
from typing import Any

import numpy as np


def     a__			(    snake_case    ):





  """simple docstring"""
  assert np.shape(snake_case    )[0] == np.shape(snake_case    )[1]

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

  # Get eigenvalues and eignevectors for a symmetric matrix.
  __SCREAMING_SNAKE_CASE     :					Any			=						np.linalg.eigh(snake_case    )

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


def     a__			(    snake_case    ):





  """simple docstring"""
  __SCREAMING_SNAKE_CASE     :					Optional[int]			=						np.random.randn(snake_case   ,	snake_case    )
  __SCREAMING_SNAKE_CASE     :					Optional[Any]			=						np.dot(snake_case   ,	random_matrix.T    )
  assert _is_matrix_spd(snake_case    )
  return spd_matrix


def     a__			(    snake_case   ,	snake_case   ,	snake_case = 1_000   ,	snake_case = 1E-8   ,	):





  """simple docstring"""
  assert np.shape(snake_case    )[0] == np.shape(snake_case    )[1]
  assert np.shape(snake_case    )[0] == np.shape(snake_case    )[0]
  assert _is_matrix_spd(snake_case    )

  # Initialize solution guess, residual, search direction.
  __SCREAMING_SNAKE_CASE     :					Union[str, Any]			=						np.zeros((np.shape(snake_case    )[0], 1)    )
  __SCREAMING_SNAKE_CASE     :					Tuple			=						np.copy(snake_case    )
  __SCREAMING_SNAKE_CASE     :					str			=						np.copy(snake_case    )

  # Set initial errors in solution guess and residual.
  __SCREAMING_SNAKE_CASE     :					Tuple			=						1E9
  __SCREAMING_SNAKE_CASE     :					int			=						1E9
  __SCREAMING_SNAKE_CASE     :					Any			=						1E9

  # Set iteration counter to threshold number of iterations.
  __SCREAMING_SNAKE_CASE     :					Optional[Any]			=						0

  while error > tol:
    # Save this value so we only calculate the matrix-vector product once.
    __SCREAMING_SNAKE_CASE     :					Optional[int]			=						np.dot(snake_case   ,	snake_case    )

    # The main algorithm.

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

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

    # Update variables.
    __SCREAMING_SNAKE_CASE     :					str			=						np.copy(snake_case    )
    __SCREAMING_SNAKE_CASE     :					Dict			=						np.copy(snake_case    )
    __SCREAMING_SNAKE_CASE     :					Dict			=						np.copy(snake_case    )

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

  return x


def     a__			(    ):





  """simple docstring"""
  __SCREAMING_SNAKE_CASE     :					str			=						3
  __SCREAMING_SNAKE_CASE     :					Union[str, Any]			=						_create_spd_matrix(snake_case    )
  __SCREAMING_SNAKE_CASE     :					Union[str, Any]			=						np.random.randn(snake_case   ,	1    )
  __SCREAMING_SNAKE_CASE     :					Tuple			=						np.dot(snake_case   ,	snake_case    )

  # Numpy solution.
  __SCREAMING_SNAKE_CASE     :					Optional[Any]			=						np.linalg.solve(snake_case   ,	snake_case    )

  # Our implementation.
  __SCREAMING_SNAKE_CASE     :					List[Any]			=						conjugate_gradient(snake_case   ,	snake_case    )

  # 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 load_tool

from .test_tools_common import ToolTesterMixin


lowercase_											=	"""
Hugging Face was founded in 2016 by French entrepreneurs Clément Delangue, Julien Chaumond, and Thomas Wolf originally as a company that developed a chatbot app targeted at teenagers.[2] After open-sourcing the model behind the chatbot, the company pivoted to focus on being a platform for machine learning.

In March 2021, Hugging Face raised $40 million in a Series B funding round.[3]

On April 28, 2021, the company launched the BigScience Research Workshop in collaboration with several other research groups to release an open large language model.[4] In 2022, the workshop concluded with the announcement of BLOOM, a multilingual large language model with 176 billion parameters.[5]
"""





class   __UpperCamelCase				(    unittest.TestCase				,		lowerCAmelCase__   ):






     """simple docstring"""







     def 				UpperCAmelCase__    (							self    :    Optional[Any]				):







       """simple docstring"""




       __SCREAMING_SNAKE_CASE     :					int			=						load_tool('''summarization'''				)
       self.tool.setup()
       __SCREAMING_SNAKE_CASE     :					Any			=						load_tool('''summarization'''      ,		remote=_A				)



     def 				UpperCAmelCase__    (							self    :    Tuple				):







       """simple docstring"""




       __SCREAMING_SNAKE_CASE     :					Dict			=						self.tool(_A				)
       self.assertEqual(
           _A      ,		'''Hugging Face was founded in 2016 by French entrepreneurs Clément Delangue, Julien Chaumond, and Thomas Wolf. In March 2021, Hugging Face raised $40 million in a Series B funding round. On April 28, 2021, the company launched the BigScience Research Workshop in collaboration with several other research groups to release an open large language model. In 2022, the workshop concluded with the announcement of BLOOM.'''      ,		)



     def 				UpperCAmelCase__    (							self    :    List[str]				):







       """simple docstring"""




       __SCREAMING_SNAKE_CASE     :					Optional[Any]			=						self.remote_tool(_A				)
       self.assertEqual(
           _A      ,		'''Hugging Face was founded in 2016 by French entrepreneurs Clément Delangue, Julien Chaumond, and Thomas Wolf. In March 2021, Hugging Face raised $40 million in a Series B funding round. On April 28, 2021, the company launched the BigScience Research Workshop in collaboration with several other research groups to release an open large language model. In 2022, the workshop concluded with the announcement of BLOOM.'''      ,		)



     def 				UpperCAmelCase__    (							self    :    List[str]				):







       """simple docstring"""




       __SCREAMING_SNAKE_CASE     :					Dict			=						self.tool(text=_A				)
       self.assertEqual(
           _A      ,		'''Hugging Face was founded in 2016 by French entrepreneurs Clément Delangue, Julien Chaumond, and Thomas Wolf. In March 2021, Hugging Face raised $40 million in a Series B funding round. On April 28, 2021, the company launched the BigScience Research Workshop in collaboration with several other research groups to release an open large language model. In 2022, the workshop concluded with the announcement of BLOOM.'''      ,		)




     def 				UpperCAmelCase__    (							self    :    Optional[int]				):







       """simple docstring"""




       __SCREAMING_SNAKE_CASE     :					str			=						self.remote_tool(text=_A				)
       self.assertEqual(
           _A      ,		'''Hugging Face was founded in 2016 by French entrepreneurs Clément Delangue, Julien Chaumond, and Thomas Wolf. In March 2021, Hugging Face raised $40 million in a Series B funding round. On April 28, 2021, the company launched the BigScience Research Workshop in collaboration with several other research groups to release an open large language model. In 2022, the workshop concluded with the announcement of BLOOM.'''      ,		)
