          # Update variables.
          a  :    Any				=						np.copy(lowerCAmelCase_       )
          a  :    List[str]				=						np.copy(lowerCAmelCase_       )
          a  :    Optional[Any]				=						np.copy(lowerCAmelCase_       )

          # Update number of iterations.
          iterations += 1
          if iterations > max_iterations:
               break

     return x







def 	UpperCAmelCase       (		)	->	None:
     a  :    List[str]				=						3
     a  :    List[str]				=						_create_spd_matrix(lowerCAmelCase_       )
     a  :    List[Any]				=						np.random.randn(lowerCAmelCase_						,      1       )
     a  :    str				=						np.dot(lowerCAmelCase_						,      lowerCAmelCase_       )

     # Numpy solution.
     a  :    Tuple				=						np.linalg.solve(lowerCAmelCase_						,      lowerCAmelCase_       )

     # Our implementation.
     a  :    int				=						conjugate_gradient(lowerCAmelCase_						,      lowerCAmelCase_       )

     # Ensure both solutions are close to x_true (and therefore one another).
     assert np.linalg.norm(x_numpy - x_true       ) <= 1e-6
     assert np.linalg.norm(x_conjugate_gradient - x_true       ) <= 1e-6


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  test_conjugate_gradient()
import unittest

from transformers import BlenderbotTokenizer, BlenderbotTokenizerFast
from transformers.utils import cached_property






class 							_SCREAMING_SNAKE_CASE(   unittest.TestCase	):
   @cached_property
   def _lowercase(    self    )	->List[str]:
        return BlenderbotTokenizer.from_pretrained('''facebook/blenderbot-3B'''    )
   @cached_property
   def _lowercase(    self    )	->str:
        return BlenderbotTokenizerFast.from_pretrained('''facebook/blenderbot-3B'''    )
   def _lowercase(    self    )	->str:
        a  :    Optional[int]				=						self.tokenizer_ab
        a  :    List[Any]				=						''' I am a small frog.'''
        a  :    Optional[Any]				=						tok([src_text]							,     padding=lowerCAmelCase_							,     truncation=lowerCAmelCase_    )['''input_ids''']
        a  :    int				=						tok.batch_decode(lowerCAmelCase_							,     skip_special_tokens=lowerCAmelCase_							,     clean_up_tokenization_spaces=lowerCAmelCase_    )[0]
        assert src_text == decoded
   def _lowercase(    self    )	->Dict:
        a  :    List[Any]				=						self.rust_tokenizer_ab
        a  :    str				=						''' I am a small frog.'''
        a  :    Tuple				=						tok([src_text]							,     padding=lowerCAmelCase_							,     truncation=lowerCAmelCase_    )['''input_ids''']
        a  :    Optional[Any]				=						tok.batch_decode(lowerCAmelCase_							,     skip_special_tokens=lowerCAmelCase_							,     clean_up_tokenization_spaces=lowerCAmelCase_    )[0]
        assert src_text == decoded
   def _lowercase(    self    )	->Tuple:
        assert self.tokenizer_ab.add_prefix_space
        assert self.tokenizer_ab([''' Sam''', '''Sam''']    ).input_ids == [[55_02, 2], [55_02, 2]]


   def _lowercase(    self    )	->Optional[Any]:
        assert self.rust_tokenizer_ab.add_prefix_space
        assert self.rust_tokenizer_ab([''' Sam''', '''Sam''']    ).input_ids == [[55_02, 2], [55_02, 2]]